Tootfinder

Next stop in our NLP timeline is 2013, the introduction of low dimensional dense word vectors - so-called "word embeddings" - based on distributed semantics, as e.g. word2vec by Mikolov et al. from Google, which enabled representation learning on text.
T. Mikolov et al. (2013). Efficient Estimation of Word Representations in Vector Space.
…

Efficient Estimation of Word Representations in Vector Space
We propose two novel model architectures for computing continuous vector representations of words from very large data sets. The quality of these representations is measured in a word similarity task, and the results are compared to the previously best performing techniques based on different types of neural networks. We observe large improvements in accuracy at much lower computational cost, i.e. it takes less than a day to learn high quality word vectors from a 1.6 billion words data set. Fur…

Proof of a conjecture on isolation of graphs with a universal vertex
Peter Borg, Alastair Farrugia
https://arxiv.org/abs/2506.09290 https://

Proof of a conjecture on isolation of graphs with a universal vertex
A copy of a graph $F$ is called an $F$-copy. For any graph $G$, the $F$-isolation number of $G$, denoted by $ι(G,F)$, is the size of a smallest subset $D$ of the vertex set of $G$ such that the closed neighbourhood $N[D]$ of $D$ in $G$ intersects the vertex sets of the $F$-copies contained by $G$ (equivalently, $G-N[D]$ contains no $F$-copy). Thus, $ι(G,K_1)$ is the domination number $γ(G)$ of $G$, and $ι(G,K_2)$ is the vertex-edge domination number of $G$. Settling a conjecture of Zhang an…

Unbounded sets of solutions of non-cooperative elliptic systems on symmetric spaces
Piotr Stefaniak
https://arxiv.org/abs/2506.08705 https://

Unbounded sets of solutions of non-cooperative elliptic systems on symmetric spaces
The aim of this paper is to show that, for a class of non-cooperative elliptic systems on compact symmetric spaces, any continuum of nontrivial solutions bifurcating from the set of trivial solutions is unbounded. The main tool is the degree for invariant strongly indefinite functionals. The analysis relies on the torus-equivariant structure of the Laplace--Beltrami eigenspaces. The result is obtained by ruling out return to the trivial branch in an equivariant version of the Rabinowitz alterna…

Prime Power Residues and Blocking Sets
Bhawesh Mishra, Paolo Santonastaso
https://arxiv.org/abs/2507.07673 https://arxiv.org/pdf/2507…

Prime Power Residues and Blocking Sets
Let $q$ be a fixed odd prime. We show that a finite subset $B$ of integers, not containing any perfect $q^{th}$ power, contains a $q^{th}$ power modulo almost every prime if and only if $B$ corresponds to a blocking set (with respect to hyperplanes) in $\mathrm{PG}(\mathbb{F}_{q}^{k})$. Here, $k$ is the number of distinct prime divisors of $q$-free parts of elements of $B$. As a consequence, the property of a subset $B$ to contain $q^{th}$ power modulo almost every prime $p$ is invariant under …

sp_colocation: Social co-locations (2018)
Network of colocations between peoople, based on the information on which RFID readers received information from the RFID tags. Namely, we define two individuals to be in co-presence if the same exact set of readers have received signals from both individuals during a 20s time window.
This network has 81 nodes and 150126 edges.
Tags: Social, Offline, Unweighted, Weighted, Temporal, Metadata

This https://arxiv.org/abs/2501.16144 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Survey of the Holroyd-Talbot Conjecture
A family of sets is intersecting if every pair of its members has an element in common. Such a family of sets is called a star if some element is in every set of the family. Given a graph $G$, let $μ(G)$ denote the size of the smallest maximal independent set of $G$. In 2005, Holroyd and Talbot conjectured the following generalization of the Erdős-Ko-Rado Theorem: for $1\le r\le μ(G)/2$, there is a maximum size intersecting family of independent $r$-sets that is a star. In this paper we pres…

Testing Suffixient Sets
Davide Cenzato, Francisco Olivares, Nicola Prezza
https://arxiv.org/abs/2506.08225 https://arxiv.org/pdf/2506…

Testing Suffixient Sets
Suffixient sets are a novel prefix array (PA) compression technique based on subsampling PA (rather than compressing the entire array like previous techniques used to do): by storing very few entries of PA (in fact, a compressed number of entries), one can prove that pattern matching via binary search is still possible provided that random access is available on the text. In this paper, we tackle the problems of determining whether a given subset of text positions is (1) a suffixient set or (2)…

Set-Based Control Barrier Functions and Safety Filters
Kim P. Wabersich, Felix Berkel, Felix Gruber, Sven Reimann
https://arxiv.org/abs/2507.07805 https://…

Set-Based Control Barrier Functions and Safety Filters
High performance and formal safety guarantees are common requirements for industrial control applications. Control barrier function (CBF) methods provide a systematic approach to the modularization of safety and performance. However, the design of such CBFs can be challenging, which limits their applicability to large-scale or data-driven systems. This paper introduces the concept of a set-based CBF for linear systems with convex constraints. By leveraging control invariant sets from reachabili…

Strength of the Upper Bounds for the Edge-Weighted Maximum Clique Problem
Fabio Ciccarelli, Valerio Dose, Fabio Furini, Marta Monaci
https://arxiv.org/abs/2507.06898

Strength of the Upper Bounds for the Edge-Weighted Maximum Clique Problem
We theoretically and computationally compare the strength of the two main upper bounds from the literature on the optimal value of the Edge-Weighted Maximum Clique Problem (EWMCP). We provide a set of instances for which the ratio between either of the two upper bounds and the optimal value of the EWMCP is unbounded. This result shows that neither of the two upper bounds can give a performance guarantee. In addition, we provide two sets of instances for which the ratio between the two upper bou…

Regular sets in Cayley sum graphs on generalized dicyclic groups
Meiqi Peng, Yuefeng Yang, Wenying Zhu
https://arxiv.org/abs/2507.07736 https://

Regular sets in Cayley sum graphs on generalized dicyclic groups
For a graph $Γ=(V(Γ),E(Γ))$, a subset $C$ of $V(Γ)$ is called an $(α,β)$-regular set in $Γ$, if every vertex of $C$ is adjacent to exactly $α$ vertices of $C$ and every vertex of $V(Γ)\setminus C$ is adjacent to exactly $β$ vertices of $C$. In particular, if $C$ is an $(α,β)$-regular set in some Cayley sum graph of a finite group $G$ with connection set $S$, then $C$ is called an $(α,β)$-regular set of $G$. In this paper, we consider a generalized dicyclic group $G$ and for each s…

Interior of distance trees over thin Cantor sets
Yeonwook Jung, Krystal Taylor
https://arxiv.org/abs/2507.07385 https://arxiv.org/pdf…

Interior of distance trees over thin Cantor sets
It is known that if a compact set $E$ in $\mathbb{R}^d$ has Hausdorff dimension greater than $(d+1)/2$, then its $n$-chain distance set $$Δ^n(E) = \left\{\left(\left|x^1-x^2\right|,\cdots, \left|x^{n}- x^{n+1}\right|\right)\in \mathbb{R}^n: x^i \in E, x^i\neq x^j \text{ for } i\neq j \right\}$$ has nonempty interior for any $n\in \mathbb{N}$. In this paper, we prove that for every Cantor set $K\subset \mathbb{R}^d$ and for every $n\in\mathbb{N}$, there exists $\widetilde{K}…

Chemistry on the Defensive Line Sets Up the Raiders Well https://www.si.com/nfl/raiders/las-vegas-malcolm-koonce-adam-butler-maxx-crosby-christian-wilkins

