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75f251c503f789f588e23c9413c20b52607d2b8c4bbc4443c0ac767e63effeba | 2026-02-02T00:00:00-05:00 | The Riemann Hypothesis in Oaxaca | arXiv:2601.22413v1 Announce Type: new Abstract: An equivalence of the Riemann Hypothesis (RH) enables a direct bridge to the Young lattice. In specific, the classical threshold $\lim_{n\to\infty} \sigma(n)/(n \log\log n) = e^{\gamma} \approx 1.78107$, derived from the asymptotic behavior of the sum-of-divisors function... | https://arxiv.org/abs/2601.22413 | Academic Papers | svg |
d6138a6896d1970ee091d2340ab89d0e49669c357b37ad22e3ab15dfe8198068 | 2026-02-02T00:00:00-05:00 | Leader-Follower Linear-Quadratic Stochastic Graphon Games | arXiv:2601.22429v1 Announce Type: new Abstract: This paper investigates leader-follower linear-quadratic stochastic graphon games, which consist of a single leader and a continuum of followers. The state equations of the followers interact through graphon coupling terms, with their diffusion coefficients depending on t... | https://arxiv.org/abs/2601.22429 | Academic Papers | svg |
813fc3a7af98bfa534ccb89bc32b41b5df609418e4a7683095d95595a03a09e3 | 2026-02-02T00:00:00-05:00 | Selective Adaptation of Beliefs and Communication on Cellular Sheaves | arXiv:2601.22431v1 Announce Type: new Abstract: We extend opinion dynamics on discourse sheaves to incorporate "directional stubbornness": agents may hold fixed positions in specified directions of their opinion stalk while remaining flexible in others. This converts the equilibrium problem from harmonic extension to a... | https://arxiv.org/abs/2601.22431 | Academic Papers | svg |
e8dea9d63d4813a1bab40ad445f61703b57512116740c54580bd0fea696956da | 2026-02-02T00:00:00-05:00 | Divergence Identity for the scalar curvature and Rigidity of Codazzi Tensors | arXiv:2601.22437v1 Announce Type: new Abstract: We introduce a local vector field on an $n$-dimensional Riemannian manifold, defined as the sum of the covariant derivatives of a local orthonormal frame, and derive an explicit identity for its divergence, decomposed into a scalar curvature term and an auxiliary term inv... | https://arxiv.org/abs/2601.22437 | Academic Papers | svg |
2c06396950c9e97be2f5611bfb484de7345cedebe618d5bdc55b3b43535ee2bd | 2026-02-02T00:00:00-05:00 | On Monogeneity of reciprocal polynomials | arXiv:2601.22453v1 Announce Type: new Abstract: Let $\mathbb{Z}_K$ denote the ring of integers of the number field $K = \mathbb{Q}(\theta)$, where $\theta$ is a root of the monic irreducible polynomial $f(x) \in \mathbb{Z}[x]$. We say that $f(x)$ is monogenic if $\mathbb{Z}_K = \mathbb{Z}[\theta]$. A polynomial $f(x) \... | https://arxiv.org/abs/2601.22453 | Academic Papers | svg |
ccfb3736a5090e90888e780a63973d0e2200c88408cbabbc01cd3c753a9ae535 | 2026-02-02T00:00:00-05:00 | Compactification of Reductive Group Schemes | arXiv:2601.22462v1 Announce Type: new Abstract: Let $\mathrm G$ be an isotrivial reductive group over a scheme $S$. We construct a smooth projective $S$-scheme containing $\mathrm G$ as a fiberwise-dense open subscheme equipped with left and right actions of $\mathrm G$ which extend the translation actions of $\mathrm ... | https://arxiv.org/abs/2601.22462 | Academic Papers | svg |
218ee5635fb522ee6c34dbac21c5eebbbe15783a6f302fe3156263e9d9ad3f19 | 2026-02-02T00:00:00-05:00 | The isomorphism problem for reduced finitary power monoids | arXiv:2601.22469v1 Announce Type: new Abstract: Let $H$ be a multiplicatively written monoid with identity $1_H$ and let $\mathcal{P}_{\text{fin},1}(H)$ denote the reduced finitary power monoid of $H$, that is, the monoid consisting of all finite subsets of $H$ containing $1_H$ with set multiplication as operation. Bui... | https://arxiv.org/abs/2601.22469 | Academic Papers | svg |
b547777ba0e917b9b856b9c0c1fc96a6cb7d3fc91971fd80bc93989227749802 | 2026-02-02T00:00:00-05:00 | Tangents to Lipschitz and Sobolev images | arXiv:2601.22473v1 Announce Type: new Abstract: We develop geometric versions of Rademacher and Calderon type differentiability theorems in two categories. A special case of our results is that for any Lipschitz or continuous $W^{1,p}$ Sobolev map $f$ from $[0,1]^n$ into a Euclidean space with $p>n$, the image $f([0,1]... | https://arxiv.org/abs/2601.22473 | Academic Papers | svg |
453e49a04329109d27a6767569d884b19b230013f8291df1e1d68acd927391b4 | 2026-02-02T00:00:00-05:00 | Grothendieck rigidity and virtual retraction of higher-rank GBS groups | arXiv:2601.22477v1 Announce Type: new Abstract: A rank $n$ generalized Baumslag-Solitar group ($GBS_n$ group) is a group that splits as a finite graph of groups such that all vertex and edge groups are isomorphic to $\mathbb{Z}^n$. This paper investigates Grothendieck rigidity and virtual retraction properties of $GBS_... | https://arxiv.org/abs/2601.22477 | Academic Papers | svg |
2a992f982efeb0c919e2b3f5a4c7e3084584acd07a2eb71ff67a8c82c4ccf8f5 | 2026-02-02T00:00:00-05:00 | Note on Euler characteristic of a toric vector bundle | arXiv:2601.22514v1 Announce Type: new Abstract: A convex chain is a finite integer linear combination of indicator functions of convex polytopes. Khovanskii-Pukhlikov extend the Ehrhart theory of convex lattice polytopes to the setting of convex chains. Extending the relationship between equivariant line bundles on pro... | https://arxiv.org/abs/2601.22514 | Academic Papers | svg |
c4e868b579a6b344e90a58c8f73122544b59505a10e9c903bca4089bd149c3b7 | 2026-02-02T00:00:00-05:00 | Local existence and nonexistence of solutions to the Hardy parabolic equation with general nonlinearity | arXiv:2601.22520v1 Announce Type: new Abstract: In this paper, we consider the Cauchy problem for the Hardy parabolic equation with general nonlinearity and establish the local existence and nonexistence results. Our results provide the optimal integrability conditions on initial function for the existence of a local-i... | https://arxiv.org/abs/2601.22520 | Academic Papers | svg |
9b43697d4cb7a7dc998c509b388c5167b480af2afb1d0da9379a50095a256d1d | 2026-02-02T00:00:00-05:00 | Transmission and Reflection coefficients for Schr\"odinger Operators with Truncated Periodic Potentials that support defect states | arXiv:2601.22544v1 Announce Type: new Abstract: We consider scattering waves through truncated periodic potentials with perturbations that support localized gap eigenstates. In a small complex neighborhood around an assumed positive bound state of the model operator, we prove the existence of a distinct zero reflection... | https://arxiv.org/abs/2601.22544 | Academic Papers | svg |
