Computational Science Research

Complex systems exhibit dynamics that typically evolve on low-dimensional attractors and may have sparse representation in some optimal basis. Recently developed compressive sensing techniques exploit this sparsity for state reconstruction and/or categorical identification from limited measurements. We argue that data-driven dimensionality reduction methods integrate naturally with sparse sensing in the context of complex systems. This…

A novel method is presented for the simulation of a discrete state space, continuous time Markov process subject to fractional diffusion. The method is based on Lie-Trotter operator splitting of the diffusion and reaction terms in the master equation. The diffusion term follows a multinomial distribution governed by a kernel that is the discretized solution…

Contact rates and patterns among individuals in a geographic area drive transmission of directly-transmitted pathogens, making it essential to understand and estimate contacts for simulation of disease dynamics. Under the uniform mixing assumption, one of two mechanisms is typically used to describe the relation between contact rate and population density: density-dependent or frequency-dependent. Based on…

The goal of compressive sensing is efficient reconstruction of data from few measurements, sometimes leading to a categorical decision. If only classification is required, reconstruction can be circumvented and the measurements needed are orders-of-magnitude sparser still. We define enhanced sparsity as the reduction in number of measurements required for classification over reconstruction. In this work,…