Learn More
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)
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)
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)
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)