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65f7700a8927827006ff47acb344ab636212badb741cfa27aa65acf9d3750ab3
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2026-01-21T00:00:00-05:00
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Structural properties of graphs and the Universal Difference Property
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arXiv:2601.14126v1 Announce Type: new Abstract: We study the Universal Difference Property (UDP) introduced by Alt{\i}nok, Anders, Arreola, Asencio, Ireland, Sar{\i}o\u{g}lan, and Smith, focusing on the relationship between the structural properties of a graph and UDP. We present condtions for when UDP must hold on unicyclic graphs. We then prove that if UDP does not hold on an edge-labeled graph, then it cannot hold on any subdivision of that graph. Additionally, we show that if an edge-labeled graph satisfies the pairwise edge-disjoint path property, then the graph satisfies UDP. Lastly, we explore the relationship between UDP and subgraphs and prove that trees and cycles are the only two families of connected graphs for which UDP must hold for any edge-labeling over any ring.
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https://arxiv.org/abs/2601.14126
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64cc630a4ece9d45dd9c95d1a90403401e3857bc174703c8892412c631d7d36e
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2026-01-21T00:00:00-05:00
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Scheme theory for commutative semirings
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arXiv:2601.14136v1 Announce Type: new Abstract: In this survey, we describe two different approaches to constructing affine schemes for commutative semirings: one based on prime ideals, and another based on prime kernels (also called subtractive ideals). We then explain how these two approaches are related through the theory of universal valuations.
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https://arxiv.org/abs/2601.14136
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e9a0dda50a05607e9ff6f49f06b08fe561680257c2163313a33deffe0070da85
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2026-01-21T00:00:00-05:00
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A global stochastic maximum principle for delayed forward-backward stochastic control systems
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arXiv:2601.14138v1 Announce Type: new Abstract: In this paper, we study a delayed forward-backward stochastic control system in which all the coefficients depend on the state and control terms, and the control domain is not necessarily convex. A global stochastic maximum principle is obtained by using a new method. More precisely, this method introduces first-order and second-order auxiliary equations and offers a novel approach to deriving the adjoint equations as well as the variational equation for $y^\e - y^*$.
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https://arxiv.org/abs/2601.14138
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1c767aca1be3c2854351361222ffd6a18328d85adc421ec3667e7d31541c1c33
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2026-01-21T00:00:00-05:00
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Symmetry Breaking and Phase Transitions in Random Non-Commutative Geometries and Related Random-Matrix Ensembles
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arXiv:2601.14141v1 Announce Type: new Abstract: Ensembles of random fuzzy non-commutative geometries may be described in terms of finite (\(N^2\)-dimensional) Dirac operators and a probability measure. Dirac operators of type \((p,q)\) are defined in terms of commutators and anti-commutators of \(2^{p+q-1}\) hermitian matrices \(H_k\) and tensor products with a representation of a Clifford algebra. Ensembles based on this idea have recently been used as a toy model for quantum gravity, and they are interesting random-matrix ensembles in their own right. We provide a complete theoretical picture of crossovers, phase transitions, and symmetry breaking in the \(N \to \infty \) limit of 1-parameter families of quartic Barrett-Glaser ensembles in the one-matrix cases \((1,0)\) and \((0,1)\) that depend on one coupling constant \(g\). Our theoretical results are in full agreement with previous and new Monte-Carlo simulations.
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https://arxiv.org/abs/2601.14141
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54fc60d24da34295d6185087fa2c3b08df0dea97aa11d5b76ebc6ab3f465d206
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2026-01-21T00:00:00-05:00
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On the $p$-adic deformation problem for the $K$-theory of semistable schemes
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arXiv:2601.14146v1 Announce Type: new Abstract: We establish a semistable generalization of the Beilinson-Bloch-Esnault-Kerz fiber square, relating the algebraic K-theory of a semistable scheme to its logarithmic topological cyclic homology. We prove that the obstruction to lifting K-theory classes is governed by the Hyodo-Kato Chern character. This answers the $p$-adic deformation problem for continuous K-theory in the semistable case, extending the work of Antieau-Mathew-Morrow-Nikolaus. As an application, we provide a purely K-theoretic proof of Yamashita's semistable $p$-adic Lefschetz $(1,1)$-theorem.
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https://arxiv.org/abs/2601.14146
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69fb400890bcfd9fbf8e7c3b915964ff07e3aab5b0027f71db257d9a841129e1
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2026-01-21T00:00:00-05:00
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Gradient Flow for Finding E-optimal Designs
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arXiv:2601.14147v1 Announce Type: new Abstract: We investigate the use of Wasserstein gradient flows for finding an $E$-optimal design for a regression model. Unlike the commonly used $D$- and $L$-optimality criteria, the $E$-criterion finds a design that maximizes the smallest eigenvalue of the information matrix, and so it is a non-differentiable criterion unless the minimum eigenvalue has geometric multiplicity equals to one. Such maximin design problems abound in statistical applications and present unique theoretical and computational challenges. Building on the differential structure of the $2$-Wasserstein space, we derive explicit formulas for the Wasserstein gradient of the $E$-optimality criterion in the simple-eigenvalue case. For higher multiplicities, we propose a Wasserstein steepest ascent direction and show that it can be computed exactly via a semidefinite programming (SDP) relaxation. We develop particle approximations that connect infinite-dimensional flows with finite-dimensional optimization, and provide approximation guarantees for empirical measures. Our framework extends naturally to constrained designs via projected Wasserstein gradient flows. Numerical experiments demonstrate that the proposed methods successfully recover $E$-optimal designs for both linear and nonlinear regression models, with competitive accuracy and scalability compared to existing heuristic approaches. This work highlights the potential of optimal transport-based dynamics as a unifying tool for studying challenging optimal design problems.
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https://arxiv.org/abs/2601.14147
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cb3faeda4d4b5c3376087cc7c267606889e3602c8d6d88acd345b8b00a7d4853
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2026-01-21T00:00:00-05:00
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A Natural Representation of Volumes Yields a Remarkable Affine Consequence
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arXiv:2601.14149v1 Announce Type: new Abstract: At the beginning of the 20th Century there was a growing interest for the investigation of the action of linear groups on the geometry of surfaces. In that context of ideas, the quest for a connection between curvature and the behaviour of linear groups rose naturally. Pursuing the original thought, we investigate how the geometric meaning of this idea is intimately related to the concept of volume of parallelepiped boxes. We show how the ratio of the Gaussian curvature divided by the fourth power of a certain distance of interest in the geometry of surfaces can be represented as a function of volumes. This geometric description explores the profound meaning of a quantity considered by {\c{T}}i{\c{t}}eica in 1907, in a work that sparked a growing interest in affine differential geometry, as an illustration of Felix Klein's Erlangen Program, in which the quest for geometric invariants was the main point of inquiry.
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https://arxiv.org/abs/2601.14149
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6e961fdf590c2f0d358f5cfd833e1d745c8a1699aa1f1fed1b649232a51bf871
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2026-01-21T00:00:00-05:00
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Achievable Burning Densities of Growing Grids
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arXiv:2601.14151v1 Announce Type: new Abstract: Graph burning is a discrete-time process on graphs where vertices are sequentially activated and burning vertices cause their neighbours to burn over time. In this work, we focus on a dynamic setting in which the graph grows over time, and at each step we burn vertices in the growing grid $G_n = [-f(n),f(n)]^2$. We investigate the set of achievable burning densities for functions of the form $f(n)=\lceil cn^\alpha\rceil$, where $\alpha \ge 1$ and $c>0$. We show that for $\alpha=1$, the set of achievable densities is $[1/(2c^2),1]$, for $1<\alpha<3/2$, every density in $[0,1]$ is achievable, and for $\alpha=3/2$, the set of achievable densities is $[0,(1+\sqrt{6}c)^{-2}]$.
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https://arxiv.org/abs/2601.14151
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38a89ff999d987f375d356e1adffbcafb364c12b0ac27474d1bfeeff77e60a9b
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2026-01-21T00:00:00-05:00
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Poisson-Dirichlet graphons and permutons
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arXiv:2601.14166v1 Announce Type: new Abstract: We introduce classes of supergraphs and superpermutations with novel universal graphon and permuton limiting objects whose construction involves the two-parameter Poisson-Dirichlet process introduced by Pitman and Yor (1997). We demonstrate the universality of these limiting objects through general invariance principles in a heavy-tailed regime and establish a comprehensive phase diagram for the asymptotic shape of superstructures.
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https://arxiv.org/abs/2601.14166
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e8cc5e9513fd3375b60ec93940bd6b9218d3f26eb6920e71a8ac1bfcc34918d0
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2026-01-21T00:00:00-05:00
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Heights on toric varieties for singular metrics: Local theory
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arXiv:2601.14167v1 Announce Type: new Abstract: We show that the (toric) local height of a toric variety with respect to a semipositive torus-invariant singular metric is given by the integral of a concave function over a compact convex set. This generalizes a result of Burgos, Philippon, and Sombra for the case of continuous metrics and answers a question raised by Burgos, Kramer, and K\"uhn in 2016.
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https://arxiv.org/abs/2601.14167
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f72ec01414a5450e5675a027b972fdac1b1a7c18d8e6afb0994d2d6514081ec5
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2026-01-21T00:00:00-05:00
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The 2-categorical S-matrix of a braided fusion 1-category is a character table
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arXiv:2601.14168v1 Announce Type: new Abstract: The semisimple module categories over a braided fusion category $\mathcal{C}$ form a connected fusion 2-category $\text{Mod}(\mathcal{C})$. Its Drinfeld center $\mathcal{Z}(\text{Mod}(\mathcal{C}))$ is a braided fusion 2-category. To any braided fusion 2-category, Johnson-Freyd and Reutter arXiv:2105.15167v3 [math.QA] have associated a matrix-valued invariant, the 2-categorical $S$-matrix. In this short note we investigate this matrix of $\mathcal{Z}(\text{Mod}(\mathcal{C}))$ as an invariant for the braided fusion 1-category $\mathcal{C}$ and show that it reduces to the character table of the M\"uger center of $\mathcal{C}$.
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https://arxiv.org/abs/2601.14168
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4f80758357c1d83e67aad239476556574e5b064de163b7f004c36d0ee9015f53
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2026-01-21T00:00:00-05:00
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Chaos propagation in genetic algorithms: An optimal transport approach
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arXiv:2601.14169v1 Announce Type: new Abstract: Genetic algorithms are high-level heuristic optimization methods which enjoy great popularity thanks to their intuitive description, flexibility, and, of course, effectiveness. The optimization procedure is based on the evolution of possible solutions following three mechanisms: selection, mutation, and crossover. In this paper, we look at the algorithm as an interacting particle system and show that it is described by a Boltzmann-type equation in the many particles limit. Specifically, we prove a propagation of chaos result with a novel technique that leverages the optimal transport formulation of the Kantorovich-Rubinstein norm and naturally incorporates the crossover mechanism into the analysis. The convergence rate is sharp with respect to the number of particles.
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https://arxiv.org/abs/2601.14169
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054436b9f3b6994eea8eb1c8250f282d4021ea7df5c03f42e3b0cdee8714b3de
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2026-01-21T00:00:00-05:00
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Wasserstein distances between ERGMs and Erd\H{o}s-R\'enyi models
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arXiv:2601.14170v1 Announce Type: new Abstract: Ferromagnetic exponential random graph models (ERGMs) are random graph models under which the presence of certain small structures (such as triangles) is encouraged; they can be constructed by tilting an Erd\H{o}s--R\'enyi model by the exponential of a particular nonlinear Hamiltonian. These models are mixtures of metastable wells which each behave macroscopically like an Erd\H{o}s--R\'enyi model, exhibiting the same laws of large numbers for subgraph counts [CD13]. However, on the microscopic scale these metastable wells are very different from Erd\H{o}s--R\'enyi models, with the total variation distance between the two measures tending to 1 [MX23]. In this article we clarify this situation by providing a sharp (up to constants) bound on the Hamming-Wasserstein distance between the two models, which is the average number of edges at which they differ, under the coupling which minimizes this average. In particular, we show that this distance is $\Theta(n^{3/2})$, quantifying exactly how these models differ. An upper bound of this form has appeared in the past [RR19], but this was restricted to the subcritical (high-temperature) regime of parameters. We extend this bound, using a new proof technique, to the supercritical (low-temperature) regime, and prove a matching lower bound which has only previously appeared in the subcritical regime of special cases of ERGMs satisfying a "triangle-free" condition [DF25]. To prove the lower bound in the presence of triangles, we introduce an approximation of the discrete derivative of the Hamiltonian, which controls the dynamical properties of the ERGM, in terms of local counts of triangles and wedges (two-stars) near an edge. This approximation is the main technical and conceptual contribution of the article, and we expect it will be useful in a variety of other contexts as well. Along the way, we also prove a bound on the marginal edge probability under the ERGM via a new bootstrapping argument. Such a bound has already appeared [FLSW25], but again only in the subcritical regime and using a different proof strategy.
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https://arxiv.org/abs/2601.14170
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3c34f56f6848e27fac4238daf018f91a99e7994627a0a4f1feb911bd9b38b49d
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2026-01-21T00:00:00-05:00
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Wavelet-Packet Content for Positive Operators
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arXiv:2601.14174v1 Announce Type: new Abstract: We give a simple way to attach ``content" to the nodes of a wavelet packet tree when a positive operator is given. At a fixed packet depth, the packet projections split the operator into positive pieces, and this decomposition induces a boundary measure on the packet path space, together with vector-dependent densities that show how energy is distributed across the tree. We then study a sequential extraction procedure and two depth-fixed greedy rules for choosing packet blocks, one based on trace weights and one based on Hilbert-Schmidt weights. The main results are explicit geometric decay estimates for the remainder under these greedy removals. In the Hilbert-Schmidt case we also isolate a coherence quantity that measures how close the operator is to being block-diagonal in the packet partition. We close with a concrete patch-based denoising procedure for images, where packet blocks are selected by these content weights computed from an empirical second-moment operator; the construction ensures that both the approximants and the remainders stay positive at every step.
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https://arxiv.org/abs/2601.14174
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d52df39f43d43861ec2042a0042538a5aa4dd44ef61420f3c2476b85a0f8ce56
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2026-01-21T00:00:00-05:00
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Quantum mixing on large Schreier graphs
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arXiv:2601.14182v1 Announce Type: new Abstract: Quantum ergodicity describes the delocalization of most eigenfunctions of Laplace-type operators on graphs or manifolds exhibiting chaotic classical dynamics. Quantum mixing is a stronger notion, additionally controlling correlations between eigenfunctions at different energy levels. In this work, we study families of finite Schreier graphs that converge to an infinite Cayley graph and establish quantum mixing under the assumption that the limiting Cayley graph has absolutely continuous spectrum. The convergence of Schreier graphs is understood in the Benjamini-Schramm sense or in the sense of strong convergence in distribution. Our proofs rely on a new approach to quantum ergodicity, based on trace computations, resolvent approximations and representation theory. We illustrate our assumptions on several examples and provide applications to Schreier graphs associated with free products of groups and right-angled Coxeter groups.
