Spin Glass Theory and Beyond

Mézard, Marc; Parisi, G.; Virasoro, M. A.

doi:10.1142/0271

Cited by 1,920 publications

(2,925 citation statements)

References 14 publications

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“…The bottom sketch shows a rough energy landscape with many energy minima each with a narrow funnel leading to it. magnetic system in which spins are randomly arrayed in a dilute alloy [28][29][30]. The interactions between spins are equally often, at random ferromagnetic (the spins want to point in the same direction) and antiferromagnetic (the spins want to point in opposite directions).…”

Section: Smoothness Roughness and The Topography Of Energy Landscmentioning

confidence: 99%

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Funnels, pathways, and the energy landscape of protein folding: A synthesis

et al. 1995

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The understanding, and even the description of protein folding is impeded by the complexity of the process. Much of this complexity can be described and understood by taking a statistical approach to the energetics of protein conformation, that is, to the energy landscape. The statistical energy landscape approach explains when and why unique behaviors, such as specific folding pathways, occur in some proteins and more generally explains the distinction between folding processes common to all sequences and those peculiar to individual sequences. This approach also gives new, quantitative insights into the interpretation of experiments and simulations of protein folding thermodynamics and kinetics. Specifically, the picture provides simple explanations for folding as a two‐state first‐order phase transition, for the origin of metastable collapsed unfolded states and for the curved Arrhenius plots observed in both laboratory experiments and discrete lattice simulations. The relation of these quantitative ideas to folding pathways, to uniexponential vs. multiexponential behavior in protein folding experiments and to the effect of mutations on folding is also discussed. The success of energy landscape ideas in protein structure prediction is also described. The use of the energy landscape approach for analyzing data is illustrated with a quantitative analysis of some recent simulations, and a qualitative analysis of experiments on the folding of three proteins. The work unifies several previously proposed ideas concerning the mechanism protein folding and delimits the regions of validity of these ideas under different thermodynamic conditions. © 1995 Wiley‐Liss, Inc.

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Section: Smoothness Roughness and The Topography Of Energy Landscmentioning

confidence: 99%

“…Systems with rough energy landscapes also exhibit effective phase transitions [28][29][30]. When the temperature of such a system is lowered, it tends to occupy the lower energy states and at a transition temperature will become trapped in one of them.…”

Section: Smoothness Roughness and The Topography Of Energy Landscmentioning

confidence: 99%

Funnels, pathways, and the energy landscape of protein folding: A synthesis

et al. 1995

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“…This is surprising since they offer a number of potentials to ethologists. Artificial neural networks can show us how small units like nerve cells can exhibit powerful computational abilities when working together (Hopfield & Tank, 1986;Mezard et al, 1987). They also provide understanding about memory and mental representations (McClelland & Rumelhart, 1985), and about mechanisms such as learning (Shanks, 1995) and stimulus control (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Artificial neural networks as models of stimulus control

Ghirlanda

Enquist

1998

Animal Behaviour

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We evaluate the ability of artificial neural network models (multi-layer perceptrons) to predict stimulus-response relationships. A variety of empirical results are considered, such as generalization, peak-shift (supernormality) and stimulus intensity effects. The networks were trained on the same tasks as the animals in the considered experiments. The subsequent generalization tests on the networks showed that the model replicates correctly the empirical results. It is concluded that these models are valuable tools in the study of animal behaviour.

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“…where we have used (28) along with normalization in the first, (39) in the second, and (39) and (40) in the last step. This proves the assertion of Proposition 3.…”

Section: Proof (Of Proposition 3)mentioning

confidence: 99%

An asymptotic maximum principle for essentially linear evolution models

Baake

Bovier

et al. 2004

J. Math. Biol.

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Abstract. Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained through a lowdimensional maximum principle in the limit N → ∞ (where N is the number of types). In order to extend this variational principle to a larger class of models, we consider here a family of reversible N × N matrices and identify conditions under which the high-dimensional Rayleigh-Ritz variational problem may be reduced to a low-dimensional one that yields the leading eigenvalue up to an error term of order 1/N . For a large class of mutation-selection models, this implies estimates for the mean fitness, as well as a concentration result for the ancestral distribution of types.

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Spin Glass Theory and Beyond

Cited by 1,920 publications

References 14 publications

Funnels, pathways, and the energy landscape of protein folding: A synthesis

Funnels, pathways, and the energy landscape of protein folding: A synthesis

Artificial neural networks as models of stimulus control

An asymptotic maximum principle for essentially linear evolution models

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