Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables

Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been attracting attention as a way of obtaining global modal descriptions of NLDSs without requiring explicit prior knowledge. However, since existing DMD algorithms are in principle formulated based on the concatenation of scalar observables, it is not directly applicable to data with dependent structures among observables, which take, for example, the form of a sequence of graphs. In this paper, we formulate Koopman spectral analysis for NLDSs with structures among observables and propose an estimation algorithm for this problem. This method can extract and visualize the underlying low-dimensional global dynamics of NLDSs with structures among observables from data, which can be useful in understanding the underlying dynamics of such NLDSs. To this end, we first formulate the problem of estimating spectra of the Koopman operator defined in vector-valued reproducing kernel Hilbert spaces, and then develop an estimation procedure for this problem by reformulating tensor-based DMD. As a special case of our method, we propose the method named as Graph DMD, which is a numerical algorithm for Koopman spectral analysis of graph dynamical systems, using a sequence of adjacency matrices. We investigate the empirical performance of our method by using synthetic and real-world data.Comment: 34 pages with 4 figures, Published in Neural Networks, 201

A Stochastic Differential Equation Model for Predator-Avoidance Fish Schooling

This paper presents a system of stochastic differential equations (SDEs) as mathematical model to describe the spatial-temporal dynamics of predator-prey system in an artificial aquatic environment with schooling behavior imposed upon the associated prey. The proposed model follows the particle-like approach where interactions among the associated units are manifested through combination of attractive and repulsive forces analogous to the ones occurred in molecular physics. Two hunting tactics of the predator are proposed and integrated into the general model, namely the center-attacking and the nearest-attacking strategy. Emphasis is placed upon demonstrating the capacity of the proposed model in: (i) discovering the predator-avoidance patterns of the schooling prey, and (ii) showing the benefit of constituting large prey school in better escaping the predator's attack. Based on numerical simulations upon the proposed model, four predator-avoidance patterns of the schooling prey are discovered, namely Split and Reunion, Split and Separate into Two Groups, Scattered, and Maintain Formation and Distance. The proposed model also successfully demonstrates the benefit of constituting large group of schooling prey in mitigating predation risk. Such findings are in agreement with real-life observations of the natural aquatic ecosystem, hence confirming the validity and exactitude of the proposed model

LightDock: a new multi-scale approach to protein–protein docking

Computational prediction of protein–protein complex structure by docking can provide structural and mechanistic insights for protein interactions of biomedical interest. However, current methods struggle with difficult cases, such as those involving flexible proteins, low-affinity complexes or transient interactions. A major challenge is how to efficiently sample the structural and energetic landscape of the association at different resolution levels, given that each scoring function is often highly coupled to a specific type of search method. Thus, new methodologies capable of accommodating multi-scale conformational flexibility and scoring are strongly needed. We describe here a new multi-scale protein–protein docking methodology, LightDock, capable of accommodating conformational flexibility and a variety of scoring functions at different resolution levels. Implicit use of normal modes during the search and atomic/coarse-grained combined scoring functions yielded improved predictive results with respect to state-of-the-art rigid-body docking, especially in flexible cases.B.J-G was supported by a FPI fellowship from the Spanish Ministry of Economy and Competitiveness. This work was supported by I+D+I Research Project grants BIO2013-48213-R and BIO2016-79930-R from the Spanish Ministry of Economy and Competitiveness. This work is partially supported by the European Union H2020 program through HiPEAC (GA 687698), by the Spanish Government through Programa Severo Ochoa (SEV-2015-0493), by the Spanish Ministry of Science and Technology (TIN2015-65316-P) and the Departament d’Innovació, Universitats i Empresa de la Generalitat de Catalunya, under project MPEXPAR: Models de Programaciói Entorns d’Execució Paral·lels (2014-SGR-1051).Peer ReviewedPostprint (author's final draft

An optimization-based model of collective motion

Computational models of collective motion have yielded many insights about the way that groups of animals or simulated particles may move together and self-organize. Recent literature has compared predictions of models with large datasets of detailed observations of animal behavior, and found that there are important discrepancies, leading researchers to reexamine some of the most widely used assumptions. We introduce FlockOpt, an optimization-based, variable-speed, self-propelled particle model of collective motion that addresses important shortcomings of earlier models. In our model, each particle adjusts its velocity by performing a constrained optimization of a locally-defined objective function, which is computed at each time step over the kinematics of the particle and the relative position of neighboring particles. Our model explains how ordered motion can arise in the absence of an explicitly prescribed alignment term and simulations performed with our model exhibit a wide variety of patterns of motion, including several not possible with popular constant-speed models. Our model predicts that variations in speed and heading of particles are coupled due to costs associated with changes in relative position. We have found that a similar coupling effect may also be present in the flight of groups of gregarious bats. The Mexican Free-tailed bat (Tadarida brasiliensis) is a gregarious bat that forms large maternity colonies, containing hundreds of thousands to millions of individuals, in the southwestern United States in the summer. We have developed a protocol for calibrating cameras used in stereo videography and developed guidelines for data collection. Our field protocol can be deployed in a single afternoon, requiring only short video segments of light, portable calibration objects. These protocols have allowed us to reconstruct the three-dimensional flight trajectories of hundreds of thousands of bats in order to use their flight as a biological study system for our model

An approach to distributed sensing in a virtual fishtank

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.Includes bibliographical references (leaves 44-45).by Mark L. Neri.M.Eng