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PubMed2005

Modeling signal transduction networks: a comparison of two stochastic kinetic simulation algorithms.

Computational efficiency of stochastic kinetic algorithms depend on factors such as the overall species population, the total number of reactions, and the average number of nodal interactions or connectivity in a network. These size measures of the network model can have a significant impact on computational efficiency. In this study, two scalable biological networks are used to compare the size scaling efficiencies of two popular and conceptually distinct stochastic kinetic simulation algorithms--the random substrate method of Firth and Bray (FB), and the Gillespie algorithm as implemented using the Gibson-Bruck method (GGB). The arithmetic computational efficiencies of these two algorithms, respectively, scale with the square of the total species population and the logarithm of the total number of active reactions. The two scalable models considered are the size scalable model (SSM), a four compartment reaction model for a signal transduction network involving receptors with single phosphorylation binding sites, and the variable connectivity model (VCM), a single compartment model where receptors possess multiple phosphorylation binding sites. The SSM has fixed species connectivity while the connectivity between species in VCM increases with the number of phosphorylation sites. For SSM, we find that, as the total species population is increased over four orders of magnitude, the GGB algorithm performs significantly better than FB for all three SSM compartment models considered. In contrast, for VCM, we find that as the overall species population decreases while the number of phosphorylation sites increases (implying an increase in network linkage) there exists a crossover point where the computational demands of the GGB method exceed that of the FB.

Computer Simulation↗

PubMed2005

An examination of the validity of nonequilibrium molecular-dynamics simulation algorithms for arbitrary steady-state flows.

Nonlinear-response theory of nonequilibrium molecular-dynamics simulation algorithms is considered under the imposition of an arbitrary steady-state flow field. It is demonstrated that the SLLOD and DOLLS algorithms cannot be used for general flows, although the SLLOD algorithm is rigorous for planar Couette flow. Following the same procedure used to establish SLLOD as the valid algorithm for planar Couette flow [D. J. Evans and E. P. Morriss, Phys. Rev. A 30, 1528 (1984)], it is demonstrated that the p-SLLOD algorithm is valid for arbitrary flows and produces the correct nonlinear response of the viscous pressure tensor.

Journal Article↗

PubMed2005

Mean-field dynamics with stochastic decoherence (MF-SD): a new algorithm for nonadiabatic mixed quantum/classical molecular-dynamics simulations with nuclear-induced decoherence.

The key factors that distinguish algorithms for nonadiabatic mixed quantum/classical (MQC) simulations from each other are how they incorporate quantum decoherence-the fact that classical nuclei must eventually cause a quantum superposition state to collapse into a pure state-and how they model the effects of decoherence on the quantum and classical subsystems. Most algorithms use distinct mechanisms for modeling nonadiabatic transitions between pure quantum basis states ("surface hops") and for calculating the loss of quantum-mechanical phase information (e.g., the decay of the off-diagonal elements of the density matrix). In our view, however, both processes should be unified in a single description of decoherence. In this paper, we start from the density matrix of the total system and use the frozen Gaussian approximation for the nuclear wave function to derive a nuclear-induced decoherence rate for the electronic degrees of freedom. We then use this decoherence rate as the basis for a new nonadiabatic MQC molecular-dynamics (MD) algorithm, which we call mean-field dynamics with stochastic decoherence (MF-SD). MF-SD begins by evolving the quantum subsystem according to the time-dependent Schrodinger equation, leading to mean-field dynamics. MF-SD then uses the nuclear-induced decoherence rate to determine stochastically at each time step whether the system remains in a coherent mixed state or decoheres. Once it is determined that the system should decohere, the quantum subsystem undergoes an instantaneous total wave-function collapse onto one of the adiabatic basis states and the classical velocities are adjusted to conserve energy. Thus, MF-SD combines surface hops and decoherence into a single idea: decoherence in MF-SD does not require the artificial introduction of reference states, auxiliary trajectories, or trajectory swarms, which also makes MF-SD much more computationally efficient than other nonadiabatic MQC MD algorithms. The unified definition of decoherence in MF-SD requires only a single ad hoc parameter, which is not adjustable but instead is determined by the spatial extent of the nonadiabatic coupling. We use MF-SD to solve a series of one-dimensional scattering problems and find that MF-SD is as quantitatively accurate as several existing nonadiabatic MQC MD algorithms and significantly more accurate for some problems.

