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b15c7082beed48db63304eb32977aab0fed358f3e6c23a431f3b7a899b55ab43 | 2026-02-02T00:00:00-05:00 | Geometric Quantization by Paths, Part III: The Metaplectic Anomaly | arXiv:2601.23259v1 Announce Type: new Abstract: In the previous parts of this work, we established the Prequantum Groupoid $\mathbf{T}_\omega$ as the universal geometric container for quantum mechanics. This approach, which we call the "Geometric Quantization by Paths" (GQbP) framework, replaces the traditional constru... | https://arxiv.org/abs/2601.23259 | Academic Papers | svg |
4edd0702b5ab316dba7350ab94e86981769d99460e40632658be2b2090e6d33b | 2026-02-02T00:00:00-05:00 | On graphs with girth at least five achieving Steffen's edge coloring bound | arXiv:2601.23274v1 Announce Type: new Abstract: Vizing and Gupta showed that the chromatic index $\chi'(G)$ of a graph $G$ is bounded above by $\Delta(G) + \mu(G)$, where $\Delta(G)$ and $\mu(G)$ denote the maximum degree and the maximum multiplicity of $G$, respectively. Steffen refined this bound, proving that $\chi'... | https://arxiv.org/abs/2601.23274 | Academic Papers | svg |
23ff4c96f7fa2358a0e6e71f1fad75aff9ab16a2274476e19f6218a9c1912d6e | 2026-02-02T00:00:00-05:00 | Variational Tail Bounds for Norms of Random Vectors and Matrices | arXiv:2503.17300v4 Announce Type: cross Abstract: We propose a variational tail bound for norms of random vectors under moment assumptions on their one-dimensional marginals. A simplified version of the bound that parametrizes the ``aggregating distribution'' using a certain pushforward of the Gaussian distribution is ... | https://arxiv.org/abs/2503.17300 | Academic Papers | svg |
47640ab38559e41b9fc49da7ef6b6bdcd55ffbf53cd197c441175771079663b7 | 2026-02-02T00:00:00-05:00 | Optimizing Shanghai's Household Waste Recycling Collection Program by Decision-Making based on Mathematical Modeling | arXiv:2507.03844v1 Announce Type: cross Abstract: In this article, we will discuss the optimization of Shanghai's recycling collection program, with the core of the task as making a decision among the choice of the alternatives. We will be showing a vivid and comprehensive application of the classical mathematical mult... | https://arxiv.org/abs/2507.03844 | Academic Papers | svg |
c48869df8c27f6b7b88bbffad329c656a3ac77ead176f9843efd2d2596510d9b | 2026-02-02T00:00:00-05:00 | Emergent spatial organization of competing species under environmental stress and cooperation | arXiv:2601.22177v1 Announce Type: cross Abstract: Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability, pollution, resource heterogeneity,... | https://arxiv.org/abs/2601.22177 | Academic Papers | svg |
3e8d476d8f5313968386061c539b56f6cc88cdf1b05c3c2197a3bea536ff3b82 | 2026-02-02T00:00:00-05:00 | Efficient learning of logical noise from syndrome data | arXiv:2601.22286v1 Announce Type: cross Abstract: Characterizing errors in quantum circuits is essential for device calibration, yet detecting rare error events requires a large number of samples. This challenge is particularly severe in calibrating fault-tolerant, error-corrected circuits, where logical error probabil... | https://arxiv.org/abs/2601.22286 | Academic Papers | svg |
87c0e3fe2ae76b5119649569eaa00201235cff065f9ab758e1ec686a05b433b2 | 2026-02-02T00:00:00-05:00 | Quantum bootstrap product codes | arXiv:2601.22363v1 Announce Type: cross Abstract: Product constructions constitute a powerful method for generating quantum CSS codes, yielding celebrated examples such as toric codes and asymptotically good low-density parity check (LDPC) codes. Since a CSS code is fully described by a chain complex, existing product ... | https://arxiv.org/abs/2601.22363 | Academic Papers | svg |
fd46ba5e64febb245aa946363d044ee81d25404d011004379de70bd2ee91bef8 | 2026-02-02T00:00:00-05:00 | Spin quantum Hall transition on random networks: exact critical exponents via quantum gravity | arXiv:2601.22639v1 Announce Type: cross Abstract: We solve the problem of the spin quantum Hall transition on random networks using a mapping to classical percolation that focuses on the boundary of percolating clusters. Using tools of two-dimensional quantum gravity, we compute critical exponents that characterize thi... | https://arxiv.org/abs/2601.22639 | Academic Papers | svg |
140702b46423f2c28830949314ecc503575fb104db5e058edaf85c31ff87071f | 2026-02-02T00:00:00-05:00 | Geometric Selection Rules for Singularity Formation in Modified Gravity | arXiv:2601.22739v1 Announce Type: cross Abstract: We argue that the polynomial degeneracies of curvature invariants can act as geometric selection rules for spacetime singularities in modified theories of gravity. The degeneracies arise purely from the algebraic structure of Riemannian geometry and impose non-trivial c... | https://arxiv.org/abs/2601.22739 | Academic Papers | svg |
7e2bc0db8f563fb0561c5b222285e1a291788a8251ec6d4d268a348d81f039cb | 2026-02-02T00:00:00-05:00 | A Framework for the Bayesian Calibration of Complex and Data-Scarce Models in Applied Sciences | arXiv:2601.22890v1 Announce Type: cross Abstract: In this work, we review the theory involved in the Bayesian calibration of complex computer models, with particular emphasis on their use for applications involving computationally expensive simulations and scarce experimental data. In the article, we present a unified ... | https://arxiv.org/abs/2601.22890 | Academic Papers | svg |
23c04294104498e587d04eae8ad5223ec246a5343cc63d5353d4ff3c8dac2b5e | 2026-02-02T00:00:00-05:00 | A categorical account of the Metropolis-Hastings algorithm | arXiv:2601.22911v1 Announce Type: cross Abstract: Metropolis-Hastings (MH) is a foundational Markov chain Monte Carlo (MCMC) algorithm. In this paper, we ask whether it is possible to formulate and analyse MH in terms of categorical probability, using a recent involutive framework for MH-type procedures as a concrete c... | https://arxiv.org/abs/2601.22911 | Academic Papers | svg |
4fbfb786e9a555c91323c0eeeb0733ca7fdd0180e335da9e7c0b06584aef4c2e | 2026-02-02T00:00:00-05:00 | Open strings on knot complements | arXiv:2601.22922v1 Announce Type: cross Abstract: Using skein valued holomorphic curve counting techniques, we give a flow loop formula for the skein valued partition function of the Lagrangian knot complement of a fibered knot (of the $A$-model open topological strings with Lagrangian $A$-branes wrapping the complemen... | https://arxiv.org/abs/2601.22922 | Academic Papers | svg |
12fa46db082abb0b14362d4923af1b889246deda78ddbd9b28d61a11e64e8266 | 2026-02-02T00:00:00-05:00 | Causal spinfoam vertex for 4d Lorentzian quantum gravity | arXiv:2601.23162v1 Announce Type: cross Abstract: We introduce a new causal spinfoam vertex for $4$d Lorentzian quantum gravity. The causal data are encoded in Toller $T$-matrices, which add to Wigner $D$-matrices $T^{(+)}+T^{(-)}=D$, and for which we provide a Feynman $\mathrm{i}\varepsilon$ representation. We discuss... | https://arxiv.org/abs/2601.23162 | Academic Papers | svg |
