Single-Step Quantum Search Using Problem Structure

The structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties. The structure of random k-SAT allows determining the asymptotic average behavior of these algorithms, showing they improve on quantum algorithms, such as amplitude amplification, that ignore detailed problem structure but remain exponential for hard problem instances. Compared to good classical methods, the algorithm performs better, on average, for weakly and highly constrained problems but worse for hard cases. The analytic techniques introduced here also apply to other quantum algorithms, supplementing the limited evaluation possible with classical simulations and showing how quantum computing can use ensemble properties of NP search problems.Comment: 39 pages, 12 figures. Revision describes further improvement with multiple steps (section 7). See also http://www.parc.xerox.com/dynamics/www/quantum.htm

Ensemble Learning for Free with Evolutionary Algorithms ?

Evolutionary Learning proceeds by evolving a population of classifiers, from which it generally returns (with some notable exceptions) the single best-of-run classifier as final result. In the meanwhile, Ensemble Learning, one of the most efficient approaches in supervised Machine Learning for the last decade, proceeds by building a population of diverse classifiers. Ensemble Learning with Evolutionary Computation thus receives increasing attention. The Evolutionary Ensemble Learning (EEL) approach presented in this paper features two contributions. First, a new fitness function, inspired by co-evolution and enforcing the classifier diversity, is presented. Further, a new selection criterion based on the classification margin is proposed. This criterion is used to extract the classifier ensemble from the final population only (Off-line) or incrementally along evolution (On-line). Experiments on a set of benchmark problems show that Off-line outperforms single-hypothesis evolutionary learning and state-of-art Boosting and generates smaller classifier ensembles

Cut Size Statistics of Graph Bisection Heuristics

We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut sizes found by ``local'' algorithms becomes peaked as the number of vertices in the graphs becomes large. Evidence is given that this distribution tends towards a Gaussian whose mean and variance scales linearly with the number of vertices of the graphs. Given the distribution of cut sizes associated with each heuristic, we provide a ranking procedure which takes into account both the quality of the solutions and the speed of the algorithms. This procedure is demonstrated for a selection of local graph bisection heuristics.Comment: 17 pages, 5 figures, submitted to SIAM Journal on Optimization also available at http://ipnweb.in2p3.fr/~martin

Average-Case Complexity

We survey the average-case complexity of problems in NP. We discuss various notions of good-on-average algorithms, and present completeness results due to Impagliazzo and Levin. Such completeness results establish the fact that if a certain specific (but somewhat artificial) NP problem is easy-on-average with respect to the uniform distribution, then all problems in NP are easy-on-average with respect to all samplable distributions. Applying the theory to natural distributional problems remain an outstanding open question. We review some natural distributional problems whose average-case complexity is of particular interest and that do not yet fit into this theory. A major open question whether the existence of hard-on-average problems in NP can be based on the P$\neq$NP assumption or on related worst-case assumptions. We review negative results showing that certain proof techniques cannot prove such a result. While the relation between worst-case and average-case complexity for general NP problems remains open, there has been progress in understanding the relation between different ``degrees'' of average-case complexity. We discuss some of these ``hardness amplification'' results

RNAiFold2T: Constraint Programming design of thermo-IRES switches

Motivation: RNA thermometers (RNATs) are cis-regulatory ele- ments that change secondary structure upon temperature shift. Often involved in the regulation of heat shock, cold shock and virulence genes, RNATs constitute an interesting potential resource in synthetic biology, where engineered RNATs could prove to be useful tools in biosensors and conditional gene regulation. Results: Solving the 2-temperature inverse folding problem is critical for RNAT engineering. Here we introduce RNAiFold2T, the first Constraint Programming (CP) and Large Neighborhood Search (LNS) algorithms to solve this problem. Benchmarking tests of RNAiFold2T against existent programs (adaptive walk and genetic algorithm) inverse folding show that our software generates two orders of magnitude more solutions, thus allow- ing ample exploration of the space of solutions. Subsequently, solutions can be prioritized by computing various measures, including probability of target structure in the ensemble, melting temperature, etc. Using this strategy, we rationally designed two thermosensor internal ribosome entry site (thermo-IRES) elements, whose normalized cap-independent transla- tion efficiency is approximately 50% greater at 42?C than 30?C, when tested in reticulocyte lysates. Translation efficiency is lower than that of the wild-type IRES element, which on the other hand is fully resistant to temperature shift-up. This appears to be the first purely computational design of functional RNA thermoswitches, and certainly the first purely computational design of functional thermo-IRES elements. Availability: RNAiFold2T is publicly available as as part of the new re- lease RNAiFold3.0 at https://github.com/clotelab/RNAiFold and http: //bioinformatics.bc.edu/clotelab/RNAiFold, which latter has a web server as well. The software is written in C++ and uses OR-Tools CP search engine.Comment: 24 pages, 5 figures, Intelligent Systems for Molecular Biology (ISMB 2016), to appear in journal Bioinformatics 201