ba159aa15dc371bc2dd6ba446ce5f42a47506ab226713f5a9362ebcc9f2c30ce | 2026-02-02T00:00:00-05:00 | Corrigendum: Strong $\mathbb A^1$-invariance of $\mathbb A^1$-connected components of reductive algebraic groups (J. Topol. 16 (2023), no. 2, 634--649.) | arXiv:2601.22555v1 Announce Type: new Abstract: The proof of Lemma 5.1 in the paper Strong $\mathbb A^1$-invariance of $\mathbb A^1$-connected components of reductive algebraic groups (J. Topol. 16 (2023), no. 2, 634--649) is incomplete as it relies on some results of Choudhury-Hagadi, the proof of which contains a gap... | https://arxiv.org/abs/2601.22555 | Academic Papers | svg |
f3d49577f9361abedb6986b11c1ca64e11928e30d281f1618400ba53c91f1dce | 2026-02-02T00:00:00-05:00 | Generalized Zalcman Conjecture for Starlike Mappings in Several Complex Variables | arXiv:2601.22558v1 Announce Type: new Abstract: Generalizing the Zalcman conjecture given by $\vert a_n^2 - a_{2n-1}\vert \leq (n-1)^2$, Ma proposed and proved that the inequality $$\vert a_n a_m-a_{n+m-1}\vert \leq (n-1)(m-1), \quad m,n \in \mathbb{N},$$ holds for functions $f(z)=z+a_2z^2 +a_3 z^3 +\cdots\in \mathcal{... | https://arxiv.org/abs/2601.22558 | Academic Papers | svg |
62e760a3826abbbe82eb11c7692b6db24d15815912d8802abee4ba2bbec759a4 | 2026-02-02T00:00:00-05:00 | Kernels of Arithmetic Jet Spaces and Frobenius Morphism | arXiv:2601.22591v1 Announce Type: new Abstract: For any $\pi$-formal group scheme $G$, the Frobenius morphism between arithmetic jet spaces restricts to generalized kernels of the projection map. Using the functorial properties of such kernels of arithmetic jet spaces, we show that this morphism is indeed induced by a ... | https://arxiv.org/abs/2601.22591 | Academic Papers | svg |
d71103c71e537917ab5c4ee9374e1742331ddc2364cf30362775b77ad2f35f1a | 2026-02-02T00:00:00-05:00 | A spectral approach for online covariance change point detection | arXiv:2601.22602v1 Announce Type: new Abstract: Change point detection in covariance structures is a fundamental and crucial problem for sequential data. Under the high-dimensional setting, most of the existing research has focused on identifying change points in historical data. However, there is a significant lack of... | https://arxiv.org/abs/2601.22602 | Academic Papers | svg |
a802dee35eb1336312802690c2a0d15713c84276424baa9f4fda4b126bfa7a79 | 2026-02-02T00:00:00-05:00 | Spectral properties and bound states of the Dirac equation on periodic quantum graphs | arXiv:2601.22603v1 Announce Type: new Abstract: We investigate nonlinear Dirac equations on a periodic quantum graph $G$ and develop a variational approach to the existence and multiplicity of bound states. After introducing the Dirac operator on $G$ with a $\mathbb Z^{d}$-periodic potential, we describe its spectral d... | https://arxiv.org/abs/2601.22603 | Academic Papers | svg |
287cbf6e099c7593a5cb20f35fc769e3e8185938dcdee6090f1c5998e6a74f7d | 2026-02-02T00:00:00-05:00 | Weighted estimates for Hodge-Maxwell systems | arXiv:2601.22604v1 Announce Type: new Abstract: We establish up to the boundary regularity estimates in weighted $L^{p}$ spaces with Muckenhoupt weights $A_{p}$ for weak solutions to the Hodge systems \begin{align*} d^{\ast}\left(Ad\omega\right) + B^{\intercal}dd^{\ast}\left(B\omega\right) = \lambda B\omega + f \quad \... | https://arxiv.org/abs/2601.22604 | Academic Papers | svg |
55d47d0985e72b8fd583db2e9f36753cdd3da39470835cf56e4f63c79f263b7d | 2026-02-02T00:00:00-05:00 | Local controllability of the Cahn-Hilliard-Burgers' equation around certain steady states | arXiv:2601.22611v1 Announce Type: new Abstract: In this article we study the local controllability of the one-dimensional Cahn-Hilliard-Navier-Stokes equation, that is Cahn-Hilliard-Burgers' equation, around a certain steady state using a localized interior control acting only in the concentration equation. To do it, w... | https://arxiv.org/abs/2601.22611 | Academic Papers | svg |
a5862d8693beb1162d099423b482eb008f8506ca02f6dbfe54cea2e78c41d46c | 2026-02-02T00:00:00-05:00 | Sequence entropy of rank one systems | arXiv:2601.22626v1 Announce Type: new Abstract: We study the sequence entropy of rank one measure-preserving systems along subexponential sequences. We prove that the sequence entropy along a large class of sequences can be infinite using Ornstein's probabilistic constructions. Moreover, we show that sequence entropy n... | https://arxiv.org/abs/2601.22626 | Academic Papers | svg |
234f6ec37787277e4ef382efcbae5147a9b77d29762290823a1f6253ea603bf0 | 2026-02-02T00:00:00-05:00 | Maximal Prikry Sequences | arXiv:2601.22643v1 Announce Type: new Abstract: In this paper we investigate the covering machinery of the Mitchell-Steel core model $K$, under the hypothesis that there is no inner model with a Woodin cardinal. In an earlier work, Mitchell and the first author showed that if $\nu>\omega_2$ is a regular cardinal in $K$... | https://arxiv.org/abs/2601.22643 | Academic Papers | svg |
323b42e3f3acaef40a852a499e93d8ec3ef3f1ab5dca44173a9f6a791b6dc2b8 | 2026-02-02T00:00:00-05:00 | On the BSE and BED properties of the Beurling algebra $L^1(G,\omega)$ | arXiv:2601.22646v1 Announce Type: new Abstract: Let $G$ be a locally compact abelian group, and let $\omega:G \to [1,\infty)$ be a weight, i.e., $\omega$ is measurable, $\omega$ is locally bounded and $\omega(s+t)\leq \omega(s)\omega(t)$ for all $s, t \in G$. If $\omega^{-1}$ is vanishing at infinity, then we show that... | https://arxiv.org/abs/2601.22646 | Academic Papers | svg |
ea69d75ca64eef94705f42a2388e20b6aca6a689e30d2d06d8f5c088a80d4259 | 2026-02-02T00:00:00-05:00 | Multisets of finite intervals and a universal category of poset representations | arXiv:2601.22649v1 Announce Type: new Abstract: For any finite totally ordered set, the multisets of intervals form an abelian category. Various classes of subcategories admit natural combinatorial descriptions, and counting them yields familiar integer sequences. Surprisingly, in some cases new integer sequences arise... | https://arxiv.org/abs/2601.22649 | Academic Papers | svg |
8a870ef543ac9c7dd4ab6fa348bb9c02a50ff08591cb86373851d5e6c699847d | 2026-02-02T00:00:00-05:00 | Sharp thresholds for Escobar and Gagliardo-Nirenberg functionals: the Escobar-Willmore mass, geometric selection, and compactness trichotomy | arXiv:2601.22665v1 Announce Type: new Abstract: We develop a unified quantitative framework for sharp threshold phenomena in boundary-critical variational problems on compact Riemannian manifolds, covering the Escobar quotient and Gagliardo-Nirenberg inequalities. Via transfer-stability-reduction, we obtain attainment-... | https://arxiv.org/abs/2601.22665 | Academic Papers | svg |
