Hongseok Yang (양홍석), DAG-symmetries and Symmetry-Preserving Neural Networks

Room B232 IBS (기초과학연구원)

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

Suil O (오수일), Eigenvalues and [a, b]-factors in regular graphs

Room B232 IBS (기초과학연구원)

For positive integers, $r \ge 3, h \ge 1,$ and $k \ge 1$, Bollobás, Saito, and Wormald proved some sufficient conditions for an $h$-edge-connected $r$-regular graph to have a k-factor in 1985. Lu gave an upper bound for the third-largest eigenvalue in a connected $r$-regular graph to have a $k$-factor in 2010. Gu found an upper bound

Jaehoon Kim (김재훈), $K_{r+1}$-saturated graphs with small spectral radius

Room B232 IBS (기초과학연구원)

For a graph $H$, a graph $G$ is $H$-saturated if $G$ does not contain $H$ as a subgraph but for any $e\in E(\overline G)$, $G+e$ contains $H$. In this note, we prove a sharp lower bound for the number of paths and walks on length 2 in $n$-vertex $K_{r+1}$-saturated graphs. We then use this bound to give a

Semin Yoo (유세민), Combinatorics of Euclidean spaces over finite fields

Room B232 IBS (기초과학연구원)

$q$-analogues of quantities in mathematics involve perturbations of classical quantities using the parameter $q$, and revert to the original quantities when $q$ goes $1$. An important example is the $q$-analogues of binomial coefficients, denoted by $\binom{n}{k}_{q}$, which give the number of $k$-dimensional subspaces in $\mathbb{F}_{q}^{n}$. When $q$ goes to $1$, this reverts to the binomial

Eun Jung Kim (김은정), A Constant-factor Approximation for Weighted Bond Cover

Room B232 IBS (기초과학연구원)

The Weighted $\mathcal F$-Vertex Deletion for a class $\mathcal F$ of graphs asks, given a weighted graph $G$, for a minimum weight vertex set $S$ such that $G-S\in\mathcal F$. The case when $\mathcal F$ is minor-closed and excludes some graph as a minor has received particular attention but a constant-factor approximation remained elusive for Weighted $\mathcal

Linda Cook, TBA

Room B232 IBS (기초과학연구원)

Sang-hyun Kim (김상현), On rational 2×2 matrices without relations

Room B232 IBS (기초과학연구원)

For a rational number q= s/r, we consider the two 2x2 matrices A=((1,0),(1,1)) and  B_q=((1,q), (0,1)). It is a long standing conjecture (traced at least back to Rimhak Ree) that A and B(q) admit a nontrivial group relation if |q|<4; the converse is classical. For the special case s≤27 and s≠24, we prove this conjecture.

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