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arXiv:2606.01209v1 Announce Type: new Abstract: We consider an open Jackson network with $n$ exchangeable single-server stations and weak all-to-all interaction through routing: upon service completion at station $i$, a job is routed to station $j$ with probability $p/n$, where $p\in(0,1)$, or leaves the system with probability $q=1-p$. We study a joint asymptotic regime in which the number of stations tends to infinity while the system ap....
arXiv:2606.01218v1 Announce Type: new Abstract: Collision statistics provide a finite-resolution view of information by measuring how often a fixed number of independent samples fall on the same state. These directly countable quantities form the basis of integer-order R\'enyi entropies. Here, we use low-order R\'enyi entropies to approximate Shannon entropy and mutual information, while characterizing what is necessarily lost when only fi....
arXiv:2606.01219v1 Announce Type: new Abstract: In this paper, we consider a network transport model in which agents moving along the edges can contribute to dynamics at nodes or bypass them. The model takes the form of a system of first-order partial differential equations coupled with a system of ordinary differential equations, and can describe a range of phenomena, from diseases in metapopulations to migratory systems with delays, to c..
arXiv:2606.01232v1 Announce Type: new Abstract: We study randomized stationary methods for symmetric positive definite linear systems in which component $j$ is selected with probability proportional to $|r_j|^\ell$. This power-weighted family interpolates continuously between uniform randomized Jacobi as $\ell \to 0$ and Gauss--Southwell greedy relaxation as $\ell \to \infty$. For the central case $\ell = 2$, we sharpen the standard one-st....
arXiv:2606.01245v1 Announce Type: new Abstract: Motivated by their applications in DNA-based storage systems, codes capable of correcting consecutive deletions have attracted significant attention. An important class of such codes consists of those that can correct multiple consecutive deletion errors, commonly referred to as multiple $b$-burst deletion-correcting codes. In this paper, we investigate the fundamental limits of multiple $b$-..
arXiv:2606.01257v1 Announce Type: new Abstract: Gradient-based algorithms are central to modern statistical estimation, yet their statistical analysis is often restricted to fixed-time behavior, such as convergence to a population target or fluctuations at a prescribed iteration. In many applications, however, uncertainty quantification is needed along the entire optimization path, especially when the stopping time is data-dependent or div....
arXiv:2606.01267v1 Announce Type: new Abstract: The Burrows--Wheeler transform is usually viewed as a clustering transform: it tends to group equal letters into long runs. We study the opposite extremal regime, where the BWT output is completely unclustered, that is, has as many equal-letter runs as positions. Known results imply, on the one hand, that the number of runs in the BWT of a Lyndon word can increase by at most a factor of two, ....
arXiv:2606.01268v1 Announce Type: new Abstract: We prove that Thompson's group $F$ satisfies the relative invariant subalgebra rigidity property with respect to its commutator subgroup: every von Neumann subalgebra of $L(F)$ that is invariant under conjugation by $[F,F]$ is of the form $L(N)$ for some normal subgroup $N \trianglelefteq F$. Along the way, we establish a general factoriality criterion for invariant subalgebras whose hypothes..
arXiv:2606.01278v1 Announce Type: new Abstract: We study the extremality properties of rays generated by tautological Chern classes of matroids in the polyhedral nef cones of the permutohedral variety. Our main result provides necessary and sufficient conditions a matroid has to meet for its tautological Chern classes to generate extremal rays. Our approach yields a new and large family of extremal rays that interpolates between two previo..
arXiv:2606.01284v1 Announce Type: new Abstract: Semantic communication has emerged as a promising paradigm for improving transmission efficiency by conveying task-relevant semantics rather than raw data. Although recent studies have achieved notable gains in communication efficiency and average task performance, reliability remains a fundamental bottleneck in dynamic and uncertain environments. In particular, most existing designs are stil....
arXiv:2606.01290v1 Announce Type: new Abstract: We study the behavior of Dehn functions of finitely presentable groups for presentations with finite generating sets and possibly infinite sets of defining relators. For the free abelian group $\mathbb Z^2$ of rank two on generators $a,b$, we prove that the infinite presentation $\langle a,b \mid [a^{2^k},b],\ k=0,1,2,\ldots\rangle$ has Dehn function of order $n\log n$. We also prove that, fo....
