Mathematics
New submissions
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New submissions for Mon, 29 Apr 24
- [1] arXiv:2404.16888 [pdf, ps, other]
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Title: On smooth infinite dimensional grassmannians, splittings and non-commutative generalized cross-ratio mappingsAuthors: Jean-Pierre MagnotSubjects: Differential Geometry (math.DG); Mathematical Physics (math-ph)
We describe basic diffeological structures related to splittings and Grassmannians for infinite dimensional vector spaces. We analyze and expand the notion of non-commutative cross-ratio and prove its smoothness. Then we illustrate this theory by examples, with some of them extracted from the existing literature related to infinite dimensional (Banach) Grassmannians, and others where the diffeological setting is a key primary step for rigorous definitions.
- [2] arXiv:2404.16889 [pdf, ps, other]
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Title: Non-associative versions of Hilbert's basis theoremComments: 9 pages. Earlier versions of arXiv:2207.07994 have been split in two; this is the second partSubjects: Rings and Algebras (math.RA)
We prove several new versions of Hilbert's basis theorem for non-associative Ore extensions and non-associative skew Laurent polynomial rings, non-associative skew power series rings, and non-associative skew Laurent series rings. For non-associative skew Laurent polynomial rings, we show that both a left and a right version of Hilbert's basis theorem hold. For non-associative Ore extensions, we show that a right version holds, but give a counterexample to a left version; a difference that does not appear in the associative setting.
- [3] arXiv:2404.16968 [pdf, ps, other]
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Title: Detecting fast vanishing loops in complex-analytic germs (and detecting germs that are inner metrically conical)Subjects: Algebraic Geometry (math.AG); Complex Variables (math.CV); Metric Geometry (math.MG)
Let X be a reduced complex-analytic germ of pure dimension n\ge2, with arbitrary singularities (not necessarily normal or complete intersection). Various homology cycles on Link_\ep[X] vanish at different speeds when \ep\to0. We give a condition ensuring fast vanishing loops on X. The condition is in terms of the discriminant and the covering data for "convenient" coverings X\to (C^n,o). No resolution of singularities is involved.
For surface germs (n=2) this condition becomes necessary and sufficient.
A corollary for surface germs that are strictly complete intersections detects fast loops via singularities of the projectivized tangent cone of X.
Fast loops are the simplest obstructions for X to be inner metrically conical. Hence we get simple necessary conditions to the IMC property. For normal surface germs these conditions are also sufficient.
We give numerous classes of non-IMC germs and IMC germs. - [4] arXiv:2404.16971 [pdf, ps, other]
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Title: Retractors in local positive logicComments: arxiv:2401.03260v1 has been divided in two papers. This is the second partSubjects: Logic (math.LO)
We study type spaces and retractors (saturated models) for local positive logic.
- [5] arXiv:2404.16978 [pdf, ps, other]
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Title: A Three-Field Multiscale MethodSubjects: Numerical Analysis (math.NA)
"A Three-Field Domain Decomposition Method" is the title of a seminal paper by F. Brezzi and L. D. Marini which introduces a three-field formulation for elliptic partial differential equations. Based on that, we propose the Multiscale-Hybrid-Hybrid Method (MH$^2$M) for the Darcy model, a multiscale finite element method that yields, after a series of formal manipulations, a symmetric positive definite formulation that depends only on the trace of the solution. We show stability and convergence results for a family of finite element spaces and establish relationships with other multiscale finite element methods.
- [6] arXiv:2404.16979 [pdf, ps, other]
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Title: A Constructive Real Projective PlaneAuthors: Mark MandelkernJournal-ref: J. Geom. 107 (2016), 19-60Subjects: Metric Geometry (math.MG)
The classical theory of plane projective geometry is examined constructively, using both synthetic and analytic methods. The topics include Desargues's Theorem, harmonic conjugates, projectivities, involutions, conics, Pascal's Theorem, poles and polars. The axioms used for the synthetic treatment are constructive versions of the traditional axioms. The analytic construction is used to verify the consistency of the axioms; it is based on the usual model in three-dimensional Euclidean space, using only constructive properties of the real numbers. The methods of strict constructivism, following principles put forward by Errett Bishop, reveal the hidden constructive content of a portion of classical geometry. A number of open problems remain for future studies.
- [7] arXiv:2404.16982 [pdf, ps, other]
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Title: Explicit formulae for generalized Stirling and Eulerian numbersAuthors: Josef KüstnerComments: 19 pagesSubjects: Combinatorics (math.CO)
In this article we generalize the $q$-difference operator due to Carlitz in order to derive explicit sum formulae for several extensions of Stirling numbers of the second kind, including complete homogeneous symmetric functions, complementary symmetric functions, $r$-Whitney numbers and elliptic analogues of rook, Stirling and Lah numbers. Furthermore, we generalize Carlitz' $q$-Eulerian numbers to a Lagrange polynomial extension. We define them by generalizing Worpitzky's identity appropriately, and derive a recursion and an explicit sum formulae. Special cases include $r$-Whitney Eulerian numbers and elliptic Eulerian numbers.
- [8] arXiv:2404.17002 [pdf, ps, other]
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Title: Quiver connections and bimodules of basic algebrasAuthors: Sean ThompsonSubjects: Category Theory (math.CT); Quantum Algebra (math.QA); Rings and Algebras (math.RA)
Motivated by the problem of classifying quantum symmetries of non-semisimple, finite-dimensional associative algebras, we define a notion of connection between bounded quivers and build a bicategory of bounded quivers and quiver connections. We prove this bicategory is equivalent to a bicategory of basic algebras, bimodules, and intertwiners with some additional structure.
- [9] arXiv:2404.17005 [pdf, ps, other]
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Title: Uncommon linear systems of two equationsComments: 62 pages, 1 figureSubjects: Combinatorics (math.CO); Number Theory (math.NT)
A system of linear equations $L$ is common over $\mathbb{F}_p$ if, as $n\to\infty$, any 2-coloring of $\mathbb{F}_p^n$ gives asymptotically at least as many monochromatic solutions to $L$ as a random 2-coloring. The notion of common linear systems is analogous to that of common graphs, i.e., graphs whose monochromatic density in 2-edge-coloring of cliques is asymptotically minimized by the random coloring. Saad and Wolf initiated a systematic study on identifying common linear systems, built upon the earlier work of Cameron-Cilleruelo-Serra. When $L$ is a single equation, Fox-Pham-Zhao gave a complete characterization of common linear equations. When $L$ consists of two equations, Kam\v{c}ev-Liebenau-Morrison showed that irredundant $2\times 4$ linear systems are always uncommon. In this work, (1) we determine commonness of all $2\times 5$ linear systems up to a small number of cases, and (2) we show that all $2\times k$ linear systems with $k$ even and girth (minimum number of nonzero coefficients of a nonzero equation spanned by the system) $k-1$ are uncommon, answering a question of Kam\v{c}ev-Liebenau-Morrison.
- [10] arXiv:2404.17006 [pdf, ps, other]
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Title: Path integral control under McKean-Vlasov dynamicsAuthors: Timothy BennettComments: 9Subjects: Optimization and Control (math.OC); Probability (math.PR)
We investigate the complexities of the McKean-Vlasov optimal control problem, exploring its various formulations such as the strong and weak formulations, as well as both Markovian and non-Markovian setups within financial markets. Furthermore, we examine scenarios where the law governing the control process impacts the dynamics of options. By conceptualizing controls as probability measures on a fitting canonical space with filtrations, we unlock the potential to devise classical measurable selection methods, conditioning strategies, and concatenation arguments within this innovative framework. These tools enable us to establish the dynamic programming principle under a wide range of conditions.
- [11] arXiv:2404.17023 [pdf, other]
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Title: Out-of-Distribution Detection using Maximum Entropy CodingAuthors: Mojtaba Abolfazli, Mohammad Zaeri Amirani, Anders Høst-Madsen, June Zhang, Andras BratincsakSubjects: Information Theory (cs.IT); Machine Learning (cs.LG)
Given a default distribution $P$ and a set of test data $x^M=\{x_1,x_2,\ldots,x_M\}$ this paper seeks to answer the question if it was likely that $x^M$ was generated by $P$. For discrete distributions, the definitive answer is in principle given by Kolmogorov-Martin-L\"{o}f randomness. In this paper we seek to generalize this to continuous distributions. We consider a set of statistics $T_1(x^M),T_2(x^M),\ldots$. To each statistic we associate its maximum entropy distribution and with this a universal source coder. The maximum entropy distributions are subsequently combined to give a total codelength, which is compared with $-\log P(x^M)$. We show that this approach satisfied a number of theoretical properties.
For real world data $P$ usually is unknown. We transform data into a standard distribution in the latent space using a bidirectional generate network and use maximum entropy coding there. We compare the resulting method to other methods that also used generative neural networks to detect anomalies. In most cases, our results show better performance. - [12] arXiv:2404.17024 [pdf, other]
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Title: Evolution of random representable matroids: minors, circuits, connectivity and the critical numberComments: 26 pagesSubjects: Combinatorics (math.CO)
We study the evolution of random matroids represented by the sequence of random matrices over ${\mathbb F}_q$ where columns are added one after the other, and each column vector is a uniformly random vector in ${\mathbb F}_q^n$, independent of each other. We study the appearance of matroid minors, the appearance of circuits, the evolution of the connectivities and the critical number. We settle several open problems in the literature.
- [13] arXiv:2404.17035 [pdf, ps, other]
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Title: Compact embeddings and Pitt's property for weighted sequence spaces of Sobolev typeAuthors: Pierre-A. VuillermotComments: 10 pagesSubjects: Functional Analysis (math.FA)
In this article we introduce a new class of weighted sequence spaces of Sobolev type and prove several compact embedding theorems for them. In all cases our proofs are based on the existence of a Schauder basis that spans all of the spaces under consideration. Our choice of spaces is primarily motivated by earlier work on infinite-dimensional dynamical systems of hyperbolic type arising in non-equilibrium statistical mechanics. We also prove a theorem of Pitt's type asserting that under some conditions every linear bounded transformation from one weighted sequence space into another is compact.
- [14] arXiv:2404.17060 [pdf, ps, other]
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Title: On convergence of a sequence of mappings with inverse modulus inequality to a discrete mappingComments: in Ukrainian languageSubjects: Complex Variables (math.CV)
We have studied the mappings that satisfy the Poletsky-type inverse inequality in the domain of the Euclidean space. It is proved that the uniform boundary of the family of such mappings is a discrete mapping. We separately considered domains that are locally connected at their boundary and regular domains in the quasiconformal sense.
- [15] arXiv:2404.17062 [pdf, other]
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Title: Equivariant Double-Slice GenusAuthors: Malcolm GabbardComments: 18 pages, 13 figures. All comments are welcome!Subjects: Geometric Topology (math.GT)
In this paper we define the equivariant double-slice genus and equivariant super-slice genus of a strongly invertible knot. We prove lower bounds for both the equivariant double-slice genus and the equivariant super-slice genus. Using these bounds we find a family of knots which are double-slice and equivariantly slice but have arbitrarily large equivariant double-slice genus. From this, we construct equivariantly knotted symmetric 3-balls as well as unknotted symmetric 2-spheres which do not bound equivariant 3-balls. Additionally, using double-slice and super-slice genus we construct properly embedded surfaces with large 1-handle stabilization distance distance rel boundary.
- [16] arXiv:2404.17067 [pdf, ps, other]
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Title: The distance function on Coxeter-like graphs and self-dual codesComments: 44 pages, 1 figureSubjects: Combinatorics (math.CO); Information Theory (cs.IT)
Let $SGL_n(\mathbb{F}_2)$ be the set of all invertible $n\times n$ symmetric matrices over the binary field $\mathbb{F}_2$. Let $\Gamma_n$ be the graph with the vertex set $SGL_n(\mathbb{F}_2)$ where a pair of matrices $\{A,B\}$ form an edge if and only if $\textrm{rank}(A-B)=1$. In particular, $\Gamma_3$ is the well-known Coxeter graph. The distance function $d(A,B)$ in $\Gamma_n$ is described for all matrices $A,B\in SGL_n(\mathbb{F}_2)$. The diameter of $\Gamma_n$ is computed. For odd $n\geq 3$, it is shown that each matrix $A\in SGL_n(\mathbb{F}_2)$ such that $d(A,I)=\frac{n+5}{2}$ and $\textrm{rank}(A-I)=\frac{n+1}{2}$ where $I$ is the identity matrix induces a self-dual code in $\mathbb{F}_2^{n+1}$. Conversely, each self-dual code $C$ induces a family ${\cal F}_C$ of such matrices $A$. The families given by distinct self-dual codes are disjoint. The identification $C\leftrightarrow {\cal F}_C$ provides a graph theoretical description of self-dual codes. A result of Janusz (2007) is reproved and strengthened by showing that the orthogonal group ${\cal O}_n(\mathbb{F}_2)$ acts transitively on the set of all self-dual codes in $\mathbb{F}_2^{n+1}$.
- [17] arXiv:2404.17069 [pdf, other]
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Title: Channel Modeling for FR3 Upper Mid-band via Generative Adversarial NetworksSubjects: Information Theory (cs.IT); Machine Learning (cs.LG); Signal Processing (eess.SP)
The upper mid-band (FR3) has been recently attracting interest for new generation of mobile networks, as it provides a promising balance between spectrum availability and coverage, which are inherent limitations of the sub 6GHz and millimeter wave bands, respectively. In order to efficiently design and optimize the network, channel modeling plays a key role since FR3 systems are expected to operate at multiple frequency bands. Data-driven methods, especially generative adversarial networks (GANs), can capture the intricate relationships among data samples, and provide an appropriate tool for FR3 channel modeling. In this work, we present the architecture, link state model, and path generative network of GAN-based FR3 channel modeling. The comparison of our model greatly matches the ray-tracing simulated data.
- [18] arXiv:2404.17076 [pdf, ps, other]
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Title: Thermodynamic formalism and hyperbolic Baker domains: Real-analyticity of the Hausdorff dimensionAuthors: Adrián Esparza-AmadorSubjects: Dynamical Systems (math.DS)
We consider the family of entire maps given by $f_{\ell,c}(z)=\ell+c-(\ell-1)\log c-e^z$, where $c\in D(\ell,1)$ and $\ell\in\mathbb N$, $\ell\geq2$. By using the property of $f_{\ell,c}$ to be dynamically projected to an infinite cylinder $\mathbb C/2\pi I\mathbb Z$, where the thermodynamic formalism tools are well-defined, we prove as a main result on this work, the real-analyticity of the map $c\mapsto HD(\mathcal{J}_r(f_{\ell,c}))$, here $\mathcal{J}_r(f_{\ell,c})$ is the radial Julia set.
- [19] arXiv:2404.17081 [pdf, other]
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Title: Collar parameters for Teichmuller Space & Measured Foliations on a Surface Research AnnouncementSubjects: Geometric Topology (math.GT)
We defined a new set of coordinates with respect to which the Thurston compactification of Teichmuller space is the radial compactification of Euclidean space.
- [20] arXiv:2404.17085 [pdf, other]
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Title: Gain distance Laplacian matrices for complex unit gain graphsAuthors: Suliman KhanComments: 18 pages, 1 figureSubjects: Combinatorics (math.CO)
A complex unit gain graph (or a $\mathbb{T}$-gain graph) $\Theta(\Sigma,\varphi)$ is a graph where the unit complex number is assign by a function $\varphi$ to every oriented edge of $\Sigma$ and assign its inverse to the opposite orientation. In this paper, we define the two gain distance Laplacian matrices $DL^{\max}_{<}(\Theta)$ and $DL^{\min}_{<}(\Theta)$ corresponding to the two gain distance matrices $D^{\max}_{<}(\Theta)$ and $D^{\min}_{<}(\Theta)$ defined for $\mathbb{T}$-gain graphs $\Theta(\Sigma,\varphi)$, for any vertex ordering $(V(\Sigma),<)$. Furthermore, we provide the characterization of singularity and find formulas for the rank of those Laplacian matrices. We also establish two types of characterization for balanced in complex unit gain graphs while using the gain distance Lapalcian matrices. Most of the results are derived by proving them more generally for weighted $\mathbb{T}$-gain graphs.
- [21] arXiv:2404.17090 [pdf, ps, other]
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Title: Killing Fields on Compact m-Quasi-Einstein ManifoldsAuthors: Eric CochranComments: 8 pagesSubjects: Differential Geometry (math.DG)
We show that given a compact, connected $m$-quasi Einstein manifold $(M,g,X)$ without boundary, the potential vector field $X$ is Killing if and only if $(M, g)$ has constant scalar curvature. This extends a result of Bahuaud-Gunasekaran-Kunduri-Woolgar, where it is shown that $X$ is Killing if $X$ is incompressible. We also provide a sufficient condition for a compact, non-gradient $m$-quasi Einstein metric to admit a Killing field. We do this by following a technique of Dunajski and Lucietti, who prove that a Killing field always exists in this case when $m=2$. This condition provides an alternate proof of the aforementioned result of Bahuaud-Gunasekaran-Kunduri-Woolgar. This alternate proof works in the $m = -2$ case as well, which was not covered in the original proof.
- [22] arXiv:2404.17096 [pdf, ps, other]
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Title: Automorphism groups of parafermion vertex operator algebras: general caseComments: 23 pagesSubjects: Quantum Algebra (math.QA); Group Theory (math.GR)
We complete the program for determining the full automorphism groups of all parafermion vertex operator algebras associated with simple Lie algebras and positive integral levels. We show that the full automorphism group of the parafermion vertex operator algebra is isomorphic to the automorphism group of the associated root system for the remaining cases: (i) the level is at least $3$; (ii) the level is $2$ and the simple Lie algebra is non simply laced.
- [23] arXiv:2404.17102 [pdf, other]
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Title: An explicit construction of optimized interpolation points on the 4-simplexSubjects: Numerical Analysis (math.NA)
In this work, a family of symmetric interpolation points are generated on the four-dimensional simplex (i.e. the pentatope). These points are optimized in order to minimize the Lebesgue constant. The process of generating these points closely follows that outlined by Warburton in "An explicit construction of interpolation nodes on the simplex," Journal of Engineering Mathematics, 2006. Here, Warburton generated optimal interpolation points on the triangle and tetrahedron by formulating explicit geometric warping and blending functions, and applying these functions to equidistant nodal distributions. The locations of the resulting points were Lebesgue-optimized. In our work, we extend this procedure to four dimensions, and construct interpolation points on the pentatope up to order ten. The Lebesgue constants of our nodal sets are calculated, and are shown to outperform those of equidistant nodal distributions.
- [24] arXiv:2404.17103 [pdf, ps, other]
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Title: Asymptotics for Sobolev extremals: the hyperdiffusive caseAuthors: Grey ErcoleComments: 13 pagesSubjects: Analysis of PDEs (math.AP)
Let $\Omega$ be a bounded, smooth domain of $\mathbb{R}^{N},$ $N\geq2.$ For $p>N$ and $1\leq q(p)<\infty$ set \[ \lambda_{p,q(p)}:=\inf\left\{ \int_{\Omega}\left\vert \nabla u\right\vert ^{p}\mathrm{d}x:u\in W_{0}^{1,p}(\Omega)\text{ \ and \ }\int_{\Omega }\left\vert u\right\vert ^{q(p)}\mathrm{d}x=1\right\} \] and let $u_{p,q(p)}$ denote a corresponding positive extremal function. We show that if $\lim\limits_{p\rightarrow\infty}q(p)=\infty$, then $\lim\limits_{p\rightarrow\infty}\lambda_{p,q(p)}^{1/p}=\left\Vert d_{\Omega }\right\Vert _{\infty}^{-1}$, where $d_{\Omega}$ denotes the distance function to the boundary of $\Omega.$ Moreover, in the hyperdiffusive case: $\lim\limits_{p\rightarrow\infty}\frac{q(p)}{p}=\infty,$ we prove that each sequence $u_{p_{n},q(p_{n})},$ with $p_{n}\rightarrow\infty,$ admits a subsequence converging uniformly in $\overline{\Omega}$ to a viscosity solution to the problem \[ \left\{ \begin{array} [c]{lll} -\Delta_{\infty}u=0 & \text{in} & \Omega\setminus M\\ u=0 & \text{on} & \partial\Omega\\ u=1 & \text{in} & M, \end{array} \right. \] where $M$ is a closed subset of the set of all maximum points of $d_{\Omega}.$
- [25] arXiv:2404.17106 [pdf, ps, other]
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Title: Edge-connectivity between (edge-)ends of infinite graphsComments: 18 pages, 1 figureSubjects: Combinatorics (math.CO)
In infinite graph theory, the notion of ends, first introduced by Freudenthal and Jung for locally finite graphs, plays an important role when generalizing statements from finite graphs to infinite ones. Nash-Willian's Tree-Packing Theorem and MacLane's Planarity Criteria are examples of results that allow a topological approach, in which ends might be considered as endpoints of rays. In fact, there are extensive works in the literature showing that classical theorems of (vertex-)connectivity for finite graphs can be discussed regarding ends, in a more general context. However, aiming to generalize results of edge-connectivity, this paper recalls the definition of edge-ends in infinite graphs due to Hahn, Laviolette and \v{S}ir\'a\v{n}. In terms of that object, we state an edge version of Menger's Theorem (following a previous work of Polat) and generalize the Lov\'asz-Cherkassky Theorem for infinite graphs with edge-ends (inspired by a paper of Jacobs, Jo\'o, Knappe, Kurkofka and Melcher).
- [26] arXiv:2404.17109 [pdf, ps, other]
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Title: An adaptive linearized alternating direction multiplier method with a relaxation step for convex programmingAuthors: Boran WangComments: arXiv admin note: substantial text overlap with arXiv:2404.11435Subjects: Optimization and Control (math.OC)
Alternating direction multiplication is a powerful technique for solving convex optimisation problems. When challenging subproblems are encountered in the real world, it is useful to solve them by introducing neighbourhood terms. When the neighbourhood matrix is positive definite, the algorithm converges but at the same time makes the iteration step small. Recent studies have revealed the potential non-positive definiteness of the neighbourhood matrix. In this paper, we present an adaptive linearized alternating direction multiplier method with a relaxation step, combining the relaxation step with an adaptive technique. The novelty of the method is to use the information of the current iteration point to dynamically select the neighbourhood matrix, increase the iteration step size, and speed up the convergence of the algorithm.We prove the global convergence of the algorithm theoretically and illustrate the effectiveness of the algorithm using numerical experiments.
