Recycling random numbers in the stochastic simulation algorithm.
Yates, Christian A; Klingbeil, Guido
2013-03-01
The stochastic simulation algorithm (SSA) was introduced by Gillespie and in a different form by Kurtz. Since its original formulation there have been several attempts at improving the efficiency and hence the speed of the algorithm. We briefly discuss some of these methods before outlining our own simple improvement, the recycling direct method (RDM), and demonstrating that it is capable of increasing the speed of most stochastic simulations. The RDM involves the statistically acceptable recycling of random numbers in order to reduce the computational cost associated with their generation and is compatible with several of the pre-existing improvements on the original SSA. Our improvement is also sufficiently simple (one additional line of code) that we hope will be adopted by both trained mathematical modelers and experimentalists wishing to simulate their model systems. PMID:23485273
Algorithmic advances in stochastic programming
Morton, D.P.
1993-07-01
Practical planning problems with deterministic forecasts of inherently uncertain parameters often yield unsatisfactory solutions. Stochastic programming formulations allow uncertain parameters to be modeled as random variables with known distributions, but the size of the resulting mathematical programs can be formidable. Decomposition-based algorithms take advantage of special structure and provide an attractive approach to such problems. We consider two classes of decomposition-based stochastic programming algorithms. The first type of algorithm addresses problems with a ``manageable`` number of scenarios. The second class incorporates Monte Carlo sampling within a decomposition algorithm. We develop and empirically study an enhanced Benders decomposition algorithm for solving multistage stochastic linear programs within a prespecified tolerance. The enhancements include warm start basis selection, preliminary cut generation, the multicut procedure, and decision tree traversing strategies. Computational results are presented for a collection of ``real-world`` multistage stochastic hydroelectric scheduling problems. Recently, there has been an increased focus on decomposition-based algorithms that use sampling within the optimization framework. These approaches hold much promise for solving stochastic programs with many scenarios. A critical component of such algorithms is a stopping criterion to ensure the quality of the solution. With this as motivation, we develop a stopping rule theory for algorithms in which bounds on the optimal objective function value are estimated by sampling. Rules are provided for selecting sample sizes and terminating the algorithm under which asymptotic validity of confidence interval statements for the quality of the proposed solution can be verified. Issues associated with the application of this theory to two sampling-based algorithms are considered, and preliminary empirical coverage results are presented.
A retrodictive stochastic simulation algorithm
Vaughan, T.G. Drummond, P.D.; Drummond, A.J.
2010-05-20
In this paper we describe a simple method for inferring the initial states of systems evolving stochastically according to master equations, given knowledge of the final states. This is achieved through the use of a retrodictive stochastic simulation algorithm which complements the usual predictive stochastic simulation approach. We demonstrate the utility of this new algorithm by applying it to example problems, including the derivation of likely ancestral states of a gene sequence given a Markovian model of genetic mutation.
RES: Regularized Stochastic BFGS Algorithm
NASA Astrophysics Data System (ADS)
Mokhtari, Aryan; Ribeiro, Alejandro
2014-12-01
RES, a regularized stochastic version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is widespread, but the number of iterations required to approximate optimal arguments can be prohibitive in high dimensional problems. Application of second order methods, on the other hand, is impracticable because computation of objective function Hessian inverses incurs excessive computational cost. BFGS modifies gradient descent by introducing a Hessian approximation matrix computed from finite gradient differences. RES utilizes stochastic gradients in lieu of deterministic gradients for both, the determination of descent directions and the approximation of the objective function's curvature. Since stochastic gradients can be computed at manageable computational cost RES is realizable and retains the convergence rate advantages of its deterministic counterparts. Convergence results show that lower and upper bounds on the Hessian egeinvalues of the sample functions are sufficient to guarantee convergence to optimal arguments. Numerical experiments showcase reductions in convergence time relative to stochastic gradient descent algorithms and non-regularized stochastic versions of BFGS. An application of RES to the implementation of support vector machines is developed.
Enhanced algorithms for stochastic programming
Krishna, A.S.
1993-09-01
In this dissertation, we present some of the recent advances made in solving two-stage stochastic linear programming problems of large size and complexity. Decomposition and sampling are two fundamental components of techniques to solve stochastic optimization problems. We describe improvements to the current techniques in both these areas. We studied different ways of using importance sampling techniques in the context of Stochastic programming, by varying the choice of approximation functions used in this method. We have concluded that approximating the recourse function by a computationally inexpensive piecewise-linear function is highly efficient. This reduced the problem from finding the mean of a computationally expensive functions to finding that of a computationally inexpensive function. Then we implemented various variance reduction techniques to estimate the mean of a piecewise-linear function. This method achieved similar variance reductions in orders of magnitude less time than, when we directly applied variance-reduction techniques directly on the given problem. In solving a stochastic linear program, the expected value problem is usually solved before a stochastic solution and also to speed-up the algorithm by making use of the information obtained from the solution of the expected value problem. We have devised a new decomposition scheme to improve the convergence of this algorithm.
Algorithm refinement for the stochastic Burgers' equation
Bell, John B.; Foo, Jasmine; Garcia, Alejandro L. . E-mail: algarcia@algarcia.org
2007-04-10
In this paper, we develop an algorithm refinement (AR) scheme for an excluded random walk model whose mean field behavior is given by the viscous Burgers' equation. AR hybrids use the adaptive mesh refinement framework to model a system using a molecular algorithm where desired while allowing a computationally faster continuum representation to be used in the remainder of the domain. The focus in this paper is the role of fluctuations on the dynamics. In particular, we demonstrate that it is necessary to include a stochastic forcing term in Burgers' equation to accurately capture the correct behavior of the system. The conclusion we draw from this study is that the fidelity of multiscale methods that couple disparate algorithms depends on the consistent modeling of fluctuations in each algorithm and on a coupling, such as algorithm refinement, that preserves this consistency.
Morton, D.P.
1994-01-01
Handling uncertainty in natural inflow is an important part of a hydroelectric scheduling model. In a stochastic programming formulation, natural inflow may be modeled as a random vector with known distribution, but the size of the resulting mathematical program can be formidable. Decomposition-based algorithms take advantage of special structure and provide an attractive approach to such problems. We develop an enhanced Benders decomposition algorithm for solving multistage stochastic linear programs. The enhancements include warm start basis selection, preliminary cut generation, the multicut procedure, and decision tree traversing strategies. Computational results are presented for a collection of stochastic hydroelectric scheduling problems. Stochastic programming, Hydroelectric scheduling, Large-scale Systems.
Chow, Sy-Miin; Lu, Zhaohua; Sherwood, Andrew; Zhu, Hongtu
2016-03-01
The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation-maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed. PMID:25416456
A Stochastic Collocation Algorithm for Uncertainty Analysis
NASA Technical Reports Server (NTRS)
Mathelin, Lionel; Hussaini, M. Yousuff; Zang, Thomas A. (Technical Monitor)
2003-01-01
This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.
A novel stochastic optimization algorithm.
Li, B; Jiang, W
2000-01-01
This paper presents a new stochastic approach SAGACIA based on proper integration of simulated annealing algorithm (SAA), genetic algorithm (GA), and chemotaxis algorithm (CA) for solving complex optimization problems. SAGACIA combines the advantages of SAA, GA, and CA together. It has the following features: (1) it is not the simple mix of SAA, GA, and CA; (2) it works from a population; (3) it can be easily used to solve optimization problems either with continuous variables or with discrete variables, and it does not need coding and decoding,; and (4) it can easily escape from local minima and converge quickly. Good solutions can be obtained in a very short time. The search process of SAGACIA can be explained with Markov chains. In this paper, it is proved that SAGACIA has the property of global asymptotical convergence. SAGACIA has been applied to solve such problems as scheduling, the training of artificial neural networks, and the optimizing of complex functions. In all the test cases, the performance of SAGACIA is better than that of SAA, GA, and CA. PMID:18244742
Stochastic structure formation in random media
NASA Astrophysics Data System (ADS)
Klyatskin, V. I.
2016-01-01
Stochastic structure formation in random media is considered using examples of elementary dynamical systems related to the two-dimensional geophysical fluid dynamics (Gaussian random fields) and to stochastically excited dynamical systems described by partial differential equations (lognormal random fields). In the latter case, spatial structures (clusters) may form with a probability of one in almost every system realization due to rare events happening with vanishing probability. Problems involving stochastic parametric excitation occur in fluid dynamics, magnetohydrodynamics, plasma physics, astrophysics, and radiophysics. A more complicated stochastic problem dealing with anomalous structures on the sea surface (rogue waves) is also considered, where the random Gaussian generation of sea surface roughness is accompanied by parametric excitation.
Bootstrap performance profiles in stochastic algorithms assessment
Costa, Lino; Espírito Santo, Isabel A.C.P.; Oliveira, Pedro
2015-03-10
Optimization with stochastic algorithms has become a relevant research field. Due to its stochastic nature, its assessment is not straightforward and involves integrating accuracy and precision. Performance profiles for the mean do not show the trade-off between accuracy and precision, and parametric stochastic profiles require strong distributional assumptions and are limited to the mean performance for a large number of runs. In this work, bootstrap performance profiles are used to compare stochastic algorithms for different statistics. This technique allows the estimation of the sampling distribution of almost any statistic even with small samples. Multiple comparison profiles are presented for more than two algorithms. The advantages and drawbacks of each assessment methodology are discussed.
Linear-scaling and parallelisable algorithms for stochastic quantum chemistry
NASA Astrophysics Data System (ADS)
Booth, George H.; Smart, Simon D.; Alavi, Ali
2014-07-01
For many decades, quantum chemical method development has been dominated by algorithms which involve increasingly complex series of tensor contractions over one-electron orbital spaces. Procedures for their derivation and implementation have evolved to require the minimum amount of logic and rely heavily on computationally efficient library-based matrix algebra and optimised paging schemes. In this regard, the recent development of exact stochastic quantum chemical algorithms to reduce computational scaling and memory overhead requires a contrasting algorithmic philosophy, but one which when implemented efficiently can achieve higher accuracy/cost ratios with small random errors. Additionally, they can exploit the continuing trend for massive parallelisation which hinders the progress of deterministic high-level quantum chemical algorithms. In the Quantum Monte Carlo community, stochastic algorithms are ubiquitous but the discrete Fock space of quantum chemical methods is often unfamiliar, and the methods introduce new concepts required for algorithmic efficiency. In this paper, we explore these concepts and detail an algorithm used for Full Configuration Interaction Quantum Monte Carlo (FCIQMC), which is implemented and available in MOLPRO and as a standalone code, and is designed for high-level parallelism and linear-scaling with walker number. Many of the algorithms are also in use in, or can be transferred to, other stochastic quantum chemical methods and implementations. We apply these algorithms to the strongly correlated chromium dimer to demonstrate their efficiency and parallelism.