a0d1363b2bc1365dd695445b74e531fd86e7c195c1708fe75f99f09c06e0cdd8 | 2026-02-02T00:00:00-05:00 | A unified theory of order flow, market impact, and volatility | arXiv:2601.23172v1 Announce Type: cross Abstract: We propose a microstructural model for the order flow in financial markets that distinguishes between {\it core orders} and {\it reaction flow}, both modeled as Hawkes processes. This model has a natural scaling limit that reconciles a number of salient empirical proper... | https://arxiv.org/abs/2601.23172 | Academic Papers | svg |
386d3e8105652fc1fcd22a65f5d276d440f0246a4f2ce8ddd9b720796d557976 | 2026-02-02T00:00:00-05:00 | Cubical approximation for directed topology I | arXiv:1012.0509v3 Announce Type: replace Abstract: Topological spaces - such as classifying spaces, configuration spaces and spacetimes - often admit extra temporal structure. Qualitative invariants on such directed spaces often are more informative yet more difficult to calculate than classical homotopy invariants on ... | https://arxiv.org/abs/1012.0509 | Academic Papers | svg |
2e42457864e9b80fb6a6d149d2058ef540f5a27f2093743f064c205f96a8c881 | 2026-02-02T00:00:00-05:00 | The Partition-Frequency Enumeration Matrix | arXiv:2102.04191v3 Announce Type: replace Abstract: We develop a calculus that gives an elementary approach to enumerate partition-like objects using an infinite upper-triangular number-theoretic matrix. We call this matrix the Partition-Frequency Enumeration (PFE) matrix. This matrix unifies a large number of results ... | https://arxiv.org/abs/2102.04191 | Academic Papers | svg |
ced94bc4851cca75042a62f214c89c9bc5b78f9d8345e2083829fdcdb9e47b3f | 2026-02-02T00:00:00-05:00 | On quasi-isospectrality of potentials and Riemannian manifolds | arXiv:2202.06110v5 Announce Type: replace Abstract: In this article, we study quasi-isospectral operators as a generalization of isospectral operators. The paper contains both expository material and original results. We begin by reviewing known results on isospectral potentials on compact manifolds and finite interval... | https://arxiv.org/abs/2202.06110 | Academic Papers | svg |
03df4170f5ff83d3fb2f2889a0001751e42de90c64ff298f806b1bebfebbcd41 | 2026-02-02T00:00:00-05:00 | On classification of continuous first order theories | arXiv:2205.12051v3 Announce Type: replace Abstract: We give several new characterizations of $IP$ (the independence property) and $SOP$ (the strict order property) for continuous first order logic and study their relations to the function theory and the Banach space theory. We suggest new dividing lines of unstable the... | https://arxiv.org/abs/2205.12051 | Academic Papers | svg |
646a251945e468aaef41fac0da9e1aca8a373db402be293951cb77bbc96e2c37 | 2026-02-02T00:00:00-05:00 | Ramification theory from homotopical point of view, I | arXiv:2206.02401v2 Announce Type: replace Abstract: We prove the compatibility of pushforward along a proper morphism of an \'{e}tale constructible sheaf and the pushforward of its characteristic cycle up to $p$-torsion. This was conjectured by Takeshi Saito. For this, we revisit the construction of the characteristic ... | https://arxiv.org/abs/2206.02401 | Academic Papers | svg |
5a6884b5174181555a87e9d8e0361a7e98f89218135b90dcd86104cc67edf6c8 | 2026-02-02T00:00:00-05:00 | Cardinal Optimizer (COPT) User Guide | arXiv:2208.14314v4 Announce Type: replace Abstract: Cardinal Optimizer is a high-performance mathematical programming solver for efficiently solving largescale optimization problem. This documentation provides basic introduction to the Cardinal Optimizer. | https://arxiv.org/abs/2208.14314 | Academic Papers | svg |
a0d3bc38e0edf1369143a5f9c58043f5b9ce30ae2b4cb5172efaf322ff77afe1 | 2026-02-02T00:00:00-05:00 | Conjectures on the reduced Kronecker coefficients | arXiv:2210.14668v4 Announce Type: replace Abstract: We formulate a series of conjectures on the stable tensor product of irreducible representations of symmetric groups, which are closely related to the reduced Kronecker coefficients. These conjectures are certain generalizations of Okounkov's conjecture on the log-con... | https://arxiv.org/abs/2210.14668 | Academic Papers | svg |
bbe2c2ac37bd1888f847a4777faecf07d95926d7ff325e6a41a455025b5b3a2c | 2026-02-02T00:00:00-05:00 | Optimal Stabilization of Periodic Orbits: A Symplectic Geometry Approach | arXiv:2211.11955v3 Announce Type: replace Abstract: In this contribution, the optimal stabilization problem of periodic orbits is studied via invariant manifold theory and symplectic geometry. The stable manifold theory for the optimal point stabilization case is generalized to the case of periodic orbit stabilization,... | https://arxiv.org/abs/2211.11955 | Academic Papers | svg |
0ab5285cc2e7c4dffbf77d8ec8a8f734e502e013606e70054bb2195791f9d555 | 2026-02-02T00:00:00-05:00 | A universal sheaf of algebras governing representations of vector fields on quasi-projective varieties | arXiv:2302.07918v2 Announce Type: replace Abstract: We construct a quasi-coherent sheaf of associative algebras which controls a category of $AV$-modules over a smooth quasi-projective variety. We establish a local structure theorem, proving that in \'etale charts these associative algebras decompose into a tensor prod... | https://arxiv.org/abs/2302.07918 | Academic Papers | svg |
a5959470dd4837d8a9ef1de202e09cffe4e4496680a5fbf796e0407b3775445c | 2026-02-02T00:00:00-05:00 | On the finite time blow-ups for solutions of nonlinear differential equations | arXiv:2303.10153v2 Announce Type: replace Abstract: We study systems of nonlinear ordinary differential equations where the dominant term, with respect to large spatial variables, causes blow-ups and is positively homogeneous of a degree $1+\alpha$ for some $\alpha>0$. We prove that the asymptotic behavior of a solutio... | https://arxiv.org/abs/2303.10153 | Academic Papers | svg |
64590f84b0ccdb84d6cecc54c36029a510983a7676e26ceead28790c19b604eb | 2026-02-02T00:00:00-05:00 | Higher topological complexity of Seifert fibered manifolds | arXiv:2304.01274v3 Announce Type: replace Abstract: In this article, we investigate the higher topological complexity of oriented Seifert fibered manifolds that are Eilenberg--MacLane spaces $K(G,1)$ with infinite fundamental group $G$. We first refine the cohomological lower bounds for higher topological complexity by... | https://arxiv.org/abs/2304.01274 | Academic Papers | svg |