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https://arxiv.org/abs/2601.14182
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acb54bb08705042b32950c939c14f3d98b5b2a99fb27f93d6f02a2a47d88fd9d
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2026-01-21T00:00:00-05:00
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The nonlinear Steklov problem in outward cuspidal domains
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arXiv:2601.14186v1 Announce Type: new Abstract: In this article, we consider the nonlinear Steklov eigenvalue problem in outward cuspidal domains. Using the compactness of the weighted trace embedding we obtain the variational characterization of the first non-trivial eigenvalue and prove the existence of a corresponding weak solution.
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https://arxiv.org/abs/2601.14186
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2de155d95fc5fb3d9cd09ccac6c6e34c430314b6ccb827ddb10b93ce3c6b1351
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2026-01-21T00:00:00-05:00
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From big q-Jacobi and Chebyshev polynomials to exponential-reproducing subdivision: new identities
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arXiv:2601.14189v1 Announce Type: new Abstract: In this paper we derive new identities satisfied by Chebyshev polynomials of the first kind and big q-Jacobi polynomials. An immediate benefit of the derived identities is the achievement of closed-form expressions for the Laurent polynomials that identify minimum-support interpolating subdivision schemes reproducing finite sets of integer powers of exponentials.
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https://arxiv.org/abs/2601.14189
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afc47ad1fd13df652976cbd6cea94f548c5e377e0be1c0c4565d56b32e97f0c0
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2026-01-21T00:00:00-05:00
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Translation invariant curvature measures of convex bodies
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arXiv:2601.14193v1 Announce Type: new Abstract: In a series of papers, Weil initiated the investigation of translation invariant curvature measures of convex bodies, which include as prime examples Federer's curvature measures. In this paper, we continue this line of research by introducing new tools to study curvature measures. Our main results suggest that the space of curvature measures, which is graded by degree and parity, is highly structured: We conjecture that each graded component has length at most $2$ as a representation of the general linear group, and we prove this in degrees $0$ and $n-2$. Beyond this conjectural picture, our methods yield a characterization of Federer's curvature measures under weaker assumptions.
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https://arxiv.org/abs/2601.14193
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d17d55e74bf3b2094fe3a2a0fecaed81af7c97c3e742ac6758495dde89d98a70
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2026-01-21T00:00:00-05:00
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Local electrical impedance tomography via projections
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arXiv:2601.14198v1 Announce Type: new Abstract: This paper introduces a method for approximately eliminating the effect that conductivity changes outside the region of interest have in electrical impedance tomography, allowing to form a local reconstruction in the region of interest only. The method considers the Jacobian matrix of the forward map, i.e., of the map that sends the discretized conductivity to the electrode measurements, at an initial guess for the conductivity. The Jacobian matrix is divided columnwise into two parts: one corresponding to the region of interest and a nuisance Jacobian corresponding to the rest of the domain. The leading idea is to project both the electrode measurements and the forward map onto the orthogonal complement of the span of a number of left-hand singular vectors for a suitably weighted nuisance Jacobian. The weighting can, e.g., account for the element sizes in a finite element discretization or to prior information on the conductivity outside the region of interest. The inverse problem is then solved by considering the projected relation between the measurements and the forward map, only reconstructing the conductivity in the region of interest. The functionality of the method is demonstrated by applying a reconstruction algorithm that combines lagged diffusivity iteration and total variation regularization to experimental data. In particular, data from a head-shaped water tank is considered, with the conductivity change in the region of interest mimicking growth of a hemorrhagic stroke and the changes outside the region of interest imitating physiological variations in the conductivity of the scalp.
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https://arxiv.org/abs/2601.14198
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435b27e7867278e1607b588a3481b07399badd6572bb1e6fe77ec363fb52c6fb
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2026-01-21T00:00:00-05:00
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Convergence analysis and a novel Lagrange multiplier partitioned method for fluid-poroelastic interaction
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arXiv:2601.14201v1 Announce Type: new Abstract: We propose a partitioned method for the monolithic formulation of the Stokes-Biot system that incorporates Lagrange multipliers enforcing the interface conditions. The monolithic system is discretized using finite elements, and we establish convergence of the resulting approximation. A Schur complement based algorithm is developed together with an efficient preconditioner, enabling the fluid and poroelastic structure subproblems to be decoupled and solved independently at each time step. The Lagrange multipliers approximate the interface fluxes and act as Neumann boundary conditions for the subproblems, yielding parallel solution of the Stokes and Biot equations. Numerical experiments demonstrate the effectiveness of the proposed algorithm and validate the theoretical error estimate.
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https://arxiv.org/abs/2601.14201
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a32538513b600c9bffcb1975da2954350cce5d30c208b06fbca4ee716c0a4d25
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2026-01-21T00:00:00-05:00
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Storage-Rate Trade-off in A-XPIR
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arXiv:2601.14202v1 Announce Type: new Abstract: We consider the storage problem in an asymmetric $X$-secure private information retrieval (A-XPIR) setting. The A-XPIR setting considers the $X$-secure PIR problem (XPIR) when a given arbitrary set of servers is communicating. We focus on the trade-off region between the average storage at the servers and the average download cost. In the case of $N=4$ servers and two non-overlapping sets of communicating servers with $K=2$ messages, we characterize the achievable region and show that the three main inequalities compared to the no-security case collapse to two inequalities in the asymmetric security case. In the general case, we derive bounds that need to be satisfied for the general achievable region for an arbitrary number of servers and messages. In addition, we provide the storage and retrieval scheme for the case of $N=4$ servers with $K=2$ messages and two non-overlapping sets of communicating servers, such that the messages are not replicated (in the sense of a coded version of each symbol) and at the same time achieve the optimal achievable rate for the case of replication. Finally, we derive the exact capacity for the case of asymmetric security and asymmetric collusion for $N=4$ servers, with the communication links $\{1,2\}$ and $\{3,4\}$, which splits the servers into two groups, i.e., $g=2$, and with the collusion links $\{1,3\}$, $\{2,4\}$, as $C=\frac{1}{3}$. More generally, we derive a capacity result for a certain family of asymmetric collusion and asymmetric security cases.
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https://arxiv.org/abs/2601.14202
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97683481bcd2e9416516af7fb48c18e531e56759b68d1a829d0922594188c958
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2026-01-21T00:00:00-05:00
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Tropical Methods for Counting Plane Curves -- Complex, Real and Quadratically Enriched
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arXiv:2601.14216v1 Announce Type: new Abstract: Since the first famous correspondence theorem by Mikhalkin appeared in 2005, tropical geometry has allowed a parallel treatment of real and complex counting problems. A prime example are the genus 0 Gromov-Witten invariants of the plane which count rational plane curves of degree d satisfying point conditions and their real counterpart, the Welschinger invariants, which both can be determined using tropical methods. Remarkably, the tropical computation of the two types of invariants works entirely in parallel. Recently, quadratically enriched enumerative geometry enables us to combine such real and complex counts under one roof, providing a simultaneous approach which can also be used for counts over other fields. Tropical geometry is a successful tool for the study and computation of such quadratically enriched enumerative invariants, too. In this survey, we provide an overview of tropical methods for plane curve counting problems over the real and complex numbers, and the new quadratically enriched counts.
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https://arxiv.org/abs/2601.14216
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46acdbf8c6202963ce53085a57060bfe62ed9326fd5ba3f5d5706b370156eb7c
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2026-01-21T00:00:00-05:00
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Symmetry Testing in Time Series using Ordinal Patterns: A U-Statistic Approach
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arXiv:2601.14223v1 Announce Type: new Abstract: We introduce a general framework for testing temporal symmetries in time series based on the distribution of ordinal patterns. While previous approaches have focused on specific forms of asymmetry, such as time reversal, our method provides a unified framework applicable to arbitrary symmetry tests. We establish asymptotic results for the resulting test statistics under a broad class of stationary processes. Comprehensive experiments on both synthetic and real data demonstrate that the proposed test achieves high sensitivity to structural asymmetries while remaining fully data-driven and computationally efficient.
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https://arxiv.org/abs/2601.14223
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941c71572fdbcdbaa2b2ecb860f0db01bbbd04c4da9fae0578307c71572c1ab9
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2026-01-21T00:00:00-05:00
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New Topological Restrictions For Spaces With Nonnegative Ricci Curvature
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arXiv:2601.14231v1 Announce Type: new Abstract: We obtain new topological restrictions for complete Riemannian manifolds with nonnegative Ricci curvature and RCD(0,n) spaces. Our main results are a Betti number rigidity theorem which answers a question open since work of M.-T. Anderson in 1990, and a vanishing theorem for the simplicial volume generalizing a theorem of M. Gromov from 1982. Combining such results we obtain a new proof of the classification of noncompact 3-manifolds with nonnegative Ricci curvature, originally due to G. Liu in 2011, which extends to the synthetic setting.
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https://arxiv.org/abs/2601.14231
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82bcae6897f0a085209bf60c99553088109c36269bfbf01d5da98320383910fc
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2026-01-21T00:00:00-05:00
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Stabilizer-Assisted Inactivation Decoding of Quantum Error-Correcting Codes with Erasures
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arXiv:2601.14236v1 Announce Type: new Abstract: In this work, we develop a reduced complexity maximum likelihood (ML) decoder for quantum low-density parity-check (QLDPC) codes over erasures. Our decoder combines classical inactivation decoding, which integrates peeling with symbolic guessing, with a new dual peeling procedure. In the dual peeling stage, we perform row operations on the stabilizer matrix to efficiently reveal stabilizer generators and their linear combinations whose support lies entirely on the erased set. Each such stabilizer identified allows us to freely fix a bit in its support without affecting the logical state of the decoded result. This removes one degree of freedom that would otherwise require a symbolic guess, reducing the number of inactivated variables and decreasing the size of the final linear system that must be solved. We further show that dual peeling combined with standard peeling alone, without inactivation, is sufficient to achieve ML for erasure decoding of surface codes. Simulations across several QLDPC code families confirm that our decoder matches ML logical failure performance while significantly reducing the complexity of inactivation decoding, including more than a 20% reduction in symbolic guesses for the B1 lifted product code at high erasure rates.
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https://arxiv.org/abs/2601.14236
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d66148c6f355b0efa6e649dad62eed8d749f501901936efd8d5d2ea2802d596d
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2026-01-21T00:00:00-05:00
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Partial Linearity in Categories
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arXiv:2601.14237v1 Announce Type: new Abstract: In this paper we study partial linearity in a category by replacing isomorphism between coproducts and products in a linear category with isomorphism between suitable monoidal structures on a category. The main results a coherence theorem and a generalization of the theory of central morphisms from unital categories to our context of partial linearity
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https://arxiv.org/abs/2601.14237
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1014e579b8b35986456fca8b5e424acd7222d0849fe0665809ce4e4fc5a5e1d4
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2026-01-21T00:00:00-05:00
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Conformal dimension and its attainment on self-similar Laakso-type fractal spaces
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arXiv:2601.14241v1 Announce Type: new Abstract: A general construction of Laakso-type fractal spaces was recently introduced by the first two authors. In this paper, we establish a simple condition characterizing when the Ahlfors regular conformal dimension of a symmetric Laakso-type fractal space is attained. The attaining metrics are constructed explicitly. This gives new examples of attainment and clarifies the possible obstructions.
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https://arxiv.org/abs/2601.14241
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7f552a18cbb9c950ccfc4552ec3588aa15fa1657c7d477788e5456f4c2e589eb
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2026-01-21T00:00:00-05:00
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Detecting Limit Tori in Non-Smooth Systems: An Analytic Approach with Applications to 3D Piecewise Linear Systems
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arXiv:2601.14247v1 Announce Type: new Abstract: This work investigates a class of non-autonomous $T$-periodic piecewise smooth differential systems and their associated time-$T$ maps. Our main result provides an analytical approach for detecting, within this class of piecewise differential systems, isolated invariant tori associated with normally hyperbolic invariant closed curves of the time-$T$ map. To achieve this, we derive sufficient conditions under which smooth near-identity maps undergo a Neimark--Sacker bifurcation. As an application of our main result, we present a family of 3D piecewise linear differential systems exhibiting attracting and repelling isolated invariant tori which, moreover, persist under small perturbations. To the best of our knowledge, this family provides the first examples in which limit tori are analytically detected in piecewise linear systems.
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https://arxiv.org/abs/2601.14247
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Academic Papers
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da557c619f154bb571fca305a99974ecdef4e33c22fe753fc01ee94927040ee9
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2026-01-21T00:00:00-05:00
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Identification capacity and rate-query tradeoffs in classification systems
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arXiv:2601.14252v1 Announce Type: new Abstract: We study a one-shot identification analogue of rate-distortion for discrete classification under three resources: tag rate L (bits of side information stored per entity), identification cost W (attribute-membership queries per identification, excluding global preprocessing and amortized caching), and distortion D (misclassification probability). The question is to characterize achievable triples (L,W,D) when a decoder must recover an entity's class from limited observations. Zero-error barrier. If two distinct classes induce the same attribute profile, then the observation pi(V) is identical for both and no decoder can identify the class from attribute queries alone. Thus, if the profile map pi is not injective on classes, zero-error identification without tags is impossible (a zero-error feasibility threshold). Achievability and converse at D=0. With k classes, nominal tags of L = ceil(log2 k) bits enable O(1) identification cost with D=0. Conversely, any scheme with D=0 must satisfy L >= log2 k bits (tight). Without tags (L=0), identification requires Omega(n) queries in the worst case and may incur D>0. Combinatorial structure. Minimal sufficient query families form the bases of a matroid; the induced distinguishing dimension is well-defined and links to zero-error source coding via graph entropy. We illustrate implications for type systems, databases, and biological taxonomy. All results are mechanized in Lean4 (6000+ lines, 0 sorry).
