Cross-validated maximum likelihood enhances crystallographic simulated annealing refinement

Recently, the target function for crystallographic refinement has been improved through a maximum likelihood analysis, which makes proper allowance for the effects of data quality, model errors, and incompleteness. The maximum likelihood target reduces the significance of false local minima during the refinement process, but it does not completely eliminate them, necessitating the use of stochastic optimization methods such as simulated annealing for poor initial models. It is shown that the combination of maximum likelihood with cross-validation, which reduces overfitting, and simulated annealing by torsion angle molecular dynamics, which simplifies the conformational search problem, results in a major improvement of the radius of convergence of refinement and the accuracy of the refined structure. Torsion angle molecular dynamics and the maximum likelihood target function interact synergistically, the combination of both methods being significantly more powerful than each method individually. This is demonstrated in realistic test cases at two typical minimum Bragg spacings (dmin = 2.0 and 2.8 Å, respectively), illustrating the broad applicability of the combined method. In an application to the refinement of a new crystal structure, the combined method automatically corrected a mistraced loop in a poor initial model, moving the backbone by 4 Å.

Using rare mutations to estimate population divergence times: A maximum likelihood approach

In this paper we propose a method to estimate by maximum likelihood the divergence time between two populations, specifically designed for the analysis of nonrecurrent rare mutations. Given the rapidly growing amount of data, rare disease mutations affecting humans seem the most suitable candidates for this method. The estimator RD, and its conditional version RDc, were derived, assuming that the population dynamics of rare alleles can be described by using a birth–death process approximation and that each mutation arose before the split of a common ancestral population into the two diverging populations. The RD estimator seems more suitable for large sample sizes and few alleles, whose age can be approximated, whereas the RDc estimator appears preferable when this is not the case. When applied to three cystic fibrosis mutations, the estimator RD could not exclude a very recent time of divergence among three Mediterranean populations. On the other hand, the divergence time between these populations and the Danish population was estimated to be, on the average, 4,500 or 15,000 years, assuming or not a selective advantage for cystic fibrosis carriers, respectively. Confidence intervals are large, however, and can probably be reduced only by analyzing more alleles or loci.

Factors affecting likelihood of applicants being offered a place in medical schools in the United Kingdom in 1996 and 1997: retrospective study

Objective To assess the relation between a range of measures and the likelihood of applicants to medical schools in the United Kingdom being offered a place overall and at each medical school, with particular emphasis on ethnic minority applicants.

Maximum likelihood estimation of a migration matrix and effective population sizes in n subpopulations by using a coalescent approach

A maximum likelihood estimator based on the coalescent for unequal migration rates and different subpopulation sizes is developed. The method uses a Markov chain Monte Carlo approach to investigate possible genealogies with branch lengths and with migration events. Properties of the new method are shown by using simulated data from a four-population n-island model and a source–sink population model. Our estimation method as coded in migrate is tested against genetree; both programs deliver a very similar likelihood surface. The algorithm converges to the estimates fairly quickly, even when the Markov chain is started from unfavorable parameters. The method was used to estimate gene flow in the Nile valley by using mtDNA data from three human populations.

Anatomy of word and sentence meaning

Reading and listening involve complex psychological processes that recruit many brain areas. The anatomy of processing English words has been studied by a variety of imaging methods. Although there is widespread agreement on the general anatomical areas involved in comprehending words, there are still disputes about the computations that go on in these areas. Examination of the time relations (circuitry) among these anatomical areas can aid in understanding their computations. In this paper, we concentrate on tasks that involve obtaining the meaning of a word in isolation or in relation to a sentence. Our current data support a finding in the literature that frontal semantic areas are active well before posterior areas. We use the subject’s attention to amplify relevant brain areas involved either in semantic classification or in judging the relation of the word to a sentence to test the hypothesis that frontal areas are concerned with lexical semantics and posterior areas are more involved in comprehension of propositions that involve several words.

Neuroimaging studies of word reading

This review discusses how neuroimaging can contribute to our understanding of a fundamental aspect of skilled reading: the ability to pronounce a visually presented word. One contribution of neuroimaging is that it provides a tool for localizing brain regions that are active during word reading. To assess the extent to which similar results are obtained across studies, a quantitative review of nine neuroimaging investigations of word reading was conducted. Across these studies, the results converge to reveal a set of areas active during word reading, including left-lateralized regions in occipital and occipitotemporal cortex, the left frontal operculum, bilateral regions within the cerebellum, primary motor cortex, and the superior and middle temporal cortex, and medial regions in the supplementary motor area and anterior cingulate. Beyond localization, the challenge is to use neuroimaging as a tool for understanding how reading is accomplished. Central to this challenge will be the integration of neuroimaging results with information from other methodologies. To illustrate this point, this review will highlight the importance of spelling-to-sound consistency in the transformation from orthographic (word form) to phonological (word sound) representations, and then explore results from three neuroimaging studies in which the spelling-to-sound consistency of the stimuli was deliberately varied. Emphasis is placed on the pattern of activation observed within the left frontal cortex, because the results provide an example of the issues and benefits involved in relating neuroimaging results to behavioral results in normal and brain damaged subjects, and to theoretical models of reading.

Training and search methods for speech recognition.

Speech recognition involves three processes: extraction of acoustic indices from the speech signal, estimation of the probability that the observed index string was caused by a hypothesized utterance segment, and determination of the recognized utterance via a search among hypothesized alternatives. This paper is not concerned with the first process. Estimation of the probability of an index string involves a model of index production by any given utterance segment (e.g., a word). Hidden Markov models (HMMs) are used for this purpose [Makhoul, J. & Schwartz, R. (1995) Proc. Natl. Acad. Sci. USA 92, 9956-9963]. Their parameters are state transition probabilities and output probability distributions associated with the transitions. The Baum algorithm that obtains the values of these parameters from speech data via their successive reestimation will be described in this paper. The recognizer wishes to find the most probable utterance that could have caused the observed acoustic index string. That probability is the product of two factors: the probability that the utterance will produce the string and the probability that the speaker will wish to produce the utterance (the language model probability). Even if the vocabulary size is moderate, it is impossible to search for the utterance exhaustively. One practical algorithm is described [Viterbi, A. J. (1967) IEEE Trans. Inf. Theory IT-13, 260-267] that, given the index string, has a high likelihood of finding the most probable utterance.

A maximum likelihood algorithm for genome mapping of cytogenetic loci from meiotic configuration data.

Frequencies of meiotic configurations in cytogenetic stocks are dependent on chiasma frequencies in segments defined by centromeres, breakpoints, and telomeres. The expectation maximization algorithm is proposed as a general method to perform maximum likelihood estimations of the chiasma frequencies in the intervals between such locations. The estimates can be translated via mapping functions into genetic maps of cytogenetic landmarks. One set of observational data was analyzed to exemplify application of these methods, results of which were largely concordant with other comparable data. The method was also tested by Monte Carlo simulation of frequencies of meiotic configurations from a monotelodisomic translocation heterozygote, assuming six different sample sizes. The estimate averages were always close to the values given initially to the parameters. The maximum likelihood estimation procedures can be extended readily to other kinds of cytogenetic stocks and allow the pooling of diverse cytogenetic data to collectively estimate lengths of segments, arms, and chromosomes.