Tootfinder

A subset generalization of the Erd\H{o}s-Kac theorem over number fields with applications
Sourabhashis Das, Wentang Kuo, Yu-Ru Liu
https://arxiv.org/abs/2506.03215

A subset generalization of the Erdős-Kac theorem over number fields with applications
Let $ω(n)$ denote the number of distinct prime factors of a natural number $n$. In 1940, Erdős and Kac established that $ω(n)$ obeys the Gaussian distribution over natural numbers. In 2004, the third author generalized their theorem to all abelian monoids. In this work, we extend the work of the third author to any subset of the set of ideals of a number field satisfying some additional conditions. Finally, we apply this theorem to prove the Erdős-Kac theorem over $h$-free and over $h$-full…

Minimum Selective Subset on Some Graph Classes
Bubai Manna
https://arxiv.org/abs/2507.00235 https://arxiv.org/pdf/2507.00235

Minimum Selective Subset on Some Graph Classes
In a connected simple graph G = (V(G),E(G)), each vertex is assigned a color from the set of colors C={1, 2,..., c}. The set of vertices V(G) is partitioned as V_1, V_2, ... ,V_c, where all vertices in V_j share the same color j. A subset S of V(G) is called Selective Subset if, for every vertex v in V(G), and if v is in V_j, at least one of its nearest neighbors in (S union (V(G)\ V_j)) has the same color as v. The Minimum Selective Subset (MSS) problem seeks to find a selective subset of mini…

Diffeomorphic approximation of piecewise affine homeomorphisms
Daniel Campbell, Luigi D'Onofrio, Tom\'a\v{s} V\'itek
https://arxiv.org/abs/2507.02854

Diffeomorphic approximation of piecewise affine homeomorphisms
Given any $f$ a locally finitely piecewise affine homeomorphism of $Ω\subset \mathbb{R}^d$ onto $Δ\subset \mathbb{R}^d$ (for $d=3, 4$) such that $f\in W^{1,p}(Ω, \mathbb{R}^d)$ and $f^{-1}\in W^{1,q}(Δ, \mathbb{R}^d)$, $1\leq p ,q < \infty$ and any $ε>0$ we construct a diffeomorphism $\tilde{f}$ such that $$\|f-\tilde{f}\|_{W^{1,p}(Ω,\mathbb{R}^d)} + \|f^{-1}-\tilde{f}^{-1}\|_{W^{1,q}(Δ,\mathbb{R}^d)} < ε.$$

Bounded powers of edge ideals: The strong exchange property
Takayuki Hibi, Seyed Amin Seyed Fakhari
https://arxiv.org/abs/2506.03480 https://

Bounded powers of edge ideals: The strong exchange property
Let $S=K[x_1, \ldots,x_n]$ denote the polynomial ring in $n$ variables over a field $K$ and $I \subset S$ a monomial ideal. Given a vector $\mathfrak{c}\in\mathbb{Z}_{>0}^n$, the ideal $I_{\mathfrak{c}}$ is the ideal generated by those monomials belonging to $I$ whose exponent vectors are componentwise bounded above by $\mathfrak{c}$. Let $δ_{\mathfrak{c}}(I)$ be the largest integer $q$ for which $(I^q)_{\mathfrak{c}}\neq 0$. Let $I(G) \subset S$ denote the edge ideal of a finite graph $G$ on …

Uniform Validity of the Subset Anderson-Rubin Test under Heteroskedasticity and Nonlinearity
Atsushi Inoue, \`Oscar Jord\`a, Guido M. Kuersteiner
https://arxiv.org/abs/2507.01167 …

Uniform Validity of the Subset Anderson-Rubin Test under Heteroskedasticity and Nonlinearity
We consider the Anderson-Rubin (AR) statistic for a general set of nonlinear moment restrictions. The statistic is based on the criterion function of the continuous updating estimator (CUE) for a subset of parameters not constrained under the Null. We treat the data distribution nonparametrically with parametric moment restrictions imposed under the Null. We show that subset tests and confidence intervals based on the AR statistic are uniformly valid over a wide range of distributions that incl…

This https://arxiv.org/abs/2505.14884 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Polar Sparsity: High Throughput Batched LLM Inferencing with Scalable Contextual Sparsity
Accelerating large language model (LLM) inference is critical for real-world deployments requiring high throughput and low latency. Contextual sparsity, where each token dynamically activates only a small subset of the model parameters, shows promise but does not scale to large batch sizes due to union of active neurons quickly approaching dense computation. We introduce Polar Sparsity, highlighting a key shift in sparsity importance from MLP to Attention layers as we scale batch size and seque…

Structured Column Subset Selection for Bayesian Optimal Experimental Design
Hugo D\'iaz, Arvind K. Saibaba, Srinivas Eswar, Vishwas Rao, Zichao Wendy Di
https://arxiv.org/abs/2506.00336

Structured Column Subset Selection for Bayesian Optimal Experimental Design
We consider optimal experimental design (OED) for Bayesian inverse problems, where the experimental design variables have a certain multiway structure. Given $d$ different experimental variables with $m_i$ choices per design variable $1 \le i\le d$, the goal is to select $k_i \le m_i$ experiments per design variable. Previous work has related OED to the column subset selection problem by mapping the design variables to the columns of a matrix $\mathbf{A}$. However, this approach is applicable o…

A generalized Birman-Schwinger principle and applications to one-dimensional Schr\"odinger operators with distributional potentials
Fritz Gesztesy, Roger Nichols
https://arxiv.org/abs/2507.02251

A generalized Birman-Schwinger principle and applications to one-dimensional Schrödinger operators with distributional potentials
Given a self-adjoint operator $H_0$ bounded from below in a complex Hilbert space $\mathcal{H}$, the corresponding scale of spaces $\mathcal{H}_{+1}(H_0) \subset \mathcal{H} \subset \mathcal{H}_{-1}(H_0) = [\mathcal{H}_{+1}(H_0)]^*$, and a fixed $V\in \mathcal{B}(\mathcal{H}_{+1}(H_0),\mathcal{H}_{-1}(H_0))$, we define the operator-valued map $A_V(\,\cdot\,):ρ(H_0)\to \mathcal{B}(\mathcal{H})$ by \[ A_V(z):=-\big(H_0-zI_{\mathcal{H}} \big)^{-1/2}V\big(H_0-zI_{\mathcal{H}} \big)^{-1/2}\in \math…

On the Visibility Polynomial of Graphs
Tonny K B, Shikhi M
https://arxiv.org/abs/2507.01851 https://arxiv.org/pdf/2507.01851

On the Visibility Polynomial of Graphs
Let G(V,E) be a simple graph and let X subset of V. Two vertices u and v are said to be X-visible if there exists a shortest u,v-path P such that V(P) intersection X is a subset of {u, v}. A set X is called a mutual-visibility set of G if every pair of vertices in X are X-visible. The visibility polynomial of a graph G is defined as nu (G)=sum_{i >= 0} r_i x^i, where r_i denotes the number of mutual-visibility sets in G of cardinality i. In the present paper, the visibility polynomial is studie…

PII Jailbreaking in LLMs via Activation Steering Reveals Personal Information Leakage
Krishna Kanth Nakka, Xue Jiang, Xuebing Zhou
https://arxiv.org/abs/2507.02332

PII Jailbreaking in LLMs via Activation Steering Reveals Personal Information Leakage
This paper investigates privacy jailbreaking in LLMs via steering, focusing on whether manipulating activations can bypass LLM alignment and alter response behaviors to privacy related queries (e.g., a certain public figure's sexual orientation). We begin by identifying attention heads predictive of refusal behavior for private attributes (e.g., sexual orientation) using lightweight linear probes trained with privacy evaluator labels. Next, we steer the activations of a small subset of these at…

This https://arxiv.org/abs/2504.04109 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Variation of cones of divisors in a family of varieties -- Fano type case
We investigate the relationship between the Fano type property on fibers over a Zariski dense subset and the global Fano type property. We establish the invariance of Néron-Severi spaces, nef cones, effective cones, movable cones, and Mori chamber decompositions for a family of Fano type varieties after a generic finite base change. Additionally, we show the uniform behavior of the minimal model program for this family. These results are applied to the boundedness problem of Fano type varietie…

This https://arxiv.org/abs/2407.10640 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDC_…