Difference of Constrained Patterns in Logically Constrained Term Rewrite Systems (Full Version)
Naoki Nishida, Misaki Kojima, Yuto Nakamura
https://arxiv.org/abs/2507.04080

Difference of Constrained Patterns in Logically Constrained Term Rewrite Systems (Full Version)
Considering patterns as sets of their instances, a difference operator over patterns computes a finite set of two given patterns, which represents the difference between the dividend pattern and the divisor pattern. A complement of a pattern is a set of patterns, the ground constructor instances of which comprise the complement set of the ground constructor instances of the former pattern. Given finitely many unconstrained linear patterns, using a difference operator over linear patterns, a kno…

A Twisted sl_2(C) Isomonodromic-Isospectral Correspondence
Mohamad Alameddine
https://arxiv.org/abs/2507.06668 https://arxiv.org/pdf/…

A Twisted sl_2(C) Isomonodromic-Isospectral Correspondence
The aim of this article is to generalize the isomonodromic-isospectral correspondence for meromorphic connections of rank $2$ over $\mathbb{P}^1$ to the twisted case. More specifically, the construction of the isospectral approach is provided for the Painlevé I hierarchy, then two maps are constructed, one linking the sets of isomonodromic and isospectral Hamiltonians, another linking the set of apparent singularities to a set of isospectral coordinates.

Universal Mass Equation for Equal-Quantum Excited-States Sets II
L. David Roper (VTech), Igor Strakovsky (GWU)
https://arxiv.org/abs/2506.06496 https://

Universal Mass Equation for Equal-Quantum Excited-States Sets II
We extend our recent study of the universal mass equation for equal-quantum excited-states sets reported by Roper and Strakovsky~\cite{Roper:2024ovj}. The masses of twelve baryon sets and sixteen meson sets, with only two equal-quantum excited states in each set, using Breit-Wigner PDG2024 masses and their uncertainties at fixed $J^P$ for baryons and $J^{PC}$ for mesons, are fitted by a simple one-parameter logarithmic function, $M_n = αLn(n) + M_1$, where $n$ is the level of radial excitation…

Minimal generating sets of groups of Kim-Manturov
Takuya Sakasai, Yuuki Tadokoro, Kokoro Tanaka
https://arxiv.org/abs/2506.05778 https://

Minimal generating sets of groups of Kim-Manturov
We consider a series of groups defined by Kim and Manturov. These groups have their background in triangulations of a surface and configurations of points, lines or circles on the surface. They are expected to have relationships to many geometric objects. In this paper, we give a minimal generating set of the group and determine the abelianization. We also introduce some related groups which might be helpful to understand the structure of the original groups.

Hausdorff dimension of self-similar measures and sets with common fixed point structure
Bal\'azs B\'ar\'any, Manuj Verma
https://arxiv.org/abs/2507.05835

Hausdorff dimension of self-similar measures and sets with common fixed point structure
In this paper, we study the Hausdorff dimension of self-similar measures and sets on the real line, where the generating iterated function system consists of some maps that share the same fixed point. In particular, we will show that out of a Hausdorff co-dimension one exceptional set of natural parameters, such systems satisfy a weak exponential separation. This significantly strengthens the previous result of the first author and Szvák. As an application, we give the Hausdorff dimension of s…

Evasive sets, twisted varieties, and container-clique trees
Jeck Lim, Jiaxi Nie, Ji Zeng
https://arxiv.org/abs/2507.07594 https://arx…

Evasive sets, twisted varieties, and container-clique trees
In the affine space $\mathbb{F}_q^n$ over the finite field of order $q$, a point set $S$ is said to be $(d,k,r)$-evasive if the intersection between $S$ and any variety, of dimension $k$ and degree at most $d$, has cardinality less than $r$. As $q$ tends to infinity, the size of a $(d,k,r)$-evasive set in $\mathbb{F}_q^n$ is at most $O\left(q^{n-k}\right)$ by a simple averaging argument. We exhibit the existence of such evasive sets of sizes at least $Ω\left(q^{n-k}\right)$ for much smaller va…

Lineal Extensions of Kakeya Sets Missing Every ee-Random Point
Neil Lutz, Spencer Park Martin, Rain White
https://arxiv.org/abs/2507.05475 https://

Lineal Extensions of Kakeya Sets Missing Every ee-Random Point
By effectivizing a Kakeya set construction, we prove the existence of lines in all directions that do not contain any double exponential time random points. This means each point on these lines has an algorithmically predictable location, to the extent that a gambler in an environment with fair payouts can, using double exponential time computing resources, amass unbounded capital placing bets on increasingly precise estimates of the point's location. Our result resolves an open question publis…

Smallest Suffixient Sets as a Repetitiveness Measure
Gonzalo Navarro, Giuseppe Romana, Cristian Urbina
https://arxiv.org/abs/2506.05638 https://

Smallest Suffixient Sets as a Repetitiveness Measure
Suffixient sets are a novel combinatorial object that capture the essential information of repetitive strings in a way that, provided with a random-access mechanism, supports various forms of pattern matching. In this paper we study the size $χ$ of the smallest suffixient set as a repetitiveness measure: we place it between known measures and study its sensitivity to various string operations.

This https://arxiv.org/abs/2503.03933 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Arithmetic properties of Cantor sets involving non-diagonal forms
We show conditions on $k$ such that any number $x$ in the interval $[0, k/2]$ can be represented in the form $x_1^{a_1} x_2^{a_2} + x_3^{a_3} x_4^{a_4} + \cdots + x_{k-1}^{a_{k-1}} x_k^{a_k}$, where the exponents $a_{2i-1}$ and $a_{2i}$ are positive integers satisfying $a_{2i-1} + a_{2i} = s$ for $i = 1, 2, \dots, k/2$, and each $x_i$ belongs to the generalized Cantor set. Moreover, we discuss different types of non-diagonal polynomials and clarify the optimal results in low-dimensional cases.

This https://arxiv.org/abs/2306.07237 has been replaced.
link: https://scholar.google.com/scholar?q=a

Three Edge-disjoint Plane Spanning Paths in a Point Set
We consider the following problem: Given a set $S$ of $n$ distinct points in the plane, how many edge-disjoint plane straight-line spanning paths can be drawn on $S$? Each spanning path must be crossing-free, but edges from different paths are allowed to intersect at arbitrary points. It is known that if the points of $S$ are in convex position, then $\lfloor n/2 \rfloor$ such paths always exist. However, for general point sets, the best known construction yields only two edge-disjoint plane sp…

Dynamics of rotationally invariant polynomial root sets under iterated differentiations
Andr\'e Galligo, Joseph Najnudel, Truong Vu
https://arxiv.org/abs/2506.06263

Dynamics of rotationally invariant polynomial root sets under iterated differentiations
We associate to an $N$-sample of a given rotationally invariant probability measure $μ_0$ with compact support in the complex plane, a polynomial $P_N$ with roots given by the sample. Then, for $t \in (0,1)$, we consider the empirical measure $μ_t^{N}$ associated to the root set of the $\lfloor t N\rfloor$-th derivative of $P_N$. A question posed by O'Rourke and Steinerberger \cite{o2021nonlocal}, reformulated as a conjecture by Hoskins and Kabluchko \cite{hoskins2021dynamics}, and recently…

Filing: neobank Chime plans to sell 26M shares in its IPO at $24 to $26, giving it a valuation between $10.3B and $11.1B; its two co-founders own 4% to 5% each (Cory Weinberg/The Information)
https://www.theinformation.com/briefings/chime-sets-ipo-…

