Related papers: Lattices with exponentially large kissing numbers …
It is shown that strongly correlated electrons on frustrated lattices like pyrochlore, checkerboard or kagome lattice can lead to the appearance of closed and open strings. They are resulting from nonlocal subsidiary conditions which…
Recently, a convergent series employing a non-Gaussian initial approximation was constructed and shown to be an effective computational tool for the finite size lattice models with a polynomial interaction. Here we numerically examine the…
We consider the number of visible lattice points under the assumption of the Extended Lindel\"{o}f Hypothesis. We get a relation between visible lattice points and the Extended Lindel\"{o}f Hypothesis. And we also get a relation between…
Given a one-dimensional shift $X$, let $|F_X(\ell)|$ be the number of follower sets of words of length $\ell$ in $X$. We call the sequence $\{|F_X(\ell)|\}_{\ell \in \mathbb{N}}$ the follower set sequence of the shift $X$. Extender sets are…
Research on Helly-type theorems in combinatorial convex geometry has produced volumetric versions of Helly's theorem using witness sets and quantitative extensions of Doignon's theorem. This paper combines these philosophies and presents…
Properties of several sorts of lattices of convex subsets of R^n are examined. The lattice of convex sets containing the origin turns out, for n>1, to satisfy a set of identities strictly between those of the lattice of all convex subsets…
We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the metric space is (i) expanding and (ii) well-spread, and (iii) a certain random variable on the…
We study different extended formulations for the set $X = \{x\in\mathbb{Z}^n \mid Ax = Ax^0\}$ in order to tackle the feasibility problem for the set $X_+=X \cap \mathbb{Z}^n_+$. Here the goal is not to find an improved polyhedral…
In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In…
Topological defects in crystalline lattices are considered. In relation to physical realizability of such defects, criteria for geometric compatibility of the lattice distortions are formulated. For 2D lattices it is shown that the answer…
For a long time, Collatz Conjecture has been assumed to be true, although a formal proof has eluded all efforts to date. In this article, evidence is presented that suggests such an assumption is incorrect. By analysing the stopping times…
Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon…
We calculate exponential growth constants describing the asymptotic behavior of several quantities enumerating classes of orientations of arrow variables on the bonds of several types of directed lattice strip graphs $G$ of finite width and…
We show that there are uncountably many countable lattices. We give a discussion of which such lattices can be modular or distributive. The method applies to show that certain other classes of structures also have uncountably many…
We extend the validity of Kiss's characterization of the commutator from congruence modular varieties to varieties with a difference term. This fixes a recently discovered gap in our paper [A finite basis theorem for difference-term…
I review recent theoretical developments and numerical results of twisted mass QCD. I argue that, combined with an efficient algorithm, twisted mass QCD can be an attractive QCD lattice action, to perform large scale simulations at small…
Recent Lattice QCD results are reviewed with an emphasis on spectroscopic results concerning the charm quark. It is demonstrated that, with accurate computations from lattice QCD in recent years that can be compared with the existing or…
A conjecture regarding the structure of expander graphs is discussed.
We give a short proof of polynomial recurrence with large intersection for additive actions of finite-dimensional vector spaces over countable fields on probability spaces, improving upon the known size and structure of the set of strong…
Contact defects are time-periodic patterns in one space dimension that resemble spatially homogeneous oscillations with an embedded defect in their core region. For theoretical and numerical purposes, it is important to understand whether…