- [27] arXiv:2404.17111 [pdf, ps, other]
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Title: Uniform bounds and the inviscid limit for the Navier-Stokes equations with Navier boundary conditionsSubjects: Analysis of PDEs (math.AP)
We consider the vanishing viscosity problem for solutions of the Navier-Stokes equations with Navier boundary conditions in the half-space. We lower the currently known conormal regularity needed to establish that the inviscid limit holds. Our requirement for the Lipschitz initial data is that the first four conormal derivatives are bounded along with two for the gradient. In addition, we establish a new class of initial data for the local existence and uniqueness for the Euler equations in the half-space or a channel for initial data in the conormal space without conormal requirements on the gradient.
- [28] arXiv:2404.17112 [pdf, ps, other]
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Title: Local well-posedness of strong solutions to the 2D nonhomogeneous primitive equations with density-dependent viscositySubjects: Analysis of PDEs (math.AP)
In this paper, we consider the initial-boundary value problem of the nonhomogeneous primitive equations with density-dependent viscosity. Local well-posedness of strong solutions is established for this system with a natural compatibility condition. The initial density does not need to be strictly positive and may contain vacuum. Meanwhile, we also give the corresponding blow-up criterion if the maximum existence interval with respect to the time is finite.
- [29] arXiv:2404.17114 [pdf, ps, other]
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Title: Upgraded free independence phenomena for random unitariesComments: 24 pagesSubjects: Operator Algebras (math.OA); Probability (math.PR)
We study upgraded free independence phenomena for unitary elements $u_1$, $u_2$, \dots in a matrix ultraproduct constructed from the large-$n$ limit of Haar random unitaries. Using a uniform asymptotic freeness argument and volumetric analysis, we establish freeness of several much larger algebras $\mathcal{A}_j$ containing $u_j$, which sheds new light on the structural properties of matrix ultraproducts, as well as free products of tracial von Neumann algebras. First, motivated by Houdayer and Ioana's results on free independence of approximate commutants in free products, we show that the commutants $\{u_j\}'\cap \prod_{n\to \mathcal{U}}\mathbb{M}_n(\mathbb{C})$ in the matrix ultraproduct are freely independent. We then prove free independence of the entire Pinsker algebras $\mathcal{P}_j$ containing $u_j$; $\mathcal{P}_j$ by definition is the maximal subalgebra containing $u_j$ with vanishing $1$-bounded entropy in the sense of Hayes, and $\mathcal{P}_j$ contains for instance any amenable algebra containing $u_j$ as well as the entire sequential commutation orbit of $u_j$, and it is closed under taking iterated wq-normalizers. Through an embedding argument, we go back and deduce analogous free independence results for $\mathcal{M}^{\mathcal{U}}$ when $\mathcal{M}$ is a free product of Connes embeddable tracial von Neumann algebras $\mathcal{M}_i$, which thus yields a generalization and a new proof of Houdayer--Ioana's results in this case.
- [30] arXiv:2404.17116 [pdf, ps, other]
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Title: Topological remarks on end and edge-end spacesComments: 28 pages, 1 figureSubjects: Combinatorics (math.CO); General Topology (math.GN)
The notion of ends in an infinite graph $G$ might be modified if we consider them as equivalence classes of infinitely edge-connected rays, rather than equivalence classes of infinitely (vertex-)connected ones. This alternative definition yields to the edge-end space $\Omega_E(G)$ of $G$, in which we can endow a natural (edge-)end topology. For every graph $G$, this paper proves that $\Omega_E(G)$ is homeomorphic to $\Omega(H)$ for some possibly another graph $H$, where $\Omega(H)$ denotes its usual end space. However, we also show that the converse statement does not hold: there is a graph $H$ such that $\Omega(H)$ is not homeomorphic to $\Omega_E(G)$ for any other graph $G$. In other words, as a main result, we conclude that the class of topological spaces $\Omega_E = \{\Omega_E(G) : G \text{ graph}\}$ is strictly contained in $\Omega = \{\Omega(H) : H \text{ graph}\}$.
- [31] arXiv:2404.17121 [pdf, ps, other]
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Title: Oberwolfach Workshop Report: Analysis, Geometry and Topology of Positive Scalar Curvature Metrcs: Limits of sequences of manifolds with nonnegative scalar curvature and other hypothesesSubjects: Differential Geometry (math.DG); Metric Geometry (math.MG)
This report contains a survey of examples of sequences of manifolds with nonnegative scalar curvature including an extreme example with Wenchuan Tian and Changliang Wang. It announces a paper with Wenchaun Tian proving the GH and SWIF convergence of the extreme example. It contains six Open Questions concerning such sequences.
- [32] arXiv:2404.17131 [pdf, ps, other]
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Title: Notes on a conjecture by Paszkiewicz on an ordered product of positive contractionsAuthors: Hiroshi AndoComments: 6 pagesSubjects: Spectral Theory (math.SP); Operator Algebras (math.OA)
Paszkiewicz's conjecture asserts that given a decreasing sequence $T_1\ge T_2\ge \dots$ of positive contractions on a separable infinite-dimensional Hilbert space $H$, the product $S_n=T_nT_{n-1}\cdots T_1$ converges in the strong operator topology. In these notes, we give an equivalent, more precise formulation of his conjecture. Moreover, we show that the conjecture is true for the following two cases: (1) $1$ is not in the essential spectrum of $T_n$ for some $n\in \mathbb{N}$. (2) The von Neumann algebra generated by $\{T_n\mid n\in \mathbb{N}\}$ admits a faithful normal tracial state. We also remark that the analogous conjecture for the weak convergence is true.
- [33] arXiv:2404.17134 [pdf, ps, other]
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Title: Boundedness of log Fano cone singularities and discreteness of local volumesComments: 20 pages. Comments are welcome!Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC); Differential Geometry (math.DG)
We prove that in any fixed dimension, K-semistable log Fano cone singularities whose volumes are bounded from below by a fixed positive number form a bounded set. As a consequence, we show that the set of local volumes of klt singularities of a fixed dimension has zero as the only accumulation point.
- [34] arXiv:2404.17135 [pdf, ps, other]
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Title: Hausdorff dimension of some exceptional sets in Lüroth expansionsSubjects: Number Theory (math.NT)
In this paper, we study the metrical theory of the growth rate of digits in L\"{u}roth expansions. More precisely, for $ x\in \left( 0,1 \right] $, let $ \left[ d_1\left( x \right) ,d_2\left( x \right) ,\cdots \right] $ denote the L\"{u}roth expansion of $ x $, we completely determine the Hausdorff dimension of the following sets \begin{align*}
E_{\mathrm{sup}}\left( \psi \right) =\Big\{ x\in \left( 0,1 \right] :\limsup\limits_{n\rightarrow \infty}\frac{\log d_n\left( x \right)}{\psi \left( n \right)}=1 \Big\} , \end{align*} \begin{align*}
E\left( \psi \right) =\Big\{ x\in \left( 0,1 \right] :\lim_{n\rightarrow \infty}\frac{\log d_n\left( x \right)}{\psi \left( n \right)}=1 \Big\} \end{align*} and \begin{align*}
E_{\mathrm{inf}}\left( \psi \right) =\Big\{ x\in \left( 0,1 \right] : \liminf_{n\rightarrow \infty}\frac{\log d_n\left( x \right)}{\psi \left( n \right)}=1 \Big\} , \end{align*} where $ \psi :\mathbb{N} \rightarrow \mathbb{R} ^+ $ is an arbitrary function satisfying $ \psi \left( n \right) \rightarrow \infty$ as $n\rightarrow \infty$. - [35] arXiv:2404.17137 [pdf, ps, other]
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Title: Global existence and geometry of constant mass aspect function foliation in perturbed Schwarzschild spacetimeAuthors: Pengyu LeComments: 110 pagesSubjects: Differential Geometry (math.DG); General Relativity and Quantum Cosmology (gr-qc)
The constant mass function foliation has been shown useful for studying the null Penrose inequality on a null hypersurface, because of the monotonicity formula of Hawking mass along such a foliation. In this paper, we show the global existence of the constant mass aspect function foliation on a nearly spherically symmetric incoming null hypersurface, emanating from a spacelike surface near the apparent horizon to the past null infinity in a vacuum perturbed Schwarzschild spacetime. Moreover, we study the geometry of the constant mass aspect function foliation, by comparing with the spherically symmetric foliation in the Schwarzschild spacetime. The knowledge about the geometry of the foliation is essential for investigating the perturbation of the constant mass aspect function foliation, which is the core in the application to the null Penrose inequality for a vacuum perturbed Schwarzschild spacetime.
- [36] arXiv:2404.17145 [pdf, other]
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Title: Finite volume simulation of a semi-linear Neumann problem (Keller-Segel model) on rectangular domainsSubjects: Mathematical Physics (math-ph)
In this study, the finite volume method is implemented for solving the problem of the semilinear equation: $-d \delta u+ u=u^q (d, q>0) $with a homogeneous Neumann boundary condition. This problem is equivalent to the known stationary Keller-Segel model, which arises in chemotaxis.After discretization, a nonlinear algebraic system is obtained and solved on the platform Matlab. As a result, many single peaked and multi-peaked shapes in 3D and contour plots can be drawn depending on the parameters d and q.
- [37] arXiv:2404.17150 [pdf, other]
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Title: A concentration phenomenon for $h$-extra edge-connectivity reliability analysis of enhanced hypercubes Q_{n,2} with exponentially many faulty linksSubjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM)
Reliability assessment of interconnection networks is critical to the design and maintenance of multiprocessor systems. The (n, k)-enhanced hypercube Q_{n,k} as a variation of the hypercube Q_{n}, was proposed by Tzeng and Wei in 1991. As an extension of traditional edge-connectivity, h-extra edge-connectivity of a connected graph G, \lambda_h(G), is an essential parameter for evaluating the reliability of interconnection networks. This article intends to study the h-extra edge-connectivity of the (n,2)-enhanced hypercube Q_{n,2}. Suppose that the link malfunction of an interconnection network Q_{n,2} does not isolate any subnetwork with no more than h-1 processors, the minimum number of these possible faulty links concentrate on a constant 2^{n-1} for each integer \lceil\frac{11\times2^{n-1}}{48}\rceil \leq h \leq 2^{n-1} and n\geq 9. That is, for about 77.083 percent values of h\leq2^{n-1}, the corresponding h-extra edge-connectivity of Q_{n,2}, \lambda_h(Q_{n,2}), presents a concentration phenomenon. Moreover, the above lower and upper bounds of h are both tight.
- [38] arXiv:2404.17155 [pdf, ps, other]
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Title: Refined distributional limit theorems for compound sumsAuthors: Vsevolod K. MalinovskiiComments: 25 pages, 3 figuresSubjects: Probability (math.PR)
The paper is a sketch of systematic presentation of distributional limit theorems and their refinements for compound sums. When analyzing, e.g., ergodic semi-Markov systems with discrete or continuous time, this allows us to separate those aspects that lie within the theory of random processes from those that relate to the classical summation theory. All these limit theorems are united by a common approach to their proof, based on the total probability rule, auxiliary multidimensional limit theorems for sums of independent random vectors, and (optionally) modular analysis.
- [39] arXiv:2404.17156 [pdf, other]
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Title: Construction of a new (3 + 1)-dimensional KdV equation and its closed-form solutions with solitary wave behaviour and conserved vectorsSubjects: Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI)
This paper discusses the construction of a new $(3+1)$-dimensional Korteweg-de Vries (KdV) equation. By employing the KdV's recursion operator, we extract two equations, and with elemental computation steps, the obtained result is $ 3u_{xyt}+3u_{xzt}-(u_{t}-6uu_{x}+u_{xxx})_{yz}-2\left(u_{x}\partial_{x}^{-1}u_{y}\right)_{xz}-2\left(u_{x}\partial_{x}^{-1}u_{z}\right)_{xy}=0 $. We then transform the new equation to a simpler one to avoid the appearance of the integral in the equation. Thereafter, we apply the Lie symmetry technique and gain a $7$-dimensional Lie algebra $L_7$ of point symmetries. The one-dimensional optimal system of Lie subalgebras is then computed and used in the reduction process to achieve seven exact solutions. These obtained solutions are graphically illustrated as 3D and 2D plots that show different propagations of solitary wave solutions such as breather, periodic, bell shape, and others. Finally, the conserved vectors are computed by invoking Ibragimov's method.
- [40] arXiv:2404.17162 [pdf, ps, other]
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Title: Group Vertex Magicness of H-join and Generalised Friendship GraphSubjects: Combinatorics (math.CO)
In this paper we have discussed the group vertex magicness of H-join of family of graphs and generalized friendship graph.
- [41] arXiv:2404.17163 [pdf, ps, other]
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Title: Intractability results for integration in tensor product spacesSubjects: Numerical Analysis (math.NA)
We study lower bounds on the worst-case error of numerical integration in tensor product spaces. As reference we use the $N$-th minimal error of linear rules that use $N$ function values. The information complexity is the minimal number $N$ of function evaluations that is necessary such that the $N$-th minimal error is less than a factor $\varepsilon$ times the initial error. We are interested to which extent the information complexity depends on the number $d$ of variables of the integrands. If the information complexity grows exponentially fast in $d$, then the integration problem is said to suffer from the curse of dimensionality.
Under the assumption of the existence of a worst-case function for the uni-variate problem we present two methods for providing good lower bounds on the information complexity. The first method is based on a suitable decomposition of the worst-case function. This method can be seen as a generalization of the method of decomposable reproducing kernels, that is often successfully applied when integration in Hilbert spaces with a reproducing kernel is studied. The second method, although only applicable for positive quadrature rules, has the advantage, that it does not require a suitable decomposition of the worst-case function. Rather, it is based on a spline approximation of the worst-case function and can be used for analytic functions.
The methods presented can be applied to problems beyond the Hilbert space setting. For demonstration purposes we apply them to several examples, notably to uniform integration over the unit-cube, weighted integration over the whole space, and integration of infinitely smooth functions over the cube. Some of these results have interesting consequences in discrepancy theory. - [42] arXiv:2404.17165 [pdf, ps, other]
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Title: Inequalities involving arithmetic functionsAuthors: S. I. DimitrovSubjects: Number Theory (math.NT)
This paper presents a brief survey of the most important and the most remarkable inequalities involving the basic arithmetic functions.
- [43] arXiv:2404.17168 [pdf, ps, other]
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Title: On the invertibility of matrices with a double saddle-point structureSubjects: Numerical Analysis (math.NA)
We establish necessary and sufficient conditions for invertiblility of symmetric three-by-three block matrices having a double saddle-point structure that guarantee the unique solvability of double saddle-point systems. We consider various scenarios, including the case where all diagonal blocks are allowed to be rank deficient. Under certain conditions related to the ranks of the blocks and intersections of their kernels, an explicit formula for the inverse is derived.
- [44] arXiv:2404.17172 [pdf, ps, other]
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Title: Geometry on deformations of S1 singularitiesAuthors: Runa ShimadaComments: 15 pages, 7 figuresSubjects: Differential Geometry (math.DG)
For a one parameter deformation of the $S_1$ singularity in the three space, we give a form using only isometric maps of the target. Using this form, we study differential geometric properties of $S_1$ singularities and the Whitney umbrellas appearing in the deformation.
- [45] arXiv:2404.17175 [pdf, ps, other]
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Title: Over-the-Air Modulation for RIS-assisted Symbiotic Radios: Design, Analysis, and OptimizationComments: 13 pages, 9 figuresSubjects: Information Theory (cs.IT); Signal Processing (eess.SP)
In reconfigurable intelligent surface (RIS)-assisted symbiotic radio (SR), an RIS is exploited to assist the primary system and to simultaneously operate as a secondary transmitter by modulating its own information over the incident primary signal from the air. Such an operation is called over-the-air modulation. The existing modulation schemes such as on-off keying and binary phase-shift keying suffer from two problems for joint detection of the primary and secondary signals in RIS-assisted SR, i.e., one is the detection ambiguity problem when the direct link is blocked, and the other is the bit error rate (BER) error-floor problem when the direct link is weak. To address the two problems, we propose a novel modulation scheme by dividing the phase-shift matrix into two parts: one is the assistance beamforming matrix for assisting the primary system and the other is the transmission beamforming matrix for delivering the secondary signal. To optimize the assistance and transmission beamforming matrices, we first introduce an assistance factor that describes the performance requirement of the primary system and then formulate a problem to minimize the BER of the secondary system, while guaranteeing the BER requirement of the primary system controlled by the assistance factor. To solve this non-convex problem, we resort to the successive convex approximation technique to obtain a suboptimal solution. Furthermore, to draw more insights, we propose a low-complexity assistance-transmission beamforming structure by borrowing the idea from the classical maximum ratio transmission and zero forcing techniques. Finally, simulation results reveal an interesting tradeoff between the BER performance of the primary and secondary systems by adjusting the assistance factor.
- [46] arXiv:2404.17185 [pdf, other]
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Title: On potential density of integral points on the complement of some subvarieties in the projective spaceAuthors: Motoya TeranishiComments: 17 pages, 2 figuresSubjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
We study some density results for integral points on the complement of a closed subvariety in the $n$-dimensional projective space over a number field. For instance, we consider a subvariety whose components consist of $n-1$ hyperplanes plus one smooth quadric hypersurface in general position, or four hyperplanes in general position plus a finite number of concurrent straight lines. In these cases, under some conditions on intersection, we show that the integral points on the complements are potentially dense. Our results are generalizations of Corvaja-Zucconi's results for complements of subvarieties in the two or three dimensional projective space.
- [47] arXiv:2404.17188 [pdf, ps, other]
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Title: Hipster Tree Growth RatesAuthors: Alexander WongComments: 9 pages, 55th Southeastern International Conference on Combinatorics, Graph Theory & ComputingSubjects: Combinatorics (math.CO)
A plane rooted tree is called a hipster tree if it has no nontrivial automorphisms. Equivalently, a tree is a hipster tree if no two siblings have isomorphic subtrees. We impose the hipster condition on various classes of rooted trees. By approximating the generating function for the number of such trees, we obtain bounds on their exponential growth rates.
- [48] arXiv:2404.17190 [pdf, other]
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Title: Delay-tolerant distributed Bregman proximal algorithmsJournal-ref: Optimization Methods and Software, 2024, pp.1-17. \&\#x27E8;10.1080/10556788.2023.2278089\&\#x27E9Subjects: Optimization and Control (math.OC)
Many problems in machine learning write as the minimization of a sum of individual loss functions over the training examples. These functions are usually differentiable but, in some cases, their gradients are not Lipschitz continuous, which compromises the use of (proximal) gradient algorithms. Fortunately, changing the geometry and using Bregman divergences can alleviate this issue in several applications, such as for Poisson linear inverse problems.However, the Bregman operation makes the aggregation of several points and gradients more involved, hindering the distribution of computations for such problems. In this paper, we propose an asynchronous variant of the Bregman proximal-gradient method, able to adapt to any centralized computing system. In particular, we prove that the algorithm copes with arbitrarily long delays and we illustrate its behavior on distributed Poisson inverse problems.
- [49] arXiv:2404.17192 [pdf, other]
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Title: A multi-scale multi-lane model for traffic regulation via autonomous vehiclesSubjects: Analysis of PDEs (math.AP)
We propose a new model for multi-lane traffic with moving bottlenecks, e.g., autonomous vehicles (AV). It consists of a system of balance laws for traffic in each lane, coupled in the source terms for lane changing, and fully coupled to ODEs for the AVs' trajectories.More precisely, each AV solves a controlled equation depending on the traffic density, while the PDE on the corresponding lane has a flux constraint at the AV's location. We prove existence of entropy weak solutions, and we characterize the limiting behavior for the source term converging to zero (without AVs), corresponding to a scalar conservation law for the total density.The convergence in the presence of AVs is more delicate and we show that the limit does not satisfy an entropic equation for the total density as in the original coupled ODE-PDE model. Finally, we illustrate our results via numerical simulations.
- [50] arXiv:2404.17197 [pdf, ps, other]
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Title: Lecture notes on martingale inequalitiesAuthors: Pavel Zorin-KranichComments: 45 pages. University of Bonn, Winter term 2021/22Subjects: Probability (math.PR)
We present a few techniques for proving $L^p$ estimates for martingales. Basic applications to It\^o integration and rough paths are included.
- [51] arXiv:2404.17201 [pdf, ps, other]
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Title: Optimal gradient estimates for the insulated conductivity problem with general convex inclusions caseComments: arXiv admin note: text overlap with arXiv:2203.10081 by other authorsSubjects: Analysis of PDEs (math.AP)
In this paper we study the insulated conductivity problem involving two adjacent convex insulators embedded in a bounded domain. It is known that the gradient of solutions may blow up as the distance between two inclusions tends to zero. For general convex insulators, we establish a pointwise upper bound and a lower bound of the gradient with optimal blow up rates, which are associated with the first nonzero eigenvalue of an elliptic operator determined by the geometry of insulators. This extends the previous result for ball insulators in \cite{DLY}.
- [52] arXiv:2404.17209 [pdf, other]
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Title: Generalized multi-view model: Adaptive density estimation under low-rank constraintsSubjects: Statistics Theory (math.ST)
We study the problem of bivariate discrete or continuous probability density estimation under low-rank constraints.For discrete distributions, we assume that the two-dimensional array to estimate is a low-rank probability matrix.In the continuous case, we assume that the density with respect to the Lebesgue measure satisfies a generalized multi-view model, meaning that it is $\beta$-H{\"o}lder and can be decomposed as a sum of $K$ components, each of which is a product of one-dimensional functions.In both settings, we propose estimators that achieve, up to logarithmic factors, the minimax optimal convergence rates under such low-rank constraints.In the discrete case, the proposed estimator is adaptive to the rank $K$. In the continuous case, our estimator converges with the $L_1$ rate $\min((K/n)^{\beta/(2\beta+1)}, n^{-\beta/(2\beta+2)})$ up to logarithmic factors, and it is adaptive to the unknown support as well as to the smoothness $\beta$ and to the unknown number of separable components $K$. We present efficient algorithms for computing our estimators.
