Research
Research
Research
Research
2,262+ open-access research outputs.
Motivated by an optimal-matching problem (Leighton-Shor) and the random-field Ising model (Aizenman-Wehr, Ding-Wirth), we consider a variational problem for graphs in $1+1$ dimension maximizing an act…
In this paper, we introduce a problem closely related to the {\emph{Cage Problem}}. We are interested in {\emph{Balanced Biregular Cages}}, which are the smallest biregular graphs of fixed girth that …
A $k$-regular graph of girth $g$ is called vertex-girth-regular if every vertex is contained in the same number of cycles of length $g$. For integers $n, k, g$ and $\lambda$, we denote such a graph on…
A graph reaction--diffusion (RD) equation is a system of differential equations that is defined on the nodes of a graph. Consider a sequence of growing graphs that converges in cut norm to a limiting …
We develop a likelihood-based inference for finite-state birth-death processes with composite birth rates, in which multiple distinct mechanisms contribute additively to the total birth intensity. Our…
We study the surjectivity of certain maps involving local cohomology modules, which we can realize as a dual version of part of the investigation developed by Bhatt, Blickle, Lyubeznik, Singh and Zhan…
Let $k$ be a field of characteristic $p,$ and $f : X \to S$ a smooth proper morphism of smooth $k$-schemes. Katz's formula gives a relationship between the Kodaira--Spencer map of $f,$ and an invarian…
In a previous submission, we established a fundamental relation between tone networks and configurations. It was shown that the Eulerian tonnetz can be represented by a $\{12_3\}$ of Daublebsky von St…
Let $G_n$ be the partition graph whose vertices are the partitions of $n$, with adjacency given by elementary transfers of one cell between parts, followed by reordering. We study the support of a par…
We study the mixing time of the Rook's Walk Markov chain on a $d$-dimensional chess board of side length $n\geq 3$, where a rook moves by first selecting an axis uniformly at random and then selecting…
This collection presents a selected set of unsolved problems in semigroup theory, a fundamental branch of modern algebra. The publication is dedicated to the 110th anniversary of the birth of E. S. Ly…
We study the persistent homology of the offset filtration generated by the range of a planar Brownian motion with constant nonzero drift. The members of this filtration are the Wiener sausages of incr…
Let $2\le k\in\mathbb{Z}$. A total coloring of a$k$-regular simple graph via $k+1$ colors is an efficient total coloring if each color yields an efficient dominating set, where the efficient dominatio…
In this paper, we investigate the prescribed curvature problem associated with a special Lin-Lu-Yau curvature on finite graphs of girth at least 6. We define the corresponding Calabi flow for this cur…
The hard-core model can be used to understand the numbers of independent sets in graphs in extremal graph theory. The occupancy fraction, defined as the logarithmic derivative of the independence poly…
Based on an almost Kodaira-type vanishing result in mixed characteristics of Bhatt, we show that, in the locally analytic completed cohomology of a general Shimura variety, sufficiently regular infini…
We introduce the notion of birth and death cochains as generalized versions of birth and death simplices in persistent cohomology. We show that birth and death cochains (unlike birth and death simplic…
We prove that there is only one translation-invariant Gibbsian point process w.r.t. to a chosen interaction if any of them satisfies a certain bound related to concentration-of-measure. This concentra…
For a non-decreasing sequence $S=(s_1,s_2,\dots,s_k)$, an $S$-packing coloring of a graph $G$ is a vertex coloring using the colors $s_1,s_2,\dots,s_k$ such that any two vertices assigned the same col…
A graph is called strongly $\Z_{2k+1}$-connected if for each boundary function $\beta: V(G)\mapsto \Z_{2k+1}$ with $\sum_{v\in V(G)}\beta(v)\equiv 0\pmod{2k+1}$, there exists an orientation $D$ of $G$…
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