The adaptive spectral estimation method IAA provides better performance than the periodogram at the cost of higher computational complexity. Current fast IAA algorithms reduce the computational complexity using Toeplitz/Vandermonde structures, but are not efficient for missing data cases when the number of missing samples is small. We considerably reduce the computational complexity compared to the state-of-the-art by using a low rank completion to transform the problem to a Toeplitz/Vandermonde structured problem.

MOTIVATION: Directed evolution, in addition to its principal application of obtaining novel biomolecules, offers significant potential as a vehicle for obtaining useful information about the topologies of biomolecular fitness landscapes. In this article, we make use of a special type of model of fitness landscapes-based on finite state machines-which can be inferred from directed evolution experiments. Importantly, the model is constructed only from the fitness data and phylogeny, not sequence or structural information, which is often absent. The model, called a landscape state machine (LSM), has already been used successfully in the evolutionary computation literature to model the landscapes of artificial optimization problems. Here, we use the method for the first time to simulate a biological fitness landscape based on experimental evaluation. RESULTS: We demonstrate in this study that LSMs are capable not only of representing the structure of model fitness landscapes such as NK-landscapes, but also the fitness landscape of real DNA oligomers binding to a protein (allophycocyanin), data we derived from experimental evaluations on microarrays. The LSMs prove adept at modelling the progress of evolution as a function of various controlling parameters, as validated by evaluations on the real landscapes. Specifically, the ability of the model to 'predict' optimal mutation rates and other parameters of the evolution is demonstrated. A modification to the standard LSM also proves accurate at predicting the effects of recombination on the evolution.

A Landscape State Machine (LSM) is a Markov model describing the transition probabilities between the fitness ` levels' of an optimization problem, when a given neighbourhood (or mutation) operator is applied. Although most optimization problems cannot be modeled precisely by an LSM, an approximate LSM can always be constructed by sampling, and can be used, subsequently, in place of real fitness evaluations in order to model the performance of any search algorithm using the given neighbourhood operator. In this paper, we provide empirical evidence that (a) LSMs constructed by simulated annealing-based sampling of a problem landscape make accurate models in few evaluations; (b) LSMs can accurately rank the performance of diverse algorithms including EAs with/without niching and SA; (c) the LSM approach works on diverse problems from MAX-SAT to NKp; (d) convergence of the LSM can be used as a guide to stopping the sampling phase; and, (e) a single LSM constructed using a low mutation-rate sample is sufficient to accurately rank the performance of search algorithms run at multiples of this mutation rate.

Identification of single nucleotide polymorphisms (SNPs) and mutations is important for the discovery of genetic predisposition to complex diseases. PCR resequencing is the method of choice for de novo SNP discovery. However, manual curation of putative SNPs has been a major bottleneck in the application of this method to high-throughput screening. Therefore it is critical to develop a more sensitive and accurate computational method for automated SNP detection. We developed a software tool, SNPdetector, for automated identification of SNPs and mutations in fluorescence-based resequencing reads. SNPdetector was designed to model the process of human visual inspection and has a very low false positive and false negative rate. We demonstrate the superior performance of SNPdetector in SNP and mutation analysis by comparing its results with those derived by human inspection, PolyPhred (a popular SNP detection tool), and independent genotype assays in three large-scale investigations. The first study identified and validated inter- and intra-subspecies variations in 4,650 traces of 25 inbred mouse strains that belong to either the Mus musculus species or the M. spretus species. Unexpected heterozygosity in CAST/Ei strain was observed in two out of 1,167 mouse SNPs. The second study identified 11,241 candidate SNPs in five ENCODE regions of the human genome covering 2.5 Mb of genomic sequence. Approximately 50% of the candidate SNPs were selected for experimental genotyping; the validation rate exceeded 95%. The third study detected ENU-induced mutations (at 0.04% allele frequency) in 64,896 traces of 1,236 zebra fish. Our analysis of three large and diverse test datasets demonstrated that SNPdetector is an effective tool for genome-scale research and for large-sample clinical studies. SNPdetector runs on Unix/Linux platform and is available publicly (http://lpg.nci.nih.gov).