Statistical analysis of shape through triangulation of landmarks: A study of sexual dimorphism in hominids

Two objects with homologous landmarks are said to be of the same shape if the configuration of landmarks of one object can be exactly matched with that of the other by translation, rotation/reflection, and scaling. In an earlier paper, the authors proposed statistical analysis of shape by considering logarithmic differences of all possible Euclidean distances between landmarks. Tests of significance for differences in the shape of objects and methods of discrimination between populations were developed with such data. In the present paper, the corresponding statistical methodology is developed by triangulation of the landmarks and by considering the angles as natural measurements of shape. This method is applied to the study of sexual dimorphism in hominids.

Building a dictionary for genomes: Identification of presumptive regulatory sites by statistical analysis

The availability of complete genome sequences and mRNA expression data for all genes creates new opportunities and challenges for identifying DNA sequence motifs that control gene expression. An algorithm, “MobyDick,” is presented that decomposes a set of DNA sequences into the most probable dictionary of motifs or words. This method is applicable to any set of DNA sequences: for example, all upstream regions in a genome or all genes expressed under certain conditions. Identification of words is based on a probabilistic segmentation model in which the significance of longer words is deduced from the frequency of shorter ones of various lengths, eliminating the need for a separate set of reference data to define probabilities. We have built a dictionary with 1,200 words for the 6,000 upstream regulatory regions in the yeast genome; the 500 most significant words (some with as few as 10 copies in all of the upstream regions) match 114 of 443 experimentally determined sites (a significance level of 18 standard deviations). When analyzing all of the genes up-regulated during sporulation as a group, we find many motifs in addition to the few previously identified by analyzing the subclusters individually to the expression subclusters. Applying MobyDick to the genes derepressed when the general repressor Tup1 is deleted, we find known as well as putative binding sites for its regulatory partners.

Statistical analysis of shape of objects based on landmark data.

Two objects with homologous landmarks are said to be of the same shape if the configurations of landmarks of one object can be exactly matched with that of the other by translation, rotation/reflection, and scaling. The observations on an object are coordinates of its landmarks with reference to a set of orthogonal coordinate axes in an appropriate dimensional space. The origin, choice of units, and orientation of the coordinate axes with respect to an object may be different from object to object. In such a case, how do we quantify the shape of an object, find the mean and variation of shape in a population of objects, compare the mean shapes in two or more different populations, and discriminate between objects belonging to two or more different shape distributions. We develop some methods that are invariant to translation, rotation, and scaling of the observations on each object and thereby provide generalizations of multivariate methods for shape analysis.

Is redshift-dependent evolution of galaxies a theoretical artifact?

The physical validity of the hypothesis of (redshift-dependent) luminosity evolution in galaxies is tested by statistical analysis of an intensively studied complete high-redshift sample of normal galaxies. The necessity of the evolution hypothesis in the frame of big-bang cosmology is confirmed at a high level of statistical significance; however, this evolution is quantitatively just as predicted by chronometric cosmology, in which there is no such evolution. Since there is no direct observational means to establish the evolution postulated in big-bang studies of higher-redshift galaxies, and the chronometric predictions involve no adjustable parameters (in contrast to the two in big-bang cosmology), the hypothesized evolution appears from the standpoint of conservative scientific methodology as a possible theoretical artifact.

Brain-wave recognition of sentences

Electrical and magnetic brain waves of two subjects were recorded for the purpose of recognizing which one of 12 sentences or seven words auditorily presented was processed. The analysis consisted of averaging over trials to create prototypes and test samples, to each of which a Fourier transform was applied, followed by filtering and an inverse transformation to the time domain. The filters used were optimal predictive filters, selected for each subject. A still further improvement was obtained by taking differences between recordings of two electrodes to obtain bipolar pairs that then were used for the same analysis. Recognition rates, based on a least-squares criterion, varied, but the best were above 90%. The first words of prototypes of sentences also were cut and pasted to test, at least partially, the invariance of a word’s brain wave in different sentence contexts. The best result was above 80% correct recognition. Test samples made up only of individual trials also were analyzed. The best result was 134 correct of 288 (47%), which is promising, given that the expected recognition number by chance is just 24 (or 8.3%). The work reported in this paper extends our earlier work on brain-wave recognition of words only. The recognition rates reported here further strengthen the case that recordings of electric brain waves of words or sentences, together with extensive mathematical and statistical analysis, can be the basis of new developments in our understanding of brain processing of language.

Evidence for nonrandom hydrophobicity structures in protein chains.

The question of whether proteins originate from random sequences of amino acids is addressed. A statistical analysis is performed in terms of blocked and random walk values formed by binary hydrophobic assignments of the amino acids along the protein chains. Theoretical expectations of these variables from random distributions of hydrophobicities are compared with those obtained from functional proteins. The results, which are based upon proteins in the SWISS-PROT data base, convincingly show that the amino acid sequences in proteins differ from what is expected from random sequences in a statistically significant way. By performing Fourier transforms on the random walks, one obtains additional evidence for nonrandomness of the distributions. We have also analyzed results from a synthetic model containing only two amino acid types, hydrophobic and hydrophilic. With reasonable criteria on good folding properties in terms of thermodynamical and kinetic behavior, sequences that fold well are isolated. Performing the same statistical analysis on the sequences that fold well indicates similar deviations from randomness as for the functional proteins. The deviations from randomness can be interpreted as originating from anticorrelations in terms of an Ising spin model for the hydrophobicities. Our results, which differ from some previous investigations using other methods, might have impact on how permissive with respect to sequence specificity protein folding process is-only sequences with nonrandom hydrophobicity distributions fold well. Other distributions give rise to energy landscapes with poor folding properties and hence did not survive the evolution.

Analysis of the relation between the sequence and secondary and three-dimensional structures of immunoglobulin molecules.

Methods of structural and statistical analysis of the relation between the sequence and secondary and three-dimensional structures are developed. About 5000 secondary structures of immunoglobulin molecules from the Kabat data base were predicted. Two statistical analyses of amino acids reveal 47 universal positions in strands and loops. Eight universally conservative positions out of the 47 are singled out because they contain the same amino acid in > 90% of all chains. The remaining 39 positions, which we term universally alternative positions, were divided into five groups: hydrophobic, charged and polar, aromatic, hydrophilic, and Gly-Ala, corresponding to the residues that occupied them in almost all chains. The analysis of residue-residue contacts shows that the 47 universal positions can be distinguished by the number and types of contacts. The calculations of contact maps in the 29 antibody structures revealed that residues in 24 of these 47 positions have contacts only with residues of antiparallel beta-strands in the same beta-sheet and residues in the remaining 23 positions always have far-away contacts with residues from other beta-sheets as well. In addition, residues in 6 of the 47 universal positions are also involved in interactions with residues of the other variable or constant domains.