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159,352
Lateral Inhibition through DeltaNotch Signaling: A Piecewise Affine Hybrid Model
, 2001
"... Biological cell networks exhibit complex combinations of both discrete and continuous behaviors: indeed, the dynamics that govern the spatial and temporal increase or decrease of protein concentration inside a single cell are continuous di#erential equations, while the activation or deactivation of ..."
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Cited by 64 (7 self)
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of these continuous dynamics are triggered by discrete switches which encode protein concentrations reaching given thresholds. In this paper, we model as a hybrid system a striking example of this behavior in a biological mechanism called DeltaNotch signaling, which is thought to be the primary mechanism of cell di
Automated Symbolic Reachability Analysis; with Application to DeltaNotch Signaling Automata
 Lecture Notes in Computer Science
, 2003
"... This paper describes the implementation of predicate abstraction techniques to automatically compute symbolic backward reachable sets of high dimensional piecewise a#ne hybrid automata, used to model DeltaNotch biological cell signaling networks. These automata are analyzed by creating an abstr ..."
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Cited by 40 (2 self)
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This paper describes the implementation of predicate abstraction techniques to automatically compute symbolic backward reachable sets of high dimensional piecewise a#ne hybrid automata, used to model DeltaNotch biological cell signaling networks. These automata are analyzed by creating
Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Deltanotch protein signalling
 Systems Biology
, 2004
"... Hybrid automata are an eminently suitable modelling framework for biological protein regulatory networks, as the protein concentration dynamics inside each biological cell are modelled using linear differential equations; inputs activate or deactivate these continuous dynamics through discrete switc ..."
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Cited by 63 (2 self)
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switches, which themselves are controlled by protein concentrations reaching given thresholds. This paper proposes an iterative refinement algorithm for computing discrete abstractions of a class of hybrid automata with piecewise affine continuous dynamics and forced discrete transitions, defined
Predictive reward signal of dopamine neurons
 Journal of Neurophysiology
, 1998
"... Schultz, Wolfram. Predictive reward signal of dopamine neurons. is called rewards, which elicit and reinforce approach behavJ. Neurophysiol. 80: 1–27, 1998. The effects of lesions, receptor ior. The functions of rewards were developed further during blocking, electrical selfstimulation, and drugs ..."
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Cited by 717 (12 self)
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Schultz, Wolfram. Predictive reward signal of dopamine neurons. is called rewards, which elicit and reinforce approach behavJ. Neurophysiol. 80: 1–27, 1998. The effects of lesions, receptor ior. The functions of rewards were developed further during blocking, electrical selfstimulation, and drugs
Reachability Analysis of DeltaNotch Lateral Inhibition using Predicate Abstraction
 In Proceedings of High Performance Computing
, 2002
"... This paper examines the feasibility of predicate abstraction as a method for the reachability analysis of hybrid systems. A hybrid system can be abstracted into a purely discrete system by mapping the continuous state space into an equivalent finite discrete state space using a finite set of Boo ..."
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Cited by 6 (4 self)
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. We also develop a computational technique for reachability analysis and apply it to a biological system of interest (the DeltaNotch lateral inhibition problem).
Modeling and simulation of genetic regulatory systems: A literature review
 JOURNAL OF COMPUTATIONAL BIOLOGY
, 2002
"... In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between ..."
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Cited by 729 (15 self)
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DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical
Markov Random Field Models in Computer Vision
, 1994
"... . A variety of computer vision problems can be optimally posed as Bayesian labeling in which the solution of a problem is defined as the maximum a posteriori (MAP) probability estimate of the true labeling. The posterior probability is usually derived from a prior model and a likelihood model. The l ..."
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Cited by 515 (18 self)
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. A variety of computer vision problems can be optimally posed as Bayesian labeling in which the solution of a problem is defined as the maximum a posteriori (MAP) probability estimate of the true labeling. The posterior probability is usually derived from a prior model and a likelihood model
Results 1  10
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159,352