Stochastic template placement algorithm for gravitational wave data analysis
Harry, I. W.; Sathyaprakash, B. S.; Allen, B.
2009-11-15
This paper presents an algorithm for constructing matched-filter template banks in an arbitrary parameter space. The method places templates at random, then removes those which are 'too close' together. The properties and optimality of stochastic template banks generated in this manner are investigated for some simple models. The effectiveness of these template banks for gravitational wave searches for binary inspiral waveforms is also examined. The properties of a stochastic template bank are then compared to the deterministically placed template banks that are currently used in gravitational wave data analysis.
Stochastic Leader Gravitational Search Algorithm for Enhanced Adaptive Beamforming Technique.
Darzi, Soodabeh; Islam, Mohammad Tariqul; Tiong, Sieh Kiong; Kibria, Salehin; Singh, Mandeep
2015-01-01
In this paper, stochastic leader gravitational search algorithm (SL-GSA) based on randomized k is proposed. Standard GSA (SGSA) utilizes the best agents without any randomization, thus it is more prone to converge at suboptimal results. Initially, the new approach randomly choses k agents from the set of all agents to improve the global search ability. Gradually, the set of agents is reduced by eliminating the agents with the poorest performances to allow rapid convergence. The performance of the SL-GSA was analyzed for six well-known benchmark functions, and the results are compared with SGSA and some of its variants. Furthermore, the SL-GSA is applied to minimum variance distortionless response (MVDR) beamforming technique to ensure compatibility with real world optimization problems. The proposed algorithm demonstrates superior convergence rate and quality of solution for both real world problems and benchmark functions compared to original algorithm and other recent variants of SGSA. PMID:26552032
Stochastic Leader Gravitational Search Algorithm for Enhanced Adaptive Beamforming Technique
Darzi, Soodabeh; Islam, Mohammad Tariqul; Tiong, Sieh Kiong; Kibria, Salehin; Singh, Mandeep
2015-01-01
In this paper, stochastic leader gravitational search algorithm (SL-GSA) based on randomized k is proposed. Standard GSA (SGSA) utilizes the best agents without any randomization, thus it is more prone to converge at suboptimal results. Initially, the new approach randomly choses k agents from the set of all agents to improve the global search ability. Gradually, the set of agents is reduced by eliminating the agents with the poorest performances to allow rapid convergence. The performance of the SL-GSA was analyzed for six well-known benchmark functions, and the results are compared with SGSA and some of its variants. Furthermore, the SL-GSA is applied to minimum variance distortionless response (MVDR) beamforming technique to ensure compatibility with real world optimization problems. The proposed algorithm demonstrates superior convergence rate and quality of solution for both real world problems and benchmark functions compared to original algorithm and other recent variants of SGSA. PMID:26552032
An exact accelerated stochastic simulation algorithm
Mjolsness, Eric; Orendorff, David; Chatelain, Philippe; Koumoutsakos, Petros
2009-01-01
An exact method for stochastic simulation of chemical reaction networks, which accelerates the stochastic simulation algorithm (SSA), is proposed. The present “ER-leap” algorithm is derived from analytic upper and lower bounds on the multireaction probabilities sampled by SSA, together with rejection sampling and an adaptive multiplicity for reactions. The algorithm is tested on a number of well-quantified reaction networks and is found experimentally to be very accurate on test problems including a chaotic reaction network. At the same time ER-leap offers a substantial speedup over SSA with a simulation time proportional to the 2∕3 power of the number of reaction events in a Galton–Watson process. PMID:19368432
Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes
NASA Technical Reports Server (NTRS)
Williams Colin P.
1999-01-01
Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.
Stochastic Evolutionary Algorithms for Planning Robot Paths
NASA Technical Reports Server (NTRS)
Fink, Wolfgang; Aghazarian, Hrand; Huntsberger, Terrance; Terrile, Richard
2006-01-01
A computer program implements stochastic evolutionary algorithms for planning and optimizing collision-free paths for robots and their jointed limbs. Stochastic evolutionary algorithms can be made to produce acceptably close approximations to exact, optimal solutions for path-planning problems while often demanding much less computation than do exhaustive-search and deterministic inverse-kinematics algorithms that have been used previously for this purpose. Hence, the present software is better suited for application aboard robots having limited computing capabilities (see figure). The stochastic aspect lies in the use of simulated annealing to (1) prevent trapping of an optimization algorithm in local minima of an energy-like error measure by which the fitness of a trial solution is evaluated while (2) ensuring that the entire multidimensional configuration and parameter space of the path-planning problem is sampled efficiently with respect to both robot joint angles and computation time. Simulated annealing is an established technique for avoiding local minima in multidimensional optimization problems, but has not, until now, been applied to planning collision-free robot paths by use of low-power computers.
Random musings on stochastics (Lorenz Lecture)
NASA Astrophysics Data System (ADS)
Koutsoyiannis, D.
2014-12-01
In 1960 Lorenz identified the chaotic nature of atmospheric dynamics, thus highlighting the importance of the discovery of chaos by Poincare, 70 years earlier, in the motion of three bodies. Chaos in the macroscopic world offered a natural way to explain unpredictability, that is, randomness. Concurrently with Poincare's discovery, Boltzmann introduced statistical physics, while soon after Borel and Lebesgue laid the foundation of measure theory, later (in 1930s) used by Kolmogorov as the formal foundation of probability theory. Subsequently, Kolmogorov and Khinchin introduced the concepts of stochastic processes and stationarity, and advanced the concept of ergodicity. All these areas are now collectively described by the term "stochastics", which includes probability theory, stochastic processes and statistics. As paradoxical as it may seem, stochastics offers the tools to deal with chaos, even if it results from deterministic dynamics. As chaos entails uncertainty, it is more informative and effective to replace the study of exact system trajectories with that of probability densities. Also, as the exact laws of complex systems can hardly be deduced by synthesis of the detailed interactions of system components, these laws should inevitably be inferred by induction, based on observational data and using statistics. The arithmetic of stochastics is quite different from that of regular numbers. Accordingly, it needs the development of intuition and interpretations which differ from those built upon deterministic considerations. Using stochastic tools in a deterministic context may result in mistaken conclusions. In an attempt to contribute to a more correct interpretation and use of stochastic concepts in typical tasks of nonlinear systems, several examples are studied, which aim (a) to clarify the difference in the meaning of linearity in deterministic and stochastic context; (b) to contribute to a more attentive use of stochastic concepts (entropy, statistical
The theory of hybrid stochastic algorithms
Kennedy, A.D. . Supercomputer Computations Research Inst.)
1989-11-21
These lectures introduce the family of Hybrid Stochastic Algorithms for performing Monte Carlo calculations in Quantum Field Theory. After explaining the basic concepts of Monte Carlo integration we discuss the properties of Markov processes and one particularly useful example of them: the Metropolis algorithm. Building upon this framework we consider the Hybrid and Langevin algorithms from the viewpoint that they are approximate versions of the Hybrid Monte Carlo method; and thus we are led to consider Molecular Dynamics using the Leapfrog algorithm. The lectures conclude by reviewing recent progress in these areas, explaining higher-order integration schemes, the asymptotic large-volume behaviour of the various algorithms, and some simple exact results obtained by applying them to free field theory. It is attempted throughout to give simple yet correct proofs of the various results encountered. 38 refs.
A hierarchical exact accelerated stochastic simulation algorithm
Orendorff, David; Mjolsness, Eric
2012-01-01
A new algorithm, “HiER-leap” (hierarchical exact reaction-leaping), is derived which improves on the computational properties of the ER-leap algorithm for exact accelerated simulation of stochastic chemical kinetics. Unlike ER-leap, HiER-leap utilizes a hierarchical or divide-and-conquer organization of reaction channels into tightly coupled “blocks” and is thereby able to speed up systems with many reaction channels. Like ER-leap, HiER-leap is based on the use of upper and lower bounds on the reaction propensities to define a rejection sampling algorithm with inexpensive early rejection and acceptance steps. But in HiER-leap, large portions of intra-block sampling may be done in parallel. An accept/reject step is used to synchronize across blocks. This method scales well when many reaction channels are present and has desirable asymptotic properties. The algorithm is exact, parallelizable and achieves a significant speedup over the stochastic simulation algorithm and ER-leap on certain problems. This algorithm offers a potentially important step towards efficient in silico modeling of entire organisms. PMID:23231214
Perspective: Stochastic algorithms for chemical kinetics
Gillespie, Daniel T.; Hellander, Andreas; Petzold, Linda R.
2013-01-01
We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not well-mixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes. PMID:23656106
Stochastic algorithms for Markov models estimation with intermittent missing data.
Deltour, I; Richardson, S; Le Hesran, J Y
1999-06-01
Multistate Markov models are frequently used to characterize disease processes, but their estimation from longitudinal data is often hampered by complex patterns of incompleteness. Two algorithms for estimating Markov chain models in the case of intermittent missing data in longitudinal studies, a stochastic EM algorithm and the Gibbs sampler, are described. The first can be viewed as a random perturbation of the EM algorithm and is appropriate when the M step is straightforward but the E step is computationally burdensome. It leads to a good approximation of the maximum likelihood estimates. The Gibbs sampler is used for a full Bayesian inference. The performances of the two algorithms are illustrated on two simulated data sets. A motivating example concerned with the modelling of the evolution of parasitemia by Plasmodium falciparum (malaria) in a cohort of 105 young children in Cameroon is described and briefly analyzed. PMID:11318215
Path sampling with stochastic dynamics: Some new algorithms
Stoltz, Gabriel . E-mail: stoltz@cermics.enpc.fr
2007-07-01
We propose here some new sampling algorithms for path sampling in the case when stochastic dynamics are used. In particular, we present a new proposal function for equilibrium sampling of paths with a Monte-Carlo dynamics (the so-called 'brownian tube' proposal). This proposal is based on the continuity of the dynamics with respect to the random forcing, and generalizes all previous approaches when stochastic dynamics are used. The efficiency of this proposal is demonstrated using some measure of decorrelation in path space. We also discuss a switching strategy that allows to transform ensemble of paths at a finite rate while remaining at equilibrium, in contrast with the usual Jarzynski like switching. This switching is very interesting to sample constrained paths starting from unconstrained paths, or to perform simulated annealing in a rigorous way.
A stochastic approximation algorithm for estimating mixture proportions
NASA Technical Reports Server (NTRS)
Sparra, J.
1976-01-01
A stochastic approximation algorithm for estimating the proportions in a mixture of normal densities is presented. The algorithm is shown to converge to the true proportions in the case of a mixture of two normal densities.
Constant-complexity stochastic simulation algorithm with optimal binning
Sanft, Kevin R.; Othmer, Hans G.