ab7d71686996085a0beac0818f4aadaf31f6d6c6634a3263209f505af918bacf | 2026-02-02T00:00:00-05:00 | Amending the Lonely Runner Spectrum Conjecture | arXiv:2306.10417v2 Announce Type: replace Abstract: Let $||x||$ be the absolute distance from $x$ to the nearest integer. For a set of distinct positive integral speeds $v_1, \ldots, v_n$, we define its maximum loneliness, also known as the gap $\delta$, to be $$ML(v_1,\ldots,v_n) = \max_{t \in \mathbb{R}}\min_{1 \leq ... | https://arxiv.org/abs/2306.10417 | Academic Papers | svg |
a4bea096c14814fd13ccbcdd51509a7089ddb2fae14c5773a86e2d6d9fc9c2ef | 2026-02-02T00:00:00-05:00 | Tilings in quasi-random $k$-partite hypergraphs | arXiv:2306.10539v2 Announce Type: replace Abstract: Given $k\ge 2$ and two $k$-graphs ($k$-uniform hypergraphs) $F$ and $H$, an $F$-factor in $H$ is a set of vertex disjoint copies of $F$ that together cover the vertex set of $H$. Lenz and Mubayi were first to study the $F$-factor problems in quasi-random $k$-graphs wi... | https://arxiv.org/abs/2306.10539 | Academic Papers | svg |
d72286bcc2947772de21b7ff28f42cded04cfcc6e4d4ba93bb91c92e31cbf9c1 | 2026-02-02T00:00:00-05:00 | Quartic Gauss sums over primes and metaplectic theta functions | arXiv:2306.11875v5 Announce Type: replace Abstract: We improve 1987 estimates of Patterson for sums of quartic Gauss sums over primes. Our Type-I and Type-II estimates feature new ideas, including use of the quadratic large sieve over $\mathbb{Q}(i)$, and Suzuki's evaluation of the Fourier-Whittaker coefficients of qua... | https://arxiv.org/abs/2306.11875 | Academic Papers | svg |
454eef2a36a0f23a878b28a1b8ed7144b18629631e825ff151798f9206aef15b | 2026-02-02T00:00:00-05:00 | The center of the asymptotic Hecke category and unipotent character sheaves | arXiv:2307.07276v3 Announce Type: replace Abstract: In 2015, Lusztig [Bull. Inst. Math. Acad. Sin. (N.S.)10(2015), no.1, 1-72] showed that for a connected reductive group over an algebraic closure of a finite field the associated (geometric) Hecke category admits a truncation in a two-sided Kazhdan--Lusztig cell, makin... | https://arxiv.org/abs/2307.07276 | Academic Papers | svg |
1c1f37ca95de9616034c7b9cbc1c1d6cbcefcc0f84ca0bc1dd2cea458b4b8982 | 2026-02-02T00:00:00-05:00 | Logarithmic Asymptotic Relations Between $p$-Values and Mutual Information | arXiv:2308.14735v2 Announce Type: replace Abstract: We establish a precise connection between statistical significance in dependence testing and information-theoretic dependence as quantified by Shannon mutual information (MI). In the absence of prior distributional information, we consider a maximum-entropy model and ... | https://arxiv.org/abs/2308.14735 | Academic Papers | svg |
565f8326d1f18b5ce26a3c6a74fc279fe9908a710cab4d3de7a774eb8f5a1c03 | 2026-02-02T00:00:00-05:00 | Frank--Wolfe algorithms for piecewise star-convex functions with a nonsmooth difference-of-convex structure | arXiv:2308.16444v4 Announce Type: replace Abstract: In the present paper, we formulate two versions of Frank--Wolfe algorithm or conditional gradient method to solve the DC optimization problem with an adaptive step size. The DC objective function consists of two components; the first is thought to be differentiable wi... | https://arxiv.org/abs/2308.16444 | Academic Papers | svg |
0fa8046c2b7cbfc44d5ffa091317b3bd9c457509d2fdfb7ea4a0b445cbcb981d | 2026-02-02T00:00:00-05:00 | High-Dimensional Bernstein Von-Mises Theorems for Covariance and Precision Matrices | arXiv:2309.08556v3 Announce Type: replace Abstract: This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis focuses on establishing asymptotic... | https://arxiv.org/abs/2309.08556 | Academic Papers | svg |
e834b3bb80c9d231cd34cea0ef6bb41e443204918096ae6e7c0877b0a007975e | 2026-02-02T00:00:00-05:00 | Imaginaries, products and the adele ring | arXiv:2309.11678v3 Announce Type: replace Abstract: We describe the imaginary sorts of infinite products in terms of imaginary sorts of the factors. We extend the result to certain reduced powers and then to infinite products $\prod_{i\in I} M_i$ enriched with a predicate for the ideal of finite subsets of $I$. As a sp... | https://arxiv.org/abs/2309.11678 | Academic Papers | svg |
fa718c1f6de10ccc484a62bff1151b99b239da3996fbc3aaf15271597711be20 | 2026-02-02T00:00:00-05:00 | Cubical Approximation for Directed Topology II | arXiv:2309.16619v4 Announce Type: replace Abstract: The paper establishes an equivalence between directed homotopy categories of (diagrams of) cubical sets and (diagrams of) directed topological spaces. This equivalence both lifts and extends an equivalence between classical homotopy categories of cubical sets and topo... | https://arxiv.org/abs/2309.16619 | Academic Papers | svg |
65cfe4d86791b48c47bb68070eb4181e966549d6b931a89a5d2113dc7959311a | 2026-02-02T00:00:00-05:00 | Balanced metrics, Zoll deformations and isosystolic inequalities in $\mathbb{C}P^n$ | arXiv:2310.10877v2 Announce Type: replace Abstract: The k-systole of a Riemannian manifold is the infimum of the volume over all homologically non-trivial k-cycles. In this paper we discuss the behavior of the dimension two and co-dimension two systole of the complex projective space for distinguished classes of metric... | https://arxiv.org/abs/2310.10877 | Academic Papers | svg |
54a3df4dea48c7dbe3125f3f6c729328106fb985cd3f885b6472c9c5bd82d1e4 | 2026-02-02T00:00:00-05:00 | Optimal sampling for stochastic and natural gradient descent | arXiv:2402.03113v2 Announce Type: replace Abstract: We consider the problem of optimising the expected value of a loss functional over a nonlinear model class of functions, assuming that we have only access to realisations of the gradient of the loss. This is a classical task in statistics, machine learning and physics... | https://arxiv.org/abs/2402.03113 | Academic Papers | svg |
fb94f9e49cd934642d139c2847d0b64d32b75bc5d9ed7e581801bfefa92d41b6 | 2026-02-02T00:00:00-05:00 | Cyclotomic Factors and LRS-Degeneracy | arXiv:2403.08751v4 Announce Type: replace Abstract: We present three new, practical algorithms for polynomials in $\mathbb{Z}[x]$: one to test if a polynomial is cyclotomic, one to determine which cyclotomic polynomials are factors, and one to determine whether the given polynomial is LRS-degenerate. A polynomial is "L... | https://arxiv.org/abs/2403.08751 | Academic Papers | svg |
ca50342dfe4f0093065ceba8d714d253bcc1e0b4419323b2a36ebe1c9b3c2545 | 2026-02-02T00:00:00-05:00 | Quasi-invariant lifts of completely positive maps for groupoid actions | arXiv:2405.07859v2 Announce Type: replace Abstract: Let $G$ be a locally compact, Hausdorff, second countable groupoid and $A$ be a separable, $C_0(G^{(0)})$-nuclear, $G$-$C^*$-algebra. We prove the existence of quasi-invariant, completely positive and contractive lifts for equivariant, completely positive and contract... | https://arxiv.org/abs/2405.07859 | Academic Papers | svg |
