Related papers: Sparseness of 4-cycle systems
Permutation $\sigma$ appears in permutation $\pi$ if there exists a subsequence of $\pi$ that is order-isomorphic to $\sigma$. The natural question is to check if $\sigma$ appears in $\pi$, and if so count the number of occurrences. We know…
We show that for any n divisible by 3, almost all order-n Steiner triple systems admit a decomposition of almost all their triples into disjoint perfect matchings (that is, almost all Steiner triple systems are almost resolvable).
Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input…
We reveal the rule with which we predicted, and verified by detailed numerical calculations on dozens of specific cases over the last decade, the emergence of hidden induced states and the formation of quartets of order parameters. The rule…
In 1976, Steinberg conjectured that planar graphs without $4$-cycles and $5$-cycles are $3$-colorable. This conjecture attracted numerous researchers for about 40 years, until it was recently disproved by Cohen-Addad et al. (2017). However,…
It is an intriguing question to see what kind of information on the structure of an oriented graph $D$ one can obtain if $D$ does not contain a fixed oriented graph $H$ as a subgraph. The related question in the unoriented case has been an…
We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…
An $r$-matrix is a matrix with symbols in $\{0,1,\ldots,r-1\}$. A matrix is simple if it has no repeated columns. Let ${\cal F}$ be a finite set of $r$-matrices. Let $\hbox{forb}(m,r,{\cal F})$ denote the maximum number of columns possible…
The distribution of holes in Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$ (SCCO) is revisited with semi-emperical reanalysis of the x-ray absorption (XAS) data and exact-diagonalized cluster calculations. A new interpretation of the XAS data leads to…
In this paper we propose a model of random compositions of cylinder maps, which in the simplified form is as follows: let $(\theta,r)\in \mathbb T\times \mathbb R=\mathbb A$ and \[ f_{\pm 1}:…
The convergence of the projection algorithm for solving the convex feasibility problem for a family of closed convex sets, is in connection with the regularity properties of the family. In the paper [18] are pointed out four cases of such a…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
A Berge-$K_4$ in a triple system is a configuration with four vertices $v_1,v_2,v_3,v_4$ and six distinct triples $\{e_{ij}: 1\le i< j \le 4\}$ such that $\{v_i,v_j\}\subset e_{ij}$ for every $1\le i<j\le 4$. We denote by $\cal{B}$ the set…
One of the fundamental problems of interest for discrete-time linear systems is whether its input sequence may be recovered given its output sequence, a.k.a. the left inversion problem. Many conditions on the state space geometry, dynamics,…
We present a new technique for efficiently removing almost all short cycles in a graph without unintentionally removing its triangles. Consequently, triangle finding problems do not become easy even in almost $k$-cycle free graphs, for any…
We study choosability with separation which is a constrained version of list coloring of graphs. A (k,d)-list assignment L on a graph G is a function that assigns to each vertex v a list L(v) of at least k colors and for any adjacent pair…
A planar graph is essentially $4$-connected if it is 3-connected and every of its 3-separators is the neighborhood of a single vertex. Jackson and Wormald proved that every essentially 4-connected planar graph $G$ on $n$ vertices contains a…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
In this paper we propose a model of random compositions of cylinder maps, which in the simplified form is as follows: $(\theta,r)\in \mathbb T\times \mathbb R=\mathbb A$ and \begin{eqnarray} \nonumber f_{\pm 1}:…
One-dimensional gapped systems are often characterized by a 'hidden' non-local order parameter, the so-called string order. Due to the gap, thermodynamic properties are robust against a weak higher-dimensional coupling between such chains…