arXiv:2606.01299v1 Announce Type: new Abstract: We study the interaction between the group law on an abelian variety and the additive structure induced on its image under a morphism to a projective space. Let $A/F$ be an abelian variety, $f:A \rightarrow \mathbb{P}^n$ be a morphism which is finite onto its image, and $\Gamma \subseteq A(F)$ be a finite-rank subgroup. We show that for any affine chart $\mathbb{A}^n \subseteq \mathbb{P}^n$ a....
arXiv:2606.01303v1 Announce Type: new Abstract: We develop a multicontinuum Generalized Multiscale Finite Element Method (MC-GMsFEM) for constructing coarse-scale models in heterogeneous media that simultaneously provide accurate numerical approximations and physically consistent macroscopic equations. Classical multiscale methods efficiently approximate fine-scale solutions on coarse grids using localized basis functions, but they do not ....
arXiv:2606.01310v1 Announce Type: new Abstract: For an algebraic function field $F$ over a large field $K$, we show: 1) if $F|K$ has a rational place, then there is a finite purely inseparable extension $K'|K$ such that $K'$ is existentially closed in $F.K'$; 2) $F|K$ has a rational place admitting local uniformization if and only if $K$ is existentially closed in $F$.
arXiv:2606.01319v1 Announce Type: new Abstract: In this note, we show that if the Bergman metric of a pseudoconvex domain in $\mathbb C^n$($n\geq 3$) has constant scalar curvature, then every strongly pseudoconvex boundary point of the domain is spherical.
arXiv:2606.01320v1 Announce Type: new Abstract: We present a non-convergence theory for probabilistic direct search, a randomized derivative-free optimization method, where non-convergence means the failure to produce iterates that achieve stationarity asymptotically. The motivation is to understand whether the submartingale-like assumption in the existing convergence theory is essential or merely an artifact of the analysis techniques. Fo....
arXiv:2606.01321v1 Announce Type: new Abstract: We consider time-dependent Kohn-Sham equations in dimension $3$ with a fractional dispersion relation $(1-\Delta)^s$, $s\in(0,\frac32)$, and a class of interaction terms including, in particular, external potentials, internal potentials associated to Hartree-type non-linearities, and exchange terms described by energy subcritical pure-power non-linearities. We prove the local existence of wea..
arXiv:2606.01324v1 Announce Type: new Abstract: The evolution toward 6G wireless networks envisions a seamlessly intelligent, Open-RAN-enabled architecture where unmanned aerial vehicles (UAVs) play a pivotal role in extending coverage, enhancing resilience, and ensuring reliable connectivity for ground users deployment. However, efficiently managing spectrum and resources in such highly dynamic UAV-assisted environments remains a major ch....
arXiv:2606.01331v1 Announce Type: new Abstract: We investigate the ill-posedness mechanism of the hard-sphere Boltzmann equation in $H_{x}^{s}$ Sobolev space. Via a direct construction, we prove a strong-weak type ill-posedness result in the low-regularity regime $s<1$, establishing a sharp threshold in connection to the local $s>1$ well-posedness result [11]. Instead of originating from the large-velocity growth of the collision kernel, t..
arXiv:2606.01335v1 Announce Type: new Abstract: We study the limitations of matrix-free algorithms that access a matrix $A$ only through forward matrix-vector products (matvecs) $x \mapsto Ax$, without access to the transpose $A^\top$ or its action. This setting arises naturally in operator learning, inverse problems, and matrix-free PDE solvers, where adjoint evaluations may be unavailable or prohibitively expensive. We show that the lack....
arXiv:2606.01337v1 Announce Type: new Abstract: The Kleshchev multipartitions arise in the representation theory for the Ariki-Koike algebras. In previous work, Li, Stanton, Xue, Yee, and the author considered a refined enumeration for the $2$-dimensional case, namely, the Kleshchev bipartitions, by invoking the $2$-residue statistic for partitions. In this paper, we make further elaboration by bounding the largest part of the bipartitions..
arXiv:2606.01343v1 Announce Type: new Abstract: In this work we study the Schwinger-Dyson equations and saddle point equations of matrix integrals that come from type $(0,1)$ random fuzzy geometries coupled to fermions or bosons. Such random fuzzy geometries are bi-tracial Hermitian matrix ensembles with a determinant contribution in the integrand. We derive the Schwinger-Dyson equations using complex analytic techniques from the saddle po..
