Spatiotemporal Barcodes for Image Sequence Analysis

Taking as input a time-varying sequence of two-dimensional (2D) binary images, we develop an algorithm for computing a spatiotemporal 0–barcode encoding lifetime of connected components on the image sequence over time. This information may not coincide with the one provided by the 0–barcode encoding the 0–persistent homology, since the latter does not respect the principle that it is not possible to move backwards in time. A cell complex K is computed from the given sequence, being the cells of K classified as spatial or temporal depending on whether they connect two consecutive frames or not. A spatiotemporal path is defined as a sequence of edges of K forming a path such that two edges of the path cannot connect the same two consecutive frames. In our algorithm, for each vertex v ∈ K, a spatiotemporal path from v to the “oldest” spatiotemporally-connected vertex is computed and the corresponding spatiotemporal 0–bar is added to the spatiotemporal 0–barcode.Junta de Andalucía FQM-369Ministerio de Economía y Competitividad MTM2012-3270

Parametric Inference for Biological Sequence Analysis

One of the major successes in computational biology has been the unification, using the graphical model formalism, of a multitude of algorithms for annotating and comparing biological sequences. Graphical models that have been applied towards these problems include hidden Markov models for annotation, tree models for phylogenetics, and pair hidden Markov models for alignment. A single algorithm, the sum-product algorithm, solves many of the inference problems associated with different statistical models. This paper introduces the \emph{polytope propagation algorithm} for computing the Newton polytope of an observation from a graphical model. This algorithm is a geometric version of the sum-product algorithm and is used to analyze the parametric behavior of maximum a posteriori inference calculations for graphical models.Comment: 15 pages, 4 figures. See also companion paper "Tropical Geometry of Statistical Models" (q-bio.QM/0311009

Fundamental principles in drawing inference from sequence analysis

Individual life courses are dynamic and can be represented as a sequence of states for some portion of their experiences. More generally, study of such sequences has been made in many fields around social science; for example, sociology, linguistics, psychology, and the conceptualisation of subjects progressing through a sequence of states is common. However, many models and sets of data allow only for the treatment of aggregates or transitions, rather than interpreting whole sequences. The temporal aspect of the analysis is fundamental to any inference about the evolution of the subjects but assumptions about time are not normally made explicit. Moreover, without a clear idea of what sequences look like, it is impossible to determine when something is not seen whether it was not actually there. Some principles are proposed which link the ideas of sequences, hypothesis, analytical framework, categorisation and representation; each one being underpinned by the consideration of time. To make inferences about sequences, one needs to: understand what these sequences represent; the hypothesis and assumptions that can be derived about sequences; identify the categories within the sequences; and data representation at each stage. These ideas are obvious in themselves but they are interlinked, imposing restrictions on each other and on the inferences which can be draw

Revealing evolutionary constraints on proteins through sequence analysis

Statistical analysis of alignments of large numbers of protein sequences has revealed "sectors" of collectively coevolving amino acids in several protein families. Here, we show that selection acting on any functional property of a protein, represented by an additive trait, can give rise to such a sector. As an illustration of a selected trait, we consider the elastic energy of an important conformational change within an elastic network model, and we show that selection acting on this energy leads to correlations among residues. For this concrete example and more generally, we demonstrate that the main signature of functional sectors lies in the small-eigenvalue modes of the covariance matrix of the selected sequences. However, secondary signatures of these functional sectors also exist in the extensively-studied large-eigenvalue modes. Our simple, general model leads us to propose a principled method to identify functional sectors, along with the magnitudes of mutational effects, from sequence data. We further demonstrate the robustness of these functional sectors to various forms of selection, and the robustness of our approach to the identification of multiple selected traits.Comment: 37 pages, 28 figure

Motion sequence analysis in the presence of figural cues

Published in final edited form as: Neurocomputing. 2015 January 5, 147: 485–491The perception of 3-D structure in dynamic sequences is believed to be subserved primarily through the use of motion cues. However, real-world sequences contain many figural shape cues besides the dynamic ones. We hypothesize that if figural cues are perceptually significant during sequence analysis, then inconsistencies in these cues over time would lead to percepts of non-rigidity in sequences showing physically rigid objects in motion. We develop an experimental paradigm to test this hypothesis and present results with two patients with impairments in motion perception due to focal neurological damage, as well as two control subjects. Consistent with our hypothesis, the data suggest that figural cues strongly influence the perception of structure in motion sequences, even to the extent of inducing non-rigid percepts in sequences where motion information alone would yield rigid structures. Beyond helping to probe the issue of shape perception, our experimental paradigm might also serve as a possible perceptual assessment tool in a clinical setting.The authors wish to thank all observers who participated in the experiments reported here. This research and the preparation of this manuscript was supported by the National Institutes of Health RO1 NS064100 grant to LMV. (RO1 NS064100 - National Institutes of Health)Accepted manuscrip