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- Vitaly Feldman, Will Perkins, Santosh Vempala
- STOC
- 2014

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)

- Irit Dinur, Subhash Khot, Will Perkins, Shmuel Safra
- 2010 IEEE 51st Annual Symposium on Foundations of…
- 2010

For every \epsilon > 0, and integer q >= 3, we show that given an N-vertex graph that has an induced q-colorable sub graph of size (1-\epsilon)N, it is NP-hard to find an independent set of size N/q^2.

- Will Perkins
- Random Struct. Algorithms
- 2015

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)

- A. Heagerty, A. Smith, +8 authors R. C. Strange
- British journal of cancer
- 1996

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)

- B P Wittgen, P W Kunst, +7 authors P E Postmus
- Journal of clinical oncology : official journal…
- 2006

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)

- Mihyun Kang, Will Perkins, Joel H. Spencer
- Random Struct. Algorithms
- 2013

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)

- C J MIGEON, W R SLAUNWHITE, +4 authors W PERKINS
- The Journal of clinical endocrinology and…
- 1955

- Laura Florescu, Will Perkins
- COLT
- 2016

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)

- Vitaly Feldman, Will Perkins, Santosh Vempala
- ArXiv
- 2014