- [53] arXiv:2404.17211 [pdf, other]
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Title: Pseudo-Observations and Super Learner for the Estimation of the Restricted Mean Survival TimeAuthors: Ariane Cwiling (MAP5 - UMR 8145), Vittorio Perduca (MAP5 - UMR 8145), Olivier Bouaziz (MAP5 - UMR 8145)Subjects: Statistics Theory (math.ST); Methodology (stat.ME); Machine Learning (stat.ML)
In the context of right-censored data, we study the problem of predicting the restricted time to event based on a set of covariates. Under a quadratic loss, this problem is equivalent to estimating the conditional Restricted Mean Survival Time (RMST). To that aim, we propose a flexible and easy-to-use ensemble algorithm that combines pseudo-observations and super learner. The classical theoretical results of the super learner are extended to right-censored data, using a new definition of pseudo-observations, the so-called split pseudo-observations. Simulation studies indicate that the split pseudo-observations and the standard pseudo-observations are similar even for small sample sizes. The method is applied to maintenance and colon cancer datasets, showing the interest of the method in practice, as compared to other prediction methods. We complement the predictions obtained from our method with our RMST-adapted risk measure, prediction intervals and variable importance measures developed in a previous work.
- [54] arXiv:2404.17219 [pdf, other]
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Title: Well-posedness and potential-based formulation for the propagation of hydro-acoustic waves and tsunamisAuthors: Juliette Dubois (RWTH), Sébastien Imperiale (LMS), Anne Mangeney (IPGP (UMR\_7154)), Jacques Sainte-Marie (LJLL (UMR\_7598))Subjects: Analysis of PDEs (math.AP); Geophysics (physics.geo-ph)
We study a linear model for the propagation of hydro-acoustic waves and tsunami in a stratified free-surface ocean. A formulation was previously obtained by linearizing the compressible Euler equations. The new formulation is obtained by studying the functional spaces and operators associated to the model. The mathematical study of this new formulation is easier and the discretization is also more efficient than for the previous formulation. We prove that both formulations are well posed and show that the solution to the first formulation can be obtained from the solution to the second. Finally, the formulations are discretized using a spectral element method, and we simulate tsunamis generation from submarine earthquakes and landslides.
- [55] arXiv:2404.17220 [pdf, other]
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Title: Infinite dimensional Slow Manifolds for a Linear Fast-Reaction SystemSubjects: Analysis of PDEs (math.AP); Dynamical Systems (math.DS)
The aim of this expository paper is twofold. We start with a concise overview of the theory of invariant slow manifolds for fast-slow dynamical systems starting with the work by Tikhonov and Fenichel to the most recent works on infinite-dimensional fast-slow systems. The main part focuses on a class of linear fast-reaction PDE, which are particular forms of fast-reaction systems. The first result shows the convergence of solutions of the linear system to the limit system as the time-scale parameter $\varepsilon$ goes to zero. Moreover, from the explicit solutions the slow manifold is constructed and the convergence to the critical manifold is proven. The subsequent result, then, states a generalized version of the Fenichel-Tikhonov theorem for linear fast-reaction systems.
- [56] arXiv:2404.17222 [pdf, other]
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Title: Asymptotic analysis for covariance parameter estimation of Gaussian processes with functional inputsSubjects: Statistics Theory (math.ST)
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend these theoretical guarantees to encompass scenarios accounting for approximation errors in the inputs, which allows robustness of practical implementations relying on conventional sampling methods or projections onto a functional basis. Loosely speaking, both consistency and normality hold when the approximation error becomes negligible, a condition that is often achieved as the number of samples or basis functions becomes large. These later asymptotic properties are illustrated through analytical examples, including one that covers the case of non-randomly perturbed grids, as well as several numerical illustrations.
- [57] arXiv:2404.17228 [pdf, ps, other]
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Title: Finite-time blowup for Keller-Segel-Navier-Stokes system in three dimensionsComments: 32 pagesSubjects: Analysis of PDEs (math.AP)
While finite-time blowup solutions have been studied in depth for the Keller-Segel equation, a fundamental model describing chemotaxis, the existence of finite-time blowup solutions to chemotaxis-fluid models remains largely unexplored. To fill this gap in the literature, we use a quantitative method to directly construct a smooth finite-time blowup solution for the Keller-Segel-Navier-Stokes system with buoyancy in 3D. The heart of the proof is to establish the non-radial finite-codimensional stability of an explicit self-similar blowup solution to 3D Keller-Segel equation with the abstract semigroup tool from [Merle-Rapha\"el-Rodnianski-Szeftel, 2022], which partially generalizes the radial stability result [Glogi\'c-Sch\"orkhuber, 2024] to the non-radial setting. Additionally, we introduce a robust localization argument to find blowup solutions with non-negative density and finite mass.
- [58] arXiv:2404.17232 [pdf, ps, other]
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Title: On the locality of formal distributions over pre-Lie and Novikov algebrasComments: 11 pagesSubjects: Quantum Algebra (math.QA)
The Dong Lemma in the theory of vertex algebras states that the locality property of formal distributions over a Lie algebra is preserved under the action of a vertex operator. A~similar statement is known for associative algebras. We study local formal distributions over pre-Lie (right-symmetric), pre-associative (dendriform), and Novikov algebras to show that the analogue of the Dong Lemma holds for Novikov algebras but does not hold for pre-Lie and pre-associative ones.
- [59] arXiv:2404.17234 [pdf, ps, other]
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Title: Generic differentiability and $P$-minimal groupsAuthors: Will JohnsonComments: 50 pagesSubjects: Logic (math.LO)
We prove generic differentiability in $P$-minimal theories, strengthening an earlier result of Kuijpers and Leenknegt. Using this, we prove Onshuus and Pillay's $P$-minimal analogue of Pillay's conjectures on o-minimal groups. Specifically, let $G$ be an $n$-dimensional definable group in a highly saturated model $M$ of a $P$-minimal theory. Then there is an open definable subgroup $H \subseteq G$ such that $H$ is compactly dominated by $H/H^{00}$, and $H/H^{00}$ is a $p$-adic Lie group of the expected dimension.
- [60] arXiv:2404.17236 [pdf, ps, other]
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Title: Stochastic solutions to Hamilton-Jacobi-Bellman Dirichlet problemsAuthors: David CriensSubjects: Analysis of PDEs (math.AP); Probability (math.PR)
We consider a nonlinear Dirichlet problem on a bounded domain whose Hamiltonian is given by a Hamilton-Jacobi-Bellman operator with merely continuous and bounded coefficients. The objective of this paper is to study the existence question from a stochastic point of view. Using a relaxed control framework, we define a candidate for a viscosity solution. We prove that this stochastic solution satisfies viscosity sub- and supersolution properties and we establish a strong Markov selection principle, which shows that the stochastic solution can be realized through a strong Markov family. Building on the selection principle, we investigate regularity properties of the stochastic solution. For certain elliptic cases, we show that the strong Markov selection is even a Feller selection, which entails the continuity of the stochastic solution.
- [61] arXiv:2404.17237 [pdf, ps, other]
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Title: Euclidean distance degree of complete intersections via Newton polytopesComments: 14 pagesSubjects: Algebraic Geometry (math.AG)
In this note, we consider a complete intersection $X=\{x\in \mathbb{R}^n : f_1(x)= \ldots = f_m(x)=0\}, n>m$ and study its Euclidean distance degree in terms of the mixed volume of the Newton polytopes. We show that if the Newton polytopes of $f_j,j=1,\ldots, m$ contain the origin then when these polynomials are generic with respect to their Newton polytopes, the Euclidean distance degree of $X$ can be computed in terms of the mixed volume of Newton polytopes associated to $f_j$. This is a generalization for the result by P. Breiding, F. Sottile and J. Woodcock in case $m=1$.
- [62] arXiv:2404.17250 [pdf, ps, other]
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Title: Omega Theorems for Logarithmic Derivatives of Zeta and L-functions Near the 1-lineSubjects: Number Theory (math.NT)
We establish an omega theorem for logarithmic derivative of the Riemann zeta function near the 1-line by resonance method. We show that the inequality $\left| \zeta^{\prime}\left(\sigma_A+it\right)/\zeta\left(\sigma_A+it\right) \right| \geqslant \left(\left(e^A-1\right)/A\right)\log_2 T + O\left(\log_2 T / \log_3 T\right)$ has a solution $t \in [T^{\beta}, T]$ for all sufficiently large $T,$ where $\sigma_A = 1 - A / \log_2 {T}.$Furthermore, we give a conditional lower bound for the measure of the set of $t$ for which the logarithmic derivative of the Riemann zeta function is large. Moreover, similar results can be generalized to Dirichlet $L$-functions.
- [63] arXiv:2404.17256 [pdf, ps, other]
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Title: Degree bounds for rational generators of invariant fields of finite abelian groupsAuthors: Ben Blum-SmithComments: 11 pagesSubjects: Commutative Algebra (math.AC)
We study degree bounds on rational but not necessarily polynomial generators for the field $\mathbf{k}(V)^G$ of rational invariants of a linear action of a finite abelian group. We show that lattice-theoretic methods used recently by the author and collaborators to study polynomial generators for the same field largely carry over, after minor modifications to the arguments. It then develops that the specific degree bounds found in that setting also carry over.
- [64] arXiv:2404.17258 [pdf, ps, other]
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Title: On Sets of Lengths in Monoids of plus-minus weighted Zero-Sum SequencesSubjects: Commutative Algebra (math.AC); Combinatorics (math.CO); Number Theory (math.NT)
Let $G$ be an additive abelian group. A sequence $S = g_1 \cdot \ldots \cdot g_{\ell}$ of terms from $G$ is a plus-minus weighted zero-sum sequence if there are $\varepsilon_1, \ldots, \varepsilon_{\ell} \in \{-1, 1\}$ such that $\varepsilon_1 g_1 + \ldots + \varepsilon_{\ell} g_{\ell}=0$. We study sets of lengths in the monoid $\mathcal B_{\pm} (G)$ of plus-minus weighted zero-sum sequences over $G$. If $G$ is finite, then sets of lengths are highly structured. If $G$ is infinite, then every finite, nonempty subset of $\mathbb N_{\ge 2}$ is the set of lengths of some sequence $S \in \mathcal B_{\pm} (G)$.
- [65] arXiv:2404.17260 [pdf, ps, other]
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Title: The evolution of the permutahedronComments: 27 pagesSubjects: Combinatorics (math.CO)
In their seminal paper introducing the theory of random graphs, Erd\H{o}s and R\'{e}nyi considered the evolution of the structure of a random subgraph of $K_n$ as the density increases from $0$ to $1$, identifying two key points in this evolution -- the \emph{percolation threshold}, where the order of the largest component seemingly jumps from logarithmic to linear in size, and the \emph{connectivity threshold}, where the subgraph becomes connected. Similar phenomena have been observed in many other random graph models, and in particular, works of Ajtai, Koml\'{o}s and Szemer\'{e}di and of Spencer and Erd\H{o}s determine corresponding thresholds for random subgraphs of the hypercube.
We study similar questions on the \emph{permutahedron}.
The permutahedron, like the hypercube, has many different equivalent representations, and arises as a natural object of study in many areas of combinatorics. In particular, as a highly-symmetric simple polytope, like the $n$-simplex and $n$-cube, this percolation model naturally generalises the Erd\H{o}s-R\'{e}nyi random graph and the percolated hypercube.
We determine the percolation threshold and the connectivity threshold for random subgraphs of the permutahedron.
Along the way we develop a novel graph exploration technique which can be used to find exponentially large clusters after percolation in high-dimensional geometric graphs and we initiate the study of the isoperimetric properties of the permutahedron. - [66] arXiv:2404.17262 [pdf, ps, other]
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Title: Spread-out percolation on transitive graphs of polynomial growthComments: 35 pagesSubjects: Probability (math.PR); Combinatorics (math.CO); Group Theory (math.GR)
Let $G$ be a vertex-transitive graph of superlinear polynomial growth. Given $r>0$, let $G_r$ be the graph on the same vertex set as $G$, with two vertices joined by an edge if and only if they are at graph distance at most $r$ apart in $G$. We show that the critical probability $p_c(G_r)$ for Bernoulli bond percolation on $G_r$ satisfies $p_c(G_r) \sim 1/\mathrm{deg}(G_r)$ as $r\to\infty$. This extends work of Penrose and Bollob\'as-Janson-Riordan, who considered the case $G=\mathbb{Z}^d$.
Our result provides an important ingredient in parallel work of Georgakopoulos in which he introduces a new notion of dimension in groups. It also verifies a special case of a conjecture of Easo and Hutchcroft. - [67] arXiv:2404.17263 [pdf, ps, other]
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Title: Multiple-Target Detection in Cell-Free Massive MIMO-Assisted ISACComments: The manuscript has been submitted to IEEE TWCSubjects: Information Theory (cs.IT); Signal Processing (eess.SP)
We propose a distributed implementation for integrated sensing and communication (ISAC) backed by a massive multiple input multiple output (CF-mMIMO) architecture without cells. Distributed multi-antenna access points (APs) simultaneously serve communication users (UEs) and emit probing signals towards multiple specified zones for sensing. The APs can switch between communication and sensing modes, and adjust their transmit power based on the network settings and sensing and communication operations' requirements. By considering local partial zero-forcing and maximum-ratio-transmit precoding at the APs for communication and sensing, respectively, we first derive closed-form expressions for the spectral efficiency (SE) of the UEs and the mainlobe-to-average-sidelobe ratio (MASR) of the sensing zones. Then, a joint operation mode selection and power control design problem is formulated to maximize the SE fairness among the UEs, while ensuring specific levels of MASR for sensing zones. The complicated mixed-integer problem is relaxed and solved via successive convex approximation approach. We further propose a low-complexity design, where AP mode selection is designed through a greedy algorithm and then power control is designed based on this chosen mode. Our findings reveal that the proposed scheme can consistently ensure a sensing success rate of $100\%$ for different network setups with a satisfactory fairness among all UEs.
- [68] arXiv:2404.17266 [pdf, ps, other]
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Title: On the Grothendieck duality for the space of holomorphic Sobolev functionsSubjects: Complex Variables (math.CV)
We describe the strong dual space $({\mathcal O}^s (D))^*$ for the space ${\mathcal O}^s (D) =
H^s (D) \cap {\mathcal O} (D)$ of holomorphic functions from the Sobolev space $H^s(D)$, $s \in \mathbb Z$, over a bounded simply connected plane domain $D$ with infinitely differential boundary $\partial D$. We identify the dual space with the space of holomorhic functions on ${\mathbb C}^n\setminus \overline D$ that belong to $H^{1-s} (G\setminus \overline D)$ for any bounded domain $G$, containing the compact $\overline D$, and vanish at the infinity. As a corollary, we obtain a description of the strong dual space $({\mathcal O}_F (D))^*$ for the space ${\mathcal O}_F (D)$ of holomorphic functions of finite order of growth in $D$ (here, ${\mathcal O}_F (D)$ is endowed with the inductive limit topology with respect to the family of spaces ${\mathcal O}^s (D)$, $s \in \mathbb Z$).
In this way we extend the classical Grothendieck-K{\"o}the-Sebasti\~{a}o e Silva duality for the space of holomorphic functions. - [69] arXiv:2404.17270 [pdf, other]
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Title: Empirical Studies of Propagation Characteristics and Modeling Based on XL-MIMO Channel Measurement: From Far-Field to Near-FieldSubjects: Information Theory (cs.IT); Signal Processing (eess.SP)
In the sixth-generation (6G), the extremely large-scale multiple-input-multiple-output (XL-MIMO) is considered a promising enabling technology. With the further expansion of array element number and frequency bands, near-field effects will be more likely to occur in 6G communication systems. The near-field radio communications (NFRC) will become crucial in 6G communication systems. It is known that the channel research is very important for the development and performance evaluation of the communication systems. In this paper, we will systematically investigate the channel measurements and modeling for the emerging NFRC. First, the principle design of massive MIMO channel measurement platform are solved. Second, an indoor XL-MIMO channel measurement campaign with 1600 array elements is conducted, and the channel characteristics are extracted and validated in the near-field region. Then, the outdoor XL-MIMO channel measurement campaign with 320 array elements is conducted, and the channel characteristics are extracted and modeled from near-field to far-field (NF-FF) region. The spatial non-stationary characteristics of angular spread at the transmitting end are more important in modeling. We hope that this work will give some reference to the near-field and far-field research for 6G.
- [70] arXiv:2404.17278 [pdf, other]
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Title: A Notion of Dimension based on Probability on GroupsAuthors: Agelos GeorgakopoulosSubjects: Probability (math.PR); Combinatorics (math.CO); Group Theory (math.GR); Geometric Topology (math.GT)
We introduce notions of dimension of an infinite group, or more generally, a metric space, defined using percolation. Roughly speaking, the percolation dimension $pdim(G)$ of a group $G$ is the fastest rate of decay of a symmetric probability measure $\mu$ on $G$, such that Bernoulli percolation on $G$ with connection probabilities proportional to $\mu$ behaves like a Poisson branching process with parameter 1 in a sense made precise below. We show that $pdim(G)$ has several natural properties: it is monotone decreasing with respect to subgroups and quotients, and coincides with the growth rate exponent for several classes of groups.
- [71] arXiv:2404.17279 [pdf, ps, other]
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Title: Bipartite powers of some classes of bipartite graphsSubjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM)
Graph powers are a well-studied concept in graph theory. Analogous to graph powers, Chandran et al.[3] introduced the concept of bipartite powers for bipartite graphs. In this paper, we will demonstrate that some well-known classes of bipartite graphs, namely the interval bigraphs, proper interval bigraphs, and bigraphs of Ferrers dimension 2, are closed under the operation of taking bipartite powers. Finally, we define strongly closed property for bipartite graphs under powers and have shown that the class of chordal bipartite graphs is strongly closed under powers.
- [72] arXiv:2404.17289 [pdf, ps, other]
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Title: The asymptotic behaviour of the Cesàro operatorSubjects: Functional Analysis (math.FA)
We study the asymptotic behaviour of orbits $(T^nx)_{n\ge0}$ of the classical Ces\`aro operator $T$ for sequences $x$ in the Banach space $c$ of convergent sequences. We give new non-probabilistic proofs, based on the Katznelson--Tzafriri theorem and one of its quantified variants, of results which characterise the set of sequences $x\in c$ that lead to convergent orbits and, for sequences satisfying a simple additional condition, we provide a rate of convergence. These results are then shown, again by operator-theoretic techniques, to be optimal in different ways. Finally, we study the asymptotic behaviour of the Ces\`aro operator defined on spaces of continuous functions, establishing new and improved results in this setting, too.
- [73] arXiv:2404.17290 [pdf, ps, other]
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Title: Efficient Orthogonal Decomposition with Automatic Basis Extraction for Low-Rank Matrix ApproximationSubjects: Numerical Analysis (math.NA)
Low-rank matrix approximation play a ubiquitous role in various applications such as image processing, signal processing, and data analysis. Recently, random algorithms of low-rank matrix approximation have gained widespread adoption due to their speed, accuracy, and robustness, particularly in their improved implementation on modern computer architectures. Existing low-rank approximation algorithms often require prior knowledge of the rank of the matrix, which is typically unknown. To address this bottleneck, we propose a low-rank approximation algorithm termed efficient orthogonal decomposition with automatic basis extraction (EOD-ABE) tailored for the scenario where the rank of the matrix is unknown. Notably, we introduce a randomized algorithm to automatically extract the basis that reveals the rank. The efficacy of the proposed algorithms is theoretically and numerically validated, demonstrating superior speed, accuracy, and robustness compared to existing methods. Furthermore, we apply the algorithms to image reconstruction, achieving remarkable results.
- [74] arXiv:2404.17295 [pdf, ps, other]
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Title: Generalized quantifiers using team semanticsAuthors: Fredrik EngströmSubjects: Logic (math.LO)
Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was only achieved for monotone increasing generalized quantifiers.
In this paper, we modify the fundamental semantical guideline of dependence logic to create a framework that adequately handles both monotone and non-monotone generalized quantifiers. We demonstrate that this new logic can interpret dependence logic and possesses the same expressive power as existential second-order logic (ESO) on the level of formulas. Additionally, we establish truth conditions for generalized quantifiers and prove that the extended logic remains conservative over first-order logic with generalized quantifiers and is able to express the branching of continuous generalized quantifiers. - [75] arXiv:2404.17301 [pdf, ps, other]
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Title: Symplectic cohomology of $cA_n$ singularitiesComments: 41 pages. Comments are welcome!Subjects: Symplectic Geometry (math.SG); Algebraic Geometry (math.AG); Geometric Topology (math.GT)
We compute the symplectic cohomology of Milnor fibers of isolated quasihomogeneous $cA_n$ singularities. As a by-product of our computations we distinguish their links as contact manifolds and we also provide further evidence to a conjecture of Evans and Lekili.
- [76] arXiv:2404.17303 [pdf, ps, other]
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Title: Partial representations of connected and smash product Hopf algebrasSubjects: Quantum Algebra (math.QA); Rings and Algebras (math.RA); Representation Theory (math.RT)
We show that every partial representation of a connected Hopf algebra is global. Some interesting classes of partial representations of smash product Hopf algebras are studied, and a description of the partial "Hopf" algebra if the first tensorand is connected is given. If $H$ is cocommutative and has finitely many grouplikes, this allows to see $H_{par}$ as the weak Hopf algebra coming from a Hopf category.
- [77] arXiv:2404.17306 [pdf, other]
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Title: Quickly excluding an apex-forestSubjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM)
We give a short proof that for every apex-forest $X$ on at least two vertices, graphs excluding $X$ as a minor have layered pathwidth at most $2|V(X)|-3$. This improves upon a result by Dujmovi\'c, Eppstein, Joret, Morin, and Wood (SIDMA, 2020). Our main tool is a structural result about graphs excluding a forest as a rooted minor, which is of independent interest. We develop similar tools for treedepth and treewidth. We discuss implications for Erd\H{o}s-P\'osa properties of rooted models of minors in graphs.
- [78] arXiv:2404.17308 [pdf, other]
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Title: $L$-space knots with positive surgeries that are not weakly symplectically fillableAuthors: Isacco NoninoComments: Comments welcome!Subjects: Geometric Topology (math.GT)
In this paper we discuss a general strategy to detect the absence of weakly symplectic fillings of $L$-spaces. We start from a generic $L$-space knot and consider (positive) Dehn surgeries on it. We compute, using arithmetic data depending only on the knot type and the surgery coefficient, the value of the relevant geometric invariants used to obstruct fillability. We also provide a new example of an infinite family of hyperbolic $L$-spaces that do not admit weakly symplectic fillings. These are manifolds that lie inside $\{\text{Tight}\}$ but not inside $\{\text{Weakly Fillable}\}$.
