Results 1  10
of
201
From Private Attitude to Public Opinion: A Dynamic Theory of Social Impact
 Psychological Review
, 1990
"... A computer simulation modeled the change of attitudes in a population resulting from the interactive, reciprocal, and reeursive operation of Latan~'s (198 I) theory of social impact, which specifies principles underlying how individuals are affected by their social environment. Surprisingly, severa ..."
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Cited by 49 (0 self)
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A computer simulation modeled the change of attitudes in a population resulting from the interactive, reciprocal, and reeursive operation of Latan~'s (198 I) theory of social impact, which specifies principles underlying how individuals are affected by their social environment. Surprisingly, several macrolevel phenomena emerged from the simple operation of this microlevei theory, including an incomplete polarization of opinions reaching a stable equilibrium, with coherent minority subgroups managing to exist near the margins of the whole population. Computer simulations, neglected in group dynamics for 20 years, may, as in modern physics, help determine the extent to which grouplevel phenomena result from individuallevel processes. Writing about social phenomena, social scientists have produced empirical generalizations and theoretical analyses of social processes representing differing levels of social reality. Some analyses concern the cognitions, feelings, and behavior of individuals; others deal with small, medium, or large groups, collectivities, and organizations; still others involve such largescale human aggregates and systems as nations, societies, or cul
Nonequilibrium critical phenomena and phase transitions into absorbing states
 ADVANCES IN PHYSICS
, 2000
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Application of the τfunction theory of Painlevé equations to random matrices
 PV, PIII, the LUE, JUE and CUE
, 2002
"... Okamoto has obtained a sequence of τfunctions for the PVI system expressed as a double Wronskian determinant based on a solution of the Gauss hypergeometric equation. Starting with integral solutions of the Gauss hypergeometric equation, we show that the determinant can be reexpressed as multidim ..."
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Cited by 42 (16 self)
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Okamoto has obtained a sequence of τfunctions for the PVI system expressed as a double Wronskian determinant based on a solution of the Gauss hypergeometric equation. Starting with integral solutions of the Gauss hypergeometric equation, we show that the determinant can be reexpressed as multidimensional integrals, and these in turn can be identified with averages over the eigenvalue probability density function for the Jacobi unitary ensemble (JUE), and the Cauchy unitary ensemble (CyUE) (the latter being equivalent to the circular Jacobi unitary ensemble (cJUE)). Hence these averages, which depend on four continuous parameters and the discrete parameter N, can be characterised as the solution of the second order second degree equation satisfied by the Hamiltonian in the PVI theory. We show that the Hamiltonian also satisfies an equation related to the discrete PV equation, thus providing an alternative characterisation in terms of a difference equation. In the case of the cJUE, the spectrum singularity scaled limit is considered, and the evaluation of a certain four parameter average is given in terms of the general PV transcendent in σ form. Applications are given to the evaluation of the spacing distribution for the circular unitary ensemble (CUE) and its scaled counterpart, giving formulas more succinct than those known previously; to expressions for the hard edge gap probability in the scaled Laguerre orthogonal ensemble (LOE) (parameter a a nonnegative
Sparse Signal Recovery Using Markov Random Fields
"... Compressive Sensing (CS) combines sampling and compression into a single subNyquist linear measurement process for sparse and compressible signals. In this paper, we extend the theory of CS to include signals that are concisely represented in terms of a graphical model. In particular, we use Markov ..."
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Cited by 39 (10 self)
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Compressive Sensing (CS) combines sampling and compression into a single subNyquist linear measurement process for sparse and compressible signals. In this paper, we extend the theory of CS to include signals that are concisely represented in terms of a graphical model. In particular, we use Markov Random Fields (MRFs) to represent sparse signals whose nonzero coefficients are clustered. Our new modelbased recovery algorithm, dubbed Lattice Matching Pursuit (LaMP), stably recovers MRFmodeled signals using many fewer measurements and computations than the current stateoftheart algorithms. 1
Towards conformal invariance of 2D lattice models
 Proceedings of the international congress of mathematicians (ICM
"... Abstract. Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, selfavoiding polymers,...This has led to numerous exact (but nonrigorous) predictions of their scaling exponents and dimensions. We will discuss how to pro ..."