arXiv:2606.01347v1 Announce Type: new Abstract: The integer lattice $\mathbb{Z}^n$ is conjectured to maximize the Gaussian mass $\Theta_L(t)=\sum_{x\in L}e^{-t\|x\|^2}$ over the set of stable lattices in $\mathbb{R}^n$, for every $t>0$. We prove this sharp inequality for every integral unimodular lattice $L$ of rank $n\leq 32$, with equality only at $L\cong\mathbb{Z}^n$, and furthermore obtain the strict inequality for every even unimodula..
arXiv:2606.01353v1 Announce Type: new Abstract: Subpacketization remains a major obstacle to the practical deployment of coded caching (CC) in multi-antenna wireless networks. In this paper, we propose a low-complexity multiple-input multiple-output (MIMO) CC scheme that enables flexible delivery rate adaptation while substantially reducing subpacketization requirements. The proposed design builds on a virtual decomposition of the broadcas....
arXiv:2606.01358v1 Announce Type: new Abstract: We review the kinetic theory of one-dimensional nonlinear oscillator chains, of which the most famous example is the Fermi-Pasta-Ulam-Tsingou equation. We provide detailed, though not rigorous, accounts of the microscopic to mesoscopic, and mesoscopic to macroscopic limits: derivation of the kinetic wave equation and hydrodynamic limit. We also present the state of the art of the mathematical..
arXiv:2606.01359v1 Announce Type: new Abstract: We develop a nonlinear potential theoretic framework for Schauder estimates for vector-valued solutions of a broad class of nonautonomous variational problems at nearly linear growth. Our approach naturally embraces the variable exponent as well as the Double and Multi phase setting, yielding new regularity results in basic models and recovering optimal regularity recently established in spec..
arXiv:2606.01368v1 Announce Type: new Abstract: We prove Cohn-Vossen-type scalar-curvature inequalities on complete noncompact Riemannian manifolds with nonnegative Ricci curvature, motivated by Yau's higher-dimensional problem. In dimensions n >= 3, we obtain a normalized O(r^{n-2}) growth estimate under the assumption that the fundamental group contains a free abelian subgroup of rank n-2. For locally conformally flat manifolds, we prove....
arXiv:2606.01369v1 Announce Type: new Abstract: In this article, using the notion of discrepancies, we study the generalized Weierstrass semigroup $\widehat{H}(\mathbf{Q})$, where $\mathbf{Q}$ is an $n$-tuple of distinct totally ramified places of degree one in a linearized function field. As a consequence, we characterize and explicitly determine the sets of absolute maximal elements $\widehat{\Gamma}(\mathbf{Q})$ and relative maximal ele..
arXiv:2606.01371v1 Announce Type: new Abstract: The behavior of representations under restriction is a central theme in Lie theory. We study wide regular subalgebras of symmetrizable Kac-Moody algebras, extending work of Douglas and Repka on semisimple Lie algebras. A subalgebra is wide if every irreducible integrable highest weight module remains indecomposable upon restriction. Let $\mathfrak{g}$ be a symmetrizable Kac-Moody algebra with....
arXiv:2606.01376v1 Announce Type: new Abstract: For every $d\geq1$ we give an explicit equal-weight spherical $5$-design in $\mathbb{S}^{d-1}\subset\mathbb{R}^d$ with at most $72d^2$ points. Our approach utilizes recent construction of complex projective $2$-designs based on Sidon sets.
arXiv:2606.01383v1 Announce Type: new Abstract: Let $\Delta$ be the Dirichlet Laplacian on a bounded domain $\Omega \subset \mathbb{R}^{N}$, and let $(-\Delta)^\alpha$ be the associated spectral fractional Laplacian with $\alpha \leq 1, \ \rho <2$. For general bounded domains with $C^2$ boundary, we prove a symmetry formula for $\alpha <1/2$, extending a result previously proven on rectangles for $\alpha <1$. As a consequence of this formu..
arXiv:2606.01384v1 Announce Type: new Abstract: In 1970, T. M. Apostol introduced the M\"{o}bius function $\mu_{k}$ of order $k$ for all positive integer $k$, as a generalization of the M\"{o}bius function $\mu = \mu_{1}$. For any integer $k \ge 2$, he proved $\sum_{n \le x} \mu_{k}(n) = A_{k} x + O_{k}(x^{1/k} \log x)$ where $A_{k}$ is a positive constant. In 2001, A. Bege conjectured both the conditional and unconditional estimates for t..