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https://arxiv.org/abs/2601.14252
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4f4a6c5c70ee7e0f0911886b395048dc841556e00a4999d2857cac50142b6455
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2026-01-21T00:00:00-05:00
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Post-Hoc Uncertainty Quantification in Pre-Trained Neural Networks via Activation-Level Gaussian Processes
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arXiv:2502.20966v1 Announce Type: cross Abstract: Uncertainty quantification in neural networks through methods such as Dropout, Bayesian neural networks and Laplace approximations is either prone to underfitting or computationally demanding, rendering these approaches impractical for large-scale datasets. In this work, we address these shortcomings by shifting the focus from uncertainty in the weight space to uncertainty at the activation level, via Gaussian processes. More specifically, we introduce the Gaussian Process Activation function (GAPA) to capture neuron-level uncertainties. Our approach operates in a post-hoc manner, preserving the original mean predictions of the pre-trained neural network and thereby avoiding the underfitting issues commonly encountered in previous methods. We propose two methods. The first, GAPA-Free, employs empirical kernel learning from the training data for the hyperparameters and is highly efficient during training. The second, GAPA-Variational, learns the hyperparameters via gradient descent on the kernels, thus affording greater flexibility. Empirical results demonstrate that GAPA-Variational outperforms the Laplace approximation on most datasets in at least one of the uncertainty quantification metrics.
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https://arxiv.org/abs/2502.20966
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920aa89d6fcc3aadb337426f3287bbe30b0bdf246acaf4dd89dc8376f0661cbb
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2026-01-21T00:00:00-05:00
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Embeddings and intersections of adelic groups
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arXiv:2510.22408v1 Announce Type: cross Abstract: We prove the embeddings of adelic groups $\mathbb{A}_I(X, \mathcal{F})\hookrightarrow \mathbb{A}_J(X, \mathcal{F})$ on an excellent scheme $X$ of special type, where $I\subset J$ and $\mathcal{F}$ is a flat quasicoherent sheaf on $X$. We prove the equality $\mathbb{A}_I(X, \mathcal{F})\cap \mathbb{A}_J(X, \mathcal{F}) = \mathbb{A}_{I\setminus 0}(X, \mathcal{F})$ for a normal excellent scheme of special type $X$ and a flat quasicoherent sheaf $\mathcal{F}$ on it, where $I\cap J = I\setminus 0$. We show that the limit of restrictions of global sections of a locally free sheaf on a Cohen-Macaulay projective scheme to power thickenings of integral subschemes is equal to the group of global sections of this sheaf. Using this result, we prove the equality $\mathbb{A}_{\dim X - 1}(X, \mathcal{F})\cap\mathbb{A}_{\dim X}(X, \mathcal{F}) = H^0(X, \mathcal{F})$ for a Cohen-Macaulay projective variety $X$ and a locally free sheaf $\mathcal{F}$ on it. Hence we deduce a theorem on intersections of adelic groups for the case of a normal projective surface. We also compute cohomology groups for a particular case of a curtailed adelic complex. Hence we show that on a three-dimensional regular projective variety over a countable field $X$ there is an equality $\mathbb{A}_I(X, \mathcal{F})\cap \mathbb{A}_J(X, \mathcal{F}) = \mathbb{A}_{I\cap J}(X, \mathcal{F})$ for any $I, J\subset \{0, 1, 2, 3\}$ and any locally free sheaf $\mathcal{F}$ on $X$.
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https://arxiv.org/abs/2510.22408
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2b4b44fefc6c6a9bce039d4ad5dcfd1b602814d36d2156a19ef3126317bcae0c
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2026-01-21T00:00:00-05:00
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Phase Space Formulation of S-matrix
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arXiv:2512.23100v1 Announce Type: cross Abstract: We establish an exact relation between the S-symplectomorphism and the S-matrix by means of the phase space formulation of quantum mechanics. The adjoint action of the S-matrix defines a fuzzy diffeomorphism on phase space whose classical limit is the S-symplectomorphism. The relation between classical and quantum eikonals is immediate via $\hbar$-deformation of each Poisson bracket in the Magnus formula. Diagrammatic computation of quantum eikonal is illustrated for quantizations in both symmetric and normal orderings.
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https://arxiv.org/abs/2512.23100
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455210a35b167a0490bf9b8607cfeee5a3e22d3a8dae3be082ec1c7053d135d6
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2026-01-21T00:00:00-05:00
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A new class of special functions arising in plasma linear susceptibility tensor calculations
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arXiv:2601.11276v1 Announce Type: cross Abstract: We investigate some fundamental properties of a peculiar class of special functions strictly related to Bessel, Anger and Weber functions, whose introduction was originally motivated by linear susceptibility tensor calculations in a hot, magnetised plasma. We show that these functions are solutions of an inhomogeneous Bessel ODE, with specified initial conditions and a distinct right-hand-side term fulfilling the Nielsen's requirement. Beside deriving recurrence relations and an alternative representation involving incomplete Anger-Weber functions, we show that these functions admit a simple series expansion in terms of Bessel functions of integer order, obtained by resorting to the Jacobi-Anger formula. In plasma applications this eventually leads to expressions involving infinite sums of products of Bessel functions, not particularly apt to numerical evaluation ought to their slow convergence rate when the particle's gyro-radius is larger than the wavelength. By exploiting the previously determined recurrence properties of the new class of functions we present a particularly simple derivation of the linear susceptibility tensor that enables to avoid this inconvenience.
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https://arxiv.org/abs/2601.11276
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a1d41cb15e321cf250a59f38cfc06a614266d46abc57ce94b4201b5231f67762
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2026-01-21T00:00:00-05:00
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From HNSW to Information-Theoretic Binarization: Rethinking the Architecture of Scalable Vector Search
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arXiv:2601.11557v1 Announce Type: cross Abstract: Modern semantic search and retrieval-augmented generation (RAG) systems rely predominantly on in-memory approximate nearest neighbor (ANN) indexes over high-precision floating-point vectors, resulting in escalating operational cost and inherent trade-offs between latency, throughput, and retrieval accuracy. This paper analyzes the architectural limitations of the dominant "HNSW + float32 + cosine similarity" stack and evaluates existing cost-reduction strategies, including storage disaggregation and lossy vector quantization, which inevitably sacrifice either performance or accuracy. We introduce and empirically evaluate an alternative information-theoretic architecture based on maximally informative binarization (MIB), efficient bitwise distance metrics, and an information-theoretic scoring (ITS) mechanism. Unlike conventional ANN systems, this approach enables exhaustive search over compact binary representations, allowing deterministic retrieval and eliminating accuracy degradation under high query concurrency. Using the MAIR benchmark across 14 datasets and 10,038 queries, we compare this architecture against Elasticsearch, Pinecone, PGVector, and Qdrant. Results demonstrate retrieval quality comparable to full-precision systems, while achieving substantially lower latency and maintaining constant throughput at high request rates. We show that this architectural shift enables a truly serverless, cost-per-query deployment model, challenging the necessity of large in-memory ANN indexes for high-quality semantic search.
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https://arxiv.org/abs/2601.11557
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7132846be78d14378ee42b7bb3ad10d5e8d7ce9f22551d237dcc852aaecbca94
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2026-01-21T00:00:00-05:00
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On Analyzing the Conditions for Stability of Opportunistic Supply Chains Under Network Growth
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arXiv:2601.11566v1 Announce Type: cross Abstract: Even large firms such as Walmart, Apple, and Coca-Cola face persistent fluctuations in costs, demand, and raw material availability. These are not \textit{rare events} and cannot be evaluated using traditional disruption models focused on infrequent events. Instead, sustained volatility induces opportunistic behavior, as firms repeatedly reconfigure partners in absence of long-term contracts, often due to trust deficits. The resulting web of transient relationships forms opportunistic supply chains (OSCs). To capture OSC evolution, we develop an integrated mathematical framework combining a Geometric Brownian Motion (GBM) model to represent stochastic price volatility, a Bayesian learning model to describe adaptive belief updates regarding partner reliability, and a Latent Order Logistic (LOLOG) network model for endogenous changes in network structure. This framework is implemented in an agent-based simulation to examine how volatility, trust, and network structure jointly shape SC resilience. Our modeling approach identifies critical volatility threshold; a tipping point beyond which the network shifts from a stable, link-preserving regime to a fragmented regime marked by rapid relationship dissolution. We analytically establish monotonic effects of volatility on profitability, trust, and link activation; derive formal stability conditions and volatility-driven phase transitions, and show how these mechanisms shape node importance and procurement behavior. These theoretical mechanisms are illustrated through computational experiments reflecting industry behaviors in fast fashion, electronics, and perishables. Overall, our contribution is to develop an integrated GBM-Bayesian-LOLOG framework to analyze OSC stability and our model can be extended to other OSCs including humanitarian, pharmaceutical, and poultry networks.
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https://arxiv.org/abs/2601.11566
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8d5054823be35593ff298279b2a1b93fd43597ce7635cfa1eb6979fb4ed57154
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2026-01-21T00:00:00-05:00
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Privacy-Preserving Black-Box Optimization (PBBO): Theory and the Model-Based Algorithm DFOp
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arXiv:2601.11570v1 Announce Type: cross Abstract: This paper focuses on solving unconstrained privacy-preserving black-box optimization (PBBO), its corresponding least Frobenius norm updating of quadratic models, and the differentially privacy mechanisms for PBBO. Optimization problems with transformed/encrypted objective functions aim to minimize F(x), which is encrypted/transformed/encrypted to F_k(x) as the output at the k-th iteration. A new derivative-free solver named DFOp, with its implementation, is proposed in this paper, which has a new updating formula for the quadratic model functions. The convergence of DFOp for solving problems with transformed/encrypted objective functions is given. Other analyses, including the new model updating formula and the analysis of the transformation's impact to model functions are presented. We propose two differentially private noise-adding mechanisms for privacy-preserving black-box optimization. Numerical results show that DFOp performs better than compared algorithms. To the best of our knowledge, DFOp is the first derivative-free solver that can solve black-box optimization problems with step-encryption and privacy-preserving black-box problems exactly, which also tries to answer the open question about the combination of derivative-free optimization and privacy.
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https://arxiv.org/abs/2601.11570
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40ec6d1bd27b0e9bb755f61b0c467f291d30f8a8233f2eafec41b9c28f03459a
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2026-01-21T00:00:00-05:00
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Exact Computation of the Catalan Number $C(2,050,572,903)$
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arXiv:2601.11621v1 Announce Type: cross Abstract: This paper presents a two-phase algorithm for computing exact Catalan numbers at an unprecedented scale. The method is demonstrated by computing $C(n)$ for $n = 2,050,572,903$ yielding a result with a targeted $1,234,567,890$ decimal digits. To circumvent the memory limitations associated with evaluating large factorials, the algorithm operates exclusively in the prime-exponent domain. Phase 1 employs a parallel segmented sieve to enumerate primes up to $2n$ and applies Legendre's formula to determine the precise prime factorization of $C(n)$. The primes are grouped by exponent and serialized to disk. Phase 2 reconstructs the final integer using a memory-efficient balanced product tree with chunking. The algorithm runs on a time complexity of $\Theta(n(\log n)^2)$ bit-operations and a space complexity of $\Theta(n \log n)$ bits. This result represents the largest exact Catalan number computed to date. Performance statistics for a single-machine execution are reported, and verification strategies -- including modular checks and SHA-256 hash validation -- are discussed. The source code and factorization data are provided to ensure reproducibility.
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https://arxiv.org/abs/2601.11621
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95349a970ed10349f0054dabb7cb4620338db23b4684fb892abb984c14f88eef
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2026-01-21T00:00:00-05:00
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Weyl Mutations in Quiver Yangians
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arXiv:2601.11736v1 Announce Type: cross Abstract: The problem of solving non-linear equations would be considerably simplified by a possibility to convert known solutions into the new ones. This could seem an element of art, but in the context of ADHM-like equations describing quiver varieties there is a systematic approach. In this note we study moduli spaces and dualities of quiver gauge theories associated to effective dynamics of D-branes compactified on Calabi-Yau resolutions. We concentrate on a subfamily of quivers $\mathfrak{Q}_{\mathfrak{g}}$ covering Dynkin diagrams for simple Lie algebras $\mathfrak{g}$, where the respective BPS algebra is expected to be the Yangian algebra $Y(\mathfrak{g})$. For Yangians labeled by quivers their representations are described by solutions of ADHM-like equations. As quivers substitute Dynkin diagrams a generalization of the Weyl group $\mathcal{W}_{\mathfrak{g}}$ acts on the ADHM solutions. Here we work with the case $\mathfrak{g}=\mathfrak{sl}_{n+1}$ and treat this group as a group of electro-magnetic Seiberg-like dualities (we call them Weyl mutations) on the respective quiver gauge theories. We lift it to the case of higher representations associated to rectangular Young diagrams. An action of Weyl mutations on the BPS Yangian algebra is also discussed.
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https://arxiv.org/abs/2601.11736
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d4b5f35b4245da02ad341d310dcb2df4c6f51943f31d6910b2ea5684e39967ef
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2026-01-21T00:00:00-05:00
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On Nonasymptotic Confidence Intervals for Treatment Effects in Randomized Experiments
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arXiv:2601.11744v1 Announce Type: cross Abstract: We study nonasymptotic (finite-sample) confidence intervals for treatment effects in randomized experiments. In the existing literature, the effective sample sizes of nonasymptotic confidence intervals tend to be looser than the corresponding central-limit-theorem-based confidence intervals by a factor depending on the square root of the propensity score. We show that this performance gap can be closed, designing nonasymptotic confidence intervals that have the same effective sample size as their asymptotic counterparts. Our approach involves systematic exploitation of negative dependence or variance adaptivity (or both). We also show that the nonasymptotic rates that we achieve are unimprovable in an information-theoretic sense.
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https://arxiv.org/abs/2601.11744
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c4c69841ce963657bdb4f0089ca358300e7af18a9392b0f27b44edd3c8781026
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2026-01-21T00:00:00-05:00
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Generalized Shiraishi--Mori construction is exhaustive for ferromagnetic quantum many-body scars
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arXiv:2601.11806v1 Announce Type: cross Abstract: Quantum many-body scars (QMBS) constitute a subtle violation of ergodicity through a set of non-thermal eigenstates, referred to as scar states, which are embedded in an otherwise thermal spectrum. In a broad class of known examples, these scar states admit a simple interpretation: they are magnon excitations of fixed momentum on top of a ferromagnetic background. In this paper we prove that any Hamiltonian hosting such ``ferromagnetic scar states'' necessarily admits a structural decomposition into a Zeeman term and an ``annihilator'' that annihilates the entire scar manifold. Moreover, we show that this annihilator must itself decompose into a sum of terms built from local projectors that locally annihilate the scar states. This architecture is closely related to the Shiraishi--Mori construction, and our main theorem establishes that an appropriate generalization of that construction is in fact essentially exhaustive for this class of scar states.
