기초과학연구원 이산수학그룹
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Let $\mathbb{F}_q$ be a finite field of order $q$ which is a prime power. In the finite field setting, we say that a function $\phi\colon \mathbb{F}_q^d\times \mathbb{F}_q^d\to \mathbb{F}_q$ is a Mattila-Sjölin type function in $\mathbb{F}_q^d$ if for any $E\subset \mathbb{F}_q^d$ with $|E|\gg q^{\frac{d}{2}}$, we have $\phi(E, E)=\mathbb{F}_q$. The main purpose of this talk is to present … |
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Recently, significant progress has been made in the area of machine learning algorithms, and they have quickly become some of the most exciting tools in a scientist’s toolbox. In particular, recent advances in the field of reinforcement learning have led computers to reach superhuman level play in Atari games and Go, purely through self-play. In … |
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An intersection digraph is a digraph where every vertex $v$ is represented by an ordered pair $(S_v, T_v)$ of sets such that there is an edge from $v$ to $w$ if and only if $S_v$ and $T_w$ intersect. An intersection digraph is reflexive if $S_v\cap T_v\neq \emptyset$ for every vertex $v$. Compared to well-known undirected … |
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An interval graph is the intersection graph of a family of intervals in the real line. Motivated by problems in ecology, Roberts defined the boxicity of a graph G to be the minimal k such that G can be written as the intersection of k interval graphs. A natural higher-dimensional generalization of interval graphs is … |
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The preservation of symmetry is one of the key tools for designing data-efficient neural networks. A representative example is convolutional neural networks (CNNs); they preserve translation symmetries, and this symmetry preservation is often attributed to their success in real-world applications. In the machine-learning community, there is a growing body of work that explores a new … |
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In this talk, we present sufficient conditions to guarantee the invertibility of rational circulant matrices with any given size. These sufficient conditions consist of linear combinations in terms of the entries in the first row with integer coefficients. Using these conditions we show the invertibility of some family of circulant matrices with particular forms of … |
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The local connectivity $ \kappa_D(r,v) $ from $ r $ to $ v $ is defined to be the maximal number of internally disjoint $r\rightarrow v $ paths in $ D $. A spanning subdigraph $ L $ of $ D $ with $ \kappa_L(r,v)=\kappa_D(r,v) $ for every $ v\in V-r $ must have at … |
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