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71
Markov Chain Monte Carlo Estimation of Exponential Random Graph Models
 Journal of Social Structure
, 2002
"... This paper is about estimating the parameters of the exponential random graph model, also known as the p # model, using frequentist Markov chain Monte Carlo (MCMC) methods. The exponential random graph model is simulated using Gibbs or MetropolisHastings sampling. The estimation procedures consider ..."
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Cited by 105 (15 self)
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This paper is about estimating the parameters of the exponential random graph model, also known as the p # model, using frequentist Markov chain Monte Carlo (MCMC) methods. The exponential random graph model is simulated using Gibbs or MetropolisHastings sampling. The estimation procedures considered are based on the RobbinsMonro algorithm for approximating a solution to the likelihood equation.
New specifications for exponential random graph models
, 2004
"... The most promising class of statistical models for expressing structural properties of social networks observed at one moment in time, is the class of Exponential Random Graph Models (ERGMs), also known as p ∗ models. The strong point of these models is that they can represent a variety of structura ..."
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Cited by 81 (16 self)
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The most promising class of statistical models for expressing structural properties of social networks observed at one moment in time, is the class of Exponential Random Graph Models (ERGMs), also known as p ∗ models. The strong point of these models is that they can represent a variety of structural tendencies, such as transitivity, that define complicated dependence patterns not easily modeled by more basic probability models. Recently, MCMC algorithms have been developed which produce approximate Maximum Likelihood estimators. Applying these models in their traditional specification to observed network data often has led to problems, however, which can be traced back to the fact that important parts of the parameter space correspond to nearly degenerate distributions, which may lead to convergence problems of estimation algorithms, and a poor fit to empirical data. This paper proposes new specifications of Exponential Random Graph Models. These specifications represent structural properties such as transitivity and heterogeneity of degrees by more complicated graph statistics than the traditional star and triangle counts. Three kinds of statistic are proposed: geometrically weighted degree distributions, alternating ktriangles, and alternating independent twopaths. Examples are presented both of modeling graphs and digraphs, in which the new specifications lead to much better results than the earlier existing specifications of the ERGM. It is concluded that the new specifications increase the range and applicability of the ERGM as a tool for the statistical analysis of social networks.
TOUCHSTONE II: A new approach to ab initio protein structure prediction
 Biophys. J
, 2003
"... ABSTRACT We have developed a new combined approach for ab initio protein structure prediction. The protein conformation is described as a lattice chain connecting Ca atoms, with attached Cb atoms and sidechain centers of mass. The model force field includes various shortrange and longrange knowle ..."
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Cited by 40 (13 self)
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ABSTRACT We have developed a new combined approach for ab initio protein structure prediction. The protein conformation is described as a lattice chain connecting Ca atoms, with attached Cb atoms and sidechain centers of mass. The model force field includes various shortrange and longrange knowledgebased potentials derived from a statistical analysis of the regularities of protein structures. The combination of these energy terms is optimized through the maximization of correlation for 30 3 60,000 decoys between the root mean square deviation (RMSD) to native and energies, as well as the energy gap between native and the decoy ensemble. To accelerate the conformational search, a newly developed parallel hyperbolic sampling algorithm with a composite movement set is used in the Monte Carlo simulation processes. We exploit this strategy to successfully fold 41/100 small proteins (36; 120 residues) with predicted structures having a RMSD from native below 6.5 A ˚ in the top five cluster centroids. To fold largersize proteins as well as to improve the folding yield of small proteins, we incorporate into the basic force field sidechain contact predictions from our threading program PROSPECTOR where homologous proteins were excluded from the data base. With these threadingbased restraints, the program can fold 83/125 test proteins (36; 174 residues) with structures having a RMSD to native below 6.5 A ˚ in the top five cluster centroids. This shows the significant improvement of folding by using predicted tertiary restraints, especially when the accuracy of sidechain contact prediction is [20%. For native fold selection, we introduce quantities dependent on the cluster density and the combination of energy and free energy, which show a higher discriminative power to select the native structure than the previously used cluster energy or cluster size, and which can be used in native structure identification in blind simulations. These procedures are readily automated and are being implemented on a genomic scale.
Models of the Small World  A Review
"... It is believed that almost any pair of people in the world can be connected to one another by a short chain of intermediate acquaintances, of typical length about six. This phenomenon, colloquially referred to as the "six degrees of separation," has been the subject of considerable recent interest w ..."
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Cited by 34 (0 self)
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It is believed that almost any pair of people in the world can be connected to one another by a short chain of intermediate acquaintances, of typical length about six. This phenomenon, colloquially referred to as the "six degrees of separation," has been the subject of considerable recent interest within the physics community. This paper provides a short review of the topic.