0773e7a51abe0f41844b16c0660540aa69cc21abf8c0468382992c557b6f7dc9 | 2026-02-02T00:00:00-05:00 | Classification of horospherical invariant measures in higher rank: The Full Story | arXiv:2601.22668v1 Announce Type: new Abstract: In this paper, we classify horospherical invariant Radon measures for Anosov subgroups of arbitrary semisimple real algebraic groups. This generalizes the works of Burger and Roblin in rank one to higher ranks. At the same time, this extends the works of Furstenberg, Veec... | https://arxiv.org/abs/2601.22668 | Academic Papers | svg |
a822f3b8d3735431ce42556013bb0401950fd995553028dc5ad54fdd4155aa8a | 2026-02-02T00:00:00-05:00 | Wall singularity of spaces with an upper curvature bound | arXiv:2601.22673v1 Announce Type: new Abstract: We study typical wall singularity of codimension one for locally compact geodesically complete metric spaces with an upper curvature bound. We provide a geometric structure theorem of codimension one singularity, and a geometric characterization of codimension two regular... | https://arxiv.org/abs/2601.22673 | Academic Papers | svg |
802fdae76528efb87aac0db675c14861e08a00e8927ea591ed7652adbcec0634 | 2026-02-02T00:00:00-05:00 | Anisotropic Minkowski Content for Countably $\mathcal{H}^k$-rectifiable Sets | arXiv:2601.22681v1 Announce Type: new Abstract: This paper investigates the existence of the anisotropic lower-dimensional Minkowski content. We establish that the $C$-anisotropic $k$-dimensional Minkowski content of a $k$-rectifiable compact set always exists and coincides with a specific functional that depends natur... | https://arxiv.org/abs/2601.22681 | Academic Papers | svg |
39090b340344e635ce11be70db2bff955f12bdd2ab31df1e86f2c5719e5ad0f5 | 2026-02-02T00:00:00-05:00 | SUN-DSBO: A Structured Unified Framework for Nonconvex Decentralized Stochastic Bilevel Optimization | arXiv:2601.22682v1 Announce Type: new Abstract: Decentralized stochastic bilevel optimization (DSBO) is a powerful tool for various machine learning tasks, including decentralized meta-learning and hyperparameter tuning. Existing DSBO methods primarily address problems with strongly convex lower-level objective functio... | https://arxiv.org/abs/2601.22682 | Academic Papers | svg |
a72021efd506c71b4d8ee28f0313fc5065ac1da3373aed0d5eb8722998d045c4 | 2026-02-02T00:00:00-05:00 | Enhancing Exploration in Global Optimization by Noise Injection in the Probability Measures Space | arXiv:2601.22753v1 Announce Type: new Abstract: McKean-Vlasov (MKV) systems provide a unifying framework for recent state-of-the-art particlebased methods for global optimization. While individual particles follow stochastic trajectories, the probability law evolves deterministically in the mean-field limit, potentiall... | https://arxiv.org/abs/2601.22753 | Academic Papers | svg |
11e039ebff9bb5a1846b2fc41615ea4275c651ac42388909c4fc36f6dc7adf46 | 2026-02-02T00:00:00-05:00 | Characterization of $n$-Lie Derivations on Generalized Matrix Algebras | arXiv:2601.22774v1 Announce Type: new Abstract: The principal objective of this paper is to determine the structure of $n$-Lie derivations ($n\geq 3$) on generalized matrix algebras.It is shown that under certain mild assumptions, every $n$-Lie derivation can be decomposed into the sum of an extremal $n$-derivation and... | https://arxiv.org/abs/2601.22774 | Academic Papers | svg |
9fd199ee513fda2086fcc962c32375843489ffdaf77d8aa502073688b6cc8f87 | 2026-02-02T00:00:00-05:00 | The Symplectic-to-Contact Dictionary | arXiv:2601.22775v1 Announce Type: new Abstract: Contact Geometry is an odd dimensional analogue of Symplectic Geometry. This vague idea can actually be formalized in a rather precise way by means of a Symplectic-to-Contact Dictionary. The aim of this review paper is discussing the basic entries in this dictionary. Surp... | https://arxiv.org/abs/2601.22775 | Academic Papers | svg |
97ad03cc61b666581f6c97618f3ebf84185c0d571b2311983e853fbc73430736 | 2026-02-02T00:00:00-05:00 | Generators for automorphisms of special groups | arXiv:2601.22789v1 Announce Type: new Abstract: Let $G$ be a (compact) special group in the sense of Haglund and Wise. We show that ${\rm Out}(G)$ is finitely generated, and provide a virtual generating set consisting of Dehn twists and ``pseudo-twists''. We exhibit instances where Dehn twists alone do not suffice and ... | https://arxiv.org/abs/2601.22789 | Academic Papers | svg |
b3340318ad0a9ffd619b5f82d61be965f73dffd276afec0d27f8fc1aa36529b2 | 2026-02-02T00:00:00-05:00 | Convergence of Multi-Level Markov Chain Monte Carlo Adaptive Stochastic Gradient Algorithms | arXiv:2601.22799v1 Announce Type: new Abstract: Stochastic optimization in learning and inference often relies on Markov chain Monte Carlo (MCMC) to approximate gradients when exact computation is intractable. However, finite-time MCMC estimators are biased, and reducing this bias typically comes at a higher computatio... | https://arxiv.org/abs/2601.22799 | Academic Papers | svg |
89a21e83d11477add0a6cc82f1fb658be9194edae4a4d8c69e7ce252058723fb | 2026-02-02T00:00:00-05:00 | Rapid stabilizability of delayed infinite-dimensional control systems | arXiv:2601.22819v1 Announce Type: new Abstract: In this paper, the rapid stabilizability of linear infinite-dimensional control system with constant-valued delay is studied. Under assumptions that the state operator generates an immediately compact semigroup and the coefficient of the delay term is constant, we mainly ... | https://arxiv.org/abs/2601.22819 | Academic Papers | svg |
a2e5460bebd7776cc50e2070a9bf9bf713f62b97de43f25c2f9a76447a2d8859 | 2026-02-02T00:00:00-05:00 | On the average number of representations of an integer as a sum of polynomials computed at prime values | arXiv:2601.22822v1 Announce Type: new Abstract: We study the average number of representations of an integer $n$ as $n = \phi(n_{1}) + \dots + \phi(n_{j})$, for polynomials $\phi \in \mathbb{Z}[n]$ with $\partial\phi = k\ge 1$, $\operatorname{lead}(\phi) = 1$, $j \ge k$, where $n_{i}$ is a prime power for each $i \in \... | https://arxiv.org/abs/2601.22822 | Academic Papers | svg |
5255b72ee5a6d02234476abbab90bf01ba7c58d7a3c4069f5ba626406574774c | 2026-02-02T00:00:00-05:00 | Simplicity of eigenvalues for elliptic problems with mixed Steklov-Robin boundary condition | arXiv:2601.22829v1 Announce Type: new Abstract: This paper investigates the spectral properties of two classes of elliptic problems characterized by mixed Steklov-Robin boundary conditions. Our main objective is to prove that, for a generic domain, all the eigenvalues are simple. This result is established by employing... | https://arxiv.org/abs/2601.22829 | Academic Papers | svg |
