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arXiv2008

A library-based Monte Carlo technique enables rapid equilibrium sampling of a protein model with atomistic components

There is significant interest in rapid protein simulations because of the time-scale limitations of all-atom methods. Exploiting the low cost and great availability of computer memory, we report a Monte Carlo technique for incorporating fully flexible atomistic protein components (e.g., peptide planes) into protein models without compromising sampling speed or statistical rigor. Building on existing approximate methods (e.g., Rosetta), the technique uses pre-generated statistical libraries of all-atom components which are swapped with the corresponding protein components during a simulation. The simple model we study consists of the three all-atom backbone residues -- Ala, Gly, and Pro -- with structure-based (Go-like) interactions. For the five different proteins considered in this study, LBMC can generate at least 30 statistically independent configurations in about a month of single CPU time. Minimal additional cost is required to add residue-specific interactions.

physics.bio-ph↗

arXiv2008

Reminiscences about numerical schemes

This preprint appeared firstly in Russian in 1997. Some truncated versions of this preprint were published in English and French, here a fully translated version is presented. The translation in English was done by O. V. Feodoritova and V. Deledicque to whom I express my gratitude. In the present paper I will describe how the first variant of the Godunov's scheme has been elaborated in 1953-1954 and tell about all modifications realized by myself (until 1969) and the group of scientists from the Institute of Applied Mathematics in Moscow (which has become the M.V.Keldysh Institute of Applied Mathematics).

physics.comp-ph↗

arXiv2008

How to compute the atomic stress objectively?

Atomistic simulation has been a powerful study tool in mechanics research, but how to objectively compute the atomic stress equivalent to Cauchy stress is still controversial, especially on the velocity-related part in the virial stress definition. In this paper, by strictly following the classical definition of the Cauchy stress for continuum medium, the fundamental Lagrangian atomic stress is proposed and can be used to obtain the correct Cauchy stress under any circumstances. Furthermore, the Lagrangian virial stress is proposed, which is still in virial form but does not include velocities to avoid controversial velocity treatments. It is also found that the widely used classical virial stress is actually the Eulerian virial stress, which includes the velocities of atoms, and is valid only when the impulse-momentum theorem is applicable to estimate the internal forces. However this requirement for the Eulerian atomic stress can not always be met in practical cases, such as the material volume element in rotation and the examples presented in this paper, but the proposed Lagrangian atomic stress can avoid these velocity-related nonobjectivities.

physics.comp-ph↗

arXiv2009

The "weighted ensemble" path sampling method is statistically exact for a broad class of stochastic processes and binning procedures

The "weighted ensemble" method, introduced by Huber and Kim, [G. A. Huber and S. Kim, Biophys. J. 70, 97 (1996)], is one of a handful of rigorous approaches to path sampling of rare events. Expanding earlier discussions, we show that the technique is statistically exact for a wide class of Markovian and non-Markovian dynamics. The derivation is based on standard path-integral (path probability) ideas, but recasts the weighted-ensemble approach as simple "resampling" in path space. Similar reasoning indicates that arbitrary nonstatic binning procedures, which merely guide the resampling process, are also valid. Numerical examples confirm the claims, including the use of bins which can adaptively find the target state in a simple model.

physics.comp-ph↗

arXiv2009

Simulated Annealing for Optimal Ship Routing

A simulated annealing based algorithm is presented for the determination of optimal ship routes through the minimization of a cost function. This cost function is a weighted sum of the time of voyage and the voyage comfort (safety is taken into account too). The latter is dependent on both the wind speed and direction and the wave height and direction. The algorithm first discretizes an initial route and optimizes it by considering small deviations which are accepted by utilizing the simulated annealing technique. Using calculus of variations we prove a key theorem which dramatically accelerates the convergence of the algorithm. Finally both simulated and real experiments are presented.

physics.comp-ph↗

arXiv2011

A Central Partition of Molecular Conformational Space. V. The Hypergraph of 3D Partition Sequences

In a previous work a procedure was decribed for dividing the $3 \times N$-dimensional conformational space of a molecular system into a number of discrete cells, this partition allowed the building of a combinatorial structure from data sampled in molecular dynamics trajectories: the graph of cells or G, encoding the set of cells in conformational space that are visited by the system in its thermal wandering. The information in G however, is encoded in a great number of fragments that must be aggregated. We describe here the algorithmic procedures 1) for aggregating the information from G into an hypergraph allowing to enumerate the relevant cells from conformational space, and 2) for puttting the data in a very compact format.

