Survivability of Deterministic Dynamical Systems

The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system does not leave a region of desirable states. We demonstrate the utility of this novel stability measure by considering models from climate science, neuronal networks and power grids. We also show that a semi-analytic lower bound for the survivability of linear systems allows a numerically very efficient survivability analysis in realistic models of power grids. Our numerical and semi-analytic work underlines that the type of stability measured by survivability is not captured by common asymptotic stability measures.Comment: 21 pages, 6 figure

Exploring the Free Energy Landscape: From Dynamics to Networks and Back

The knowledge of the Free Energy Landscape topology is the essential key to understand many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers are, how the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times or rate constants, and the hierarchical relationship among basins, complete the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, the dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press

Survivability : A Unifiying Concept for the Transient Resilience of Deterministic Dynamical Systems

16 pagesNon peer reviewedPreprin

Discovery and Strategic Partnership Group Concept Mapping: 2014-2015 Progress Report

In 2014, New York State received funding from the U.S. Department of Education, Office of Special Education and Rehabilitative Services to begin the NYS PROMISE (Promote the Readiness of Minors in Supplemental Security Income) research initiative. The goal of this initiative is to coordinate the system of support surrounding these youths to better catalyze their potential to transition from Supplemental Security Income (SSI) to a sustainable future of living and earning as independent adults. To guide strategy and support PROMISE priorities over the course of the initiative, NYS PROMISE convened the NYS PROMISE Steering Committee, comprised of appointed liaisons from agencies who are connected to the NYS PROMISE initiative. To support sustainable partnership development for greater progress and impact on the goals of NYS PROMISE, the Steering Committee engaged in a structured, time sensitive strategic planning and partnership framework development effort. To develop the elements of a prioritized strategy, the group used Group Concept Mapping (GCM), and constructed a visual framework, or concept map, that served as the basis for prioritization and strategy development throughout the process. The GCM approach employs a group process to capture individual contributions for consensus around a given topic, using a structured approach with a specific sequence of steps that support timely and consistent engagement in the process. GCM incorporates opinions and values, and presents the results in ways that are understandable and usable. 25 individuals from 8 member agencies took part in the concept map development, contributing elements in response to the following prompt: “To yield enduring individual outcomes, a viable system to support youth with disabilities in their transition from high school to successful adult lives needs to include…