b9a696afbe0a864797ff84c5f02220fb572a3adbd2b026c44d5f5ef6b822c068 | 2026-02-02T00:00:00-05:00 | Asymmetric conformal prediction with penalized kernel sum-of-squares | arXiv:2601.22834v1 Announce Type: new Abstract: Conformal prediction (CP) is a distribution-free method to construct reliable prediction intervals that has gained significant attention in recent years. Despite its success and various proposed extensions, a significant practical feature which has been overlooked in prev... | https://arxiv.org/abs/2601.22834 | Academic Papers | svg |
cc5c710c9183ef9523bcbdd22d712ac03769b417e4ed19966c2e2e7cda8a0671 | 2026-02-02T00:00:00-05:00 | Vidinli algebras | arXiv:2601.22839v1 Announce Type: new Abstract: A new class of nonassociative algebras, Vidinli algebras, is defined based on recent work of Co\c{s}kun and Eden. These algebras are conic (or quadratic) algebras with the extra restriction that the commutator of any two elements is a scalar multiple of the unity. Over fi... | https://arxiv.org/abs/2601.22839 | Academic Papers | svg |
0e4b4aaae61472149e713a8031f75b67fb465687b461870da0c12e4283ef532c | 2026-02-02T00:00:00-05:00 | Distance Optimization in the Grassmannian of Lines | arXiv:2601.22843v1 Announce Type: new Abstract: The square of a skew-symmetric matrix is a symmetric matrix whose eigenvalues have even multiplicities. When the matrices have rank two, they represent the Grassmannian of lines, and the squaring operation takes Pl\"ucker coordinates to projection coordinates. We develop ... | https://arxiv.org/abs/2601.22843 | Academic Papers | svg |
4d2425d4c025d03f957ec3ae1b7228ab08c3f470b24364904cbc6f0a8b8aa5f4 | 2026-02-02T00:00:00-05:00 | Unconditional well-posedness of the master equation for monotone mean field games of controls | arXiv:2601.22845v1 Announce Type: new Abstract: We establish the first unconditional well-posedness result for the master equation associated with a general class of mean field games of controls. Our analysis covers games with displacement monotone or Lasry--Lions monotone data, as well as those with a small time horiz... | https://arxiv.org/abs/2601.22845 | Academic Papers | svg |
01363877c58454102d95cc4b44ceb0340227b5ddb78c377e3b517a49c4cb5e05 | 2026-02-02T00:00:00-05:00 | Relative Kazhdan Lusztig isomorphism for $GL_{2n}/Sp_{2n}$ | arXiv:2601.22846v1 Announce Type: new Abstract: The Kazhdan Lusztig isomorphism, relating the affine Hecke algebra of a $p$-adic group to the equivariant $K$ theory of the Steinberg variety of its Langlands dual, played a key role in the proof of the Deligne Langlands conjectures concerning the classification of smooth... | https://arxiv.org/abs/2601.22846 | Academic Papers | svg |
92b54211a4ba8f733c8e4d9ab55e001662ffaba275582606894b7a4b0a8f7ad7 | 2026-02-02T00:00:00-05:00 | Existence of a solution of the TV Wasserstein gradient flow | arXiv:2601.22847v1 Announce Type: new Abstract: On the flat torus in any dimension we prove existence of a solution to the TV Wasserstein gradient flow equation, only assuming that the initial density $\rho_0$ is bounded from below and above by strictly positive constants. This solution preserves upper and lower bounds... | https://arxiv.org/abs/2601.22847 | Academic Papers | svg |
411964c531e4ffed2acec85d0c9edd96eadbb8a3729d9f6e5e8d7aa11790a966 | 2026-02-02T00:00:00-05:00 | Convergence Rates for the Alternating Minimization Algorithm in Structured Nonsmooth and Nonconvex Optimization | arXiv:2601.22850v1 Announce Type: new Abstract: This paper is devoted to developing the alternating minimization algorithm for problems of structured nonconvex optimization proposed by Attouch, Bolt\'e, Redont, and Soubeyran in 2010. Our main result provides significant improvements of the convergence rate of the algor... | https://arxiv.org/abs/2601.22850 | Academic Papers | svg |
e5d7fc554d4aee2c73d4070d0783099ea6c18033d7b5bb3d5333943a61d41d4c | 2026-02-02T00:00:00-05:00 | The two-nest ants process on triangle-series-parallel graphs | arXiv:2601.22855v1 Announce Type: new Abstract: The ants process is a stochastic process introduced by Kious, Mailler and Schapira as a model for the phenomenon of ants finding shortest paths between their nest and a source of food (seen as two marked nodes in a finite graph), with no other means of communications besi... | https://arxiv.org/abs/2601.22855 | Academic Papers | svg |
f819c7d4c4f8775bd2b8243da55f50e6029e5075174976d7b22164f885f2e192 | 2026-02-02T00:00:00-05:00 | Global Well-posedness of Strong Solutions to the Cauchy Problem of 2D Nonhomogeneous Navier-Stokes Equations with Density-Dependent Viscosity and Vacuum | arXiv:2601.22877v1 Announce Type: new Abstract: This paper is concerned with the Cauchy problem for the modified two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity. By fully using the structure of the system, we can obtain the key estimates of $\|\nabla \rho\|_{L... | https://arxiv.org/abs/2601.22877 | Academic Papers | svg |
1f029d8a6730a43dfa7e641d7d115e46637a3ff4b5cef95cff9b0d0c0cee55e4 | 2026-02-02T00:00:00-05:00 | Arbitrary harmonic functions as Bose--Einstein condensates | arXiv:2601.22883v1 Announce Type: new Abstract: We show that a suitable choice of boundary conditions for the Laplacian allows for the appearance of an an arbitrary number of condensates, described by arbitrary harmonic functions, in the thermodynamic limit of an ideal Bose gas. | https://arxiv.org/abs/2601.22883 | Academic Papers | svg |
aa6fdf6895ee70d6df0ac8e75790919dfba654ace08f1e7dc6ab9ee00333894f | 2026-02-02T00:00:00-05:00 | Uncoupled Dirac-Yang-Mills Pairs on Closed Riemannian Spin Manifolds | arXiv:2601.22886v1 Announce Type: new Abstract: We study the Dirac-Yang-Mills equations on closed spin manifolds with a focus on uncoupled solutions, i.e. solutions for which the connection form satisfies the Yang-Mills equation. Such solutions require the Dirac current, a quadratic form on the spinor bundle, to vanish... | https://arxiv.org/abs/2601.22886 | Academic Papers | svg |
d2de9cdb114a86f7a43fc9ec0cf19db6012857e24788817ac4dfffaa29ce1d7a | 2026-02-02T00:00:00-05:00 | Grassmannian Geometry and Global Convergence of Variable Projection for Neural Networks | arXiv:2601.22897v1 Announce Type: new Abstract: Training deep neural networks and Physics-Informed Neural Networks (PINNs) often leads to ill-conditioned and stiff optimization problems. A key structural feature of these models is that they are linear in the output-layer parameters and nonlinear in the hiddenlayer para... | https://arxiv.org/abs/2601.22897 | Academic Papers | svg |
a2c1058c7355b8b283ba6039618cdc596e2bd31d701efd8cacc2e5b114ba01a7 | 2026-02-02T00:00:00-05:00 | Rigidity of circle polyhedra and hyperideal polyhedra: the tangency case | arXiv:2601.22903v1 Announce Type: new Abstract: We prove the global rigidity of proper triangulated convex hyperbolic circle polyhedra on the sphere $\mathbb{S}^2$. These circle polyhedra correspond to proper triangulated convex hyperbolic polyhedra in the Beltrami-Klein model $\mathbb{B}^{3}$ of hyperbolic space with ... | https://arxiv.org/abs/2601.22903 | Academic Papers | svg |
