Results 1  10
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93
COPASI  a COmplex PAthway SImulator
 BIOINFORMATICS
, 2006
"... Motivation: Simulation and modeling is becoming a standard approach to understand complex biochemical processes. Therefore, there is a big need for software tools that allow access to diverse simulation and modeling methods as well as support for the usage of these methods. Results: Here, we present ..."
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Cited by 256 (6 self)
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Motivation: Simulation and modeling is becoming a standard approach to understand complex biochemical processes. Therefore, there is a big need for software tools that allow access to diverse simulation and modeling methods as well as support for the usage of these methods. Results: Here, we present COPASI, a platformindependent and userfriendly biochemical simulator that offers several unique features. We discuss numerical issues with these features, in particular the criteria to switch between stochastic and deterministic simulation methods, hybrid deterministicstochastic methods, and the importance of random number generator numerical resolution in stochastic simulation. Availability: The complete software is available in binary (executable) for MS Windows, OS X, Linux (Intel), and Sun Solaris (SPARC), as well as the full source code under an open source license from
Brightness Perception, Illusory Contours, and Corticogeniculate Feedback
, 1995
"... A neural network model is developed to explain how visual thalamocortical interactions give rise to boundary percepts such as illusory contours and surface percepts such as filledin brightnesses. Topdown feedback interactions are needed in addition to bottomup feedforward interactions to simulat ..."
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Cited by 95 (52 self)
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A neural network model is developed to explain how visual thalamocortical interactions give rise to boundary percepts such as illusory contours and surface percepts such as filledin brightnesses. Topdown feedback interactions are needed in addition to bottomup feedforward interactions to simulate these data. One feedback loop is modeled between lateral geniculate nucleus (LGN) and cortical area VI, and another within cortical areas VI and V2. The first feedback loop realizes a matching process which enhances LGN cell activities that are consistent with those of active cortical cells, and suppresses LGN activities that are not. This corticogeniculate feedback, being endstopped and oriented, also enhances LGN ON cell activations at the ends of thin dark lines, thereby leading to enhanced cortical brightness percepts when the lines group into closed illusory contours. The second feedback loop generates boundary representations, including illusory contours, that coherently bind distributed cortical features together. Brightness percepts form within the surface representations through a diffusive fillingin process that is contained by resistive gating signals from the boundary representations. The model is used to simulate illusory contours and surface brightnesses induced by Ehrenstein disks, Kanizsa squares, Glass patterns, and cafe wall patterns in single contrast, reverse contrast, and mixed contrast configurations. These examples illustrate how boundary
Theory and implementation of numerical methods based on RungeKutta integration for solving optimal control problems
, 1996
"... ..."
The adaptive explicitimplicit tauleaping method with automatic tau selection
 J. Chem. Phys
, 2007
"... The existing tauselection strategy, which was designed for explicit tauleaping, is here modified to apply to implicit tauleaping, allowing for longer steps when the system is stiff. Further, an adaptive strategy is proposed that identifies stiffness and automatically chooses between the explicit ..."
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Cited by 27 (2 self)
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The existing tauselection strategy, which was designed for explicit tauleaping, is here modified to apply to implicit tauleaping, allowing for longer steps when the system is stiff. Further, an adaptive strategy is proposed that identifies stiffness and automatically chooses between the explicit and the (new) implicit tauselection methods to achieve better efficiency. Numerical testing demonstrates the advantages of the adaptive method for stiff systems. ∗ Author to whom correspondence should be addressed.
Broadband criticality of human brain network synchronization, PLoS
 Comput. Biol
, 2009
"... Selforganized criticality is an attractive model for human brain dynamics, but there has been little direct evidence for its existence in largescale systems measured by neuroimaging. In general, critical systems are associated with fractal or power law scaling, longrange correlations in space and ..."
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Cited by 26 (2 self)
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Selforganized criticality is an attractive model for human brain dynamics, but there has been little direct evidence for its existence in largescale systems measured by neuroimaging. In general, critical systems are associated with fractal or power law scaling, longrange correlations in space and time, and rapid reconfiguration in response to external inputs. Here, we consider two measures of phase synchronization: the phaselock interval, or duration of coupling between a pair of (neurophysiological) processes, and the lability of global synchronization of a (brain functional) network. Using computational simulations of two mechanistically distinct systems displaying complex dynamics, the Ising model and the Kuramoto model, we show that both synchronization metrics have power law probability distributions specifically when these systems are in a critical state. We then demonstrate power law scaling of both pairwise and global synchronization metrics in functional MRI and magnetoencephalographic data recorded from normal volunteers under resting conditions. These results strongly suggest that human brain functional systems exist in an endogenous state of dynamical criticality, characterized by a greater than random probability of both prolonged periods of phaselocking and occurrence of large rapid changes in the state of global synchronization, analogous to the neuronal ‘‘avalanches’ ’ previously described in cellular systems. Moreover, evidence for critical dynamics was identified consistently in neurophysiological systems operating at frequency intervals ranging from 0.05–0.11 to 62.5–125 Hz, confirming that criticality is a property of human
Event location for ordinary differential equations
 Comp. & Maths. with Appls
"... An initial value problem for y ′ = f(t, y) may have an associated event function g(t, y). An event is said to occur at t ∗ when g(t∗, y(t∗)) = 0. We consider problems for which the definition of f(t, y) changes at the time of an event. A number of solvers locate events and restart the integration ..."