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https://arxiv.org/abs/2601.11806
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2aecd841d2f596ba0b8bc3bf212e2083a6fec03071c320412a2939521e69cbd2
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2026-01-21T00:00:00-05:00
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Analysis of a Random Local Search Algorithm for Dominating Set
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arXiv:2601.11841v1 Announce Type: cross Abstract: Dominating Set is a well-known combinatorial optimization problem which finds application in computational biology or mobile communication. Because of its $\mathrm{NP}$-hardness, one often turns to heuristics for good solutions. Many such heuristics have been empirically tested and perform rather well. However, it is not well understood why their results are so good or even what guarantees they can offer regarding their runtime or the quality of their results. For this, a strong theoretical foundation has to be established. We contribute to this by rigorously analyzing a Random Local Search (RLS) algorithm that aims to find a minimum dominating set on a graph. We consider its performance on cycle graphs with $n$ vertices. We prove an upper bound for the expected runtime until an optimum is found of $\mathcal{O}\left(n^4\log^2(n)\right)$. In doing so, we introduce several models to represent dominating sets on cycles that help us understand how RLS explores the search space to find an optimum. For our proof we use techniques which are already quite popular for the analysis of randomized algorithms. We further apply a special method to analyze a reversible Markov Chain, which arises as a result of our modeling. This method has not yet found wide application in this kind of runtime analysis.
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https://arxiv.org/abs/2601.11841
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2580ba1aa5e1f27c712b6a8f052d1144b128d5797253eaa0c0df20afc0ce26c6
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2026-01-21T00:00:00-05:00
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Necessity of Cooperative Transmissions for Wireless MapReduce
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arXiv:2601.11844v1 Announce Type: cross Abstract: The paper presents an improved upper bound (achievability result) on the optimal tradeoff between Normalized Delivery Time (NDT) and computation load for distributed computing MapReduce systems in certain ranges of the parameters. The upper bound is based on interference alignment combined with zero-forcing. The paper further provides a lower bound (converse) on the optimal NDT-computation tradeoff that can be achieved when IVAs are partitioned into sub-IVAs, and these sub-IVAs are then transmitted (in an arbitrary form) by a single node, without cooperation among nodes. For appropriate linear functions (e.g., XORs), such non-cooperative schemes can achieve some of the best NDT-computation tradeoff points so far obtained in the literature. However, as our lower bound shows, any non-cooperative scheme achieves a worse NDT-computation tradeoff than our new proposed scheme for certain parameters, thus proving the necessity of cooperative schemes like zero-forcing to attain the optimal NDT-computation tradeoff.
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https://arxiv.org/abs/2601.11844
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9e623440ca5cd86a37efa45bb302fe965b5f845c5b722ae606c2b1693322c46f
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2026-01-21T00:00:00-05:00
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Least-Squares Multi-Step Koopman Operator Learning for Model Predictive Control
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arXiv:2601.11901v1 Announce Type: cross Abstract: MPC is widely used in real-time applications, but practical implementations are typically restricted to convex QP formulations to ensure fast and certified execution. Koopman-based MPC enables QP-based control of nonlinear systems by lifting the dynamics to a higher-dimensional linear representation. However, existing approaches rely on single-step EDMD. Consequently, prediction errors may accumulate over long horizons when the EDMD operator is applied recursively. Moreover, the multi-step prediction loss is nonconvex with respect to the single-step EDMD operator, making long-horizon model identification particularly challenging. This paper proposes a multi-step EDMD framework that directly learns the condensed multi-step state-control mapping required for Koopman-MPC, thereby bypassing explicit identification of the lifted system matrices and subsequent model condensation. The resulting identification problem admits a convex least-squares formulation. We further show that the problem decomposes across prediction horizons and state coordinates, enabling parallel computation and row-wise $\ell_1$-regularization for automatic dictionary pruning. A non-asymptotic finite-sample analysis demonstrates that, unlike one-step EDMD, the proposed method avoids error compounding and yields error bounds that depend only on the target multi-step mapping. Numerical examples validate improved long-horizon prediction accuracy and closed-loop performance.
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https://arxiv.org/abs/2601.11901
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dbe0f564e7e521bb3bf7a79d7b786ed344d8f21bb598a7ce17cb353b5b0a8a7b
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2026-01-21T00:00:00-05:00
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LIBRA: Language Model Informed Bandit Recourse Algorithm for Personalized Treatment Planning
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arXiv:2601.11905v1 Announce Type: cross Abstract: We introduce a unified framework that seamlessly integrates algorithmic recourse, contextual bandits, and large language models (LLMs) to support sequential decision-making in high-stakes settings such as personalized medicine. We first introduce the recourse bandit problem, where a decision-maker must select both a treatment action and a feasible, minimal modification to mutable patient features. To address this problem, we develop the Generalized Linear Recourse Bandit (GLRB) algorithm. Building on this foundation, we propose LIBRA, a Language Model-Informed Bandit Recourse Algorithm that strategically combines domain knowledge from LLMs with the statistical rigor of bandit learning. LIBRA offers three key guarantees: (i) a warm-start guarantee, showing that LIBRA significantly reduces initial regret when LLM recommendations are near-optimal; (ii) an LLM-effort guarantee, proving that the algorithm consults the LLM only $O(\log^2 T)$ times, where $T$ is the time horizon, ensuring long-term autonomy; and (iii) a robustness guarantee, showing that LIBRA never performs worse than a pure bandit algorithm even when the LLM is unreliable. We further establish matching lower bounds that characterize the fundamental difficulty of the recourse bandit problem and demonstrate the near-optimality of our algorithms. Experiments on synthetic environments and a real hypertension-management case study confirm that GLRB and LIBRA improve regret, treatment quality, and sample efficiency compared with standard contextual bandits and LLM-only benchmarks. Our results highlight the promise of recourse-aware, LLM-assisted bandit algorithms for trustworthy LLM-bandits collaboration in personalized high-stakes decision-making.
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https://arxiv.org/abs/2601.11905
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1d8c20ad03b01ec9d5eddfd140c82703bed4ebc6cbdc7583da223ad38f184a9a
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2026-01-21T00:00:00-05:00
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A Constraint Programming Model for the Super-Agile Earth Observation Satellite Imaging Scheduling Problem
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arXiv:2601.11967v1 Announce Type: cross Abstract: As the dependence on satellite imaging continues to grow, modern satellites have become increasingly agile, with the new generation, namely super-agile Earth observation satellites (SAEOS), providing unprecedented imaging flexibility. The highly dynamic capabilities of these satellites introduce additional challenges to the scheduling of observation tasks, as existing approaches for conventional agile satellites do not account for variable observation durations and multiple imaging directions. Although some efforts have been made in this regard, the SAEOS imaging scheduling problem (SAEOS-ISP) remains largely unexplored, and no exact approaches have yet been proposed. In this context, this study presents the first exact Constraint Programming formulation for the SAEOS-ISP, considering flexible observation windows, multiple pointing directions and sequence-dependent transition times across multiple satellites. Computational experiments on a newly generated benchmark set demonstrate that the model can be solved efficiently and within very short computational times. Moreover, the results also show that the proposed approach has the potential to achieve higher computational performance compared to the non-exact approaches that are currently considered state-of-the-art.
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https://arxiv.org/abs/2601.11967
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b184e435ec0daa2e15214088da90bc9b70fa4e8cf37d2943c27331dad2a22cf6
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2026-01-21T00:00:00-05:00
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Parameterized Complexity of Scheduling Problems in Robotic Process Automation
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arXiv:2601.11984v1 Announce Type: cross Abstract: This paper studies the growing domain of Robotic Process Automation (RPA) problems. Motivated by scheduling problems arising in RPA, we study the parameterized complexity of the single-machine problem $1|\text{prec},r_j,d_j|*$. We focus on parameters naturally linked to RPA systems, including chain-like precedences, the number of distinct processing times, and the structure of the time windows. We show that the problem is W[2]-hard parameterized by the number of chains, even with only two prescribed processing times and two distinct time-window lengths. This hardness remains even for distinct processing times and time windows under prec-consistent time windows. On the positive side, we obtain polynomial-time algorithm when all jobs share a single time-window length and FPT when the processing times, release times and deadlines are chain-uniform. We also show that the problem lies in XP when parameterized by the width of the precedence relation.
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https://arxiv.org/abs/2601.11984
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08734ae5c4fc0d0337728a89aa425b11ddc03d27dd1e86e3cc1e0063bcbb3d71
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2026-01-21T00:00:00-05:00
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A method for optimizing the structure of the software and hardware complex of a distributed process control system for large industrial enterprises
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arXiv:2601.12070v1 Announce Type: cross Abstract: The article proposes a method for optimizing the structure of the software and hardware complex of an automated control system for continuous technological processes for large industrial enterprises. General information is given on the relevance of the problem of choosing the structure of a system built on the basis of serially produced components, a formal description of the optimization problem is given, the criterion and limitations are highlighted. A solution method using the metaheuristic algorithm of ant colonies is described. A numerical example of the solution is given, the results of the algorithm are analyzed, and directions for further research are determined.
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https://arxiv.org/abs/2601.12070
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cb329a9f92b8f74ea77c562e9d18e19448eb85e698f211b5d3db162a4dadafe7
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2026-01-21T00:00:00-05:00
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Peres-type Criterion of Einstein-Podolsky-Rosen Steering for Two Qubits
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arXiv:2601.12085v1 Announce Type: cross Abstract: Quantum nonlocality manifests in multipartite systems through entanglement, Bell's nonlocality, and Einstein-Podolsky-Rosen (EPR) steering. While Peres's positive-partial-transpose criterion provides a simple and powerful test for entanglement, a comparably elegant spectral criterion for detecting EPR steering remains an open challenge. In this work, we systematically explore whether a Peres-type criterion can be established for EPR steering in the two-qubit system. Focusing on rank-2 (including rank-1) states and the two-qubit Werner state, we analyze the eigenvalues of their partially transposed density matrices and construct a significant steering criterion based on symmetric combinations of these eigenvalues. We prove that this criterion serves as a necessary and sufficient condition for steerability for the Werner state, all two-qubit pure states, all two-qubit rank-2 states. Furthermore, we validate the criterion for higher-rank states (rank-3 and rank-4) and show that the results align with known steering inequalities. Our findings suggest a more unified framework for detecting quantum nonlocality via partial transposition and open avenues for further theoretical and numerical investigations into steering detection.
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https://arxiv.org/abs/2601.12085
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665a30e955557ea34c4ef865d9f95317af2bc783b59e4770cdc83ee7aba3cbb9
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2026-01-21T00:00:00-05:00
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Tensionless spinning string: emergence of world-sheet torsion and covariant density of energy-momentum tensor
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arXiv:2601.12086v1 Announce Type: cross Abstract: The action of tensionless spinning string invariant under reparametrizions, both local supersymmetry and dilatations, is considered. The density of energy-momentum tensor is constructed and vanishing of its covariant divergence is proved. This result arises from mutual cancellation of the bosonic and fermionic contributions. Differences in the geometry of worldsheets swept by tensionless and tensionfull spinning strings are analyzed. Shown is emergence of covariant trace of a torsion tensor on w-s of the tensionless spinning string. It is derived from the condition for the fermionic scalar density to be a composite one including the 2-dim. w-s density simulating the 4-dim. Rarita-Schwinger field. The said condition is accompanied with the Noether condition for covariant divergence of the vector metric density to vanish.
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https://arxiv.org/abs/2601.12086
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41beacd0baa3728a1fdf05e5ded64f5c415e54f2179d2fcaeac5352965ba3a96
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2026-01-21T00:00:00-05:00
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On the Provable Suboptimality of Momentum SGD in Nonstationary Stochastic Optimization
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arXiv:2601.12238v1 Announce Type: cross Abstract: While momentum-based acceleration has been studied extensively in deterministic optimization problems, its behavior in nonstationary environments -- where the data distribution and optimal parameters drift over time -- remains underexplored. We analyze the tracking performance of Stochastic Gradient Descent (SGD) and its momentum variants (Polyak heavy-ball and Nesterov) under uniform strong convexity and smoothness in varying stepsize regimes. We derive finite-time bounds in expectation and with high probability for the tracking error, establishing a sharp decomposition into three components: a transient initialization term, a noise-induced variance term, and a drift-induced tracking lag. Crucially, our analysis uncovers a fundamental trade-off: while momentum can suppress gradient noise, it incurs an explicit penalty on the tracking capability. We show that momentum can substantially amplify drift-induced tracking error, with amplification that becomes unbounded as the momentum parameter approaches one, formalizing the intuition that using 'stale' gradients hinders adaptation to rapid regime shifts. Complementing these upper bounds, we establish minimax lower bounds for dynamic regret under gradient-variation constraints. These lower bounds prove that the inertia-induced penalty is not an artifact of analysis but an information-theoretic barrier: in drift-dominated regimes, momentum creates an unavoidable 'inertia window' that fundamentally degrades performance. Collectively, these results provide a definitive theoretical grounding for the empirical instability of momentum in dynamic environments and delineate the precise regime boundaries where SGD provably outperforms its accelerated counterparts.
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https://arxiv.org/abs/2601.12238
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c4bc7ddf1d738fb09ae1720db90945ecb0bccd90ea4279a8f568a1749fe9f542
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2026-01-21T00:00:00-05:00
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DeepRAHT: Learning Predictive RAHT for Point Cloud Attribute Compression
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arXiv:2601.12255v1 Announce Type: cross Abstract: Regional Adaptive Hierarchical Transform (RAHT) is an effective point cloud attribute compression (PCAC) method. However, its application in deep learning lacks research. In this paper, we propose an end-to-end RAHT framework for lossy PCAC based on the sparse tensor, called DeepRAHT. The RAHT transform is performed within the learning reconstruction process, without requiring manual RAHT for preprocessing. We also introduce the predictive RAHT to reduce bitrates and design a learning-based prediction model to enhance performance. Moreover, we devise a bitrate proxy that applies run-length coding to entropy model, achieving seamless variable-rate coding and improving robustness. DeepRAHT is a reversible and distortion-controllable framework, ensuring its lower bound performance and offering significant application potential. The experiments demonstrate that DeepRAHT is a high-performance, faster, and more robust solution than the baseline methods. Project Page: https://github.com/zb12138/DeepRAHT.
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https://arxiv.org/abs/2601.12255
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35e098bd8a728311c0182347cec83a60472cc18f89c40f82f584e73685aab141
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2026-01-21T00:00:00-05:00
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Topological quantum color code model on infinite lattice
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arXiv:2601.12409v1 Announce Type: cross Abstract: The color code model is a crucial instance of a Calderbank--Shor--Steane (CSS)-type topological quantum error-correcting code, which notably supports transversal implementation of the full Clifford group. Its robustness against local noise is rooted in the structure of its topological excitations. From the perspective of quantum phases of matter, it is essential to understand these excitations in the thermodynamic limit. In this work, we analyze the color code model on an infinite lattice within the quasi-local $C^{*}$-algebra framework, using a cone-localized Doplicher-Haag-Roberts (DHR) analysis. We classify its irreducible anyon superselection sectors and construct explicit string operators that generate anyonic excitations from the ground state. We further examine the fusion and braiding properties of these excitations. Our results show that the topological order of the color code is described by $\mathsf{Rep}(D(\mathbb{Z}_2 \times \mathbb{Z}_2)) \simeq \mathsf{Rep}(D(\mathbb{Z}_2)) \boxtimes \mathsf{Rep}(D(\mathbb{Z}_2))$, which is equivalent to a double layer of the toric code and consistent with established analyses on finite lattices.