6b953b623243ce0dc0dbd55cc749d11c781fa6cc5fa55737eed6a5ce153b766b | 2026-02-02T00:00:00-05:00 | Examples of finitely presented groups with strong fixed point properties and property (T) | arXiv:2601.22907v1 Announce Type: new Abstract: We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the simplicity requirement. | https://arxiv.org/abs/2601.22907 | Academic Papers | svg |
a9772e942d7470c0ff36e93f5c4033fbeb5b4db4d301d48e2ee25275fdb1d803 | 2026-02-02T00:00:00-05:00 | Reducibility of self-maps in monoid and its related invariants | arXiv:2601.22908v1 Announce Type: new Abstract: Given a positive integer $k$, we investigate the $k$-redcibility of self-maps in the monoid $\AA^k(X\vee Y)$, consisting of self-maps that induce isomorphisms on homology groups up to degree $k$. In general, verifying $k$-reducibility is a subtle problem. We show that the... | https://arxiv.org/abs/2601.22908 | Academic Papers | svg |
c8a34ece507e6e83c447e5bd879a12a8cb763ea547dbce4a96fe70cbd1b814e0 | 2026-02-02T00:00:00-05:00 | Left Ehresmann monoids with a proper basis | arXiv:2601.22923v1 Announce Type: new Abstract: This article gives an abstract characterisation of a class of left Ehresmann monoids possessing certain universal properties. It is known that every left Ehresmann monoid has a cover, that is, a projection separating preimage, of the form $\mathcal{P}_{\ell}(T,X)$, where ... | https://arxiv.org/abs/2601.22923 | Academic Papers | svg |
a4fa07a47839f0ca74231c35e6b90cc13594ddfff48e9f6f96e0ace96edf8773 | 2026-02-02T00:00:00-05:00 | Poset modules of the $0$-Hecke algebras of type $B$ | arXiv:2601.22926v1 Announce Type: new Abstract: In 2001, Chow developed the theory of the $B_n$ posets $P$ and the type $B$ $P$-partition enumerators $K^B_P$. To provide a representation-theoretic interpretation of $K^B_P$, we define the poset modules $M^B_P$ of the 0-Hecke algebra $H_n^B(0)$ of type $B$ by endowing th... | https://arxiv.org/abs/2601.22926 | Academic Papers | svg |
93275aa3417a3ac4c0ee5c5e52d4cb387176b8d5d2996db02fe59c5d1d1147a4 | 2026-02-02T00:00:00-05:00 | Prescribed $T$-curvature flow on the four-dimensional unit ball | arXiv:2601.22934v1 Announce Type: new Abstract: In this paper, we study the prescribed $T$-curvature problem on the unit ball $\mathbb{B}^4$ of $\mathbb{R} ^4$ via the $T$-curvature flow approach. By combining Ache-Chang's inequality with the Morse-theoretic approach of Malchiodi-Struwe, we establish existence results ... | https://arxiv.org/abs/2601.22934 | Academic Papers | svg |
f73ce1d5c8f96c9c461dc1129bcc3e2bdbcea93d9ff6cbb88a590643ee84b2bb | 2026-02-02T00:00:00-05:00 | Local Well-posedness and Blow-up for the Restricted Fourth-Order Prandtl Equation | arXiv:2601.22940v1 Announce Type: new Abstract: We prove local well-posedness and finite-time blow-up for a restricted fourth-order Prandtl equation posed on the half-line with clamped boundary conditions. The equation arises from a two-dimensional fourth-order Prandtl system via an ansatz reduction, and its nonlineari... | https://arxiv.org/abs/2601.22940 | Academic Papers | svg |
197102a0958480f215b681fe70aad1b87a54c0be5adbb1cea70d43b83e25ee66 | 2026-02-02T00:00:00-05:00 | Compact group Rohlin actions and $G$-kernels on von Neumann algebras | arXiv:2601.22941v1 Announce Type: new Abstract: We provide a new construction of a topological group model for the string group of a compact, simple, and simply-connected Lie group, by solving the obstruction realization problem for compact group $G$-kernels on full factors. Furthermore, we introduce the Rohlin propert... | https://arxiv.org/abs/2601.22941 | Academic Papers | svg |
25e3e70f4073c4ba44b747383d7156f8ec590a05bcdfca2272f8aa6616675603 | 2026-02-02T00:00:00-05:00 | On polynomial functors and polynomial comonads over infinity groupoids | arXiv:2601.22968v1 Announce Type: new Abstract: We show that single-variable polynomial functors over the category $\mathcal{S}$ of infinity groupoids, as defined by Gepner-Haugseng-Kock, are exactly colimits of representable copresheaves indexed by infinity groupoid. This allows us to establish certain categorical pro... | https://arxiv.org/abs/2601.22968 | Academic Papers | svg |
5e89fdb3633c968d0e400665e73a165231b1a05dd0a686da2f061c093237f254 | 2026-02-02T00:00:00-05:00 | Periods of Ehrhart coefficients of rational polytopes | arXiv:2601.22992v1 Announce Type: new Abstract: Let $\mathcal{P} \subseteq \mathbb{R}^{n}$ be a polytope whose vertices have rational coordinates. By a seminal result of E. Ehrhart, the number of integer lattice points in the $k$th dilate of $\mathcal{P}$ ($k$ a positive integer) is a quasi-polynomial function of $k$ -... | https://arxiv.org/abs/2601.22992 | Academic Papers | svg |
ebc2cec96172d9a2bd72f2cf916e74ff9757ebbc15755744b3dbb878efa17a07 | 2026-02-02T00:00:00-05:00 | A Remark on Stability Conditions on Smooth Projective Varieties | arXiv:2601.22994v1 Announce Type: new Abstract: Let $X$ be a smooth projective variety over $\mathbb C$. In this paper, we prove that $\mathrm{D}^b(X)$, the bounded derived category of coherent sheaves on $X$, always admits stability conditions in the sense of Bridgeland. | https://arxiv.org/abs/2601.22994 | Academic Papers | svg |
6e24479a594ca75101db3a36390ecd57b7fdf0f9ea08be856b9989ccf895d1c3 | 2026-02-02T00:00:00-05:00 | Baire-type properties of topological vector spaces | arXiv:2601.23008v1 Announce Type: new Abstract: Burzyk, Kli\'{s} and Lipecki proved that every topological vector space (tvs) $E$ with the property $(K)$ is a Baire space. K\c{a}kol and S\'{a}nchez Ruiz proved that every sequentially complete Fr\'{e}chet--Urysohn locally convex space (lcs) is Baire. Being motivated by ... | https://arxiv.org/abs/2601.23008 | Academic Papers | svg |
2436671508f17a55de0300da1f8da1964e3ad2859dbd0f9515378947342e4ef4 | 2026-02-02T00:00:00-05:00 | On the finiteness of prime trees and their relation to modular forms | arXiv:2601.23016v1 Announce Type: new Abstract: In this paper, we introduce the prime trees associated with a finite subset $P$ of the set of all prime numbers, and provide conditions under which the tree is of finite type. Moreover, we compute the density of finite-type subsets $P$. As an application, we show that for... | https://arxiv.org/abs/2601.23016 | Academic Papers | svg |
93d16fc663623231986c3bce0bcd20cacf44935ef83fe61b0e3cb027d8d99817 | 2026-02-02T00:00:00-05:00 | The uniqueness theorem for Kasparov theory | arXiv:2601.23029v1 Announce Type: new Abstract: Answering a question of Carri\'on et al in their recent landmark paper on C*-algebra classification, we prove a general uniqueness theorem for $KK$-theory. Given arbitrary separable C*-algebras $A$ and $B$ and a Cuntz pair consisting of two absorbing representations $\var... | https://arxiv.org/abs/2601.23029 | Academic Papers | svg |
