M. C. Davis, R. Carretero-González, Z. Shi, K. J. H. Law, P. G. Kevrekidis, and B. P. Anderson Department of Mathematics and Statistics and Computational Science Research Center, Nonlinear Dynamical Systems Group, San Diego State University, San Diego, California 92182-7720, USA Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003, USA College of O...

We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relat...

R. Carretero-González, B. P. Anderson, P. G. Kevrekidis, D. J. Frantzeskakis, and C. N. Weiler Nonlinear Dynamical Systems Group,*Department of Mathematics and Statistics, and Computational Science Research Center, San Diego State University, San Diego, California 92182-7720, USA College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA Department of Mathematics and Statist...

Computing Scan Statistic p Values Using Importance Sampling, with Applications to Genetics and Medical Image Analysis Author(s): Daniel Q. Naiman and Carey E. Priebe Source: Journal of Computational and Graphical Statistics, Vol. 10, No. 2 (Jun., 2001), pp. 296328 Published by: American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of America Stable URL...

H. XU1, P.G. KEVREKIDIS1,a, Q. ZHOU1, D.J. FRANTZESKAKIS2,*, V. ACHILLEOS2, R. CARRETERO-GONZÁLEZ3 1Department of Mathematics and Statistics, University of Massachusetts, Amherst MA 01003-4515, USA E-mail: [email protected] 2Department of Physics, University of Athens, Panepistimiopolis, Zografos, GR-15784 Athens, Greece E-mail∗: [email protected] (corresponding author) 3Nonlinear Dynamical ...

Scattering and leapfrogging of vortex rings in a superfluid R. M. Caplan,1 J. D. Talley,2 R. Carretero-González,2 and P. G. Kevrekidis3 1Predictive Science Inc., 9990 Mesa Rim Road Suite 170, San Diego, California 92121, USA 2Nonlinear Dynamical Systems Group, Computational Science Research Center, and Department of Mathematics and Statistics, San Diego State University, San Diego, California 9...

R. Carretero-González, N. Whitaker, P. G. Kevrekidis, and D. J. Frantzeskakis Nonlinear Dynamical Systems Group,* Department of Mathematics and Statistics, and Computational Science Research Center, San Diego State University, San Diego, California 92182-7720, USA Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA Department of Physics,...

We show how martingale techniques (both old and new) can be used to obtain otherwise hard-to-get information for the moments and distributions of waiting times for patterns in independent or Markov sequences. In particular, we show how these methods provide moments and distribution approximations for certain scan statistics, including about variable length scan statistics. Each general problem ...

Biochemical reaction networks are often modelled using discrete-state, continuoustime Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie’s di...

We consider a simple model of cooperation among agents called Coalitional Skill Games (CSGs). This is a restricted form of coalitional games, where each agent has a set of skills that are required to complete various tasks. Each task requires a set of skills in order to be completed, and a coalition can accomplish the task only if the coalition’s agents cover the set of required skills for the ...