23 research outputs found
Identification of Amino Acid Sequences with Good Folding Properties in an Off-Lattice Model
Folding properties of a two-dimensional toy protein model containing only two
amino-acid types, hydrophobic and hydrophilic, respectively, are analyzed. An
efficient Monte Carlo procedure is employed to ensure that the ground states
are found. The thermodynamic properties are found to be strongly sequence
dependent in contrast to the kinetic ones. Hence, criteria for good folders are
defined entirely in terms of thermodynamic fluctuations. With these criteria
sequence patterns that fold well are isolated. For 300 chains with 20 randomly
chosen binary residues approximately 10% meet these criteria. Also, an analysis
is performed by means of statistical and artificial neural network methods from
which it is concluded that the folding properties can be predicted to a certain
degree given the binary numbers characterizing the sequences.Comment: 15 pages, 8 Postscript figures. Minor change
Interacting Multiple Try Algorithms with Different Proposal Distributions
We propose a new class of interacting Markov chain Monte Carlo (MCMC)
algorithms designed for increasing the efficiency of a modified multiple-try
Metropolis (MTM) algorithm. The extension with respect to the existing MCMC
literature is twofold. The sampler proposed extends the basic MTM algorithm by
allowing different proposal distributions in the multiple-try generation step.
We exploit the structure of the MTM algorithm with different proposal
distributions to naturally introduce an interacting MTM mechanism (IMTM) that
expands the class of population Monte Carlo methods. We show the validity of
the algorithm and discuss the choice of the selection weights and of the
different proposals. We provide numerical studies which show that the new
algorithm can perform better than the basic MTM algorithm and that the
interaction mechanism allows the IMTM to efficiently explore the state space
Phase transition between synchronous and asynchronous updating algorithms
We update a one-dimensional chain of Ising spins of length with
algorithms which are parameterized by the probability for a certain site to
get updated in one time step. The result of the update event itself is
determined by the energy change due to the local change in the configuration.
In this way we interpolate between the Metropolis algorithm at zero temperature
for of the order of 1/L and for large , and a synchronous deterministic
updating procedure for . As function of we observe a phase transition
between the stationary states to which the algorithm drives the system. These
are non-absorbing stationary states with antiferromagnetic domains for ,
and absorbing states with ferromagnetic domains for . This means
that above this transition the stationary states have lost any remnants to the
ferromagnetic Ising interaction. A measurement of the critical exponents shows
that this transition belongs to the universality class of parity conservation.Comment: 5 pages, 3 figure
Phase Transitions of Hard Disks in External Periodic Potentials: A Monte Carlo Study
The nature of freezing and melting transitions for a system of hard disks in
a spatially periodic external potential is studied using extensive Monte Carlo
simulations. Detailed finite size scaling analysis of various thermodynamic
quantities like the order parameter, its cumulants etc. are used to map the
phase diagram of the system for various values of the density and the amplitude
of the external potential. We find clear indication of a re-entrant liquid
phase over a significant region of the parameter space. Our simulations
therefore show that the system of hard disks behaves in a fashion similar to
charge stabilized colloids which are known to undergo an initial freezing,
followed by a re-melting transition as the amplitude of the imposed, modulating
field produced by crossed laser beams is steadily increased. Detailed analysis
of our data shows several features consistent with a recent dislocation
unbinding theory of laser induced melting.Comment: 36 pages, 16 figure
Cosmological parameters from SDSS and WMAP
We measure cosmological parameters using the three-dimensional power spectrum
P(k) from over 200,000 galaxies in the Sloan Digital Sky Survey (SDSS) in
combination with WMAP and other data. Our results are consistent with a
``vanilla'' flat adiabatic Lambda-CDM model without tilt (n=1), running tilt,
tensor modes or massive neutrinos. Adding SDSS information more than halves the
WMAP-only error bars on some parameters, tightening 1 sigma constraints on the
Hubble parameter from h~0.74+0.18-0.07 to h~0.70+0.04-0.03, on the matter
density from Omega_m~0.25+/-0.10 to Omega_m~0.30+/-0.04 (1 sigma) and on
neutrino masses from <11 eV to <0.6 eV (95%). SDSS helps even more when
dropping prior assumptions about curvature, neutrinos, tensor modes and the
equation of state. Our results are in substantial agreement with the joint
analysis of WMAP and the 2dF Galaxy Redshift Survey, which is an impressive
consistency check with independent redshift survey data and analysis
techniques. In this paper, we place particular emphasis on clarifying the
physical origin of the constraints, i.e., what we do and do not know when using
different data sets and prior assumptions. For instance, dropping the
assumption that space is perfectly flat, the WMAP-only constraint on the
measured age of the Universe tightens from t0~16.3+2.3-1.8 Gyr to
t0~14.1+1.0-0.9 Gyr by adding SDSS and SN Ia data. Including tensors, running
tilt, neutrino mass and equation of state in the list of free parameters, many
constraints are still quite weak, but future cosmological measurements from
SDSS and other sources should allow these to be substantially tightened.Comment: Minor revisions to match accepted PRD version. SDSS data and ppt
figures available at http://www.hep.upenn.edu/~max/sdsspars.htm
Side chain-positioning as an integer programming problem
Abstract. An important aspect of homology modeling and protein design algorithms is the correct positioning of protein side chains on a fixed backbone. Homology modeling methods are necessary to complement large scale structural genomics projects. Recently it has been shown that in automatic protein design it is of the uttermost importance to find the global solution to the side chain positioning problem [1]. If a suboptimal solution is found the difference in free energy between different sequences will be smaller than the error of the side chain positioning. Several different algorithms have been developed to solve this problem. The most successful methods use a discrete representation of the conformational space. Today, the best methods to solve this problem, are based on the dead end elimination theorem. Here we introduce an alternative method. The problem is formulated as a linear integer program. This programming problem can then be solved by efficient polynomial time methods, using linear programming relaxation. If the solution to the relaxed problem is integral it corresponds to the global minimum energy conformation (GMEC). In our experimental results, the solution to the relaxed problem has always been integral.
Computational Methods for Complex Stochastic Systems: A Review of Some Alternatives to MCMC.
We consider analysis of complex stochastic models based upon partial information. MCMC and reversible jump MCMC are often the methods of choice for such problems, but in some situations they can be difficult to implement; and suffer from problems such as poor mixing, and the difficulty of diagnosing convergence. Here we review three alternatives to MCMC methods: importance sampling, the forward-backward algorithm, and sequential Monte Carlo (SMC). We discuss how to design good proposal densities for importance sampling, show some of the range of models for which the forward-backward algorithm can be applied, and show how resampling ideas from SMC can be used to improve the efficiency of the other two methods. We demonstrate these methods on a range of examples, including estimating the transition density of a diffusion and of a discrete-state continuous-time Markov chain; inferring structure in population genetics; and segmenting genetic divergence data