2015-08-21
At the molecular level, biochemical processes are governed by random interactions between reactant molecules, and the dynamics of such systems are inherently stochastic. When the copy numbers of reactants are large, a deterministic description is adequate, but when they are small, such systems are often modeled as continuous-time Markov jump processes that can be described by the chemical master equation. Gillespie’s Stochastic Simulation Algorithm (SSA) generates exact trajectories of these systems, but the amount of computational work required for each step of the original SSA is proportional to the number of reaction channels, leading to computational complexity that scales linearly with the problem size. The original SSA is therefore inefficient for large problems, which has prompted the development of several alternative formulations with improved scaling properties. We describe an exact SSA that uses a table data structure with event time binning to achieve constant computational complexity with respect to the number of reaction channels for weakly coupled reaction networks. We present a novel adaptive binning strategy and discuss optimal algorithm parameters. We compare the computational efficiency of the algorithm to existing methods and demonstrate excellent scaling for large problems. This method is well suited for generating exact trajectories of large weakly coupled models, including those that can be described by the reaction-diffusion master equation that arises from spatially discretized reaction-diffusion processes.
Second-order stochastic leapfrog algorithm for multiplicative noise brownian motion
Qiang; Habib
2000-11-01
A stochastic leapfrog algorithm for the numerical integration of Brownian motion stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a second-order convergence of moments in a finite time interval and requires the sampling of only one uniformly distributed random variable per time step. The noise may be white or colored. We apply the algorithm to a study of the approach towards equilibrium of an oscillator coupled nonlinearly to a heat bath and investigate the effect of the multiplicative noise (arising from the nonlinear coupling) on the relaxation time. This allows us to test the regime of validity of the energy-envelope approximation method. PMID:11102105
Second-order stochastic leapfrog algorithm for multiplicative noise Brownian motion
NASA Astrophysics Data System (ADS)
Qiang, Ji; Habib, Salman
2000-11-01
A stochastic leapfrog algorithm for the numerical integration of Brownian motion stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a second-order convergence of moments in a finite time interval and requires the sampling of only one uniformly distributed random variable per time step. The noise may be white or colored. We apply the algorithm to a study of the approach towards equilibrium of an oscillator coupled nonlinearly to a heat bath and investigate the effect of the multiplicative noise (arising from the nonlinear coupling) on the relaxation time. This allows us to test the regime of validity of the energy-envelope approximation method.
Stochastic Formal Correctness of Numerical Algorithms
NASA Technical Reports Server (NTRS)
Daumas, Marc; Lester, David; Martin-Dorel, Erik; Truffert, Annick
2009-01-01
We provide a framework to bound the probability that accumulated errors were never above a given threshold on numerical algorithms. Such algorithms are used for example in aircraft and nuclear power plants. This report contains simple formulas based on Levy's and Markov's inequalities and it presents a formal theory of random variables with a special focus on producing concrete results. We selected four very common applications that fit in our framework and cover the common practices of systems that evolve for a long time. We compute the number of bits that remain continuously significant in the first two applications with a probability of failure around one out of a billion, where worst case analysis considers that no significant bit remains. We are using PVS as such formal tools force explicit statement of all hypotheses and prevent incorrect uses of theorems.
Parameter identification using a creeping-random-search algorithm
NASA Technical Reports Server (NTRS)
Parrish, R. V.
1971-01-01
A creeping-random-search algorithm is applied to different types of problems in the field of parameter identification. The studies are intended to demonstrate that a random-search algorithm can be applied successfully to these various problems, which often cannot be handled by conventional deterministic methods, and, also, to introduce methods that speed convergence to an extremal of the problem under investigation. Six two-parameter identification problems with analytic solutions are solved, and two application problems are discussed in some detail. Results of the study show that a modified version of the basic creeping-random-search algorithm chosen does speed convergence in comparison with the unmodified version. The results also show that the algorithm can successfully solve problems that contain limits on state or control variables, inequality constraints (both independent and dependent, and linear and nonlinear), or stochastic models.
Exploratory Analysis of Stochastic Local Search Algorithms in Biobjective Optimization
NASA Astrophysics Data System (ADS)
López-Ibáñez, Manuel; Paquete, Luís; Stützle, Thomas
This chapter introduces two Perl programs that implement graphical tools for exploring the performance of stochastic local search algorithms for biobjective optimization problems. These tools are based on the concept of the empirical attainment function (EAF), which describes the probabilistic distribution of the outcomes obtained by a stochastic algorithm in the objective space. In particular, we consider the visualization of attainment surfaces and differences between the first-order EAFs of the outcomes of two algorithms. This visualization allows us to identify certain algorithmic behaviors in a graphical way. We explain the use of these visualization tools and illustrate them with examples arising from practice.
Stochastic reaction–diffusion algorithms for macromolecular crowding
NASA Astrophysics Data System (ADS)
Sturrock, Marc
2016-06-01
Compartment-based (lattice-based) reaction–diffusion algorithms are often used for studying complex stochastic spatio-temporal processes inside cells. In this paper the influence of macromolecular crowding on stochastic reaction–diffusion simulations is investigated. Reaction–diffusion processes are considered on two different kinds of compartmental lattice, a cubic lattice and a hexagonal close packed lattice, and solved using two different algorithms, the stochastic simulation algorithm and the spatiocyte algorithm (Arjunan and Tomita 2010 Syst. Synth. Biol. 4, 35–53). Obstacles (modelling macromolecular crowding) are shown to have substantial effects on the mean squared displacement and average number of molecules in the domain but the nature of these effects is dependent on the choice of lattice, with the cubic lattice being more susceptible to the effects of the obstacles. Finally, improvements for both algorithms are presented.
Random Walk-Based Solution to Triple Level Stochastic Point Location Problem.
Jiang, Wen; Huang, De-Shuang; Li, Shenghong
2016-06-01
This paper considers the stochastic point location (SPL) problem as a learning mechanism trying to locate a point on a real line via interacting with a random environment. Compared to the stochastic environment in the literatures that confines the learning mechanism to moving in two directions, i.e., left or right, this paper introduces a general triple level stochastic environment which not only tells the learning mechanism to go left or right, but also informs it to stay unmoved. It is easy to understand, as we will prove in this paper, that the environment reported in the previous literatures is just a special case of the triple level environment. And a new learning algorithm, named as random walk-based triple level learning algorithm, is proposed to locate an unknown point under this new type of environment. In order to examine the performance of this algorithm, we divided the triple level SPL problems into four distinguished scenarios by the properties of the unknown point and the stochastic environment, and proved that even under the triple level nonstationary environment and the convergence condition having not being satisfied for some time, which are rarely considered in existing SPL problems, the proposed learning algorithm is still working properly whenever the unknown point is static or evolving with time. Extensive experiments validate our theoretical analyses and demonstrate that the proposed learning algorithms are quite effective and efficient. PMID:26168455
Cao Yang . E-mail: ycao@cs.ucsb.edu; Gillespie, Dan . E-mail: GillespieDT@mailaps.org; Petzold, Linda . E-mail: petzold@engineering.ucsb.edu
2005-07-01
In this paper, we introduce a multiscale stochastic simulation algorithm (MSSA) which makes use of Gillespie's stochastic simulation algorithm (SSA) together with a new stochastic formulation of the partial equilibrium assumption (PEA). This method is much more efficient than SSA alone. It works even with a very small population of fast species. Implementation details are discussed, and an application to the modeling of the heat shock response of E. Coli is presented which demonstrates the excellent efficiency and accuracy obtained with the new method.
Random attractor of non-autonomous stochastic Boussinesq lattice system
Zhao, Min Zhou, Shengfan
2015-09-15
In this paper, we first consider the existence of tempered random attractor for second-order non-autonomous stochastic lattice dynamical system of nonlinear Boussinesq equations effected by time-dependent coupled coefficients and deterministic forces and multiplicative white noise. Then, we establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.
Designing Stochastic Optimization Algorithms for Real-world Applications
NASA Astrophysics Data System (ADS)
Someya, Hiroshi; Handa, Hisashi; Koakutsu, Seiichi
This article presents a review of recent advances in stochastic optimization algorithms. Novel algorithms achieving highly adaptive and efficient searches, theoretical analyses to deepen our understanding of search behavior, successful implementation on parallel computers, attempts to build benchmark suites for industrial use, and techniques applied to real-world problems are included. A list of resources is provided.
Webster, Clayton G; Gunzburger, Max D
2013-01-01
We present a scalable, parallel mechanism for stochastic identification/control for problems constrained by partial differential equations with random input data. Several identification objectives will be discussed that either minimize the expectation of a tracking cost functional or minimize the difference of desired statistical quantities in the appropriate $L^p$ norm, and the distributed parameters/control can both deterministic or stochastic. Given an objective we prove the existence of an optimal solution, establish the validity of the Lagrange multiplier rule and obtain a stochastic optimality system of equations. The modeling process may describe the solution in terms of high dimensional spaces, particularly in the case when the input data (coefficients, forcing terms, boundary conditions, geometry, etc) are affected by a large amount of uncertainty. For higher accuracy, the computer simulation must increase the number of random variables (dimensions), and expend more effort approximating the quantity of interest in each individual dimension. Hence, we introduce a novel stochastic parameter identification algorithm that integrates an adjoint-based deterministic algorithm with the sparse grid stochastic collocation FEM approach. This allows for decoupled, moderately high dimensional, parameterized computations of the stochastic optimality system, where at each collocation point, deterministic analysis and techniques can be utilized. The advantage of our approach is that it allows for the optimal identification of statistical moments (mean value, variance, covariance, etc.) or even the whole probability distribution of the input random fields, given the probability distribution of some responses of the system (quantities of physical interest). Our rigorously derived error estimates, for the fully discrete problems, will be described and used to compare the efficiency of the method with several other techniques. Numerical examples illustrate the theoretical
Evolving Stochastic Learning Algorithm based on Tsallis entropic index
NASA Astrophysics Data System (ADS)
Anastasiadis, A. D.; Magoulas, G. D.
2006-03-01
In this paper, inspired from our previous algorithm, which was based on the theory of Tsallis statistical mechanics, we develop a new evolving stochastic learning algorithm for neural networks. The new algorithm combines deterministic and stochastic search steps by employing a different adaptive stepsize for each network weight, and applies a form of noise that is characterized by the nonextensive entropic index q, regulated by a weight decay term. The behavior of the learning algorithm can be made more stochastic or deterministic depending on the trade off between the temperature T and the q values. This is achieved by introducing a formula that defines a time-dependent relationship between these two important learning parameters. Our experimental study verifies that there are indeed improvements in the convergence speed of this new evolving stochastic learning algorithm, which makes learning faster than using the original Hybrid Learning Scheme (HLS). In addition, experiments are conducted to explore the influence of the entropic index q and temperature T on the convergence speed and stability of the proposed method.
On stochastic approximation algorithms for classes of PAC learning problems
Rao, N.S.V.; Uppuluri, V.R.R.; Oblow, E.M.