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https://arxiv.org/abs/2601.12409
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3a4dd584267f6461e1e37a64d324d4f421e4cbc0a676f03c2b702c12868a6ba1
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2026-01-21T00:00:00-05:00
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A Mixture of Experts Vision Transformer for High-Fidelity Surface Code Decoding
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arXiv:2601.12483v1 Announce Type: cross Abstract: Quantum error correction is a key ingredient for large scale quantum computation, protecting logical information from physical noise by encoding it into many physical qubits. Topological stabilizer codes are particularly appealing due to their geometric locality and practical relevance. In these codes, stabilizer measurements yield a syndrome that must be decoded into a recovery operation, making decoding a central bottleneck for scalable real time operation. Existing decoders are commonly classified into two categories. Classical algorithmic decoders provide strong and well established baselines, but may incur substantial computational overhead at large code distances or under stringent latency constraints. Machine learning based decoders offer fast GPU inference and flexible function approximation, yet many approaches do not explicitly exploit the lattice geometry and local structure of topological codes, which can limit performance. In this work, we propose QuantumSMoE, a quantum vision transformer based decoder that incorporates code structure through plus shaped embeddings and adaptive masking to capture local interactions and lattice connectivity, and improves scalability via a mixture of experts layer with a novel auxiliary loss. Experiments on the toric code demonstrate that QuantumSMoE outperforms state-of-the-art machine learning decoders as well as widely used classical baselines.
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https://arxiv.org/abs/2601.12483
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30fa0f47b028d041c1ad4eda1ca36a92e828cc598d9baa613c09457b1ddbf8a9
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2026-01-21T00:00:00-05:00
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Rerandomization for quantile treatment effects
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arXiv:2601.12540v1 Announce Type: cross Abstract: Although complete randomization is widely regarded as the gold standard for causal inference, covariate imbalance can still arise by chance in finite samples. Rerandomization has emerged as an effective tool to improve covariate balance across treatment groups and enhance the precision of causal effect estimation. While existing work focuses on average treatment effects, quantile treatment effects (QTEs) provide a richer characterization of treatment heterogeneity by capturing distributional shifts in outcomes, which is crucial for policy evaluation and equity-oriented research. In this article, we establish the asymptotic properties of the QTE estimator under rerandomization within a finite-population framework, without imposing any distributional or modeling assumptions on the covariates or outcomes.The estimator exhibits a non-Gaussian asymptotic distribution, represented as a linear combination of Gaussian and truncated Gaussian random variables. To facilitate inference, we propose a conservative variance estimator and construct corresponding confidence interval. Our theoretical analysis demonstrates that rerandomization improves efficiency over complete randomization under mild regularity conditions. Simulation studies further support the theoretical findings and illustrate the practical advantages of rerandomization for QTE estimation.
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https://arxiv.org/abs/2601.12540
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1f5a2308476c026bf515c1490e1a799273c512d6825b6c5709c4fdba683d385c
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2026-01-21T00:00:00-05:00
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Quantum Filtering for Squeezed Noise Inputs
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arXiv:2601.12564v1 Announce Type: cross Abstract: We derive the quantum filter for a quantum open system undergoing quadrature measurements (homodyning) where the input field is in a general quasi-free state. This extends previous work for thermal input noise and allows for squeezed inputs. We introduce a convenient class of Bogoliubov transformations which we refer to as balanced and formulate the quantum stochastic model with squeezed noise as an Araki-Woods type representation. We make an essential use of the Tomita-Takesaki theory to construct the commutant of the C*-algebra describing the inputs and obtain the filtering equations using the quantum reference probability technique. The derived quantum filter must be independent of the choice of representation and this is achieved by fixing an independent quadrature in the commutant algebra.
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https://arxiv.org/abs/2601.12564
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ef6e40f65b22c6f8189ede8cc203fdb0a1cf7793af2326cddaf5490effa27e85
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2026-01-21T00:00:00-05:00
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Partial Identification under Stratified Randomization
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arXiv:2601.12566v1 Announce Type: cross Abstract: This paper develops a unified framework for partial identification and inference in stratified experiments with attrition, accommodating both equal and heterogeneous treatment shares across strata. For equal-share designs, we apply recent theory for finely stratified experiments to Lee bounds, yielding closed-form, design-consistent variance estimators and properly sized confidence intervals. Simulations show that the conventional formula can overstate uncertainty, while our approach delivers tighter intervals. When treatment shares differ across strata, we propose a new strategy, which combines inverse probability weighting and global trimming to construct valid bounds even when strata are small or unbalanced. We establish identification, introduce a moment estimator, and extend existing inference results to stratified designs with heterogeneous shares, covering a broad class of moment-based estimators which includes the one we formulate. We also generalize our results to designs in which strata are defined solely by observed labels.
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https://arxiv.org/abs/2601.12566
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88582ddc96b0fe78f0470d0c4a964ddbbda229764ed4cdacbc23e62ce12dfa4a
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2026-01-21T00:00:00-05:00
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Angular Sensing by Highly Reconfigurable Pixel Antennas with Joint Radiating Aperture and Feeding Ports Reconfiguration
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arXiv:2601.12867v1 Announce Type: cross Abstract: Angular sensing capability is realized using highly reconfigurable pixel antenna (HRPA) with joint radiating aperture and feeding ports reconfiguration. Pixel antennas represent a general class of reconfigurable antenna designs in which the radiating surface, regardless of its shape or size, is divided into sub-wavelength elements called pixels. Each pixel is connected to its neighboring elements through radio frequency switches. By controlling pixel connections, the pixel antenna topology can be flexibly adjusted so that the resulting radiation pattern can be reconfigured. However, conventional pixel antennas have only a single, fixed-position feeding port, which is not efficient for angular sensing. Therefore, in this work, we further extend the reconfigurability of pixel antennas by introducing the HRPA, which enables both geometry control of the pixel antenna and switching of its feeding ports. The model of the proposed HRPA, including both circuit and radiation parameters, is derived. A codebook is then defined, consisting of pixel connection states and feeding port positions for each sensing area. Based on this codebook, an efficient optimization approach is developed to minimize the Cram\acute{\mathrm{\mathbf{e}}}r-Rao lower bound (CRLB) and obtain the optimal HRPA geometries for angular sensing within a given area. Numerical results show that the HRPA reduces the angle estimation error by more than 50% across the full three-dimensional sphere when compared with a conventional uniform planar array of the same size. This demonstrates the effectiveness of the proposed approach and highlights the potential of HRPA for integrated sensing and communication systems.
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https://arxiv.org/abs/2601.12867
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82fd460da80f66363e03ba647d648657d712276410a0d7dbf9ce195cf48a1bb1
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2026-01-21T00:00:00-05:00
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Transverse modulation in electrovac Brinkmann pp-waves: Maxwell consistency and curvature universality
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arXiv:2601.12949v1 Announce Type: cross Abstract: Electrovac pp--waves in Brinkmann form provide exact Einstein--Maxwell solutions for co--propagating null radiation. Motivated by lensing or scattering, one often ``modulates'' a plane electromagnetic wave by a weak transverse envelope $1+\gamma f(x,y)$. We show that, within the aligned null pp--wave ansatz ($A_v=0$, no $v$--dependence, $F_{xy}=0$) and enforcing the source--free Maxwell equations to $\mathcal O(\gamma)$, a generic profile $f(x,y)$ is incompatible with Maxwell: the transverse field $F_{ui}$ must be both divergence--free and curl--free on the transverse plane, hence $F_{ui}=\partial_i\Phi$ with $\Delta_\perp\Phi=0$. We give a minimal, polarization--agnostic gauge completion of the modulated potential and prove a cancellation theorem: under standard decay/regularity (or zero--mode) conditions that exclude additional harmonic transverse modes, all $\mathcal O(\gamma)$ dependence on $f$ drops out of $F_{ui}$ and therefore out of the electrovac source $T_{uu}$. Consequently, the electromagnetic contribution to the Brinkmann profile is universal at $\mathcal O(\gamma)$: the familiar cycle--averaged isotropic $r^2$ term plus an isotropic oscillatory correction at frequency $2\omega$, present only for non-circular polarisation. We isolate the residual Maxwell--admissible freedom as harmonic (holomorphic) transverse data and, by Kerr--Schild linearity, superpose an arbitrary co--propagating vacuum gravitational pp--wave, relating TT--gauge strain to Brinkmann amplitudes. Modelling genuinely localised beams, therefore, requires currents, non-null components, or more general Kundt/gyraton geometries.
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https://arxiv.org/abs/2601.12949
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7fbd92a2ec6bc6bd2f3d94c8cc61cd03d7146acdcab24c014cc84b31ad220d8d
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2026-01-21T00:00:00-05:00
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When Is Distributed Nonlinear Aggregation Private? Optimality and Information-Theoretical Bounds
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arXiv:2601.13001v1 Announce Type: cross Abstract: Nonlinear aggregation is central to modern distributed systems, yet its privacy behavior is far less understood than that of linear aggregation. Unlike linear aggregation where mature mechanisms can often suppress information leakage, nonlinear operators impose inherent structural limits on what privacy guarantees are theoretically achievable when the aggregate must be computed exactly. This paper develops a unified information-theoretic framework to characterize privacy leakage in distributed nonlinear aggregation under a joint adversary that combines passive (honest-but-curious) corruption and eavesdropping over communication channels. We cover two broad classes of nonlinear aggregates: order-based operators (maximum/minimum and top-$K$) and robust aggregation (median/quantiles and trimmed mean). We first derive fundamental lower bounds on leakage that hold without sacrificing accuracy, thereby identifying the minimum unavoidable information revealed by the computation and the transcript. We then propose simple yet effective privacy-preserving distributed algorithms, and show that with appropriate randomized initialization and parameter choices, our proposed approaches can attach the derived optimal bounds for the considered operators. Extensive experiments validate the tightness of the bounds and demonstrate that network topology and key algorithmic parameters (including the stepsize) govern the observed leakage in line with the theoretical analysis, yielding actionable guidelines for privacy-preserving nonlinear aggregation.
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https://arxiv.org/abs/2601.13001
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3872904900d24146ed5a5caf7335ea0998718a210052a6e8ab1d270412f7a2f6
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2026-01-21T00:00:00-05:00
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On nonlinear self-duality in $4p$ dimensions
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arXiv:2601.13022v1 Announce Type: cross Abstract: We demonstrate that every model for self-dual nonlinear electrodynamics in four dimensions has a $\mathsf{U}(1)$ duality-invariant extension to $4p>4$ dimensions.
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https://arxiv.org/abs/2601.13022
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ccce744452a61b96b551bd030eabc3850bc643daffff6e8354e15f3311aae672
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2026-01-21T00:00:00-05:00
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Failure of the mean-field Hartree approximation for a bosonic many-body system with non-Hermitian Hamiltonian
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arXiv:2601.13038v1 Announce Type: cross Abstract: Mean-field Hartree theory is a central tool for reducing interacting many-body dynamics to an effective nonlinear one-particle evolution. This approximation has been employed also when the Hamiltonian that governs the many-body dynamics is not Hermitian. Indeed, non-Hermitian Hamiltonians model particle gain/loss or the evolution of open quantum systems between consecutive quantum jumps. Furthermore, the validity of the Hartree approximation for generic non-Hermitian Hamiltonians lies at the basis of a quantum algorithm for nonlinear differential equations. In this work, we show that this approximation can fail. We analytically solve a model of $N$ bosonic qubits with two-body interactions generated by a purely anti-Hermitian Hamiltonian, determine an analytic expression for the limit for $N\to\infty$ of the one-particle marginal state and show that such a limit does not agree with the solution of the non-Hermitian Hartree evolution equation. We further show that there exists an initial condition such that the exact one-particle marginal state undergoes a finite-time transition to a mixed state, a phenomenon that is completely absent in the case of Hermitian Hamiltonians. Our findings challenge the validity of the mean-field Hartree approximation for non-Hermitian Hamiltonians, and call for additional conditions for the validity of the mean-field regime to model the dynamics of particle gain and loss and the open-system dynamics in bosonic many-body systems.
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https://arxiv.org/abs/2601.13038
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0319bfe851f9ac8ce40917816c550560c8bbc68c353b0420408f45a9c6629303
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2026-01-21T00:00:00-05:00
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Approximate full conformal prediction in RKHS
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arXiv:2601.13102v1 Announce Type: cross Abstract: Full conformal prediction is a framework that implicitly formulates distribution-free confidence prediction regions for a wide range of estimators. However, a classical limitation of the full conformal framework is the computation of the confidence prediction regions, which is usually impossible since it requires training infinitely many estimators (for real-valued prediction for instance). The main purpose of the present work is to describe a generic strategy for designing a tight approximation to the full conformal prediction region that can be efficiently computed. Along with this approximate confidence region, a theoretical quantification of the tightness of this approximation is developed, depending on the smoothness assumptions on the loss and score functions. The new notion of thickness is introduced for quantifying the discrepancy between the approximate confidence region and the full conformal one.
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https://arxiv.org/abs/2601.13102
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c685618bed5a7a6a8a7045217365341dbeeb5830e9c68b70fce40136bca7acb8
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2026-01-21T00:00:00-05:00
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Global stability of a Hebbian/anti-Hebbian network for principal subspace learning
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arXiv:2601.13170v1 Announce Type: cross Abstract: Biological neural networks self-organize according to local synaptic modifications to produce stable computations. How modifications at the synaptic level give rise to such computations at the network level remains an open question. Pehlevan et al. [Neur. Comp. 27 (2015), 1461--1495] proposed a model of a self-organizing neural network with Hebbian and anti-Hebbian synaptic updates that implements an algorithm for principal subspace analysis; however, global stability of the nonlinear synaptic dynamics has not been established. Here, for the case that the feedforward and recurrent weights evolve at the same timescale, we prove global stability of the continuum limit of the synaptic dynamics and show that the dynamics evolve in two phases. In the first phase, the synaptic weights converge to an invariant manifold where the `neural filters' are orthonormal. In the second phase, the synaptic dynamics follow the gradient flow of a non-convex potential function whose minima correspond to neural filters that span the principal subspace of the input data.
