Related papers: Using the Incompressibility Method to obtain Local…
We consider the recent formulation of the Algorithmic Lov\'asz Local Lemma [10,2,3] for finding objects that avoid `bad features', or `flaws'. It extends the Moser-Tardos resampling algorithm [17] to more general discrete spaces. At each…
The resampling algorithm of Moser \& Tardos is a powerful approach to develop constructive versions of the Lov\'{a}sz Local Lemma (LLL). We generalize this to partial resampling: when a bad event holds, we resample an appropriately-random…
We investigate the incompressible and compressible heat conducting boundary layer with applying the two-dimensional self-similar Ansatz. Analytic solutions can be found for the incompressible case which can be expressed with special…
The Local Lemma is a fundamental tool of probabilistic combinatorics and theoretical computer science, yet there are hardly any natural problems known where it provides an asymptotically tight answer. The main theme of our paper is to…
We establish the incompressible limit of weakly asymmetric simple exclusion processes coupled through particle collisions. The incompressible limit depends on various parameters in the particle system and is linked to fluid dynamics…
Satisfiability of word equations is an important problem in the intersection of formal languages and algebra: Given two sequences consisting of letters and variables we are to decide whether there is a substitution for the variables that…
The problem of variable-rate lossless data compression is considered, for codes with and without prefix constraints. Sharp bounds are derived for the best achievable compression rate of memoryless sources, when the excess-rate probability…
The Lovasz Local Lemma (LLL) is a powerful tool in probability theory to show the existence of combinatorial objects meeting a prescribed collection of "weakly dependent" criteria. We show that the LLL extends to a much more general…
In this paper, we develop a general approach to proving global and local uniform limit theorems for the Horvitz-Thompson empirical process arising from complex sampling designs. Global theorems such as Glivenko-Cantelli and Donsker…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…
We generalize the notion of relational precompact expansions of Fra\"iss\'e classes via functorial means, inspired by the technique outlined by Laflamme, Nguyen Van Th\'e and Sauer in their paper Partition properties of the dense local…
This paper investigates the problem of variable-length lossy source coding allowing a positive excess distortion probability and an overflow probability of codeword lengths. Novel one-shot achievability and converse bounds of the optimal…
We analyze a macroscopic model with a maximal density constraint which describes short range repulsion in biological systems. This system aims at modeling finite-size particles which cannot overlap and repel each other when they are too…
We develop tools for analyzing focused stochastic local search algorithms. These are algorithms which search a state space probabilistically by repeatedly selecting a constraint that is violated in the current state and moving to a random…
The Lov\'{a}sz Local Lemma (LLL) is a powerful tool in probabilistic combinatorics which can be used to establish the existence of objects that satisfy certain properties. The breakthrough paper of Moser and Tardos and follow-up works…
This work continues the study of the relationship between sample compression schemes and statistical learning, which has been mostly investigated within the framework of binary classification. The central theme of this work is establishing…
The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…
This article discusses some recent trends in Ramsey theory on infinite structures. Trees and their Ramsey theory have been vital to these investigations. The main ideas behind the author's recent method of trees with coding nodes are…
In this paper we investigate the extent to which the Lov\'asz Local Lemma (an important tool in probabilistic combinatorics) can be adapted for the measurable setting. In most applications, the Lov\'asz Local Lemma is used to produce a…
The local behavior of the lowest order boundary element method on quasi-uniform meshes for Symm's integral equation and the stabilized hyper-singular integral equation on polygonal/polyhedral Lipschitz domains is analyzed. We prove local a…