102 research outputs found
An efficient algorithm for numerical computations of continuous densities of states
In Wang-Landau type algorithms, Monte-Carlo updates are performed with respect to the density of states, which is iteratively refined during simulations. The partition function and thermodynamic observables are then obtained by standard integration. In this work, our recently introduced method in this class (the LLR approach) is analysed and further developed. Our approach is a histogram free method particularly suited for systems with continuous degrees of freedom giving rise to a continuum density of states, as it is commonly found in Lattice Gauge Theories and in some Statistical Mechanics systems. We show that the method possesses an exponential error suppression that allows us to estimate the density of states over several orders of magnitude with nearly-constant relative precision. We explain how ergodicity issues can be avoided and how expectation values of arbitrary observables can be obtained within this framework. We then demonstrate the method using Compact U(1) Lattice Gauge Theory as a show case. A thorough study of the algorithm parameter dependence of the results is performed and compared with the analytically expected behaviour. We obtain high precision values for the critical coupling for the phase transition and for the peak value of the specific heat for lattice sizes ranging from 84 to 204. Our results perfectly agree with the reference values reported in the literature, which covers lattice sizes up to 184. Robust results for the 204 volume are obtained for the first time. This latter investigation, which, due to strong metastabilities developed at the pseudo-critical coupling of the system, so far has been out of reach even on supercomputers with importance sampling approaches, has been performed to high accuracy with modest computational resources. This shows the potential of the method for studies of first order phase transitions. Other situations where the method is expected to be superior to importance sampling techniques are pointed out
An effective all-atom potential for proteins
We describe and test an implicit solvent all-atom potential for simulations
of protein folding and aggregation. The potential is developed through studies
of structural and thermodynamic properties of 17 peptides with diverse
secondary structure. Results obtained using the final form of the potential are
presented for all these peptides. The same model, with unchanged parameters, is
furthermore applied to a heterodimeric coiled-coil system, a mixed alpha/beta
protein and a three-helix-bundle protein, with very good results. The
computational efficiency of the potential makes it possible to investigate the
free-energy landscape of these 49--67-residue systems with high statistical
accuracy, using only modest computational resources by today's standards
Homochirality and the need of energy
The mechanisms for explaining how a stable asymmetric chemical system can be
formed from a symmetric chemical system, in the absence of any asymmetric
influence other than statistical fluctuations, have been developed during the
last decades, focusing on the non-linear kinetic aspects. Besides the absolute
necessity of self-amplification processes, the importance of energetic aspects
is often underestimated. Going down to the most fundamental aspects, the
distinction between a single object -- that can be intrinsically asymmetric --
and a collection of objects -- whose racemic state is the more stable one --
must be emphasized. A system of strongly interacting objects can be described
as one single object retaining its individuality and a single asymmetry; weakly
or non-interacting objects keep their own individuality, and are prone to
racemize towards the equilibrium state. In the presence of energy fluxes,
systems can be maintained in an asymmetric non-equilibrium steady-state. Such
dynamical systems can retain their asymmetry for times longer than their
racemization time.Comment: 8 pages, 7 figures, submitted to Origins of Life and Evolution of
Biosphere
On the Coupling Time of the Heat-Bath Process for the Fortuin–Kasteleyn Random–Cluster Model
We consider the coupling from the past implementation of the random-cluster
heat-bath process, and study its random running time, or coupling time. We
focus on hypercubic lattices embedded on tori, in dimensions one to three, with
cluster fugacity at least one. We make a number of conjectures regarding the
asymptotic behaviour of the coupling time, motivated by rigorous results in one
dimension and Monte Carlo simulations in dimensions two and three. Amongst our
findings, we observe that, for generic parameter values, the distribution of
the appropriately standardized coupling time converges to a Gumbel
distribution, and that the standard deviation of the coupling time is
asymptotic to an explicit universal constant multiple of the relaxation time.