- [79] arXiv:2404.17312 [pdf, ps, other]
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Title: Conjugacy geodesics and growth in dihedral Artin groupsSubjects: Group Theory (math.GR)
In this paper we describe conjugacy geodesic representatives in any dihedral Artin group $G(m)$, $m\geq 3$, which we then use to calculate asymptotics for the conjugacy growth of $G(m)$, and show that the conjugacy growth series of $G(m)$ with respect to the `free product' generating set $\{x, y\}$ is transcendental. This, together with recent results on Artin groups and contracting elements, implies that all Artin groups of XXL-type have transcendental conjugacy growth series for some generating set.
We prove two additional properties of $G(m)$ that connect to conjugacy, namely that the permutation conjugator length function is constant, and that the falsification by fellow traveler property (FFTP) holds with respect to $\{x, y\}$. These imply that the language of all conjugacy geodesics in $G(m)$ with respect to $\{x, y\}$ is regular. - [80] arXiv:2404.17314 [pdf, ps, other]
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Title: The pro-Nisnevich topologyAuthors: Klaus MattisComments: 10 pages, Comments welcome!Subjects: Algebraic Geometry (math.AG)
We construct the pro-Nisnevich topology, an analog of the pro-\'etale topology. We then show that the Nisnevich $\infty$-topos embeds into the pro-Nisnevich $\infty$-topos, and that the pro-Nisnevich $\infty$-topos is locally of homotopy dimension $0$.
- [81] arXiv:2404.17318 [pdf, other]
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Title: Performance Bounds of Near-Field Sensing with Circular ArraysComments: 6 pages, 6 figures. arXiv admin note: text overlap with arXiv:2404.05076Subjects: Information Theory (cs.IT); Signal Processing (eess.SP)
The performance bounds of near-field sensing are studied for circular arrays, focusing on the impact of bandwidth and array size. The closed-form Cramer-Rao bound (CRBs) for angle and distance estimation are derived, revealing the scaling laws of the CRBs with bandwidth and array size. Contrary to expectations, enlarging array size does not always enhance sensing performance. Furthermore, the asymptotic CRBs are analyzed under different conditions, unveiling that the derived expressions include the existing results as special cases. Finally, the derived expressions are validated through numerical results.
- [82] arXiv:2404.17321 [pdf, other]
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Title: Fractional Order Sunflower Equation: Stability, Bifurcation and ChaosComments: 10 pages, 28 figuresSubjects: Dynamical Systems (math.DS)
The sunflower equation describes the motion of the tip of a plant due to the auxin transportation under the influence of gravity. This work proposes the fractional-order generalization to this delay differential equation. The equation contains two fractional orders and infinitely many equilibrium points. The coefficients in the linearized equation near the equilibrium points are delay-dependent. We provide a detailed stability analysis of each equilibrium point. We observed the following bifurcation phenomena: stable for all the delay values, a single stable region in the delayed interval, and a stability switch. We also observed a multi-scroll chaotic attractor for some values of the parameters.
- [83] arXiv:2404.17322 [pdf, ps, other]
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Title: Filtered Boolean powers of finite simple non-abelian Mal'cev algebrasSubjects: Logic (math.LO); Group Theory (math.GR); Rings and Algebras (math.RA)
Let $\mathbf{A}$ be a finite simple non-abelian Mal'cev algebra (e.g. a group, loop, ring). We investigate the Boolean power $\mathbf{D}$ of $\mathbf{A}$ by the countable atomless Boolean algebra $\mathbf{B}$ filtered at some idempotents $e_1,\dots,e_n$ of $\mathbf{A}$. When $e_1,\dots,e_n$ are all idempotents of $\mathbf{A}$ we establish two concrete representations of $\mathbf{D}$: as the Fra\"iss\'e limit of the class of finite direct powers of $\mathbf{A}$, and as congruence classes of the countable free algebra in the variety generated by $\mathbf{A}$. Further, for arbitrary $e_1,\dots,e_n$, we show that $\mathbf{D}$ is $\omega$-categorical and that its automorphism group has the small index property, strong uncountable cofinality and the Bergman property. As necessary background we establish some general properties of congruences and automorphisms of filtered Boolean powers of $\mathbf{A}$ by any Boolean algebra $\mathbf{B}$, including a semidirect decomposition for their automorphism groups.
- [84] arXiv:2404.17341 [pdf, other]
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Title: Free curves in Fano hypersurfaces must have high degreeAuthors: Raymond ChengComments: 4 pages, comments welcome!Subjects: Algebraic Geometry (math.AG)
The purpose of this note is to show that the minimal $e$ for which every smooth Fano hypersurface of dimension $n$ contains a free rational curve of degree at most $e$ cannot be bounded by a linear function in $n$ when the base field has positive characteristic. This is done by providing a super-linear bound on the minimal possible degree of a free curve in certain Fermat hypersurfaces.
- [85] arXiv:2404.17349 [pdf, other]
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Title: RectangulotopesComments: 23 pages, 14 figuresSubjects: Combinatorics (math.CO); Computational Geometry (cs.CG); Discrete Mathematics (cs.DM)
Rectangulations are decompositions of a square into finitely many axis-aligned rectangles. We describe realizations of (n-1)-dimensional polytopes associated with two combinatorial families of rectangulations composed of n rectangles. They are defined as quotientopes of natural lattice congruences on the weak Bruhat order on permutations in S_n, and their skeleta are flip graphs on rectangulations. We give simple vertex and facet descriptions of these polytopes, in particular elementary formulas for computing the coordinates of the vertex corresponding to each rectangulation, in the spirit of J.-L. Loday's realization of the associahedron.
- [86] arXiv:2404.17351 [pdf, ps, other]
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Title: On the index of power compositional polynomialsSubjects: Number Theory (math.NT); Commutative Algebra (math.AC)
The index of a monic irreducible polynomial $f(x)\in\mathbb{Z}[x]$ having a root $\theta$ is the index $[\mathbb{Z}_K:\mathbb{Z}[\theta]]$, where $\mathbb{Z}_K$ is the ring of algebraic integers of the number field $K=\mathbb{Q}(\theta)$. If $[\mathbb{Z}_K:\mathbb{Z}[\theta]]=1$, then $f(x)$ is monogenic. In this paper, we give necessary and sufficient conditions for a monic irreducible power compositional polynomial $f(x^k)$ belonging to $\mathbb{Z}[x]$, to be monogenic. As an application of our results, for a polynomial $f(x)=x^d+A\cdot h(x)\in\mathbb{Z}[x],$ with $d>1, \operatorname{deg} h(x)<d$ and $|h(0)|=1$, we prove that for each positive integer $k$ with $\operatorname{rad}(k)\mid \operatorname{rad}(A)$, the power compositional polynomial $f(x^k)$ is monogenic if and only if $f(x)$ is monogenic, provided that $f(x^k)$ is irreducible. At the end of the paper, we give infinite families of polynomials as examples.
- [87] arXiv:2404.17356 [pdf, other]
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Title: Phase and amplitude responses for delay equations using harmonic balanceComments: 5 pages, 2 figuresSubjects: Dynamical Systems (math.DS)
Robust delay induced oscillations, common in nature, are often modeled by delay-differential equations (DDEs). Motivated by the success of phase-amplitude reductions for ordinary differential equations with limit cycle oscillations, there is now a growing interest in the development of analogous approaches for DDEs to understand their response to external forcing. When combined with Floquet theory, the fundamental quantities for this reduction are phase and amplitude response functions. Here, we develop a framework for their construction that utilises the method of harmonic balance.
- [88] arXiv:2404.17359 [pdf, ps, other]
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Title: Relations between Kondratiev spaces and refined localization Triebel-Lizorkin spacesComments: 26 pagesSubjects: Analysis of PDEs (math.AP); Functional Analysis (math.FA); Numerical Analysis (math.NA)
We investigate the close relation between certain weighted Sobolev spaces (Kondratiev spaces) and refined localization spaces from introduced by Triebel [39,40]. In particular, using a characterization for refined localization spaces from Scharf [32], we considerably improve an embedding from Hansen [17]. This embedding is of special interest in connection with convergence rates for adaptive approximation schemes.
- [89] arXiv:2404.17366 [pdf, ps, other]
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Title: An introduction to extended Gevrey regularitySubjects: Analysis of PDEs (math.AP); Functional Analysis (math.FA)
Gevrey classes are the most common choice when considering the regularities of smooth functions that are not analytic. However, in various situations, it is important to consider smoothness properties that go beyond Gevrey regularity, for example when initial value problems are ill-posed in Gevrey settings. Extended Gevrey classes provide a convenient framework for studying smooth functions that possess weaker regularity than any Gevrey function. Since the available literature on this topic is scattered, our aim is to provide an overview to extended Gevrey regularity, highlighting its most important features. Additionally, we consider related dual spaces of ultradistributions and review some results on micro-local analysis in the context of extended Gevrey regularity. We conclude the paper with a few selected applications that may motivate further study of the topic.
- [90] arXiv:2404.17372 [pdf, other]
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Title: CEM-GMsFEM for Poisson equations in heterogeneous perforated domainsSubjects: Numerical Analysis (math.NA)
In this paper, we propose a novel multiscale model reduction strategy tailored to address the Poisson equation within heterogeneous perforated domains. The numerical simulation of this intricate problem is impeded by its multiscale characteristics, necessitating an exceptionally fine mesh to adequately capture all relevant details. To overcome the challenges inherent in the multiscale nature of the perforations, we introduce a coarse space constructed using the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM). This involves constructing basis functions through a sequence of local energy minimization problems over eigenspaces containing localized information pertaining to the heterogeneities. Through our analysis, we demonstrate that the oversampling layers depend on the local eigenvalues, thereby implicating the local geometry as well. Additionally, we provide numerical examples to illustrate the efficacy of the proposed scheme.
- [91] arXiv:2404.17375 [pdf, ps, other]
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Title: Properties of the complementarity set for the cone of copositive matricesAuthors: O.I. KostyukovaComments: 26 pagesSubjects: Optimization and Control (math.OC)
For a proper cone $K$ and its dual cone $K^*$ in $\mathbb R^n$, the complementarity set of $K$ is defined as
${\mathbb C}(K)=\{(x,y): x\in K,\; y\in K^*,\, x^\top y=0\}$. It is known that ${\mathbb C}(K)$ is an $n$-dimensional manifold in the space $\mathbb R^{2n}$. If $ K$ is a symmetric cone, points in ${\mathbb C}(K)$ must satisfy at least $n$ linearly independent bi-linear identities. Since this knowledge comes in handy when optimizing over such cones, it makes sense to search for similar relationships for non-symmetric cones.
In this paper, we study properties of the complementarity set for the dual cones of copositive and completely positive matrices. Despite these cones are of great interest due to their applications in optimization, they have not yet been sufficiently studied. - [92] arXiv:2404.17383 [pdf, ps, other]
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Title: Counterexamples to generalizations of the Erdős $B+B+t$ problemAuthors: Ethan AckelsbergComments: 8 pagesSubjects: Combinatorics (math.CO); Number Theory (math.NT)
Following their resolution of the Erd\H{o}s $B+B+t$ problem, Kra Moreira, Richter, and Robertson posed a number of questions and conjectures related to infinite configurations in positive density subsets of the integers and other amenable groups. We give a negative answer to several of these questions and conjectures by producing families of counterexamples based on a construction of Ernst Straus.
Included among our counterexamples, we exhibit, for any $\varepsilon > 0$, a set $A \subseteq \mathbb{N}$ with multiplicative upper Banach density at least $1 - \varepsilon$ such that $A$ does not contain any dilated product set $\{b_1b_2t : b_1, b_2 \in B, b_1 \ne b_2\}$ for an infinite set $B \subseteq \mathbb{N}$ and $t \in \mathbb{Q}_{>0}$. We also prove the existence of a set $A \subseteq \mathbb{N}$ with additive upper Banach density at least $1 - \varepsilon$ such that $A$ does not contain any polynomial configuration $\{b_1^2 + b_2 + t : b_1, b_2 \in B, b_1 < b_2\}$ for an infinite set $B \subseteq \mathbb{N}$ and $t \in \mathbb{Z}$. Counterexamples to some closely related problems are also discussed. - [93] arXiv:2404.17385 [pdf, ps, other]
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Title: Extremal problems for intersecting families of subspaces with a measureComments: 20 pagesSubjects: Combinatorics (math.CO)
We introduce a measure for subspaces of a vector space over a $q$-element field, and propose some extremal problems for intersecting families. These are $q$-analogue of Erd\H{o}s-Ko-Rado type problems, and we answer some of the basic questions.
- [94] arXiv:2404.17386 [pdf, other]
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Title: Stochastic Bregman Subgradient Methods for Nonsmooth Nonconvex Optimization ProblemsComments: 28 pages, 6 figuresSubjects: Optimization and Control (math.OC)
This paper focuses on the problem of minimizing a locally Lipschitz continuous function. Motivated by the effectiveness of Bregman gradient methods in training nonsmooth deep neural networks and the recent progress in stochastic subgradient methods for nonsmooth nonconvex optimization problems \cite{bolte2021conservative,bolte2022subgradient,xiao2023adam}, we investigate the long-term behavior of stochastic Bregman subgradient methods in such context, especially when the objective function lacks Clarke regularity. We begin by exploring a general framework for Bregman-type methods, establishing their convergence by a differential inclusion approach. For practical applications, we develop a stochastic Bregman subgradient method that allows the subproblems to be solved inexactly. Furthermore, we demonstrate how a single timescale momentum can be integrated into the Bregman subgradient method with slight modifications to the momentum update. Additionally, we introduce a Bregman proximal subgradient method for solving composite optimization problems possibly with constraints, whose convergence can be guaranteed based on the general framework. Numerical experiments on training nonsmooth neural networks are conducted to validate the effectiveness of our proposed methods.
- [95] arXiv:2404.17387 [pdf, ps, other]
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Title: Well-posedness and convergence of entropic approximation of semi-geostrophic equationsSubjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Optimization and Control (math.OC)
We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic equations as the entropic parameter vanishes. Convergence is also proved for discretizations that can be computed numerically in practice as shown recently in [6].
- [96] arXiv:2404.17389 [pdf, ps, other]
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Title: Skellam compound Poisson approximation to the sums of symmetric Markov dependent random variablesSubjects: Probability (math.PR)
The sum of symmetric Markov dependent three-point random variables is approximated by the difference of two independent Poisson random variables (Skellam random variable). The accuracy is estimated in local, total variation and Wasserstein metrics. Properties of convolutions of measures is used for the proof.
- [97] arXiv:2404.17393 [pdf, other]
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Title: Equivariant Lagrangian Floer homology via multiplicative flow treesAuthors: Guillem CazassusComments: 29 pages, 22 figures, comments are welcomeSubjects: Symplectic Geometry (math.SG); Geometric Topology (math.GT)
We provide constructions of equivariant Lagrangian Floer homology groups, by constructing and exploiting an $A_\infty$-module structure on the Floer complex.
- [98] arXiv:2404.17404 [pdf, ps, other]
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Title: A Breiman's theorem for conditional dependent random vector and its applications to risk theorySubjects: Probability (math.PR)
In this paper, we give a Breiman's theorem for conditional dependent random vector, where one component has a regularly-varying-tailed distribution with the index $\alpha\ge0$ and its slowly varying function satisfies a relaxed condition, while the other component is non-negative and its tail distribution is lighter than the former. This result substantially extends and improves Theorem 2.1 of Yang and Wang (Extremes,\ 2013). %with a lower moment condition requirement for many occasions. We also provide some concrete examples and some interesting properties of conditional dependent random vector. Further, we apply the above Breiman's theorem to risk theory, and obtain two asymptotic estimates of the finite-time ruin probability and the infinite-time ruin probability of a discrete-time risk model, in which the corresponding net loss and random discount are conditionally dependent.
- [99] arXiv:2404.17406 [pdf, other]
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Title: Stability of partially congested travelling wave solutions for the extended Aw-Rascle systemSubjects: Analysis of PDEs (math.AP)
We prove the non-linear stability of a class of travelling-wave solutions to the extended Aw-Rascle system with a singular offset function, which is formally equivalent to the compressible pressureless Navier-Stokes system with a singular viscosity. These solutions encode the effect of congestion by connecting a congested left state to an uncongested right state, and may also be viewed as approximations of solutions to the 'hard-congestion model'. By using carefully weighted energy estimates we are able to prove the non-linear stability of viscous shock waves to the Aw-Rascle system under a small zero integral perturbation, which in particular extends previous results that do not handle the case where the viscosity is singular.
- [100] arXiv:2404.17407 [pdf, other]
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Title: Interior regularity of area minimizing currents within a $C^{2,α}$-submanifoldComments: 3 figures, comments are welcomeSubjects: Analysis of PDEs (math.AP); Differential Geometry (math.DG)
Given an area-minimizing integral $m$-current in $\Sigma$, we prove that the Hausdorff dimension of the interior singular set of $T$ cannot exceed $m-2$, provided that $\Sigma$ is an embedded $(m+\bar{n})$-submanifold of $\mathbb{R}^{m+n}$ of class $C^{2,\alpha}$, where $\alpha>0$. This result establishes the complete counterpart, in the arbitrary codimension setting, of the interior regularity theory for area-minimizing integral hypercurrents within a Riemannian manifold of class $C^{2,\alpha}$.
- [101] arXiv:2404.17408 [pdf, ps, other]
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Title: Dirac cohomology of minimal representationsAuthors: Xuanchen ZhaoComments: arXiv admin note: text overlap with arXiv:2305.03254 by other authorsSubjects: Representation Theory (math.RT)
In this paper, we study the Dirac cohomology of minimal representations for all real reductive groups G. The Dirac indices of these representations are also studied when G is of equal rank, giving some counterexamples of a conjecture of Huang proposed in 2015.
- [102] arXiv:2404.17414 [pdf, ps, other]
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Title: Multifractal analysis of the power-2-decaying Gauss-like expansionAuthors: Xue-Jiao WangSubjects: Dynamical Systems (math.DS)
Each real number $x\in[0,1]$ admits a unique power-2-decaying Gauss-like expansion (P2GLE for short) as $x=\sum_{i\in\mathbb{N}} 2^{-(d_1(x)+d_2(x)+\cdots+d_i(x))}$, where $d_i(x)\in\mathbb{N}$. For any $x\in(0,1]$, the Khintchine exponent $\gamma(x)$ is defined by $\gamma(x):=\lim_{n\to\infty}\frac{1}{n}\sum_{j=1}^nd_j(x)$ if the limit exists. We investigate the sizes of the level sets $E(\xi):=\{x\in(0,1]:\gamma(x)=\xi\}$ for $\xi\geq 1$. Utilizing the Ruelle operator theory, we obtain the Khintchine spectrum $\xi\mapsto\dim_H E(\xi)$, where $\dim_H$ denotes the Hausdorff dimension. We establish the remarkable fact that the Khintchine spectrum has exactly one inflection point, which was never proved for the corresponding spectrum in continued fractions. As a direct consequence, we also obtain the Lyapunov spectrum. Furthermore, we find the Hausdorff dimensions of the level sets $\{x\in(0,1]:\lim_{n\to\infty}\frac{1}{n}\sum_{j=1}^{n}\log(d_j(x))=\xi\}$ and $\{x\in(0,1]:\lim_{n\to\infty}\frac{1}{n}\sum_{j=1}^{n}2^{d_j(x)}=\xi\}$.
- [103] arXiv:2404.17424 [pdf, ps, other]
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Title: Équations en diviseursAuthors: Patrick LetendreComments: in French languageSubjects: Number Theory (math.NT)
Let $d(n) \subset \mathbb{N}$ be the set of the $\tau(n)$ divisors of $n$. We generalize a method of Tenenbaum and de la Bret\`eche for the study of the set $d(n)$. Among other things, we establish that $$ |\{(d_1,d_2,d_3) \in d(n)^3 : d_1+d_2=d_3\}| \le \tau(n)^{2-\delta} $$ with $\delta=0.045072$.
- [104] arXiv:2404.17432 [pdf, ps, other]
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Title: Shellability of Kohnert posetsSubjects: Combinatorics (math.CO)
In this paper, we are concerned with identifying among the family of posets associated with Kohnert polynomials, those whose order complex has a certain combinatorial property. In particular, for numerous families of Kohnert polynomials, including key polynomials, we determine when the associated Kohnert posets are (EL-)shellable. Interestingly, under certain diagram restrictions, (EL-)shellability of a Kohnert poset is equivalent to multiplcity freeness of the associated Kohnert polynomial.
- [105] arXiv:2404.17441 [pdf, other]
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Title: Comparison results for Markov tree distributionsSubjects: Statistics Theory (math.ST); Probability (math.PR)
We develop comparison results for Markov tree distributions extending ordering results from the literature on discrete time Markov processes and recently studied ordering results for conditionally independent factor models to tree structures. Based on fairly natural positive dependence conditions, our main contribution is a comparison result with respect to the supermodular order. Since this order is a pure dependence order, it has many applications in optimal transport, finance, and insurance. As an illustrative example, we consider hidden Markov models and study distributional robustness for functionals of the random walk under model uncertainty. Further, we show that, surprisingly, more general comparison results via the recently established rearrangement-based Schur order for conditional distributions, which implies an ordering of Chatterjee's rank correlation, do not carry over from star structures to trees. Several examples and a detailed discussion of the assumptions demonstrate the generality of our results and provide further insights into the behavior of multidimensional distributions.
- [106] arXiv:2404.17455 [pdf, other]
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Title: Averaged observations and turnpike phenomenon for parameter-dependent systemsSubjects: Optimization and Control (math.OC)
Our main contribution in this article is the achievement of the turnpike property in its integral and exponential forms for parameter-dependent systems with averaged observations in the cost functional. Namely, under suitable assumptions with respect to the matrices that defined the dynamics and the cost functional, we prove that the optimal control and state for the evolutionary problem converge in average to the optimal pair of an associated stationary problem. Moreover, we characterize the closeness between these two optimal solutions, proving that over a large time interval, they are exponentially close.