Chime Sets Tentative IPO Price at Around $10.7 Billion
Banking app Chime plans to sell shares in an initial public offering at a price that would value it at between $10.3 billion and $11.1 billion, on a fully-diluted basis, the company said in a new securities filing Monday. The company set the price range ahead of a roadshow to meet investors over the next week, ahead of its IPO. The per-share price of the range, between $24 and $26, is more

Context-aware gate set tomography: Improving the self-consistent characterization of trapped-ion universal gate sets by leveraging non-Markovianity
Pablo Vi\~nas, Alejandro Bermudez
https://arxiv.org/abs/2507.02542

Context-aware gate set tomography: Improving the self-consistent characterization of trapped-ion universal gate sets by leveraging non-Markovianity
To progress in the characterization of noise for current quantum computers, gate set tomography (GST) has emerged as a self-consistent tomographic protocol that can accurately estimate the complete set of noisy quantum gates, state preparations, and measurements. In its original incarnation, GST improves the estimation precision by applying the gates sequentially, provided that the noise makes them a set of fixed completely-positive and trace preserving (CPTP) maps independent of the history of…

This https://arxiv.org/abs/2505.10090 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sombor index of clean graphs
Let $G = (V, E)$ be a graph with the vertex set $V (G)$ and edge set $E(G)$. The Sombor index of $G$, $SO(G)$, is defined as $\sum_{uv\in E(G)} \sqrt{deg(u)^2 + deg(v)^2}$, where $deg(u)$ is the degree of vertex $u$ in $V (G)$. The clean graph of a ring R, denoted by $Cl(R)$, is a graph with vertex set $\{(e, u) : e \in Id(R), u \in U(R)\}$ and two distinct vertices $(e, u)$ and$(f, v)$ are adjacent if and only if $ef = 0$ or $uv = 1$ ($Id(R)$ and $U(R)$ are the sets of idempotents and unit ele…

Effective Versions of Strong Measure Zero
Matthew Rayman
#toXiv_bot_toot

What a game…
https://www.theguardian.com/sport/live/2025/jun/08/french-open-2025-mens-final-jannik-sinner-v-carlos-alcaraz-tennis-live?CMP=Share_iOSApp_Other

Hausdorff Dimension of non-conical and Myrberg limit sets
Mahan Mj, Wenyuan Yang
https://arxiv.org/abs/2506.04955 https://arxiv.org/p…

Hausdorff Dimension of non-conical and Myrberg limit sets
In this paper, we develop techniques to study the Hausdorff dimensions of non-conical and Myrberg limit sets for groups acting on negatively curved spaces. We establish maximality of the Hausdorff dimension of the non-conical limit set of $G$ in the following cases. 1. $M$ is a finite volume complete Riemannian manifold of pinched negative curvature and $G$ is an infinite normal subgroups of infinite index in $π_1(M)$. 2. $G$ acts on a regular tree $X$ with $X/G$ infinite and amenable (dimensi…

Controlled Reach-avoid Set Computation for Discrete-time Polynomial Systems via Convex Optimization
Taoran Wu, Yiling Xue, Dejin Ren, Arvind Easwaran, Martin Fr\"anzle, Bai Xue
https://arxiv.org/abs/2506.06679

Controlled Reach-avoid Set Computation for Discrete-time Polynomial Systems via Convex Optimization
This paper addresses the computation of controlled reach-avoid sets (CRASs) for discrete-time polynomial systems subject to control inputs. A CRAS is a set encompassing initial states from which there exist control inputs driving the system into a target set while avoiding unsafe sets. However, efficiently computing CRASs remains an open problem, especially for discrete-time systems. In this paper, we propose a novel framework for computing CRASs which takes advantage of a probabilistic perspec…

Frobenius theorem and fine structure of tangency sets to non-involutive distributions
Giovanni Alberti, Annalisa Massaccesi, Andrea Merlo
https://arxiv.org/abs/2506.03715

Frobenius theorem and fine structure of tangency sets to non-involutive distributions
In this paper we provide a complete answer to the question whether Frobenius' Theorem can be generalized to surfaces below the $C^{1,1}$ threshold. We study the fine structure of the tangency set in terms of involutivity of a given distribution and we highlight a tradeoff behavior between the regularity of a tangent surface and that of the tangency set. First of all, we prove a Frobenius-type result, that is, given a $k$-dimensional surface $S$ of class $C^1$ and a non-involutive $k$-distributi…

This https://arxiv.org/abs/2407.01101 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Packing Density of Sets With Only Two Nonmixed Gaps
For a finite set of integers such that the first few gaps between its consecutive elements equal $a$, while the remaining gaps equal $b$, we study dense packings of its translates on the line. We obtain an explicit lower bound on the corresponding optimal density, conjecture its tightness, and prove it in case one of the gap lengths, $a$ or $b$, appears only once. This is equivalent to a Motzkin problem on the independence ratio of certain integer distance graphs.

Operators of stochastic adding machines and Julia sets
Danilo Caprio, Ali Messaoudi, Ioannis Tsokanos, Glauco Valle
https://arxiv.org/abs/2506.05703 https:…

Operators of stochastic adding machines and Julia sets
A stochastic adding machine is a Markov chain on the set of non-negative integers $\mathbb{Z}_{+}$ that models the process of adding one by successively updating the digits of a number's expansion in a given numeration system. At each step, random failures may occur, interrupting the procedure and preventing it from continuing beyond a certain point. The first model of such a stochastic adding machine, constructed for the binary base, was introduced by Killeen and Taylor. Their work was motiv…

Norming Sets for Tensor and Polynomial Sketching
Yifan Zhang, Joe Kileel
https://arxiv.org/abs/2506.05174 https://arxiv.org/pdf/2506.…

Norming Sets for Tensor and Polynomial Sketching
This paper develops the sketching (i.e., randomized dimension reduction) theory for real algebraic varieties and images of polynomial maps, including, e.g., the set of low rank tensors and tensor networks. Through the lens of norming sets, we provide a framework for controlling the sketching dimension for \textit{any} sketch operator used to embed said sets, including sub-Gaussian, fast Johnson-Lindenstrauss, and tensor structured sketch operators. Leveraging norming set theory, we propose a ne…

2-Segal sets and pseudomonoids in the bicategory of spans
Sophia E Marx, Rajan Amit Mehta
https://arxiv.org/abs/2505.22832 https://ar…

2-Segal sets and pseudomonoids in the bicategory of spans
In this survey article, we give an introduction to the notion of a 2-Segal set and prove that 2-Segal sets are equivalent to pseudomonoids in the bicategory of spans. The proof utilizes graphical techniques for 2-Segal sets and spans that should be useful in more general settings. There are procedures for obtaining an associative algebra from a 2-Segal set (satisfying finiteness conditions). We describe these procedures and give several examples of algebras arising from 2-Segal sets. Wherev…

An Efficient Candidate-Free R-S Set Similarity Join Algorithm with the Filter-and-Verification Tree and MapReduce
Yuhong Feng, Fangcao Jian, Yixuan Cao, Xiaobin Jian, Jia Wang, Haiyue Feng, Chunyan Miao
https://arxiv.org/abs/2506.03893

An Efficient Candidate-Free R-S Set Similarity Join Algorithm with the Filter-and-Verification Tree and MapReduce
Given two different collections of sets, the exact set similarity R-S Join finds all set pairs with similarity no less than a given threshold, which has widespread applications. While existing algorithms accelerate large-scale R-S Joins using a two-stage filter-and-verification framework along with the parallel and distributed MapReduce framework, they suffer from excessive candidate set pairs, leading to significant I/O, data transfer, and verification overhead, and ultimately degrading the pe…

Classification by Separating Hypersurfaces: An Entropic Approach
Argimiro Arratia, Mahmoud El Daou, Henryk Gzyl
https://arxiv.org/abs/2507.02732 https://…

Classification by Separating Hypersurfaces: An Entropic Approach
We consider the following classification problem: Given a population of individuals characterized by a set of attributes represented as a vector in ${\mathbb R}^N$, the goal is to find a hyperplane in ${\mathbb R}^N$ that separates two sets of points corresponding to two distinct classes. This problem, with a history dating back to the perceptron model, remains central to machine learning. In this paper we propose a novel approach by searching for a vector of parameters in a bounded $N$-dimensi…

Generic mean curvature flow with obstacles
Tim Laux, Keisuke Takasao
https://arxiv.org/abs/2507.06150 https://arxiv.org/pdf/2507.0615…

Generic mean curvature flow with obstacles
We study the obstacle problem associated to mean curvature flow. We add to the geometric vanishing-viscosity approximation of Evans and Spruck a singular perturbation that penalizes the violation of the constraint, and pass to the limit. The resulting level set formulation has unique solutions - up to fattening. Extending the work of Evans and Spruck and a work by Ullrich and one of the authors, we show that generic level sets of this flow are distributional solutions of the obstacle problem.

