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Order of Magnitude Reasoning in Qualitative Differential Equations
, 1987
"... We present a theory that combines order of magnitude reasoning with envisionment of qualitative differential equations. Such a theory can be used to reason qualitatively about dynamical systems containing parameters of widely varying magnitudes. We present an a mathematical analysis of envisionment ..."
Abstract

Cited by 17 (2 self)
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We present a theory that combines order of magnitude reasoning with envisionment of qualitative differential equations. Such a theory can be used to reason qualitatively about dynamical systems containing parameters of widely varying magnitudes. We present an a mathematical analysis of envisionment
Closed Form Solution of Qualitative Differential Equations
"... Numerical simulation, phasespace analysis, and analytic techniques are three methods used to solve quantitative differential equations. Most work in Qualitative Reasoning has dealt with analogs of the first two techniques, producing capabilities applicable to a wide range of systems. Although poten ..."
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Numerical simulation, phasespace analysis, and analytic techniques are three methods used to solve quantitative differential equations. Most work in Qualitative Reasoning has dealt with analogs of the first two techniques, producing capabilities applicable to a wide range of systems. Although
QPC: A Compiler from Physical Models into Qualitative Differential Equations
 In Proceedings of the Eighth National Conference on Artificial Intelligence
, 1990
"... Qualitative reasoning can, and should, be decomposed into a modelbuilding task, which creates a qualitative differential equation (QDE) as a model of a physical situation, and a qualitative simulation task, which starts with a QDE, and predicts the possible behaviors following from the model. In su ..."
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Cited by 68 (17 self)
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Qualitative reasoning can, and should, be decomposed into a modelbuilding task, which creates a qualitative differential equation (QDE) as a model of a physical situation, and a qualitative simulation task, which starts with a QDE, and predicts the possible behaviors following from the model
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 719 (14 self)
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, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rulebased formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems.
2001 Kluwer Academic Publishers. Printed in the Netherlands. Integration of case studies on Global Change by means of qualitative differential equations
, 2000
"... We present a novel methodology to integrate qualitative knowledge from different case studies on Global Change related issues into a single framework. The method is based on the concept of qualitative differential equations (QDEs) which represents a mathematically welldefined approach to investigat ..."
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We present a novel methodology to integrate qualitative knowledge from different case studies on Global Change related issues into a single framework. The method is based on the concept of qualitative differential equations (QDEs) which represents a mathematically welldefined approach
USER’S GUIDE TO VISCOSITY SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
, 1992
"... The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking argume ..."
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Cited by 1372 (16 self)
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The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking
An iterative method for the solution of the eigenvalue problem of linear differential and integral
, 1950
"... The present investigation designs a systematic method for finding the latent roots and the principal axes of a matrix, without reducing the order of the matrix. It is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the ..."
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Cited by 526 (0 self)
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the process of "minimized iterations". Moreover, the method leads to a well convergent successive approximation procedure by which the solution of integral equations of the Fredholm type and the solution of the eigenvalue problem of linear differential and integral operators may be accomplished. I.
New results in linear filtering and prediction theory
 TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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Cited by 581 (0 self)
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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary
Impulses and Physiological States in Theoretical Models of Nerve Membrane
 Biophysical Journal
, 1961
"... ABSTRACT Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of nonlinear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model " has two variables of state, representing excitabi ..."
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Cited by 494 (0 self)
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ABSTRACT Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of nonlinear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model " has two variables of state, representing
Results 1  10
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1,444,877