88e10ef0178caf1e7616c7cb0c7e1f2fe33d53cb6231a6fe581d26b95a69ee75 | 2026-02-02T00:00:00-05:00 | Asymptotic vanishing of cohomology in triangulated categories | arXiv:2405.12763v2 Announce Type: replace Abstract: Given a graded-commutative ring acting centrally on a triangulated category, our main result shows that if cohomology of a pair of objects of the triangulated category is finitely generated over the ring acting centrally, then the asymptotic vanishing of the cohomolog... | https://arxiv.org/abs/2405.12763 | Academic Papers | svg |
64fa69c606749080135ceccda86357218f509de08fe826c552f5e48074a9db77 | 2026-02-02T00:00:00-05:00 | SLE and its partition function in multiply connected domains via the Gaussian Free Field and restriction measures | arXiv:2405.20148v2 Announce Type: replace Abstract: One way to uniquely define Schramm-Loewner Evolution (SLE) in multiply connected domains is to use the restriction property. This gives an implicit definition of a $\sigma$-finite measure on curves; yet it is in general not clear how to construct such measures nor whe... | https://arxiv.org/abs/2405.20148 | Academic Papers | svg |
d1be80a5d754322c8ecebe6da55d3bc6545c7dd99d46a053021c065cae2374b2 | 2026-02-02T00:00:00-05:00 | Enumeration of minimal transversals of hypergraphs of bounded VC-dimension | arXiv:2407.00694v4 Announce Type: replace Abstract: We consider the problem of enumerating all minimal transversals (also called minimal hitting sets) of a hypergraph $\mathcal{H}$. An equivalent formulation of this problem known as the \emph{transversal hypergraph} problem (or \emph{hypergraph dualization} problem) is... | https://arxiv.org/abs/2407.00694 | Academic Papers | svg |
1af3e5ebb14413d4cc815044104a8d752d8a50b6c3032c5ff86417025805ef6d | 2026-02-02T00:00:00-05:00 | A unified theory of regular functions of a hypercomplex variable | arXiv:2408.01523v2 Announce Type: replace Abstract: This work proposes a unified theory of regularity in one hypercomplex variable: the theory of $T$-regular functions. In the special case of quaternion-valued functions of one quaternionic variable, this unified theory comprises Fueter-regular functions, slice-regular ... | https://arxiv.org/abs/2408.01523 | Academic Papers | svg |
ad335e9d14ee5ec2e42d39d2093910f7880b8f3a45f779ee92931c9328ff797a | 2026-02-02T00:00:00-05:00 | Homogenization of Poisson-Nernst-Planck equations for multiple species in a porous medium | arXiv:2408.08831v3 Announce Type: replace Abstract: We rigorously derive a homogenized model for the Poisson--Nernst--Planck (PNP) equations for the case of multiple species defined on a periodic porous medium in spatial dimensions two and three. This extends the previous homogenization results for the PNP equations co... | https://arxiv.org/abs/2408.08831 | Academic Papers | svg |
4c81044926293a33ae700b9b87a34a26fc66a25d68c94017a295df0ff3182030 | 2026-02-02T00:00:00-05:00 | Lannes' $T$-functor and mod-$p$ cohomology of profinite groups | arXiv:2408.12488v2 Announce Type: replace Abstract: The Lannes-Quillen theorem relates the mod-$p$ cohomology of a finite group $G$ with the mod-$p$ cohomology of centralizers of abelian elementary $p$-subgroups of $G$, for $p>0$ a prime number. This theorem was extended to profinite groups whose mod-$p$ cohomology alg... | https://arxiv.org/abs/2408.12488 | Academic Papers | svg |
628af47f8e6a9596708a6853d2030fb4a5f4fc571d25dd1f5b24bc85581bf7ea | 2026-02-02T00:00:00-05:00 | Multivariate functorial difference | arXiv:2409.09494v2 Announce Type: replace Abstract: Partial difference operators for a large class of functors between presheaf categories are introduced, extending our difference operator from \cite{Par24} to the multivariable case. These combine into the Jacobian profunctor which provides the setting for a lax chain ... | https://arxiv.org/abs/2409.09494 | Academic Papers | svg |
5ca7b65bdd6f85010fb8142bfc6a34324ac5cffa585677022d3dd6c8c19c0a17 | 2026-02-02T00:00:00-05:00 | Positively closed $Sh(B)$-valued models | arXiv:2409.11231v3 Announce Type: replace Abstract: We study positively closed and strongly positively closed topos-valued models of coherent theories. Positively closed is a global notion (it is defined in terms of all possible outgoing homomorphisms), while strongly positively closed is a local notion (it only concer... | https://arxiv.org/abs/2409.11231 | Academic Papers | svg |
a6ab91406717f5cb75b1c6b91d1d6e0d7eb44bbe82b9dc264fff8c5b760a6886 | 2026-02-02T00:00:00-05:00 | On the tails of log-concave density estimators | arXiv:2409.17910v3 Announce Type: replace Abstract: It is shown that the nonparametric maximum likelihood estimator of a univariate log-concave probability density satisfies desirable consistency properties in the tail regions. Specifically, let $P$ and $f$ denote the true underlying distribution and density, respectiv... | https://arxiv.org/abs/2409.17910 | Academic Papers | svg |
4342f52debdfd1138b15a18b3f31d49bea3830586852854eccc610e1129d7eea | 2026-02-02T00:00:00-05:00 | On the Uniqueness of the Norton-Sullivan Quasiconformal extension | arXiv:2409.19805v2 Announce Type: replace Abstract: We show that the extension map \[ \mathcal{E}_{NS}(f)(z)=\frac{f(x+y)+f(x-y)}{2}+i\frac{f(x+y)-f(x-y)}{2}\mbox{ for all }z=x+iy\in\mathbb{H}\,, \] defined by Norton and Sullivan in '96, is the only locally linear extension map taking bi-Lipschitz functions on $\mathbb... | https://arxiv.org/abs/2409.19805 | Academic Papers | svg |
f17e3af352f01e999a27b5627bdbda35123f1388e14157eb4b8f3157b3d73970 | 2026-02-02T00:00:00-05:00 | Large Deviations of Mean-Field Jump-Markov Processes on Structured Sparse Disordered Graphs | arXiv:2410.13682v2 Announce Type: replace Abstract: We prove a Large Deviation Principle for {\color{blue} jump-Markov } Processes on sparse large disordered network with disordered connectivity. The network is embedded in a geometric space, with the probability of a connection a (scaled) function of the spatial positi... | https://arxiv.org/abs/2410.13682 | Academic Papers | svg |
7bd26e8715944660910e8135cc315466fbd7d5843544cc9eb7daeeb022aab389 | 2026-02-02T00:00:00-05:00 | Zarankiewicz bounds from distal regularity lemma | arXiv:2410.13695v3 Announce Type: replace Abstract: Since K\H{o}v\'ari, S\'os, and Tur\'an proved upper bounds for the Zarankiewicz problem in 1954, much work has been undertaken to improve these bounds, and some have done so by restricting to particular classes of graphs. In 2017, Fox, Pach, Sheffer, Suk, and Zahl pro... | https://arxiv.org/abs/2410.13695 | Academic Papers | svg |