Journal Article↗

PubMed1994

A fast random cost algorithm for physical mapping.

Ordering clones from a genomic library into physical maps of whole chromosomes presents a central computational/statistical problem in genetics. Here we present a physical mapping algorithm for creating ordered genomic libraries or contig maps by using a random cost approach [Berg, A. (1993) Nature (London) 361, 708-710]. This random cost algorithm is 5-10 times faster than existing physical mapping algorithms and has optimization performance comparable to existing procedures. The speedup in the algorithm makes practical the widespread use of bootstrap resampling to assess the statistical reliability of links in the physical map as well as the use of more elaborate physical mapping criteria to improve map quality. The random cost algorithm is illustrated by its application in assembling a physical map of chromosome IV from the filamentous fungus Aspergillus nidulans.

Aspergillus nidulans↗

PubMed2003

Evaluation of a schizophrenia medication algorithm in a state hospital.

Provider's practice behaviors before and after physician and staff training in the use of a schizophrenia medication algorithm and the effects of education on physician adherence to the algorithm were evaluated. Medical records of 30 patients admitted between September 1 and November 30, 1999, and 30 patients admitted from September 1 to November 30, 2000, with an admitting and discharge diagnosis of schizophrenia and a minimum length of stay of 14 days were randomly selected and analyzed. Clinical data, including prescribed psychotropic medications and dosages, documentation of target symptoms and severity, adverse drug effects, appropriate clinical ratings, patient's response to treatment, and reason for medication change, were collected and compared with the recommendations in the schizophrenia medication algorithm. Efforts to implement the schizophrenia algorithm included staff education and uniform documentation. Progress notes were evaluated before and after training. After physician and staff training, only 5 of 359 progress notes were written using the recommended documentation form. The number of progress notes containing no documentation of symptoms decreased from 66 to 41, and those documenting three to five target symptoms increased from 74 to 140. Documentation of physician assessment of the presence or absence of adverse effects and their severity decreased from 35.2% to 18.7% and from 22.3% to 17.0%, respectively. Physicians increased the documentation of their clinical global impressions from 12.1% to 20.3%. The recording of medication changes increased twofold, but the difference was not significant. Physician and staff education alone did not significantly alter providers' practice behavior. Inadequate and inconsistent documentation of clinical outcomes made it difficult to assess physician adherence to the treatment algorithm.

Adolescent↗

PubMed1986

An efficient string matching algorithm with k differences for nucleotide and amino acid sequences.

There are a few algorithms designed to solve the problem of the optimal alignment of one sequence, the pattern, of length m, with another, longer sequence the text, of length n. These algorithms allow mismatches, deletions and insertions. Algorithms to date run in O(mn) time. Let us define an integer, k, which is the maximal number of differences allowed. We present a simple algorithm showing that sequences can be optimally aligned in O(k2n) time. For long sequences the gain factor over the currently used algorithms is very large.

Amino Acid Sequence↗

PubMed1986

A microcomputer algorithm for solving compartmental models involving radionuclide transformations.

An algorithm for solving first-order non-recycling compartment models is described. Given the initial amounts of a radioactive material in each compartment and the fundamental transfer rate constants between each compartment, the algorithm gives both the amount of material remaining at any time t and the integrated number of transformations that would occur up to time t. The method is analytical, and consequently, is ideally suited for implementation on a microcomputer. For a typical microcomputer with 64 kilobytes of random access memory, a model containing up to 100 compartments, with any number of interconnecting translocation routes, can be solved in a few seconds; providing that no recycling occurs. An example computer program, written in 30 lines of Microsoft BASIC, is included in an appendix to demonstrate the use of the algorithm. A detailed description is included to show how the algorithm is modified to satisfy the requirements commonly encountered in compartment modelling, for example, continuous intake, partitioning of activity, and transformations from radioactive progeny. Although the algorithm does not solve models involving recycling, it is often possible to represent such cases by a non-recycling model which is mathematically equivalent.