1994-03-01
The classical stochastic approximation methods are shown to yield algorithms to solve several formulations of the PAC learning problem defined on the domain [o,1]{sup d}. Under some assumptions on different ability of the probability measure functions, simple algorithms to solve some PAC learning problems are proposed based on networks of non-polynomial units (e.g. artificial neural networks). Conditions on the sizes of these samples required to ensure the error bounds are derived using martingale inequalities.
Fast Quantum Algorithms for Numerical Integrals and Stochastic Processes
NASA Technical Reports Server (NTRS)
Abrams, D.; Williams, C.
1999-01-01
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known classical deterministic algotithms and a quadratic speed increase incomparison to classical Monte Carlo methods.
Point group identification algorithm in dynamic response analysis of nonlinear stochastic systems
NASA Astrophysics Data System (ADS)
Li, Tao; Chen, Jian-bing; Li, Jie
2016-03-01
The point group identification (PGI) algorithm is proposed to determine the representative point sets in response analysis of nonlinear stochastic dynamic systems. The PGI algorithm is employed to identify point groups and their feature points in an initial point set by combining subspace clustering analysis and the graph theory. Further, the representative point set of the random-variate space is determined according to the minimum generalized F-discrepancy. The dynamic responses obtained by incorporating the algorithm PGI into the probability density evolution method (PDEM) are compared with those by the Monte Carlo simulation method. The investigations indicate that the proposed method can reduce the number of the representative points, lower the generalized F-discrepancy of the representative point set, and also ensure the accuracy of stochastic structural dynamic analysis.
Quantum stochastic walks: A generalization of classical random walks and quantum walks
NASA Astrophysics Data System (ADS)
Aspuru-Guzik, Alan
2010-03-01
We introduce the quantum stochastic walk (QSW), which determines the evolution of generalized quantum mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical and quantum-stochastic transitions from a vertex as defined by its connectivity. We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases, but also includes more general probability distributions. As an example, we study the QSW on a line, the QW to CRW transition and transitions to genearlized QSWs that go beyond the CRW and QW. QSWs provide a new framework to the study of quantum algorithms as well as of quantum walks with environmental effects.
Random search optimization based on genetic algorithm and discriminant function
NASA Technical Reports Server (NTRS)
Kiciman, M. O.; Akgul, M.; Erarslanoglu, G.
1990-01-01
The general problem of optimization with arbitrary merit and constraint functions, which could be convex, concave, monotonic, or non-monotonic, is treated using stochastic methods. To improve the efficiency of the random search methods, a genetic algorithm for the search phase and a discriminant function for the constraint-control phase were utilized. The validity of the technique is demonstrated by comparing the results to published test problem results. Numerical experimentation indicated that for cases where a quick near optimum solution is desired, a general, user-friendly optimization code can be developed without serious penalties in both total computer time and accuracy.
Randomized Algorithms for Matrices and Data
NASA Astrophysics Data System (ADS)
Mahoney, Michael W.
2012-03-01
This chapter reviews recent work on randomized matrix algorithms. By “randomized matrix algorithms,” we refer to a class of recently developed random sampling and random projection algorithms for ubiquitous linear algebra problems such as least-squares (LS) regression and low-rank matrix approximation. These developments have been driven by applications in large-scale data analysis—applications which place very different demands on matrices than traditional scientific computing applications. Thus, in this review, we will focus on highlighting the simplicity and generality of several core ideas that underlie the usefulness of these randomized algorithms in scientific applications such as genetics (where these algorithms have already been applied) and astronomy (where, hopefully, in part due to this review they will soon be applied). The work we will review here had its origins within theoretical computer science (TCS). An important feature in the use of randomized algorithms in TCS more generally is that one must identify and then algorithmically deal with relevant “nonuniformity structure” in the data. For the randomized matrix algorithms to be reviewed here and that have proven useful recently in numerical linear algebra (NLA) and large-scale data analysis applications, the relevant nonuniformity structure is defined by the so-called statistical leverage scores. Defined more precisely below, these leverage scores are basically the diagonal elements of the projection matrix onto the dominant part of the spectrum of the input matrix. As such, they have a long history in statistical data analysis, where they have been used for outlier detection in regression diagnostics. More generally, these scores often have a very natural interpretation in terms of the data and processes generating the data. For example, they can be interpreted in terms of the leverage or influence that a given data point has on, say, the best low-rank matrix approximation; and this
A random search algorithm for laboratory computers
NASA Technical Reports Server (NTRS)
Curry, R. E.
1975-01-01
The small laboratory computer is ideal for experimental control and data acquisition. Postexperimental data processing is often performed on large computers because of the availability of sophisticated programs, but costs and data compatibility are negative factors. Parameter optimization can be accomplished on the small computer, offering ease of programming, data compatibility, and low cost. A previously proposed random-search algorithm ('random creep') was found to be very slow in convergence. A method is proposed (the 'random leap' algorithm) which starts in a global search mode and automatically adjusts step size to speed convergence. A FORTRAN executive program for the random-leap algorithm is presented which calls a user-supplied function subroutine. An example of a function subroutine is given which calculates maximum-likelihood estimates of receiver operating-characteristic parameters from binary response data. Other applications in parameter estimation, generalized least squares, and matrix inversion are discussed.
A fast and convergent stochastic MLP learning algorithm.
Sakurai, A
2001-12-01
We propose a stochastic learning algorithm for multilayer perceptrons of linear-threshold function units, which theoretically converges with probability one and experimentally exhibits 100% convergence rate and remarkable speed on parity and classification problems with typical generalization accuracy. For learning the n bit parity function with n hidden units, the algorithm converged on all the trials we tested (n=2 to 12) after 5.8 x 4.1(n) presentations for 0.23 x 4.0(n-6) seconds on a 533MHz Alpha 21164A chip on average, which is five to ten times faster than Levenberg-Marquardt algorithm with restarts. For a medium size classification problem known as Thyroid in UCI repository, the algorithm is faster in speed and comparative in generalization accuracy than the standard backpropagation and Levenberg-Marquardt algorithms. PMID:11852440
Stochastic search in structural optimization - Genetic algorithms and simulated annealing
NASA Technical Reports Server (NTRS)
Hajela, Prabhat
1993-01-01
An account is given of illustrative applications of genetic algorithms and simulated annealing methods in structural optimization. The advantages of such stochastic search methods over traditional mathematical programming strategies are emphasized; it is noted that these methods offer a significantly higher probability of locating the global optimum in a multimodal design space. Both genetic-search and simulated annealing can be effectively used in problems with a mix of continuous, discrete, and integer design variables.
NASA Astrophysics Data System (ADS)
El-Wakil, S. A.; Sallah, M.; El-Hanbaly, A. M.
2015-10-01
The stochastic radiative transfer problem is studied in a participating planar finite continuously fluctuating medium. The problem is considered for specular- and diffusly-reflecting boundaries with linear anisotropic scattering. Random variable transformation (RVT) technique is used to get the complete average for the solution functions, that are represented by the probability-density function (PDF) of the solution process. In the RVT algorithm, a simple integral transformation to the input stochastic process (the extinction function of the medium) is applied. This linear transformation enables us to rewrite the stochastic transport equations in terms of the optical random variable (x) and the optical random thickness (L). Then the transport equation is solved deterministically to get a closed form for the solution as a function of x and L. So, the solution is used to obtain the PDF of the solution functions applying the RVT technique among the input random variable (L) and the output process (the solution functions). The obtained averages of the solution functions are used to get the complete analytical averages for some interesting physical quantities, namely, reflectivity and transmissivity at the medium boundaries. In terms of the average reflectivity and transmissivity, the average of the partial heat fluxes for the generalized problem with internal source of radiation are obtained and represented graphically.
NASA Astrophysics Data System (ADS)
Liang, Rui; Schruff, Tobias; Jia, Xiaodong; Schüttrumpf, Holger; Frings, Roy M.
2015-11-01
Porosity as one of the key properties of sediment mixtures is poorly understood. Most of the existing porosity predictors based upon grain size characteristics have been unable to produce satisfying results for fluvial sediment porosity, due to the lack of consideration of other porosity-controlling factors like grain shape and depositional condition. Considering this, a stochastic digital packing algorithm was applied in this work, which provides an innovative way to pack particles of arbitrary shapes and sizes based on digitization of both particles and packing space. The purpose was to test the applicability of this packing algorithm in predicting fluvial sediment porosity by comparing its predictions with outcomes obtained from laboratory measurements. Laboratory samples examined were two natural fluvial sediments from the Rhine River and Kall River (Germany), and commercial glass beads (spheres). All samples were artificially combined into seven grain size distributions: four unimodal distributions and three bimodal distributions. Our study demonstrates that apart from grain size, grain shape also has a clear impact on porosity. The stochastic digital packing algorithm successfully reproduced the measured variations in porosity for the three different particle sources. However, the packing algorithm systematically overpredicted the porosity measured in random dense packing conditions, mainly because the random motion of particles during settling introduced unwanted kinematic sorting and shape effects. The results suggest that the packing algorithm produces loose packing structures, and is useful for trend analysis of packing porosity.
Stochastic deletion-insertion algorithm to construct dense linkage maps
Wu, Jixiang; Lou, Xiang-Yang; Gonda, Michael
2011-01-01
In this study, we proposed a stochastic deletion-insertion (SDI) algorithm for constructing large-scale linkage maps. This SDI algorithm was compared with three published approximation approaches, the seriation (SER), neighbor mapping (NM), and unidirectional growth (UG) approaches, on the basis of simulated F2 data with different population sizes, missing genotype rates, and numbers of markers. Simulation results showed that the SDI method had a similar or higher percentage of correct linkage orders than the other three methods. This SDI algorithm was also applied to a real dataset and compared with the other three methods. The total linkage map distance (cM) obtained by the SDI method (148.08 cM) was smaller than the distance obtained by SER (225.52 cM) and two published distances (150.11 cM and 150.38 cM). Since this SDI algorithm is stochastic, a more accurate linkage order can be quickly obtained by repeating this algorithm. Thus, this SDI method, which combines the advantages of accuracy and speed, is an important addition to the current linkage mapping toolkit for constructing improved linkage maps. PMID:21927641
Gotway, C.A.; Rutherford, B.M.