6fa1fa729fc2de2ca97b3c645197c3ee7e01f08b4cb435b135ed1b4bb2a6fa02 | 2026-02-02T00:00:00-05:00 | State Estimation Using Sparse DEIM and Recurrent Neural Networks | arXiv:2410.15982v3 Announce Type: replace Abstract: Sparse Discrete Empirical Interpolation Method (S-DEIM) was recently proposed for state estimation in dynamical systems when only a sparse subset of the state variables can be observed. The S-DEIM estimate involves a kernel vector whose optimal value is inferred throu... | https://arxiv.org/abs/2410.15982 | Academic Papers | svg |
9019772725da3a3efd6920f39049806d4e391c14f682bc87864b4898f36d430f | 2026-02-02T00:00:00-05:00 | Gelfand-Fuks cohomology of vector fields on algebraic varieties | arXiv:2410.20316v2 Announce Type: replace Abstract: For an affine algebraic variety, we introduce algebraic Gelfand-Fuks cohomology of polynomial vector fields with coefficients in differentiable $AV$-modules. Its complex is given by cochains that are differential operators in the sense of Grothendieck. Using the jets ... | https://arxiv.org/abs/2410.20316 | Academic Papers | svg |
06f487da2ce5ccf4b8168a6641a19a61289adae25a10f37bbd486f5ad4450718 | 2026-02-02T00:00:00-05:00 | On uniqueness in structured model learning | arXiv:2410.22009v3 Announce Type: replace Abstract: This paper addresses the problem of uniqueness in learning physical laws for systems of partial differential equations (PDEs). Contrary to most existing approaches, it considers a framework of structured model learning, where existing, approximately correct physical m... | https://arxiv.org/abs/2410.22009 | Academic Papers | svg |
34d0f6fcb5b8c25c0a20f91c22850236366cd1dad8c324db3e375e87d6773f5c | 2026-02-02T00:00:00-05:00 | Generalized random processes related to Hadamard operators and Le Roy measures | arXiv:2410.22880v3 Announce Type: replace Abstract: The definition of generalized random processes in Gel'fand sense allows to extend well-known stochastic models, such as the fractional Brownian motion, and study the related fractional pde's, as well as stochastic differential equations in distributional sense. By ana... | https://arxiv.org/abs/2410.22880 | Academic Papers | svg |
3001454712d321b529efd2a58648dad3ca0d8d37085bfba9843493d62f98d91d | 2026-02-02T00:00:00-05:00 | Index estimates for constant mean curvature surfaces in three-manifolds by energy comparison | arXiv:2411.02932v2 Announce Type: replace Abstract: We prove a linear upper bound on the Morse index of closed constant mean curvature (CMC) surfaces in orientable three-manifolds in terms of genus, number of branch points and a Willmore-type energy. | https://arxiv.org/abs/2411.02932 | Academic Papers | svg |
052c157d8c30154248835bfa67dae554b1b3b8ae95fc15843d808daaa8042478 | 2026-02-02T00:00:00-05:00 | Well-Posedness of the Linear Regularized 13-Moment Equations Using Tensor-Valued Korn Inequalities | arXiv:2501.14108v2 Announce Type: replace Abstract: In this paper, we finally prove the well-posedness of the linearized R13 moment model, which describes, e.g., rarefied gas flows. As an extension of the classical fluid equations, moment models are robust and have been frequently used, yet they are challenging to anal... | https://arxiv.org/abs/2501.14108 | Academic Papers | svg |
57154cccf5b9803c05dfbea046926ef05c903c6ce0ec17424be8e9a6449a70ed | 2026-02-02T00:00:00-05:00 | Families of singular algebraic varieties that are rationally elliptic spaces | arXiv:2501.17970v3 Announce Type: replace Abstract: We discuss families of hypersurfaces with isolated singularities in projective space with the property that the sum of the ranks of the rational homotopy and the homology groups is finite. They represent infinitely many distinct homotopy types with all hypersurfaces h... | https://arxiv.org/abs/2501.17970 | Academic Papers | svg |
b1a66250bfc905b9073d87c7bddbbf32b07ea929daa72ac471fb0af2a5e8a384 | 2026-02-02T00:00:00-05:00 | Inexact Moreau Envelope Lagrangian Method for Non-Convex Constrained Optimization under Local Error Bound Conditions on Constraint Functions | arXiv:2502.19764v2 Announce Type: replace Abstract: In this paper, we investigate how structural properties of the constraint system impact the oracle complexity of smooth non-convex optimization problems with convex inequality constraints over a simple polytope. In particular, we show that, under a local error bound c... | https://arxiv.org/abs/2502.19764 | Academic Papers | svg |
d43f2a3b3d408032cb164fa6132b1ea7ae5f5966166093041fe3db193194136f | 2026-02-02T00:00:00-05:00 | Dynamic Programming in Ordered Vector Space | arXiv:2503.06055v2 Announce Type: replace Abstract: New approaches to the theory of dynamic programming view dynamic programs as families of policy operators acting on partially ordered sets. In this paper, we extend these ideas by shifting from arbitrary partially ordered sets to ordered vector spaces. The integrated ... | https://arxiv.org/abs/2503.06055 | Academic Papers | svg |
fbdcb7b42a5790e9b5cf5f2ca060c219ed9ab909abeb0dcecca694dd8dd4df7a | 2026-02-02T00:00:00-05:00 | Supersimplicity and arithmetic progressions | arXiv:2503.08258v3 Announce Type: replace Abstract: The main motivation for this article is to explore the connections between the existence of certain combinatorial patterns (as in van der Corputs's theorem on arithmetic progressions of length $3$) with well-known tools and theorems for definable groups in simple theo... | https://arxiv.org/abs/2503.08258 | Academic Papers | svg |
abf898b1ec75cc1d9423edea3efeefcfe19a605c225e8578010f04e3640c14c2 | 2026-02-02T00:00:00-05:00 | Some Geometric Aspects Related to Lim's Condition | arXiv:2504.09464v2 Announce Type: replace Abstract: In their seminal work, Lau and Mah (1986) study $w^*$-normal structure in the space of operators $\mathcal{L}(H)$, on a Hilbert space $H$, using a geometric property of the dual unit ball called Lim's condition. In this paper, we study a weaker form of Lim's condition... | https://arxiv.org/abs/2504.09464 | Academic Papers | svg |
add656c85a6a014aa999524475b8866204998b5361e8f2a18ca9f8139580ebf3 | 2026-02-02T00:00:00-05:00 | On anti-coproximinal and strongly anti-coproximinal subspaces of function spaces | arXiv:2504.13464v2 Announce Type: replace Abstract: The purpose of this article is to study the anti-coproximinal and strongly anti-coproximinal subspaces of the Banach space of all bounded (continuous) functions. We obtain a tractable necessary condition for a subspace to be stronsgly anti-coproximinal. We prove that ... | https://arxiv.org/abs/2504.13464 | Academic Papers | svg |
fdf3415be737f6e1117758bea7c498aa39da821a59e929623021604051378f4b | 2026-02-02T00:00:00-05:00 | Geometry of regular semisimple Lusztig varieties | arXiv:2504.15868v2 Announce Type: replace Abstract: Lusztig varieties are subvarieties in flag manifolds $G/B$ associated to an element $w$ in the Weyl group $W$ and an element $x$ in $G$, introduced in Lusztig's papers on character sheaves. We study the geometry of these varieties when $x$ is regular semisimple. In th... | https://arxiv.org/abs/2504.15868 | Academic Papers | svg |