Computers↗

PubMed1999

Algorithm for normal random numbers.

We propose a simple algorithm for generating normally distributed pseudorandom numbers. The algorithm simulates N molecules that exchange energy among themselves following a simple stochastic rule. We prove that the system is ergodic, and that a Maxwell-like distribution that may be used as a source of normally distributed random deviates follows in the N-->infinity limit. The algorithm passes various performance tests, including Monte Carlo simulation of a finite two-dimensional Ising model using Wolff's algorithm. It only requires four simple lines of computer code, and is approximately ten times faster than the Box-Muller algorithm.

Journal Article↗

PubMed2000

Cluster algorithm for potts models with fixed spin densities

A cluster algorithm is presented for the simulation of the q-state Potts models in which the number of spins is conserved in each state. The algorithm constructs Fortuin-Kasteleyn cluster configurations from spin configurations, in a way identical to the Swendsen-Wang algorithm; the spin assignment to these clusters is, however, different, and conserves the number of spins for each state. Compared to traditional nonlocal spin-exchange algorithms, the cluster algorithm presented here suffers less from critical slowing down, and consequently is more efficient near the critical temperature.

Journal Article↗

PubMed2000

Adaptive box-assisted algorithm for correlation-dimension estimation

An algorithm is presented for efficient computation of the correlation dimension from a time series. The main feature of the algorithm is the use of a variable number of points in order to keep the number of close pairs approximately constant at the various scales and at the various embedding dimensions. The procedure consists of a number of steps with decreasing cutoff distance; at each step only neighboring pairs are considered, using a box-assisted approach. The algorithm is tested by performing some trials on time series from known model attractors. With respect to the standard algorithm, the one proposed here yields more uniform precision in the various correlation integral values, improving the statistics at the smallest distances. Moreover, it gives a substantial reduction in computation time, allowing execution of trials with a very large number of points, and exploitation of shorter length scales. The algorithm can be easily adapted for the computation of q-order generalized dimensions.

Journal Article↗

PubMed2000

Fourth-order algorithms for solving the multivariable Langevin equation and the Kramers equation.

We develop a fourth-order simulation algorithm for solving the stochastic Langevin equation. The method consists of identifying solvable operators in the Fokker-Planck equation, factorizing the evolution operator for small time steps to fourth order, and implementing the factorization process numerically. A key contribution of this paper is to show how certain double commutators in the factorization process can be simulated in practice. The method is general, applicable to the multivariable case, and systematic, with known procedures for doing fourth-order factorizations. The fourth-order convergence of the resulting algorithm allowed very large time steps to be used. In simulating the Brownian dynamics of 121 Yukawa particles in two dimensions, the converged result of a first-order algorithm can be obtained by using time steps 50 times as large. To further demonstrate the versatility of our method, we derive two new classes of fourth-order algorithms for solving the simpler Kramers equation without requiring the derivative of the force. The convergence of many fourth-order algorithms for solving this equation are compared.

Journal Article↗

PubMed2002

Fast algorithm for generating long self-affine profiles.

We introduce a fast algorithm for generating long self-affine profiles. The algorithm, which is based on the fast wavelet transform, is faster than the conventional Fourier filtering algorithm. In addition to increased performance for large systems, the algorithm, named the wavelet filtering algorithm, a priori gives rise to profiles for which the long-range correlation extends throughout the entire system independently of the length scale.

Journal Article↗

PubMed2002

First- and last-passage Monte Carlo algorithms for the charge density distribution on a conducting surface.