1993-09-01
Stochastic simulation has been suggested as a viable method for characterizing the uncertainty associated with the prediction of a nonlinear function of a spatially-varying parameter. Geostatistical simulation algorithms generate realizations of a random field with specified statistical and geostatistical properties. A nonlinear function is evaluated over each realization to obtain an uncertainty distribution of a system response that reflects the spatial variability and uncertainty in the parameter. Crucial management decisions, such as potential regulatory compliance of proposed nuclear waste facilities and optimal allocation of resources in environmental remediation, are based on the resulting system response uncertainty distribution. Many geostatistical simulation algorithms have been developed to generate the random fields, and each algorithm will produce fields with different statistical properties. These different properties will result in different distributions for system response, and potentially, different managerial decisions. The statistical properties of the resulting system response distributions are not completely understood, nor is the ability of the various algorithms to generate response distributions that adequately reflect the associated uncertainty. This paper reviews several of the algorithms available for generating random fields. Algorithms are compared in a designed experiment using seven exhaustive data sets with different statistical and geostatistical properties. For each exhaustive data set, a number of realizations are generated using each simulation algorithm. The realizations are used with each of several deterministic transfer functions to produce a cumulative uncertainty distribution function of a system response. The uncertainty distributions are then compared to the single value obtained from the corresponding exhaustive data set.
Random attractors for the stochastic coupled fractional Ginzburg-Landau equation with additive noise
Shu, Ji E-mail: 530282863@qq.com; Li, Ping E-mail: 530282863@qq.com; Zhang, Jia; Liao, Ou
2015-10-15
This paper is concerned with the stochastic coupled fractional Ginzburg-Landau equation with additive noise. We first transform the stochastic coupled fractional Ginzburg-Landau equation into random equations whose solutions generate a random dynamical system. Then we prove the existence of random attractor for random dynamical system.
Stochastic Kinetic Monte Carlo algorithms for long-range Hamiltonians
Mason, D R; Rudd, R E; Sutton, A P
2003-10-13
We present a higher order kinetic Monte Carlo methodology suitable to model the evolution of systems in which the transition rates are non- trivial to calculate or in which Monte Carlo moves are likely to be non- productive flicker events. The second order residence time algorithm first introduced by Athenes et al.[1] is rederived from the n-fold way algorithm of Bortz et al.[2] as a fully stochastic algorithm. The second order algorithm can be dynamically called when necessary to eliminate unproductive flickering between a metastable state and its neighbors. An algorithm combining elements of the first order and second order methods is shown to be more efficient, in terms of the number of rate calculations, than the first order or second order methods alone while remaining statistically identical. This efficiency is of prime importance when dealing with computationally expensive rate functions such as those arising from long- range Hamiltonians. Our algorithm has been developed for use when considering simulations of vacancy diffusion under the influence of elastic stress fields. We demonstrate the improved efficiency of the method over that of the n-fold way in simulations of vacancy diffusion in alloys. Our algorithm is seen to be an order of magnitude more efficient than the n-fold way in these simulations. We show that when magnesium is added to an Al-2at.%Cu alloy, this has the effect of trapping vacancies. When trapping occurs, we see that our algorithm performs thousands of events for each rate calculation performed.
Implementing Quality Control on a Random Number Stream to Improve a Stochastic Weather Generator
Technology Transfer Automated Retrieval System (TEKTRAN)
For decades stochastic modelers have used computerized random number generators to produce random numeric sequences fitting a specified statistical distribution. Unfortunately, none of the random number generators we tested satisfactorily produced the target distribution. The result is generated d...
A random walk approach to quantum algorithms.
Kendon, Vivien M
2006-12-15
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial; pure quantum dynamics is deterministic, so randomness only enters during the measurement phase, i.e. when converting the quantum information into classical information. The outcome of a quantum random walk is very different from the corresponding classical random walk owing to the interference between the different possible paths. The upshot is that quantum walkers find themselves further from their starting point than a classical walker on average, and this forms the basis of a quantum speed up, which can be exploited to solve problems faster. Surprisingly, the effect of making the walk slightly less than perfectly quantum can optimize the properties of the quantum walk for algorithmic applications. Looking to the future, even with a small quantum computer available, the development of quantum walk algorithms might proceed more rapidly than it has, especially for solving real problems. PMID:17090467
Random migration processes between two stochastic epidemic centers.
Sazonov, Igor; Kelbert, Mark; Gravenor, Michael B
2016-04-01
We consider the epidemic dynamics in stochastic interacting population centers coupled by random migration. Both the epidemic and the migration processes are modeled by Markov chains. We derive explicit formulae for the probability distribution of the migration process, and explore the dependence of outbreak patterns on initial parameters, population sizes and coupling parameters, using analytical and numerical methods. We show the importance of considering the movement of resident and visitor individuals separately. The mean field approximation for a general migration process is derived and an approximate method that allows the computation of statistical moments for networks with highly populated centers is proposed and tested numerically. PMID:26877075
Efficient stochastic Galerkin methods for random diffusion equations
Xiu Dongbin Shen Jie
2009-02-01
We discuss in this paper efficient solvers for stochastic diffusion equations in random media. We employ generalized polynomial chaos (gPC) expansion to express the solution in a convergent series and obtain a set of deterministic equations for the expansion coefficients by Galerkin projection. Although the resulting system of diffusion equations are coupled, we show that one can construct fast numerical methods to solve them in a decoupled fashion. The methods are based on separation of the diagonal terms and off-diagonal terms in the matrix of the Galerkin system. We examine properties of this matrix and show that the proposed method is unconditionally stable for unsteady problems and convergent for steady problems with a convergent rate independent of discretization parameters. Numerical examples are provided, for both steady and unsteady random diffusions, to support the analysis.
An adaptive multi-level simulation algorithm for stochastic biological systems
Lester, C. Giles, M. B.; Baker, R. E.; Yates, C. A.
2015-01-14
Discrete-state, continuous-time Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms (SSA) to estimate system statistics. The Gillespie algorithm is exact, but computationally costly as it simulates every single reaction. As such, approximate stochastic simulation algorithms such as the tau-leap algorithm are often used. Potentially computationally more efficient, the system statistics generated suffer from significant bias unless tau is relatively small, in which case the computational time can be comparable to that of the Gillespie algorithm. The multi-level method [Anderson and Higham, “Multi-level Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics,” SIAM Multiscale Model. Simul. 10(1), 146–179 (2012)] tackles this problem. A base estimator is computed using many (cheap) sample paths at low accuracy. The bias inherent in this estimator is then reduced using a number of corrections. Each correction term is estimated using a collection of paired sample paths where one path of each pair is generated at a higher accuracy compared to the other (and so more expensive). By sharing random variables between these paired paths, the variance of each correction estimator can be reduced. This renders the multi-level method very efficient as only a relatively small number of paired paths are required to calculate each correction term. In the original multi-level method, each sample path is simulated using the tau-leap algorithm with a fixed value of τ. This approach can result in poor performance when the reaction activity of a system changes substantially over the timescale of interest. By introducing a novel adaptive time-stepping approach where τ is chosen according to the stochastic behaviour of each sample path, we extend the applicability of the multi-level method to such cases. We demonstrate the
An adaptive multi-level simulation algorithm for stochastic biological systems
NASA Astrophysics Data System (ADS)
Lester, C.; Yates, C. A.; Giles, M. B.; Baker, R. E.
2015-01-01
Discrete-state, continuous-time Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms (SSA) to estimate system statistics. The Gillespie algorithm is exact, but computationally costly as it simulates every single reaction. As such, approximate stochastic simulation algorithms such as the tau-leap algorithm are often used. Potentially computationally more efficient, the system statistics generated suffer from significant bias unless tau is relatively small, in which case the computational time can be comparable to that of the Gillespie algorithm. The multi-level method [Anderson and Higham, "Multi-level Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics," SIAM Multiscale Model. Simul. 10(1), 146-179 (2012)] tackles this problem. A base estimator is computed using many (cheap) sample paths at low accuracy. The bias inherent in this estimator is then reduced using a number of corrections. Each correction term is estimated using a collection of paired sample paths where one path of each pair is generated at a higher accuracy compared to the other (and so more expensive). By sharing random variables between these paired paths, the variance of each correction estimator can be reduced. This renders the multi-level method very efficient as only a relatively small number of paired paths are required to calculate each correction term. In the original multi-level method, each sample path is simulated using the tau-leap algorithm with a fixed value of τ. This approach can result in poor performance when the reaction activity of a system changes substantially over the timescale of interest. By introducing a novel adaptive time-stepping approach where τ is chosen according to the stochastic behaviour of each sample path, we extend the applicability of the multi-level method to such cases. We demonstrate the
NASA Astrophysics Data System (ADS)
Roh, Min K.; Daigle, Bernie J.; Gillespie, Dan T.; Petzold, Linda R.
2011-12-01
In recent years there has been substantial growth in the development of algorithms for characterizing rare events in stochastic biochemical systems. Two such algorithms, the state-dependent weighted stochastic simulation algorithm (swSSA) and the doubly weighted SSA (dwSSA) are extensions of the weighted SSA (wSSA) by H. Kuwahara and I. Mura [J. Chem. Phys. 129, 165101 (2008)], 10.1063/1.2987701. The swSSA substantially reduces estimator variance by implementing system state-dependent importance sampling (IS) parameters, but lacks an automatic parameter identification strategy. In contrast, the dwSSA provides for the automatic determination of state-independent IS parameters, thus it is inefficient for systems whose states vary widely in time. We present a novel modification of the dwSSA—the state-dependent doubly weighted SSA (sdwSSA)—that combines the strengths of the swSSA and the dwSSA without inheriting their weaknesses. The sdwSSA automatically computes state-dependent IS parameters via the multilevel cross-entropy method. We apply the method to three examples: a reversible isomerization process, a yeast polarization model, and a lac operon model. Our results demonstrate that the sdwSSA offers substantial improvements over previous methods in terms of both accuracy and efficiency.
Weighted Flow Algorithms (WFA) for stochastic particle coagulation
DeVille, R.E.L.; Riemer, N.; West, M.
2011-09-20
Stochastic particle-resolved methods are a useful way to compute the time evolution of the multi-dimensional size distribution of atmospheric aerosol particles. An effective approach to improve the efficiency of such models is the use of weighted computational particles. Here we introduce particle weighting functions that are power laws in particle size to the recently-developed particle-resolved model PartMC-MOSAIC and present the mathematical formalism of these Weighted Flow Algorithms (WFA) for particle coagulation and growth. We apply this to an urban plume scenario that simulates a particle population undergoing emission of different particle types, dilution, coagulation and aerosol chemistry along a Lagrangian trajectory. We quantify the performance of the Weighted Flow Algorithm for number and mass-based quantities of relevance for atmospheric sciences applications.
NASA Astrophysics Data System (ADS)
Wei, Fengying; Chen, Fangxiang
2016-07-01
This article discusses a stochastic SIQS epidemic model with saturated incidence. We assume that random perturbations always fluctuate at the endemic equilibrium. The existence of a global positive solution is obtained by constructing a suitable Lyapunov function. Under some suitable conditions, we derive the stochastic boundedness and stochastic permanence of the solutions of a stochastic SIQS model. Some numerical simulations are carried out to check our results.