Error Bounds for the Network Scale-Up Method
Epidemiologists and social scientists have used the Network Scale-Up Method (NSUM) for over thirty years to estimate the size of a hidden sub-population within a social network. This method involves querying a subset of network nodes about the number of their neighbours belonging to the hidden sub-population. In general, NSUM assumes that the social network topology and the hidden sub-population distribution are well-behaved; hence, the NSUM estimate is close to the actual value. However, bound…

This https://arxiv.org/abs/2501.16815 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Best Subset Selection: Optimal Pursuit for Feature Selection and Elimination
This paper introduces two novel criteria: one for feature selection and another for feature elimination in the context of best subset selection, which is a benchmark problem in statistics and machine learning. From the perspective of optimization, we revisit the classical selection and elimination criteria in traditional best subset selection algorithms, revealing that these classical criteria capture only partial variations of the objective function after the entry or exit of features. By form…

Vietoris--Rips Shadow for Euclidean Graph Reconstruction
Rafal Komendarczyk, Sushovan Majhi, Atish Mitra
https://arxiv.org/abs/2506.01603 https://

Vietoris--Rips Shadow for Euclidean Graph Reconstruction
The shadow of an abstract simplicial complex $K$ with vertices in $\mathbb R^N$ is a subset of $\mathbb R^N$ defined as the union of the convex hulls of simplices of $K$. The Vietoris--Rips complex of a metric space $(S,d)$ at scale $β$ is an abstract simplicial complex whose each $k$-simplex corresponds to $(k+1)$ points of $S$ within diameter $β$. In case $S\subset\mathbb R^2$ and $d(a,b)=\|a-b\|$ standard Euclidean, the natural shadow projection of the Vietoris--Rips is already p…

Inverse matroid optimization under subset constraints
Krist\'of \'iB\'erczi, Lydia Mirabel Mendoza-Cadena, Jos\'e Soto
https://arxiv.org/abs/2507.00930

Inverse matroid optimization under subset constraints
In the Inverse Matroid problem, we are given a matroid, a fixed basis $B$, and an initial weight function, and the goal is to minimally modify the weights -- measured by some function -- so that $B$ becomes a maximum-weight basis. The problem arises naturally in settings where one wishes to explain or enforce a given solution by minimally perturbing the input. We extend this classical problem by replacing the fixed basis with a subset $S_0$ of the ground set and imposing various structural co…

Multishot Capacity of Networks with Restricted Adversaries
Giuseppe Cotardo, Gretchen L. Matthews, Alberto Ravagnani, Julia Shapiro
https://arxiv.org/abs/2506.03361

Multishot Capacity of Networks with Restricted Adversaries
We investigate adversarial network coding and decoding, focusing on the multishot regime and when the adversary is restricted to operate on a vulnerable region of the network. Errors can occur on a proper subset of the network edges and are modeled via an adversarial channel. The paper contains both bounds and capacity-achieving schemes for the Diamond Network, the Mirrored Diamond Network, and generalizations of these networks. We also initiate the study of the capacity of 3-level networks in …

Calibrated Recommendations: Survey and Future Directions
Diego Corr\^ea da Silva, Dietmar Jannach
https://arxiv.org/abs/2507.02643 https://

Calibrated Recommendations: Survey and Future Directions
The idea of calibrated recommendations is that the properties of the items that are suggested to users should match the distribution of their individual past preferences. Calibration techniques are therefore helpful to ensure that the recommendations provided to a user are not limited to a certain subset of the user's interests. Over the past few years, we have observed an increasing number of research works that use calibration for different purposes, including questions of diversity, biases, …

Introduction to moduli spaces and Dirac geometry
Eckhard Meinrenken
https://arxiv.org/abs/2506.04150 https://arxiv.org/pdf/2506.04150…

Introduction to moduli spaces and Dirac geometry
Let $G$ be a Lie group, with an invariant metric on its Lie algebra $\mathfrak{g}$. Given a surface $Σ$ with boundary, and a collection of base points $\mathcal{V}\subset Σ$ meeting every boundary component, the moduli space (representation variety) $\mathcal{M}_G(Σ,\mathcal{V})$ carries a distinguished `quasi-symplectic' 2-form. We shall explain the finite-dimensional construction of this 2-form and discuss its basic properties, using quasi-Hamiltonian techniques and Dirac geometry. This ar…

Finiteness properties of stabilisers of oligomorphic actions
Francesco Fournier-Facio, Peter H. Kropholler, Robert Alonzo Lyman, Matthew C. B. Zaremsky
https://arxiv.org/abs/2506.02319

Finiteness properties of stabilisers of oligomorphic actions
An action of a group on a set is oligomorphic if it has finitely many orbits of $n$-element subsets for all $n$. We prove that for a large class of groups (including all groups of finite virtual cohomological dimension and all countable linear groups), for any oligomorphic action of such a group on an infinite set there exists a finite subset whose stabiliser is not of type $\mathrm{FP}_\infty$. This leads to obstructions on finiteness properties for permutational wreath products and twisted Br…

Power Enhancement of Permutation-Augmented Partial-Correlation Tests via Fixed-Row Permutations
Tianyi Wang, Guanghui Wang, Zhaojun Wang, Changliang Zou
https://arxiv.org/abs/2506.02906

Power Enhancement of Permutation-Augmented Partial-Correlation Tests via Fixed-Row Permutations
Permutation-based partial-correlation tests guarantee finite-sample Type I error control under any fixed design and exchangeable noise, yet their power can collapse when the permutation-augmented design aligns too closely with the covariate of interest. We remedy this by fixing a design-driven subset of rows and permuting only the remainder. The fixed rows are chosen by a greedy algorithm that maximizes a lower bound on power. This strategy reduces covariate-permutation collinearity while prese…

Boundary blow-up and degenerate equations
Satyanad Kichenassamy (LMR)
https://arxiv.org/abs/2507.02485 https://arxiv.org/pdf/2507.024…

Boundary blow-up and degenerate equations
Let $Ω\subset\mathbb R^2$ be a bounded domain of class $C^{2+α}$, $0<α<1$. We show that if $u$ is the solution of $Δu = 4\exp(2u)$ which tends to $+\infty$ as $(x,y)\to\partialΩ$, then the hyperbolic radius $v=\exp(-u)$ is also of class $C^{2+α}$ up to the boundary. The proof relies on new Schauder estimates for degenerate elliptic equations of Fuchsian type.

This https://arxiv.org/abs/2503.20158 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qbi…

RxRx3-core: Benchmarking drug-target interactions in High-Content Microscopy
High Content Screening (HCS) microscopy datasets have transformed the ability to profile cellular responses to genetic and chemical perturbations, enabling cell-based inference of drug-target interactions (DTI). However, the adoption of representation learning methods for HCS data has been hindered by the lack of accessible datasets and robust benchmarks. To address this gap, we present RxRx3-core, a curated and compressed subset of the RxRx3 dataset, and an associated DTI benchmarking task. At…

This https://arxiv.org/abs/2305.19415 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Euclidean nets under isometric embeddings
Suppose that there exists a discrete subset $X$ of a complete, connected, $n$-dimensional Riemannian manifold $M$ such that the Riemannian distances between points of $X$ correspond to the Euclidean distances of a net in $\mathbb{R}^{n}$. What can then be derived about the geometry of $M$? In arXiv:2004.08621 it was shown that if $n=2$ then $M$ is isometric to $\mathbb{R}^{2}$. In this paper we show two consequential geometric properties that the manifold $M$ shares with the Euclidean space in …

Classification of exact structures using the Ziegler spectrum
Julia Sauter
https://arxiv.org/abs/2506.02304 https://arxiv.org/pdf/250…

Classification of exact structures using the Ziegler spectrum
Given an idempotent complete additive category, we show the there is an explicitly constructed topological space such that the lattice of exact substructures is anti-isomorphic to the lattice of closed subsets. In the special case that the additive category has weak cokernels, this topological space is an open subset of the Ziegler spectrum and this is a result of Kevin Schlegel. We also look at some module categories of rings where the Ziegler spectrum is known and calculate the global dimensi…

This https://arxiv.org/abs/2209.03243 has been replaced.
link: https://scholar.google.com/scholar?q=a

Adapted Wasserstein distance between the laws of SDEs
We consider the bicausal optimal transport problem between the laws of scalar time-homogeneous stochastic differential equations, and we establish the optimality of the synchronous coupling between these laws. The proof of this result is based on time-discretisation and reveals a novel connection between the synchronous coupling and the celebrated discrete-time Knothe--Rosenblatt rearrangement. We also prove a result on equality of topologies restricted to a certain subset of laws of continuous…

