Results 1  10
of
39
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
Abstract

Cited by 585 (13 self)
 Add to MetaCart
(Show Context)
Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree, but only approximate when the factor graph has cycles. We show that BP fixed points correspond to the stationary points of the Bethe approximation of the free energy for a factor graph. We explain how to obtain regionbased free energy approximations that improve the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms. We emphasize the conditions a free energy approximation must satisfy in order to be a “valid ” or “maxentnormal ” approximation. We describe the relationship between four different methods that can be used to generate valid approximations: the “Bethe method, ” the “junction graph method, ” the “cluster variation method, ” and the “region graph method.” Finally, we explain how to tell whether a regionbased approximation, and its corresponding GBP algorithm, is likely to be accurate, and describe empirical results showing that GBP can significantly outperform BP.
MeanField Equations for Spin Models with Orthogonal Interaction Matrices
 Matrices, J. Phys. A (Math. Gen
, 1995
"... We study the metastable states in Ising spin models with orthogonal interaction matrices. We focus on three realizations of this model, the random case and two nonrandom cases, i.e. the fullyfrustrated model on an infinite dimensional hypercube and the socalled sinemodel. We use the meanfield ( ..."
Abstract

Cited by 18 (4 self)
 Add to MetaCart
We study the metastable states in Ising spin models with orthogonal interaction matrices. We focus on three realizations of this model, the random case and two nonrandom cases, i.e. the fullyfrustrated model on an infinite dimensional hypercube and the socalled sinemodel. We use the meanfield (or tap) equations which we derive by resuming the hightemperature expansion of the Gibbs free energy. In some special nonrandom cases, we can find the absolute minimum of the free energy. For the random case we compute the average number of solutions to the tap equations. We find that the configurational entropy (or complexity) is extensive in the range T RSB ! T ! TM . Finally we present an apparently unrelated replica calculation which reproduces the analytical expression for the total number of tap solutions. condmat/9503009 potters@roma1.infn.it The aim of this paper is to study the mean field equations (the tap equations) for the local magnetization for the fully frustrated Ising...
Zerotemperature dynamics of ±J spin glasses and related models
 Commun. Math. Phys
, 2000
"... We study zerotemperature, stochastic Ising models σt on Zd with (disordered) nearestneighbor couplings independently chosen from a distribution µ on R and an initial spin configuration chosen uniformly at random. Given d, call µ type I (resp., type F) if, for every x in Zd, σt x flips infinitely ( ..."
Abstract

Cited by 14 (11 self)
 Add to MetaCart
We study zerotemperature, stochastic Ising models σt on Zd with (disordered) nearestneighbor couplings independently chosen from a distribution µ on R and an initial spin configuration chosen uniformly at random. Given d, call µ type I (resp., type F) if, for every x in Zd, σt x flips infinitely (resp., only finitely) many times as t → ∞ (with probability one) — or else mixed type M. Models of type I and M exhibit a zerotemperature version of “local nonequilibration”. For d = 1, all types occur and the type of any µ is easy to determine. The main result of this paper is a proof that for d = 2, ±J models (where µ = αδJ +(1 −α)δ−J) are type M, unlike homogeneous models (type I) or continuous (finite mean) µ’s (type F). We also prove that all other noncontinuous disordered systems are type M for any d ≥ 2. The ±J proof is noteworthy in that it is much less “local ” than the other (simpler) proof. Homogeneous and ±J models for d ≥ 3 remain an open problem. KEY WORDS: spin glass; nonequilibrium dynamics; deep quench; mixed type. I. INTRODUCTION AND RESULTS
Blending Heuristics with a PopulationBased Approach: A "Memetic" Algorithm for the Traveling Salesman Problem
 REPORT 9212, UNIVERSIDAD NACIONAL DE LA PLATA, C.C. 75, 1900 LA PLATA
, 1994
"... Very recently many researchers, with backgrounds in parallel computing, started to develop hybrids of traditional genetic algorithms. The main departure from standard genetic algorithms is that these new methods incorporate specific heuristics for the problem at hand (drawing on a tradition which ha ..."
Abstract