- [107] arXiv:2404.17458 [pdf, other]
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Title: Pullback of symplectic forms to the space of circle patternsAuthors: Wai Yeung LamComments: 23 pages, 3 figuresSubjects: Geometric Topology (math.GT); Complex Variables (math.CV); Symplectic Geometry (math.SG)
We consider circle patterns on surfaces with complex projective structures. We investigate two symplectic forms pulled back to the deformation space of circle patterns. The first one is Goldman's symplectic form on the space of complex projective structures on closed surfaces. The other is the Weil-Petersson symplectic form on the Teichm\"uller space of punctured surfaces. We show that their pullbacks to the space of circle patterns coincide. It is applied to prove the smoothness of the deformation space, which is an essential step to the conjecture that the space of circle patterns is homeomorphic to the Teichm\"uller space of the closed surface. We further conjecture that the pullback of the symplectic forms is non-degenerate and defines a symplectic structure on the space of circle patterns.
- [108] arXiv:2404.17467 [pdf, ps, other]
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Title: Around the positive graph conjectureComments: 14 pagesSubjects: Combinatorics (math.CO)
A graph $H$ is said to be positive if the homomorphism density $t_H(G)$ is non-negative for all weighted graphs $G$. The positive graph conjecture proposes a characterisation of such graphs, saying that a graph is positive if and only if it is symmetric, in the sense that it is formed by gluing two copies of some subgraph along an independent set. We prove several results relating to this conjecture. First, we make progress towards the conjecture itself by showing that any connected positive graph must have a vertex of even degree. We then make use of this result to identify some new counterexamples to the analogue of Sidorenko's conjecture for hypergraphs. In particular, we show that, for $r$ odd, every $r$-uniform tight cycle is a counterexample, generalising a recent result of Conlon, Lee and Sidorenko that dealt with the case $r=3$. Finally, we relate the positive graph conjecture to the emerging study of graph codes by showing that any positive graph has vanishing graph code density, thereby improving a result of Alon who proved the same result for symmetric graphs. Our proofs make use of a variety of tools and techniques, including the properties of independence polynomials, hypergraph quasirandomness and discrete Fourier analysis.
- [109] arXiv:2404.17468 [pdf, ps, other]
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Title: On Elliptical and Inverse Elliptical Wishart distributions: Review, new results, and applicationsSubjects: Statistics Theory (math.ST); Methodology (stat.ME)
This paper deals with matrix-variate distributions, from Wishart to Inverse Elliptical Wishart distributions over the set of symmetric definite positive matrices. Similar to the multivariate scenario, (Inverse) Elliptical Wishart distributions form a vast and general family of distributions, encompassing, for instance, Wishart or $t$-Wishart ones. The first objective of this study is to present a unified overview of Wishart, Inverse Wishart, Elliptical Wishart, and Inverse Elliptical Wishart distributions through their fundamental properties. This involves leveraging the stochastic representation of these distributions to establish key statistical properties of the Normalized Wishart distribution. Subsequently, this enables the computation of expectations, variances, and Kronecker moments for Elliptical Wishart and Inverse Elliptical Wishart distributions. As an illustrative application, the practical utility of these generalized Elliptical Wishart distributions is demonstrated using a real electroencephalographic dataset. This showcases their effectiveness in accurately modeling heterogeneous data.
- [110] arXiv:2404.17470 [pdf, ps, other]
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Title: Lorentzian homogeneous structures with indecomposable holonomyComments: 30 pages, comments welcomeSubjects: Differential Geometry (math.DG)
For a Lorentzian homogeneous space, we study how algebraic conditions on the isotropy group affect the geometry and curvature of the homogeneous space. More specifically, we prove that a Lorentzian locally homogeneous space is locally isometric to a plane wave if it admits an Ambrose--Singer connection with indecomposable, non-irreducible holonomy. This generalises several existing results that require a certain algebraic type of the torsion of the Ambrose--Singer connection and moreover is in analogy to the fact that a Lorentzian homogeneous space with irreducible isotropy has constant sectional curvature.
- [111] arXiv:2404.17471 [pdf, other]
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Title: Multicontinuum homogenization in perforated domainsSubjects: Numerical Analysis (math.NA)
In this paper, we develop a general framework for multicontinuum homogenization in perforated domains. The simulations of problems in perforated domains are expensive and, in many applications, coarse-grid macroscopic models are developed. Many previous approaches include homogenization, multiscale finite element methods, and so on. In our paper, we design multicontinuum homogenization based on our recently proposed framework. In this setting, we distinguish different spatial regions in perforations based on their sizes. For example, very thin perforations are considered as one continua, while larger perforations are considered as another continua. By differentiating perforations in this way, we are able to predict flows in each of them more accurately. We present a framework by formulating cell problems for each continuum using appropriate constraints for the solution averages and their gradients. These cell problem solutions are used in a multiscale expansion and in deriving novel macroscopic systems for multicontinuum homogenization. Our proposed approaches are designed for problems without scale separation. We present numerical results for two continuum problems and demonstrate the accuracy of the proposed methods.
- [112] arXiv:2404.17473 [pdf, other]
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Title: Consistent Second Moment Methods with Scalable Linear Solvers for Radiation TransportSubjects: Numerical Analysis (math.NA)
Second Moment Methods (SMMs) are developed that are consistent with the Discontinuous Galerkin (DG) spatial discretization of the discrete ordinates (or \Sn) transport equations. The low-order (LO) diffusion system of equations is discretized with fully consistent \Pone, Local Discontinuous Galerkin (LDG), and Interior Penalty (IP) methods. A discrete residual approach is used to derive SMM correction terms that make each of the LO systems consistent with the high-order (HO) discretization. We show that the consistent methods are more accurate and have better solution quality than independently discretized LO systems, that they preserve the diffusion limit, and that the LDG and IP consistent SMMs can be scalably solved in parallel on a challenging, multi-material benchmark problem.
- [113] arXiv:2404.17491 [pdf, other]
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Title: Computationally Efficient Algorithms for Simulating Isotropic Gaussian Random Fields on Graphs with Euclidean EdgesSubjects: Statistics Theory (math.ST)
This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three general algorithms that allow to reconstruct a wide spectrum of random fields having a covariance function that depends on a specific metric, called resistance metric, and proposed in recent literature. The algorithms are applied to a synthetic case study consisting of a street network. They prove to be fast and accurate in that they reproduce the target covariance function and provide random fields whose finite-dimensional distributions are approximately Gaussian.
- [114] arXiv:2404.17500 [pdf, ps, other]
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Title: On the integrability of generalized $N$-center problemsComments: 15 pagesSubjects: Dynamical Systems (math.DS)
In this paper, we study the rational integrability of the $N$-center problem with rational weak and moderate forces. We show that the problem is not rationally integrable for all but a finite number of values $\alpha\in]0,2[$, where $\alpha$ is the order of the singularities. We identify the remaining cases and give the necessary conditions for integrability.
- [115] arXiv:2404.17506 [pdf, other]
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Title: Chemotaxis-inspired PDE model for airborne infectious disease transmission: analysis and simulationsSubjects: Analysis of PDEs (math.AP); Dynamical Systems (math.DS); Populations and Evolution (q-bio.PE)
Partial differential equation (PDE) models for infectious disease have received renewed interest in recent years. Most models of this type extend classical compartmental formulations with additional terms accounting for spatial dynamics, with Fickian diffusion being the most common such term. However, while diffusion may be appropriate for modeling vector-borne diseases, or diseases among plants or wildlife, the spatial propagation of airborne diseases in human populations is heavily dependent on human contact and mobility patterns, which are not necessarily well-described by diffusion. By including an additional chemotaxis-inspired term, in which the infection is propagated along the positive gradient of the susceptible population (from regions of low- to high-density of susceptibles), one may provide a more suitable description of these dynamics. This article introduces and analyzes a mathematical model of infectious disease incorporating a modified chemotaxis-type term. The model is analyzed mathematically and the well-posedness of the resulting PDE system is demonstrated. A series of numerical simulations are provided, demonstrating the ability of the model to naturally capture important phenomena not easily observed in standard diffusion models, including propagation over long spatial distances over short time scales and the emergence of localized infection hotspots
- [116] arXiv:2404.17512 [pdf, other]
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Title: On the spectral edge of non-Hermitian random matricesComments: 50 pagesSubjects: Probability (math.PR)
For general non-Hermitian random matrices $X$ and deterministic deformation matrices $A$, we prove that the local eigenvalue statistics of $A+X$ close to the typical edge points of its spectrum are universal. Furthermore, we show that under natural assumptions on $A$ the spectrum of $A+X$ does not have outliers at a distance larger than the natural fluctuation scale of the eigenvalues. As a consequence, the number of eigenvalues in each component of $\mathrm{Spec}(A+X)$ is deterministic.
- [117] arXiv:2404.17514 [pdf, other]
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Title: On the impossibility of certain $({n^2+n+k}_{n+1})$ configurationsSubjects: Combinatorics (math.CO)
This paper investigates the impossibility of certain $({n^2+n+k}_{n+1})$ configurations. Firstly, for $k=2$, the result of \cite{gropp1992non} that $\frac{n^2+n}{2}$ is even and $n+1$ is a perfect square or $\frac{n^2+n}{2}$ is odd and $n-1$ is a perfect square is reproved using the incidence matrix $N$ and analysing the form of $N^TN$. Then, for all $k$, configurations where paralellism is a transitive property are considered. It is then analogously established that if $n\equiv0$ or $n\equiv k-1$ mod $k$ for $k$ even, then $\frac{n^2+n}{k}$ is even and $n+1$ is a perfect square or $\frac{n^2+n}{k}$ is odd and $n-(k-1)$ is a perfect square. Finally, the case $k=3$ is investigated in full generality.
- [118] arXiv:2404.17516 [pdf, ps, other]
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Title: An order analysis of hyperfinite Borel equivalence relationsSubjects: Logic (math.LO)
In this paper we first consider hyperfinite Borel equivalence relations with a pair of Borel $\mathbb{Z}$-orderings. We define a notion of compatibility between such pairs, and prove a dichotomy theorem which characterizes exactly when a pair of Borel $\mathbb{Z}$-orderings are compatible with each other. We show that, if a pair of Borel $\mathbb{Z}$-orderings are incompatible, then a canonical incompatible pair of Borel $\mathbb{Z}$-orderings of $E_0$ can be Borel embedded into the given pair. We then consider hyperfinite-over-finite equivalence relations, which are countable Borel equivalence relations admitting Borel $\mathbb{Z}^2$-orderings. We show that if a hyperfinite-over-hyperfinite equivalence relation $E$ admits a Borel $\mathbb{Z}^2$-ordering which is compatible with itself, then $E$ is hyperfinite.
- [119] arXiv:2404.17518 [pdf, other]
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Title: Manin pairs and moment maps revisitedComments: 42 pagesSubjects: Differential Geometry (math.DG)
The notion of quasi-Poisson $G$-spaces with $D/G$-valued moment maps was introduced by Alekseev and Kosmann-Schwarzbach in 1999. Our main result is a \emph{Lifting Theorem}, establishing a bijective correspondence between the categories of quasi-Poisson $G$-spaces with $D/G$-valued moment maps and of quasi-Poisson $G\times G$-spaces with $D$-valued moment maps. Using this result, we give simple constructions of fusion and conjugation for these spaces, and new examples coming from moduli spaces.
- [120] arXiv:2404.17519 [pdf, other]
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Title: Interpreting Deepcode, a learned feedback codeComments: Accepted to the 2024 ISIT conferenceSubjects: Information Theory (cs.IT); Signal Processing (eess.SP)
Deep learning methods have recently been used to construct non-linear codes for the additive white Gaussian noise (AWGN) channel with feedback. However, there is limited understanding of how these black-box-like codes with many learned parameters use feedback. This study aims to uncover the fundamental principles underlying the first deep-learned feedback code, known as Deepcode, which is based on an RNN architecture. Our interpretable model based on Deepcode is built by analyzing the influence length of inputs and approximating the non-linear dynamics of the original black-box RNN encoder. Numerical experiments demonstrate that our interpretable model -- which includes both an encoder and a decoder -- achieves comparable performance to Deepcode while offering an interpretation of how it employs feedback for error correction.
- [121] arXiv:2404.17527 [pdf, other]
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Title: Reduction of the effective population size in a branching particle system in the moderate mutation-selection regimeComments: 38 pages, 4 figuresSubjects: Probability (math.PR)
We consider a system of particles performing a one-dimensional dyadic branching Brownian motion with positive drift $\beta\in(0,1)$, branching rate 1/2, killed at $L(\beta)>0$, and reflected at 0. The killing boundary $L(\beta)$ is chosen so that the total population size is approximately constant, proportional to $N\in\mathbb{N}$. This branching system is interpreted as a population accumulating deleterious mutations.
We prove that, when the typical width of the cloud of particles is of order $c\log(N)$, $c\in(0,1)$, the demographic fluctuations of the system converge to a Feller diffusion on the time scale $N^{1-c}$. In addition, we show that the limiting genealogy of the system comprises only binary mergers and that these mergers are concentrated in the vicinity of the reflective boundary. This model is a version of the branching Brownian motion with absorption studied by Berestycki, Berestycki and Schweinsberg to describe the effect of natural selection on the genealogy of a population accumulating beneficial mutations. In the latter case, the genealogical structure of the system is described by a Bolthausen-Sznitman coalescent on a logarithmic time scale. In this work, we show that, when the population size in the fittest class is mesoscopic, namely of order $N^{1-c}$, the genealogy of the system is given by a Kingman coalescent on a polynomial time scale. - [122] arXiv:2404.17529 [pdf, ps, other]
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Title: Kaledin classes and formality criteriaAuthors: Coline EmprinComments: 46 pagesSubjects: Algebraic Topology (math.AT); Algebraic Geometry (math.AG); Quantum Algebra (math.QA)
We develop a general obstruction theory to the formality of algebraic structures over any commutative ground ring. It relies on the construction of Kaledin obstruction classes that faithfully detect the formality of differential graded algebras over operads or properads, possibly colored in groupoids. The present treatment generalizes the previous obstruction classes in two directions: outside characteristic zero and including a wider range of algebraic structures. This enables us to establish novel formality criteria, including formality descent with torsion coefficients, formality in families, intrinsic formality, and criteria in terms of chain-level lifts of homology automorphism.
- [123] arXiv:2404.17533 [pdf, other]
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Title: Rigidity of spin fill-ins with non-negative scalar curvatureComments: 20 pagesSubjects: Differential Geometry (math.DG); General Relativity and Quantum Cosmology (gr-qc)
We establish new mean curvature rigidity theorems of spin fill-ins with non-negative scalar curvature using two different spinorial techniques. Our results address two questions by Miao and Gromov, respectively. The first technique is based on extending boundary spinors satisfying a generalized eigenvalue equation via the Fredholm alternative for an APS boundary value problem, while the second is a comparison result in the spirit of Llarull and Lott using index theory. We also show that the latter implies a new Witten-type integral inequality for the mass of an asymptotically Schwarzschild manifold which holds even when the scalar curvature is not assumed to be non-negative.
- [124] arXiv:2404.17536 [pdf, other]
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Title: Besicovitch's 1/2 problem and linear programmingComments: 42 pages + appendix, 10 figures. Comments are welcomeSubjects: Classical Analysis and ODEs (math.CA); Analysis of PDEs (math.AP); Metric Geometry (math.MG)
We consider the following classical conjecture of Besicovitch: a $1$-dimensional Borel set in the plane with finite Hausdorff $1$-dimensional measure $\mathcal{H}^1$ which has lower density strictly larger than $\frac{1}{2}$ almost everywhere must be countably rectifiable. We improve the best known bound, due to Preiss and Ti\v{s}er, showing that the statement is indeed true if $\frac{1}{2}$ is replaced by $\frac{7}{10}$ (in fact we improve the Preiss-Ti\v{s}er bound even for the corresponding statement in general metric spaces). More importantly, we propose a family of variational problems to produce the latter and many other similar bounds and we study several properties of them, paving the way for further improvements.
- [125] arXiv:2404.17537 [pdf, ps, other]
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Title: Artinian rings which are not generalized RickartAuthors: Ali ShahidikiaSubjects: Rings and Algebras (math.RA)
In this note, we show that there exist non-unital right artinian rings which are not generalized Rickart. In particular, we provide examples to show that, [16, Corollary 2.31] is not true for non-unital artinian rings.
- [126] arXiv:2404.17540 [pdf, ps, other]
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Title: Schwarz Modular Operads Revisited: $\mathcal{SM}=\mathcal{S}\circ\mathcal{M}$Subjects: Algebraic Topology (math.AT); Category Theory (math.CT)
We prove that the Feynman category encoding Schwarz's variant of modular operads is Koszul. Our proof uses a generalization of the theory of distributive laws to the groupoid colored setting.
- [127] arXiv:2404.17541 [pdf, ps, other]
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Title: Applications of Lifted Nonlinear Cuts to Convex Relaxations of the AC Power Flow EquationsSubjects: Optimization and Control (math.OC); Systems and Control (eess.SY)
We demonstrate that valid inequalities, or lifted nonlinear cuts (LNC), can be projected to tighten the Second Order Cone (SOC), Convex DistFlow (CDF), and Network Flow (NF) relaxations of the AC Optimal Power Flow (AC-OPF) problem. We conduct experiments on 36 cases from the PGLib-OPF library for two objective functions, (1) power generation maximization and (2) generation cost minimization. Significant optimality gap improvements are shown for the maximization problem, where the LNC strengthen the SOC and CDF relaxations in 100% of the test cases, with average and maximum differences in the optimality gaps of 23.1% and 93.5% respectively. The NF relaxation is strengthened in 79.2% of test cases, with average and maximum differences in the optimality gaps of 3.45% and 21.2% respectively. We also study the trade-off between relaxation quality and solve time, demonstrating that the strengthened CDF relaxation outperforms the strengthened SOC formulation in terms of runtime and number of iterations needed, while the strengthened NF formulation is the most scalable with the lowest relaxation quality provided by these LNC.
- [128] arXiv:2404.17543 [pdf, ps, other]
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Title: Complexity of Minimizing Regularized Convex Quadratic FunctionsSubjects: Optimization and Control (math.OC)
In this work, we study the iteration complexity of gradient methods minimizing the class of uniformly convex regularized quadratic functions. We prove lower bounds on the functional residual of the form $\Omega(N^{-2p/(p-2)})$, where $p > 2$ is the power of the regularization term, and $N$ is the number of calls to a first-order oracle. A special case of our problem class is $p=3$, which is the minimization of cubically regularized convex quadratic functions. It naturally appears as a subproblem at each iteration of the cubic Newton method. The corresponding lower bound for $p = 3$ becomes $\Omega(N^{-6})$. Our result matches the best-known upper bounds on this problem class, rendering a sharp analysis of the minimization of uniformly convex regularized quadratic functions. We also establish new lower bounds on minimizing the gradient norm within our framework.
- [129] arXiv:2404.17564 [pdf, other]
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Title: Half-space separation in monophonic convexityComments: 22 pages, 11 figuresSubjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM); Data Structures and Algorithms (cs.DS)
We study half-space separation in the convexity of chordless paths of a graph, i.e., monophonic convexity. In this problem, one is given a graph and two (disjoint) subsets of vertices and asks whether these two sets can be separated by complementary convex sets, called half-spaces. While it is known this problem is $\mathbf{NP}$-complete for geodesic convexity -- the convexity of shortest paths -- we show that it can be solved in polynomial time for monophonic convexity.
- [130] arXiv:2404.17566 [pdf, ps, other]
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Title: Extended genus fields of abelian extensions of rational function fieldsComments: 23 pagesSubjects: Number Theory (math.NT)
In this paper we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power degree. Next, we use that the extended genus fields of a composite of two cyclotomic extensions of a global rational function field is equal to the composite of their respective extended genus fields, to obtain our main result. This result is that the extended genus field of a general finite abelian extension of a global rational function field, is given explicitly in terms of the field and of the extended genus field of its "cyclotomic projection".
- [131] arXiv:2404.17572 [pdf, ps, other]
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Title: On liftings of modules of finite projective dimensionSubjects: Commutative Algebra (math.AC)
We introduce and study a notion of dimly liftable modules; these are modules that are liftable to the right dimension to a regular local ring. We establish special new cases of Serre's positivity conjecture over ramified regular local rings by proving it for dimly liftable modules. Furthermore, we show that the length of a nonzero finite length dimly liftable module is bounded below by the Hilbert-Samuel multiplicity of the local ring. This establishes special cases of the Length Conjecture of Iyengar-Ma-Walker.
- [132] arXiv:2404.17573 [pdf, other]
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Title: Spectrum occupies pseudospectrum for random matrices with diagonal deformation and variance profileComments: 41 pages, 2 figuresSubjects: Probability (math.PR); Mathematical Physics (math-ph); Functional Analysis (math.FA); Operator Algebras (math.OA)
We consider $n\times n$ non-Hermitian random matrices with independent entries and a variance profile, as well as an additive deterministic diagonal deformation. We show that the support of the asymptotic eigenvalue distribution in the complex plane exactly coincides with the $\varepsilon$-pseudospectrum in the consecutive limits $n \to \infty$ and $\varepsilon \to 0$. Furthermore, we provide a description of this support in terms of a single real-valued function on the complex plane. As a level set of this locally real analytic function, the spectral edge is a real analytic variety of dimension at most one.
- [133] arXiv:2404.17577 [pdf, ps, other]
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Title: On Quasi-Locality and Decay of Correlations for Long-Range Models of Open Quantum Spin SystemsComments: 25 pagesSubjects: Mathematical Physics (math-ph)
We consider models of open quantum spin systems with irreversible dynamics and show that general quasi-locality results for long-range models, e.g. as proven for the Heisenberg dynamics associated to quantum systems in [27], naturally extend to this setting. Given these bounds, we provide two applications. First, we use these results to obtain estimates on a strictly local approximation of these finite-volume, irreversible dynamics. Next, we show how these bounds can be used to estimate correlation decay in various states.