Fluid Democracy in Federated Data Aggregation
Aditya Vema Reddy Kesari, Krishna Reddy Kesari
https://arxiv.org/abs/2507.02710 https://

Fluid Democracy in Federated Data Aggregation
Federated learning (FL) mechanisms typically require each client to transfer their weights to a central server, irrespective of how useful they are. In order to avoid wasteful data transfer costs from clients to the central server, we propose the use of consensus based protocols to identify a subset of clients with most useful model weights at each data transfer step. First, we explore the application of existing fluid democracy protocols to FL from a performance standpoint, comparing them with…

This https://arxiv.org/abs/2505.23240 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Joint estimation of smooth graph signals from partial linear measurements
Given an undirected and connected graph $G$ on $T$ vertices, suppose each vertex $t$ has a latent signal $x_t \in \mathbb{R}^n$ associated to it. Given partial linear measurements of the signals, for a potentially small subset of the vertices, our goal is to estimate $x_t$'s. Assuming that the signals are smooth w.r.t $G$, in the sense that the quadratic variation of the signals over the graph is small, we obtain non-asymptotic bounds on the mean squared error for jointly recovering $x_t$'s, fo…

Algebraic approximations to linear combinations of S-units
Parvathi S Nair, Veekesh Kumar, S. S. Rout
https://arxiv.org/abs/2506.02898 https://

Algebraic approximations to linear combinations of S-units
Let $Γ\subset \bar{\mathbb{Q}}^{\times}$ be a finitely generated multiplicative group of algebraic numbers, let $α_1,\ldots,α_m\in K$ be given algebraic numbers and not all zero, and let $\varepsilon >0$ be fixed. In this paper, we prove that there exist only finitely many tuples $(u_1, \ldots, u_m, q, p)\in Γ^m\times\mathbb{Z}^2$ with $d = [\mathbb{Q}(u_1, \ldots, u_m):\mathbb{Q}]$ such that $\max\{|α_1 qu_1|, \ldots, |α_m qu_m|\}>1$, the tuple $(α_1qu_1, \ldots, α_…

Optimization Strategies for Variational Quantum Algorithms in Noisy Landscapes
Vojt\v{e}ch Nov\'ak, Ivan Zelinka, V\'aclav Sn\'a\v{s}el
https://arxiv.org/abs/2506.01715

Optimization Strategies for Variational Quantum Algorithms in Noisy Landscapes
Variational Quantum Algorithms (VQAs) are a promising tool in the NISQ era, leveraging quantum computing across diverse fields. However, their performance is hindered by optimization challenges like local minima, barren plateaus, and noise from current quantum hardware. Variational Quantum Eigensolver (VQE), a key subset of VQAs, approximates molecular ground-state energies by minimizing a Hamiltonian, enabling quantum chemistry applications. Beyond this, VQE contributes to condensed matter phy…

Spatial tangible user interfaces for cognitive assessment and training
Ehud Sharlin, Yuichi Itoh, Benjamin Watson, Yoshifumi Kitamura, Steve Sutphen, Lili Liu, Fumio Kishino
https://arxiv.org/abs/2507.01944

Spatial tangible user interfaces for cognitive assessment and training
This paper discusses Tangible User Interfaces (TUIs) and their potential impact on cognitive assessment and cognitive training. We believe that TUIs, and particularly a subset that we dub spatial TUIs, can extend human computer interaction beyond some of its current limitations. Spatial TUIs exploit human innate spatial and tactile ability in an intuitive and direct manner, affording interaction paradigms that are practically impossible using current interface technology. As proof-of-concept we…

Spherical designs for finite quaternionic unit groups and their applications to modular forms
Masatake Hirao, Hiroshi Nozaki, Koji Tasaka
https://arxiv.org/abs/2507.01358

Spherical designs for finite quaternionic unit groups and their applications to modular forms
For a finite subset $X$ of the $d$-dimensional unit sphere, the harmonic strength $T(X)$ of $X$ is the set of $\ell\in \mathbb{N}$ such that $\sum_{x\in X} P(x)=0$ for all harmonic polynomials $P$ of homogeneous degree $\ell$. We will study three exceptional finite groups of unit quaternions, called the binary tetrahedral group $2T$ of order 24, the octahedral group $2O$ of order 48, and the icosahedral group $2I$ of order 120, which can be viewed as a subset of the 3-dimensional unit sphere. F…

Abelianized Descent Obstruction for 0-Cycles
Hui Zhang
https://arxiv.org/abs/2506.22980 https://arxiv.org/pdf/2506.22980

Abelianized Descent Obstruction for 0-Cycles
Classical descent theory of Colliot-Thélène and Sansuc for rational points tells that, over a smooth variety $X$, the algebraic Brauer-Manin subset equals the descent obstruction subset defined by a universal torsor. Moreover, Harari shows that the Brauer-Manin subset equals the descent obstruction subset defined by torsors under connected linear groups. By using the abelian cohomology theory by Borovoi, we define abelianized descent obstructions by torsors under connected linear groups. As a…

facebook_wall: Facebook wall posts (2009)
Friendship relationships and interactions (wall posts) for a subset of the Facebook social network in 2009, recorded over a 2 year period. Edge directed edge represents a post by one user on another user's FB wall.
This network has 46952 nodes and 876993 edges.
Tags: Social, Online, Temporal, Multigraph

Memory-Efficient Split Federated Learning for LLM Fine-Tuning on Heterogeneous Mobile Devices
Xiaopei Chen, Liang Li, Fei Ji, Wen Wu
https://arxiv.org/abs/2506.02940

Memory-Efficient Split Federated Learning for LLM Fine-Tuning on Heterogeneous Mobile Devices
In this paper, we propose an edge-assisted split federated learning framework to facilitate large language model (LLM) fine-tuning on heterogeneous mobile devices while alleviating memory pressures on both mobile devices and the edge server. Specifically, mobile devices perform low-rank adaptation (LoRA) fine-tuning on only a subset of lower layers of the pre-trained LLM, tailored to their individual capacities. On the server, a full LLM is maintained, and the corresponding LoRA modules are sel…

Reentrant localization in a quasiperiodic chain with correlated hopping sequences
Sourav Karmakar, Sudin Ganguly, Santanu K. Maiti
https://arxiv.org/abs/2506.02716

Reentrant localization in a quasiperiodic chain with correlated hopping sequences
Quasiperiodic systems are known to exhibit localization transitions in low dimensions, wherein all electronic states become localized beyond a critical disorder strength. Interestingly, recent studies have uncovered a reentrant localization (RL) phenomenon: upon further increasing the quasiperiodic disorder strength beyond the localization threshold, a subset of previously localized states can become delocalized again within a specific parameter window. While RL transitions have been primarily …

Extensions of Schr\"odinger operators that generate $C_0$ contraction semigroups
Lawrence Frolov
https://arxiv.org/abs/2506.00231 https://

Extensions of Schrödinger operators that generate $C_0$ contraction semigroups
Consider a non-relativistic quantum particle with wave function $ψ$ in a bounded $C^2$ region $Ω\subset \mathbb{R}^n$, and suppose detectors are placed along the boundary $\partial Ω$. Assume the detection process is irreversible, its mechanism is time independent and also hard, i.e., detections occur only along the boundary $\partial Ω$. Under these conditions Tumulka argued that the dynamics of $ψ$ must be governed by a $C_0$ contraction semigroup that weakly solves the Schrödinger equa…

GORACS: Group-level Optimal Transport-guided Coreset Selection for LLM-based Recommender Systems
Tiehua Mei, Hengrui Chen, Peng Yu, Jiaqing Liang, Deqing Yang
https://arxiv.org/abs/2506.04015

GORACS: Group-level Optimal Transport-guided Coreset Selection for LLM-based Recommender Systems
Although large language models (LLMs) have shown great potential in recommender systems, the prohibitive computational costs for fine-tuning LLMs on entire datasets hinder their successful deployment in real-world scenarios. To develop affordable and effective LLM-based recommender systems, we focus on the task of coreset selection which identifies a small subset of fine-tuning data to optimize the test loss, thereby facilitating efficient LLMs' fine-tuning. Although there exist some intuitive …

This https://arxiv.org/abs/2410.11470 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