Perhaps surprisingly, we observe these results to hold both off criticality,
where the coupling time closely mimics the coupon collector's problem, and also
at the critical point, provided the cluster fugacity is below the value at
which the transition becomes discontinuous. Finally, we consider analogous
questions for the single-spin Ising heat-bath process
Conjectures on exact solution of three - dimensional (3D) simple orthorhombic Ising lattices
We report the conjectures on the three-dimensional (3D) Ising model on simple
orthorhombic lattices, together with the details of calculations for a putative
exact solution. Two conjectures, an additional rotation in the fourth curled-up
dimension and the weight factors on the eigenvectors, are proposed to serve as
a boundary condition to deal with the topologic problem of the 3D Ising model.
The partition function of the 3D simple orthorhombic Ising model is evaluated
by spinor analysis, by employing these conjectures. Based on the validity of
the conjectures, the critical temperature of the simple orthorhombic Ising
lattices could be determined by the relation of KK* = KK' + KK'' + K'K'' or
sinh 2K sinh 2(K' + K'' + K'K''/K) = 1. For a simple cubic Ising lattice, the
critical point is putatively determined to locate exactly at the golden ratio
xc = exp(-2Kc) = (sq(5) - 1)/2, as derived from K* = 3K or sinh 2K sinh 6K = 1.
If the conjectures would be true, the specific heat of the simple orthorhombic
Ising system would show a logarithmic singularity at the critical point of the
phase transition. The spontaneous magnetization and the spin correlation
functions of the simple orthorhombic Ising ferromagnet are derived explicitly.
The putative critical exponents derived explicitly for the simple orthorhombic
Ising lattices are alpha = 0, beta = 3/8, gamma = 5/4, delta = 13/3, eta = 1/8
and nu = 2/3, showing the universality behavior and satisfying the scaling
laws. The cooperative phenomena near the critical point are studied and the
results obtained based on the conjectures are compared with those of the
approximation methods and the experimental findings. The 3D to 2D crossover
phenomenon differs with the 2D to 1D crossover phenomenon and there is a
gradual crossover of the exponents from the 3D values to the 2D ones.Comment: 176 pages, 4 figure
Scaling Properties of the Number of Random Sequential Adsorption Iterations Needed to Generate Saturated Random Packing
A novel method to compare protein structures using local descriptors
<p>Abstract</p> <p>Background</p> <p>Protein structure comparison is one of the most widely performed tasks in bioinformatics. However, currently used methods have problems with the so-called "difficult similarities", including considerable shifts and distortions of structure, sequential swaps and circular permutations. There is a demand for efficient and automated systems capable of overcoming these difficulties, which may lead to the discovery of previously unknown structural relationships.</p> <p>Results</p> <p>We present a novel method for protein structure comparison based on the formalism of local descriptors of protein structure - DEscriptor Defined Alignment (DEDAL). Local similarities identified by pairs of similar descriptors are extended into global structural alignments. We demonstrate the method's capability by aligning structures in difficult benchmark sets: curated alignments in the SISYPHUS database, as well as SISY and RIPC sets, including non-sequential and non-rigid-body alignments. On the most difficult RIPC set of sequence alignment pairs the method achieves an accuracy of 77% (the second best method tested achieves 60% accuracy).</p> <p>Conclusions</p> <p>DEDAL is fast enough to be used in whole proteome applications, and by lowering the threshold of detectable structure similarity it may shed additional light on molecular evolution processes. It is well suited to improving automatic classification of structure domains, helping analyze protein fold space, or to improving protein classification schemes. DEDAL is available online at <url>http://bioexploratorium.pl/EP/DEDAL</url>.</p
Bayesian Computation with Intractable Likelihoods
This article surveys computational methods for posterior inference with
intractable likelihoods, that is where the likelihood function is unavailable
in closed form, or where evaluation of the likelihood is infeasible. We review
recent developments in pseudo-marginal methods, approximate Bayesian
computation (ABC), the exchange algorithm, thermodynamic integration, and
composite likelihood, paying particular attention to advancements in
scalability for large datasets. We also mention R and MATLAB source code for
implementations of these algorithms, where they are available.Comment: arXiv admin note: text overlap with arXiv:1503.0806
Weak Glycolipid Binding of a Microdomain-Tracer Peptide Correlates with Aggregation and Slow Diffusion on Cell Membranes
10.1371/journal.pone.0051222PLoS ONE712
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