NASA Astrophysics Data System (ADS)
Arsenault, Richard; Brissette, François P.; Poulin, Annie; Côté, Pascal; Martel, Jean-Luc
2014-05-01
The process of hydrological model parameter calibration is routinely performed with the help of stochastic optimization algorithms. Many such algorithms have been created and they sometimes provide varying levels of performance (as measured by an efficiency metric such as Nash-Sutcliffe). This is because each algorithm is better suited for one type of optimization problem rather than another. This research project's aim was twofold. First, it was sought upon to find various features in the calibration problem fitness landscapes to map the encountered problem types to the best possible optimization algorithm. Second, the optimal number of model evaluations in order to minimize resources usage and maximize overall model quality was investigated. A total of five stochastic optimization algorithms (SCE-UA, CMAES, DDS, PSO and ASA) were used to calibrate four lumped hydrological models (GR4J, HSAMI, HMETS and MOHYSE) on 421 basins from the US MOPEX database. Each of these combinations was performed using three objective functions (Log(RMSE), NSE, and a metric combining NSE, RMSE and BIAS) to add sufficient diversity to the fitness landscapes. Each run was performed 30 times for statistical analysis. With every parameter set tested during the calibration process, the validation value was taken on a separate period. It was then possible to outline the calibration skill versus the validation skill for the different algorithms. Fitness landscapes were characterized by various metrics, such as the dispersion metric, the mean distance between random points and their respective local minima (found through simple hill-climbing algorithms) and the mean distance between the local minima and the best local optimum found. These metrics were then compared to the calibration score of the various optimization algorithms. Preliminary results tend to show that fitness landscapes presenting a globally convergent structure are more prevalent than other types of landscapes in this
A parallel algorithm for random searches
NASA Astrophysics Data System (ADS)
Wosniack, M. E.; Raposo, E. P.; Viswanathan, G. M.; da Luz, M. G. E.
2015-11-01
We discuss a parallelization procedure for a two-dimensional random search of a single individual, a typical sequential process. To assure the same features of the sequential random search in the parallel version, we analyze the former spatial patterns of the encountered targets for different search strategies and densities of homogeneously distributed targets. We identify a lognormal tendency for the distribution of distances between consecutively detected targets. Then, by assigning the distinct mean and standard deviation of this distribution for each corresponding configuration in the parallel simulations (constituted by parallel random walkers), we are able to recover important statistical properties, e.g., the target detection efficiency, of the original problem. The proposed parallel approach presents a speedup of nearly one order of magnitude compared with the sequential implementation. This algorithm can be easily adapted to different instances, as searches in three dimensions. Its possible range of applicability covers problems in areas as diverse as automated computer searchers in high-capacity databases and animal foraging.
Efficient generation and optimization of stochastic template banks by a neighboring cell algorithm
NASA Astrophysics Data System (ADS)
Fehrmann, Henning; Pletsch, Holger J.
2014-12-01
Placing signal templates (grid points) as efficiently as possible to cover a multidimensional parameter space is crucial in computing-intensive matched-filtering searches for gravitational waves, but also in similar searches in other fields of astronomy. To generate efficient coverings of arbitrary parameter spaces, stochastic template banks have been advocated, where templates are placed at random while rejecting those too close to others. However, in this simple scheme, for each new random point its distance to every template in the existing bank is computed. This rapidly increasing number of distance computations can render the acceptance of new templates computationally prohibitive, particularly for wide parameter spaces or in large dimensions. This paper presents a neighboring cell algorithm that can dramatically improve the efficiency of constructing a stochastic template bank. By dividing the parameter space into subvolumes (cells), for an arbitrary point an efficient hashing technique is exploited to obtain the index of its enclosing cell along with the parameters of its neighboring templates. Hence only distances to these neighboring templates in the bank are computed, massively lowering the overall computing cost, as demonstrated in simple examples. Furthermore, we propose a novel method based on this technique to increase the fraction of covered parameter space solely by directed template shifts, without adding any templates. As is demonstrated in examples, this method can be highly effective.
Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs
Gade, Dinakar; Hackebeil, Gabriel; Ryan, Sarah M.; Watson, Jean -Paul; Wets, Roger J.-B.; Woodruff, David L.
2016-04-02
We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. In conclusion, we report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds.
Fast state estimation subject to random data loss in discrete-time nonlinear stochastic systems
NASA Astrophysics Data System (ADS)
Mahdi Alavi, S. M.; Saif, Mehrdad
2013-12-01
This paper focuses on the design of the standard observer in discrete-time nonlinear stochastic systems subject to random data loss. By the assumption that the system response is incrementally bounded, two sufficient conditions are subsequently derived that guarantee exponential mean-square stability and fast convergence of the estimation error for the problem at hand. An efficient algorithm is also presented to obtain the observer gain. Finally, the proposed methodology is employed for monitoring the Continuous Stirred Tank Reactor (CSTR) via a wireless communication network. The effectiveness of the designed observer is extensively assessed by using an experimental tested-bed that has been fabricated for performance evaluation of the over wireless-network estimation techniques under realistic radio channel conditions.
Stochastic simulations of sediment connectivity using random forests
NASA Astrophysics Data System (ADS)
Masselink, Rens; Keesstra, Saskia; Temme, Arnaud
2016-04-01
Modelling sediment connectivity, i.e. determining sediment sources, sinks and pathways has often been done by applying spatially explicit models to catchments and calibrating those models using data obtained at a catchment outlet. This means that modelled locations of sediment sources, sinks and pathways are directly derived from the input data of the model (especially the digital elevation model) and the calibration parameters. On the other hand, measured sediment transport data, e.g. from erosion plots or sediment tracers (e.g. Be7, Cs137, Rare earth oxides) is often only available from small plots or hillslopes. Extrapolation of these measured values often lead to an overestimation of erosion at catchment scale. There is a need to link both the small scale erosion/deposition measurements with large scale catchment scale sediment yield. In this study we propose using random forests (RF) for multivariable regression for determining to which extent certain variables influence sediment transport. The independent variables for the RF are derivatives of a high-resolution digital elevation model and vegetation parameters and the independent variables are sediment erosion and deposition data. For the erosion and deposition data we use sediment tracers (rare-earth oxides) applied at a single hillslope in the winter of 2014/2015. Subsequently, we will do stochastic simulations (e.g. sequential Gaussian simulation) for the entire catchment using the RF output and its residuals. These simulations will then be compared to the total suspended sediment output at the catchment outlet. This way, we hope to get a better view of both sediment yield at the catchment scale and locations of sediment sources, sinks and pathways.
Note on coefficient matrices from stochastic Galerkin methods for random diffusion equations
Zhou Tao; Tang Tao
2010-11-01
In a recent work by Xiu and Shen [D. Xiu, J. Shen, Efficient stochastic Galerkin methods for random diffusion equations, J. Comput. Phys. 228 (2009) 266-281], the Galerkin methods are used to solve stochastic diffusion equations in random media, where some properties for the coefficient matrix of the resulting system are provided. They also posed an open question on the properties of the coefficient matrix. In this work, we will provide some results related to the open question.
Fluorescence microscopy image noise reduction using a stochastically-connected random field model
Haider, S. A.; Cameron, A.; Siva, P.; Lui, D.; Shafiee, M. J.; Boroomand, A.; Haider, N.; Wong, A.
2016-01-01
Fluorescence microscopy is an essential part of a biologist’s toolkit, allowing assaying of many parameters like subcellular localization of proteins, changes in cytoskeletal dynamics, protein-protein interactions, and the concentration of specific cellular ions. A fundamental challenge with using fluorescence microscopy is the presence of noise. This study introduces a novel approach to reducing noise in fluorescence microscopy images. The noise reduction problem is posed as a Maximum A Posteriori estimation problem, and solved using a novel random field model called stochastically-connected random field (SRF), which combines random graph and field theory. Experimental results using synthetic and real fluorescence microscopy data show the proposed approach achieving strong noise reduction performance when compared to several other noise reduction algorithms, using quantitative metrics. The proposed SRF approach was able to achieve strong performance in terms of signal-to-noise ratio in the synthetic results, high signal to noise ratio and contrast to noise ratio in the real fluorescence microscopy data results, and was able to maintain cell structure and subtle details while reducing background and intra-cellular noise. PMID:26884148
A new stochastic algorithm for inversion of dust aerosol size distribution
NASA Astrophysics Data System (ADS)
Wang, Li; Li, Feng; Yang, Ma-ying
2015-08-01
Dust aerosol size distribution is an important source of information about atmospheric aerosols, and it can be determined from multiwavelength extinction measurements. This paper describes a stochastic inverse technique based on artificial bee colony (ABC) algorithm to invert the dust aerosol size distribution by light extinction method. The direct problems for the size distribution of water drop and dust particle, which are the main elements of atmospheric aerosols, are solved by the Mie theory and the Lambert-Beer Law in multispectral region. And then, the parameters of three widely used functions, i.e. the log normal distribution (L-N), the Junge distribution (J-J), and the normal distribution (N-N), which can provide the most useful representation of aerosol size distributions, are inversed by the ABC algorithm in the dependent model. Numerical results show that the ABC algorithm can be successfully applied to recover the aerosol size distribution with high feasibility and reliability even in the presence of random noise.
Emergence of patterns in random processes. II. Stochastic structure in random events
NASA Astrophysics Data System (ADS)
Newman, William I.
2014-06-01
Random events can present what appears to be a pattern in the length of peak-to-peak sequences in time series and other point processes. Previously, we showed that this was the case in both individual and independently distributed processes as well as for Brownian walks. In addition, we introduced the use of the discrete form of the Langevin equation of statistical mechanics as a device for connecting the two limiting sets of behaviors, which we then compared with a variety of observations from the physical and social sciences. Here, we establish a probabilistic framework via the Smoluchowski equation for exploring the Langevin equation and its expected peak-to-peak sequence lengths, and we introduce a concept we call "stochastic structure in random events," or SSRE. We extend the Brownian model to include antipersistent processes via autoregressive (AR) models. We relate the latter to describe the behavior of Old Faithful Geyser in Yellowstone National Park, and we devise a further test for the validity of the Langevin and AR models. Given our analytic results, we show how the Langevin equation can be adapted to describe population cycles of three to four years observed among many mammalian species in biology.
Emergence of patterns in random processes. II. Stochastic structure in random events.
