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Probabilistic abstract interpretation is a theory used to extract particular properties of a computer program when it is infeasible to test every single inputs. In this paper we apply the theory on neural networks for the same purpose: to…

Artificial Intelligence · Computer Science 2026-03-27 Zhuofan Zhang , Herbert Wiklicky

We apply the semidefinite programming method to derive bounds for projective codes over a finite field.

Information Theory · Computer Science 2013-11-05 Christine Bachoc , Alberto Passuello , Frank Vallentin

A subgraph of the $n$-dimensional hypercube is called 'layered' if it is a subgraph of a layer of some hypercube. In this paper we show that there exist subgraphs of the cube of arbitrarily large girth that are not layered. This answers a…

Combinatorics · Mathematics 2024-04-30 Natalie Behague , Imre Leader , Natasha Morrison , Kada Williams

We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the sum with respect to…

Algebraic Geometry · Mathematics 2021-01-22 Hao Wen , Chunhui Liu

We consider large uniform labeled random graphs in different classes with prescribed decorations in their modular decomposition. Our main result is the estimation of the number of copies of every graph as an induced subgraph. As a…

Combinatorics · Mathematics 2023-10-25 Théo Lenoir

Hypergraphs, as a generalization of simplicial complexes, have long been a subject of interest in their geometric interpretation. The subdivision of simplicial complexes can, to some extent, provide insights into the geometry of simplicial…

Algebraic Topology · Mathematics 2023-11-17 Jian Liu , Ran Liu , Jie Wu

We present a method for generating random hypergraphs in context-free hypergraph languages. It is obtained by adapting Mairson's generation algorithm for context-free string grammars to the setting of hyperedge replacement grammars. Our…

Logic in Computer Science · Computer Science 2024-10-02 Federico Vastarini , Detlef Plump

We find the exact formula for the minimal number of edges of hypergraph which guaranteed fractional matching of cardinality $s$ in the case when $sn$ is integer.

Combinatorics · Mathematics 2015-03-27 Vladimir Blinovsky

Defeasible reasoning is the mode of reasoning where conclusions can be overturned by taking into account new evidence. A commonly used method in cognitive science and logic literature is to handcraft argumentation supporting inference…

Computation and Language · Computer Science 2021-06-01 Aman Madaan , Dheeraj Rajagopal , Niket Tandon , Yiming Yang , Eduard Hovy

Pseudo-variograms appear naturally in the context of multivariate Brown-Resnick processes, and are a useful tool for analysis and prediction of multivariate random fields. We give a necessary and sufficient criterion for a matrix-valued…

Statistics Theory · Mathematics 2021-12-07 Christopher Dörr , Martin Schlather

In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in…

Dynamical Systems · Mathematics 2023-09-19 Joshua Pickard , Amit Surana , Anthony Bloch , Indika Rajapakse

For a positive integer $n$, a graph with at least $n$ vertices is $n$-existentially closed or simply $n$-e.c. if for any set of vertices $S$ of size $n$ and any set $T\subseteq S$, there is a vertex $x\not\in S$ adjacent to each vertex of…

Combinatorics · Mathematics 2024-07-09 Andrea C. Burgess , Robert D. Luther , David A. Pike

Let H be a 3-uniform hypergraph with N vertices. A tight Hamilton cycle C \subset H is a collection of N edges for which there is an ordering of the vertices v_1, ..., v_N such that every triple of consecutive vertices {v_i, v_{i+1},…

Combinatorics · Mathematics 2010-06-09 Alan Frieze , Michael Krivelevich , Po-Shen Loh

For any $S\subset [n]$, we compute the probability that the subgraph of $\mathcal{G}_{n,d}$ induced by $S$ is a given graph $H$ on the vertex set $S$. The result holds for any $d=o(n^{1/3})$ and is further extended to $\mathcal{G}_{{\bf…

Combinatorics · Mathematics 2010-11-30 Pu Gao , Yi Su , Nicholas Wormald

In this paper we describe all rotation $H$-hypersurfaces in $H^n \times R$ and use them as barriers to prove existence and characterization of certain vertical $H$-graphs and to give symmetry and uniqueness results for compact…

Differential Geometry · Mathematics 2019-10-07 Pierre Bérard , Ricardo Sa Earp

A $d$-dimensional hypercube drawing of a graph represents the vertices by distinct points in $\{0,1\}^d$, such that the line-segments representing the edges do not cross. We study lower and upper bounds on the minimum number of dimensions…

Combinatorics · Mathematics 2007-05-23 David R. Wood

We initiate the study of pseudofiniteness in continuous logic. We introduce a related concept, namely that of pseudocompactness, and investigate the relationship between the two concepts. We establish some basic properties of…

Logic · Mathematics 2016-02-10 Isaac Goldbring , Vinicius Cifu Lopes

Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…

Combinatorics · Mathematics 2011-04-06 Gareth A. Jones

Multisequences over finite fields play a pushing role in the applications that relate to parallelization, such as word-based stream ciphers and pseudorandom vector generation. It is interesting to study the complexity measures for…

Information Theory · Computer Science 2020-01-30 Yang Yan , Qiuyan Wang , Chenhuang Wu

We construct compact descriptions of function fields and number fields.

Number Theory · Mathematics 2020-11-04 Jean-Marc Couveignes