accc9c7c9c217ab5ee676d4d5258f432145ba103d13cd370b699b1dfac19dfb4 | 2026-02-02T00:00:00-05:00 | Breaking the Stochasticity Barrier: An Adaptive Variance-Reduced Method for Variational Inequalities | arXiv:2601.23034v1 Announce Type: new Abstract: Stochastic non-convex non-concave optimization, formally characterized as Stochastic Variational Inequalities (SVIs), presents unique challenges due to rotational dynamics and the absence of a global merit function. While adaptive step-size methods (like Armijo line-searc... | https://arxiv.org/abs/2601.23034 | Academic Papers | svg |
69ea95c212db4114bee41583b55bfd37740bc575db2e6f5a2dd8ca91f3ffaaac | 2026-02-02T00:00:00-05:00 | Accelerated Inertial Gradient Algorithms with Vanishing Tikhonov Regularization | arXiv:2601.23035v1 Announce Type: new Abstract: In this paper, we study an explicit Tikhonov-regularized inertial gradient algorithm for smooth convex minimization with Lipschitz continuous gradient. The method is derived via an explicit time discretization of a damped inertial system with vanishing Tikhonov regulariza... | https://arxiv.org/abs/2601.23035 | Academic Papers | svg |
bb181f5065e8658763ad96431bdfa6a2cde9bbc3a3c0acccea8b3e5123d3abe5 | 2026-02-02T00:00:00-05:00 | Stationary Mean-Field singular control of an Ornstein-Uhlenbeck process | arXiv:2601.23036v1 Announce Type: new Abstract: Motivated by continuous-time optimal inventory management, we study a class of stationary mean-field control problems with singular controls. The dynamics are modeled by a mean-reverting Ornstein-Uhlenbeck process, and the performance criterion is given by a quadratic lon... | https://arxiv.org/abs/2601.23036 | Academic Papers | svg |
a50ac2236ab421d90fd73852b6d2ed221da87544435cb982eced8506713a9f80 | 2026-02-02T00:00:00-05:00 | Instability of two-dimensional Taylor-Green Vortices | arXiv:2601.23040v1 Announce Type: new Abstract: For a wide class of linear Hamiltonian operators we develop a general criterion that characterizes the unstable eigenvalues as the zeros of a holomorphic function given by the determinant of a finite-dimensional matrix. We apply the latter result to prove the spectral ins... | https://arxiv.org/abs/2601.23040 | Academic Papers | svg |
77ba48df79fcc68ed54fdc873c07224cdbfa10bfc1466ac093223be1f84d5dba | 2026-02-02T00:00:00-05:00 | On two-dimensional Dirac operators with critical delta-shell interactions | arXiv:2601.23053v1 Announce Type: new Abstract: We study two-dimensional Dirac operators with singular interactions of electrostatic and Lorentzscalar type, supported either on a straight line or a circle. For certain critical values of the interaction strengths, the essential spectrum of such operators comprises an is... | https://arxiv.org/abs/2601.23053 | Academic Papers | svg |
677660a6a6d60d92bb7bcba89204d4fe318523968996d15ba63a3fbb021d809c | 2026-02-02T00:00:00-05:00 | Some elementary amenable subgroups of interval exchange transformations | arXiv:2601.23054v1 Announce Type: new Abstract: In this paper, we study a family of finitely generated elementary amenable iet-groups. These groups are generated by finitely many rationals iets and rotations. For them, we state criteria for not virtual nilpotency or solvability, and we give conditions to ensure that th... | https://arxiv.org/abs/2601.23054 | Academic Papers | svg |
166212226dca438f440c41060b076fd1fb07ddb6f0935a4617551a320a143ec7 | 2026-02-02T00:00:00-05:00 | Spectrum of bidual uniform algebras | arXiv:2601.23055v1 Announce Type: new Abstract: We obtain a description of the spectrum of bidual algebra $A^{**}$ of a uniform algebra $A$. This spectrum turns out to be a quotient space of the hyper-Stonean envelope of the spectrum of $A$. | https://arxiv.org/abs/2601.23055 | Academic Papers | svg |
d042c4ec2e85f07d3c1571663f626afb6f1edb6ef66d789d2b17d0dc581b455a | 2026-02-02T00:00:00-05:00 | Some notes on plump ordinals | arXiv:2601.23070v1 Announce Type: new Abstract: In this exposition, we attempt to formalise a treatment of Paul Taylor's notion of plump ordinals in weak intuitionistic axiomatic set theories such as IKP. We will explore basic properties of plump ordinals, especially in relation to G\"odel's constructible universe $L$ ... | https://arxiv.org/abs/2601.23070 | Academic Papers | svg |
b17b73dcbbd01fb2b13a478b0e374f840bb0a44940ef2360253db2ebd514f53b | 2026-02-02T00:00:00-05:00 | The $L^p$- regularity problem for the Bergman projection of two-dimensional Rudin ball quotients | arXiv:2601.23074v1 Announce Type: new Abstract: We solve the $L^p$-regularity problem of the Bergman projection of two-dimensional Rudin ball quotients. | https://arxiv.org/abs/2601.23074 | Academic Papers | svg |
1603ef686632936a59f4bace58e43d52d7b5e18094595c8956e40bf509b26f63 | 2026-02-02T00:00:00-05:00 | Mermin-Wagner theorems for quantum systems with multipole symmetries | arXiv:2601.23078v1 Announce Type: new Abstract: We prove Mermin-Wagner-type theorems for quantum lattice systems in the presence of multipole symmetries. These theorems show that the presence of higher-order symmetries protects against the breaking of lower-order ones. In particular, we prove that the critical dimensio... | https://arxiv.org/abs/2601.23078 | Academic Papers | svg |
de7d446ddf212c714a47787aee3820cd78318db6583ebf79c16c4e5e0e37bf40 | 2026-02-02T00:00:00-05:00 | Lifting property for finite groups | arXiv:2601.23089v1 Announce Type: new Abstract: We classify all finite groups that have lifting property of mod $p$ representations to mod $p^2$ representations for all prime $p$. | https://arxiv.org/abs/2601.23089 | Academic Papers | svg |
965f49260025a403cf6d2f6e699aaff1d0acddd02ae00db1cefd40d1ed912683 | 2026-02-02T00:00:00-05:00 | Existence of Traveling Waves in Infinite Range FPUT Lattices | arXiv:2601.23091v1 Announce Type: new Abstract: We prove the existence of solitary waves in a lattice where all particles interact with each other by pair-wise repulsive forces that decay with distance. The variational existence proof is based on constrained optimization and provides a one-parameter family of unimodal ... | https://arxiv.org/abs/2601.23091 | Academic Papers | svg |
022baac651615030d28fc0bf61f874cfaa43f47f9a78039ec8b45f00abe4ded2 | 2026-02-02T00:00:00-05:00 | Seminoetherian Modules over Non-Primitive HNP rings | arXiv:2601.23099v1 Announce Type: new Abstract: We study the structure of seminoetherian modules. Seminoetherian modules over non-primitive hereditary noetherian prime rings are completely described. | https://arxiv.org/abs/2601.23099 | Academic Papers | svg |
