1,721,043 research outputs found
sin[n Delta t sin (n Delta t1)] as a source of unpredictable dynamics.
No full textWe investigate the ability of the function sin[n Delta t sin (n Delta t1)], where n is an integer and growing number, to produce unpredictable sequences of numbers. Classical mathematical tools for distinguishing periodic from chaotic or random behaviour, such as sensitivity to the initial conditions, Fourier analysis, and autocorrelation are used. Moreover, the function acos{sin[n Delta t sin (n Delta t1)]}/pigreek is introduced to have an uniform density of numbers in the interval [0,1], so it can be submitted to a battery of widely used tests for random number generators. All these tools show that a proper choice of Delta t and Delta t1, can produce a sequence of numbers behaving as unpredictable dynamics
sin[n Delta t sin (n Delta t1)] as a source of unpredictable dynamics
No full textWe investigate the ability of the function sin[n Delta t sin (n Delta t1)], where n is an integer and growing number, to produce unpredictable sequences of numbers. Classical mathematical tools for distinguishing periodic from chaotic or random behaviour, such as sensitivity to the initial conditions, Fourier analysis, and autocorrelation are used. Moreover, the function acos{ sin[n Delta t sin (n Delta t1)]}/pi is introduced to have an uniform density of numbers in the interval [0,1], so it can be submitted to a battery of widely used tests for random number generators. All these tools show that a proper choice of Delta t and Delta t1, can produce a sequence of numbers behaving as unpredictable dynamics
Discrete Haar transform and protein structure
No full textThe discrete Haar transform of the sequence of the backbone dihedral angles (phi and psi) was performed over a set of X-ray protein structures of high resolution from the Brookhaven Protein Data Bank. Afterwards, the new dihedral angles were calculated by the inverse transform, using a growing number of Haar functions, from the lower to the higher degree. New structures were obtained using these dihedral angles, with standard values for bond lengths and angles, and with omega = 0 degree. The reconstructed structures were compared with the experimental ones, and analyzed by visual inspection and statistical analysis. When half of the Haar coefficients were used, all the reconstructed structures were not yet collapsed to a tertiary folding, but they showed yet realized most of the secondary motifs. These results indicate a substantial separation of structural information in the space of Haar transform, with the secondary structural information mainly present in the Haar coefficients of lower degrees, and the tertiary one present in the higher degree coefficients. Because of this separation, the representation of the folded structures in the space of Haar transform seems a promising candidate to encompass the problem of premature convergence in genetic algorithms
A simple procedure to weight empirical potentials in a fitness function so as to optimize its performance in ab initio protein-folding problem
No full textIn an approach to the protein folding problem by a Genetic Algorithm, the fitness function plays a critical role. Empirical potentials are generally used to build the fitness function, and they must be weighted to obtain a valuable one. The weights are generally found by the comparison with a set of misfolded structures (decoys), but a dependence of the obtained fitness generally arises on the used decoys. Here we describe a general procedure to find out, from a given set of potentials, their better linear combination that could either identify the wild structure or prove their powerlessness. We use topological considerations over the hyperspace of the potentials, and a multiple linear inequalities solver. The iterated method flows through the following steps: it determines a direction in the hyperspace of the potentials, which identifies the native structure as a vertex among a set of misfolded decoys. A multiple linear inequalities solver obtains the direction. A Genetic Algorithm, tailored to the specific problem, uses the fitness function defined by this direction and generally reaches a new structure better than the experimental one, which is added to the ensemble. The decoys so generated are not dependent on a deterministic criterion. This iterative procedure can be stopped either by identifying an effective fitness function or by proving the impossibility of its achievement. In order to test the method under the hardest conditions, we choose numerous and heterogeneous quantities as components of the fitness function. This method could be a useful tool for the scientific community in order to test any fitness proposed and to recognize the most important components on which it is built
A method for building simple physical models: representing the structures of nucleic acid
No full textAn improved low-resoln. phys. model for representing the structures of nucleic acids in presented. The models are inexpensive and easy to construct and show flexibility in application
RECOGNITION OF THE FOLDING CONSENSUS IN RNA SECONDARY STRUCTURES BY THE TOPOLOGICAL-FILTERING METHOD
No full textFunctionally homologous RNA sequences can substantially diverge in their primary sequences but it can be reasonably assumed that they are related in their higher-degree structures. The problem to find such structures and simultaneously satisfy as far as possible the free-energy-minimization criterion, is considered here in two aspects. Firstly a quantitative measure of the folding consensus among secondary structures is defined, translating each structure into a linear representation and using the correlation theorem to compare them. Secondly an algorithm for the parallel search for secondary structures according to the free-energy-minimization criterion, but with a filtering action on the basis of the folding consensus measure is presented. The method is tested on groups of RNA sequences different in origin and in functions, for which proposals of homologous secondary structures based on experimental data exist. A comparison of the results with a blank consisting of a search on the basis of the free energy minimization alone is always performed. In these tests the method shows its ability in obtaining, from different sequences, secondary structures characterized by a high-folding consensus measure also when lower free energy but not homologous structures are possible. Two applications are also shown. The first demonstrates the transfer of experimental data available for one sequence, to a functionally related and therefore homologous one. The second application is the possibility of using a topological probe in the search for precise structural motifs
Three-dimensional folding of Tetrahymena thermophila rRNA IVS sequence: A proposal
No full textWe studied the Tetrahymena thermophila rRNA IVS sequence with the aim of obtaining a model of the structure characterized by the bases proximity of the self-reactions sites. The considered sequence kept up those fragments essential for its catalytic activity as demonstrated by deletion mutants. The first step was the theoretical analysis with a computer method previously proposed, to find optimal free energy secondary structures with the required features, under the suitable constrains. Then we tried folding the obtained secondary structures, in low resolution tertiary models, which kept up the proximity of the catalytic sites also in the space. The proposed tertiary folding seems to provide for a better explanation to the transesterification mechanisms and moreover it is in good agreement with the experimental data (activity of mutants, enzymatic cleavages, phylogenetically conserved regions)
Simple testing procedure to identigy a minimal frustrated fitness function in ab inizio protein folding problem
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