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Cited by 37 (4 self)
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Abstract. Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, selfavoiding polymers,...This has led to numerous exact (but nonrigorous) predictions of their scaling exponents and dimensions. We will discuss how to prove the conformal invariance conjectures, especially in relation to SchrammLoewner Evolution.
Rigorous probabilistic analysis of equilibrium crystal shapes
 J. Math. Phys
, 2000
"... Abstract. The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom construct ..."
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Cited by 35 (14 self)
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Abstract. The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom constructions can be derived from the microscopic description provided by the equilibrium statistical mechanics of lattice gases. We focus on the main conceptual issues and describe the central ideas of the existing
Image Processing with Multiscale Stochastic Models
, 1993
"... In this thesis, we develop image processing algorithms and applications for a particular class of multiscale stochastic models. First, we provide background on the model class, including a discussion of its relationship to wavelet transforms and the details of a twosweep algorithm for estimation. A ..."
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Cited by 29 (3 self)
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In this thesis, we develop image processing algorithms and applications for a particular class of multiscale stochastic models. First, we provide background on the model class, including a discussion of its relationship to wavelet transforms and the details of a twosweep algorithm for estimation. A multiscale model for the error process associated with this algorithm is derived. Next, we illustrate how the multiscale models can be used in the context of regularizing illposed inverse problems and demonstrate the substantial computational savings that such an approach offers. Several novel features of the approach are developed including a technique for choosing the optimal resolution at which to recover the object of interest. Next, we show that this class of models contains other widely used classes of statistical models including 1D Markov processes and 2D Markov random fields, and we propose a class of multiscale models for approximately representing Gaussian Markov random fields...
Statistical Mechanics, ThreeDimensionality and NPcompleteness I. Universality of Intractability for the Partition Function of the Ising Model Across NonPlanar Lattices (Extended Abstract)
"... This work provides an exact characterization, across crystal lattices, of the computational tractability frontier for the partition functions of several Ising models. Our results show that beyond planarity computing partition functions is NPcomplete. We provide rigorous solutions to several working ..."
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Cited by 28 (1 self)
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This work provides an exact characterization, across crystal lattices, of the computational tractability frontier for the partition functions of several Ising models. Our results show that beyond planarity computing partition functions is NPcomplete. We provide rigorous solutions to several working conjectures in the statistical mechanics literature, such as the CrossedBonds conjecture, and the impossibility to compute effectively the partition functions for any threedimensional lattice Ising model � these conjectures apply to the Onsager algebraic method, the Fermion operators method, and the combinatorial method based on Pfaffians. The fundamental results of the area, including those of Onsager, Kac, Feynman, Fisher, Kasteleyn, Temperley, Green, Hurst and more recently Barahona: for every Planar crystal lattice the partition functions for the nite sublattices can be computed in polynomialtime, paired with the results of this paper: for every NonPlanar crystal lattice computing the parition functions for the finite sublattices is NPcomplete, provide an exact characterization for several of the most studied Ising models. Our results settle at once, for several models, (1) the 2D nonplanar vs. 2D planar, (2) the nextnearest neighbour
The central limit theorem for local linear s tatistics in classical compact groups and related combinatorial identities
 Ann. Probab
, 2000
"... We discuss CLT for the global and local linear statistics of random matrices from classical compact groups. The main part of our proofs are certain combinatorial identities much in the spirit of works by Kac and Spohn. 1 ..."
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Cited by 27 (2 self)
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We discuss CLT for the global and local linear statistics of random matrices from classical compact groups. The main part of our proofs are certain combinatorial identities much in the spirit of works by Kac and Spohn. 1
Diffraction of Random Tilings: Some Rigorous Results
 J. STAT. PHYS
, 1999
"... The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of stochastic product tilings built from cuboids, and of planar rando ..."
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Cited by 26 (16 self)
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The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of stochastic product tilings built from cuboids, and of planar random tilings based on solvable dimer models, augmented by a brief outline of the diraction from the classical 2D Ising lattice gas. We also give a summary of the measure theoretic approach to mathematical diraction theory which underlies the unique decomposition of the diffraction spectrum into its pure point, singular continuous and absolutely continuous parts.