Higher homotopy wild sets
Jeremy Brazas, Atish Mitra
https://arxiv.org/abs/2505.23665 https://arxiv.org/pdf/2505.23665

Higher homotopy wild sets
The $π_n$-wild set $\mathbf{w}_{n}(X)$ of a topological space $X$ is the subspace of $X$ consisting of the points at which there exists a shrinking sequence of essential based maps $S^n\to X$. In this paper, we show that the homotopy type of $\mathbf{w}_{n}(X)$ is a homotopy invariant of $X$ and, in analogy to the known one-dimensional case, we show that for certain $n$-dimensional $π_n$-shape injective metric spaces, the homeomorphism type of $\mathbf{w}_{n}(X)$ is a homotopy invariant of $X…

This https://arxiv.org/abs/2410.12201 has been replaced.
link: https://scholar.google.com/scholar?q=a

Data-light Uncertainty Set Merging with Admissibility: Synthetics, Aggregation, and Test Inversion
This article introduces a Synthetics, Aggregation, and Test inversion (SAT) approach for merging diverse and potentially dependent uncertainty sets into a single unified set. The procedure is data-light, relying only on initial sets and control levels, and it adapts to any user-specified initial uncertainty sets, accommodating potentially varying coverage levels. SAT is motivated by the challenge of integrating uncertainty sets when only the initial sets and their control levels are available -…

Critical elements in algebras of numerical events
Dietmar Dorninger, Helmut L\"anger
https://arxiv.org/abs/2507.00194 https://ar…

Critical elements in algebras of numerical events
The probability p(s) of the occurrence of an event pertaining to a physical system which is observed in different states s determines a function p from the set S of states of the system to [0,1]. The function p is called a numerical event or more precisely an S-probability. When appropriately structured, sets P of numerical events form so-called algebras of S-probabilities, which are orthomodular posets that can serve as quantum logics. If one deals with a classical physical system, then P will…

a friend let me take a picture of his whiteboard

RefTok: Reference-Based Tokenization for Video Generation
Xiang Fan, Xiaohang Sun, Kushan Thakkar, Zhu Liu, Vimal Bhat, Ranjay Krishna, Xiang Hao
https://arxiv.org/abs/2507.02862 …

RefTok: Reference-Based Tokenization for Video Generation
Effectively handling temporal redundancy remains a key challenge in learning video models. Prevailing approaches often treat each set of frames independently, failing to effectively capture the temporal dependencies and redundancies inherent in videos. To address this limitation, we introduce RefTok, a novel reference-based tokenization method capable of capturing complex temporal dynamics and contextual information. Our method encodes and decodes sets of frames conditioned on an unquantized re…

Corrections to Published Values of Frequency Sampling Filter Transition Coefficients
C. S. Ramalingam
https://arxiv.org/abs/2507.02556 https://

Corrections to Published Values of Frequency Sampling Filter Transition Coefficients
Tables of optimal transition coefficients and peak sidelobe level (PSL, in dB) associated with frequency sampling filter (FSF) design were published by Rabiner et al. (Jun 1970), and reproduced, for example, in the book Digital Signal Processing by Proakis and Manolakis (4/e, 2007). A set of values are also given in Appendix H of Understanding Digital Signal Processing} by Lyons (3/e, 2011), but there are significant differences between these two sets. For example, for $N=16$ and BW$=4$, two di…

This https://arxiv.org/abs/2502.16673 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the asymptotic validity of confidence sets for linear functionals of solutions to integral equations
This paper examines the construction of confidence sets for parameters defined as linear functionals of a function of W and X whose conditional mean given Z and X equals the conditional mean of another variable Y given Z and X. Many estimands of interest in causal inference can be expressed in this form, including the average treatment effect in proximal causal inference and treatment effect contrasts in instrumental variable models. We derive a necessary condition for a confidence set to be un…

On the convergence of critical points on real algebraic sets and applications to optimization
Saugata Basu, Ali Mohammad-Nezhad
https://arxiv.org/abs/2506.20565

On the convergence of critical points on real algebraic sets and applications to optimization
Let $F \in \R[X_1,\ldots,X_n]$ and the zero set $V=\zero(\mathcal{P},\R^n)$, where $\mathcal{P}:=\{P_1,\ldots,P_s\} \subset \R[X_1,\ldots,X_n]$ is a finite set of polynomials. We investigate existence of critical points of $F$ on an infinitesimal perturbation $V_ξ = \zero(\{P_1-ξ_1.\ldots,P_s-ξ_s\},\R^n)$. Our motivation is to understand the limiting behavior of central paths in polynomial optimization, which is an important problem in the theory of interior point methods for polynomial opti…

A family of non Minkowski measurable fractals in $\mathbb{R}^2$
Uta Freiberg, Jonas Lippold
https://arxiv.org/abs/2506.02640 https://…

A family of non Minkowski measurable fractals in $\mathbb{R}^2$
A long-standing conjecture of Lapidus asserts that, under certain conditions, a self-similar fractal set is not Minkowski measurable if and only if it is of lattice-type. For self-similar sets in $\mathbb{R}$, the Lapidus conjecture has been confirmed. However, in higher dimensions, it remains unclear whether all lattice-type self-similar sets are not Minkowski measurable. This work presents a family of lattice-type subsets in $\mathbb{R}^2$ that are not Minkowski measurable, hence providing fu…

The Erd\H{o}s-Falconer distance problem between arbitrary sets and $k$-coordinatable sets in finite fields
Hunseok Kang, Doowon Koh, Firdavs Rakhmonov
https://arxiv.org/abs/2506.07251

The Erdős-Falconer distance problem between arbitrary sets and $k$-coordinatable sets in finite fields
In this paper, we study the cardinality of the distance set $Δ(A, B)$ determined by two subsets $A$ and $B$ of the $d$-dimensional vector space over a finite field $\mathbb{F}_q$. Assuming that $A$ or $B$ lies in a $k$-coordinate plane up to translations and rotations, we prove that if $|A||B| > 2q^d$, then $|Δ(A, B)| > q/2$, where $|Δ(A, B)|$ denotes the number of distinct distances between elements of $A$ and $B$. In particular, we show that our resu…

sp_colocation: Social co-locations (2018)
Network of colocations between peoople, based on the information on which RFID readers received information from the RFID tags. Namely, we define two individuals to be in co-presence if the same exact set of readers have received signals from both individuals during a 20s time window.
This network has 100 nodes and 394247 edges.
Tags: Social, Offline, Unweighted, Weighted, Temporal, Metadata