ad98f0e66e2791ffbc0e0830781a0836615b03947c48f7caa7f1eee145e59ed4 | 2026-02-02T00:00:00-05:00 | Discrete analogues of second-order Riesz transforms | arXiv:2504.18739v2 Announce Type: replace Abstract: Discrete analogues of classical operators in harmonic analysis have been widely studied, revealing deep connections with areas such as ergodic theory and analytic number theory. This line of research is commonly known as \emph{Discrete Analogues in Harmonic Analysis (... | https://arxiv.org/abs/2504.18739 | Academic Papers | svg |
2b31a92ee2c9684bc9d9e453733ff288b786cc162b0d4c8cefd5e6450fe20de3 | 2026-02-02T00:00:00-05:00 | Weakly Einstein curvature tensors | arXiv:2504.18752v2 Announce Type: replace Abstract: We classify weakly Einstein algebraic curvature tensors in an oriented Euclidean 4-space, defined by requiring that the three-index contraction of the curvature tensor against itself be a multiple of the inner product. This algebraic formulation parallels the geometri... | https://arxiv.org/abs/2504.18752 | Academic Papers | svg |
f9cc38c952e7785b30279a0250d441dfa90bfe3d79358b9158665612cc964823 | 2026-02-02T00:00:00-05:00 | Sharp asymptotics for $N$-point correlation functions of coalescing heavy-tailed random walk | arXiv:2505.05000v2 Announce Type: replace Abstract: We study a system of coalescing continuous-time random walks starting from every site on $\mathbb{Z}$, where the jump increments lie in the domain of attraction of an $\alpha$-stable distribution with $\alpha\in(0,1]$. We establish sharp asymptotics for the $N$-point ... | https://arxiv.org/abs/2505.05000 | Academic Papers | svg |
81774848c78b48231475e070fc6ff5f87f443d1cd580dd8d982dc5a481f25ce3 | 2026-02-02T00:00:00-05:00 | A Dantzig-Wolfe Decomposition Method for Quasi-Variational Inequalities | arXiv:2505.08108v2 Announce Type: replace Abstract: We propose an algorithm to solve quasi-variational inequality problems, based on the Dantzig-Wolfe decomposition paradigm. Our approach solves in the subproblems variational inequalities, which is a simpler problem, while restricting quasi-variational inequalities in ... | https://arxiv.org/abs/2505.08108 | Academic Papers | svg |
a88da1bd6b0da8b0db6e3f87671ca6d7f000fcd3346b7cbea75da8a60400dbbf | 2026-02-02T00:00:00-05:00 | Bias-Optimal Bounds for SGD: A Computer-Aided Lyapunov Analysis | arXiv:2505.17965v2 Announce Type: replace Abstract: The non-asymptotic analysis of Stochastic Gradient Descent (SGD) typically yields bounds that decompose into a bias term and a variance term. In this work, we focus on the bias component and study the extent to which SGD can match the optimal convergence behavior of d... | https://arxiv.org/abs/2505.17965 | Academic Papers | svg |
a94eefd88b5806b5a5efc5bd4d21727bd85c0b1c1ffe2b0ff9ffa400ab64defe | 2026-02-02T00:00:00-05:00 | Calder\'{o}n-Zygmund estimates for double phase problems with matrix weights | arXiv:2505.20856v3 Announce Type: replace Abstract: We establish an optimal Calder\'{o}n-Zygmund theory for nonuniformly elliptic double phase problems with matrix weights. For $11$, $$ (|\M F|^p+a(x)|\M F|^q)\in L^\gamma_{\mathrm{loc}} \;\Longrightarrow\; (|\M Du|^p+a(x)|\M Du|^q)\in L^\gamma_{\mathrm{loc}}. $$ Our ar... | https://arxiv.org/abs/2505.20856 | Academic Papers | svg |
26f86005980561b45bba2c26c3d66a4d1c2910096640c9fa8ea1bf36e26afeb0 | 2026-02-02T00:00:00-05:00 | Classification of exact structures using the Ziegler spectrum | arXiv:2506.02304v2 Announce Type: replace Abstract: Given an idempotent complete additive category, we show the there is an explicitly constructed topological space such that the lattice of exact substructures is anti-isomorphic to the lattice of closed subsets. In the special case that the additive category has weak c... | https://arxiv.org/abs/2506.02304 | Academic Papers | svg |
76d5c5e911b9e7909c829a3498c9cacea891c8f685bbaebe15529bce13eaa1d1 | 2026-02-02T00:00:00-05:00 | On some results of Harish-Chandra for representations of p-adic groups, extended to their central extensions | arXiv:2506.21334v2 Announce Type: replace Abstract: The aim of this article is to give a complete proof of results of Harish-Chandra linking the irreducibility of parabolic induction of a supercuspidal representation of a p-adic group to the analytic behavior of the mu-function of Harish-Chandra and to show that the pr... | https://arxiv.org/abs/2506.21334 | Academic Papers | svg |
e072d939df577f0f7fba6d1e1e11f19084829f027aea71637f7b26e164d8883c | 2026-02-02T00:00:00-05:00 | Illumination number of 3-dimensional cap bodies | arXiv:2507.08712v2 Announce Type: replace Abstract: The illumination conjecture asserts that any convex body in $n$-dimensional Euclidean space can be illuminated by at most $2^n$ external light sources or parallel beams of light. Despite recent progress on the illumination conjecture, it remains open in general, as we... | https://arxiv.org/abs/2507.08712 | Academic Papers | svg |
6e3c7aaa0ce018e2c5ce72cd2cd130bbca4102b575d8a9438e0f611aaf75ae18 | 2026-02-02T00:00:00-05:00 | Twisted periods of modular forms | arXiv:2507.17041v2 Announce Type: replace Abstract: Let $S_k$ denote the space of cusp forms of weight $k$ and level one. For $0\leq t\leq k-2$ and primitive Dirichlet character $\chi$ mod $D$, we introduce twisted periods $r_{t,\chi}$ on $S_k$. We show that for a fixed natural number $n$, if $k$ is sufficiently large ... | https://arxiv.org/abs/2507.17041 | Academic Papers | svg |
a5b19c8ebe6f6b9ad8738066e0d8d0c373f52cfa43e2e65f8b4b8f99124939c0 | 2026-02-02T00:00:00-05:00 | Self-Similar Solutions to the Hele-Shaw Problem with Surface Tension | arXiv:2507.19443v2 Announce Type: replace Abstract: We consider the Hele-Shaw problem with surface tension in an infinite domain. We prove the existence of a family of self-similar solutions. At $t=0$, these solutions have a corner of angle $\theta$ with $ 0 0$, the solutions are smooth. | https://arxiv.org/abs/2507.19443 | Academic Papers | svg |
825df2bb03cc0e2d87875d70f2732173704dc50b77eecad8c6351faf7a0ec8c3 | 2026-02-02T00:00:00-05:00 | A Generalized Analytical Framework for the Nonlinear Best-Worst Method | arXiv:2508.06048v2 Announce Type: replace Abstract: The nonlinear model of the best-worst method frequently produces multiple optimal weight sets, which are conventionally determined through optimization software. While an analytical approach exists that provides both a closed-form expression for the optimal interval-w... | https://arxiv.org/abs/2508.06048 | Academic Papers | svg |