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Cited by 17 (3 self)
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An initial value problem for y ′ = f(t, y) may have an associated event function g(t, y). An event is said to occur at t ∗ when g(t∗, y(t∗)) = 0. We consider problems for which the definition of f(t, y) changes at the time of an event. A number of solvers locate events and restart the integration there so as to deal with the changes in f, but there is little theoretical support for what is done. Here we prove that with reasonable assumptions about the problem and the solver, the error of the numerical solution is qualitatively the same whether or not events occur. Numerical results obtained with a wide range of solvers confirm the theory developed here. 1
Numerical and Analytical Studies of the Dynamics of Gaseous Detonations
 UNIVERSITY OF CALIFORNIA PRESS
, 2001
"... This thesis examines two dynamic parameters of gaseous detonations, critical energy and cell size. The first part is concerned with the direct initiation of gaseous detonations by a blast wave and the associated critical energy. Numerical simulations of the spherically symmetric direct initiation ev ..."
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Cited by 16 (4 self)
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This thesis examines two dynamic parameters of gaseous detonations, critical energy and cell size. The first part is concerned with the direct initiation of gaseous detonations by a blast wave and the associated critical energy. Numerical simulations of the spherically symmetric direct initiation event with a simple chemical reaction model are presented. Local analysis of the computed unsteady reaction zone structure identifies a competition between heat release rate, front curvature and unsteadiness. The primary failure mechanism is found to be unsteadiness in the induction zone arising from the deceleration of the shock front. On this basis, simplifying assumptions are applied to the governing equations, permitting solution of an analytical model for the critical shock decay rate. The local analysis is validated by integration of reaction zone structure equations with detailed chemical kinetics and prescribed unsteadiness. The model is then applied to the global initiation problem to produce an analytical equation for the critical energy. Unlike previous phenomenological models, this equation is not dependent on other experimentally determined parameters. For di#erent fueloxidizer mixtures, it is found to give agreement with experimental data to within an order of magnitude. The second part of the thesis is concerned with the development of improved reaction models for accurate quantitative simulations of detonation cell size and cellular structure. The mechanism reduction method of Intrinsic LowDimensional Manifolds, originally developed for flame calculations, is shown to be a viable option for detonation simulations when coupled with a separate model in the induction zone. The agreement with detailed chemistry calculations of constant volume reactions and onedim...
Parameter estimation for a mathematical model of the cell cycle in frog eggs
 Journal of Computational Biology
, 2005
"... Parameter values for a kinetic model of the nuclear replication–division cycle in frog eggs are estimated by fitting solutions of the kinetic equations (nonlinear ordinary differential equations) to a suite of experimental observations. A set of optimal parameter values is found by minimizing an obj ..."
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Cited by 11 (2 self)
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Parameter values for a kinetic model of the nuclear replication–division cycle in frog eggs are estimated by fitting solutions of the kinetic equations (nonlinear ordinary differential equations) to a suite of experimental observations. A set of optimal parameter values is found by minimizing an objective function defined as the orthogonal distance between the data and the model. The differential equations are solved by LSODAR and the objective function is minimized by ODRPACK. The optimal parameter values are close to the “guesstimates” of the modelers who first studied this problem. These tools are sufficiently general to attack more complicated problems, where guesstimation is impractical or unreliable. Key words: cyclindependent kinase, Mphase promoting factor, orthogonal distance regression, LevenbergMarquardt method. 1.
Timedependent outward current in guinea pig ventricular myocytes. Gating kinetics of the delayed
, 1990
"... ABSTRACT Several conflicting models have been used to characterize the gating behavior of the cardiac delayed rectifier. In this study, whole.cell delayed rectifier currents were measured in voltageclamped guinea pig ventricular myocytes, and a minimal model which reproduced the observed kinetic be ..."
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Cited by 8 (2 self)
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ABSTRACT Several conflicting models have been used to characterize the gating behavior of the cardiac delayed rectifier. In this study, whole.cell delayed rectifier currents were measured in voltageclamped guinea pig ventricular myocytes, and a minimal model which reproduced the observed kinetic behavior was identified. First, whole.cell potassium currents between10 and +70 mV were recorded using external solutions designed to eliminate Na and Ca currents and two components of timedependent outward current were found. One component was a La3+sensitive current which inactivated and resembled the transient outward current described in other cell types; singlechannel observations confirmed the presence of a transient outward current in these guinea pig ventricular cells (3, 9.9 pS, [K] o = 4.5 mM). Analysis of envelopes of tail amplitudes demonstrated that this component was absent in solutions containing 30100/~M La s+. The remaining timedependent current, IK, activated with a sigmoidal time course that was wellcharacterized by three time constants. Nonlinear leastsquares fits of a