Newman, William I
2014-06-01
Random events can present what appears to be a pattern in the length of peak-to-peak sequences in time series and other point processes. Previously, we showed that this was the case in both individual and independently distributed processes as well as for Brownian walks. In addition, we introduced the use of the discrete form of the Langevin equation of statistical mechanics as a device for connecting the two limiting sets of behaviors, which we then compared with a variety of observations from the physical and social sciences. Here, we establish a probabilistic framework via the Smoluchowski equation for exploring the Langevin equation and its expected peak-to-peak sequence lengths, and we introduce a concept we call "stochastic structure in random events," or SSRE. We extend the Brownian model to include antipersistent processes via autoregressive (AR) models. We relate the latter to describe the behavior of Old Faithful Geyser in Yellowstone National Park, and we devise a further test for the validity of the Langevin and AR models. Given our analytic results, we show how the Langevin equation can be adapted to describe population cycles of three to four years observed among many mammalian species in biology. PMID:25019731
Manca, Gian Mario; Vallisneri, Michele
2010-01-15
The efficient placement of signal templates in source-parameter space is a crucial requisite for exhaustive matched-filtering searches of modeled gravitational-wave sources, as well as other searches based on more general detection statistics. Unfortunately, the current placement algorithms based on regular parameter-space meshes are difficult to generalize beyond simple signal models with few parameters. Various authors have suggested that a general, flexible, yet efficient alternative can be found in randomized placement strategies such as random placement and stochastic placement, which enhances random placement by selectively rejecting templates that are too close to others. In this article we explore several theoretical and practical issues in randomized placement: the size and performance of the resulting template banks; the very general, purely geometric effects of parameter-space boundaries; the use of quasirandom (self-avoiding) number sequences; most important, the implementation of these algorithms in curved signal manifolds with and without the use of a Riemannian signal metric, which may be difficult to obtain. Specifically, we show how the metric can be replaced with a discrete triangulation-based representation of local geometry. We argue that the broad class of randomized placement algorithms offers a promising answer to many search problems, but that the specific choice of a scheme and its implementation details will still need to be fine-tuned separately for each problem.
One-dimensional random field Ising model and discrete stochastic mappings
Behn, U.; Zagrebnov, V.A.
1987-06-01
Previous results relating the one-dimensional random field Ising model to a discrete stochastic mapping are generalized to a two-valued correlated random (Markovian) field and to the case of zero temperature. The fractal dimension of the support of the invariant measure is calculated in a simple approximation and its dependence on the physical parameters is discussed.
Quantum stochastic walks: A generalization of classical random walks and quantum walks
NASA Astrophysics Data System (ADS)
Whitfield, James D.; Rodríguez-Rosario, César A.; Aspuru-Guzik, Alán
2010-02-01
We introduce the quantum stochastic walk (QSW), which determines the evolution of a generalized quantum-mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical, and quantum-stochastic transitions from a vertex as defined by its connectivity. We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases but also includes more general probability distributions. As an example, we study the QSW on a line and the glued tree of depth three to observe the behavior of the QW-to-CRW transition.
Evaluation of a Geothermal Prospect Using a Stochastic Joint Inversion Algorithm
NASA Astrophysics Data System (ADS)
Tompson, A. F.; Mellors, R. J.; Ramirez, A.; Dyer, K.; Yang, X.; Trainor-Guitton, W.; Wagoner, J. L.
2013-12-01
A stochastic joint inverse algorithm to analyze diverse geophysical and hydrologic data for a geothermal prospect is developed. The purpose is to improve prospect evaluation by finding an ensemble of hydrothermal flow models that are most consistent with multiple types of data sets. The staged approach combines Bayesian inference within a Markov Chain Monte Carlo (MCMC) global search algorithm. The method is highly flexible and capable of accommodating multiple and diverse datasets as a means to maximize the utility of all available data to understand system behavior. An initial application is made at a geothermal prospect located near Superstition Mountain in the western Salton Trough in California. Readily available data include three thermal gradient exploration boreholes, borehole resistivity logs, magnetotelluric and gravity geophysical surveys, surface heat flux measurements, and other nearby hydrologic and geologic information. Initial estimates of uncertainty in structural or parametric characteristics of the prospect are used to drive large numbers of simulations of hydrothermal fluid flow and related geophysical processes using random realizations of the conceptual geothermal system. Uncertainty in the results is represented within a ranked subset of model realizations that best match all available data within a specified norm or tolerance. Statistical (posterior) characteristics of these solutions reflect reductions in the perceived (prior) uncertainties. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-641792.
NASA Technical Reports Server (NTRS)
Jacobson, R. A.
1975-01-01
Difficulties arise in guiding a solar electric propulsion spacecraft due to nongravitational accelerations caused by random fluctuations in the magnitude and direction of the thrust vector. These difficulties may be handled by using a low thrust guidance law based on the linear-quadratic-Gaussian problem of stochastic control theory with a minimum terminal miss performance criterion. Explicit constraints are imposed on the variances of the control parameters, and an algorithm based on the Hilbert space extension of a parameter optimization method is presented for calculation of gains in the guidance law. The terminal navigation of a 1980 flyby mission to the comet Encke is used as an example.
A new model for realistic random perturbations of stochastic oscillators
NASA Astrophysics Data System (ADS)
Dieci, Luca; Li, Wuchen; Zhou, Haomin
2016-08-01
Classical theories predict that solutions of differential equations will leave any neighborhood of a stable limit cycle, if white noise is added to the system. In reality, many engineering systems modeled by second order differential equations, like the van der Pol oscillator, show incredible robustness against noise perturbations, and the perturbed trajectories remain in the neighborhood of a stable limit cycle for all times of practical interest. In this paper, we propose a new model of noise to bridge this apparent discrepancy between theory and practice. Restricting to perturbations from within this new class of noise, we consider stochastic perturbations of second order differential systems that -in the unperturbed case- admit asymptotically stable limit cycles. We show that the perturbed solutions are globally bounded and remain in a tubular neighborhood of the underlying deterministic periodic orbit. We also define stochastic Poincaré map(s), and further derive partial differential equations for the transition density function.
D-leaping: Accelerating stochastic simulation algorithms for reactions with delays
Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros
2009-09-01
We propose a novel, accelerated algorithm for the approximate stochastic simulation of biochemical systems with delays. The present work extends existing accelerated algorithms by distributing, in a time adaptive fashion, the delayed reactions so as to minimize the computational effort while preserving their accuracy. The accuracy of the present algorithm is assessed by comparing its results to those of the corresponding delay differential equations for a representative biochemical system. In addition, the fluctuations produced from the present algorithm are comparable to those from an exact stochastic simulation with delays. The algorithm is used to simulate biochemical systems that model oscillatory gene expression. The results indicate that the present algorithm is competitive with existing works for several benchmark problems while it is orders of magnitude faster for certain systems of biochemical reactions.
Genetic algorithms as global random search methods
NASA Technical Reports Server (NTRS)
Peck, Charles C.; Dhawan, Atam P.
1995-01-01
Genetic algorithm behavior is described in terms of the construction and evolution of the sampling distributions over the space of candidate solutions. This novel perspective is motivated by analysis indicating that that schema theory is inadequate for completely and properly explaining genetic algorithm behavior. Based on the proposed theory, it is argued that the similarities of candidate solutions should be exploited directly, rather than encoding candidate solution and then exploiting their similarities. Proportional selection is characterized as a global search operator, and recombination is characterized as the search process that exploits similarities. Sequential algorithms and many deletion methods are also analyzed. It is shown that by properly constraining the search breadth of recombination operators, convergence of genetic algorithms to a global optimum can be ensured.
Genetic algorithms as global random search methods
NASA Technical Reports Server (NTRS)
Peck, Charles C.; Dhawan, Atam P.
1995-01-01
Genetic algorithm behavior is described in terms of the construction and evolution of the sampling distributions over the space of candidate solutions. This novel perspective is motivated by analysis indicating that the schema theory is inadequate for completely and properly explaining genetic algorithm behavior. Based on the proposed theory, it is argued that the similarities of candidate solutions should be exploited directly, rather than encoding candidate solutions and then exploiting their similarities. Proportional selection is characterized as a global search operator, and recombination is characterized as the search process that exploits similarities. Sequential algorithms and many deletion methods are also analyzed. It is shown that by properly constraining the search breadth of recombination operators, convergence of genetic algorithms to a global optimum can be ensured.
Ariyawansa, K.A.; Hudson, D.D.
1989-01-01
We describe a benchmark parallel version of the Van Slyke and Wets algorithm for two-stage stochastic programs and an implementation of that algorithm on the Sequent/Balance. We also report results of a numerical experiment using random test problems and our implementation. These performance results, to the best of our knowledge, are the first available for the Van Slyke and Wets algorithm on a parallel processor. They indicate that the benchmark implementation parallelizes well, and that even with the use of parallel processing, problems with random variables having large numbers of realizations can take prohibitively large amounts of computation for solution. Thus, they demonstrate the need for exploiting both parallelization and approximation for the solution of stochastic programs. 15 refs., 18 tabs.
Investigation of stochastic radiation transport methods in random heterogeneous mixtures
NASA Astrophysics Data System (ADS)
Reinert, Dustin Ray
Among the most formidable challenges facing our world is the need for safe, clean, affordable energy sources. Growing concerns over global warming induced climate change and the rising costs of fossil fuels threaten conventional means of electricity production and are driving the current nuclear renaissance. One concept at the forefront of international development efforts is the High Temperature Gas-Cooled Reactor (HTGR). With numerous passive safety features and a meltdown-proof design capable of attaining high thermodynamic efficiencies for electricity generation as well as high temperatures useful for the burgeoning hydrogen economy, the HTGR is an extremely promising technology. Unfortunately, the fundamental understanding of neutron behavior within HTGR fuels lags far behind that of more conventional water-cooled reactors. HTGRs utilize a unique heterogeneous fuel element design consisting of thousands of tiny fissile fuel kernels randomly mixed with a non-fissile graphite matrix. Monte Carlo neutron transport simulations of the HTGR fuel element geometry in its full complexity are infeasible and this has motivated the development of more approximate computational techniques. A series of MATLAB codes was written to perform Monte Carlo simulations within HTGR fuel pebbles to establish a comprehensive understanding of the parameters under which the accuracy of the approximate techniques diminishes. This research identified the accuracy of the chord length sampling method to be a function of the matrix scattering optical thickness, the kernel optical thickness, and the kernel packing density. Two new Monte Carlo methods designed to focus the computational effort upon the parameter conditions shown to contribute most strongly to the overall computational error were implemented and evaluated. An extended memory chord length sampling routine that recalls a neutron's prior material traversals was demonstrated to be effective in fixed source calculations containing
Multi-Parent Clustering Algorithms from Stochastic Grammar Data Models
NASA Technical Reports Server (NTRS)
Mjoisness, Eric; Castano, Rebecca; Gray, Alexander
1999-01-01
We introduce a statistical data model and an associated optimization-based clustering algorithm which allows data vectors to belong to zero, one or several "parent" clusters. For each data vector the algorithm makes a discrete decision among these alternatives. Thus, a recursive version of this algorithm would place data clusters in a Directed Acyclic Graph rather than a tree. We test the algorithm with synthetic data generated according to the statistical data model. We also illustrate the algorithm using real data from large-scale gene expression assays.
Simple randomized algorithms for online learning with kernels.