a99b650145a08cca2e62167b50492bcc89bed2562daf96e837af254320dc71d3 | 2026-02-02T00:00:00-05:00 | A bottleneck model with shared autonomous vehicles: Scale economies and price regulations | arXiv:2508.08848v2 Announce Type: replace Abstract: This study examines how scale economies in the operation of shared autonomous vehicles (SAVs) affect the efficiency of a transportation system where SAVs coexist with normal vehicles (NVs). We develop a bottleneck model where commuters choose their departure times and... | https://arxiv.org/abs/2508.08848 | Academic Papers | svg |
542146290d8b2167d1fb55160f00f6cdbbc9059db7354a5135be111870d29c97 | 2026-02-02T00:00:00-05:00 | Relative braid group symmetries on modified iquantum groups and their modules | arXiv:2508.12041v2 Announce Type: replace Abstract: We present a comprehensive generalization of Lusztig's braid group symmetries for quasi-split iquantum groups. Specifically, we give 3 explicit rank one formulas for symmetries acting on integrable modules over a quasi-split iquantum group of arbitrary Kac-Moody type ... | https://arxiv.org/abs/2508.12041 | Academic Papers | svg |
d0919ee975349cbe9ee7509b0e87a196bf1da897c57792c762b543bc0b2e8274 | 2026-02-02T00:00:00-05:00 | Cycles of Length 4 or 8 in Graphs with Diameter 2 and Minimum Degree at Least 3 | arXiv:2508.19302v4 Announce Type: replace Abstract: In this short note it is shown that every graph of diameter 2 and minimum degree at least 3 contains a cycle of length 4 or 8. This result contributes to the study of the Erd\H{o}s-Gy\'arf\'as Conjecture by confirming it for the class of diameter-2 graphs. | https://arxiv.org/abs/2508.19302 | Academic Papers | svg |
87a0db0279e84acd030575ed9350bfc36cba7a20f90df0fa3ff78f0ca7e95483 | 2026-02-02T00:00:00-05:00 | The Tautochrone of Huygens and Abel: From Constructive Geometry to Fractional Calculus | arXiv:2509.05308v2 Announce Type: replace Abstract: In this paper, we explore the connections between Christiaan Huygens and Niels Henrik Abel through the tautochrone problem. The problem -- determining the curve along which a particle descends under gravity in the same time, regardless of its starting point -- has bee... | https://arxiv.org/abs/2509.05308 | Academic Papers | svg |
20e5a7d4777c6eaba630c76fd975d6512e9c1274785fbda20683b5041a64d5a2 | 2026-02-02T00:00:00-05:00 | Carryless Pairing: Additive Pairing in the Fibonacci Basis | arXiv:2509.10382v4 Announce Type: replace Abstract: We define a pairing map $\pi : \mathbb{N}^2\to\mathbb{N}$ that encodes $x$ and $y$ into disjoint index bands inside the Zeckendorf support of a single integer. Evaluation and inversion use only addition, comparison, and bounded scans of supports; no multiplication, fa... | https://arxiv.org/abs/2509.10382 | Academic Papers | svg |
370c33304b1389fbf51560f63e5fbbea72d5bf172f7ec2bd451e3395d13d04f8 | 2026-02-02T00:00:00-05:00 | Rough stochastic filtering | arXiv:2509.11825v2 Announce Type: replace Abstract: This article is concerned with the well-posedness of the "filtering equations", due to Zakai and Kushner-Stratonovich, arising in nonlinear stochastic filtering. In general situations, notably in correlated diffusion models and when signal coefficients depend on the o... | https://arxiv.org/abs/2509.11825 | Academic Papers | svg |
bdd44085ae3312f7af402375f6dd4d1c65b64f27dc8155c1fca5ed0aa2fb97ab | 2026-02-02T00:00:00-05:00 | Haussdorff consistency of MLE in folded normal and Gaussian mixtures | arXiv:2509.12206v2 Announce Type: replace Abstract: We develop a constant-tracking likelihood theory for two nonregular models: the folded normal and finite Gaussian mixtures. For the folded normal, we prove boundary coercivity for the profiled likelihood, show that the profile path of the location parameter exists and... | https://arxiv.org/abs/2509.12206 | Academic Papers | svg |
75b15bd62b939276d3d91faa35d9d0b4d89bd006ee8f9d2a8ff9e2f0ff121c5b | 2026-02-02T00:00:00-05:00 | Error Analysis of Discrete Flow with Generator Matching | arXiv:2509.21906v2 Announce Type: replace Abstract: Discrete flow models offer a powerful framework for learning distributions over discrete state spaces and have demonstrated superior performance compared to the discrete diffusion models. However, their convergence properties and error analysis remain largely unexplor... | https://arxiv.org/abs/2509.21906 | Academic Papers | svg |
717de269c2d9fa1eff65720ff5d9b681675e7d061155f3a007b235042d579b91 | 2026-02-02T00:00:00-05:00 | Abstract Integration in Net Convergence Structures | arXiv:2509.24430v2 Announce Type: replace Abstract: In this article, we propose a general theory of integration of the Riemann and Lebesgue types with respect to arbitrary measures and functions, connected by a continuous bilinear product, with values in abstract vector spaces endowed with a convergence structure given... | https://arxiv.org/abs/2509.24430 | Academic Papers | svg |
2dce6f43353362f9997a636c225e50bdde4590de098d8d85f445d7b93f1df7eb | 2026-02-02T00:00:00-05:00 | Multifractality in the Tree of Life: A Branching-Process RIFS Proof | arXiv:2509.26637v2 Announce Type: replace Abstract: We study a branching-process random iterated function system (RIFS) defined by a recursive replacement of leaves by finite subtrees at strictly smaller contraction scales. This construction yields a tree-valued, infinite-depth random geometry that unifies classical br... | https://arxiv.org/abs/2509.26637 | Academic Papers | svg |
9cf3a84fb82c4111b8572e8b340b0d2f02bbe637866d98702456bd531cc236fd | 2026-02-02T00:00:00-05:00 | The Magmoid of Normalized Stochastic Kernels | arXiv:2510.01131v2 Announce Type: replace Abstract: Normalization, $D(X + 1) \to D(X) + 1$, is almost a distributive law; but because one of the distributive law axioms only holds up-to-idempotent, it yields a non-associative composition of normalized kernels. We introduce the Markov magmoid of normalized stochastic ke... | https://arxiv.org/abs/2510.01131 | Academic Papers | svg |
971c77c46d8f801d7b87668342bd137d689206aec4b77e888b3dbe65a4436099 | 2026-02-02T00:00:00-05:00 | Absolutely Abelian Hilbert Class Fields and $\ell-$torsion conjecture | arXiv:2510.10725v2 Announce Type: replace Abstract: There are several recent works where authors have shown that number fields $K$ with `sufficiently many' units and cyclic class group contain a Euclidean ideal class provided the Hilbert class field $H(K)$ is absolutely abelian. In this article, we explore the latter h... | https://arxiv.org/abs/2510.10725 | Academic Papers | svg |
7ba887ebde4f609b5c84f00455f3a3d00f86873d753b8c1d74e8247a409a3715 | 2026-02-02T00:00:00-05:00 | On estimation of weighted cumulative residual Tsallis entropy for complete and censored samples | arXiv:2510.12442v2 Announce Type: replace Abstract: Recently, weighted cumulative residual Tsallis entropy has been introduced in the literature as a generalization of weighted cumulative residual entropy. We study some new properties of weighted cumulative residual Tsallis entropy measure. Next, we propose some non-pa... | https://arxiv.org/abs/2510.12442 | Academic Papers | svg |
