Randall Pruim

A genome-wide association study of type 2 diabetes in Finns detects multiple susceptibility variants.

Identifying the genetic variants that increase the risk of type 2 diabetes (T2D) in humans has been a formidable challenge. Adopting a genome-wide association strategy, we genotyped 1161 Finnish T2D cases and 1174 Finnish normal glucose-tolerant (NGT) controls with >315,000 single-nucleotide polymorphisms (SNPs) and imputed genotypes for an additional >2 million autosomal SNPs. We carried out association analysis with these SNPs to identify genetic variants that predispose to T2D, compared our T2D association results with the results of two similar studies, and genotyped 80 SNPs in an additional 1215 Finnish T2D cases and 1258 Finnish NGT controls. We identify T2D-associated variants in an intergenic region of chromosome 11p12, contribute to the identification of T2D-associated variants near the genes IGF2BP2 and CDKAL1 and the region of CDKN2A and CDKN2B, and confirm that variants near TCF7L2, SLC30A8, HHEX, FTO, PPARG, and KCNJ11 are associated with T2D risk. This brings the number of T2D loci now confidently identified to at least 10.

Relativized separation of EQP from P NP

Abstract An oracle is constructed relative to which quantum polynomial time ( EQP ) is not polynomial-time Turing reducible to NP . That is, there is an A such that EQP A ⊈ P NP A . This generalizes and simplifies previous separations of EQP from NP and ZPP , due to Berthiaume and Brassard. A key element of the proof is the use of a special property of Grovers algorithm for database search, in order to show that the test language is in EQP A .

Computing for STEM majors: enhancing non CS majors' computing skills

One of the challenges facing the U.S. technological workforce is that as fewer students take computing courses, fewer college graduates are being prepared for computing careers. Besides trying to attract more CS majors, another approach is to (i) design a computing curriculum that appeals to students and faculty from other (non-CS) disciplines, (ii) use special scholarships to attract students to that curriculum, and (iii) sponsor faculty development workshops for non-CS departments. In this paper, we detail this approach, using a new introductory course oriented to science majors, and scholarships funded by the National Science Foundation Scholarships for Science, Technology, Engineering, and Mathematics (NSF S-STEM) program to motivate non-CS majors to take CS courses. We also present several success stories that this approach has produced in its first two years.

The Pebble Game

The Pebble game is a model for successive execution of a computation with the use of an auxiliary storage devise. The game can be used to study trade-off effects between the memory use and running time for a particular computation. We will show a lower bound originally proved by Paul, Tarjan, and Celoni (1977) which says that certain graphs, based on superconcentrators, require many pebbles.

Spectral Problems and Descriptive Complexity Theory

This chapter begins with a question from predicate logic, namely to determine the set of all (sizes of) finite models of a given formula. It turns out that there is an amazingly close relationship between this question and the world of P and NP.

Challenge to the Established Curriculum: A Collection of Reflections

We invited a number of prominent statisticians and statistics educators to glimpse into the future to discuss what they see as the significant challenges to the established statistics curriculum that enculturate students into statistical practices that underpin the activity of statisticians. Peng, Kreuter, and Gould discuss various developments, which are already gaining traction in current society and will support the notion of immersion in a data-rich curriculum. The influence of MOOCs, “big data,” and Bayesian approaches is primarily discussed by these writers in relation to an undergraduate curriculum. Pruim raises some key questions about teaching computation in statistics with a particular emphasis on undergraduates and programming. In the final piece of writing, Witmer and Cobb discuss the increasing influence of Bayesian inference with an emphasis on a curriculum that fosters statistical reasoning and the evaluation of arguments.

Hyper-polynomial hierarchies and the polynomial jump

Abstract Assuming that the polynomial hierarchy (PH) does not collapse, we show the existence of ascending sequences of ptime Turing degrees of length ω 1 CK in PSPACE such that successors are polynomial jumps of their predecessors. Moreover these ptime degrees are all uniformly hard for PH. This is analogous to the hyperarithmetic hierarchy, which is defined similarly but with the (computable) Turing degrees. The lack of uniform least upper bounds for ascending sequences of ptime degrees causes the limit levels of our hyper-polynomial hierarchy to be inherently non-canonical. This problem is investigated in depth, and various possible structures for hyper-polynomial hierarchies are explicated, as are properties of the polynomial jump operator on the languages which are in PSPACE but not in PH.

The BP-Operator and the Power of Counting Classes

With the help of the BP· operator, Toda (1989) achieved an astonishing result: the classes ⊕P and #P are, in a sense, at least as expressive as the entire polynomial hierarchy.

Quantum Search Algorithms

Widespread interest in quantum computation was sparked by an algorithm of P. Shor for factoring integers on a quantum computer. We investigate here a more recent quantum algorithm of L. Grover for searching a database. This algorithm demonstrates a proven speed-up against the best possible classical algorithm for the same task.

Superconcentrators and the Marriage Theorem

We want to study graphs with special, extreme connectivity properties, prove that they exist, and approximate their size. In the next topic, the existence of these graphs will be used to obtain certain lower bounds.