This https://arxiv.org/abs/2306.09536 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On two definitions of wave-front sets for $p$-adic groups
The wave-front set for an irreducible admissible representation of a $p$-adic reductive group is the set of maximal nilpotent orbits which appear in the local character expansion. By Mœglin-Waldspurger, they are also the maximal nilpotent orbits whose associated degenerate Whittaker models are non-zero. However, in the literature there are two versions commonly used, one defining maximality using analytic closure and the other using Zariski closure. We show that these two definitions are non-e…

The Price of Being Partial: Complexity of Partial Generalized Dominating Set on Bounded-Treewidth Graphs
Jakob Greilhuber, D\'aniel Marx
https://arxiv.org/abs/2506.01645

The Price of Being Partial: Complexity of Partial Generalized Dominating Set on Bounded-Treewidth Graphs
The $(σ, ρ)$-domination framework introduced by Telle [Nord. J. Comput.'94] captures many classical graph problems. For fixed sets $σ, ρ$ of non-negative integers, a $(σ,ρ)$-set of a graph $G$ is a set $S$ such that for every $v\in V(G)$, we have (1) if $v \in S$, then $|N(v) \cap S| \in σ$, and (2) if $v \not\in S$, then $|N(v) \cap S| \in ρ$. We initiate the study of a natural partial variant of the problem, in which the constraints given by $σ, ρ$ need not be fu…

Finitary codings and stochastic domination for Poisson representable processes
Yinon Spinka
https://arxiv.org/abs/2506.04797 https://…

Finitary codings and stochastic domination for Poisson representable processes
Construct a random set by independently selecting each finite subset of the integers with some probability depending on the set up to translations and taking the union of the selected sets. We show that when the only sets selected with positive probability are pairs, such a random set is a finitary factor of an IID process, answering a question of Forsström, Gantert and Steif. More generally, we show that this is the case whenever the distribution induced by the size of the selected sets has s…

This https://arxiv.org/abs/2505.22251 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Evaluation of LLMs in Speech is Often Flawed: Test Set Contamination in Large Language Models for Speech Recognition
Recent work suggests that large language models (LLMs) can improve performance of speech tasks compared to existing systems. To support their claims, results on LibriSpeech and Common Voice are often quoted. However, this work finds that a substantial amount of the LibriSpeech and Common Voice evaluation sets appear in public LLM pretraining corpora. This calls into question the reliability of findings drawn from these two datasets. To measure the impact of contamination, LLMs trained with or w…

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 $K$.

I have this idea of building a "Luddite Library". A set of information, tools and processes to harness luddite thinking when analyzing technological developments and "innovation".
Something that interested parties could use to understand that there might be a different way to think about what tech is/should be/can be/mustn't be for us. Think for example sets of questions to use to analyze a new thing being pushed on you and similar tools.
I'm thinking …

On orbit sets generated by semigroups of one-dimensional affine functions
Karim F. Shamazov, Alexey L. Talambutsa
https://arxiv.org/abs/2507.06875 https://…

On orbit sets generated by semigroups of one-dimensional affine functions
The one-dimensional orbit set $\langle F : s \rangle$ is formed by the images of a number $s$ under the action of a semigroup generated by the integer affine functions $f_i=a_i x+b_i$ taken from the set $F=\{f_1,\ldots,f_n\}$. P.Erdös established an upper bound $O(x^{σ+ε})$ for the growth function $|\langle F : s \rangle\cap[0,x]|$, where $1/a_1^σ+1/a_2^σ+\ldots + 1/a_n^σ=1$ and $\varepsilon>0$, which was extended to orbit multisets and real affine functions by J.Lagarias. We co…

This https://arxiv.org/abs/2409.11231 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Positively closed $Sh(B)$-valued models
We study positively closed and strongly positively closed topos-valued models of coherent theories. Positively closed is a global notion (it is defined in terms of all possible outgoing homomorphisms), while strongly positively closed is a local notion (it only concerns the definable sets inside the model). For $\mathbf{Set}$-valued models of coherent theories they coincide. We prove that if $\mathcal{E}=Sh(X)$ for an extremally disconnected Stone space (or equivalently $\mathcal{E}=Sh(B,τ_{…

A few good choices
Thanh Nguyen, Haoyu Song, Young-San Lin
https://arxiv.org/abs/2506.22133 https://arxiv.org/pdf/2506.22133

A few good choices
A Condorcet winning set addresses the Condorcet paradox by selecting a few candidates--rather than a single winner--such that no unselected alternative is preferred to all of them by a majority of voters. This idea extends to $α$-undominated sets, which ensure the same property for any $α$-fraction of voters and are guaranteed to exist in constant size for any $α$. However, the requirement that an outsider be preferred to every member of the set can be overly restrictive and difficult to jus…

$J$-class weighted translations on locally compact groups
M. R. Azimi, I. Akbarbaglu, A. R. Imanzadeh Fard
https://arxiv.org/abs/2506.04730 https://…

$J$-class weighted translations on locally compact groups
A bounded linear operator $T$ on a Banach space $X$ (not necessarily separable) is said to be $J$-class operator whenever the extended limit set, say $J_T(x)$ equals $X$ for some vector $x\in X$. Practically, the extended limit sets localize the dynamical behavior of operators. In this paper, using the extended limit sets we will examine the necessary and sufficient conditions for the weighted translation $T_{a,ω}$ to be $J$-class on a locally compact group $G$, within the setting of $ L^p$-sp…

This https://arxiv.org/abs/2407.18293 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

On the relation between magnetic field strength and gas density in the interstellar medium: A multiscale analysis
The magnetic field strength to gas density relation in the interstellar medium is of fundamental importance. We present and compare Bayesian analyses of the B-n relation for two comprehensive observational data sets: a Zeeman data set and 700 observations using the Davis-Chandrasekhar-Fermi (DCF) method. Using a hierarchical Bayesian analysis we present a general, multi-scale broken power-law relation, $B=B_0(n/n_0)^α$ , with $α=α_1$ for $nn_0$, and with $B_0$ the fie…

$p$-adic alternate Julia sets
Rui-Xi Wang
https://arxiv.org/abs/2507.02133 https://arxiv.org/pdf/2507.02133

$p$-adic alternate Julia sets
The study of dynamical systems involves analyzing how functions behave under iteration in different mathematical spaces. In the context of complex dynamics, tools such as Julia sets and filled Julia sets are used to understand the long-term behavior of functions in the complex Euclidean field. In this paper, we will present a review of Julia sets and filled Julia sets, provide an overview of the mathematical formulation of the alternate Julia set introduced in the work of Danca-Romera-Pastor, e…

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…

Egyptian fractions for few primes
Agustina Czenky, Emily McGovern, Julia Plavnik, Eric Rowell, Abigail Watkins
https://arxiv.org/abs/2507.03727 https://

Egyptian fractions for few primes
We study solutions to the Egyptian fractions equation with the prime factors of the denominators constrained to lie in a fixed set of primes. We evaluate the effectiveness of the greedy algorithm in establishing bounds on such solutions. Additionally, we present improved algorithms for generating low-rank solutions and solutions restricted to specific prime sets. Computational results obtained using these algorithms are provided, alongside a discussion on their performance.