c2e4548749cfbbef13e4c0d1e7526fde37b6abe38aa09227a34ac959bf38fcac | 2026-02-02T00:00:00-05:00 | Bipartite Graphs Are Not Well-Ordered by Bipartite Minors | arXiv:2601.23101v1 Announce Type: new Abstract: In "Bipartite minors," Chudnovsky etal. introduced the bipartite minor relation, a partial order on the set of bipartite graphs somewhat analogous the minor relation on general graphs and asked whether it is a well-order. We answer this question negatively by giving an in... | https://arxiv.org/abs/2601.23101 | Academic Papers | svg |
97dc247f260c7334b85fd1ed838678a91e8bb981c9f67b0e224e1814aa84fa46 | 2026-02-02T00:00:00-05:00 | Series-Parallel and Planar Graphs for Efficient Broadcasting | arXiv:2601.23104v1 Announce Type: new Abstract: The broadcasting problem concerns the efficient dissemination of information in graphs. In classical broadcasting, a single originator vertex initially has a message to be transmitted to all vertices. Every vertex which has received the message informs at most one uninfor... | https://arxiv.org/abs/2601.23104 | Academic Papers | svg |
83d0838d4930cd432770b68ef3bec436a8130aeb9a8551dd54c403f81c922bc8 | 2026-02-02T00:00:00-05:00 | Lifts of endomorphisms of Weyl algebras modulo $p^2$ | arXiv:2601.23110v1 Announce Type: new Abstract: Let $\varphi$ denote a $k$-algebra endomorphism of the $n$-th Weyl algebra $A_n(k)$ over a perfect field $k$ of positive characteristic $p$. We prove that $\varphi$ can be lifted to an endomorphism of the Weyl algebra $A_n(W_2(k))$ over the Witt vectors $W_2(k)$ of length... | https://arxiv.org/abs/2601.23110 | Academic Papers | svg |
fd15db3c8f94e2c3120ca4ab88b1810d9be7c40527c3669643ddcecf4f8409e9 | 2026-02-02T00:00:00-05:00 | The Coxeter Flag Variety | arXiv:2601.23111v1 Announce Type: new Abstract: For a Coxeter element $c$ in a Weyl group $W$, we define the $c$-Coxeter flag variety $\operatorname{CFl}_c\subset G/B$ as the union of left-translated Richardson varieties $w^{-1}X^{wc}_w$. This is a complex of toric varieties whose geometry is governed by the lattice $\... | https://arxiv.org/abs/2601.23111 | Academic Papers | svg |
5461f5483feb1fbf945c79a0b2e98b418bd8fc0ba01c17407a08ff13593733b3 | 2026-02-02T00:00:00-05:00 | Graded Lie superalgebras from embedding tensors | arXiv:2601.23113v1 Announce Type: new Abstract: We show how various constructions of $\mathbb{Z}$-graded Lie superalgebras are related to each other. These Lie superalgebras have a Lie algebra $\mathfrak{g}$ as the subalgebra at degree 0, an odd $\mathfrak{g}$-module V as the subspace at degree 1, and an embedding tens... | https://arxiv.org/abs/2601.23113 | Academic Papers | svg |
74013151098ed1cb5fc9dc5de24d01aa47ef492f81c24f9b37ce52e6cba032b9 | 2026-02-02T00:00:00-05:00 | Nonlinear Schr\"odinger Equation with magnetic potential on metric graphs | arXiv:2601.23115v1 Announce Type: new Abstract: In this manuscript, we shall investigate the Nonlinear Magnetic Schr\"odinger Equation on noncompact metric graphs, focusing on the existence of ground states. We prove that the magnetic Hamiltonian is variationally equivalent to a non-magnetic operator with additional re... | https://arxiv.org/abs/2601.23115 | Academic Papers | svg |
dd7f87e2e596ae2fdcc02ad23748265a4a69da9e12a1eb69b7a8ac45b708cc00 | 2026-02-02T00:00:00-05:00 | Log canonical thresholds at infinity | arXiv:2601.23118v1 Announce Type: new Abstract: The paper considers a global version of the notion of log canonical threshold for plurisubharmonic functions $u$ of logarithmic growth in $\mathbb{C}^n$, aiming at description of the range of all $p>0$ such that $e^{-u}\in L^p(\mathbb{C}^n)$. Explicit formulas are obtaine... | https://arxiv.org/abs/2601.23118 | Academic Papers | svg |
82ffd8f8136517125cfeafeaa18f6adc3142bba7503223971a5658586b5235a3 | 2026-02-02T00:00:00-05:00 | A General Tikhonov Regularized Second-Order Dynamical System for Convex-Concave Bilinear Saddle Point Problems | arXiv:2601.23120v1 Announce Type: new Abstract: In this paper, we propose a general Tikhonov regularized second-order dynamical system with viscous damping, time scaling and extrapolation coefficients for the convex-concave bilinear saddle point problem. By the Lyapunov function approach, we show that the convergence p... | https://arxiv.org/abs/2601.23120 | Academic Papers | svg |
75d4627e19ca783985b506ae0ebb7791a2cdee880fd47893eb030feaece69a20 | 2026-02-02T00:00:00-05:00 | Learning and Teaching Calculus Through Its History | arXiv:2601.23122v1 Announce Type: new Abstract: This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like infinity, area, motion, and cont... | https://arxiv.org/abs/2601.23122 | Academic Papers | svg |
b6b03d0a6b87243c8b3ad5288658b8ab61b2fe76f56acd1851de70c5dc3bd12c | 2026-02-02T00:00:00-05:00 | Semi-knockoffs: a model-agnostic conditional independence testing method with finite-sample guarantees | arXiv:2601.23124v1 Announce Type: new Abstract: Conditional independence testing (CIT) is essential for reliable scientific discovery. It prevents spurious findings and enables controlled feature selection. Recent CIT methods have used machine learning (ML) models as surrogates of the underlying distribution. However, ... | https://arxiv.org/abs/2601.23124 | Academic Papers | svg |
620197f62f5f92f32281bd0f8e054f944181cf641da27d35d4dc73027eda4381 | 2026-02-02T00:00:00-05:00 | On the b-function with respect to weights of annihilating ideals in the Weyl algebra | arXiv:2601.23125v1 Announce Type: new Abstract: Given a polynomial $f\in\mathbb{C}[x_1,\ldots,x_n]$ and an integer $\ell\in\mathbb{Z}$, we study some properties of the b-function with respect to weights of the annihilating ideal Ann$(f^\ell)$. In some particular cases the expression of the b-function is given explicitl... | https://arxiv.org/abs/2601.23125 | Academic Papers | svg |
241b156f63f863d3f79363e0237bae77284ccd5ce6b39dfaf129a45abc3830e9 | 2026-02-02T00:00:00-05:00 | Hyperbolic partial differential equations with complex characteristics on Fourier Lebesgue spaces | arXiv:2601.23138v1 Announce Type: new Abstract: The aim of this paper is to establish well-posedness properties for hyperbolic PDEs on Fourier Lebesgue spaces. We consider hyperbolic operators with complex characteristics. Since our approach comes from harmonic analysis, we establish boundedness properties of Fourier i... | https://arxiv.org/abs/2601.23138 | Academic Papers | svg |
760742a05dc9e07725b8e3a57d04c9e7596fead34a78c85146abba7f73606094 | 2026-02-02T00:00:00-05:00 | 2-covering numbers of some finite solvable groups | arXiv:2601.23144v1 Announce Type: new Abstract: A 2-covering for a finite group $G$ is a set of proper subgroups of $G$ such that every pair of elements of $G$ is contained in at least one subgroup in the set. The minimal number of subgroups needed to 2-cover a group $G$ is called the 2-covering number and denoted by $... | https://arxiv.org/abs/2601.23144 | Academic Papers | svg |