Almost Optimal Fully Dynamic $k$-Center Clustering with Recourse
In this paper, we consider the \emph{metric $k$-center} problem in the fully dynamic setting, where we are given a metric space $(V,d)$ evolving via a sequence of point insertions and deletions and our task is to maintain a subset $S \subseteq V$ of at most $k$ points that minimizes the objective $\max_{x \in V} \min_{y \in S}d(x, y)$. We want to design our algorithm so that we minimize its \emph{approximation ratio}, \emph{recourse} (the number of changes it makes to the solution $S$), and \em…

Maximal stretch and Lipschitz maps on Riemannian manifolds of negative curvature
Xian Dai, Gerhard Knieper
https://arxiv.org/abs/2507.02617 https://…

Maximal stretch and Lipschitz maps on Riemannian manifolds of negative curvature
In his seminal work on Teichmüller spaces (\cite{Th98}), Thurston introduced the maximal stretch for a pair of hyperbolic metrics on a closed surface of genus $\geq 2$ and showed that the logarithm of this quantity induces an asymmetric metric in the Teichmüller space. He also showed that the subset of the surface on which the maximal stretch is attained is a geodesic lamination. In this paper, we define the maximal stretch analogously for closed manifolds equipped with Riemannian metrics of …

Renormalized variational principles and Hardy-type inequalities
Satyanad Kichenassamy (LMR)
https://arxiv.org/abs/2507.02486 https://…

Renormalized variational principles and Hardy-type inequalities
Let $Ω\subset{\mathbb R}^2$ be a bounded domain on which Hardy's inequality holds. We prove that $[\exp(u^2)-1]/δ^2\in L^1(Ω)$ if $u\in H^1_0(Ω)$, where $δ$ denotes the distance to $\partialΩ$. The corresponding higher-dimensional result is also given. These results contain both Hardy's and Trudinger's inequalities, and yield a new variational characterization of the maximal solution of the Liouville equation on smooth domains, in terms of a renormalized functional. A global $H^1$ bound o…

Counterfactual Explanation of Shapley Value in Data Coalitions
Michelle Si, Jian Pei
https://arxiv.org/abs/2507.01267 https://arxiv.o…

Counterfactual Explanation of Shapley Value in Data Coalitions
The Shapley value is widely used for data valuation in data markets. However, explaining the Shapley value of an owner in a data coalition is an unexplored and challenging task. To tackle this, we formulate the problem of finding the counterfactual explanation of Shapley value in data coalitions. Essentially, given two data owners $A$ and $B$ such that $A$ has a higher Shapley value than $B$, a counterfactual explanation is a smallest subset of data entries in $A$ such that transferring the sub…

This https://arxiv.org/abs/2504.21760 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Bounded powers of edge ideals: Gorenstein toric rings
Let $S=K[x_1, \ldots,x_n]$ denote the polynomial ring in $n$ variables over a field $K$ and $I \subset S$ a monomial ideal. Given a vector $\mathfrak{c}\in\mathbb{N}^n$, the ideal $I_{\mathfrak{c}}$ is the ideal generated by those monomials belonging to $I$ whose exponent vectors are componentwise bounded above by $\mathfrak{c}$. Let $δ_{\mathfrak{c}}(I)$ be the largest integer $q$ for which $(I^q)_{\mathfrak{c}}\neq 0$. For a finite graph $G$, its edge ideal is denoted by $I(G)$. Let $\mathca…

Bivariate polynomial histopolation techniques on Padua, Fekete and Leja triangles
Ludovico Bruni Bruno, Francesco Dell'Accio, Wolfgang Erb, Federico Nudo
https://arxiv.org/abs/2506.03025

Bivariate polynomial histopolation techniques on Padua, Fekete and Leja triangles
This paper explores the reconstruction of a real-valued function $f$ defined over a domain $Ω\subset \mathbb{R}^2$ using bivariate polynomials that satisfy triangular histopolation conditions. More precisely, we assume that only the averages of $f$ over a given triangulation $\mathcal{T}_N$ of $Ω$ are available and seek a bivariate polynomial that approximates $f$ using a histopolation approach, potentially flanked by an additional regression technique. This methodology relies on the selectio…

Boundary behavior in the Loewner-Nirenberg problem
Satyanad Kichenassamy (LMR)
https://arxiv.org/abs/2507.02484 https://arxiv.org/pdf…

Boundary behavior in the Loewner-Nirenberg problem
Let $Ω\subset\mathbb R^n$ be a bounded domain of class $C^{2+α}$, $0<α<1$. We show that if $n\geq 3$ and $u_Ω$ is the maximal solution of equation $Δu = n(n-2)u^{(n+2)/(n-2)}$ in $Ω$, then the hyperbolic radius $v_Ω=u_Ω^{-2/(n-2)}$ is of class $C^{2+α}$ up to the boundary. The argument rests on a reduction to a nonlinear Fuchsian elliptic PDE.

The birth of young radio jets in changing-look AGN: a population study
Sufia Birmingham, Charlotte Ward, Kristina Nyland, Dougal Dobie, Matthew J. Graham, David L. Kaplan, Tara Murphy
https://arxiv.org/abs/2507.01355

The birth of young radio jets in changing-look AGN: a population study
Changing-Look Active Galactic Nuclei (CLAGN) are a rare subset of AGN that show significant changes to the flux of broad Balmer emission lines. Recent studies of CLAGN, such as 1ES 1927+654 and Mrk 590, have revealed that changes in the optically observed accretion rate are accompanied by changes in radio activity. We present a time-domain population study of 474 spectroscopically confirmed CLAGN at radio wavelengths using the Australia SKA Pathfinder Variable and Slow Transients Survey and the…

Gr\"obner-Shirshov bases of Rota-Baxter algebra of weight $\lambda$ with spectrum lying in $\{0,-\lambda\}$
H. Alhussein
https://arxiv.org/abs/2507.01614

Gröbner-Shirshov bases of Rota-Baxter algebra of weight $λ$ with spectrum lying in $\{0,-λ\}$
It is known that if $A$ is a finite-dimensional unital algebra equipped with a Rota-Baxter operator $R$ of weight $λ$, then spectrum of $R$ is a subset of $\{0,-λ\}$. We are interested on finding all consequences of the Rota-Baxter relation and the relation of the form $R^k(R+λ{\rm id})^l = 0$. In 2024, H.~Qiu, S. Zheng, Y. Dan solved this problem for $k = l = 1$ and $λ\neq0$. We find a Gröbner-Shirshov basis of the ideal generated by these two relations in general case.

The Local Structure Theorem for Graph Minors with Finite Index
Christophe Paul, Evangelos Protopapas, Dimitrios M. Thilikos, Sebastian Wiederrecht
https://arxiv.org/abs/2507.02769

The Local Structure Theorem for Graph Minors with Finite Index
The Local Structure Theorem (LST) for graph minors roughly states that every $H$-minor free graph $G$ that contains a sufficiently large wall $W$, there is a set of few vertices $A$ such that, upon removing $A$, the resulting graph $G':=G - A$ admits an "almost embedding" $δ$ into a surface $Σ$ in which $H$ does not embed. By almost embedding, we mean that there exists a hypergraph $\mathcal{H}$ whose vertex set is a subset of the vertex set of $G$ and an embedding of $\mathcal{H}$ in $Σ$ su…

Information Geometry on the $\ell^2$-Simplex via the $q$-Root Transform
Levin Maier
https://arxiv.org/abs/2506.00485 https://arxiv.or…

Information Geometry on the $\ell^2$-Simplex via the $q$-Root Transform
In this paper, we introduce \emph{$\ell^p$-information geometry}, an infinite dimensional framework that shares key features with the geometry of the space of probability densities \( \mathrm{Dens}(M) \) on a closed manifold, while also incorporating aspects of measure-valued information geometry. We define the \emph{$\ell^2$-probability simplex} with a noncanonical differentiable structure induced via the \emph{$q$-root transform} from an open subset of the $\ell^p$-sphere. This structure rend…

Inequalities in Fourier analysis on binary cubes
Ton\'ci Crmari\'c, Vjekoslav Kova\v{c}, Shobu Shiraki
https://arxiv.org/abs/2507.01359 https://

Inequalities in Fourier analysis on binary cubes
This paper studies two classical inequalities, namely the Hausdorff-Young inequality and equal-exponent Young's convolution inequality, for discrete functions supported in the binary cube $\{0,1\}^d\subset\mathbb{Z}^d$. We characterize the exact ranges of Lebesgue exponents in which sharp versions of these two inequalities hold, and present several immediate consequences. First, if the functions are specialized to be the indicator of some set $A\subseteq\{0,1\}^d$, then we obtain sharp upper bo…

