John W. Clark

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We investigate the recently proposed label-propagation algorithm (LPA) for identifying network communities. We reformulate the LPA as an equivalent optimization problem, giving an objective function whose maxima correspond to community solutions. By considering properties of the objective function, we identify conceptual and practical drawbacks of the(More)
We have developed a mathematical model of the human atria myocyte based on averaged voltage-clamp data recorded from isolated single myocytes. Our model consists of a Hodgkin-Huxley-type equivalent circuit for the sarcolemma, coupled with a fluid compartment model, which accounts for changes in ionic concentrations in the cytoplasm as well as in the(More)
1. An equivalent circuit model of the R15 bursting neuron in Aplysia has been combined with a fluid compartment model, resulting in a model that incorporates descriptions of most of the membrane ion channels that are known to exist in the somata of R15, as well as providing a Ca2+ balance on the cell. 2. A voltage-activated, calcium-inactivated Ca2+ current(More)
A mathematical model of midbrain dopamine neurons has been developed to understand the mechanisms underlying two types of calcium-dependent firing patterns that these cells exhibit in vitro. The first is the regular, pacemaker-like firing exhibited in a slice preparation, and the second is a burst firing pattern sometimes exhibited in the presence of(More)
1. Neurons of the nodose ganglia provide the sole connection between many types of visceral sensory inputs and the central nervous system. Electrophysiological studies of isolated nodose neurons provide a practical means of measuring individual cell membrane currents and assessing their putative contributions to the overall response properties of the neuron(More)
In order to assess the relative contributions to pattern-generation of the intrinsic properties of individual neurons and of their connectivity, we examined a ring circuit composed of four complex physiologically based oscillators. This circuit produced patterns that correspond to several quadrupedal gaits, including the walk, the bound, and the gallop. An(More)
The essential dynamics of some biological central pattern generators (CPGs) can be captured by a model consisting of N neurons connected in a ring. These circuits, like many oscillatory nonlinear circuits of sufficient complexity, are capable of multistability, that is, of generating different firing patterns distinguished by the phasic relationships(More)
Canavier et al. (1997) used phase response curves (PRCs) of individual oscillators to characterize the possible modes of phase-locked entrainment of an N-oscillator ring network. We extend this work by developing a mathematical criterion to determine the local stability of such a mode based on the PRCs. Our method does not assume symmetry; neither the(More)
This paper introduces a novel nonlinear multiscale wavelet diffusion method for ultrasound speckle suppression and edge enhancement. This method is designed to utilize the favorable denoising properties of two frequently used techniques: the sparsity and multiresolution properties of the wavelet, and the iterative edge enhancement feature of nonlinear(More)
Chaotic regimens have been observed experimentally in neurons as well as in deterministic neuronal models. The R15 bursting cell in the abdominal ganglion of Aplysia has been the subject of extensive mathematical modeling. Previously, the model of Plant and Kim has been shown to exhibit both bursting and beating modes of electrical activity. In this report,(More)