Related papers: Computational lower limits on small Ramsey numbers
Convergence rate estimates in limit theorems for sums of independent random variables are considered.
We present a brief introduction to the theory of operator limits of random matrices to non-experts. Several open problems and conjectures are given. Connections to statistics, integrable systems, orthogonal polynomials, and more, are…
In this article we give the generalized triangle Ramsey numbers R(K3,G) of 12 005 158 of the 12 005 168 graphs of order 10. There are 10 graphs remaining for which we could not determine the Ramsey number. Most likely these graphs need…
In many high-dimensional problems, like sparse-PCA, planted clique, or clustering, the best known algorithms with polynomial time complexity fail to reach the statistical performance provably achievable by algorithms free of computational…
We develop an approach to finding upper bounds for the number of arithmetic operations necessary for doing harmonic analysis on permutation modules of finite groups. The approach takes advantage of the intrinsic orbital structure of…
In these lectures I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to…
Optimization seeks extremal points in a function. When there are superextensively many optima, optimization algorithms are liable to get stuck. Under these conditions, generic algorithms tend to find marginal optima, which have many nearly…
We investigate conditions under which a co-computably enumerable closed set in a computable metric space is computable and prove that in each locally computable computable metric space each co-computably enumerable compact manifold with…
We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…
The ordered Ramsey number of a graph $G^<$ with a linearly ordered vertex set is the smallest positive integer $N$ such that any two-coloring of the edges of the ordered complete graph on $N$ vertices contains a monochromatic copy of $G^<$…
We present a construction of 1-perfect binary codes, which gives a new lower bound on the number of such codes. We conjecture that this lower bound is asymptotically tight.
We describe a new variation of a mathematical card trick, whose analysis leads to new lower bounds for data compression and estimating the entropy of Markov sources.
In this paper, we present perturbation analysis and randomized algorithms for the total least squares (TLS) problems. We derive the perturbation bound and check its sharpness by numerical experiments. Motivated by the recently popular…
Locally-biased graph algorithms are algorithms that attempt to find local or small-scale structure in a large data graph. In some cases, this can be accomplished by adding some sort of locality constraint and calling a traditional graph…
In this paper cyclic codes are established with respect to the Mannheim metric over some finite rings by using Gaussian integers and the decoding algorithm for these codes is given.
In this paper we prove tight bounds on the combinatorial and topological complexity of sets defined in terms of $n$ definable sets belonging to some fixed definable family of sets in an o-minimal structure. This generalizes the…
We prove that a formula predicted on the basis of non-rigorous physics arguments [Zdeborova and Krzakala: Phys. Rev. E (2007)] provides a lower bound on the chromatic number of sparse random graphs. The proof is based on the interpolation…
Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of "steps" involved, the physical limit has an operational meaning in agreement with the…
In this paper, we investigate three extensions of Ramsey numbers to other combinatorial settings. We first consider ordered Ramsey numbers. Here, we ask for a monochromatic copy of a linearly ordered graph $G$ in every $2$-edge-coloring of…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…