Results 1  10
of
142
Funnels, Pathways and the Energy Landscape of Protein Folding: A Synthesis
 PROTEINS
, 1994
"... 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 lan ..."
Abstract

Cited by 154 (11 self)
 Add to MetaCart
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 twostate firstorder 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.
Landscapes and Their Correlation Functions
, 1996
"... Fitness landscapes are an important concept in molecular evolution. Many important examples of landscapes in physics and combinatorial optimation, which are widely used as model landscapes in simulations of molecular evolution and adaptation, are "elementary", i.e., they are (up to an addi ..."
Abstract

Cited by 105 (16 self)
 Add to MetaCart
Fitness landscapes are an important concept in molecular evolution. Many important examples of landscapes in physics and combinatorial optimation, which are widely used as model landscapes in simulations of molecular evolution and adaptation, are "elementary", i.e., they are (up to an additive constant) eigenfuctions of a graph Laplacian. It is shown that elementary landscapes are characterized by their correlation functions. The correlation functions are in turn uniquely determined by the geometry of the underlying configuration space and the nearest neighbor correlation of the elementary landscape. Two types of correlation functions are investigated here: the correlation of a time series sampled along a random walk on the landscape and the correlation function with respect to a partition of the set of all vertex pairs.
Fitness landscapes and evolvability
 Evolutionary Computation
, 2001
"... In this paper, we develop techniques based on evolvability statistics of the tness landscape surrounding sampled solutions. Averaging the measures over a sample of equal tness solutions allows us to build up tness evolvability portraits of the tness landscape, which we show can be used to compare ..."
Abstract

Cited by 52 (2 self)
 Add to MetaCart
In this paper, we develop techniques based on evolvability statistics of the tness landscape surrounding sampled solutions. Averaging the measures over a sample of equal tness solutions allows us to build up tness evolvability portraits of the tness landscape, which we show can be used to compare both the ruggedness and neutrality in a set of tunably rugged and tunably neutral landscapes. We further show that the techniques can be used with solution samples collected through both random sampling of the landscapes and online sampling during optimization. Finally, we apply the techniques to two real evolutionary electronics search spaces and highlight differences between the two search spaces, comparing with the time taken to nd good solutions through search.
The power of quantum systems on a line
, 2009
"... We study the computational strength of quantum particles (each of finite dimensionality) arranged on a line. First, we prove that it is possible to perform universal adiabatic quantum computation using a onedimensional quantum system (with 9 states per particle). This might have practical implicati ..."
Abstract

Cited by 46 (7 self)
 Add to MetaCart
We study the computational strength of quantum particles (each of finite dimensionality) arranged on a line. First, we prove that it is possible to perform universal adiabatic quantum computation using a onedimensional quantum system (with 9 states per particle). This might have practical implications for experimentalists interested in constructing an adiabatic quantum computer. Building on the same construction, but with some additional technical effort and 12 states per particle, we show that the problem of approximating the ground state energy of a system composed of a line of quantum particles is QMAcomplete; QMA is a quantum analogue of NP. This is in striking contrast to the fact that the analogous classical problem, namely, one dimensional MAX2SAT with nearest neighbor constraints, is in P. The proof of the QMAcompleteness result requires an additional idea beyond the usual techniques in the area: Not all illegal configurations can be ruled out by local checks, so instead we rule out such illegal configurations because they would, in the future, evolve into a state which can be seen locally to be illegal. Since it is unlikely that quantum computers can efficiently solve QMA problems, our construction gives a onedimensional system which takes an exponential time to relax to its ground state at any temperature. This makes it a candidate for a onedimensional spin glass.
Combinatorial Landscapes
 SIAM REVIEW
, 2002
"... Fitness landscapes have proven to be a valuable concept in evolutionary biology, combinatorial optimization, and the physics of disordered systems. A fitness landscape is a mapping from a configuration space into the real numbers. The configuration space is equipped with some notion of adjacency, ne ..."
Abstract

Cited by 36 (2 self)
 Add to MetaCart
Fitness landscapes have proven to be a valuable concept in evolutionary biology, combinatorial optimization, and the physics of disordered systems. A fitness landscape is a mapping from a configuration space into the real numbers. The configuration space is equipped with some notion of adjacency, nearness, distance or accessibility. Landscape theory has emerged as an attempt to devise suitable mathematical structures for describing the "static" properties of landscapes as well as their influence on the dynamics of adaptation. In this review we focus on the connections of landscape theory with algebraic combinatorics and random graph theory, where exact results are available.
The algebraic theory of recombination spaces
, 2000
"... A new mathematical representation is proposed for the configuration space structure induced by recombination which we called "Pstructure". It consists of a mapping of pairs of objects to the power set of all objects in the search space. The mapping assigns to each pair of parental "g ..."
Abstract