physics.comp-ph↗

arXiv2008

Mott Scattering of polarized electrons in a circularly polarized laser field

We present a study of Mott scattering of polarized electrons in the presence of a laser field with circular polarization using the helicity formalism and the introduction of the well known concept of non flip differential cross section as well as that of flip differential cross section. The results we have obtained in the presence of a laser field are coherent with those obtained in the absence of a laser field. We have studied the relativistic regime as well as the non relativistic regime that are precisely defined in the text. Two important consistency checks have been carried out successfully. The first one is that the sum of both differential cross sections (one with spin up, the other with spin down) always gives the unpolarized differential cross section. The second one is that the relativistic unpolarized differential cross section converges to the non relativistic differential cross section in the limit of small velocities. Moreover, the results obtained using the sofware Reduce \cite{8} gave rise to non contracted coefficients that have been dealt with using the geometry chosen.

physics.atom-ph↗

arXiv2009

Accurate calculations of the dissociation energy, equilibrium distance and spectroscopic constants for the Yb dimer

The dissociation energy, equilibrium distance, and spectroscopic constants for the $^1Σ_g^+$ ground state of the Yb$_2$ molecule are calculated. The relativistic effects are introduced through generalized relativistic effective core potentials with very high precision. The scalar relativistic coupled cluster method particularly well suited for closed-shell van-der-Waals systems is used for the correlation treatment. Extensive generalized correlation basis sets were constructed and employed. The relatively small corrections for high-order cluster amplitudes and spin-orbit interactions are taken into account using smaller basis sets and the spin-orbit density functional theory.

physics.chem-ph↗

arXiv2010

Study of Proton Transfer Reaction Dynamics in Pyrrole 2-Carboxyldehyde

Photophysical and photochemical dynamics of ground state and excited state proton transfer reaction is reported for Pyrrole 2-Carboxyldehyde (PCL). Steady state absorption and emission measurements are conducted in PCL. The theoretical investigation is done by using different quantum mechanical methods (e.g. Hartree Fock, DFT, MP2, CCSD etc.). The reaction pathway and two dimensional potential energy surfaces are computed in various level of theory. A transition state is also reported in gas phase and reaction filed calculation. It is established that PCL forms different emitting species in different media. A large Stokes shifted emission band, which is attributed to species undergoing excited state intramolecular proton transfer, is observed in hydrocarbon solvent. Intermolecular proton transfer is observed in hydroxylic polar solvent. Experimental observations yield all possible signatures of intramolecular and intermolecular proton transfer in excited state of PCL. The origins of these signatures have been explained successfully using corresponding quantum mechanical theories.

physics.atm-clus↗

arXiv2009

The acoustic wave equation in the expanding universe. Sachs-Wolfe theorem

In this paper the acoustic field propagating in the early hot ($p=ε/$) universe of arbitrary space curvature ($K=0, \pm 1$) is considered. The field equations are reduced to the d'Alembert equation in an auxiliary static Roberson-Walker space-time. Symbolic computation in {\em Mathematica} is applied.

cs.SC↗

arXiv2009

Adaptive Finite Element Simulation of the Time-dependent Simplified PN Equations

The steady-state simplified $P_N$ approximation to the radiative transport equation has been successfully applied to many problems involving radiation. Recently, time-dependent simplified $P_N$ equations have been derived by an asymptotic analysis similar to the asymptotic derivation of the steady-state $SP_N$ equations \cite{FraKlaLarYas07}. In this paper, we present computational results for the time-dependent $SP_N$ equations in two dimensions, obtained by using an adaptive finite element approach. Several numerical comparisons with other existing models are shown.

physics.comp-ph↗

arXiv2009

Communities in Networks

We survey some of the concepts, methods, and applications of community detection, which has become an increasingly important area of network science. To help ease newcomers into the field, we provide a guide to available methodology and open problems, and discuss why scientists from diverse backgrounds are interested in these problems. As a running theme, we emphasize the connections of community detection to problems in statistical physics and computational optimization.

physics.soc-ph↗

arXiv2009

Breakthrough in Interval Data Fitting II. From Ranges to Means and Standard Deviations

Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all. Worse yet, if this happens, then we are left in the state of complete ignorance concerning the unknown parameters of interest. This is in sharp contrast with widespread statistical methods of data analysis. In this paper I show the connections between those two approaches: how to process experimental data rigorously, using interval methods, and present the final results either as intervals (guaranteed, rigorous results) or in a more familiar probabilistic form: as a mean value and its standard deviation.

physics.data-an↗

arXiv2009

Joint use of the Weniger transformation and hyperasymptotics for accurate asymptotic evaluations of a class of saddle-point integrals. II. Higher-order transformations

The use of hyperasymptotics and the Weniger transformation has been proposed, in a joint fashion, for decoding the divergent asymptotic series generated by the steepest descent on a wide class of saddle-point integrals {evaluated across Stokes sets} [R. Borghi, Phys. Rev. E {\bf 78,} 026703 (2008)]. In the present sequel, the full development of the H-WT up to the second order in H is derived. Numerical experiments, carried out on several classes of saddle-point integrals, including the swallowtail diffraction catastrophe, show the effectiveness of the 2nd-level H-WT, in particular when the integrals are evaluated beyond the asymptotic realm.

physics.comp-ph↗

arXiv2009

Altruism and reputation: cooperation within groups

In our recent model, the cooperation emerges as a positive feedback between a not-too-bad reputation and an altruistic attitude. Here we introduce a bias of altruism as to favorize members of the same group. The matrix F(i,j) of frequency of cooperation between agents i and j reveals the structure of communities. The Newman algorithm reproduces the initial bias. The method based on differential equations detects two groups of agents cooperating within their groups, leaving the uncooperative ones aside.

physics.soc-ph↗

arXiv2009

Precision and Stability Issues in VBL, the Virtual Biophysics Lab simulation program

The network of biochemical reactions inside living organisms is characterized by an overwhelming complexity which stems from the sheer number of reactions and from the complicated topology of biochemical cycles. However the high speed of computers and the sophisticated computational methods that are available today are powerful tools that allow the numerical exploration of these exceedingly interesting dynamical systems. We are now developing a program, the Virtual Biophysics Lab (VBL), that simulates tumor spheroids, and which includes a reduced - but still quite complex - description of the biochemistry of individual cells, plus many diffusion processes that bring oxygen and nutrients into cells and metabolites into the environment. Each simulation step requires the integration of nonlinear differential equations that describe the individual cell's clockwork and the integration of the diffusion equations. These integrations are carried out under widely different conditions, in a changing environment, and for this reason they need integrators that are both unconditionally stable and that do not display unwanted algorithmic artifacts. These conditions are not always fulfilled in the existing literature, and we feel that a review of the underlying mathematical principles may be important not just for us but for other workers in the field of system biology as well.

physics.bio-ph↗

arXiv2009

Prisoner's Dilemma: non-trivial results for the lowest temptation level in the Darwinian and Pavlovian evolutionary strategies

The lowest temptation level (T = 1) is considered a trivial case for the Prisoner's Dilemma. Here, we show that this statement is true only for a very particular case, where the players interact with only one player. Otherwise, if the players interact with more than one player, the system presents the same possible behaviors observed for $T > 1$. In the steady state, the system can reach the cooperative, chaotic or defective phases, when adopting the Darwinian Evolutionary Strategy and the cooperative or quasi-regular phases, adopting the Pavlovian Evolutionary Strategy.

physics.soc-ph↗

arXiv2009

Intrinsic relationships between broken symmetry energies

The present paper deals with the use of the so-called broken symmetry method for the estimation of the Heisemberg exchange coupling constants. Tetra-nuclear model (square-H4) and chemical (Bis(di-mu-ethoxo-bis(3,5-di-tert-butylsemiquinonato)dicopper(II))) molecules are considered for the analysis. The overdetermination of the problem at hand was exploited to lead to intrinsic relationships between BS energies (independent of spin or exchange couplings). It is demonstrated that only 2 sets of exchange coupling parameters can be obtained from the calculations. The singular values decomposition (SVD) is proposed for the collection of the best parameters that satisfy all linear equations, within modern computers accuracy. Numerical applications as well as the composition of broken symmetry determinants as function of real spin states are discussed.

physics.chem-ph↗