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https://arxiv.org/abs/2601.13170
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f0a51a6a9ed0a2a71307409bc8c37e8d11f639f3d8eb26a838cde1911425750e
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2026-01-21T00:00:00-05:00
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Decentralized Cooperative Beamforming for BDRIS-Assisted Cell-Free MIMO OFDM Systems
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arXiv:2601.13201v1 Announce Type: cross Abstract: In this paper, a wideband cell-free multi-stream multi-user Multiple-Input Multiple-Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) system is considered operating within a smart wireless environment enabled by multiple Beyond Diagonal Reconfigurable Intelligent Surfaces (BDRISs). A novel decentralized active and passive beamforming framework, robust to imperfect channel state availability and with minimal cooperation among the system's multiple Base Stations (BSs) for deciding the final configurations of the shared BDRISs, is proposed, which aims to substantially reduce the overhead inherent in centralized solutions necessitating a central processing unit of high computational power. By considering a Dynamic Group-Connected (DGC) BDRIS architecture with frequency-selective responses per unit element, we formulate the system's sum-rate maximization problem with respect to the tunable capacitances and permutation matrices of the BDRISs as well as the precoding matrices of the BSs, which is solved via successive concave approximation and alternating projections as well as consensus-based updates for the BDRISs' design. Through extensive simulation results, it is showcased that the proposed robust decentralized cooperative approach with diverse BDRIS architectures outperforms non-cooperation benchmarks. It is also demonstrated that the considered DGC BDRIS architecture is able to provide sum-rate performance gains sufficiently close to the more complex fully-connected BDRIS structure.
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https://arxiv.org/abs/2601.13201
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5094db56418956663926c9d5230d39909704153bd36e24b6c458d078017fa436
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2026-01-21T00:00:00-05:00
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Bihamiltonian tests for integrable systems associated to rank-$1$ F-CohFTs
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arXiv:2601.13203v1 Announce Type: cross Abstract: Double ramification (DR) hierarchies associated to rank-$1$ F-CohFTs are important integrable perturbations of the Riemann--Hopf hierarchy. In this paper, we perform bihamiltonian tests for these DR hierarchies, and conjecture that the ones that are bihamiltonian form a $2$-parameter family. Remarkably, our computations suggest that there is a $1$-parameter subfamily of the rank-$1$ F-CohFTs, where the corresponding DR hierarchy is conjecturally Miura equivalent to the Camassa--Holm hierarchy. We also prove a conjecture regarding bihamiltonian Hodge hierarchies. Finally, we systematically study Miura invariants, and for another $1$-parameter subfamily propose a conjectural relation to the Degasperis--Procesi hierarchy.
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https://arxiv.org/abs/2601.13203
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c9707dce5dc7d0f6bad90ac9d7ec67fd6c44cef62cf4836026d387944339ad11
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2026-01-21T00:00:00-05:00
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Hierarchical Sparse Vector Transmission for Ultra Reliable and Low Latency Communications
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arXiv:2601.13204v1 Announce Type: cross Abstract: Sparse vector transmission (SVT) is a promising candidate technology for achieving ultra-reliable low-latency communication (URLLC). In this paper, a hierarchical SVT scheme is proposed for multi-user URLLC scenarios. The hierarchical SVT scheme partitions the transmitted bits into common and private parts. The common information is conveyed by the indices of non-zero sections in a sparse vector, while each user's private information is embedded into non-zero blocks with specific block lengths. At the receiver, the common bits are first recovered from the detected non-zero sections, followed by user-specific private bits decoding based on the corresponding non-zero block indices. Simulation results show the proposed scheme outperforms state-of-the-art SVT schemes in terms of block error rate.
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https://arxiv.org/abs/2601.13204
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4881ad662ba2b910c61d40fdd24f36e58606e7206094b6c8748a7cd95bdf74a9
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2026-01-21T00:00:00-05:00
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The table maker's quantum search
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arXiv:2601.13306v1 Announce Type: cross Abstract: We show that quantum search can be used to compute the hardness to round an elementary function, that is, to determine the minimum working precision required to compute the values of an elementary function correctly rounded to a target precision of $n$ digits for all possible precision-$n$ floating-point inputs in a given interval. For elementary functions $f$ related to the exponential function, quantum search takes time $\tilde O(2^{n/2} \log (1/\delta))$ to return, with probability $1-\delta$, the hardness to round $f$ over all $n$-bit floating-point inputs in a given binade. For periodic elementary functions in large binades, standalone quantum search yields an asymptotic speedup over the best known classical algorithms and heuristics.
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https://arxiv.org/abs/2601.13306
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c81690d05e4d447e1204bce0a44eb03a4c6e3c256e20474765af9ea07ccb54d6
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2026-01-21T00:00:00-05:00
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Renewal theory for Brownian motion across a stochastically gated interface
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arXiv:2601.13414v1 Announce Type: cross Abstract: Stochastically gated interfaces play an important role in a variety of cellular diffusion processes. Examples include intracellular transport via stochastically gated ion channels and pores in the plasma membrane of a cell, intercellular transport between cells coupled by stochastically gated gap junctions, and oxygen transport in insect respiration. Most studies of stochastically-gated interfaces are based on macroscopic models that track the particle concentration averaged with respect to different realisations of the gate dynamics. In this paper we use renewal theory to develop a probabilistic model of single-particle Brownian motion (BM) through a stochastically gated interface. We proceed by constructing a renewal equation for 1D BM with an interface at the origin, which effectively sews together a sequence of BMs on the half-line with a totally absorbing boundary at $x=0$. Each time the particle is absorbed, the stochastic process is immediately restarted according to the following rule: if the gate is closed then BM restarts on the same side of the interface, whereas if the gate is open then BM restarts on either side of the interface with equal probability. In order to ensure that diffusion restarts in a state that avoids immediate re-absorption. we assume that whenever the particle reaches the interface it is instantaneously shifted a distance $\epsilon$ from the origin. We explicitly solve the renewal equation for $\epsilon>0$ and show how the solution of a corresponding forward Kolmogorov equation is recovered in the limit $\epsilon\rightarrow 0$. However, the renewal equation provides a more general mathematical framework by explicitly separating the first passage time problem of detecting the gated interface (absorption) and the subsequent rule for restarting BM. We conclude by extending the theory to higher-dimensional interfaces.
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https://arxiv.org/abs/2601.13414
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cbe4de976e71d57363f7298b42d7fe3efd33653f468804c010ba0d947d68cb11
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2026-01-21T00:00:00-05:00
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Optimal estimation of generalized causal effects in cluster-randomized trials with multiple outcomes
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arXiv:2601.13428v1 Announce Type: cross Abstract: Cluster-randomized trials (CRTs) are widely used to evaluate group-level interventions and increasingly collect multiple outcomes capturing complementary dimensions of benefit and risk. Investigators often seek a single global summary of treatment effect, yet existing methods largely focus on single-outcome estimands or rely on model-based procedures with unclear causal interpretation or limited robustness. We develop a unified potential outcomes framework for generalized treatment effects with multiple outcomes in CRTs, accommodating both non-prioritized and prioritized outcome settings. The proposed cluster-pair and individual-pair causal estimands are defined through flexible pairwise contrast functions and explicitly account for potentially informative cluster sizes. We establish nonparametric estimation via weighted clustered U-statistics and derive efficient influence functions to construct covariate-adjusted estimators that integrate debiased machine learning with U-statistics. The resulting estimators are consistent and asymptotically normal, attain the semiparametric efficiency bounds under mild regularity conditions, and have analytically tractable variance estimators that are proven to be consistent under cross-fitting. Simulations and an application to a CRT for chronic pain management illustrate the practical utility of the proposed methods.
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https://arxiv.org/abs/2601.13428
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15c543de1e58cd5cdb56e5159c276bcbeee6e4b9cc00aa36702f8add7d712628
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2026-01-21T00:00:00-05:00
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Distribution-Free Confidence Ellipsoids for Ridge Regression with PAC Bounds
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arXiv:2601.13436v1 Announce Type: cross Abstract: Linearly parametrized models are widely used in control and signal processing, with the least-squares (LS) estimate being the archetypical solution. When the input is insufficiently exciting, the LS problem may be unsolvable or numerically unstable. This issue can be resolved through regularization, typically with ridge regression. Although regularized estimators reduce the variance error, it remains important to quantify their estimation uncertainty. A possible approach for linear regression is to construct confidence ellipsoids with the Sign-Perturbed Sums (SPS) ellipsoidal outer approximation (EOA) algorithm. The SPS EOA builds non-asymptotic confidence ellipsoids under the assumption that the noises are independent and symmetric about zero. This paper introduces an extension of the SPS EOA algorithm to ridge regression, and derives probably approximately correct (PAC) upper bounds for the resulting region sizes. Compared with previous analyses, our result explicitly show how the regularization parameter affects the region sizes, and provide tighter bounds under weaker excitation assumptions. Finally, the practical effect of regularization is also demonstrated via simulation experiments.
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https://arxiv.org/abs/2601.13436
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2db52718bb4d85e9eef539d61a8dfb216059a3eec583317d145150d4eab6cb98
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2026-01-21T00:00:00-05:00
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Labels or Preferences? Budget-Constrained Learning with Human Judgments over AI-Generated Outputs
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arXiv:2601.13458v1 Announce Type: cross Abstract: The increasing reliance on human preference feedback to judge AI-generated pseudo labels has created a pressing need for principled, budget-conscious data acquisition strategies. We address the crucial question of how to optimally allocate a fixed annotation budget between ground-truth labels and pairwise preferences in AI. Our solution, grounded in semi-parametric inference, casts the budget allocation problem as a monotone missing data framework. Building on this formulation, we introduce Preference-Calibrated Active Learning (PCAL), a novel method that learns the optimal data acquisition strategy and develops a statistically efficient estimator for functionals of the data distribution. Theoretically, we prove the asymptotic optimality of our PCAL estimator and establish a key robustness guarantee that ensures robust performance even with poorly estimated nuisance models. Our flexible framework applies to a general class of problems, by directly optimizing the estimator's variance instead of requiring a closed-form solution. This work provides a principled and statistically efficient approach for budget-constrained learning in modern AI. Simulations and real-data analysis demonstrate the practical benefits and superior performance of our proposed method.
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https://arxiv.org/abs/2601.13458
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77f8f15df5d7d5e6ab3d7a9f577d80fa3260f2527e9c4324d9f700a1121b1202
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2026-01-21T00:00:00-05:00
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Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards an Entanglement-Sensitive Langlands Correspondence
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arXiv:2601.13467v1 Announce Type: cross Abstract: Recently, quantum entanglement has been presented as a cohomological obstruction to reconstructing a global quantum state from locally compatible information, where sheafification provides a functor that is forgetful with regards to global-from-local signatures while acting faithfully with respect to within-patch multipartite structures. Nontrivial connections to Hecke modifications and the geometric Langlands program are explored in the process. The aim of this work is to validate and extend a number of the claims made in [arXiv:2511.04326] through both theoretical analysis and numerical simulations, employing concrete perspectives from condensed matter physics.
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https://arxiv.org/abs/2601.13467
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db7c6a6ccc9acbda55559bb616749bb13450fdbd91142bbbab817f8abd7baef6
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2026-01-21T00:00:00-05:00
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Resampling-free Inference for Time Series via RKHS Embedding
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arXiv:2601.13468v1 Announce Type: cross Abstract: In this article, we study nonparametric inference problems in the context of multivariate or functional time series, including testing for goodness-of-fit, the presence of a change point in the marginal distribution, and the independence of two time series, among others. Most methodologies available in the existing literature address these problems by employing a bandwidth-dependent bootstrap or subsampling approach, which can be computationally expensive and/or sensitive to the choice of bandwidth. To address these limitations, we propose a novel class of kernel-based tests by embedding the data into a reproducing kernel Hilbert space, and construct test statistics using sample splitting, projection, and self-normalization (SN) techniques. Through a new conditioning technique, we demonstrate that our test statistics have pivotal limiting null distributions under absolute regularity and mild moment assumptions. We also analyze the limiting power of our tests under local alternatives. Finally, we showcase the superior size accuracy and computational efficiency of our methods as compared to some existing ones.
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https://arxiv.org/abs/2601.13468
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b8f948f395492d6e2ae361aef09bd4ee61c427b7a561ba878fa748d925c3b3ba
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2026-01-21T00:00:00-05:00
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Small Gradient Norm Regret for Online Convex Optimization
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arXiv:2601.13519v1 Announce Type: cross Abstract: This paper introduces a new problem-dependent regret measure for online convex optimization with smooth losses. The notion, which we call the $G^\star$ regret, depends on the cumulative squared gradient norm evaluated at the decision in hindsight $\sum_{t=1}^T \|\nabla \ell(x^\star)\|^2$. We show that the $G^\star$ regret strictly refines the existing $L^\star$ (small loss) regret, and that it can be arbitrarily sharper when the losses have vanishing curvature around the hindsight decision. We establish upper and lower bounds on the $G^\star$ regret and extend our results to dynamic regret and bandit settings. As a byproduct, we refine the existing convergence analysis of stochastic optimization algorithms in the interpolation regime. Some experiments validate our theoretical findings.
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https://arxiv.org/abs/2601.13519
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4c2a02afff925cfe4be6f76401f5b83c0156848024a02bb5b15592a8f1c59c7c
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2026-01-21T00:00:00-05:00
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Near-field Physical Layer Security: Robust Beamforming under Location Uncertainty
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arXiv:2601.13549v1 Announce Type: cross Abstract: In this paper, we study robust beamforming design for near-field physical-layer-security (PLS) systems, where a base station (BS) equipped with an extremely large-scale array (XL-array) serves multiple near-field legitimate users (Bobs) in the presence of multiple near-field eavesdroppers (Eves). Unlike existing works that mostly assume perfect channel state information (CSI) or location information of Eves, we consider a more practical and challenging scenario, where the locations of Bobs are perfectly known, while only imperfect location information of Eves is available at the BS. We first formulate a robust optimization problem to maximize the sum-rate of Bobs while guaranteeing a worst-case limit on the eavesdropping rate under location uncertainty. By transforming Cartesian position errors into the polar domain, we reveal an important near-field angular-error amplification effect: for the same location error, the closer the Eve, the larger the angle error, severely degrading the performance of conventional robust beamforming methods based on imperfect channel state information. To address this issue, we first establish the conditions for which the first-order Taylor approximation of the near-field channel steering vector under location uncertainty is largely accurate. Then, we propose a two-stage robust beamforming method, which first partitions the uncertainty region into multiple fan-shaped sub-regions, followed by the second stage to formulate and solve a refined linear-matrix-inequality (LMI)-based robust beamforming optimization problem. In addition, the proposed method is further extended to scenarios with multiple Bobs and multiple Eves. Finally, numerical results validate that the proposed method achieves a superior trade-off between rate performance and secrecy robustness, hence significantly outperforming existing benchmarks under Eve location uncertainty.