Cross-lists for Mon, 29 Apr 24
- [134] arXiv:2404.16839 (cross-list from cs.CR) [pdf, ps, other]
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Title: Immersed in Reality Secured by Design -- A Comprehensive Analysis of Security Measures in AR/VR EnvironmentsComments: Cybersecurity. Augmented Reality on, Virtual Reality Implementation errors, Data security and efficiencySubjects: Cryptography and Security (cs.CR); Information Theory (cs.IT)
Virtual reality and related technologies such as mixed and augmented reality have received extensive coverage in both mainstream and fringe media outlets. When the subject goes to a new AR headset, another AR device, or AR glasses, the talk swiftly shifts to the technical and design details. Unfortunately, no one seemed to care about security. Data theft and other forms of cyberattack pose serious threats to virtual reality systems. Virtual reality goggles are just specialist versions of computers or Internet of Things devices, whereas virtual reality experiences are software packages. As a result, AR systems are just as vulnerable as any other Internet of Things (IoT) device we use on a daily basis, such as computers, tablets, and phones. Preventing and responding to common cybersecurity threats and assaults is crucial. Cybercriminals can exploit virtual reality headsets just like any other computer system. This paper analysis the data breach induced by these assaults could result in a variety of concerns, including but not limited to identity theft, the unauthorized acquisition of personal information or network credentials, damage to hardware and software, and so on. Augmented reality (AR) allows for real-time monitoring and visualization of network activity, system logs, and security alerts. This allows security professionals to immediately identify threats, monitor suspicious activities, and fix any issues that develop. This data can be displayed in an aesthetically pleasing and intuitively structured format using augmented reality interfaces, enabling for faster analysis and decision-making.
- [135] arXiv:2404.16861 (cross-list from nlin.AO) [pdf, other]
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Title: Universal resonancelike emergence of chaos in complex networks of damped-driven nonlinear systemsComments: 11 pages (including supplemental material) with included figuresSubjects: Adaptation and Self-Organizing Systems (nlin.AO); Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD)
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological networks. Here, we solve a critical outstanding problem in this multidisciplinary research field: The emergence and persistence of spatio-temporal chaos in complex networks of damped-driven nonlinear oscillators in the significant weak-coupling regime, while they exhibit regular behavior when uncoupled. By developing a comprehensive theory with the aid of standard analytical methods, a hierarchy of lower-dimensional effective models, and extensive numerical simulations, we uncover and characterize the basic physical mechanisms concerning both heterogeneity-induced and impulse-induced emergence, enhancement, and suppression of chaos in starlike and scale-free networks of periodically driven, dissipative nonlinear oscillators.
- [136] arXiv:2404.16878 (cross-list from cs.DM) [pdf, other]
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Title: tinygarden -- A java package for testing properties of spanning treesSubjects: Discrete Mathematics (cs.DM); Combinatorics (math.CO)
Spanning trees are fundamental objects in graph theory. The spanning tree set size of an arbitrary graph can be very large. This limitation discourages its analysis. However interesting patterns can emerge in small cases. In this article we introduce \emph{tinygarden}, a java package for validating hypothesis, testing properties and discovering patterns from the spanning tree set of an arbitrary graph.
- [137] arXiv:2404.16881 (cross-list from cs.LG) [pdf, other]
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Title: On uncertainty-penalized Bayesian information criterionComments: 4 pages, 2 figuresSubjects: Machine Learning (cs.LG); Statistics Theory (math.ST)
The uncertainty-penalized information criterion (UBIC) has been proposed as a new model-selection criterion for data-driven partial differential equation (PDE) discovery. In this paper, we show that using the UBIC is equivalent to employing the conventional BIC to a set of overparameterized models derived from the potential regression models of different complexity measures. The result indicates that the asymptotic property of the UBIC and BIC holds indifferently.
- [138] arXiv:2404.16900 (cross-list from eess.IV) [pdf, other]
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Title: Space-Variant Total Variation boosted by learning techniques in few-view tomographic imagingSubjects: Image and Video Processing (eess.IV); Machine Learning (cs.LG); Numerical Analysis (math.NA); Optimization and Control (math.OC)
This paper focuses on the development of a space-variant regularization model for solving an under-determined linear inverse problem. The case study is a medical image reconstruction from few-view tomographic noisy data. The primary objective of the proposed optimization model is to achieve a good balance between denoising and the preservation of fine details and edges, overcoming the performance of the popular and largely used Total Variation (TV) regularization through the application of appropriate pixel-dependent weights. The proposed strategy leverages the role of gradient approximations for the computation of the space-variant TV weights. For this reason, a convolutional neural network is designed, to approximate both the ground truth image and its gradient using an elastic loss function in its training. Additionally, the paper provides a theoretical analysis of the proposed model, showing the uniqueness of its solution, and illustrates a Chambolle-Pock algorithm tailored to address the specific problem at hand. This comprehensive framework integrates innovative regularization techniques with advanced neural network capabilities, demonstrating promising results in achieving high-quality reconstructions from low-sampled tomographic data.
- [139] arXiv:2404.16920 (cross-list from cs.NI) [pdf, other]
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Title: Structured Reinforcement Learning for Delay-Optimal Data Transmission in Dense mmWave NetworksComments: IEEE Transactions on Wireless CommunicationsSubjects: Networking and Internet Architecture (cs.NI); Information Theory (cs.IT); Machine Learning (cs.LG); Signal Processing (eess.SP)
We study the data packet transmission problem (mmDPT) in dense cell-free millimeter wave (mmWave) networks, i.e., users sending data packet requests to access points (APs) via uplinks and APs transmitting requested data packets to users via downlinks. Our objective is to minimize the average delay in the system due to APs' limited service capacity and unreliable wireless channels between APs and users. This problem can be formulated as a restless multi-armed bandits problem with fairness constraint (RMAB-F). Since finding the optimal policy for RMAB-F is intractable, existing learning algorithms are computationally expensive and not suitable for practical dynamic dense mmWave networks. In this paper, we propose a structured reinforcement learning (RL) solution for mmDPT by exploiting the inherent structure encoded in RMAB-F. To achieve this, we first design a low-complexity and provably asymptotically optimal index policy for RMAB-F. Then, we leverage this structure information to develop a structured RL algorithm called mmDPT-TS, which provably achieves an \tilde{O}(\sqrt{T}) Bayesian regret. More importantly, mmDPT-TS is computation-efficient and thus amenable to practical implementation, as it fully exploits the structure of index policy for making decisions. Extensive emulation based on data collected in realistic mmWave networks demonstrate significant gains of mmDPT-TS over existing approaches.
- [140] arXiv:2404.16956 (cross-list from cs.LG) [pdf, other]
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Title: A Notion of Uniqueness for the Adversarial Bayes ClassifierAuthors: Natalie S. FrankComments: 46 pages, 7 figuresSubjects: Machine Learning (cs.LG); Statistics Theory (math.ST); Machine Learning (stat.ML)
We propose a new notion of uniqueness for the adversarial Bayes classifier in the setting of binary classification. Analyzing this notion of uniqueness produces a simple procedure for computing all adversarial Bayes classifiers for a well-motivated family of one dimensional data distributions. This characterization is then leveraged to show that as the perturbation radius increases, certain notions of regularity improve for adversarial Bayes classifiers. We demonstrate with various examples that the boundary of the adversarial Bayes classifier frequently lies near the boundary of the Bayes classifier.
- [141] arXiv:2404.16991 (cross-list from quant-ph) [pdf, ps, other]
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Title: Efficient Variational Quantum Linear Solver for Structured Sparse MatricesSubjects: Quantum Physics (quant-ph); Numerical Analysis (math.NA)
We develop a novel approach for efficiently applying variational quantum linear solver (VQLS) in context of structured sparse matrices. Such matrices frequently arise during numerical solution of partial differential equations which are ubiquitous in science and engineering. Conventionally, Pauli basis is used for linear combination of unitary (LCU) decomposition of the underlying matrix to facilitate the evaluation the global/local VQLS cost functions. However, Pauli basis in worst case can result in number of LCU terms that scale quadratically with respect to the matrix size. We show that by using an alternate basis one can better exploit the sparsity and underlying structure of matrix leading to number of tensor product terms which scale only logarithmically with respect to the matrix size. Given this new basis is comprised of non-unitary operators, we employ the concept of unitary completion to design efficient quantum circuits for computing the global/local VQLS cost functions. We compare our approach with other related concepts in the literature including unitary dilation and measurement in Bell basis, and discuss its pros/cons while using VQLS applied to Heat equation as an example.
- [142] arXiv:2404.17012 (cross-list from cs.CC) [pdf, other]
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Title: Computational hardness of detecting graph lifts and certifying lift-monotone properties of random regular graphsComments: 64 pages, 1 table, 4 figuresSubjects: Computational Complexity (cs.CC); Data Structures and Algorithms (cs.DS); Combinatorics (math.CO); Probability (math.PR)
We introduce a new conjecture on the computational hardness of detecting random lifts of graphs: we claim that there is no polynomial-time algorithm that can distinguish between a large random $d$-regular graph and a large random lift of a Ramanujan $d$-regular base graph (provided that the lift is corrupted by a small amount of extra noise), and likewise for bipartite random graphs and lifts of bipartite Ramanujan graphs. We give evidence for this conjecture by proving lower bounds against the local statistics hierarchy of hypothesis testing semidefinite programs. We then explore the consequences of this conjecture for the hardness of certifying bounds on numerous functions of random regular graphs, expanding on a direction initiated by Bandeira, Banks, Kunisky, Moore, and Wein (2021). Conditional on this conjecture, we show that no polynomial-time algorithm can certify tight bounds on the maximum cut of random 3- or 4-regular graphs, the maximum independent set of random 3- or 4-regular graphs, or the chromatic number of random 7-regular graphs. We show similar gaps asymptotically for large degree for the maximum independent set and for any degree for the minimum dominating set, finding that naive spectral and combinatorial bounds are optimal among all polynomial-time certificates. Likewise, for small-set vertex and edge expansion in the limit of very small sets, we show that the spectral bounds of Kahale (1995) are optimal among all polynomial-time certificates.
- [143] arXiv:2404.17013 (cross-list from cs.CC) [pdf, ps, other]
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Title: Two-Source and Affine Non-Malleable Extractors for Small EntropyComments: To appear in ICALP 24. Abstract shortened due to arXiv requirementSubjects: Computational Complexity (cs.CC); Combinatorics (math.CO)
Non-malleable extractors are generalizations and strengthening of standard randomness extractors, that are resilient to adversarial tampering. Such extractors have wide applications in cryptography and explicit construction of extractors. In the well-studied models of two-source and affine non-malleable extractors, the previous best constructions only work for entropy rate $>2/3$ and $1-\gamma$ respectively by Li (FOCS' 23).
We present explicit constructions of two-source and affine non-malleable extractors that match the state-of-the-art constructions of standard ones for small entropy. Our main results include two-source and affine non-malleable extractors (over $\mathsf{F}_2$) for sources on $n$ bits with min-entropy $k \ge \log^C n$ and polynomially small error, matching the parameters of standard extractors by Chattopadhyay and Zuckerman (STOC' 16, Annals of Mathematics' 19) and Li (FOCS' 16), as well as those with min-entropy $k = O(\log n)$ and constant error, matching the parameters of standard extractors by Li (FOCS' 23).
Our constructions significantly improve previous results, and the parameters (entropy requirement and error) are the best possible without first improving the constructions of standard extractors. In addition, our improved affine non-malleable extractors give strong lower bounds for a certain kind of read-once linear branching programs, recently introduced by Gryaznov, Pudl\'{a}k, and Talebanfard (CCC' 22) as a generalization of several well-studied computational models. These bounds match the previously best-known average-case hardness results given by Chattopadhyay and Liao (CCC' 23) and Li (FOCS' 23), where the branching program size lower bounds are close to optimal, but the explicit functions we use here are different.\ Our results also suggest a possible deeper connection between non-malleable extractors and standard ones. - [144] arXiv:2404.17039 (cross-list from cs.MS) [pdf, other]
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Title: Differentiating Through Linear SolversSubjects: Mathematical Software (cs.MS); Numerical Analysis (math.NA)
Computer programs containing calls to linear solvers are a known challenge for automatic differentiation. Previous publications advise against differentiating through the low-level solver implementation, and instead advocate for high-level approaches that express the derivative in terms of a modified linear system that can be solved with a separate solver call. Despite this ubiquitous advice, we are not aware of prior work comparing the accuracy of both approaches. With this article we thus empirically study a simple question: What happens if we ignore common wisdom, and differentiate through linear solvers?
- [145] arXiv:2404.17057 (cross-list from physics.comp-ph) [pdf, other]
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Title: Portable, Massively Parallel Implementation of a Material Point Method for Compressible FlowsComments: 36 pages, 11 figuresSubjects: Computational Physics (physics.comp-ph); Distributed, Parallel, and Cluster Computing (cs.DC); Numerical Analysis (math.NA)
The recent evolution of software and hardware technologies is leading to a renewed computational interest in Particle-In-Cell (PIC) methods such as the Material Point Method (MPM). Indeed, provided some critical aspects are properly handled, PIC methods can be cast in formulations suitable to the requirements of data locality and fine-grained parallelism of modern hardware accelerators as Graphics Processing Units (GPUs). Such a rapid and continuous technological development increases also the importance of generic and portable implementations. While continuum mechanics simulations have already shown the capabilities of MPM on a wide range of phenomena, the use of the method in compressible fluid dynamics is less frequent, especially in the supersonic regime. In this paper we present a portable, highly parallel, GPU based MPM solver for compressible gas dynamics. The implementation aims to reach a good compromise between portability and efficiency and to give a first assessment of the potential of this approach in reproducing high speed gas flows, also taking into account solid obstacles. The proposed model constitutes a new step towards the realization of a monolithic MPM solver for Fluid-Structure Interaction (FSI) problems at all Mach numbers up to the supersonic regime.
- [146] arXiv:2404.17061 (cross-list from hep-th) [pdf, other]
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Title: Gauge origami and quiver W-algebras II: Vertex function and beyond quantum $q$-Langlands correspondenceComments: 30 pagesSubjects: High Energy Physics - Theory (hep-th); Algebraic Geometry (math.AG); Quantum Algebra (math.QA)
We continue the study of generalized gauge theory called gauge origami, based on the quantum algebraic approach initiated in [arXiv:2310.08545]. In this article, we in particular explore the D2 brane system realized by the screened vertex operators of the corresponding W-algebra. The partition function of this system given by the corresponding conformal block is identified with the vertex function associated with quasimaps to Nakajima quiver varieties and generalizations, that plays a central role in the quantum $q$-Langlands correspondence. Based on the quantum algebraic perspective, we address three new aspects of the correspondence: (i) Direct equivalence between the electric and magnetic blocks by constructing stable envelopes from the chamber structure of the vertex operators, (ii) Double affine generalization of quantum $q$-Langlands correspondence, and (iii) Conformal block realization of the origami vertex function associated with intersection of quasimaps, that realizes the higher-rank multi-leg Pandharipande-Thomas vertices of 3-fold and 4-fold.
- [147] arXiv:2404.17075 (cross-list from gr-qc) [pdf, ps, other]
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Title: Non-Particulate Quantum States of the Electromagnetic Field in Expanding Space-TimeSubjects: General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
A quantum field has been coupled to a space-time with accelerating expansion. Dynamical modes are destabilised successively at shorter material wavelengths as they metamorphose from oscillators to repellers. Due to degeneracy of energy levels, the number of unstable modes increases at an accelerating rate, sufficient to account for a significant proportion of cosmic energy. For the subsystem spanned by a finite basis of unstable runaway modes, the quantum Hamiltonian is unbounded below. There is no Bogoliubov transformation by which that subsystem Hamiltonian can be expressed as a linear combination of number operators. For the remaining subsystem spanned by an infinite number of oscillator modes, there is an appropriate vacuum state in a Fock-Cook representation of the field algebra. The massless quantum vector field of electromagnetism is considered when it is minimally or more generally coupled to an expanding space-time. For a significant class of models, including minimal coupling models and the exponential de Sitter universe coupled to the Ricci curvature tensor, the field equations are equivalent to the Proca equation with time-dependent mass.
- [148] arXiv:2404.17080 (cross-list from cs.DM) [pdf, other]
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Title: Solving the Graph Burning Problem for Large GraphsAuthors: Felipe de Carvalho Pereira, Pedro Jussieu de Rezende, Tallys Yunes, Luiz Fernando Batista MoratoComments: 10 pages, 1 figure and 2 tablesSubjects: Discrete Mathematics (cs.DM); Data Structures and Algorithms (cs.DS); Combinatorics (math.CO)
We propose an exact algorithm for the Graph Burning Problem ($\texttt{GBP}$), an NP-hard optimization problem that models the spread of influence on social networks. Given a graph $G$ with vertex set $V$, the objective is to find a sequence of $k$ vertices in $V$, namely, $v_1, v_2, \dots, v_k$, such that $k$ is minimum and $\bigcup_{i = 1}^{k} \{u\! \in\! V\! : d(u, v_i) \leq k - i\} = V$, where $d(u,v)$ denotes the distance between $u$ and $v$. We formulate the problem as a set covering integer programming model and design a row generation algorithm for the $\texttt{GBP}$. Our method exploits the fact that a very small number of covering constraints is often sufficient for solving the integer model, allowing the corresponding rows to be generated on demand. To date, the most efficient exact algorithm for the $\texttt{GBP}$, denoted here by $\texttt{GDCA}$, is able to obtain optimal solutions for graphs with up to 14,000 vertices within two hours of execution. In comparison, our algorithm finds provably optimal solutions approximately 236 times faster, on average, than $\texttt{GDCA}$. For larger graphs, memory space becomes a limiting factor for $\texttt{GDCA}$. Our algorithm, however, solves real-world instances with almost 200,000 vertices in less than 35 seconds, increasing the size of graphs for which optimal solutions are known by a factor of 14.
- [149] arXiv:2404.17082 (cross-list from physics.soc-ph) [pdf, other]
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Title: Evolutionary game dynamics with environmental feedback in a network with two communitiesComments: 8 figures, 2 tablesSubjects: Physics and Society (physics.soc-ph); Social and Information Networks (cs.SI); Dynamical Systems (math.DS); Populations and Evolution (q-bio.PE)
Recent developments of eco-evolutionary models have shown that evolving feedbacks between behavioral strategies and the environment of game interactions, leading to changes in the underlying payoff matrix, can impact the underlying population dynamics in various manners. We propose and analyze an eco-evolutionary game dynamics model on a network with two communities such that players interact with other players in the same community and those in the opposite community at different rates. In our model, we consider two-person matrix games with pairwise interactions occurring on individual edges and assume that the environmental state depends on edges rather than on nodes or being globally shared in the population. We analytically determine the equilibria and their stability under a symmetric population structure assumption, and we also numerically study the replicator dynamics of the general model. The model shows rich dynamical behavior, such as multiple transcritical bifurcations, multistability, and anti-synchronous oscillations. Our work offers insights into understanding how the presence of community structure impacts the eco-evolutionary dynamics within and between niches.
- [150] arXiv:2404.17231 (cross-list from physics.soc-ph) [pdf, ps, other]
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Title: Network shell structure based on hub and non-hub nodesSubjects: Physics and Society (physics.soc-ph); General Topology (math.GN)
The shell structure holds significant importance in various domains such as information dissemination, supply chain management, and transportation. This study focuses on investigating the shell structure of hub and non-hub nodes, which play important roles in these domains. Our framework explores the topology of Erd\"{o}s-R\'{e}nyi (ER) and Scale-Free (SF) networks, considering source node selection strategies dependent on the nodes' degrees. We define the shell $l$ in a network as the set of nodes at a distance $l$ from a given node and represent $r_l$ as the fraction of nodes outside shell $l$. Statistical properties of the shells are examined for a selected node, taking into account the node's degree. For a network with a given degree distribution, we analytically derive the degree distribution and average degree of nodes outside shell $l$ as functions of $r_l$. Moreover, we discover that $r_l$ follows an iterative functional form $r_l = \phi(r_{l-1})$, where $\phi$ is expressed in terms of the generating function of the original degree distribution of the network.
- [151] arXiv:2404.17309 (cross-list from cond-mat.stat-mech) [pdf, other]
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Title: On sequences of convex records in the planeComments: 29 pages, 19 figuresSubjects: Statistical Mechanics (cond-mat.stat-mech); Probability (math.PR)
Convex records have an appealing purely geometric definition. In a sequence of $d$-dimensional data points, the $n$-th point is a convex record if it lies outside the convex hull of all preceding points. We specifically focus on the bivariate (i.e., two-dimensional) setting. For iid (independent and identically distributed) points, we establish an identity relating the mean number $\mean{R_n}$ of convex records up to time $n$ to the mean number $\mean{N_n}$ of vertices in the convex hull of the first $n$ points. By combining this identity with extensive numerical simulations, we provide a comprehensive overview of the statistics of convex records for various examples of iid data points in the plane: uniform points in the square and in the disk, Gaussian points and points with an isotropic power-law distribution. In all these cases, the mean values and variances of $N_n$ and $R_n$ grow proportionally to each other, resulting in finite limit Fano factors $F_N$ and $F_R$. We also consider planar random walks, i.e., sequences of points with iid increments. For both the Pearson walk in the continuum and the P\'olya walk on a lattice, we characterise the growth of the mean number $\mean{R_n}$ of convex records and demonstrate that the ratio $R_n/\mean{R_n}$ keeps fluctuating with a universal limit distribution.
- [152] arXiv:2404.17344 (cross-list from cs.LG) [pdf, other]
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Title: Fast Evaluation of Additive Kernels: Feature Arrangement, Fourier Methods, and Kernel DerivativesComments: Official code this https URLSubjects: Machine Learning (cs.LG); Numerical Analysis (math.NA)
One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel matrices typically deteriorate in their performance if the feature vectors reside in higher-dimensional feature spaces. We here present a technique based on the non-equispaced fast Fourier transform (NFFT) with rigorous error analysis. We show that this approach is also well suited to allow the approximation of the matrix that arises when the kernel is differentiated with respect to the kernel hyperparameters; a problem often found in the training phase of methods such as Gaussian processes. We also provide an error analysis for this case. We illustrate the performance of the additive kernel scheme with fast matrix vector products on a number of data sets. Our code is available at https://github.com/wagnertheresa/NFFTAddKer
- [153] arXiv:2404.17358 (cross-list from cs.LG) [pdf, ps, other]
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Title: Adversarial Consistency and the Uniqueness of the Adversarial Bayes ClassifierAuthors: Natalie S. FrankComments: 17 pagesSubjects: Machine Learning (cs.LG); Statistics Theory (math.ST); Machine Learning (stat.ML)
Adversarial training is a common technique for learning robust classifiers. Prior work showed that convex surrogate losses are not statistically consistent in the adversarial context -- or in other words, a minimizing sequence of the adversarial surrogate risk will not necessarily minimize the adversarial classification error. We connect the consistency of adversarial surrogate losses to properties of minimizers to the adversarial classification risk, known as \emph{adversarial Bayes classifiers}. Specifically, under reasonable distributional assumptions, a convex loss is statistically consistent for adversarial learning iff the adversarial Bayes classifier satisfies a certain notion of uniqueness.
