We study generalisations of a simple, combinatorial proof of a Chernoff bound similar to the one by Impagliazzo and Kabanets (RANDOM, 2010). In particular, we prove a randomized version of the hitting property of expander random walks and use it to obtain an optimal expander random walk concentration bound settling a question asked by Impagliazzo and Kabanets. Next, we obtain an upper tail boun...

We investigate the sparse recovery problem of reconstructing a high-dimensional non-negative sparse vector from lower dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes are crucial in applications, such as DNA microarrays and sensor networks, where dense measurements are not practically feasible. One possible construction uses ...

The central goal of this thesis is to better understand, and explicitly construct, expanding towers G1,G2, . . ., which are expander families with the additional constraint that Gn+1 is a lift of Gn . A lift G of H is a graph that locally looks like H , but may be globally di erent; lifts have been proposed as a more structured setting for elementary explicit constructions of expanders, and the...

background neck reconstruction is considered as one of the most important surgeries in cosmetic and reconstructive surgery. the present study aimed to assess the results of reconstructive surgery of extensive face and neck burning scars using tissue expanders. methods this descriptive prospective study was conducted on 36 patients with extensive burning scars on the neck and face. operation for...

INTRODUCTION: Nearly 75% of breast reconstruction procedures performed by ASPS members in 2015 involved tissue expanders. Despite the advantages of expander-based reconstruction, complications are common and can require early removal of the tissue expander. Patient preference and oncologic factors may also prompt unanticipated removal of the tissue expander. We present our experience with tissu...

This paper introduces an extended notion of expansion suitable for radio networks. A graph G = (V,E) is said to be an (αw, βw)-wireless expander if for every subset S ⊆ V s.t. |S| ≤ αw · |V |, there exists a subset S′ ⊆ S s.t. there are at least βw · |S| vertices in V \S that are adjacent in G to exactly one vertex in S′. The main question we ask is the following: to what extent are ordinary ex...

In this paper we provide a new method to generate hard k-SAT instances. We incrementally construct a high girth bipartite incidence graph of the k-SAT instance. Having high girth assures high expansion for the graph, and high expansion implies high resolution width. We have extended this approach to generate hard n-ary CSP instances and we have also adapted this idea to increase the expansion o...

Let G be a given graph (modelling a communication network) which we assume suuers from static edge faults: That is we let each edge of G be present independently with probability p (or absent with fault probability f = 1 ? p). In particular we are interested in ro-bustness results for the case that the graph G itself is a random member of the class of all regular graphs with given degree d. Her...

We revisit the classical question of the relationship between the diameter of a graph and its expansion properties. One direction is well understood: expander graphs exhibit essentially the lowest possible diameter. We focus on the reverse direction. We show that “sufficiently large” graphs of fixed diameter and degree must be “good” expanders. We prove this statement for various definitions of...

We prove tail estimates for variables of the form ∑ i f(Xi), where (Xi)i is the trajectory of a random walk on an undirected graph (or, equivalently, a reversible Markov chain). The estimates are in terms of the range of the function f , its variance, and the spectrum of the graph. The purpose of our estimates is to determine the number of random walk generated samples which are required for ap...