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https://arxiv.org/abs/2601.13549
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3cb2c7424c11ee6c214a4a3badfd643c8c13dbb52cd5e31e55faa65375af8ac1
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2026-01-21T00:00:00-05:00
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Additive-Functional Approach to Transport in Periodic and Tilted Periodic Potentials
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arXiv:2601.13561v1 Announce Type: cross Abstract: We present a unified theoretical framework for effective transport in periodic and tilted periodic potentials based on additive functionals of stochastic processes. By systematically combining the Poisson equation, corrector construction, and martingale decomposition, we show that both the long-time drift and diffusion of overdamped Brownian motion can be derived within a single and transparent scheme. In the absence of external tilt, the formalism naturally recovers the classical Lifson-Jackson formula for the effective diffusion coefficient. When a constant bias is applied, breaking detailed balance and inducing a finite stationary current, the same approach yields the Stratonovich expressions for the effective drift and diffusion in tilted periodic potentials. Beyond one dimension, we demonstrate that the same additive-functional structure extends directly to two-dimensional and general N dimensional periodic diffusions, leading to the standard homogenized drift and diffusion tensor expressed in terms of vector-valued correctors. Our derivation highlights the central role of additive functionals in separating bounded microscopic corrections from unbounded macroscopic transport and clarifies the connection between reversible and nonequilibrium steady states. This work provides a conceptually unified and mathematically controlled route to transport coefficients in periodic media, with direct relevance to stochastic transport, soft matter, and nonequilibrium statistical physics.
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https://arxiv.org/abs/2601.13561
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4df5d654566ae6a279d2d19a1dd59e076076d9b964cb10f22e112b8ba6352cd1
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2026-01-21T00:00:00-05:00
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Cost-Effectiveness of Adult Hepatitis A Vaccination Strategies in Korea Under an Aging Susceptibility Profile
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arXiv:2601.13714v1 Announce Type: cross Abstract: Hepatitis A severity increases sharply with age, while Korea is experiencing a cohort shift in which low seroprevalence adult cohorts are aging into older, higher fatality age groups. This demographic and immunological transition creates an urgent policy question regarding how adult vaccination should be prioritized under resource constraints. We evaluated three adult vaccination scenarios targeting low seroprevalence age groups (S1) 20 to 39 years, (S2) 40 to 59 years, and (S3) 20 to 59 years. Using an age structured dynamic transmission model calibrated to Korean data, we derived dynamically feasible vaccination allocation trajectories under realistic capacity constraints using an optimal control framework and linked these trajectories to long term transmission model simulations. We conducted DALY based cost effectiveness analyses over a lifetime horizon from both healthcare system and societal perspectives, and characterized uncertainty using probabilistic sensitivity analysis (PSA) and cost effectiveness acceptability curves (CEACs). Robustness was examined using one way sensitivity analyses. In the base case, S2 consistently yields the most favorable and robust cost effectiveness profile under both perspectives, with the lowest ICER. S3 achieved the largest reduction in DALYs but requires substantially higher incremental costs, resulting in a higher ICER than S2. S1 produces the smallest DALY reduction and is the least efficient strategy. PSA and CEACs confirm that S2 remains the preferred option across most willingness to pay ranges. S2 offers the most balanced and robustly cost effective strategy in Korea, capturing substantial mortality reduction while limiting additional program costs. S3 may be justified when higher budgets or willingness to pay thresholds are acceptable, but S2 provides the clearest value for money under epidemiological and economic conditions.
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https://arxiv.org/abs/2601.13714
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e4f9caa6fc0e0628d6dceda947678cc8d9424b00d5684068ed277536bf3a2174
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2026-01-21T00:00:00-05:00
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Soliton dynamics in the ABS nonlinear spinor model with external fields
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arXiv:2601.13783v1 Announce Type: cross Abstract: We consider the novel nonlinear model in (1 + 1)-dimensions for Dirac spinors recently introduced by Alexeeva, Barashenkov, and Saxena [1] (ABS model), which admits an exact explicit solitary-wave (soliton for short) solution. The charge, the momentum, and the energy of this solution are conserved. We investigate the dynamics of the soliton subjected to several potentials: a ramp, a harmonic, and a periodic potential. We develop a Collective Coordinates Theory by making an ansatz for a moving soliton where the position, rapidity, and momentum, are functions of time. We insert the ansatz into the Lagrangian density of the model, integrate over space and obtain a Lagrangian as a function of the collective coordinates. This Lagrangian differs only in the charge and mass with the Lagrangian of a collective coordinates theory for the Gross-Neveu equation. Thus the soliton dynamics in the ABS spinor model is qualitatively the same as in the Gross-Neveu equation, but quantitatively it differs. These results of the collective coordinates theory are confirmed by simulations, i.e., by numerical solutions for solitons of the ABS spinor model, subjected to the above potentials.
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https://arxiv.org/abs/2601.13783
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ab7e3c3e31923064cd363baf3f74989096e27f3a27484eaf673f87624ca4ba86
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2026-01-21T00:00:00-05:00
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Composing $p$-adic qubits: from representations of SO(3)$_p$ to entanglement and universal quantum logic gates
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arXiv:2601.13808v1 Announce Type: cross Abstract: In the context of $p$-adic quantum mechanics, we investigate composite systems of $p$-adic qubits and $p$-adically controlled quantum logic gates. We build on the notion of a single $p$-adic qubit as a two-dimensional irreducible representation of the compact $p$-adic special orthogonal group SO(3)$_p$. We show that the classification of these representations reduces to the finite case, as they all factorise through some finite quotient SO(3)$_p$ mod $p^k$. Then, we tackle the problem of $p$-adic qubit composition and entanglement, fundamental for a $p$-adic formulation of quantum information processing. We classify the representations of SO(3)$_p$ mod $p$, and analyse tensor products of two $p$-adic qubit representations lifted from SO(3)$_p$ mod $p$. We solve the Clebsch-Gordan problem for such systems, revealing that the coupled bases decompose into singlet and doublet states. We further study entanglement arising from those stable subsystems. For $p=3$, we construct a set of gates from $4$-dimensional irreducible representations of SO(3)$_p$ mod $p$ that we prove to be universal for quantum computation.
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https://arxiv.org/abs/2601.13808
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3ef8bd01c5d2e6bb2a5404268805f7c67f256bd68cdc3811e950dcdeaeb1d35e
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2026-01-21T00:00:00-05:00
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Achieving Full Multipath Diversity by Random Constellation Rotation: a Theoretical Perspective
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arXiv:2601.13997v1 Announce Type: cross Abstract: Diversity is an essential concept associated with communication reliability in multipath channels since it determines the slope of bit error rate performance in the medium to high signal-to-noise ratio regions. However, most of the existing analytical frameworks were developed for specific modulation schemes while the efficient validation of full multipath diversity for general modulation schemes remains an open problem. To fill this research gap, we propose to utilize random constellation rotation to ease the conditions for full-diversity modulation designs. For linearly precoded cyclic-prefix orthogonal frequency division multiplexing (OFDM) systems, we prove that maximum multipath diversity can be attained as long as the spread matrix does not have zero entries, which is a sufficient but easily satisfied condition. Furthermore, we derive the sufficient and necessary condition for general modulation schemes, whose verification can be divided into validation tasks for each column of the modulation matrix. Based on the proposed conditions, maximum diversity order can be attained with the probability of 1 by enabling a randomly generated rotation pattern for both time and doubly dispersive channels. The theoretical analysis in this paper also demonstrates that the diversity evaluation can be concentrated on the pairwise error probability when the number of error symbols is one, which reduces the complexity of diversity-driven design and performance analysis for novel modulation schemes significantly in both time and doubly dispersive channels. Finally, numerical results for various modulation schemes confirm that the theoretical analysis holds in both time and doubly dispersive channels. Furthermore, when employing practical detectors, the random constellation rotation technique consistently enhance the transmission reliability for both coded and uncoded systems.
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https://arxiv.org/abs/2601.13997
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535d8dce95a9c51405025998fee06c5bf428545a846a07735e05dad6e1dd89f0
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2026-01-21T00:00:00-05:00
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The rate of purification of quantum trajectories
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arXiv:2601.14023v1 Announce Type: cross Abstract: We investigate the behavior of quantum trajectories conditioned on measurement outcomes. Under a condition related to the absence of so-called dark subspaces, K\"{u}mmerer and Maassen had shown that such trajectories almost surely purify in the long run. In this article, we first present a simple alternative proof of this result using Lyapunov methods. We then strengthen the conclusion by proving that purification actually occurs at an exponential rate in expectation, again using a Lyapunov approach. Furthermore, we address the quantum state estimation problem by propagating two trajectories under the same measurement record--one from the true initial state and the other from an arbitrary initial guess--and show that the estimated trajectory converges exponentially fast to the true one, thus quantifying the rate at which information is progressively revealed through the measurement process.
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https://arxiv.org/abs/2601.14023
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cb147f2debe8fb5ea576cfe2fd60ebad614084a6b13baaedbc478ef1abe2f546
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2026-01-21T00:00:00-05:00
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Performance enhancing of hybrid quantum-classical Benders approach for MILP optimization
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arXiv:2601.14024v1 Announce Type: cross Abstract: Mixed-integer linear programming problems are extensively used in industry for a wide range of optimization tasks. However, as they get larger, they present computational challenges for classical solvers within practical time limits. Quantum annealers can, in principle, accelerate the solution of problems formulated as quadratic unconstrained binary optimization instances, but their limited scale currently prevents achieving practical speedups. Quantum-classical algorithms have been proposed to take advantage of both paradigms and to allow current quantum computers to be used in larger problems. In this work, a hardware-agnostic Benders' decomposition algorithm and a series of enhancements with the goal of taking the most advantage of quantum computing are presented. The decomposition consists of a master problem with integer variables, which is reformulated as a quadratic unconstrained binary optimization problem and solved with a quantum annealer, and a linear subproblem solved by a classical computer. The enhancements consist, among others, of different embedding processes that substantially reduce the pre-processing time of the embedding computation without compromising solution quality, a conservative handling of cut constraints, and a stopping criterion that accounts for the limited size of current quantum computers and their heuristic nature. The proposed algorithm is benchmarked against classical approaches using a D-Wave quantum annealer for a scalable family of transmission network expansion planning problems.
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https://arxiv.org/abs/2601.14024
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60d55d856807ca5a07c76bba12905b69a2f478acb52dab0ce216d59383f0c029
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2026-01-21T00:00:00-05:00
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Generalised contextuality of continuous variable quantum theory can be revealed with a single projective measurement
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arXiv:2601.14067v1 Announce Type: cross Abstract: Generalized contextuality is a possible indicator of non-classical behaviour in quantum information theory. In finite-dimensional systems, this is justified by the fact that noncontextual theories can be embedded into some simplex, i.e. into a classical theory. We show that a direct application of the standard definition of generalized contextuality to continuous variable systems does not envelope the statistics of some basic measurements, such as the position observable. In other words, we construct families of fully classical, i.e. commuting, measurements that nevertheless can be used to show contextuality of quantum theory. To overcome the apparent disagreement between the two notions of classicality, that is commutativity and noncontextuality, we propose a modified definition of generalised contextuality for continuous-variable systems. The modified definition is based on a physically-motivated approximation procedure, that uses only finite sets of measurement effects. We prove that in the limiting case this definition corresponds exactly to an extension of noncontextual models that benefits from non-constructive response functions. In the process, we discuss the extension of a known connection between contextuality and no-broadcasting to the continuous-variable scenario, and prove structural results regarding fixed points of infinite-dimensional entanglement breaking channels.
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https://arxiv.org/abs/2601.14067
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23ed4c40791de506aedd168a2a3ca6bf5b984295469989ab852244da88d6b595
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2026-01-21T00:00:00-05:00
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Sharp Inequalities for Schur-Convex Functionals of Partial Traces over Unitary Orbits
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arXiv:2601.14158v1 Announce Type: cross Abstract: While many bounds have been proved for partial trace inequalities over the last decades for a large variety of quantities, recent problems in quantum information theory demand sharper bounds. In this work, we study optimal bounds for partial trace quantities in terms of the spectrum; equivalently, we determine the best bounds attainable over unitary orbits of matrices. We solve this question for Schur-convex functionals acting on a single partial trace in terms of eigenvalues for self-adjoint matrices and then we extend these results to singular values of general matrices. We subsequently extend the study to Schur-convex functionals that act on several partial traces simultaneously and present sufficient conditions for sharpness. In cases where closed-form maximizers cannot be identified, we present quadratic programs that yield new computable upper bounds for any Schur-convex functional. We additionally present examples demonstrating improvements over previously known bounds. Finally, we conclude with the study of optimal bounds for an $n$-qubit system and its subsystems of dimension $2$.
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https://arxiv.org/abs/2601.14158
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1b2d9ba531cf698dbd0ed8ccd05926bbff66a10edc4dd5838806029caf3d5f8c
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2026-01-21T00:00:00-05:00
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Purity of branch and critical locus
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arXiv:1003.5872v5 Announce Type: replace Abstract: To a dominant morphism $X/S \to Y/S$ of N\oe therian integral $S$-schemes one has the inclusion $C_{X/Y}\subset B_{X/Y}$ of the critical locus in the branch locus of $X/Y$. Starting from the notion of locally complete intersection morphisms, we give conditions on the modules of relative differentials $\Omega_{X/Y}$, $\Omega_{X/S}$, and $\Omega_{Y/S}$ that imply bounds on the codimensions of $ C_{X/Y}$ and $ B_{X/Y}$. These bounds generalise to a wider class of morphisms the classical purity results for finite morphisms by Zariski-Nagata-Auslander, and Faltings and Grothendieck, and van der Waerden's purity for birational morphisms.
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https://arxiv.org/abs/1003.5872
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35a303662b08ea20444aa469d5ac80d069b959b2bd49c6c0c7c17b9c814984d8
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2026-01-21T00:00:00-05:00
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On the birational geometry of the parameter space for codimension 2 complete intersections
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arXiv:1212.4862v2 Announce Type: replace Abstract: Codimension 2 complete intersections in P^N have a natural parameter space \bar{H}: a projective bundle over a projective space given by the choice of the lower degree equation and of the higher degree equation up to a multiple of the first. Motivated by the question of existence of complete families of smooth complete intersections, we study the birational geometry of \bar{H}. In a first part, we show that the first contraction of the MMP for \bar{H} always exists and we describe it. Then, we show that it is possible to run the full MMP for \bar{H}, and we describe it, in two degenerate cases. As an application, we prove the existence of complete curves in the punctual Hilbert scheme of complete intersection subschemes of A^2.