- [154] arXiv:2404.17429 (cross-list from stat.ML) [pdf, other]
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Title: Separation capacity of linear reservoirs with random connectivity matrixAuthors: Youness BoutaibSubjects: Machine Learning (stat.ML); Machine Learning (cs.LG); Probability (math.PR)
We argue that the success of reservoir computing lies within the separation capacity of the reservoirs and show that the expected separation capacity of random linear reservoirs is fully characterised by the spectral decomposition of an associated generalised matrix of moments. Of particular interest are reservoirs with Gaussian matrices that are either symmetric or whose entries are all independent. In the symmetric case, we prove that the separation capacity always deteriorates with time; while for short inputs, separation with large reservoirs is best achieved when the entries of the matrix are scaled with a factor $\rho_T/\sqrt{N}$, where $N$ is the dimension of the reservoir and $\rho_T$ depends on the maximum length of the input time series. In the i.i.d. case, we establish that optimal separation with large reservoirs is consistently achieved when the entries of the reservoir matrix are scaled with the exact factor $1/\sqrt{N}$. We further give upper bounds on the quality of separation in function of the length of the time series. We complement this analysis with an investigation of the likelihood of this separation and the impact of the chosen architecture on separation consistency.
- [155] arXiv:2404.17449 (cross-list from physics.hist-ph) [pdf, ps, other]
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Title: On the Meaning of Local Symmetries: Epistemic-Ontological DialecticComments: 21 pagesSubjects: History and Philosophy of Physics (physics.hist-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Differential Geometry (math.DG)
We propose our account of the meaning of local symmetries. We argue that the general covariance principle and gauge principle both are principles of democratic epistemic access to the law of physics, leading to ontological insights about the objective nature of spacetime. We further argue that relationality is a core notion of general-relativistic gauge field theory, tacitly encoded by its (active) local symmetries.
- [156] arXiv:2404.17474 (cross-list from eess.SY) [pdf, other]
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Title: Establishing best practices for modeling long duration energy storage in deeply decarbonized energy systemsAuthors: Gabriel Mantegna, Wilson Ricks, Aneesha Manocha, Neha Patankar, Dharik Mallapragada, Jesse JenkinsComments: Working paperSubjects: Systems and Control (eess.SY); Optimization and Control (math.OC)
Long duration energy storage (LDES) may become a critical technology for the decarbonization of the power sector, as current commercially available Li-ion battery storage technologies cannot cost-effectively shift energy to address multi-day or seasonal variability in demand and renewable energy availability. LDES is difficult to model in existing energy system planning models (such as electricity system capacity expansion models), as it is much more dependent on an accurate representation of chronology than other resources. Techniques exist for modeling LDES in these planning models; however, it is not known how spatial and temporal resolution affect the performance of these techniques, creating a research gap. In this study we examine what spatial and temporal resolution is necessarily to accurately capture the full value of LDES, in the context of a continent-scale capacity expansion model. We use the results to draw conclusions and present best practices for modelers seeking to accurately model LDES in a macro-energy systems planning context. Our key findings are: 1) modeling LDES with linked representative periods is crucial to capturing its full value, 2) LDES value is highly sensitive to the cost and availability of other resources, and 3) temporal resolution is more important than spatial resolution for capturing the full value of LDES, although how much temporal resolution is needed will depend on the specific model context.
- [157] arXiv:2404.17542 (cross-list from physics.flu-dyn) [pdf, other]
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Title: A mesh-constrained discrete point method for incompressible flows with moving boundariesSubjects: Fluid Dynamics (physics.flu-dyn); Numerical Analysis (math.NA); Computational Physics (physics.comp-ph)
Particle-based methods are a practical tool in computational fluid dynamics, and novel types of methods have been proposed. However, widely developed Lagrangian-type formulations suffer from the nonuniform distribution of particles, which is enhanced over time and result in problems in computational efficiency and parallel computations. To mitigate these problems, a mesh-constrained discrete point (MCD) method was developed for stationary boundary problems (Matsuda et al., 2022). Although the MCD method is a meshless method that uses moving least-squares approximation, the arrangement of particles (or discrete points (DPs)) is specialized so that their positions are constrained in background meshes to obtain a closely uniform distribution. This achieves a reasonable approximation for spatial derivatives with compact stencils without encountering any ill-posed condition and leads to good performance in terms of computational efficiency. In this study, a novel meshless method based on the MCD method for incompressible flows with moving boundaries is proposed. To ensure the mesh constraint of each DP in moving boundary problems, a novel updating algorithm for the DP arrangement is developed so that the position of DPs is not only rearranged but the DPs are also reassigned the role of being on the boundary or not. The proposed method achieved reasonable results in numerical experiments for well-known moving boundary problems.
- [158] arXiv:2404.17562 (cross-list from stat.ME) [pdf, other]
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Title: Boosting e-BH via conditional calibrationSubjects: Methodology (stat.ME); Statistics Theory (math.ST)
The e-BH procedure is an e-value-based multiple testing procedure that provably controls the false discovery rate (FDR) under any dependence structure between the e-values. Despite this appealing theoretical FDR control guarantee, the e-BH procedure often suffers from low power in practice. In this paper, we propose a general framework that boosts the power of e-BH without sacrificing its FDR control under arbitrary dependence. This is achieved by the technique of conditional calibration, where we take as input the e-values and calibrate them to be a set of "boosted e-values" that are guaranteed to be no less -- and are often more -- powerful than the original ones. Our general framework is explicitly instantiated in three classes of multiple testing problems: (1) testing under parametric models, (2) conditional independence testing under the model-X setting, and (3) model-free conformalized selection. Extensive numerical experiments show that our proposed method significantly improves the power of e-BH while continuing to control the FDR. We also demonstrate the effectiveness of our method through an application to an observational study dataset for identifying individuals whose counterfactuals satisfy certain properties.
Replacements for Mon, 29 Apr 24
- [159] arXiv:1510.05734 (replaced) [pdf, ps, other]
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Title: The p-cycle of Holonomic D-modules and Quantization of Exact Algebraic LagrangiansAuthors: Christopher DoddComments: Newest Version. Completely rewritten. Comments welcome!Subjects: Algebraic Geometry (math.AG)
- [160] arXiv:1706.08941 (replaced) [pdf, other]
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Title: Hybrid Localized Spectral Decomposition for multiscale problemsSubjects: Numerical Analysis (math.NA)
- [161] arXiv:1805.03413 (replaced) [pdf, ps, other]
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Title: Topological finiteness properties of monoids. Part 2: special monoids, one-relator monoids, amalgamated free products, and HNN extensionsComments: 36 pages, incorporates referee's suggestionsSubjects: Group Theory (math.GR); Algebraic Topology (math.AT); Rings and Algebras (math.RA)
- [162] arXiv:1812.11880 (replaced) [src]
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Title: On the zeros of sum from n=1 to 00 of lambda_P(n)/n^sComments: There is an error in the proof of the main result that cannot be repairedSubjects: Number Theory (math.NT)
- [163] arXiv:1902.02018 (replaced) [pdf, ps, other]
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Title: Restriction of $p$-modular representations of $U(2, 1)$ to a Borel subgroupAuthors: Peng XuComments: We complete the proof of (2) of Theorem 1.2. Comments are welcomeSubjects: Representation Theory (math.RT)
- [164] arXiv:1907.13283 (replaced) [pdf, other]
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Title: A globally conservative finite element MHD code and its application to the study of compact torus formation, levitation and magnetic compressionComments: 50 pages, 78 figures, partially presented in conference posters C. Dunlea et al., Magnetic Compression at General Fusion - Experiment & Simulation with a neutral fluid, APS_DPP 2017, EPS 2018, ICPP_2018Subjects: Numerical Analysis (math.NA); Plasma Physics (physics.plasm-ph)
- [165] arXiv:2010.07205 (replaced) [pdf, ps, other]
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Title: On coarse embeddings of amenable groups into hyperbolic graphsAuthors: Romain TesseraComments: 9 ppSubjects: Group Theory (math.GR); Metric Geometry (math.MG)
- [166] arXiv:2011.11669 (replaced) [pdf, ps, other]
- [167] arXiv:2012.02303 (replaced) [pdf, other]
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Title: Decentralized State-Dependent Markov Chain Synthesis with an Application to Swarm GuidanceComments: arXiv admin note: text overlap with arXiv:2012.01928Subjects: Optimization and Control (math.OC); Multiagent Systems (cs.MA); Dynamical Systems (math.DS); Probability (math.PR)
- [168] arXiv:2012.06729 (replaced) [pdf, ps, other]
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Title: A remark on Gibbs measures with log-correlated Gaussian fieldsComments: 41 pages. Minor modifications. Published in Forum Math. SigmaJournal-ref: Forum Math. Sigma. 12 (2024), e50, 40 ppSubjects: Probability (math.PR); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)
- [169] arXiv:2102.01056 (replaced) [pdf, ps, other]
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Title: Wall-crossing for zero-dimensional sheaves and Hilbert schemes of points on Calabi-Yau 4-foldsAuthors: Arkadij BojkoSubjects: Algebraic Geometry (math.AG); K-Theory and Homology (math.KT); Representation Theory (math.RT)
- [170] arXiv:2104.03943 (replaced) [src]
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Title: Un exemple de somme de série de vecteurs propres à valeurs propres de module un, non récurrenteComments: After submitting to arXiv, we found a trivial proof for the main resultSubjects: Complex Variables (math.CV); Dynamical Systems (math.DS)
- [171] arXiv:2105.07422 (replaced) [pdf, ps, other]
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Title: More than 60% of zeros of Dirichlet $L$-functions are on the critical lineAuthors: Keiju SonoComments: Comments are always welcomedSubjects: Number Theory (math.NT)
- [172] arXiv:2106.11392 (replaced) [pdf, ps, other]
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Title: Noncommutative geometry of elliptic surfacesAuthors: Igor NikolaevComments: an updateSubjects: Algebraic Geometry (math.AG); Number Theory (math.NT); Operator Algebras (math.OA)
- [173] arXiv:2107.06674 (replaced) [pdf, ps, other]
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Title: Growth in linear groupsComments: 39 pages, final version incorporating referees' corrections, to appear in Duke Math. JSubjects: Group Theory (math.GR); Combinatorics (math.CO)
- [174] arXiv:2107.06714 (replaced) [pdf, other]
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Title: Robust Data-Driven CARA OptimizationComments: 40 pages, 5 figuresSubjects: Optimization and Control (math.OC)
- [175] arXiv:2108.06777 (replaced) [pdf, other]
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Title: Stochastic quantization of the $Φ^3_3$-modelComments: 115 pages. Minor modifications. To appear in Mem. Eur. Math. SocSubjects: Probability (math.PR); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)
- [176] arXiv:2110.02380 (replaced) [pdf, ps, other]
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Title: Differential Norms and Rieffel AlgebrasComments: We introduced one more example (Example 3.14), changed a sign in the definition of the Heisenberg group and, correspondingly, changed a sign in Equation (3.22)Subjects: Operator Algebras (math.OA); Functional Analysis (math.FA)
- [177] arXiv:2111.08108 (replaced) [pdf, other]
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Title: Physics-informed neural networks via stochastic Hamiltonian dynamics learningComments: To be published in Springer series "Lecture Notes in Networks and Systems"Subjects: Optimization and Control (math.OC); Artificial Intelligence (cs.AI)
- [178] arXiv:2111.11521 (replaced) [pdf, ps, other]
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Title: The Brownian transport mapComments: 49 pages, some edits to the introduction and minor fixesSubjects: Probability (math.PR); Functional Analysis (math.FA)
- [179] arXiv:2201.11328 (replaced) [pdf, ps, other]
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Title: On the weak convergence of conditioned Bessel bridgesComments: 39 pagesSubjects: Probability (math.PR)
- [180] arXiv:2202.11996 (replaced) [pdf, ps, other]
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Title: Supersolvable posets and fiber-type abelian arrangementsComments: 33 pages, 11 figuresSubjects: Combinatorics (math.CO); Algebraic Topology (math.AT)
- [181] arXiv:2203.10860 (replaced) [pdf, ps, other]
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Title: Propagation of regularity for transport equations. A Littlewood-Paley approachComments: revised versionSubjects: Analysis of PDEs (math.AP)
- [182] arXiv:2205.11421 (replaced) [pdf, other]
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Title: Transference for loose Hamilton cycles in random $3$-uniform hypergraphsComments: 29 pages, 3 figuresSubjects: Combinatorics (math.CO)
- [183] arXiv:2205.12826 (replaced) [pdf, other]
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Title: Two Ramsey problems in blowups of graphsComments: 13 pages, 1 figure, author accepted manuscript, to appear in European Journal of CombinatoricsSubjects: Combinatorics (math.CO)
- [184] arXiv:2207.04235 (replaced) [pdf, other]
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Title: A Class of Rearrangement Groups that are not Invariably GeneratedComments: Small changes that reflect the published version (especially theorem numeration)Journal-ref: Bull. London Math. Soc. (2024)Subjects: Group Theory (math.GR)
- [185] arXiv:2207.11634 (replaced) [pdf, ps, other]
- [186] arXiv:2208.06912 (replaced) [pdf, other]
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Title: Variations on Ramsey numbers and minimum numbers of monochromatic triangles in line $2$-colorings of configurationsComments: Revisions after referee commentsJournal-ref: Electronic Journal of Graph Theory and Applications (EJGTA) 11, no. 2 (2023): 431-445Subjects: Combinatorics (math.CO)
- [187] arXiv:2209.01262 (replaced) [pdf, ps, other]
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Title: On metric approximate subgroupsSubjects: Group Theory (math.GR); Logic (math.LO)
- [188] arXiv:2210.02626 (replaced) [pdf, ps, other]
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Title: Decision Making under Cumulative Prospect Theory: An Alternating Direction Method of MultipliersComments: 32 pagesSubjects: Optimization and Control (math.OC)
- [189] arXiv:2210.11098 (replaced) [pdf, ps, other]
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Title: The definable content of homological invariants II: Čech cohomology and homotopy classificationComments: 63 pages; revised and accepted to Forum of Mathematics, PiSubjects: Logic (math.LO); Algebraic Topology (math.AT); Geometric Topology (math.GT); K-Theory and Homology (math.KT)
- [190] arXiv:2210.14100 (replaced) [pdf, ps, other]
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Title: The capacity of a finite field matrix channelComments: 32 pages, 1 figure. Typos corrected, minor changes to proofs for clarity, more discussion addedSubjects: Information Theory (cs.IT); Discrete Mathematics (cs.DM); Combinatorics (math.CO)
- [191] arXiv:2211.02713 (replaced) [pdf, other]
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Title: A degree 4 sum-of-squares lower bound for the clique number of the Paley graphComments: 62 pages, 3 figures, 1 table; closest to version published in CCC 2023Subjects: Data Structures and Algorithms (cs.DS); Computational Complexity (cs.CC); Number Theory (math.NT); Optimization and Control (math.OC)
- [192] arXiv:2212.01485 (replaced) [pdf, other]
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Title: A Theory of Semantic CommunicationComments: Keywords: Semantic communication, joint source-channel coding, semantic decoding, semantic encoding, large language modelSubjects: Information Theory (cs.IT)
- [193] arXiv:2212.04204 (replaced) [pdf, ps, other]
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Title: Maximal subgroups of finitely presented special inverse monoidsComments: 25 pages, 2 figures; incorporates referee's suggestions including minor changes to the title and abstractSubjects: Group Theory (math.GR)
- [194] arXiv:2212.12754 (replaced) [pdf, ps, other]
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Title: Sárközy's Theorem in Various Finite Field SettingsSubjects: Number Theory (math.NT); Combinatorics (math.CO)
- [195] arXiv:2301.03314 (replaced) [pdf, other]
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Title: Sign involutions on para-abelian varietiesComments: 16 pages, Introduction expanded, otherwise minor changes, to appear in Indag. MathSubjects: Algebraic Geometry (math.AG)
- [196] arXiv:2301.09002 (replaced) [pdf, ps, other]
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Title: The Gysin braid for $S^3$-actions on manifoldsSubjects: Algebraic Topology (math.AT)
- [197] arXiv:2302.04078 (replaced) [pdf, ps, other]
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Title: Generalisations of Thompson's group V arising from purely infinite groupoidsComments: 25 pages. v2: One of the conditions in Theorem A was removed, since it is not equivalent to the remaining ones. Otherwise only minor changesSubjects: Group Theory (math.GR); Dynamical Systems (math.DS); Operator Algebras (math.OA)
- [198] arXiv:2302.11160 (replaced) [pdf, other]
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Title: Proof of the Ginzburg-Kazhdan conjectureAuthors: Tom GannonComments: To appear in Advances in MathematicsSubjects: Algebraic Geometry (math.AG); Representation Theory (math.RT); Symplectic Geometry (math.SG)
- [199] arXiv:2302.14779 (replaced) [pdf, ps, other]
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Title: Twisted Drinfeld Centers and Framed String-NetsComments: Small typos fixed, one reference addedSubjects: Quantum Algebra (math.QA); Mathematical Physics (math-ph)
- [200] arXiv:2303.02432 (replaced) [pdf, other]
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Title: Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystemComments: 23 pages, 10 figures, comments welcome! Version 3 contains added clarifications and an additional proof of the Gaussian heuristic for a class of NTRU-like latticesSubjects: Quantum Physics (quant-ph); Cryptography and Security (cs.CR); Information Theory (cs.IT)
- [201] arXiv:2303.05236 (replaced) [pdf, other]
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Title: Layer separation of the 3D incompressible Navier-Stokes equation in a bounded domainComments: 33 pages, 2 figuresSubjects: Analysis of PDEs (math.AP); Fluid Dynamics (physics.flu-dyn)
- [202] arXiv:2303.14056 (replaced) [pdf, other]
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Title: Chiral basis for qubits and spin-helix decayComments: 5 pages, 2 figures; v2: major revision and new material, title changed and an author added; v3: revised version, accepted for publication by Phys. Rev. Lett., title changed again, references added, supplemental material appendedSubjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)
- [203] arXiv:2304.03334 (replaced) [pdf, ps, other]
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Title: Extension of Arakelyan's TheoremAuthors: Spyros PasiasSubjects: Complex Variables (math.CV)
- [204] arXiv:2304.05360 (replaced) [pdf, ps, other]
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Title: A Third Information-Theoretic Approach to Finite de Finetti TheoremsComments: 11 pages, no figures. In the second version the introduction is slightly extended, two new references and Section 2.4 have been addedSubjects: Information Theory (cs.IT); Probability (math.PR); Quantum Physics (quant-ph)
- [205] arXiv:2304.09400 (replaced) [pdf, other]
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Title: On the Capacity Region of Reconfigurable Intelligent Surface Assisted Symbiotic RadiosSubjects: Information Theory (cs.IT)
- [206] arXiv:2305.02287 (replaced) [pdf, ps, other]
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Title: The unipotent mixing conjectureComments: 26 pages, small inaccuracy fixed before Prop 5.1Subjects: Number Theory (math.NT)
- [207] arXiv:2305.02434 (replaced) [pdf, other]
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Title: Uncertainty Quantification and Confidence Intervals for Naive Rare-Event EstimatorsSubjects: Methodology (stat.ME); Statistics Theory (math.ST)
- [208] arXiv:2305.09278 (replaced) [pdf, other]
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Title: Multi-domain FEM-BEM coupling for acoustic scatteringSubjects: Numerical Analysis (math.NA)
- [209] arXiv:2305.10416 (replaced) [pdf, ps, other]
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Title: Minimax rate for multivariate data under componentwise local differential privacy constraintsSubjects: Statistics Theory (math.ST)
- [210] arXiv:2305.13474 (replaced) [pdf, other]
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Title: Allen-Cahn Solutions with Triple Junction Structure at InfinitySubjects: Analysis of PDEs (math.AP)
- [211] arXiv:2306.01379 (replaced) [pdf, ps, other]
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Title: Hard congestion limit of the dissipative Aw-Rascle system with a polynomial offset functionAuthors: Muhammed Ali MehmoodSubjects: Analysis of PDEs (math.AP)
- [212] arXiv:2306.04367 (replaced) [pdf, other]
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Title: Solving NP-hard Problems on \textsc{GaTEx} Graphs: Linear-Time Algorithms for Perfect Orderings, Cliques, Colorings, and Independent SetsSubjects: Discrete Mathematics (cs.DM); Computational Complexity (cs.CC); Data Structures and Algorithms (cs.DS); Combinatorics (math.CO)
- [213] arXiv:2306.06187 (replaced) [pdf, ps, other]
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Title: Faber-Krahn inequalities, the Alt-Caffarelli-Friedman formula, and Carleson's $\varepsilon^2$ conjecture in higher dimensionsComments: In this version we correct the statements of some of the main results. For example, we forgot to mention that $H^n(B)=H^n(\Omega)$ in Theorems A and B from the previous versionSubjects: Analysis of PDEs (math.AP); Classical Analysis and ODEs (math.CA)
- [214] arXiv:2306.08142 (replaced) [pdf, other]
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Title: Latent mutations in the ancestries of alleles under selectionComments: 47 pages, 3 figuresSubjects: Probability (math.PR); Populations and Evolution (q-bio.PE)
- [215] arXiv:2306.08931 (replaced) [pdf, ps, other]
- [216] arXiv:2306.12416 (replaced) [pdf, other]
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Title: Quantum soft-covering lemma with applications to rate-distortion coding, resolvability and identification via quantum channelsComments: 30 pages, 3 figures; v2 fixes an error in Definition 36 and various typos and minor issues throughout; v3 fixes some further minor points and provides a proof of Lemma 11 due to F. Dupuis, it is the version accepted by IJQI (special issue in honour of Alexander S. Holevo)Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT)
