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It has become widely accepted that the most dangerous cardiac arrhythmias are due to re-entrant waves, i.e., electrical wave(s) that re-circulate repeatedly throughout the tissue at a higher frequency than the waves produced by the heart's natural pacemaker (sinoatrial node). However, the complicated structure of cardiac tissue, as well as the complex ionic(More)
We describe a useful setting for interactive, real-time study of mathematical models of cardiac electrical activity, using implicit and explicit integration schemes implemented in JAVA. These programs are intended as a teaching aid for the study and understanding of general excitable media. Particularly for cardiac cell models and the ionic currents(More)
A simplified quantitative ionic model of cardiac action potential, which reproduces accurate restitution curves, is used in conjunction with global tissue characteristics such as rotational cell anisotropy and periodic boundaries to study the transition from ventricular tachychardia (VT) to ventricular fibrillation (VF). We give an explanation for the(More)
Biological systems routinely solve problems involving pattern recognition and feature extraction. Such problems do not appear to admit similarly routine algorithmic solutions; the power of biological systems in this regard apparently arises from nonalgorithmic dynamics. It is our intention to explore, and to develop principles of, functional characteristics(More)
We develop worst-case and typical estimates for the rate of convergence of annealing algorithms. The worst-case estimates extend results of Geman and Geman (1983) for pattern recognition. However, as Geman and Geman observe, and empirical results imply, simulated annealing usually displays much faster convergence (and thus allows much faster cooling) than(More)
We explore the potential of modifications to standard fishery models (for example Gordon-Schafer-Munro) to help understand events such as the collapse of the North Atlantic cod fishery. In particular we find that quota-driven and similar harvesting strategies induce an effective strong Allee effect (collapse if the population falls below a critical level).(More)
The purpose of this research was to explore the unstirred, ferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction as an experimental model for the response of excitable media to small perturbations (slightly larger than the threshold for excitations). Following Showalter et al. (Showalter, K.; Noyes, R. M.; Turner, H. J.Am. Chem. Soc. 1979, 101, 7463-69), we(More)
The prototype experimental example of "spontaneous" pattern formation in an unstirred chemical medium is the oscillatory Belousov-Zhabotinsky (BZ) reaction: target patterns of outward-moving concentric rings are readily observed when the reaction is run in a thin layer in a Petri dish. In many experimental runs, new target centers appeared to form closer to(More)
Heart disease is one of the most prevalent diseases in the world and is the leading cause of death in industrialized countries. In the United States alone, cardiovascular disease affects about 68 million people, roughly 25% of the total population, from both sexes, and all races and ages, and costs an estimated $117 billion annually. It is currently(More)
abstract Discordant alternans, the phenomenon of separate cardiac tissue locations exhibiting action potential duration (APD) alternans of opposite phase, appears to be a potential mechanism for electrocardiographic T wave alternans, but its initiation mechanism is unknown. We studied behavior of one-and two-dimensional cardiac tissue spatially homogeneous(More)