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https://arxiv.org/abs/1212.4862
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e78e590e1f168a570bf245316ac4ddcc45743606d30d46419f579ee365e9b809
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2026-01-21T00:00:00-05:00
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Hyperbolicity via Geodesic Stability
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arXiv:1504.06863v3 Announce Type: replace Abstract: A geodesic $g$ is Morse, for every $L \geq 1, A \geq 0$ there exists a $C=C_g(L,A)$ such that any $(L,A)$-quasi-geodesic connecting two points on $g$ stays $C$-close to $g$. The Morse lemma implies that in a hyperbolic space every geodesic is Morse. Here we prove the converse: If a homogeneous proper geodesic space is such that for every geodesic $g$ and every $L\geq 1, A \geq 0$ there exists a constant $C=C_g(L,A)$ such that any $(L,A)$-quasi-geodesic between any two points on $g$ stays $C$-close, then the space is hyperbolic. This applies in particular to infinite groups in which all geodesics are Morse.
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https://arxiv.org/abs/1504.06863
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c6dd6b818ac98a8d198ac0160748d44333b6a544043721be35a8ee1a39e27e28
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2026-01-21T00:00:00-05:00
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Chernoff bounds for branching random walks
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arXiv:1604.00056v4 Announce Type: replace Abstract: Concentration inequalities, which have proved very useful in a variety of fields, provide fairly tight bounds on large deviation probabilities while central limit theorem (CLT) describes the asymptotic distribution around the mean (at the $\sqrt{n}$ scale). Harris (1963) conjectured that for a supercritical branching random walk (BRW) of i.i.d offspring and i.i.d displacements, positions of individuals in $nth$ generation approach to Gaussian distribution -- central limit theorem. This conjecture was later proved by Stam (1966) and Kaplan \& Asmussen (1976). Refinements and extensions followed. However, to the best of our knowledge, there is no corresponding existing work on concentration inequalities for BRWs. In this note, we propose a new definition of BRW, providing a more general framework. Owing to this definition, a Chernoff-type (subgaussian) bound for BRWs follows directly from the Chernoff bound for random walk. The relation between RW (random walk) and BRW is discussed.
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https://arxiv.org/abs/1604.00056
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83bee6fcd5566e2edb191c5aa4e43c40e795314078488cf947663dbd6a30ba7c
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2026-01-21T00:00:00-05:00
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Some properties of the A$_{\infty}$-nerve
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arXiv:1609.00566v2 Announce Type: replace Abstract: The aim of this paper is to prove that the A$_{\infty}$-nerve of two quasi-equivalent A$_{\infty}$-categories (linear over a commutative ring) are weak-equivalent in the Joyal model structure. As a consequence we prove that the A$_{\infty}$-nerve of a pretriangulated A$_{\infty}$-category is a stable $\infty$-category.
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https://arxiv.org/abs/1609.00566
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f91fb6e6269887d2fd3f97164c591a68606f44bc728b90950581c143e12de531
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2026-01-21T00:00:00-05:00
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On a certain subclass of strongly starlike functions
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arXiv:1811.01271v4 Announce Type: replace Abstract: Let $\mathcal{S}^*(\alpha_1,\alpha_2)$, where $ \alpha_1, \alpha_2 \in (0,1]$, represent the class of functions $f$ that are analytic in the open unit disk $\mathbb{D}$, normalized by $f(0) = f'(0) - 1=0$, and satisfying the following double-sided inequality: \begin{equation*} -\frac{\pi\alpha_1}{2}< \arg\left\{\frac{zf'(z)}{f(z)}\right\} <\frac{\pi\alpha_2}{2}, \quad (z\in\mathbb{D}). \end{equation*} In this manuscript, we estimate the coefficients and logarithmic coefficients associated with functions that belong to the class $\mathcal{S}^*(\alpha_1,\alpha_2)$. As a result, we provide a general bound for the coefficients of a strongly starlike function, which has been an open question until now. Finally, we derive upper and lower bounds for the expression ${\rm Re}\{zf'(z)/f(z)\}$, where $f\in \mathcal{S}^*(\alpha_1,\alpha_2)$.
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https://arxiv.org/abs/1811.01271
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bb79cd14f23d13d469c506433915f7ed479330cd11ccf53653862595d332362b
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2026-01-21T00:00:00-05:00
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Linear resolution of products of monomial ideals related to maximal minors
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arXiv:1902.09748v3 Announce Type: replace Abstract: Let $ X $ be an $ m \times n $ matrix of distinct indeterminates over a field $ K $, where $ m \le n $. Set the polynomial ring $ K[X] := K[X_{ij} : 1 \le i \le m, 1 \le j \le n] $. Let $ 1 \le k < l \le n $ be such that $ l - k + 1 \ge m $. Consider the submatrix $ Y_{kl} $ of consecutive columns of $ X $ from $ k $th column to $ l $th column. Let $ J_{kl} $ be the ideal generated by `diagonal monomials' of all $ m \times m $ submatrices of $ Y_{kl} $, where the diagonal monomial of a square matrix means product of its main diagonal entries. We show that $ J_{k_1 l_1} J_{k_2 l_2} \cdots J_{k_s l_s} $ has a linear free resolution, where $ k_1 \le k_2 \le \cdots \le k_s $ and $ l_1 \le l_2 \le \cdots \le l_s $. This result is a variation of a theorem due to Bruns and Conca. Moreover, our proof is self-contained, elementary and combinatorial.
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https://arxiv.org/abs/1902.09748
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33cf19ca0e1bbb04e694d9825a4fe147bde866c1780c3ed0eabcc7a3c253af09
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2026-01-21T00:00:00-05:00
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Branching rules for winding subalgebras of the affine Kac--Moody algebras $A^{(1)}_1$ and $A^{(2)}_2$
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arXiv:1911.03316v5 Announce Type: replace Abstract: We study branching problems for affine Kac--Moody algebras. Unlike the finite-dimensional case, an affine Kac--Moody algebra may contain proper subalgebras isomorphic to itself, such as winding subalgebras obtained by rescaling the loop parameter. We investigate the restriction of integrable highest-weight representations to such subalgebras. The restriction remains integrable and decomposes into irreducible components with finite multiplicities, encoded by pairs of highest weights. We show that this set is closed under addition, extending a result of Brion and Knop to the affine setting. We also give a partial description of this set and provide explicit results for types $A^{(1)}_1$ and $A^{(2)}_2$.
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https://arxiv.org/abs/1911.03316
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01bd1e76412c04eb4a4958658d80612e88c4c5d8d9c626893d3938862c0cd90f
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2026-01-21T00:00:00-05:00
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Boosted optimal weighted least-squares
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arXiv:1912.07075v3 Announce Type: replace Abstract: This paper is concerned with the approximation of a function $u$ in a given approximation space $V_m$ of dimension $m$ from evaluations of the function at $n$ suitably chosen points. The aim is to construct an approximation of $u$ in $V_m$ which yields an error close to the best approximation error in $V_m$ and using as few evaluations as possible. Classical least-squares regression, which defines a projection in $V_m$ from $n$ random points, usually requires a large $n$ to guarantee a stable approximation and an error close to the best approximation error. This is a major drawback for applications where $u$ is expensive to evaluate. One remedy is to use a weighted least squares projection using $n$ samples drawn from a properly selected distribution. In this paper, we introduce a boosted weighted least-squares method which allows to ensure almost surely the stability of the weighted least squares projection with a sample size close to the interpolation regime $n=m$. It consists in sampling according to a measure associated with the optimization of a stability criterion over a collection of independent $n$-samples, and resampling according to this measure until a stability condition is satisfied. A greedy method is then proposed to remove points from the obtained sample. Quasi-optimality properties are obtained for the weighted least-squares projection, with or without the greedy procedure. The proposed method is validated on numerical examples and compared to state-of-the-art interpolation and weighted least squares methods.
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https://arxiv.org/abs/1912.07075
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c1f801f332418c9c1a8b7f1f86bc68ea97cffb3902943257c1f5233ed3669c63
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2026-01-21T00:00:00-05:00
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A Control-Theoretic Perspective on Optimal High-Order Optimization
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arXiv:1912.07168v5 Announce Type: replace Abstract: We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a convex function in a finite-dimensional Euclidean space. Given a function $\Phi: \mathbb{R}^d \rightarrow \mathbb{R}$ that is convex and twice continuously differentiable, we study a closed-loop control system that is governed by the operators $\nabla \Phi$ and $\nabla^2 \Phi$ together with a feedback control law $\lambda(\cdot)$ satisfying the algebraic equation $(\lambda(t))^p\|\nabla\Phi(x(t))\|^{p-1} = \theta$ for some $\theta \in (0, 1)$. Our first contribution is to prove the existence and uniqueness of a local solution to this system via the Banach fixed-point theorem. We present a simple yet nontrivial Lyapunov function that allows us to establish the existence and uniqueness of a global solution under certain regularity conditions and analyze the convergence properties of trajectories. The rate of convergence is $O(1/t^{(3p+1)/2})$ in terms of objective function gap and $O(1/t^{3p})$ in terms of squared gradient norm. Our second contribution is to provide two algorithmic frameworks obtained from discretization of our continuous-time system, one of which generalizes the large-step A-HPE framework and the other of which leads to a new optimal $p$-th order tensor algorithm. While our discrete-time analysis can be seen as a simplification and generalization of~\citet{Monteiro-2013-Accelerated}, it is largely motivated by the aforementioned continuous-time analysis, demonstrating the fundamental role that the feedback control plays in optimal acceleration and the clear advantage that the continuous-time perspective brings to algorithmic design. A highlight of our analysis is that we show that all of the $p$-th order optimal tensor algorithms that we discuss minimize the squared gradient norm at a rate of $O(k^{-3p})$, which complements the recent analysis.
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https://arxiv.org/abs/1912.07168
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Academic Papers
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35a7c7e7394be9398db5b8a204c787e24423ad28c561473bdab349cdffa0b66f
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2026-01-21T00:00:00-05:00
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Hochschild homology and the derived de Rham complex revisited
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arXiv:2007.02576v3 Announce Type: replace Abstract: We characterize two objects by universal property: the derived de Rham complex and Hochschild homology together with its Hochschild-Kostant-Rosenberg (HKR) filtration. This involves endowing these objects with extra structure, built on notions of "homotopy-coherent cochain complex" and "filtered circle action" that we study here. We use these universal properties to give a conceptual proof that the associated graded of the HKR filtration identifies with the derived de Rham complex, as well as to give a new construction of the filtrations on cyclic, negative cyclic, and periodic cyclic homology that relate these invariants to derived de Rham cohomology.
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https://arxiv.org/abs/2007.02576
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Academic Papers
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18d03a266ad9c20a8dcfd29ba2f89f13cd9b5ca065ddffeb22af05a351e5e84d
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2026-01-21T00:00:00-05:00
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A new characterization of the Hardy space and of other spaces of analytic functions
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arXiv:2009.10937v2 Announce Type: replace Abstract: The Fock space can be characterized (up to a positive multiplicative factor) as the only Hilbert space of entire functions in which the adjoint of derivation is multiplication by the complex variable. Similarly (and still up to a positive multiplicative factor) the Hardy space is the only space of functions analytic in the open unit disk for which the adjoint of the backward shift operator is the multiplication operator. In the present paper we characterize the Hardy space and some related reproducing kernel Hilbert spaces in terms of the adjoint of the differentiation operator. We use reproducing kernel methods, which seem to also give a new characterization of the Fock space.
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https://arxiv.org/abs/2009.10937
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Academic Papers
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0bebaa583927a4fa159c6fd19667325b288339ee75ba2936b430f325bb99fc3e
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2026-01-21T00:00:00-05:00
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Invertibility Conditions for the Admittance Matrices of Balanced Power Systems
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arXiv:2012.04087v5 Announce Type: replace Abstract: The admittance matrix encodes the network topology and electrical parameters of a power system in order to relate the current injection and voltage phasors. Since admittance matrices are central to many power engineering analyses, their characteristics are important subjects of theoretical studies. This paper focuses on the key characteristic of \emph{invertibility}. Previous literature has presented an invertibility condition for admittance matrices. This paper first identifies and fixes a technical issue in the proof of this previously presented invertibility condition. This paper then extends this previous work by deriving new conditions that are applicable to a broader class of systems with lossless branches and transformers with off-nominal tap ratios.
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https://arxiv.org/abs/2012.04087
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Academic Papers
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svg
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f33dc20d4717665179ad5f086142452515ea3ece0e78bafe5343b27afeb1d7a1
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2026-01-21T00:00:00-05:00
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Moduli space of homologically trivial parabolic (Higgs) bundles on the projective line and applications
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arXiv:2101.01913v3 Announce Type: replace Abstract: We establish an isomorphism between the moduli space of homologically trivial parabolic (Higgs) bundles on $\mathbb{P}^1$ and the quiver variety associated to a star-shaped quiver. As applications, we deduce a closed formula for the Littlewood-Richardson coefficients from the Verlinde formula, and solve the nilpotent case of the Deligne-Simpson problem via geometric methods.
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https://arxiv.org/abs/2101.01913
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Academic Papers
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svg
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d5302a18dbfe9dbcccfd4d79685d86cba633c1a94061eb85cbea8492ee8953ce
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2026-01-21T00:00:00-05:00
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Coarse Ricci curvature of hypergraphs and its generalization
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arXiv:2102.00698v5 Announce Type: replace Abstract: In the present paper, we introduce a concept of Ricci curvature on hypergraphs for a nonlinear Laplacian. We prove that our definition of the Ricci curvature is a generalization of Lin-Lu-Yau coarse Ricci curvature for graphs to hypergraphs. We also show a lower bound of nonzero eigenvalues of Laplacian, gradient estimate of heat flow, and diameter bound of Bonnet-Myers type for our curvature notion. This research leads to understanding how nonlinearity of Laplacian causes complexity of curvatures.
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https://arxiv.org/abs/2102.00698
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Academic Papers
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svg
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56d5ae73f31c3bb077a8b12da2111179c9d45523884ea53724664f16ae7ef7ea
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2026-01-21T00:00:00-05:00
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Value existence for zero-sum ergodic stochastic differential games
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arXiv:2106.15894v4 Announce Type: replace Abstract: In this paper we investigate two-player zero-sum stochastic differential games with an ergodic payoff, in which the diffusion coefficient does not need to be non-degenerate. We first establish the existence of a viscosity solution to the associated ergodic Hamilton-Jacobi-Bellman-Isaacs equation under a dissipativity condition. With the help of this viscosity solution, we then derive estimates for the upper and the lower ergodic value functions by constructing a series of non-degenerate approximating processes combined with the sup- and inf-convolution techniques. Finally, we prove the existence of a value for the game under the Isaacs condition and provide its representation formulae. As an application, we study the pollution accumulation problem with a long-run average social welfare to illustrate our theoretical results.
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https://arxiv.org/abs/2106.15894
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Academic Papers
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