39668622dd497f24db4f6d77026e9c8a8a243218baf73be6edc1fc3d9b2399c2 | 2026-02-02T00:00:00-05:00 | The spectrum of Dirichlet-to-Neumann maps for radial conductivities | arXiv:2510.22585v2 Announce Type: replace Abstract: The problem of characterizing sequences of real numbers that arise as spectra of Dirichlet-to-Neumann (DtN) maps for elliptic operators has attracted considerable attention over the past fifty years. In this article, we address this question in the simple setting of D... | https://arxiv.org/abs/2510.22585 | Academic Papers | svg |
81570ce28825421978d7f5295da48fcb782a7c760133649d93ede5a4b61ceef0 | 2026-02-02T00:00:00-05:00 | Prime and Semiprime Ideals in Commutative Ternary $\Gamma$-Semirings: Quotients, Radicals, Spectrum | arXiv:2510.23885v2 Announce Type: replace Abstract: The theory of ternary $\Gamma$-semirings extends classical ring and semiring frameworks by introducing a ternary product controlled by a parameter set $\Gamma$. Building on the foundational axioms recently established by Rao, Rani, and Kiran (2025), this paper develop... | https://arxiv.org/abs/2510.23885 | Academic Papers | svg |
7467bef8fdfa166b7d8e8cff4eebfafb5c9142ba65dfc13a1e5e9668bf7dfd20 | 2026-02-02T00:00:00-05:00 | Uniqueness of the non-commutative divergence cocycle | arXiv:2511.06903v2 Announce Type: replace Abstract: We show that, for $n \geq 3 $, 1-cocycles of degree zero on the Lie algebra of derivations of the free associative algebra $T(A_n)$ with values in $ \rvert T(A_n) \rvert \otimes \rvert T(A_n) \rvert $ are linear combinations of the non-commutative divergence and its s... | https://arxiv.org/abs/2511.06903 | Academic Papers | svg |
a1e7b6d2aeef09a8dc1f29cc0b10e8bc88947915e6609055ee06a6a3fb3dee08 | 2026-02-02T00:00:00-05:00 | Generalized ovals, 2.5-dimensional additive codes, and multispreads | arXiv:2511.15843v2 Announce Type: replace Abstract: We present constructions and bounds for additive codes over a finite field in terms of their geometric counterpart, i.e., projective systems. It is known that the maximum number of $(h-1)$-spaces in PG$(2,q)$, such that no hyperplane contains three, is given by $q^h+1... | https://arxiv.org/abs/2511.15843 | Academic Papers | svg |
5e828b135045414010f65c3dc121cfe2e47343b2f9e6eecbd212b53f1df96dfd | 2026-02-02T00:00:00-05:00 | On finiteness properties of separating semigroup of real curve | arXiv:2511.18545v2 Announce Type: replace Abstract: A real morphism $f$ from a real algebraic curve $X$ to $\mathbb{P}^1$ is called separating if $f^{-1}(\mathbb{R} \mathbb{P}^1) = \mathbb{R} X$. A separating morphism defines a covering $\mathbb{R} X \to \mathbb{R} \mathbb{P}^1$. Let $X_1, \ldots, X_r$ denote the compo... | https://arxiv.org/abs/2511.18545 | Academic Papers | svg |
2c331fe9318755d9ed322db9be69b0345d84232b68a548c0bd54808bb66022eb | 2026-02-02T00:00:00-05:00 | Covariance Estimation for Matrix-variate Data via Fixed-rank Core Covariance Geometry | arXiv:2512.01070v3 Announce Type: replace Abstract: We study the geometry of the fixed-rank core covariance manifold and propose a novel covariance estimator for matrix-variate data leveraging this geometry. To generalize the separable covariance model, Hoff, McCormack, and Zhang (2023) showed that every covariance mat... | https://arxiv.org/abs/2512.01070 | Academic Papers | svg |
7a1344e6baa208e33b0e851aa4711d1ff577892eae469cbdd278acd53419b681 | 2026-02-02T00:00:00-05:00 | On the complex zeros and the computational complexity of approximating the reliability polynomial | arXiv:2512.11504v2 Announce Type: replace Abstract: In this paper we relate the location of the complex zeros of the reliability polynomial to parameters at which a certain family of rational functions derived from the reliability polynomial exhibits chaotic behaviour. We use this connection to prove new results about ... | https://arxiv.org/abs/2512.11504 | Academic Papers | svg |
eadaf3f90cd3967a70d7bd1ce237f4f72bb70040676180cfe1d8437ae724b52f | 2026-02-02T00:00:00-05:00 | Taylor polynomials on left-quotients of Carnot groups | arXiv:2512.12239v2 Announce Type: replace Abstract: We prove classical Taylor polynomial theorems for sub-Riemannian manifolds that are obtained as the submetric image of a Carnot group. For these theorems we also prove a sufficient condition for real analyticity and a result on L-harmonicity of Taylor polynomials. | https://arxiv.org/abs/2512.12239 | Academic Papers | svg |
b0219ef410d1c4af0b48e91dbbc06727be848159d3cd94981435c176428b8df7 | 2026-02-02T00:00:00-05:00 | A Note on the Sum-Product Problem and the Convex Sumset Problem | arXiv:2512.13849v2 Announce Type: replace Abstract: We provide a new exponent for the Sum-Product conjecture on $\mathbb{R} $. Namely for $A \subset \mathbb{R}$ finite, \[ \max \left\{ \left\lvert A+A \right\rvert , \left\lvert AA \right\rvert \right\} \gg_{\epsilon} \left\lvert A \right\rvert ^{\frac{4}{3} + \frac{10}... | https://arxiv.org/abs/2512.13849 | Academic Papers | svg |
544a360deff76050aa77e5f276a299b7962b4872afc5ce3590cf75d786f170ee | 2026-02-02T00:00:00-05:00 | Higher Order Dualities between Prime Ideals | arXiv:2512.22346v2 Announce Type: replace Abstract: Extending the works of Alladi and Sweeting and Woo, we state and prove the general higher order duality between prime ideals in number rings. We then use the second order duality to obtain the a new formula for the Chebotarev Density involving sums of the generalized ... | https://arxiv.org/abs/2512.22346 | Academic Papers | svg |
b4fbfd602a460fdcae5de106a9bd747ee0ac6d0184569f83ea4ee24b668c50d8 | 2026-02-02T00:00:00-05:00 | Tameness of actions on finite rank median algebras | arXiv:2601.01681v2 Announce Type: replace Abstract: We prove that for (compact) finite-rank median algebras the geometric rank equals the independence number of all (continuous) median-preserving functions to $[0,1]$. Combined with Rosenthal's dichotomy, this yields a generalized Helly selection principle: for finite-r... | https://arxiv.org/abs/2601.01681 | Academic Papers | svg |
d13406e2113fe18c00dd5cc09a472810edb63bf896cbb7bfe19c94c6874dcf0e | 2026-02-02T00:00:00-05:00 | Singular basins in multiscale systems: tunneling between stable states | arXiv:2601.02001v2 Announce Type: replace Abstract: Real-world systems often evolve on different timescales and possess multiple coexisting stable states. Whether or not a system returns to a given stable state after being perturbed away from it depends on the shape and extent of its basin of attraction. We show that b... | https://arxiv.org/abs/2601.02001 | Academic Papers | svg |
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