The lion's share of bacteria in various environments cannot be cloned in the laboratory and thus cannot be sequenced using existing technologies. A major goal of single-cell genomics is to complement gene-centric metagenomic data with whole-genome assemblies of uncultivated organisms. Assembly of single-cell data is challenging because of highly non-uniform… (More)
In this paper we present a new approach to proving upper bounds for the maximum 2-satisfiability problem (MAX-2-SAT). We present a new 2<sup><i>K</i>/5.5</sup>-time algorithm for MAX-2-SAT, where <i>K</i> is the number of clauses in an input formula. We also obtain a 2<sup><i>N</i>/6</sup> bound, where <i>N</i> is the number of variables in an input… (More)
A weakened version of the Cutting Plane (CP) proof system with a restriction on the degree of falsity of intermediate inequalities was introduced by Goerdt. He proved an exponential lower bound for CP proofs with degree of falsity bounded by n log 2 n+1 , where n is the number of variables. Hirsch and Nikolenko strengthened this result by establishing a… (More)
In this paper we present relatively simple proofs of the following new upper bounds.
Effects of severe and mild hypothyroidism on the immobile response to inescapable stress were examined in male Wistar rats using the forced swim paradigm. Rats were exposed to two sessions of inescapable swim stress: pretest (for 15 min) followed by test (for 5 min) 24 h later. Surgically thyroidectomized rats showed a significant increase (by 90%) in… (More)
A Boolean function f : F n 2 → F2 is called an affine disperser of dimension d, if f is not constant on any affine subspace of F n 2 of dimension at least d. Recently Ben-Sasson and Kopparty gave an explicit construction of an affine disperser for sublinear d. The main motivation for studying such functions comes from extracting randomness from structured… (More)
The study was aimed at investigating the repercussions of deficiency in thyroid function with and without thyroid hormone (TH) replacement on the neurochemical entities which underly serotonin (5-HT) neutrotransmission, namely 5-HT1A, 5-HT2A receptors, 5-HT transporter and tryptophan hydroxylase (TPH) in the mature brain. Surgically thyroidectomized male… (More)
In this note, we present improved upper bounds on the circuit complexity of symmetric Boolean functions. In particular, we describe circuits of size 4.5n + o(n) for any symmetric function of n variables, as well as circuits of size 3n for MOD n 3 function.
We prove that, if a graph with e edges contains m vertex-disjoint edges, then m 2 /e complete bipartite subgraphs are necessary to cover all its edges. Similar lower bounds are also proved for fractional covers. For sparse graphs, this improves the well-known fooling set lower bound in communication complexity. We also formulate several open problems about… (More)