arXiv:2606.01388v1 Announce Type: new Abstract: We define the analogue of Lie-Rinehart algebras over $C^\infty$-rings. We show that given a Poisson $C^\infty$-ring $\mathcal{A}$ its module $\Omega_{\mathcal{A}}^{1}$ of $C^\infty$-K\"{a}hler differentials is (part of) a Lie-Rinehart algebra. Conversely, given a Lie-Rinehart algebra $\mathcal{M} \xrightarrow{\rho} C^\infty\mathrm{Der}(\mathcal{A})$ over a $C^\infty$-ring $\mathcal{A}$, there....
arXiv:2606.01392v1 Announce Type: new Abstract: Starting from Maxwell's and linear momentum balance equations, we derive a ferrofluid model using the generalized Onsager's principle. Guided by a discrete perturbation estimate, we design and analyze families of Galerkin schemes that converge to sufficiently regular solutions and derive error estimates. Finally, we numerically explore the model with our proposed method.
arXiv:2606.01395v1 Announce Type: new Abstract: We give a straightforward, self-contained, and natural construction of the Big Witt ring using the e\~ne product that is defined through the action on zeros of polynomials. This is in contrast with classical constructions of the Big Witt ring that use formulas out of nowhere.
arXiv:2606.01415v1 Announce Type: new Abstract: We study rational hypersurfaces $\mathscr{S}$ defined as the closure of the image of a generically finite rational map $\phi:\mathscr{X}\rightarrow \mathbb{P}^{n+1}$, where $\mathscr{X}$ is an $n$-dimensional toric variety. We provide matrix representations for the implicitization of $\mathscr{S}$ that are constructed from the coefficients of linear syzygies and quadratic syzygies of the para..
arXiv:2606.01420v1 Announce Type: new Abstract: Riemann integration remains a well-known part of mathematics for both historical and conceptual reasons. We study basic properties like boundedness of Riemann integrable functions and related classes in mathematical logic. On one hand, weak logical systems already establish that a Riemann integrable function on the unit interval is bounded or dominated by a continuous function. On the other h....
arXiv:2606.01422v1 Announce Type: new Abstract: We give a formula for $X$-products of attractors using $\mathbb{F}_1$-geometry.
arXiv:2606.01430v1 Announce Type: new Abstract: We present a variational approach to ferronematics in a three dimensional setting. The ferronematic energy functional is described by two established theories: the Landau-de Gennes energy to explain the nematic part, the micromagnetic energy to explain the magnetic part, and coupling energies between them. We explicitly include the nonlocal stray field energy in a bulk setting and the couplin..
arXiv:2606.01431v1 Announce Type: new Abstract: If $f$ is a continuous selection for the Vietoris hyperspace $\mathcal{F}(X)$ of the nonempty closed subsets of a space $X$, then the point $p=f(X)\in X$ is not as arbitrary as it might seem at first glance. In fact, the set $\mathcal{O}_{cs}(X)$ of all these points reveals certain information about the variety of Vietoris continuous selections for $\mathcal{F}(X)$. Another result of this pap..
arXiv:2606.01433v1 Announce Type: new Abstract: For complex geometries, the coarse problem of geometric multigrid can be too large to be solved by a direct solver. Here, we report on the use of domain decomposition applied to the multigrid coarse problem. Additive overlapping Schwarz methods are domain decomposition methods for the iterative solution of partial differential equations whose numerical and parallel scalability can be improved....
arXiv:2606.01447v1 Announce Type: new Abstract: For real multivariate polynomials $P$ and $Q$ both vanishing at a point, if the zero set of $Q$ is contained in the zero set of $P$, then there exists a rational function of the form $P^{p}/Q^{q}$ which is locally bounded and such that its extension that vanishes on the zero set of $Q$ is discontinuous. The proof uses inequalities of Lojasiewicz.
arXiv:2606.01448v1 Announce Type: new Abstract: The Boltzmann equation describing the transport of electrons in semiconductor devices with an external electrostatic potential is considered when the spatial variable is in a torus and the wave vector is in the Brillouin zone. We prove the exponential time decay of solutions towards the global equilibrium in a weighted $L^2$ space. Our result holds for wide classes of energy functions of elec..
arXiv:2606.01449v1 Announce Type: new Abstract: The main aim of this paper is to establish the H\"older continuity and the Harnack inequality for weak solutions to Dirichlet problems associated with superposition operators of mixed fractional order, thereby complementing our previous work \cite{BGKL2026}. To achieve this, we extend the De Giorgi--Nash--Moser theory to the framework of superposition operators by introducing a novel {\it no....
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