Related papers: A Survey on Almost Difference Sets
Recent works have shown that supervised models often exploit data artifacts to achieve good test scores while their performance severely degrades on samples outside their training distribution. Contrast sets (Gardneret al., 2020) quantify…
A $(v, k, \lambda)$ symmetric design is said to have the symmetric difference property (SDP) if the symmetric difference of any three blocks is either a block or the complement of a block. Symmetric designs fulfilling this property have the…
This paper studies the discovery of approximate rules in property graphs. We propose a semantically meaningful measure of error for mining graph entity dependencies (GEDs) at almost hold, to tolerate errors and inconsistencies that exist in…
We call the dimension data $\mathscr{D}_{H_{1}}$ and $\mathscr{D}_{H_{2}}$ of two closed subgroups $H_{1}$ and $H_{2}$ of a given compact Lie group $G$ {\it almost equal} if $\mathscr{D}_{H_{1}}(\rho)=\mathscr{D}_{H_{2}}(\rho)$ for all but…
A quasi-automatic semigroup is defined by a finite set of generators, a rational (regular) set of representatives, such that if a is a generator or neutral, then the graph of right multiplication by a on the set of representatives is a…
Let $\mathcal{X}$ be a set of $(h-1)$-dimensional subspaces of $\mathrm{PG}(kh-1,q)$ with the property that every hyperplane contains at most $t$ elements of $\mathcal{X}$. We prove the upper bound $|\mathcal{X}| \leq (t-k+2)q^h + t$, and…
A $k-$quasiperfect dominating set ($k\ge 1$) of a graph $G$ is a vertex subset $S$ such that every vertex not in $S$ is adjacent to at least one and at most k vertices in $S$. The cardinality of a minimum k-quasiperfect dominating set in…
A semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities having real coefficients and is a union of finitely many maximally connected components. We consider the problem of deciding whether two…
We use basic tools of descriptive set theory to prove that a closed set $\mathcal S$ of marked groups has $2^{\aleph_0}$ quasi-isometry classes provided every non-empty open subset of $\mathcal S$ contains at least two non-quasi-isometric…
A real-valued set function is (additively) approximately submodular if it satisfies the submodularity conditions with an additive error. Approximate submodularity arises in many settings, especially in machine learning, where the function…
This paper presents a novel approach to address the constrained coding challenge of generating almost-balanced sequences. While strictly balanced sequences have been well studied in the past, the problem of designing efficient algorithms…
We investigate the relationship between the sizes of the sum and difference sets attached to a subset of {0,1,...,N}, chosen randomly according to a binomial model with parameter p(N), with N^{-1} = o(p(N)). We show that the random subset…
This study aims at characterizing a reachable set of a hybrid dynamical system with a lag constraint in the switch control. The setting does not consider any controllability assumptions and uses a level-set approach. The approach consists…
In this article, we characterize the distortion elements of the group of smooth diffeomorphisms of the circle and of the group of compactly supported smooth diffeomorphisms of the real line. More precisely, we prove that, in this context,…
In this paper, we introduce almost $\cal D$-split sequences and establish an elementary but somewhat surprising connection between derived equivalences and Auslander-Reiten sequences via BB-tilting modules. In particular, we obtain derived…
To each finitely generated group $G$, we associate a quasi-isometric invariant called the \emph{Dehn spectrum} of $G$. If $G$ is finitely presented, our invariant is closely related to the Dehn function of $G$, but provides more information…
A cycle of length $t$ in a hypergraph is an alternating sequence $v_1,e_1,v_2\dots,v_t,e_t$ of distinct vertices $v_i$ and distinct edges $e_i$ so that $\{v_i,v_{i+1}\}\subseteq e_i$ (with $v_{t+1}:=v_1$). Let $\lambda K_n^h$ be the…
Semi-regular sequences over $\mathbb{F}_2$ are sequences of homogeneous elements of the algebra $ B^{(n)}=\mathbb{F}_2[X_1,...,X_n]/(X_1^2,...,X_n^2) $, which have as few relations between them as possible. They were introduced in order to…
We define a pseudo quasi-3 design as a symmetric design with the property that the derived and residual designs with respect to at least one block are quasi-symmetric. Quasi-symmetric designs can be used to construct optimal self…
A vertex subset $S$ of a graph $G$ is a perfect (resp. quasiperfect) dominating set in $G$ if each vertex $v$ of $G\setminus S$ is adjacent to only one vertex ($d_v\in\{1,2\}$ vertices) of $S$. Perfect and quasiperfect dominating sets in…