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The problem of identifying a planted assignment given a random k-SAT formula consistent with the assignment exhibits a large algorithmic gap: while the planted solution can always be identified given a formula with O(n log n) clauses, there are distributions over clauses for which the best known efficient algorithms require n<sup>k/2</sup> clauses. We(More)
Vindicating a sophisticated but non-rigorous physics approach called the cavity method, we establish a formula for the mutual information in statistical inference problems induced by random graphs. This general result implies the conjecture on the information-theoretic threshold in the disassortative stochastic block model [Decelle et al.: Phys. Rev. E(More)
We study an Achlioptas-process version of the random k-SAT process: a bounded number of k-clauses are drawn uniformly at random at each step, and exactly one added to the growing formula according to a particular rule. We prove the existence of a rule that shifts the satisfiability threshold. This extends a well-studied area of probabilistic combinatorics(More)
The factors that determine development of single and multiple primary cutaneous basal cell carcinomas (BCCs) are unclear. We describe a case-control study firstly, to examine the influence of allelism at the glutathione S-transferase GSTM1 and GSTT1 and cytochrome P450 CYP2D6 loci on susceptibility to these tumours and, secondly, to identify interactions(More)
7131 Background: Investigate the safety and pharmacokinetics of aerosolized SLIT (Sustained release Lipid Inhalation Targeting) cisplatin in patients with carcinoma of the lung. METHODS In this single-center, dose-escalating study patients received SLIT cisplatin for a maximum of 6 cycles. The dose level defines the cycle duration and number of(More)
The incidence of antituberculosis drug resistance in South Texas has been tabulated. Age, sex, and ethnic group were not found to significantly influence the incidence of resistance. The incidence of resistance to isoniazid (NH) was 16.4%, ethambutol, 3.9%, rifampin, 10.6%, and streptomycin, 7.8%. There was a 7.3% rate of resistance to INH and/or ethambutol(More)
The Erd˝ os-Rényi process begins with an empty graph on n vertices, with edges added randomly one at a time to the graph. A classical result of Erd˝ os and Rényi states that the Erd˝ os-Rényi process undergoes a phase transition, which takes place when the number of edges reaches n/2 (we say at time 1) and a giant component emerges. Since this sem-inal work(More)
1 We consider a bipartite stochastic block model on vertex sets V 1 and V 2 , with planted partitions in each, and ask at what densities efficient algorithms can recover the partition of the smaller vertex set. When |V 2 | |V 1 |, multiple thresholds emerge. We first locate a sharp threshold for detection of the partition, in the sense of the results of(More)