Cited by 10 (4 self)
 Add to MetaCart
Very recently many researchers, with backgrounds in parallel computing, started to develop hybrids of traditional genetic algorithms. The main departure from standard genetic algorithms is that these new methods incorporate specific heuristics for the problem at hand (drawing on a tradition which has roots outside the genetic framework) and which we apply within a stochastic game that exerts a selective pressure. The heuristics are used for periods of individual optimization, that is when agents do not interact. New computational results for the Traveling Salesman Problem will be presented in this paper. The approach is prepared to include Tabu Search techniques, introducing a new crossover operator (which is called Random Respectful Corner Recombination) and a special pair of a topology and set of rules for the interaction between agents. The approach has a natural parallelism and a feature called superlinear speedup will also be discussed.
The Global Minimum of Energy Is Not Always a Sum of Local Minima  a Note on Frustration
, 1997
"... . A classical lattice gas model with translationinvariant finite range competing interactions, for which there does not exist an equivalent translationinvariant finite range nonfrustrated potential, is constructed. The construction uses the structure of nonperiodic ground state configurations of t ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
. A classical lattice gas model with translationinvariant finite range competing interactions, for which there does not exist an equivalent translationinvariant finite range nonfrustrated potential, is constructed. The construction uses the structure of nonperiodic ground state configurations of the model. In fact, the model does not have any periodic ground state configurations. However, its ground state  a translationinvariant probability measure supported by ground state configurations  is unique. KEY WORDS: Frustration; mpotential; nonperiodic ground states; tilings. 1 Introduction Low temperature behavior of systems of many interacting particles results from the competition between energy and entropy, i.e., the minimization of the free energy. At zero temperature this reduces to the minimization of the energy density. Configurations of a system which minimize its energy density are called ground state configurations. One of the important problems of statistical mechanics ...
Crossover between discrete and continuous protein structure space: insights into automatic classification and networks of protein structures
 PloS Comput. Biol
, 2009
"... Structural classifications of proteins assume the existence of the fold, which is an intrinsic equivalence class of protein domains. Here, we test in which conditions such an equivalence class is compatible with objective similarity measures. We base our analysis on the transitive property of the eq ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
(Show Context)
Structural classifications of proteins assume the existence of the fold, which is an intrinsic equivalence class of protein domains. Here, we test in which conditions such an equivalence class is compatible with objective similarity measures. We base our analysis on the transitive property of the equivalence relationship, requiring that similarity of A with B and B with C implies that A and C are also similar. Divergent gene evolution leads us to expect that the transitive property should approximately hold. However, if protein domains are a combination of recurrent short polypeptide fragments, as proposed by several authors, then similarity of partial fragments may violate the transitive property, favouring the continuous view of the protein structure space. We propose a measure to quantify the violations of the transitive property when a clustering algorithm joins elements into clusters, and we find out that such violations present a well defined and detectable crossover point, from an approximately transitive regime at high structure similarity to a regime with large transitivity violations and large differences in length at low similarity. We argue that protein structure space is discrete and hierarchic classification is justified up to this crossover point, whereas at lower similarities the structure space is continuous and it should be represented as a network. We have tested the qualitative behaviour of this measure, varying all the choices involved in the automatic classification procedure, i.e., domain decomposition, alignment algorithm, similarity score, and clustering algorithm, and we have found out that this behaviour is quite robust. The final classification depends on the chosen
Combining Local Search with CoEvolution in a Remarkably Simple Way
 in Proceedings of the 2000 Congress on Evolutionary Computation, p. 1576, IEEE
, 2000
"... We explore a new generalpurpose heuristic for finding highquality solutions to hard optimization problems. The method, called extremal optimization, is inspired by "selforganized criticality", a concept introduced to describe emergent complexity in physical systems. In contrast to genet ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
We explore a new generalpurpose heuristic for finding highquality solutions to hard optimization problems. The method, called extremal optimization, is inspired by "selforganized criticality", a concept introduced to describe emergent complexity in physical systems. In contrast to genetic algorithms, which operate on an entire "genepool" of possible solutions, extremal optimization successively replaces extremely undesirable elements of a single suboptimal solution with new, random ones. Large fluctuations, or "avalanches", ensue that efficiently explore many local optima. Drawing upon models used to simulate farfromequilibrium dynamics, extremal optimization complements heuristics inspired by equilibrium statistical physics, such as simulated annealing. With only one adjustable parameter, its performance has proved competitive with more elaborate methods, especially near phase transitions. Phase transitions are found in many combinatorial optimization problems, and have been co...
Frustration vs. Clusterability in TwoMode Signed Networks (Signed Bipartite Graphs)
, 2010
"... Abstract. Mrvar and Doreian recently defined a notion of bipartite clustering in bipartite signed graphs that gives a measure of imbalance of the signed graph, different from previous measures (the “frustration index ” or “line index of balance”, l, and Davis’s clusterability). A biclustering of a b ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
Abstract. Mrvar and Doreian recently defined a notion of bipartite clustering in bipartite signed graphs that gives a measure of imbalance of the signed graph, different from previous measures (the “frustration index ” or “line index of balance”, l, and Davis’s clusterability). A biclustering of a bipartite signed graph is a pair (π1, π2) of partitions of the two color classes; the sets of the partitions are called clusters. The majority biclusterability index M(k1, k2) is the minimum number of edges that are inconsistent, in a certain definition, with a biclustering, over all biclusterings with π1  = k1 and π2  = k2. Theorems: M(1, k2) ≥ l, while M(k1, k2) ≤ l if k1, k2 ≥ 2. For K2,n with n ≥ 2, M(2, 2) = l in about 1/3 of all signatures. If n> 2, then for every signature of K2,n there exists a biclustering with π1  = π2  = 2 such that M(π1, π2) = l. There are many open questions. Keywords. Twomode signed network, signed bipartite graph, frustration index, majority clusterability, bipartite clusterability, biclustering. Mathematics Subject Classifications (2010): Primary 05C22; Secondary 91D30. 1
Models and Search Strategies for Applied Molecular Evolution
 Annual Reports in Combinatorial Chemistry and Molecular Diversity
, 1997
"... Introduction In just a few years, molecular diversity techniques have revolutionized pharmaceutical design and experimental methods for studying receptor binding, consensus sequences, genetic regu latory mechanisms, and many other issues in biochemistry and chemistry [30, 69 71, 78, 79]. Because o ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Introduction In just a few years, molecular diversity techniques have revolutionized pharmaceutical design and experimental methods for studying receptor binding, consensus sequences, genetic regu latory mechanisms, and many other issues in biochemistry and chemistry [30, 69 71, 78, 79]. Because of the enormous libraries of ligands that can be used and the rapidity of the techniques, methods of applied molecular evolution such as SELEX and phage display have become particularly popular [30, 78, 86,126,127, 142,151]. These methods have been enormously successful, yet the theoretical work developed for them so far is quite limited. The success of these methods is not trivial: the huge number of sequences being searched through, the low concentrations of individual species, and the noise and biases inherent in the techniques would seem to make these experiments very difficult. Understanding why they work so well, and showing how they can perform better and for more complex molecular se