Results 11  20
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22,590
The Geometry of Dissipative Evolution Equations: The Porous Medium Equation
"... We show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural. In order to convince the reader that it is mathematically natural, we show the time asymptotic behavior can be easily understood in this framework. We use the intuition and the ..."
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Cited by 405 (11 self)
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We show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural. In order to convince the reader that it is mathematically natural, we show the time asymptotic behavior can be easily understood in this framework. We use the intuition
Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex
 J. Neurosci
, 1982
"... The development of stimulus selectivity in the primary sensory cortex of higher vertebrates is considered in a general mathematical framework. A synaptic evolution scheme of a new kind is proposed in which incoming patterns rather than converging afferents compete. The change in the efficacy of a gi ..."
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Cited by 432 (20 self)
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The development of stimulus selectivity in the primary sensory cortex of higher vertebrates is considered in a general mathematical framework. A synaptic evolution scheme of a new kind is proposed in which incoming patterns rather than converging afferents compete. The change in the efficacy of a
Statistical shape influence in geodesic active contours
 In Proc. 2000 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), Hilton Head, SC
, 2000
"... A novel method of incorporating shape information into the image segmentation process is presented. We introduce a representation for deformable shapes and define a probability distribution over the variances of a set of training shapes. The segmentation process embeds an initial curve as the zero l ..."
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Cited by 396 (4 self)
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A novel method of incorporating shape information into the image segmentation process is presented. We introduce a representation for deformable shapes and define a probability distribution over the variances of a set of training shapes. The segmentation process embeds an initial curve as the zero
Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation
, 1991
"... This paper addresses the problem of parametric representation and estimation of complex planar curves in 2D, surfaces in 3D and nonplanar space curves in 3D. Curves and surfaces can be defined either parametrically or implicitly, and we use the latter representation. A planar curve is the set o ..."
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Cited by 314 (2 self)
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This paper addresses the problem of parametric representation and estimation of complex planar curves in 2D, surfaces in 3D and nonplanar space curves in 3D. Curves and surfaces can be defined either parametrically or implicitly, and we use the latter representation. A planar curve is the set
Approximate accelerated stochastic simulation of chemically reacting systems
 J. Chem. Phys
, 2001
"... The stochastic simulation algorithm ͑SSA͒ is an essentially exact procedure for numerically simulating the time evolution of a wellstirred chemically reacting system. Despite recent major improvements in the efficiency of the SSA, its drawback remains the great amount of computer time that is ofte ..."
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Cited by 346 (6 self)
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The stochastic simulation algorithm ͑SSA͒ is an essentially exact procedure for numerically simulating the time evolution of a wellstirred chemically reacting system. Despite recent major improvements in the efficiency of the SSA, its drawback remains the great amount of computer time
Unifying Evolutionary Dynamics
, 2002
"... Darwinian evolution is based on three fundamental principles, reproduction, mutation and selection, which describe how populations change over time and how new forms evolve out of old ones. There are numerous mathematical descriptions of the resulting evolutionary dynamics. In this paper, we show th ..."
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Cited by 315 (33 self)
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Volterra equation of ecology and the quasispecies equation of molecular evolution.
The Variational Formulation of the FokkerPlanck Equation
 SIAM J. Math. Anal
, 1999
"... The FokkerPlanck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of timedependent systems in which randomness plays a role. In this paper, ..."
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Cited by 282 (22 self)
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The FokkerPlanck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of timedependent systems in which randomness plays a role. In this paper
The radiance lighting simulation and rendering system
 In Proceedings of SIGGRAPH 94, ACM SIGGRAPH / ACM
, 1994
"... This paper describes a physicallybased rendering system tailored to the demands of lighting design and architecture. The simulation uses a lightbackwards raytracing method with extensions to efficiently solve the rendering equation under most conditions. This includes specular, diffuse and direct ..."
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Cited by 298 (8 self)
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This paper describes a physicallybased rendering system tailored to the demands of lighting design and architecture. The simulation uses a lightbackwards raytracing method with extensions to efficiently solve the rendering equation under most conditions. This includes specular, diffuse
Quantized Feedback Stabilization of Linear Systems
 IEEE Trans. Automat. Control
, 2000
"... This paper addresses feedback stabilization problems for linear timeinvariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation that ..."
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Cited by 293 (27 self)
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This paper addresses feedback stabilization problems for linear timeinvariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation
Empirical equations for some soil hydraulic properties
 Water Resour. Res
, 1978
"... The soil moisture characteristic may be modeled as a power curve combined with a short parabolic section near saturation to represent gradual air entry. This twopart functionmtogether with a power function relating soil moisture and hydraulic conductivitymis used to derive a formula for the wetting ..."
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Cited by 234 (0 self)
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The soil moisture characteristic may be modeled as a power curve combined with a short parabolic section near saturation to represent gradual air entry. This twopart functionmtogether with a power function relating soil moisture and hydraulic conductivitymis used to derive a formula
Results 11  20
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22,590