Scalable Subset Selection in Linear Mixed Models
Ryan Thompson, Matt P. Wand, Joanna J. J. Wang
https://arxiv.org/abs/2506.20425 https://

Scalable Subset Selection in Linear Mixed Models
Linear mixed models (LMMs), which incorporate fixed and random effects, are key tools for analyzing heterogeneous data, such as in personalized medicine or adaptive marketing. Nowadays, this type of data is increasingly wide, sometimes containing thousands of candidate predictors, necessitating sparsity for prediction and interpretation. However, existing sparse learning methods for LMMs do not scale well beyond tens or hundreds of predictors, leaving a large gap compared with sparse methods fo…

Universality of span 2-categories and the construction of 6-functor formalisms
Bastiaan Cnossen, Tobias Lenz, Sil Linskens
https://arxiv.org/abs/2505.19192

Universality of span 2-categories and the construction of 6-functor formalisms
Given an $\infty$-category $C$ equipped with suitable wide subcategories $I, P \subset E\subset C$, we show that the $(\infty,2)$-category $\text{S}{\scriptstyle\text{PAN}}_2(C,E)_{P,I}$ of higher (or iterated) spans defined by Haugseng has the universal property that 2-functors $\text{S}{\scriptstyle\text{PAN}}_2(C,E)_{P,I} \to \mathbb D$ correspond precisely to $(I, P)$-biadjointable functors $C^\text{op} \to \mathbb D$, i.e. functors $F$ where $F(i)$ for $i \in I$ admits a left adjoint and $…

A generating set of Reidemeister moves of oriented virtual knots
Danish Ali
https://arxiv.org/abs/2505.24094 https://arxiv.org/pdf/25…

A generating set of Reidemeister moves of oriented virtual knots
In oriented knot theory, verifying a quantity is an invariant involves checking its invariance under all oriented Reidemeister moves, a process that can be intricate and time-consuming. A generating set of oriented moves simplifies this by requiring verification for only a minimal subset from which all other moves can be derived. While generating sets for classical oriented Reidemeister moves are well-established, their virtual counterparts are less explored. In this study, we enumerate the ori…

Hello Afrika: Speech Commands in Kinyarwanda
George Igwegbe, Martins Awojide, Mboh Bless, Nirel Kadzo
https://arxiv.org/abs/2507.01024 https://

Hello Afrika: Speech Commands in Kinyarwanda
Voice or Speech Commands are a subset of the broader Spoken Word Corpus of a language which are essential for non-contact control of and activation of larger AI systems in devices used in everyday life especially for persons with disabilities. Currently, there is a dearth of speech command models for African languages. The Hello Afrika project aims to address this issue and its first iteration is focused on the Kinyarwanda language since the country has shown interest in developing speech recog…

A Methodological Framework for Capturing Cognitive-Affective States in Collaborative Learning
Sifatul Anindho, Videep Venkatesha, Nathaniel Blanchard
https://arxiv.org/abs/2507.01166

A Methodological Framework for Capturing Cognitive-Affective States in Collaborative Learning
Identification of affective and attentional states of individuals within groups is difficult to obtain without disrupting the natural flow of collaboration. Recent work from our group used a retrospect cued recall paradigm where participants spoke about their cognitive-affective states while they viewed videos of their groups. We then collected additional participants where their reports were constrained to a subset of pre-identified cognitive-affective states. In this latter case, participants…

This https://arxiv.org/abs/2504.05655 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multi-bubble solutions for the Dirichlet problem of the $H$-system with higher degree
We consider a Dirichlet problem of the $H$-system \begin{equation*} \begin{cases} Δv = 2v_x\wedge v_y ~& \text{ in }\mathcal{D},\\ v=\varepsilon \tilde g ~& \text{ on }\partial{\mathcal{D}}, \end{cases} \end{equation*} where $\mathcal D\subset \mathbb{R}^2$ is the unit disk, $v:\mathcal D\to \mathbb{R}^3$, and $\tilde g:\partial \mathcal D\to \mathbb{R}^3$ is a given smooth map. As $\varepsilon\to 0^+$, we construct multi-bubble solutions concentrating at distinct points, taking around each po…

Dual realizations of Bergman spaces on strongly convex domains
Agniva Chatterjee
https://arxiv.org/abs/2506.02913 https://arxiv.org/p…

Dual realizations of Bergman spaces on strongly convex domains
The Fantappiè and Laplace transforms realize isomorphisms between analytic functionals supported on a convex compact set $K\subset{\mathbb C}^n$ and certain spaces of holomorphic functions associated with $K$. Viewing the Bergman space of a bounded domain in ${\mathbb C}^n$ as a subspace of the space of analytic functionals supported on its closure, the images of the restrictions of these transforms have been studied in the planar setting. For the Fantappiè transform, this was done for simply…

Andrews-Curtis Groups
Robert H. Gilman, Alexei G. Myasnikov
https://arxiv.org/abs/2506.23031 https://arxiv.org/pdf/2506.23031

Andrews-Curtis Groups
For any group $G$ and integer $k\ge 2$ the Andrews-Curtis transformations act as a permutation group, termed the Andrews-Curtis group $AC_k(G)$, on the subset $N_k(G) \subset G^k$ of all $k$-tuples that generate $G$ as a normal subgroup (provided $N_k(G)$ is non-empty). The famous Andrews-Curtis Conjecture is that if $G$ is free of rank $k$, then $AC_k(G)$ acts transitively on $N_k(G)$. The set $N_k(G)$ may have a rather complex structure, so it is easier to study the full Andrews-Curtis group …

Is spreadsheet syntax better than numeric indexing for cell selection?
Philip Heltweg, Dirk Riehle, Georg-Daniel Schwarz
https://arxiv.org/abs/2505.23296 h…

Is spreadsheet syntax better than numeric indexing for cell selection?
Selecting a subset of cells is a common task in data engineering, for example, to remove errors or select only specific parts of a table. Multiple approaches to express this selection exist. One option is numeric indexing, commonly found in general programming languages, where a tuple of numbers identifies the cell. Alternatively, the separate dimensions can be referred to using different enumeration schemes like "A1" for the first cell, commonly found in software such as spreadsheet systems. …

Scaling Self-Supervised Representation Learning for Symbolic Piano Performance
Louis Bradshaw, Honglu Fan, Alexander Spangher, Stella Biderman, Simon Colton
https://arxiv.org/abs/2506.23869

Scaling Self-Supervised Representation Learning for Symbolic Piano Performance
We study the capabilities of generative autoregressive transformer models trained on large amounts of symbolic solo-piano transcriptions. After first pretraining on approximately 60,000 hours of music, we use a comparatively smaller, high-quality subset, to finetune models to produce musical continuations, perform symbolic classification tasks, and produce general-purpose contrastive MIDI embeddings by adapting the SimCLR framework to symbolic music. When evaluating piano continuation coherence…

Mutli-Level Autoencoder: Deep Learning Based Channel Coding and Modulation
Ahmad Abdel-Qader, Anas Chaaban, Mohamed S. Shehata
https://arxiv.org/abs/2506.23511

Mutli-Level Autoencoder: Deep Learning Based Channel Coding and Modulation
In this paper, we design a deep learning-based convolutional autoencoder for channel coding and modulation. The objective is to develop an adaptive scheme capable of operating at various signal-to-noise ratios (SNR)s without the need for re-training. Additionally, the proposed framework allows validation by testing all possible codes in the codebook, as opposed to previous AI-based encoder/decoder frameworks which relied on testing only a small subset of the available codes. This limitation in …

Model-Based Diagnosis: Automating End-to-End Diagnosis of Network Failures
Changrong Wu, Yiyao Yu, Myungjin Lee, Jayanth Srinivasa, Ennan Zhai, George Varghese, Yuval Tamir
https://arxiv.org/abs/2506.23083

Model-Based Diagnosis: Automating End-to-End Diagnosis of Network Failures
Fast diagnosis and repair of enterprise network failures is critically important since disruptions cause major business impacts. Prior works focused on diagnosis primitives or procedures limited to a subset of the problem, such as only data plane or only control plane faults. This paper proposes a new paradigm, model-based network diagnosis, that provides a systematic way to derive automated procedures for identifying the root cause of network failures, based on reports of end-to-end user-level…