Cited by 35 (16 self)
 Add to MetaCart
A new mathematical representation is proposed for the configuration space structure induced by recombination which we called "Pstructure". It consists of a mapping of pairs of objects to the power set of all objects in the search space. The mapping assigns to each pair of parental "genotypes" the set of all recombinant genotypes obtainable from the parental ones. It is shown that this construction allows a Fourierdecomposition of fitness landscapes into a superposition of "elementary landscapes". This decomposition is analogous to the Fourier decomposition of fitness landscapes on mutation spaces. The elementary landscapes are obtained as eigenfunctions of a Laplacian operator defined for Pstructures. For binary string recombination the elementary landscapes are exactly the pspin functions (Walsh functions), i.e. the same as the elementary landscapes of the string point mutation spaces (i.e. the hypercube). This supports the notion of a strong homomorphisms between string mutation ...
Landscapes  Complex Optimization Problems and Biopolymer Structures
 Computers Chem
, 1993
"... The evolution of RNA molecules in replication assays, viroids and RNA viruses can be viewed as an adaptation process on a 'fitness' landscape. The dynamics of evolution is hence tightly linked to the structure of the underlying landscape. Global features of landscapes can be described by s ..."
Abstract

Cited by 33 (16 self)
 Add to MetaCart
The evolution of RNA molecules in replication assays, viroids and RNA viruses can be viewed as an adaptation process on a 'fitness' landscape. The dynamics of evolution is hence tightly linked to the structure of the underlying landscape. Global features of landscapes can be described by statistical measures like number of optima, lengths of walks, and correlation functions. The evolution of a quasispecies on such landscapes exhibits three dynamical regimes depending on the replication fidelity: Above the "localization threshold" the population is centered around a (local) optimum. Between localization and "dispersion threshold" the population is still centered around a consensus sequence, which, however, changes in time. For very large mutation rates the population spreads in sequence space like a gas. The critical mutation rates separating the three domains depend strongly on characteristics properties of the fitness landscapes. Statistical characteristics of RNA landscapes are acces...
Exact ground states of Ising spin glasses: New experimental results with a branch and cut algorithm
, 1995
"... In this paper we study 2dimensional Ising spin glasses on a grid with nearest neighbor and periodic boundary interactions, based on a Gaussian bond distribution, and an exterior magnetic field. We show how using a technique called branch and cut, the exact ground states of grids of sizes up to 100 ..."
Abstract

Cited by 28 (3 self)
 Add to MetaCart
In this paper we study 2dimensional Ising spin glasses on a grid with nearest neighbor and periodic boundary interactions, based on a Gaussian bond distribution, and an exterior magnetic field. We show how using a technique called branch and cut, the exact ground states of grids of sizes up to 100 x 100 can be determined in a moderate amount of computation time, and we report on extensive computational tests. With our method we produce results based on more than 20 000 experiments on the properties of spin glasses whose errors depend only on the assumptions on the model and not on the computational process. This feature is a clear advantage of the method over other more popular ways to compute the ground state, like Monte Carlo simulation including simulated annealing, evolutionary, and genetic algorithms, that provide only approximate ground states with a degree of accuracy that cannot be determined a priori. Our ground state energy estimation at zero field is 1.317.
Analyzing probabilistic models in hierarchical boa on traps and spin glasses
 Genetic and Evolutionary Computation Conference (GECCO2007), I
, 2007
"... The hierarchical Bayesian optimization algorithm (hBOA) can solve nearly decomposable and hierarchical problems of bounded difficulty in a robust and scalable manner by building and sampling probabilistic models of promising solutions. This paper analyzes probabilistic models in hBOA on two common t ..."
Abstract

Cited by 25 (17 self)
 Add to MetaCart
(Show Context)
The hierarchical Bayesian optimization algorithm (hBOA) can solve nearly decomposable and hierarchical problems of bounded difficulty in a robust and scalable manner by building and sampling probabilistic models of promising solutions. This paper analyzes probabilistic models in hBOA on two common test problems: concatenated traps and 2D Ising spin glasses with periodic boundary conditions. We argue that although Bayesian networks with local structures can encode complex probability distributions, analyzing these models in hBOA is relatively straightforward and the results of such analyses may provide practitioners with useful information about their problems. The results show that the probabilistic models in hBOA closely correspond to the structure of the underlying problem, the models do not change significantly in subsequent iterations of BOA, and creating adequate probabilistic models by hand is not straightforward even with complete knowledge of the optimization problem. Categories and Subject Descriptors
From neuron to neural network dynamics
, 2006
"... This paper presents an overview of some techniques and concepts coming from dynamical system theory and used for the analysis of dynamical neural networks models. In a first section, we describe the dynamics of the neuron, starting from the HodgkinHuxley description, which is somehow the canonical ..."
Abstract

Cited by 21 (8 self)
 Add to MetaCart
This paper presents an overview of some techniques and concepts coming from dynamical system theory and used for the analysis of dynamical neural networks models. In a first section, we describe the dynamics of the neuron, starting from the HodgkinHuxley description, which is somehow the canonical description for the “biological neuron”. We discuss some models reducing