- [217] arXiv:2306.13523 (replaced) [pdf, other]
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Title: Weak error expansion of a stopped numerical scheme for singular Langevin processAuthors: Lucas JournelSubjects: Probability (math.PR)
- [218] arXiv:2306.15945 (replaced) [pdf, ps, other]
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Title: Permutation Polynomial Interleaved Zadoff-Chu SequencesComments: Submitted to IEEE Transactions on Information TheorySubjects: Information Theory (cs.IT); Signal Processing (eess.SP)
- [219] arXiv:2306.16026 (replaced) [pdf, other]
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Title: Self-similar fractals and common hypercyclicityAuthors: Fernando Costa JrComments: 42 pages, 14 figuresJournal-ref: Journal of Functional Analysis, 2024, 110473, ISSN 0022-1236Subjects: Functional Analysis (math.FA)
- [220] arXiv:2307.02282 (replaced) [pdf, ps, other]
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Title: Denseness of $g$-vector cones from weighted orbifoldsAuthors: Toshiya YurikusaComments: 21 pages. this article draws heavily from arXiv:1904.12479, v2: minor correctionsSubjects: Combinatorics (math.CO); Geometric Topology (math.GT); Rings and Algebras (math.RA); Representation Theory (math.RT)
- [221] arXiv:2307.06196 (replaced) [pdf, ps, other]
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Title: A volume-renormalized mass for asymptotically hyperbolic manifoldsComments: 45 pages; v2: presentation clarified and typos fixedSubjects: Differential Geometry (math.DG); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
- [222] arXiv:2307.06910 (replaced) [pdf, ps, other]
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Title: Transferring CompactnessComments: Accepted versionSubjects: Logic (math.LO)
- [223] arXiv:2308.00731 (replaced) [pdf, other]
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Title: The contact process with an asymptomatic stateComments: 22 pages, 4 figures, 3 tablesSubjects: Probability (math.PR); Populations and Evolution (q-bio.PE)
- [224] arXiv:2308.11581 (replaced) [pdf, ps, other]
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Title: Dynamical Low-Rank Approximation for Stochastic Differential EquationsComments: 41 pagesSubjects: Numerical Analysis (math.NA)
- [225] arXiv:2309.07691 (replaced) [pdf, ps, other]
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Title: Infinitely many commensurability classes of compact Coxeter polyhedra in $\mathbb{H}^4$ and $\mathbb{H}^5$Comments: Final version, to appear in Advances in MathematicsSubjects: Group Theory (math.GR); Geometric Topology (math.GT); Number Theory (math.NT)
- [226] arXiv:2309.08490 (replaced) [pdf, ps, other]
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Title: Bessel Periods on $U(2,1) \times U(1,1)$, Relative Trace Formula and Non-Vanishing of Central L-valuesComments: 152 pages; references added to the introductionSubjects: Number Theory (math.NT)
- [227] arXiv:2309.16506 (replaced) [pdf, ps, other]
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Title: On the local linearization of the one-dimensional stochastic wave equation with a multiplicative space-time white noise forcingComments: 12 pages. A title modified. Remark 1.2 has been added. The proof of Lemma 1.2 is simplified. To appear in Proc. Amer. Math. SocSubjects: Analysis of PDEs (math.AP); Probability (math.PR)
- [228] arXiv:2310.01522 (replaced) [pdf, other]
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Title: Property-preserving numerical approximations of a Cahn-Hilliard-Navier-Stokes model with variable densities and degenerate mobilityComments: 32 pages, 11 figures, 2 tablesSubjects: Numerical Analysis (math.NA)
- [229] arXiv:2310.10270 (replaced) [pdf, other]
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Title: $h$-function, Hilbert-Kunz density function and Frobenius-Poincaré functionComments: v2: substantial changes: applications added, results improvedSubjects: Commutative Algebra (math.AC); Algebraic Geometry (math.AG); Classical Analysis and ODEs (math.CA)
- [230] arXiv:2310.11519 (replaced) [pdf, ps, other]
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Title: On some counterparts of Rickart $*$-algebrasComments: 17 pagesSubjects: Rings and Algebras (math.RA); Operator Algebras (math.OA)
- [231] arXiv:2310.12339 (replaced) [pdf, ps, other]
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Title: Remarks on the Hilbert depth of squarefree monomial idealsComments: 10 pages; major changes (we realized that our results hold only in the squarefree case and we modified accordingly); one coauthor addedSubjects: Commutative Algebra (math.AC)
- [232] arXiv:2310.17823 (replaced) [pdf, ps, other]
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Title: On the Construction of Relativistic Quantum Wave Equation and General Solution of the Second Order Differential EquationAuthors: Nikolaos D. BagisComments: 34 pagesSubjects: General Mathematics (math.GM)
- [233] arXiv:2310.19632 (replaced) [pdf, ps, other]
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Title: The enumeration of inversion sequences avoiding the patterns 201 and 210Authors: Jay PantoneSubjects: Combinatorics (math.CO)
- [234] arXiv:2311.01167 (replaced) [pdf, ps, other]
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Title: Modulation Design and Optimization for RIS-Assisted Symbiotic RadiosComments: 16 pages,16 figuresSubjects: Information Theory (cs.IT); Signal Processing (eess.SP)
- [235] arXiv:2311.01194 (replaced) [pdf, other]
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Title: Predictive Modelling of Critical Variables for Improving HVOF Coating using Gamma Regression ModelsComments: 37 pages, 7 figuresSubjects: Applications (stat.AP); Numerical Analysis (math.NA); Applied Physics (physics.app-ph)
- [236] arXiv:2311.04043 (replaced) [pdf, ps, other]
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Title: Gaitsgory's central functor and the Arkhipov-Bezrukavnikov equivalence in mixed characteristicComments: 53 pages, prove perversity now for general parahoricsSubjects: Number Theory (math.NT); Algebraic Geometry (math.AG); Representation Theory (math.RT)
- [237] arXiv:2311.04730 (replaced) [pdf, other]
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Title: Predicting Properties of Nodes via Community-Aware FeaturesComments: 21 pages, 3 figures, 7 tablesSubjects: Social and Information Networks (cs.SI); Machine Learning (cs.LG); Combinatorics (math.CO)
- [238] arXiv:2311.06108 (replaced) [pdf, other]
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Title: Nonparametric consistency for maximum likelihood estimation and clustering based on mixtures of elliptically-symmetric distributionsSubjects: Statistics Theory (math.ST); Machine Learning (stat.ML)
- [239] arXiv:2311.06934 (replaced) [pdf, other]
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Title: Are all Weakly Convex and Decomposable Polyhedral Surfaces Infinitesimally Rigid?Authors: Jilly KevoComments: 20 pages, 17 figuresSubjects: Differential Geometry (math.DG); Metric Geometry (math.MG)
- [240] arXiv:2311.07310 (replaced) [pdf, other]
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Title: Dynamic Optimization on Quantum Hardware: Feasibility for a Process Industry Use CaseComments: 21 pages, 6 figuresJournal-ref: Computers and Chemical Engineering, 2024, 108704, ISSN 0098-1354Subjects: Optimization and Control (math.OC); Emerging Technologies (cs.ET)
- [241] arXiv:2311.08142 (replaced) [pdf, ps, other]
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Title: Intermediate long wave equation in negative Sobolev spacesComments: 16 pages. Minor modifications. To appear in Proc. Amer. Math. SocSubjects: Analysis of PDEs (math.AP)
- [242] arXiv:2311.16568 (replaced) [pdf, ps, other]
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Title: Active Reconfigurable Intelligent Surface Enhanced Spectrum Sensing for Cognitive Radio NetworksSubjects: Information Theory (cs.IT); Signal Processing (eess.SP)
- [243] arXiv:2311.17774 (replaced) [pdf, ps, other]
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Title: Enumeration of Minimum Weight Codewords of Pre-Transformed Polar Codes by Tree IntersectionComments: 8 pages, 4 figures, extended version of the CISS 2024 paperSubjects: Information Theory (cs.IT)
- [244] arXiv:2311.17835 (replaced) [pdf, ps, other]
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Title: A semigroup with linearithmic Dehn functionAuthors: Roman RepeevComments: 16 pagesSubjects: Group Theory (math.GR); Rings and Algebras (math.RA)
- [245] arXiv:2312.01253 (replaced) [pdf, ps, other]
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Title: On Merits of Faster-than-Nyquist Signaling in the Finite Blocklength RegimeAuthors: Yong Jin Daniel KimSubjects: Information Theory (cs.IT)
- [246] arXiv:2312.03683 (replaced) [pdf, other]
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Title: The discrete nonlinear Schrödinger equation with linear gain and nonlinear loss: the infinite lattice with nonzero boundary conditions and its finite dimensional approximationsAuthors: Georgios Fotopoulos, Nikos I. Karachalios, Vassilis Koukouloyannis, Paris Kyriazopoulos, Kostas VetasComments: 23 pages, 10 figuresSubjects: Mathematical Physics (math-ph); Pattern Formation and Solitons (nlin.PS)
- [247] arXiv:2312.06831 (replaced) [pdf, other]
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Title: Slab percolation for the Ising model revisitedAuthors: Franco SeveroComments: 10 pages, 1 figure. Version accepted for publication in ECPSubjects: Probability (math.PR)
- [248] arXiv:2312.08902 (replaced) [pdf, other]
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Title: Coarse geometry of quasi-transitive graphs beyond planarityComments: 15 pages, 1 figure. Final versionSubjects: Combinatorics (math.CO); Metric Geometry (math.MG)
- [249] arXiv:2312.10699 (replaced) [pdf, ps, other]
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Title: Some Properties of normal subgroups determined from character tablesSubjects: Group Theory (math.GR)
- [250] arXiv:2312.13122 (replaced) [pdf, other]
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Title: Screwon spectral statistics and dispersion relation in the quantum Rajeev-Ranken modelComments: 17 pages, 21 figure files, Discussion section expandedJournal-ref: Physica D, 463 (2024) 134170Subjects: Exactly Solvable and Integrable Systems (nlin.SI); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
- [251] arXiv:2312.16011 (replaced) [pdf, other]
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Title: Assigning Stationary Distributions to Sparse Stochastic MatricesComments: 29 pages, code available from this https URL In this third version, we have added clarifications, corrections and remarks suggested to us by anonymous reviewersSubjects: Numerical Analysis (math.NA); Optimization and Control (math.OC); Probability (math.PR); Computation (stat.CO)
- [252] arXiv:2312.16536 (replaced) [pdf, ps, other]
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Title: Weighted norm inequalities for integral transforms with splitting kernelsAuthors: Alberto Debernardi PinosSubjects: Classical Analysis and ODEs (math.CA); Functional Analysis (math.FA)
- [253] arXiv:2312.17023 (replaced) [pdf, other]
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Title: Tensorial structure of the lifting doctrine in constructive domain theoryAuthors: Jonathan SterlingComments: Minor errors fixedSubjects: Category Theory (math.CT); Logic in Computer Science (cs.LO)
- [254] arXiv:2401.00699 (replaced) [pdf, other]
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Title: Quantum walk on simplicial complexes for simplicial community detectionAuthors: Euijun SongComments: 14 pages, manuscript revisedSubjects: Quantum Physics (quant-ph); Algebraic Topology (math.AT); Data Analysis, Statistics and Probability (physics.data-an); Physics and Society (physics.soc-ph)
- [255] arXiv:2401.03260 (replaced) [pdf, ps, other]
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Title: Completeness in local positive logicComments: arxiv:2401.03260v1 has been divided in two papers. This is the first partSubjects: Logic (math.LO)
- [256] arXiv:2401.03556 (replaced) [pdf, other]
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Title: An Incentive Regulation Approach for Balancing Stakeholder Interests in Transmission InvestmentJournal-ref: 23rd Power Systems Computation Conference, PSCC2024Subjects: Optimization and Control (math.OC)
- [257] arXiv:2401.07282 (replaced) [pdf, ps, other]
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Title: Half-Space Modeling with Reflecting Surface in Molecular CommunicationComments: 9 pages, 10 figuresSubjects: Information Theory (cs.IT); Emerging Technologies (cs.ET)
- [258] arXiv:2402.00207 (replaced) [pdf, other]
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Title: Optimal vaccination strategies on networks and in metropolitan areasComments: 29 pages, 23 figuresSubjects: Populations and Evolution (q-bio.PE); Optimization and Control (math.OC); Quantitative Methods (q-bio.QM)
- [259] arXiv:2402.01015 (replaced) [pdf, ps, other]
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Title: An optimal advertising model with carryover effect and mean field termsSubjects: Optimization and Control (math.OC); Probability (math.PR)
- [260] arXiv:2402.02301 (replaced) [pdf, ps, other]
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Title: MATLAB Simulator of Level-Index ArithmeticAuthors: Mantas MikaitisSubjects: Mathematical Software (cs.MS); Hardware Architecture (cs.AR); Numerical Analysis (math.NA)
- [261] arXiv:2402.02990 (replaced) [pdf, ps, other]
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Title: Poisson-Lie analogues of spin Sutherland models revisitedAuthors: L. FeherComments: 32 pages, v2: slightly modified the abstract and corrected small typosSubjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Symplectic Geometry (math.SG); Exactly Solvable and Integrable Systems (nlin.SI)
- [262] arXiv:2402.09040 (replaced) [pdf, ps, other]
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Title: A new approach in two-dimensional heavy-tailed distributionsSubjects: Probability (math.PR)
- [263] arXiv:2402.10197 (replaced) [pdf, ps, other]
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Title: Bulk universality for complex eigenvalues of real non-symmetric random matrices with i.i.d. entriesComments: 67 pages, revised version, updated referencesSubjects: Probability (math.PR); Mathematical Physics (math-ph)
- [264] arXiv:2402.12898 (replaced) [pdf, ps, other]
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Title: Explicit formula for the Benjamin--Ono equation with square integrable and real valued initial data and applications to the zero dispersion limitAuthors: Xi Chen (LMO)Subjects: Analysis of PDEs (math.AP)
- [265] arXiv:2403.01154 (replaced) [pdf, ps, other]
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Title: Boundedness of klt complements on Fano fibrations over surfacesAuthors: Bingyi ChenComments: Version 2, showed that Shokurov's conjecture implies Birkar's conjecture, so they are equivalent (see Theorem 1.6). Version 3, added Example 1.10 to indicate that the order O(\epsilon^2) in Theorem 1.7 is optimal. arXiv admin note: text overlap with arXiv:1811.10709 by other authorsSubjects: Algebraic Geometry (math.AG)
- [266] arXiv:2403.01957 (replaced) [pdf, ps, other]
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Title: Sur l'asymptotique des sommes de Kempner pour de grandes basesAuthors: Jean-François BurnolComments: 9 pages, in French. v2 corrects a typo in the abstract (sigh...), modifies parts of the introduction and adds referencesSubjects: Number Theory (math.NT); Classical Analysis and ODEs (math.CA)
- [267] arXiv:2403.02862 (replaced) [pdf, other]
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Title: Numerical investigation of stabilization in the Hybridizable Discontinuous Galerkin method for linear anisotropic elastic equationComments: 34 pages, 9 figuresSubjects: Analysis of PDEs (math.AP); Numerical Analysis (math.NA)
- [268] arXiv:2403.04046 (replaced) [pdf, ps, other]
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Title: Operator algebras over the p-adic integersComments: 56 pages, improved exposition, adding some new materialSubjects: Operator Algebras (math.OA)
- [269] arXiv:2403.04681 (replaced) [pdf, ps, other]
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Title: On the rigidity of the complex GrassmanniansComments: v1: 30 pages. v2: 31 pages, corrected numerical error introduced in arXiv:2305.07391, simplified discussion at the endSubjects: Differential Geometry (math.DG)
- [270] arXiv:2403.08052 (replaced) [pdf, other]
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Title: A Computational Method for $H_2$-optimal Estimator and State Feedback Controller Synthesis for PDEsSubjects: Optimization and Control (math.OC); Analysis of PDEs (math.AP); Dynamical Systems (math.DS)
- [271] arXiv:2403.09453 (replaced) [pdf, other]
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Title: Combinatorics of Essential Sets for PositroidsSubjects: Combinatorics (math.CO)
- [272] arXiv:2403.13161 (replaced) [pdf, ps, other]
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Title: Sharp local propagation of chaos for mean field particles with $W^{-1,\infty}$ kernelsAuthors: Songbo WangComments: 33 pages; time-uniform chaos for 2D vortex added in this version, with other minor changesSubjects: Probability (math.PR); Analysis of PDEs (math.AP)
- [273] arXiv:2403.20206 (replaced) [pdf, other]
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Title: Scaled Brownian motion with random anomalous diffusion exponentComments: 18 pages, 13 figuresSubjects: Probability (math.PR); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)
- [274] arXiv:2404.00222 (replaced) [pdf, ps, other]
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Title: Positivity preservers over finite fieldsComments: 29 pages, LaTeX; fixed typos and made minor corrections to the proof of Theorem 5.3 and of Theorem CSubjects: Combinatorics (math.CO); Commutative Algebra (math.AC)
- [275] arXiv:2404.00663 (replaced) [pdf, ps, other]
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Title: Geometrizations of quantum groups and dual semicanonical basesAuthors: Yingjin BiComments: 10 pages. Any comments welcomeSubjects: Representation Theory (math.RT); Algebraic Geometry (math.AG); Quantum Algebra (math.QA); Rings and Algebras (math.RA)
- [276] arXiv:2404.04357 (replaced) [pdf, other]
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Title: Why does the two-timescale Q-learning converge to different mean field solutions? A unified convergence analysisComments: 34 pages. Updated version for submission. We added more numerical results and fixed several minor mistakesSubjects: Optimization and Control (math.OC)
- [277] arXiv:2404.04641 (replaced) [pdf, ps, other]
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Title: On blow-up conditions for solutions of systems of quasilinear second-order elliptic inequalitiesSubjects: Analysis of PDEs (math.AP)
- [278] arXiv:2404.06245 (replaced) [pdf, ps, other]
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Title: On cubic graphs having the maximal coalition numberSubjects: Combinatorics (math.CO)
- [279] arXiv:2404.07240 (replaced) [pdf, other]
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Title: Interactions Between Brauer Configuration Algebras and Classical Cryptanalysis to Analyze Bach's CanonsAuthors: Agustín Moreno Cañadas, Pedro Fernando Fernández Espinosa, José Gregorio Rodríguez Nieto, Odette M. Mendez, Ricardo Hugo Arteaga-BastidasComments: 50 pagesSubjects: History and Overview (math.HO); Cryptography and Security (cs.CR)
- [280] arXiv:2404.07830 (replaced) [pdf, ps, other]
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Title: Global solution and singularity formation for the supersonic expanding wave of compressible Euler equations with radial symmetryComments: Make some minor changes from the last versionSubjects: Analysis of PDEs (math.AP)
- [281] arXiv:2404.08115 (replaced) [pdf, ps, other]
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Title: An extension theorem for weak solutions of the 3d incompressible Euler equations and applications to singular flowsSubjects: Analysis of PDEs (math.AP)
- [282] arXiv:2404.08502 (replaced) [pdf, ps, other]
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Title: Twisted correlations of the divisor function via discrete averages of $\operatorname{SL}_2(\mathbb{R})$ Poincaré seriesComments: v2: minor correctionsSubjects: Number Theory (math.NT)
- [283] arXiv:2404.09224 (replaced) [pdf, ps, other]
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Title: Quotient Modules of Finite Length and Their Relation to Fredholm Elements in Semiprime RingsAuthors: Niklas LudwigSubjects: Rings and Algebras (math.RA); Functional Analysis (math.FA); Operator Algebras (math.OA)
- [284] arXiv:2404.09985 (replaced) [pdf, ps, other]
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Title: $L^p$-asymptotic behaviour of solutions of the fractional heat equation on Riemannian symmetric spaces of noncompact typeComments: 36 pages, contains main theorems for $p>2$ as wellSubjects: Classical Analysis and ODEs (math.CA)
- [285] arXiv:2404.10759 (replaced) [pdf, other]
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Title: Laplace-HDC: Understanding the geometry of binary hyperdimensional computingComments: 23 pages, 7 figuresSubjects: Machine Learning (cs.LG); Probability (math.PR); Machine Learning (stat.ML)
- [286] arXiv:2404.12604 (replaced) [pdf, ps, other]
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Title: Transmitter Side Beyond-Diagonal RIS for mmWave Integrated Sensing and CommunicationsSubjects: Information Theory (cs.IT); Signal Processing (eess.SP)
- [287] arXiv:2404.13249 (replaced) [pdf, ps, other]
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Title: Additive Complementary Pairs of CodesSubjects: Information Theory (cs.IT)
- [288] arXiv:2404.14806 (replaced) [pdf, other]
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Title: Variational Dynamic Programming for Stochastic Optimal ControlSubjects: Optimization and Control (math.OC)
- [289] arXiv:2404.15080 (replaced) [pdf, ps, other]
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Title: Flexible Field Sizes in Secure Distributed Matrix Multiplication via Efficient Interference CancellationAuthors: Okko MakkonenComments: 11 pagesSubjects: Information Theory (cs.IT)
- [290] arXiv:2404.15145 (replaced) [pdf, ps, other]
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Title: Dihedral-product groups of nonabelian simple groupsAuthors: Hao YuSubjects: Combinatorics (math.CO); Group Theory (math.GR)
- [291] arXiv:2404.15261 (replaced) [pdf, other]
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Title: All You Need is Resistance: On the Equivalence of Effective Resistance and Certain Optimal Transport Problems on GraphsComments: 35 pages, 7 figuresSubjects: Optimization and Control (math.OC); Discrete Mathematics (cs.DM); Machine Learning (cs.LG); Probability (math.PR)
- [292] arXiv:2404.15800 (replaced) [pdf, ps, other]
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Title: The Grothendieck group of a triangulated categoryComments: comments welcomeSubjects: Representation Theory (math.RT); Category Theory (math.CT)
- [293] arXiv:2404.16161 (replaced) [pdf, other]
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Title: Discrete iterated integrals and cyclic sum formulasAuthors: Hanamichi KawamuraSubjects: Number Theory (math.NT)
- [294] arXiv:2404.16347 (replaced) [pdf, other]
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Title: Enhancing Arterial Blood Flow Simulations through Physics-Informed Neural NetworksSubjects: Numerical Analysis (math.NA); Fluid Dynamics (physics.flu-dyn)
- [295] arXiv:2404.16431 (replaced) [pdf, ps, other]
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Title: Secure Coded Distributed ComputingComments: 6 pagesSubjects: Information Theory (cs.IT)
- [296] arXiv:2404.16460 (replaced) [src]
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Title: The tangent space in sub-Finsler geometry and applicationsComments: Substantial overlap with this https URLSubjects: Differential Geometry (math.DG); Metric Geometry (math.MG)
- [297] arXiv:2404.16798 (replaced) [pdf, other]
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Title: A Test Problem for Flow CodesSubjects: Numerical Analysis (math.NA); Computational Physics (physics.comp-ph); Fluid Dynamics (physics.flu-dyn)
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