Biomedical subjects

Peter Grassberger

Publications and source records attributed to Peter Grassberger.

8 recordsLinked to original sources

PubMed2003

Structure optimization in an off-lattice protein model.

We study an off-lattice protein toy model with two species of monomers interacting through modified Lennard-Jones interactions. Low energy configurations are optimized using the pruned-enriched-Rosenbluth method (PERM), hitherto employed to native state searches only for off-lattice models. For two dimensions we found states with lower energy than previously proposed putative ground states for all chain lengths >/=13. This indicates that PERM has the potential to produce native states also for more realistic protein models. For d=3, where no published ground states exist, we present some putative lowest energy states for future comparison with other methods.

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PubMed2003

Growth-based optimization algorithm for lattice heteropolymers.

An improved version of the pruned-enriched-Rosenbluth method (PERM) is proposed and tested on finding lowest energy states in simple models of lattice heteropolymers. It is found to outperform not only the previous version of PERM, but also all other fully blind general purpose stochastic algorithms which have been employed on this problem. In many cases, it found new lowest energy states missed in previous papers. Limitations are discussed.

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PubMed2003

Critical percolation in high dimensions.

We present Monte Carlo estimates for site and bond percolation thresholds in simple hypercubic lattices with 4-13 dimensions. For d<6 they are preliminary, for d>or =6 they are between 20 and 10(4) times more precise than the best previous estimates. This was achieved by three ingredients: (i) simple and fast hashing that allowed us to simulate clusters of millions of sites on computers with less than 500 Mbytes memory; (ii) a histogram method that allowed us to obtain information for several p values from a single simulation; and (iii) a variance reduction technique that is especially efficient at high dimensions where it reduces error bars by a factor of up to approximately 30 and more. Based on these data we propose a scaling law for finite cluster size corrections.

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PubMed2002

Heat conduction and entropy production in a one-dimensional hard-particle gas.

We present large scale simulations for a one-dimensional chain of hard-point particles with alternating masses and correct several claims in recent literature based on much smaller simulations. We find heat conductivities kappa to diverge with the number N of particles. These depended strongly on the mass ratio, and extrapolations to N--> infinity, and t--> infinity, are difficult due to very large finite-size and finite-time corrections. Nevertheless, our data seem compatible with a universal power law kappa approximately N(alpha) with alpha approximately 0.33 suggesting a relation to the Kardar-Parisi-Zhang model. We finally discuss why the system leads nevertheless to energy dissipation and entropy production, in spite of not being chaotic in the usual sense.

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PubMed2002

Trapping reaction with mobile traps.

We present the Monte Carlo results for the two-species trapping reaction A+B-->B with diffusing A and B on lattices in one, two, and three dimensions. We use an algorithm that permits one to simulate the survival probabilities of A particles down to <10(-30) with high accuracy. The results for the survival probability agree much better with the exact asymptotic predictions of Bramson and Lebowitz [Phys. Rev. Lett. 61, 2397 (1988)] than with the heuristics of Kang and Redner [J. Phys. A 17, L451 (1984)]. But there are very large deviations from either, which show that even these simulations are far from asymptotia. This is supported by the rms displacement of A particles, which clearly shows that the asymptotic regime has not been reached, at least for d=2 and d=3.

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PubMed2002

Stretched polymers in a poor solvent.

Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest-neighbor attraction. The bias corresponds to opposite forces applied to the first and last monomers. We show that both in d=2 and d=3 a phase transition occurs as this force is increased beyond a critical value, where the polymer changes from a collapsed globule to a stretched configuration. This transition is second order in d=2 and first order in d=3. For d=2 we predict the transition point quantitatively from properties of the unstretched polymer. This is not possible in d=3, but even there we can estimate the transition point precisely, and we can study the scaling at temperatures slightly below the collapse temperature of the unstretched polymer. We find very large finite size corrections that would make very difficult the estimate of the transition point from straightforward simulations.

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PubMed1996

Entropy estimation of symbol sequences.

We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our interest is in describing their convergence with sequence length, assuming no limits for the space and time complexities of the compression algorithms. A scaling law is proposed for extrapolation from finite sample lengths. This is applied to sequences of dynamical systems in non-trivial chaotic regimes, a 1-D cellular automaton, and to written English texts. (c)1996 American Institute of Physics.

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PubMed1993

On noise reduction methods for chaotic data.

Recently proposed noise reduction methods for nonlinear chaotic time sequences with additive noise are analyzed and generalized. All these methods have in common that they work iteratively, and that in each step of the iteration the noise is suppressed by requiring locally linear relations among the delay coordinates, i.e., by moving the delay vectors towards some smooth manifold. The different methods can be compared unambiguously in the case of strictly hyperbolic systems corrupted by measurement noise of infinitesimally low level. It was found that all proposed methods converge in this ideal case, but not equally fast. Different problems arise if the system is not hyperbolic, and at higher noise levels. A new scheme which seems to avoid most of these problems is proposed and tested, and seems to give the best noise reduction so far. Moreover, large improvements are possible within the new scheme and the previous schemes if their parameters are not kept fixed during the iteration, and if corrections are included which take into account the curvature of the attracting manifold. Finally, the fact that comparison with simple low-pass filters tends to overestimate the relative achievements of these nonlinear noise reduction schemes is stressed, and it is suggested that they should be compared to Wiener-type filters.

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