A Framework for ThreeDimensional Simulation of Morphogenesis
, 2004
"... We present COMPUCELL3D, a software framework for threedimensional simulation of morphogenesis in different organisms. COMPUCELL3D employs biologically relevant models for cell clustering, growth, and interaction with chemical fields. COMPUCELL3D uses design patterns for speed, efficient memory m ..."
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Cited by 19 (10 self)
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We present COMPUCELL3D, a software framework for threedimensional simulation of morphogenesis in different organisms. COMPUCELL3D employs biologically relevant models for cell clustering, growth, and interaction with chemical fields. COMPUCELL3D uses design patterns for speed, efficient memory management, extensibility, and flexibility, permitting the simulation of various organisms. We verify COMPUCELL3D by building a model of growth and skeletal pattern formation in the avian (chicken) limb bud. Binaries and source code are available, along with documentation and input files for sample simulations, at http://www.nd.edu/lcls/compucell.
Gibbs sampling, exponential families and orthogonal polynomials
 Statistical Sciences
, 2008
"... Abstract. We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their conjugate priors. In each case, the transition operator is explicitly diagonalizable with classical ort ..."
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Cited by 19 (6 self)
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Abstract. We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their conjugate priors. In each case, the transition operator is explicitly diagonalizable with classical orthogonal polynomials as eigenfunctions. Key words and phrases: Gibbs sampler, running time analyses, exponential families, conjugate priors, location families, orthogonal polynomials, singular value decomposition. 1.
Markov Chain Monte Carlo for Statistical Inference
 University of Washington, Center for
, 2000
"... These notes provide an introduction to Markov chain Monte Carlo methods that are useful in both Bayesian and frequent... ..."
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Cited by 18 (0 self)
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These notes provide an introduction to Markov chain Monte Carlo methods that are useful in both Bayesian and frequent...
THE MARKOV CHAIN MONTE CARLO REVOLUTION
"... Abstract. The use of simulation for highdimensional intractable computations has revolutionized applied mathematics. Designing, improving and understanding the new tools leads to (and leans on) fascinating mathematics, from representation theory through microlocal analysis. 1. ..."
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Cited by 18 (1 self)
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Abstract. The use of simulation for highdimensional intractable computations has revolutionized applied mathematics. Designing, improving and understanding the new tools leads to (and leans on) fascinating mathematics, from representation theory through microlocal analysis. 1.
Experimental design in systems biology, based on parameter sensitivity analysis using a Monte Carlo method: A case study for the TNFαmediated NFκB signal transduction pathway
 SIMULATION
, 2003
"... Mathematical modeling and dynamic simulation of signal transduction pathways is a central theme in systems biology and is increasingly attracting attention in the postgenomic era. The estimation of model parameters from experimental data remains a bottleneck for a major breakthrough in this area. Th ..."
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Cited by 15 (0 self)
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Mathematical modeling and dynamic simulation of signal transduction pathways is a central theme in systems biology and is increasingly attracting attention in the postgenomic era. The estimation of model parameters from experimental data remains a bottleneck for a major breakthrough in this area. This study’s aim is to introduce a new strategy for experimental design based on parameter sensitivity analysis. The approach identifies key parameters/variables in a signal transduction pathway model and can thereby provide experimental biologists with guidance on which proteins to consider for measurement. The article focuses on applying this approach to the TNFαmediated NFκB pathway, which plays an important role in immunity and inflammation and in the control of cell proliferation, differentiation, and apoptosis. A mathematical model of this pathway is proposed, and the sensitivity analysis of model parameters is illustrated for this model by employing the Monte Carlo method over a broad range of parameter values.
Glassy dynamics of kinetically constrained models
 Adv. Phys
"... We review the use of kinetically constrained models (KCMs) for the study of dynamics in glassy systems. The characteristic feature of KCMs is that they have trivial, often noninteracting, equilibrium behaviour but interesting slow dynamics due to restrictions on the allowed transitions between conf ..."
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Cited by 15 (2 self)
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We review the use of kinetically constrained models (KCMs) for the study of dynamics in glassy systems. The characteristic feature of KCMs is that they have trivial, often noninteracting, equilibrium behaviour but interesting slow dynamics due to restrictions on the allowed transitions between configurations. The basic question which KCMs ask is therefore how much glassy physics can be understood without an underlying ‘equilibrium glass transition’. After a brief review of glassy phenomenology, we describe the main model classes, which include spinfacilitated (Ising) models, constrained lattice gases, models inspired by cellular structures such as soap froths, models obtained via mappings from interacting systems without constraints, and finally related models such as urn, oscillator, tiling and needle models. We then describe the broad range of techniques that have been applied to KCMs, including exact solutions, adiabatic approximations, projection and modecoupling techniques, diagrammatic approaches and mappings to quantum systems or effective models. Finally, we give a survey of the known