This https://arxiv.org/abs/2405.03536 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Extensional and Non-extensional Functions as Processes
Following Milner's seminal paper, the representation of functions as processes has received considerable attention. For pure $λ$-calculus, the process representations yield (at best) non-extensional $λ$-theories (i.e., $β$ rule holds, whereas $η$ does not). In the paper, we study how to obtain extensional representations, and how to move between extensional and non-extensional representations. Using Internal $π$, $\mathrm{I}π$ (a subset of the $π$-calculus in which all outputs are boun…

A dynamical coherency gate for state recovery: Statistical requiem for the long arc of cislunar orbital mis-prediction
Binyamin Stivi, Vishnuu Mallik, Lamberto Dell'Elce, Aaron J. Rosengren
https://arxiv.org/abs/2506.22748

A dynamical coherency gate for state recovery: Statistical requiem for the long arc of cislunar orbital mis-prediction
We present a statistically grounded methodology for recovering physically consistent initial conditions from historical two-line element sets (TLEs), enabling accurate long-arc trajectory reconstruction for distant and highly eccentric Earth satellites. The approach combines numerical averaging of osculating orbital elements with Gaussian-mixture-model (GMM) filtering with robust fallback strategies to isolate a dynamically coherent subset of mean elements at a common reference epoch. From this…

On Groups of Linear Fractional Transformations Stabilizing Finite Sets of Four Elements
Patrick Nyadjo Fonga
https://arxiv.org/abs/2506.00729 https://

On Groups of Linear Fractional Transformations Stabilizing Finite Sets of Four Elements
Let $E$ be a subset of the projective line over a commutative field $\mathbb{K}$. When $\mathbb{K}$ has infinite cardinality, it is well known that if $E$ contains at most three elements, then the group of linear fractional transformations preserving $E$ is either infinite or isomorphic to the symmetric group on three elements. In this work, we investigate the case where $E$ consists of four elements. We show that the group of projective linear transformations stabilizing $E$ is, depending on t…

This https://arxiv.org/abs/2411.15174 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Regularity for Weak Solutions to First-Order Local Mean Field Games
We establish interior regularity results for first-order, stationary, local mean-field game (MFG) systems. Specifically, we study solutions of the coupled system consisting of a Hamilton-Jacobi-Bellman equation $H(x, Du, m) = 0$ and a transport equation $-\operatorname{div}(m D_pH(x, Du, m)) = 0$ in a domain $Ω\subset \mathbb{R}^d$. Under suitable structural assumptions on the Hamiltonian $H$, without requiring monotonicity of the system, convexity of the Hamiltonian, separability in variables…

A finite Linear Dependence of Discrete Series Multiplicities
Kaustabh Mondal, Gunja Sachdeva
https://arxiv.org/abs/2506.00542 https://

A finite Linear Dependence of Discrete Series Multiplicities
Let $G$ be a connected semisimple simply connected Lie group with a compact Cartan subgroup and let $Γ$ be a uniform lattice in $G$. Let $\widehat{G}_d$ denote the set of equivalence classes of unitary discrete series representations of $G$. We prove that for any finite subset of $\widehat{G}_d$ satisfying a certain condition, the associated finite set of discrete series multiplicities in $L^2(Γ\backslash G)$ determines all discrete series multiplicities in $L^2(Γ\backslash G)$. This allows …

Sources: Google is using its expansive library of YouTube videos to train Gemini and Veo 3; Google says it only uses a subset of videos for the training (Zach Vallese/CNBC)
https://www.cnbc.com/2025/06/19/google-youtube-ai-training-veo-3.html
…

Google is using YouTube videos to train its AI video generator
Google is using its expansive library of YouTube videos to train its AI models, including Gemini and the Veo 3 video and audio generator, CNBC has learned.

Kinematic Distortions of the High-Redshift Universe as Seen from Quasar Proper Motions
Valeri V. Makarov
https://arxiv.org/abs/2507.01798 https://

Kinematic Distortions of the High-Redshift Universe as Seen from Quasar Proper Motions
Advances in optical astrometry allow us to infer the non-radial kinematic structure of the Universe directly from observations. Here I use a supervised machine learning neural network method to predict 1.57 million redshifts based on several photometric and metadata classifier parameters from the unWISE mid-infrared database and from Gaia. These estimates are used to divide the sample into three redshift bins: 1-2, 2-3, and $>3$. For each subset, all available Gaia proper motions are used in a …

Data Efficacy for Language Model Training
Yalun Dai, Yangyu Huang, Xin Zhang, Wenshan Wu, Chong Li, Wenhui Lu, Shijie Cao, Li Dong, Scarlett Li
https://arxiv.org/abs/2506.21545

Data Efficacy for Language Model Training
Data is fundamental to the training of language models (LM). Recent research has been dedicated to data efficiency, which aims to maximize performance by selecting a minimal or optimal subset of training data. Techniques such as data filtering, sampling, and selection play a crucial role in this area. To complement it, we define Data Efficacy, which focuses on maximizing performance by optimizing the organization of training data and remains relatively underexplored. This work introduces a gene…

This https://arxiv.org/abs/2409.07527 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Can slow pulsars in Milky Way globular clusters form via partial recycling?
Alongside the population of several hundred radio millisecond pulsars currently known in Milky Way globular clusters, a subset of six slowly spinning pulsars (spin periods $0.3-4\,$s) are also observed. With inferred magnetic fields $\gtrsim 10^{11}\,$G and characteristic ages $\lesssim10^8\,$yr, explaining the formation of these apparently young pulsars in old stellar populations poses a major challenge. One popular explanation is that these objects are not actually young but instead have been…

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups
E. A. Ladeishchikov, L. V. Lokutsievskiy, N. V. Prilepin
https://arxiv.org/abs/2507.00250

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups
In this paper, we consider the problem of finding geodesics in a series of left-invariant problems endowed with sub-Lorentzian and Finsler structures. Explicit formulas for extremals are obtained in terms of convex trigonometric functions. In the sub-Lorentzian setting, the new trigonometric functions $\cosh_Ω$ and $\sinh_Ω$, developed here, prove especially useful; they generalize the classical $\cosh$ and $\sinh$ to the case of an unbounded convex set $Ω\subset\mathbb{R}^2$.

The independence and clique cover numbers of the squarefree graph
Boris Alexeev, Dustin G. Mixon, Will Sawin
https://arxiv.org/abs/2507.01928 https://

The independence and clique cover numbers of the squarefree graph
We determine the largest subset $A\subseteq \{1,\dotsc,n\}$ such that for all $a,b\in A$, the product $ab$ is not squarefree. Specifically, the maximum size is achieved by the \emph{complement} of the odd squarefree numbers. This resolves a problem of Paul Erdős and András Sárközy from 1992.

Stability and rigidity results of space-like hypersurface in the Minkowski space
Jianhua Chen, Haiyun Deng, Haiqin Xie, Jiabin Yin
https://arxiv.org/abs/2506.01012

Stability and rigidity results of space-like hypersurface in the Minkowski space
In this paper, we establish some rigidity theorems for space-like hypersurfaces in Minkowski space by using a Weinberger-type approach with P-functions and integral identities. Firstly, for space-like hypersurfaces $M$ represented as graphs $x_{n+1}=u(x)$ over domain $Ω\subset\mathbb R^n$, if higher-order mean curvature ratio $\frac{H_{k}}{H_l}(l

Geometric implications of weak tiling
Mihail N. Kolountzakis, Nir Lev, M\'at\'e Matolcsi
https://arxiv.org/abs/2506.23631 https://

Geometric implications of weak tiling
The notion of weak tiling played a key role in the proof of Fuglede's spectral set conjecture for convex domains, due to the fact that every spectral set must weakly tile its complement. In this paper, we revisit the notion of weak tiling and establish some geometric properties of sets that weakly tile their complement. If $A \subset \mathbb{R}^d$ is a convex polytope, we give a direct and self-contained proof that $A$ must be symmetric and have symmetric facets. If $A \subset \mathbb{R}$ is a …

Combinatorial Multi-Access Coded Caching with Private Caches under Intersecting Index Constraints
Dhruv Pratap Singh, Anjana A. Mahesh, B. Sundar Rajan
https://arxiv.org/abs/2506.24060

Combinatorial Multi-Access Coded Caching with Private Caches under Intersecting Index Constraints
We consider the coded caching system where each user, equipped with a private cache, accesses a distinct r-subset of access caches. A central server housing a library of files populates both private and access caches using uncoded placement. In this work, we focus on a constrained indexing regime, referred to as the intersection class, in which the sets used to index the demands of each user must have a nonempty intersection. This regime models resource-limited IoT scenarios such as edge-assist…