b5fa863629ea39248e5eaf7c7310af3ce515139953c402daf7c7d2b6dae953fa | 2026-02-02T00:00:00-05:00 | Some series representing the zeta function for $\Re s>1$ | arXiv:2601.23158v1 Announce Type: new Abstract: We present series converging to the Riemann zeta function in its half-plane of convergence, and possessing remainders whose sizes decrease geometrically. They are easy to implement numerically, using only polynomial and power functions, and are efficient for obtaining doz... | https://arxiv.org/abs/2601.23158 | Academic Papers | svg |
1b4323a399eb3b73bc8988517f8508b00c1a9cdcb2d9965e6a175c0e0c5fe6a1 | 2026-02-02T00:00:00-05:00 | Class choice and the surprising weakness of Kelley-Morse set theory | arXiv:2601.23165v1 Announce Type: new Abstract: Kelley-Morse set theory KM is weaker than generally supposed and fails to prove several principles that may be desirable in a foundational second-order set theory. Even though KM includes the global choice principle, for example, (i) KM does not prove the class choice sch... | https://arxiv.org/abs/2601.23165 | Academic Papers | svg |
96ceb93605daa781e194002a89b0458e2d1f24d526d69dbd016d506483ec2360 | 2026-02-02T00:00:00-05:00 | The Total Chromatic Quasisymmetric Functions of a Graph | arXiv:2601.23170v1 Announce Type: new Abstract: In this paper, we introduce and study two variants of the chromatic quasisymmetric function of a graph: the total chromatic quasisymmetric function via vertex labeling and via acyclic orientations. The original definition of the chromatic quasisymmetric function of a grap... | https://arxiv.org/abs/2601.23170 | Academic Papers | svg |
9b203cd0d2d9f046e6e1620515dc911f78fd4495e2d97c2e228a491b8575a1e6 | 2026-02-02T00:00:00-05:00 | Interacting dynamical systems on networks and fractals: discrete and continuous models, mean-field limit, and convergence rates | arXiv:2601.23175v1 Announce Type: new Abstract: We develop a continuum limit and mean-field theory for interacting particle systems (IPS) on self-similar networks, a new class of discrete models whose large-scale behavior gives rise to nonlocal evolution equations on fractal domains. This work extends the graphon-based... | https://arxiv.org/abs/2601.23175 | Academic Papers | svg |
aa0972bcbe819cf580c11f61ad85f6718bd9094f8c456e1be9dfd2ada168560a | 2026-02-02T00:00:00-05:00 | Noetherianity for powers of algebraic representations | arXiv:2601.23186v1 Announce Type: new Abstract: Powers of a polynomial $\operatorname{GL}$-representation are topologically Noetherian under the action of $\operatorname{Sym} \times \operatorname{GL}$. We show that this result extends to powers of algebraic representations of the orthogonal and the symplectic groups. T... | https://arxiv.org/abs/2601.23186 | Academic Papers | svg |
e58902b6995ae4a1c449cab34ae9a93a4780550faae020c42fab8316da9ca0cb | 2026-02-02T00:00:00-05:00 | General Optimal Stopping without Time Consistency | arXiv:2601.23187v1 Announce Type: new Abstract: In this paper, we propose a new framework for solving a general dynamic optimal stopping problem without time consistency. A sophisticated solution is proposed and is well-defined for any time setting with general flows of objectives. A backward iteration is proposed to f... | https://arxiv.org/abs/2601.23187 | Academic Papers | svg |
5cd6b3c747112a56fe8b190dddf21ca7d0d7849544743eb55785b6b0a72342e3 | 2026-02-02T00:00:00-05:00 | Schopieray's Galois-modular extension conjecture | arXiv:2601.23192v1 Announce Type: new Abstract: Plavnik, Schopieray, Yu, and Zhang have drawn attention to those (automatically premodular) fusion subcategories of modular fusion categories which are submodules for the Galois action on the ambient category. In particular, they showed that a subcategory is a Galois subm... | https://arxiv.org/abs/2601.23192 | Academic Papers | svg |
25da02c7f868e0f12aecbefeec4e359bf5458e6014ac6883dbc0898250d7bd01 | 2026-02-02T00:00:00-05:00 | Non-uniformly elliptic variational problems on BV | arXiv:2601.23195v1 Announce Type: new Abstract: We establish $\mathrm{W}^{1,1}$-regularity and higher gradient integrability for relaxed minimizers of convex integral functionals on $\mathrm{BV}$. Unlike classical examples such as the minimal surface integrand, we only require linear growth from below but not necessari... | https://arxiv.org/abs/2601.23195 | Academic Papers | svg |
b6bca2c37bac1529e13d235675666517d1aa33db3a90a870cc94869c5b5b6506 | 2026-02-02T00:00:00-05:00 | Vector-valued Gelfand-Kazhdan criterion | arXiv:2601.23199v1 Announce Type: new Abstract: The Gelfand-Kazhdan criterion is a fundamental tool for studying multiplicity-one properties of local periods of representations. However, it does not apply to many cases arising in the relative Langlands program. Generalizing the usual Gelfand-Kazhdan criterion, we formu... | https://arxiv.org/abs/2601.23199 | Academic Papers | svg |
0319fe64157c7f9ebd48252b50bd3e116c8b8992a002513d08a6b4d1f1913210 | 2026-02-02T00:00:00-05:00 | Eigenweights for arithmetic Hirzebruch Proportionality | arXiv:2601.23245v1 Announce Type: new Abstract: Prior work of Feng--Yun--Zhang established a (Higher) Arithmetic Hirzebruch Proportionality Principle, expressing the arithmetic volumes of moduli stacks of shtukas in terms of differential operators applied to $L$-functions. This formula involves certain "eigenweights" w... | https://arxiv.org/abs/2601.23245 | Academic Papers | svg |
2725291ae8f3abe620b5adc62a18038ad27567bd3264174e5469b96029145309 | 2026-02-02T00:00:00-05:00 | Radicals and Nilpotents in Equivariant Algebra | arXiv:2601.23247v1 Announce Type: new Abstract: Associated to each Tambara functor $T$ is its Nakaoka spectrum $\mathrm{Spec}(T)$, analogous to the Zariski spectrum of a commutative ring. We establish that this topological space is spectral. This result follows from an analysis of the notion of nilpotence in Tamabra fu... | https://arxiv.org/abs/2601.23247 | Academic Papers | svg |
c2a5421b38de1b21373e28ea10ceaf326d298b0e208bc17ecfe41cfaf803acf0 | 2026-02-02T00:00:00-05:00 | Theoretical Challenges in Learning for Branch-and-Cut | arXiv:2601.23249v1 Announce Type: new Abstract: Machine learning is increasingly used to guide branch-and-cut (B&C) for mixed-integer linear programming by learning score-based policies for selecting branching variables and cutting planes. Many approaches train on local signals from lookahead heuristics such as str... | https://arxiv.org/abs/2601.23249 | Academic Papers | svg |
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