Recent research shows that Monte Carlo diffusion methods are often the most efficient algorithms for solving certain elliptic boundary value problems. In this paper, we extend this research by providing two efficient algorithms based on the concept of "last-passage diffusion." These algorithms are qualitatively compared with each other (and with the best first-passage diffusion algorithm) in solving the classical problem of computing the charge distribution on a conducting disk held at unit voltage. All three algorithms show detailed agreement with the known analytic solution to this problem.

Journal Article↗

PubMed2002

Coarse-grained loop algorithms for Monte Carlo simulation of quantum spin systems.

Recently, Syljuåsen and Sandvik [Phys. Rev. E. (to be published)] proposed a new framework for constructing algorithms of quantum Monte Carlo simulation. While it includes new classes of powerful algorithms, it is not straightforward to find an efficient algorithm for a given model. Based on their framework, we propose an algorithm that is a natural extension of the conventional loop algorithm with the split-spin representation. A complete table of the vertex density and the worm-scattering probability is presented for the general XXZ model of an arbitrary S with a uniform magnetic field.

Journal Article↗

PubMed2004

Efficient algorithms for the laboratory discovery of optimal quantum controls.

The laboratory closed-loop optimal control of quantum phenomena, expressed as minimizing a suitable cost functional, is currently implemented through an optimization algorithm coupled to the experimental apparatus. In practice, the most commonly used search algorithms are variants of genetic algorithms. As an alternative choice, a direct search deterministic algorithm is proposed in this paper. For the simple simulations studied here, it outperforms the existing approaches. An additional algorithm is introduced in order to reveal some properties of the cost functional landscape.

Journal Article↗

PubMed2005

Simulation algorithms for the random-cluster model.

We compare the performance of Monte Carlo algorithms for the simulation of the random-cluster representation of the q-state Potts model for continuous values of q. In particular we consider a local bond update method, a statistical reweighting method of percolation configurations, and a cluster algorithm, all of which generate Boltzmann statistics. The dynamic exponent z of the cluster algorithm appears to be quite small, and to assume the values of the Swendsen-Wang algorithm for q = 2 and 3. The cluster algorithm appears to be much more efficient than our versions of the other two methods for the simulation of the random-cluster model. The higher efficiency of the cluster method with respect to the local method is primarily due to the fact that the computer time usage of the local method increases more rapidly with system size; the difference between the dynamic exponents is less important.

Journal Article↗

PubMed2005

Fourth-order algorithms for solving the imaginary-time Gross-Pitaevskii equation in a rotating anisotropic trap.

By implementing the exact density matrix for the rotating anisotropic harmonic trap, we derive a class of very fast and accurate fourth-order algorithms for evolving the Gross-Pitaevskii equation in imaginary time. Such fourth-order algorithms are possible only with the use of forward, positive time step factorization schemes. These fourth-order algorithms converge at time-step sizes an order-of-magnitude larger than conventional second-order algorithms. Our use of time-dependent factorization schemes provides a systematic way of devising algorithms for solving this type of nonlinear equations.

Journal Article↗

PubMed2005

Statistical-mechanical iterative algorithms on complex networks.

The Ising models have been applied for various problems on information sciences, social sciences, and so on. In many cases, solving these problems corresponds to minimizing the Bethe free energy. To minimize the Bethe free energy, a statistical-mechanical iterative algorithm is often used. We study the statistical-mechanical iterative algorithm on complex networks. To investigate effects of heterogeneous structures on the iterative algorithm, we introduce an iterative algorithm based on information of heterogeneity of complex networks, in which higher-degree nodes are likely to be updated more frequently than lower-degree ones. Numerical experiments clarified that the usage of the information of heterogeneity affects the algorithm in Barabási and Albert networks, but does not influence that in Erdös and Rényi networks. It is revealed that information of the whole system propagates rapidly through such high-degree nodes in the case of Barabási-Albert's scale-free networks.

Journal Article↗