Logrithmic Versions of Ginzburg's Sharp Operation for Free Divisors
Xia Liao, Xiping Zhang
https://arxiv.org/abs/2505.24236 https://

Logrithmic Versions of Ginzburg's Sharp Operation for Free Divisors
Let $M$ be a complex manifold, $D\subset M$ a free divisor and $U=M\setminus D$ its complement. In this paper we study the characteristic cycle $\textup{CC}(γ\cdot \ind_U)$ of the restriction of a constructible function $γ$ on $U$. We globalise Ginzburg's local sharp construction and introduce the log transversality condition, which is a new transversality condition about the relative position of $γ$ and $D$. We prove that the log transversality condition is satisfied if either $D$ is normal…

On compact sets possessing $q$-convex functions
Thomas Pawlaschyk, Nikolay Shcherbina
https://arxiv.org/abs/2505.24588 https://arxiv.…

On compact sets possessing $q$-convex functions
We show that there exists a $q$-convex function in a neighborhood of a compact set $K$ in a complex manifold $\mathcal{M}$ if and only if the $q$-nucleus of this compact set is empty. The latter can be characterized as the maximal $q$-pseudoconcave subset of $K$, i.e., a subset of $K$ containing all other compact $q$-pseudoconcave subsets in $K$.

On $L$-$\omega$-nonexpansive maps
Cleon S. Barroso, Jeimer V. Bedoya, Carlos S. R. da Silva
https://arxiv.org/abs/2507.00859 https://…

On $L$-$ω$-nonexpansive maps
We consider $L$-$ω$-nonexpansive maps $T\colon K\to K$ on a convex subset $K$ of a Banach space $X$, i.e., maps in which $ω_T(δ)\leq Lδ+ω(δ)$ with $L\in [0,1]$, $ω$ being a modulus of continuity and $ω_T$ is the minimal modulus of continuity of $T$. Both AFPP and FPP are studied. For moduli $ω$ with $ω'(0)=\infty$, we show that if $X$ contains an isomorphic copy of $\co$ then it fails the FPP for $0$-$ω$-nonexpansive maps with minimal displacement zero. In the affirmative direction, …

Multipacking in Hypercubes
Deepak Rajendraprasad, Varun Sani, Birenjith Sasidharan, Jishnu Sen
https://arxiv.org/abs/2507.01565 https://

Multipacking in Hypercubes
For an undirected graph $G$, a dominating broadcast on $G$ is a function $f : V(G) \rightarrow \mathbb{N}$ such that for any vertex $u \in V(G)$, there exists a vertex $v \in V(G)$ with $f(v) \geqslant 1$ and $d(u,v) \leqslant f(v)$. The cost of $f$ is $\sum_{v \in V} f(v)$. The minimum cost over all the dominating broadcasts on $G$ is defined as the broadcast domination number $γ_b(G)$ of $G$. A multipacking in $G$ is a subset $M \subseteq V(G)$ such that, for every vertex $v \in V(G)$ and ev…

This https://arxiv.org/abs/2502.10382 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On creating convexity in high dimensions
Given a subset $A$ of $\mathbb{R}^n$, we define \begin{align*} \mathrm{conv}_k(A) := \left\{ λ_1 s_1 + \cdots + λ_k s_k : λ_i \in [0,1], \sum_{i=1}^k λ_i = 1 , s_i \in A \right\} \end{align*} to be the set of vectors in $\mathbb{R}^n$ that can be written as a $k$-fold convex combination of vectors in $A$. Let $γ_n$ denote the standard Gaussian measure on $\mathbb{R}^n$. We show that for every $\varepsilon > 0$, there exists a subset $A$ of $\mathbb{R}^n$ with Gaussian measure $γ_n(A) \geq…

On the (In)Approximability of the Monitoring Edge Geodetic Set Problem
Davide Bil\`o, Giodano Colli, Luca Forlizzi, Stefano Leucci
https://arxiv.org/abs/2507.00708

On the (In)Approximability of the Monitoring Edge Geodetic Set Problem
We study the minimum \emph{Monitoring Edge Geodetic Set} (\megset) problem introduced in [Foucaud et al., CALDAM'23]: given a graph $G$, we say that an edge is monitored by a pair $u,v$ of vertices if \emph{all} shortest paths between $u$ and $v$ traverse $e$; the goal of the problem consists in finding a subset $M$ of vertices of $G$ such that each edge of $G$ is monitored by at least one pair of vertices in $M$, and $|M|$ is minimized. In this paper, we prove that all polynomial-t…

Counting abelian number fields with restricted ramification type
Julie Tavernier
https://arxiv.org/abs/2507.00448 https://arxiv.org/p…

Counting abelian number fields with restricted ramification type
We count abelian number fields ordered by arbitrary height function whose generator of tame inertia is restricted to lie in a given subset of the Galois group, and find an explicit formula for the leading constant. We interpret our results as a version of the Batyrev-Manin conjecture on $BG$ and rephrase our result on number fields with restricted ramification type in terms of integral points on $BG$. We also prove that such number fields are equidistributed with respect to suitable collections…

Efficient Estimation of Causal Effects Under Two-Phase Sampling with Error-Prone Outcome and Treatment Measurements
Keith Barnatchez, Kevin P. Josey, Nima S. Hejazi, Bryan E. Shepherd, Giovanni Parmigiani, Rachel Nethery
https://arxiv.org/abs/2506.21777

Efficient Estimation of Causal Effects Under Two-Phase Sampling with Error-Prone Outcome and Treatment Measurements
Measurement error is a common challenge for causal inference studies using electronic health record (EHR) data, where clinical outcomes and treatments are frequently mismeasured. Researchers often address measurement error by conducting manual chart reviews to validate measurements in a subset of the full EHR data -- a form of two-phase sampling. To improve efficiency, phase-two samples are often collected in a biased manner dependent on the patients' initial, error-prone measurements. In this …

Deciding Robust Instances of an Escape Problem for Dynamical Systems in Euclidean Space
Eike Neumann
https://arxiv.org/abs/2506.21481 https://

Deciding Robust Instances of an Escape Problem for Dynamical Systems in Euclidean Space
We study the problem of deciding whether a point escapes a closed subset of $\mathbb{R}^d$ under the iteration of a continuous map $f \colon \mathbb{R}^d \to \mathbb{R}^d$ in the bit-model of real computation. We give a sound partial decision method for this problem which is complete in the sense that its halting set contains the halting set of all sound partial decision methods for the problem. Equivalently, our decision method terminates on all problem instances whose answer is robust under a…

facebook_wall: Facebook wall posts (2009)
Friendship relationships and interactions (wall posts) for a subset of the Facebook social network in 2009, recorded over a 2 year period. Edge directed edge represents a post by one user on another user's FB wall.
This network has 46952 nodes and 876993 edges.
Tags: Social, Online, Temporal, Multigraph

Local H\"older Regularity for Quasilinear Elliptic Equations with Mixed Local-Nonlocal Operators, Variable Exponents, and Weights
Juan Pablo Alcon Apaza
https://arxiv.org/abs/2507.01899

Local Hölder Regularity for Quasilinear Elliptic Equations with Mixed Local-Nonlocal Operators, Variable Exponents, and Weights
We establish local boundedness and local Hölder continuity of weak solutions to the following prototype problem: $$ -\operatorname{div}\left(|x|^{-2 β}|\nabla u|^{\mathbf{q}-2} \nabla u\right)+(-Δ)_{p(\cdot, \cdot), β}^{s(\cdot, \cdot)} u=0 \quad \text { in } \quad Ω, $$ where $Ω\subset \mathbb{R}^n, n \geq 2$, is a bounded domain. The nonlocal operator is defined by $$ (-Δ)_{p(\cdot, \cdot), β}^{s(\cdot, \cdot)} u(x):=\mathrm{P} . \mathrm{V} . \int_Ω \frac{&#…

An approximation theory for Markov chain compression
Mark Fornace, Michael Lindsey
https://arxiv.org/abs/2506.22918 https://arxiv.org…

An approximation theory for Markov chain compression
We develop a framework for the compression of reversible Markov chains with rigorous error control. Given a subset of selected states, we construct reduced dynamics that can be lifted to an approximation of the full dynamics, and we prove simple spectral and nuclear norm bounds on the recovery error in terms of a suitably interpreted Nyström approximation error. We introduce two compression schemes: a projective compression based on committor functions and a structure-preserving compression de…