The infinite dimensional geometry of conjugation invariant generating sets
Sabine Chu, George Domat, Christine Gao, Ananya Prasanna, Alex Wright
https://arxiv.org/abs/2506.18618

The infinite dimensional geometry of conjugation invariant generating sets
We consider a number of examples of groups together with an infinite conjugation invariant generating set, including: the free group with the generating set of all separable elements; surface groups with the generating set of all non-filling curves; mapping class groups and outer automorphism groups of free groups with the generating sets of all reducible elements; and groups with suitable actions on Gromov hyperbolic spaces with a generating set of elliptic elements. In these Cayley graphs we …

On cubic vertex-transitive graphs of given girth
Ted Dobson, Ademir Hujdurovi\'c, Wilfried Imrich, Ronald Ortner
https://arxiv.org/abs/2507.05821 https…

On cubic vertex-transitive graphs of given girth
A set of vertices of a graph is distinguishing if the only automorphism that preserves it is the identity. The minimal size of such sets, if they exist, is the distinguishing cost. The distinguishing costs of vertex transitive cubic graphs are well known if they are 1-arc-transitive, or if they have two edge orbits and either have girth 3 or vertex-stabilizers of order 1 or 2. There are many results about vertex-transitive cubic graphs of girth 4 with two edge orbits, but for larger girth alm…

Connected components in d-minimal structures
Masato Fujita
https://arxiv.org/abs/2506.21846 https://arxiv.org/pdf/2506.21846

Connected components in d-minimal structures
For a given d-minimal expansion $\mathfrak R$ of the ordered real field, we consider the expansion $\mathfrak R^\natural$ of $\mathfrak R$ generated by the sets of the form $\bigcup_{S \in \mathcal C}S$, where $\mathcal C$ is a subfamily of the collection of connected components of an $\mathfrak R$-definable set. We prove that $\mathfrak R^{\natural}$ is d-minimal. A similar assertion holds for almost o-minimal expansions of ordered groups.

Estimation of Optimal Causal Bounds via Covariate-Assisted Optimal Transport
Sirui Lin, Zijun Gao, Jose Blanchet, Peter Glynn
https://arxiv.org/abs/2506.00257

Estimation of Optimal Causal Bounds via Covariate-Assisted Optimal Transport
We study the estimation of causal estimand involving the joint distribution of treatment and control outcomes for a single unit. In typical causal inference settings, it is impossible to observe both outcomes simultaneously, which places our estimation within the domain of partial identification (PI). Pre-treatment covariates can substantially reduce estimation uncertainty by shrinking the partially identified set. Recently, it was shown that covariate-assisted PI sets can be characterized thro…

The overflow in the Katona Theorem
Peter Frankl, Jian Wang
https://arxiv.org/abs/2506.05704 https://arxiv.org/pdf/2506.05704

The overflow in the Katona Theorem
Let $n>2r>0$ be integers. We consider families $\mathcal{F}$ of subsets of an $n$-element set, in which the union of any two members has size at most $2r$. One of our results states that for $n\geq 6r$ the number of members of size exceeding $r$ in $\mathcal{F}$ is at most $\binom{n-2}{r-1}$. Another result shows that for $n>3.5r$ the number of sets of size at least $r$ is at most $\binom{n}{r}$. Both bounds are best possible and the latter sharpens the classical Katona Theorem. Similar results…

On gap sets in arbitrary Kummer extensions of $K(x)$
Ethan Cotterill, Erik A. R. Mendoza, Pietro Speziali
https://arxiv.org/abs/2506.19169 https://

On gap sets in arbitrary Kummer extensions of $K(x)$
Let $K$ be an algebraically closed field, and let $F/K(x)$ be a Kummer extension of function fields of genus $g$. We provide a compact and explicit description of the gap set $G(Q)$ at any totally ramified place $Q$ of the extension $F/K(x)$. As a consequence, we deduce structural properties of the Weierstrass semigroup $H(Q)$; in particular, we determine a generating set for $H(Q)$, and we characterize its symmetry in certain cases. We also generalize a formula due to Towse that describes the …

This https://arxiv.org/abs/2505.05702 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Hypergraph Neural Sheaf Diffusion: A Symmetric Simplicial Set Framework for Higher-Order Learning
The absence of intrinsic adjacency relations and orientation systems in hypergraphs creates fundamental challenges for constructing sheaf Laplacians of arbitrary degrees. We resolve these limitations through symmetric simplicial sets derived directly from hypergraphs, which encode all possible oriented subrelations within each hyperedge as ordered tuples. This construction canonically defines adjacency via facet maps while inherently preserving hyperedge provenance. We establish that the normal…

Control of Power Grids With Switching Equilibria: $\Omega$-Limit Sets and Input-to-State Stability
Mahmoud Abdelgalil, Vishal Shenoy, Guido Cavraro, Emiliano Dall'Anese, Jorge I. Poveda
https://arxiv.org/abs/2507.00240

Control of Power Grids With Switching Equilibria: $Ω$-Limit Sets and Input-to-State Stability
This paper studies a power transmission system with both conventional generators (CGs) and distributed energy assets (DEAs) providing frequency control. We consider an operating condition with demand aggregating two dynamic components: one that switches between different values on a finite set, and one that varies smoothly over time. Such dynamic operating conditions may result from protection scheme activations, external cyber-attacks, or due to the integration of dynamic loads, such as data c…

The dimension of random subsets of self-similar sets generated by branching random walk
Pieter Allaart, Lauritz Streck
https://arxiv.org/abs/2506.22959 htt…

The dimension of random subsets of self-similar sets generated by branching random walk
Given a self-similar set $Λ$ that is the attractor of an iterated function system (IFS) $\{f_1,\dots,f_N\}$, consider the following method for constructing a random subset of $Λ$: Let $\mathbf{p}=(p_1,\dots,p_N)$ be a probability vector, and label all edges of a full $M$-ary tree independently at random with a number from $\{1,2,\dots,N\}$ according to $\mathbf{p}$, where $M\geq 2$ is an arbitrary integer. Then each infinite path in the tree starting from the root receives a random label sequ…

This https://arxiv.org/abs/2107.07544 has been replaced.
link: https://scholar.google.com/scholar?q=a

On Boundaries of $\varepsilon$-neighbourhoods of Planar Sets, Part II: Global Structure and Curvature
We study the global topological structure and smoothness of the boundaries of $\varepsilon$-neighbourhoods $E_\varepsilon = \{x \in \mathbb{R}^2 \, : \, \textrm{dist}(x, E) \leq \varepsilon \}$ of planar sets $E \subset \mathbb{R}^2$. We show that for a compact set $E$ and $\varepsilon > 0$ the boundary $\partial E_\varepsilon$ can be expressed as a disjoint union of an at most countably infinite union of Jordan curves and a possibly uncountable, totally disconnected set of singularities. We al…

A Linear Time Algorithm for Finding Minimum Flip Sequences between Plane Spanning Paths in Convex Point Sets
Oswin Aichholzer, Joseph Dorfer
https://arxiv.org/abs/2507.02740

A Linear Time Algorithm for Finding Minimum Flip Sequences between Plane Spanning Paths in Convex Point Sets
We provide a linear time algorithm to determine the flip distance between two plane spanning paths on a point set in convex position. At the same time, we show that the happy edge property does not hold in this setting. This has to be seen in contrast to several results for reconfiguration problems where the absence of the happy edge property implies algorithmic hardness of the flip distance problem. Further, we show that our algorithm can be adapted for (1) compatible flips (2) local flips and…

Curvature Rigidity Through Level Sets of Lyapunov Exponents in Geodesic Flows
Sergio Roma\~na
https://arxiv.org/abs/2507.02482 https://

Curvature Rigidity Through Level Sets of Lyapunov Exponents in Geodesic Flows
In this paper, we establish new geometric rigidity results through the study of Lyapunov exponent level sets via invariant measures. First, we prove that for a manifold $M$ without focal points, if the zero Lyapunov exponent level set has full measure with respect to a fully supported invariant measure, then $M$ must be flat. This result recovers and extends a result of Freire and Mañé (cf. [9]). Second, we prove that if the level set of the Lyapunov exponents has full measure with respect to…

