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Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
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Cited by 2083 (10 self)
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Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 548 (13 self)
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For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has run for M steps, with M sufficiently large, the distribution governing the state of the chain approximates the desired distribution. Unfortunately it can be difficult to determine how large M needs to be. We describe a simple variant of this method that determines on its own when to stop, and that outputs samples in exact accordance with the desired distribution. The method uses couplings, which have also played a role in other sampling schemes; however, rather than running the coupled chains from the present into the future, one runs from a distant point in the past up until the present, where the distance into the past that one needs to go is determined during the running of the al...
On the statistical mechanics of an
, 2003
"... Different descriptions of an adiabatic process based on statistical thermodynamics and statistical mechanics are discussed. Equality of the socalled adiabatic and isolated susceptibilities and its generalization as well as adiabatic invariants are essentially used to describe adiabatic processes ..."
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Different descriptions of an adiabatic process based on statistical thermodynamics and statistical mechanics are discussed. Equality of the socalled adiabatic and isolated susceptibilities and its generalization as well as adiabatic invariants are essentially used to describe adiabatic processes
On the statistical analysis of dirty pictures
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY B
, 1986
"... ..."
Statistical Mechanics
"... While kinetic theory, as we discussed in the preceding chapter, gives a powerful description of some statistical features of matter, other features are outside its realm and must be treated using the more sophisticated tools of statistical mechanics. Examples are: (i) Correlations: Kinetic theory’s ..."
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While kinetic theory, as we discussed in the preceding chapter, gives a powerful description of some statistical features of matter, other features are outside its realm and must be treated using the more sophisticated tools of statistical mechanics. Examples are: (i) Correlations: Kinetic theory’s
Statistical Mechanics
"... While kinetic theory, as we discussed in the preceding chapter, gives a powerful description of some statistical features of matter, other features are outside its realm and must be treated using the more sophisticated tools of statistical mechanics. Examples are: (i) Correlations: Kinetic theory’s ..."
Abstract
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While kinetic theory, as we discussed in the preceding chapter, gives a powerful description of some statistical features of matter, other features are outside its realm and must be treated using the more sophisticated tools of statistical mechanics. Examples are: (i) Correlations: Kinetic theory’s
Relations between the statistics of natural images and the response properties of cortical cells
 J. Opt. Soc. Am. A
, 1987
"... The relative efficiency of any particular imagecoding scheme should be defined only in relation to the class of images that the code is likely to encounter. To understand the representation of images by the mammalian visual system, it might therefore be useful to consider the statistics of images f ..."
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Cited by 820 (17 self)
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The relative efficiency of any particular imagecoding scheme should be defined only in relation to the class of images that the code is likely to encounter. To understand the representation of images by the mammalian visual system, it might therefore be useful to consider the statistics of images
High confidence visual recognition of persons by a test of statistical independence
 IEEE Trans. on Pattern Analysis and Machine Intelligence
, 1993
"... Abstruct A method for rapid visual recognition of personal identity is described, based on the failure of a statistical test of independence. The most unique phenotypic feature visible in a person’s face is the detailed texture of each eye’s iris: An estimate of its statistical complexity in a samp ..."
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Cited by 596 (8 self)
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Abstruct A method for rapid visual recognition of personal identity is described, based on the failure of a statistical test of independence. The most unique phenotypic feature visible in a person’s face is the detailed texture of each eye’s iris: An estimate of its statistical complexity in a
Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics
 J. Geophys. Res
, 1994
"... . A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The ..."
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Cited by 782 (22 self)
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. A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter
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