This https://arxiv.org/abs/2408.14648 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Induced Saturation of the Poset 2C_2
Given a set $X$, the power set $\mathbb{P}(X)$, and a finite poset $P$, a family $F\subset \mathbb{P}(X)$ is said to be induced-$P$-free if there is no injection $ϕ: P\rightarrow \mathbb{F}$ such that $ϕ(p)\subseteqϕ(q)$ if and only if $p\leq_{P} q$, for all $p, q \in P$. The family $F$ is induced-$P$-saturated if it is maximal with respect to being induced-$P$-free. If $n=|X|$, then the size of the smallest induced-$P$-saturated family in $\mathbb{P}(X)$ is denoted $sat(n,P)$. T…

On Fine-Grained Distinct Element Estimation
Ilias Diakonikolas, Daniel M. Kane, Jasper C. H. Lee, Thanasis Pittas, David P. Woodruff, Samson Zhou
https://arxiv.org/abs/2506.22608 …

On Fine-Grained Distinct Element Estimation
We study the problem of distributed distinct element estimation, where $α$ servers each receive a subset of a universe $[n]$ and aim to compute a $(1+\varepsilon)$-approximation to the number of distinct elements using minimal communication. While prior work establishes a worst-case bound of $Θ\left(α\log n+\fracα{\varepsilon^2}\right)$ bits, these results rely on assumptions that may not hold in practice. We introduce a new parameterization based on the number $C = \fracβ{\varepsilon^2}$ …

Integrability of the magnetic geodesic flow on the sphere with a constant 2-form
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
https://arxiv.org/abs/2506.23312

Integrability of the magnetic geodesic flow on the sphere with a constant 2-form
We prove a recent conjecture of Dragovic et al arXiv2504.20515 stating that the magnetic geodesic flow on the standard sphere $S^n\subset \mathbb R^{n+1}$ whose magnetic 2-form is the restriction of a constant 2-form from $\mathbb{R}^{n+1}$ is Liouville integrable. The integrals are quadratic and linear in momenta.

A converse to Cartan's Theorem B: The extension property for real analytic and Nash sets
Jos\'e F. Fernando, Riccardo Ghiloni
https://arxiv.org/abs/2506.18347

A converse to Cartan's Theorem B: The extension property for real analytic and Nash sets
In 1957 Cartan proved his celebrated Theorem B and deduced that if $Ω\subset{\mathbb R}^n$ is an open set and $X$ is a coherent real analytic subset of $Ω$, then $X$ has the analytic extension property, that is, each real analytic function on $X$ extends to a real analytic function on $Ω$. The converse implication in its full generality remains unproven. In the literature only special cases of non-coherent real analytic sets $X\subsetΩ$ without the extension property appear, some of them du…

A Refined Kernel for $d$-Hitting Set
Yuxi Liu, Mingyu Xiao
https://arxiv.org/abs/2506.24114 https://arxiv.org/pdf/2506.24114

A Refined Kernel for $d$-Hitting Set
The $d$-Hitting Set problem is a fundamental problem in parameterized complexity, which asks whether a given hypergraph contains a vertex subset $S$ of size at most $k$ that intersects every hyperedge (i.e., $S \cap e \neq \emptyset$ for each hyperedge $e$). The best known kernel for this problem, established by Abu-Khzam [1], has $(2d - 1)k^{d - 1} + k$ vertices. This result has been very widely used in the literature as many problems can be modeled as a special $d$-Hitting Set problem. In thi…

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow
Elena M\"ader-Baumdicker, Jona Seidel
https://arxiv.org/abs/2506.23359

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow
We study the sublevel sets of the Willmore energy on the space of smoothly immersed $ 2 $-spheres in Euclidean $ 3 $-space. We show that the subset of immersions with energy at most $ 12π$ consists of four regular homotopy classes. Moreover, we show that in certain regular homotopy classes, all singularities of the Willmore flow are avoidable, that is, the initial surface admits a regular homotopy to a round sphere whose Willmore energy does not exceed that of the initial surface. This yields …

This https://arxiv.org/abs/2412.05757 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Global existence of weak solutions to incompressible anisotropic Cahn-Hilliard-Navier-Stokes system
We study the anisotropic, incompressible Cahn-Hilliard-Navier-Stokes system with variable density in a bounded smooth domain $Ω\subset \mathbb{R}^d$. This work extends previous studies on the isotropic case by incorporating anisotropic surface energy, represented by $\mathfrak{F}= \int_Ω \fracε{2}\, Γ^2(\nabla ϕ) $. The thermodynamic consistency of this system, as well as its modeling background and physical motivation, has been established in [3,5,7]. Using a Galerkin approximation scheme…

This https://arxiv.org/abs/2401.13116 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the second-order regularity of solutions to widely singular or degenerate elliptic equations
We consider local weak solutions to PDEs of the type \[ -\,\mathrm{div}\left((\vert Du\vert-λ)_{+}^{p-1}\frac{Du}{\vert Du\vert}\right)=f\,\,\,\,\,\,\,\text{in}\,\,Ω, \] where $1

Near-Optimal Vertex Fault-Tolerant Labels for Steiner Connectivity
Koustav Bhanja, Asaf Petruschka
https://arxiv.org/abs/2506.23215 https://

Near-Optimal Vertex Fault-Tolerant Labels for Steiner Connectivity
We present a compact labeling scheme for determining whether a designated set of terminals in a graph remains connected after any $f$ (or less) vertex failures occur. An $f$-FT Steiner connectivity labeling scheme for an $n$-vertex graph $G=(V,E)$ with terminal set $U \subseteq V$ provides labels to the vertices of $G$, such that given only the labels of any subset $F \subseteq V$ with $|F| \leq f$, one can determine if $U$ remains connected in $G-F$. The main complexity measure is th…

On the Exceptional Sets of Transcendental Analytic Functions in Several Variables with Integer Coefficients
Jean Lelis, Bruno De Paula Miranda, Carlos Gustavo Moreira
https://arxiv.org/abs/2506.15914

On the Exceptional Sets of Transcendental Analytic Functions in Several Variables with Integer Coefficients
In 2020, Marques and Moreira proved that every subset of $\overline{\mathbb{Q}} \cap B(0,1)$, which is closed under complex conjugation and contains $0$, is the exceptional set of uncountably many transcendental analytic functions with integer coefficients. In this paper, we extend this result to transcendental analytic functions in several variables. In particular, we show that every subset of $\overline{\mathbb{Q}}^m$ contained in the unit polydisc $Δ(0;1)$, closed under complex conjugation …

How Trees on Atoms of Subset Algebras Define Minimal Forests and Their Growth
Vasily Buslov
https://arxiv.org/abs/2506.17921 https://…

How Trees on Atoms of Subset Algebras Define Minimal Forests and Their Growth
A complete description is given of how minimal trees on atoms of the algebra of subsets $\mathfrak{A}_k$ generated by minimal spanning $k$-component forests of a weighted digraph $V$ determine the form of these forests and how forests grow with increasing number of arcs (that is with a decrease in the number of trees). Precise bounds are established on what can be extracted about the tree structure of the original graph if the minimal trees on the atoms of a single algebra $\mathfrak{A}_k$ are …

Fault-Tolerant Matroid Bases
Matthias Bentert, Fedor V. Fomin, Petr A. Golovach, Laure Morelle
https://arxiv.org/abs/2506.22010 https://

Fault-Tolerant Matroid Bases
We investigate the problem of constructing fault-tolerant bases in matroids. Given a matroid M and a redundancy parameter k, a k-fault-tolerant basis is a minimum-size set of elements such that, even after the removal of any k elements, the remaining subset still spans the entire ground set. Since matroids generalize linear independence across structures such as vector spaces, graphs, and set systems, this problem unifies and extends several fault-tolerant concepts appearing in prior research. …

This https://arxiv.org/abs/2505.19677 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Perfect codes in quartic Cayley graphs of generalized dihedral groups
For a graph $Γ=(VΓ,EΓ)$, a subset $D$ of $VΓ$ is a perfect code in $Γ$ if every vertex of $Γ$ is dominated by exactly one vertex in $D$. In this paper, we classify all connected quartic Cayley graphs on generalized dihedral groups admitting a perfect code, and determine all perfect codes in such graphs.