Dynamics of discrete spacetimes with Quantum-enhanced Markov Chain Monte Carlo
Stuart Ferguson, Arad Nasiri, Petros Wallden
https://arxiv.org/abs/2506.19538

Dynamics of discrete spacetimes with Quantum-enhanced Markov Chain Monte Carlo
Quantum algorithms offer the potential for significant computational advantages; however, in many cases, it remains unclear how these advantages can be practically realized. Causal Set Theory is a discrete, Lorentz-invariant approach to quantum gravity which may be well positioned to benefit from quantum computing. In this work, we introduce a quantum algorithm that investigates the dynamics of causal sets by sampling the space of causal sets, improving on classical methods. Our approach builds…

This https://arxiv.org/abs/2401.13412 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Poisson Representable Processes
Motivated by Alain-Sol Sznitman's interlacement process, we consider the set of $\{0,1\}$-valued processes which can be constructed in an analogous way, namely as a union of sets coming from a Poisson process on a collection of sets. Our main focus is to determine which processes are representable in this way. Some of our results are as follows. (1) All positively associated Markov chains and a large class of renewal processes are so representable. (2) Whether an average of two product measures…

This https://arxiv.org/abs/2311.14022 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Invariable generation of certain branch groups
Let $G$ be a group. Then $S\subseteq G$ is an invariable generating set of $G$ if every subset $S'$ obtained from $S$ by replacing each element with a conjugate is also a generating set of $G$. We investigate invariable generation among key examples of branch groups. In particular, we prove that all generating sets of the torsion Grigorchuk groups, of the branch Grigorchuk-Gupta-Sidki groups and of the torsion multi-EGS groups (which are natural generalisations of the Grigorchuk-Gupta-Sidki gro…

Witnessing and guiding sets of tangles
Annegret Seibt
https://arxiv.org/abs/2507.04394 https://arxiv.org/pdf/2507.04394

Witnessing and guiding sets of tangles
Tangles o er a way to indirectly but precisely capture cluster-like though possibly fuzzy substructures in discrete data. In this paper, we analyze witnessing and guiding sets of tangles that can help to find proper cluster candidates for given tangles. We show that every k-tangle has a witnessing set whose size is bounded in an exponential function in k which improves a result of Grohe and Schweizer. Further, we generalize a result of Diestel, Elbracht and Jacobs by providing a characterizatio…

Dominating Set Knapsack: Profit Optimization on Dominating Sets
Sipra Singh
https://arxiv.org/abs/2506.24032 https://arxiv.org/pdf/25…

Dominating Set Knapsack: Profit Optimization on Dominating Sets
In a large-scale network, we want to choose some influential nodes to make a profit by paying some cost within a limited budget so that we do not have to spend more budget on some nodes adjacent to the chosen nodes; our problem is the graph-theoretic representation of it. We define our problem Dominating Set Knapsack by attaching Knapsack Problem with Dominating Set on graphs. Each vertex is associated with a cost factor and a profit amount. We aim to choose some vertices within a fixed budget …

Cofibrant generation of pure monomorphisms in presheaf categories
Sean Cox, Jonathan Feigert, Mark Kamsma, Marcos Mazari-Armida, Ji\v{r}\'i Rosick\'y
https://arxiv.org/abs/2506.20278

Cofibrant generation of pure monomorphisms in presheaf categories
We characterise when the pure monomorphisms in a presheaf category $\mathbf{Set}^\mathcal{C}$ are cofibrantly generated in terms of the category $\mathcal{C}$. In particular, when $\mathcal{C}$ is a monoid $S$ this characterises cofibrant generation of pure monomorphisms between sets with an $S$-action in terms of $S$: this happens if and only if for all $a, b \in S$ there is $c \in S$ such that $a = cb$ or $ca = b$. We give a model-theoretic proof: we prove that our characterisation is equival…

A canonical Makanin-Razborov diagram and a pseudo topology for sets of tuples in free groups, semigroups, associative algebras and Lie algebras I
Z. Sela
https://arxiv.org/abs/2505.22755

A canonical Makanin-Razborov diagram and a pseudo topology for sets of tuples in free groups, semigroups, associative algebras and Lie algebras I
The JSJ decomposition and the Makanin-Razborov diagram were proved to be essential in studying varieties over free groups, semigroups and associative algebras. In this paper we suggest a unified conceptual approach to the applicability of these structures over all these algebraic categories. With a variety over each of these algebraic categories we naturally associate a set of tuples in a free group. Then we show how to associate a Makanin-Razborov diagram with any set of tuples over a free gro…

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 …

This https://arxiv.org/abs/2412.09107 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Divisibility of the Multiplicative Order Modulo Monic Irreducible Polynomials Over Finite Fields
We consider the set of monic irreducible polynomials $P$ over a finite field $\mathbb{F}_q$ such that the multiplicative order modulo $P$ of some a in $\mathbb{F}_q(T)$ is divisible by a fixed positive integer $d$. Call $R_q(a,d)$ this set. We show the existence or non-existence of the density of $R_q(a,d)$ for three distinct notions of density. In particular, the sets $R_q(a,d)$ have a Dirichlet density. Under some assumptions, we prove simple formulas for the density values.

This https://arxiv.org/abs/2012.13515 has been replaced.
link: https://scholar.google.com/scholar?q=a

On Boundaries of $\varepsilon$-neighbourhoods of Planar Sets: Singularities, Global Structure, and Curvature
We study the geometry, topological properties and smoothness of the boundaries of closed $\varepsilon$-neighbourhoods $E_\varepsilon = \{x \in \mathbb{R}^2 \, : \, \textrm{dist}(x, E) \leq \varepsilon \}$ of compact planar sets $E \subset \mathbb{R}^2$. We develop a novel technique for analysing the boundary, and use this to obtain a classification of singularities (i.e.~non-smooth points) on $\partial E_\varepsilon$ into eight categories. We show that the set of singularities is either countab…

This https://arxiv.org/abs/2409.06581 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Velocity surface disorder of large deviation rate functions of the random walk in strongly mixing environment
In this work, we establish the existence of large deviation principles of random walk in strongly mixing environments. The quenched and annealed rate functions have the same zero set whose shape is either a singleton point or a line segment, with an illustrative example communicated and given by F. Rassoul-Agha. Whenever the level of disorder is controlled, the two rate functions are shown to conform on compact sets at the boundary and in the interior both under strongly mixing conditions.

Cardinalities of the total number of independent sets
Benedek Kov\'acs, Zolt\'an L\'or\'ant Nagy
https://arxiv.org/abs/2505.24794 https://

Cardinalities of the total number of independent sets
We study the set of numbers the total number of independent sets can admit in $n$-vertex graphs. In this paper, we prove that the cardinality of this set $\mathcal{N}i(n)$ is very close to $2^n$ in the following sense: $\mathcal{N}i(n)/2^n = O(n^{-1/5})$ while for infinitely many $n$, we have $\log_2(\mathcal{N}i(n)/2^n)\ge -2^{(1+o(1)\sqrt{\log_2 n}}$. This set is also precisely the set of possible values of the independence polynomial $I_G(x)$ at $x=1$ for $n$-vertex graphs $G$. As an applica…

This https://arxiv.org/abs/2303.07133 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Braid stability for periodic orbits of area-preserving surface diffeomorphisms
We consider an area-preserving diffeomorphism of a compact surface, which is assumed to be an irrational rotation near each boundary component. A finite set of periodic orbits of the diffeomorphism gives rise to a braid in the mapping torus. We show that under some nondegeneracy hypotheses, the isotopy classes of braids that arise from finite sets of periodic orbits are stable under Hamiltonian perturbations that are small with respect to the Hofer metric. A corollary is that for a Hamiltonian …

VC-dimension of generalized progressions in some nonabelian groups
Gabriel Conant, Aycin Iplikci Arodirik, Tora Ozawa, David Zeng
https://arxiv.org/abs/2505.21789

VC-dimension of generalized progressions in some nonabelian groups
We analyze generalized progressions in some nonabelian groups using a measure of complexity called VC-dimension, which was originally introduced in statistical learning theory by Vapnik and Chervonenkis. Here by a "generalized progression" in a group $G$, we mean a finite subset of $G$ built from a fixed set of generators in analogy to a (multidimensional) arithmetic progression of integers. These sets play an important role in additive combinatorics and, in particular, the study of approximate…

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…

Dynamical covering sets in self-similar sets
Balazs Barany, Henna Koivusalo, Sascha Troscheit
https://arxiv.org/abs/2506.18447 https://

Dynamical covering sets in self-similar sets
We study the size of \emph{dynamical covering sets} on a self-similar set. Dynamical covering sets are limsup sets generated by placing shrinking target sets around points along an orbit in a dynamical system. In the case when the target sets are balls with sizes depending on the centre, we determine the size of the dynamical covering set as a function of the shrinking rate. In particular, we find sharp conditions guaranteeing when full Dvoretzky-type covering, and full measure occur. We also c…

On the Erd\H{o}s-Ko-Rado problem of flags with type $\{1, n-3 \}$ of finite sets
Philipp Heering
https://arxiv.org/abs/2506.20556 https://

On the Erdős-Ko-Rado problem of flags with type $\{1, n-3 \}$ of finite sets
A flag of a finite set $S$ is a set $f$ of non-empty, proper subsets of $S$, such that $X\subseteq Y$ or $Y\subseteq X$ for all $X,Y\in f$. Two flags $f_1$ and $f_2$ of $S$ are opposite if $X_1\cap X_2=\emptyset$, or $X_1\cup X_2=S$ for all $X_1\in f_1$ and $X_2\in f_2$. The set $\{|X| \mid X\in f \}$ is the type of a flag $f$. A set of pairwise non-opposite flags is an Erdős-Ko-Rado set. In 2022 Metsch posed the problem of determining the maximum size of all Erdős-Ko-Rado sets of f…

Statistics of maximal independent sets in grid-like graphs
Levi Axelrod, Nathan Bickel, Anastasia Halfpap, Luke Hawranick, Alex Parker, Cole Swain
https://arxiv.org/abs/2506.22317

Statistics of maximal independent sets in grid-like graphs
An independent set $I$ in a graph $G$ is maximal if $I$ is not properly contained in any other independent set of $G$. The study of maximal independent sets (MIS's) in various graphs is well-established, often focusing upon enumeration of the set of MIS's. For an arbitrary graph $G$, it is typically quite difficult to understand the number and structure of MIS's in $G$; however, when $G$ has regular structure, the problem may be more tractable. One class of graphs for which enumeration of MIS's…

This https://arxiv.org/abs/2412.15950 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Maximal independent sets in graphs with given matching number
A maximal independent set in a graph $G$ is an independent set that cannot be extended to a larger independent set by adding any vertex from $G$. This paper investigates the problem of determining the maximum number of maximal independent sets in terms of the matching number of a graph. We establish the maximum number of maximal independent sets for general graphs, connected graphs, triangle-free graphs, and connected triangle-free graphs with a given matching number, and characterize the extre…

This https://arxiv.org/abs/2409.19908 has been replaced.
link: https://scholar.google.com/scholar?q=a

Independent Sets in Hypergraphs
A theorem of Shearer states that every $n$-vertex triangle-free graph of maximum degree $d \geq 2$ contains an independent set of size at least $(d\log d - d + 1)/(d - 1)^2 \cdot n$. Ajtai, Komlós, Pintz, Spencer and Szemerédi proved that every $(r + 1)$-uniform $n$-vertex ``uncrowded'' hypergraph of maximum degree $d \geq 1$ has an independent set of size at least $c_r(\log d)^{1/r}/d^{1/r} \cdot n$ for some $c_r > 0$ depending only on $r$. Shearer asked whether his method for triangle-free …

This https://arxiv.org/abs/2003.11202 has been replaced.
link: https://scholar.google.com/scholar?q=a

Set System Blowups
We prove that given a constant $k \ge 2$ and a large set system $\mathcal{F}$ of sets of size at most $w$, a typical $k$-tuple of sets $(S_1, \cdots, S_k)$ from $\mathcal{F}$ can be ``blown up" in the following sense: for each $1 \le i \le k$, we can find a large subfamily $\mathcal{F}_i$ containing $S_i$ so that for $i \neq j$, if $T_i \in \mathcal{F}_i$ and $T_j \in \mathcal{F}_j$ , then $T_i \cap T_j=S_i \cap S_j$. We also show that the answer to the multicolor version of the sunflower conje…

Hamiltonian laceability with a set of faulty edges in hypercubes
Abid Ali, Weihua Yang
https://arxiv.org/abs/2506.21391 https://arxiv…

Hamiltonian laceability with a set of faulty edges in hypercubes
Faulty networks are useful because link or node faults can occur in a network. This paper examines the Hamiltonian properties of hypercubes under certain conditional faulty edges. Let consider the hypercube \( Q_n \), for \( n \geq 5 \) and set of faulty edges \( F \) such that \( |F| \leq 4n - 17 \). We prove that a Hamiltonian path exists connecting any two vertices in \( Q_n - F \) from distinct partite sets if they verify the next two conditions: (i) in $Q_n - F$ any vertex has a …

A note on the second-largest number of dissociation sets in connected graphs
Pingshan Li, Ke Yang, Wei Jin
https://arxiv.org/abs/2506.12740 https://…

A note on the second-largest number of dissociation sets in connected graphs
A subset of vertices is called a dissociation set if it induces a subgraph with vertex degree at most one. Recently, Yuan et al. established the upper bound of the maximum number of dissociation sets among all connected graphs of order n and characterized the corresponding extremal graphs.They also proposed a question regarding the second-largest number of dissociation sets among all connected graphs of order n and the corresponding extremal graphs. In this paper, we give a positive answer to t…

$s$-almost cross-$t$-intersecting families for finite sets
Dehai Liu, Kaishun Wang, Tian Yao
https://arxiv.org/abs/2506.21993 https://

$s$-almost cross-$t$-intersecting families for finite sets
Two families $\mathcal{F}$ and $\mathcal{G}$ of $k$-subsets of an $n$-set are called $s$-almost cross-$t$-intersecting if each member in $\mathcal{F}$ (resp. $\mathcal{G}$) is $t$-disjoint with at most $s$ members in $\mathcal{G}$ (resp. $\mathcal{F}$). In this paper, we characterize the $s$-almost cross-$t$-intersecting families with the maximum product of their sizes. Furthermore, we provide a corresponding stability result after studying the $s$-almost cross-$t$-intersecting families which a…

This https://arxiv.org/abs/2501.06935 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Feedback Arc Sets and Feedback Arc Set Decompositions in Weighted and Unweighted Oriented Graphs
For any arc-weighted oriented graph $D=(V(D), A(D),w)$, we write ${\rm fas}_w(D)$ to denote the minimum weight of a feedback arc set in $D$. In this paper, we consider upper bounds on ${\rm fas}_w(D)$ for arc-weight oriented graphs $D$ with bounded maximum degrees and directed girth. We obtain such bounds by introducing a new parameter ${\rm fasd}(D)$, which is the maximum integer such that $A(D)$ can be partitioned into ${\rm fasd}(D)$ feedback arc sets. This new parameter seems to be intere…