He, Wenwu; Kwok, James T
2014-12-01
In online learning with kernels, it is vital to control the size (budget) of the support set because of the curse of kernelization. In this paper, we propose two simple and effective stochastic strategies for controlling the budget. Both algorithms have an expected regret that is sublinear in the horizon. Experimental results on a number of benchmark data sets demonstrate encouraging performance in terms of both efficacy and efficiency. PMID:25108150
Stochastic algorithms for the analysis of numerical flame simulations
Bell, John B.; Day, Marcus S.; Grcar, Joseph F.; Lijewski, Michael J.
2004-04-26
Recent progress in simulation methodologies and high-performance parallel computers have made it is possible to perform detailed simulations of multidimensional reacting flow phenomena using comprehensive kinetics mechanisms. As simulations become larger and more complex, it becomes increasingly difficult to extract useful information from the numerical solution, particularly regarding the interactions of the chemical reaction and diffusion processes. In this paper we present a new diagnostic tool for analysis of numerical simulations of reacting flow. Our approach is based on recasting an Eulerian flow solution in a Lagrangian frame. Unlike a conventional Lagrangian view point that follows the evolution of a volume of the fluid, we instead follow specific chemical elements, e.g., carbon, nitrogen, etc., as they move through the system . From this perspective an ''atom'' is part of some molecule of a species that is transported through the domain by advection and diffusion. Reactions cause the atom to shift from one chemical host species to another and the subsequent transport of the atom is given by the movement of the new species. We represent these processes using a stochastic particle formulation that treats advection deterministically and models diffusion and chemistry as stochastic processes. In this paper, we discuss the numerical issues in detail and demonstrate that an ensemble of stochastic trajectories can accurately capture key features of the continuum solution. The capabilities of this diagnostic are then demonstrated by applications to study the modulation of carbon chemistry during a vortex-flame interaction, and the role of cyano chemistry in rm NO{sub x} production for a steady diffusion flame.
A stochastic multiscale framework for modeling flow through random heterogeneous porous media
Ganapathysubramanian, B.; Zabaras, N.
2009-02-01
Flow through porous media is ubiquitous, occurring from large geological scales down to the microscopic scales. Several critical engineering phenomena like contaminant spread, nuclear waste disposal and oil recovery rely on accurate analysis and prediction of these multiscale phenomena. Such analysis is complicated by inherent uncertainties as well as the limited information available to characterize the system. Any realistic modeling of these transport phenomena has to resolve two key issues: (i) the multi-length scale variations in permeability that these systems exhibit, and (ii) the inherently limited information available to quantify these property variations that necessitates posing these phenomena as stochastic processes. A stochastic variational multiscale formulation is developed to incorporate uncertain multiscale features. A stochastic analogue to a mixed multiscale finite element framework is used to formulate the physical stochastic multiscale process. Recent developments in linear and non-linear model reduction techniques are used to convert the limited information available about the permeability variation into a viable stochastic input model. An adaptive sparse grid collocation strategy is used to efficiently solve the resulting stochastic partial differential equations (SPDEs). The framework is applied to analyze flow through random heterogeneous media when only limited statistics about the permeability variation are given.
Hybrid discrete/continuum algorithms for stochastic reaction networks
NASA Astrophysics Data System (ADS)
Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; Najm, Habib N.
2015-01-01
Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. The performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.
Hybrid discrete/continuum algorithms for stochastic reaction networks
Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; Najm, Habib N.
2014-10-22
Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.
Hybrid discrete/continuum algorithms for stochastic reaction networks
Safta, Cosmin Sargsyan, Khachik Debusschere, Bert Najm, Habib N.
2015-01-15
Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker–Planck equation. The Fokker–Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. The performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.
Global Mapping Analysis: Stochastic Gradient Algorithm in Multidimensional Scaling
NASA Astrophysics Data System (ADS)
Matsuda, Yoshitatsu; Yamaguchi, Kazunori
In order to implement multidimensional scaling (MDS) efficiently, we propose a new method named “global mapping analysis” (GMA), which applies stochastic approximation to minimizing MDS criteria. GMA can solve MDS more efficiently in both the linear case (classical MDS) and non-linear one (e.g., ALSCAL) if only the MDS criteria are polynomial. GMA separates the polynomial criteria into the local factors and the global ones. Because the global factors need to be calculated only once in each iteration, GMA is of linear order in the number of objects. Numerical experiments on artificial data verify the efficiency of GMA. It is also shown that GMA can find out various interesting structures from massive document collections.
Hybrid discrete/continuum algorithms for stochastic reaction networks
Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; Najm, Habib N.
2014-10-22
Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discretemore » and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.« less
A stochastic model of randomly accelerated walkers for human mobility.
Gallotti, Riccardo; Bazzani, Armando; Rambaldi, Sandro; Barthelemy, Marc
2016-01-01
Recent studies of human mobility largely focus on displacements patterns and power law fits of empirical long-tailed distributions of distances are usually associated to scale-free superdiffusive random walks called Lévy flights. However, drawing conclusions about a complex system from a fit, without any further knowledge of the underlying dynamics, might lead to erroneous interpretations. Here we show, on the basis of a data set describing the trajectories of 780,000 private vehicles in Italy, that the Lévy flight model cannot explain the behaviour of travel times and speeds. We therefore introduce a class of accelerated random walks, validated by empirical observations, where the velocity changes due to acceleration kicks at random times. Combining this mechanism with an exponentially decaying distribution of travel times leads to a short-tailed distribution of distances which could indeed be mistaken with a truncated power law. These results illustrate the limits of purely descriptive models and provide a mechanistic view of mobility. PMID:27573984
Stochastic EM algorithm for nonlinear state estimation with model uncertainties
NASA Astrophysics Data System (ADS)
Zia, Amin; Kirubarajan, Thiagalingam; Reilly, James P.; Shirani, Shahram
2004-01-01
In most solutions to state estimation problems like, for example, target tracking, it is generally assumed that the state evolution and measurement models are known a priori. The model parameters include process and measurement matrices or functions as well as the corresponding noise statistics. However, there are situations where the model parameters are not known a priori or are known only partially (i.e., with some uncertainty). Moreover, there are situations where the measurement is biased. In these scenarios, standard estimation algorithms like the Kalman filter and the extended Kalman Filter (EKF), which assume perfect knowledge of the model parameters, are not accurate. In this paper, the problem with uncertain model parameters is considered as a special case of maximum likelihood estimation with incomplete-data, for which a standard solution called the expectation-maximization (EM) algorithm exists. In this paper a new extension to the EM algorithm is proposed to solve the more general problem of joint state estimation and model parameter identification for nonlinear systems with possibly non-Gaussian noise. In the expectation (E) step, it is shown that the best variational distribution over the state variables is the conditional posterior distribution of states given all the available measurements and inputs. Therefore, a particular type of particle filter is used to estimate and update the posterior distribution. In the maximization (M) step the nonlinear measurement process parameters are approximated using a nonlinear regression method for adjusting the parameters of a mixture of Gaussians (MofG). The proposed algorithm is used to solve a nonlinear bearing-only tracking problem similar to the one reported recently with uncertain measurement process. It is shown that the algorithm is capable of accurately tracking the state vector while identifying the unknown measurement dynamics. Simulation results show the advantages of the new technique over standard
Stochastic EM algorithm for nonlinear state estimation with model uncertainties
NASA Astrophysics Data System (ADS)
Zia, Amin; Kirubarajan, Thiagalingam; Reilly, James P.; Shirani, Shahram
2003-12-01
In most solutions to state estimation problems like, for example, target tracking, it is generally assumed that the state evolution and measurement models are known a priori. The model parameters include process and measurement matrices or functions as well as the corresponding noise statistics. However, there are situations where the model parameters are not known a priori or are known only partially (i.e., with some uncertainty). Moreover, there are situations where the measurement is biased. In these scenarios, standard estimation algorithms like the Kalman filter and the extended Kalman Filter (EKF), which assume perfect knowledge of the model parameters, are not accurate. In this paper, the problem with uncertain model parameters is considered as a special case of maximum likelihood estimation with incomplete-data, for which a standard solution called the expectation-maximization (EM) algorithm exists. In this paper a new extension to the EM algorithm is proposed to solve the more general problem of joint state estimation and model parameter identification for nonlinear systems with possibly non-Gaussian noise. In the expectation (E) step, it is shown that the best variational distribution over the state variables is the conditional posterior distribution of states given all the available measurements and inputs. Therefore, a particular type of particle filter is used to estimate and update the posterior distribution. In the maximization (M) step the nonlinear measurement process parameters are approximated using a nonlinear regression method for adjusting the parameters of a mixture of Gaussians (MofG). The proposed algorithm is used to solve a nonlinear bearing-only tracking problem similar to the one reported recently with uncertain measurement process. It is shown that the algorithm is capable of accurately tracking the state vector while identifying the unknown measurement dynamics. Simulation results show the advantages of the new technique over standard
NASA Astrophysics Data System (ADS)
Ding, Derui; Shen, Yuxuan; Song, Yan; Wang, Yongxiong
2016-07-01
This paper is concerned with the state estimation problem for a class of discrete time-varying stochastic nonlinear systems with randomly occurring deception attacks. The stochastic nonlinearity described by statistical means which covers several classes of well-studied nonlinearities as special cases is taken into discussion. The randomly occurring deception attacks are modelled by a set of random variables obeying Bernoulli distributions with given probabilities. The purpose of the addressed state estimation problem is to design an estimator with hope to minimize the upper bound for estimation error covariance at each sampling instant. Such an upper bound is minimized by properly designing the estimator gain. The proposed estimation scheme in the form of two Riccati-like difference equations is of a recursive form. Finally, a simulation example is exploited to demonstrate the effectiveness of the proposed scheme.
Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains
NASA Astrophysics Data System (ADS)
Brzeźniak, Z.; Caraballo, T.; Langa, J. A.; Li, Y.; Łukaszewicz, G.; Real, J.
We show that the stochastic flow generated by the 2-dimensional Stochastic Navier-Stokes equations with rough noise on a Poincaré-like domain has a unique random attractor. One of the technical problems associated with the rough noise is overcomed by the use of the corresponding Cameron-Martin (or reproducing kernel Hilbert) space. Our results complement the result by Brzeźniak and Li (2006) [10] who showed that the corresponding flow is asymptotically compact and also generalize Caraballo et al. (2006) [12] who proved existence of a unique attractor for the time-dependent deterministic Navier-Stokes equations.
Random Volumetric MRI Trajectories via Genetic Algorithms
Curtis, Andrew Thomas; Anand, Christopher Kumar
2008-01-01
A pseudorandom, velocity-insensitive, volumetric k-space sampling trajectory is designed for use with balanced steady-state magnetic resonance imaging. Individual arcs are designed independently and do not fit together in the way that multishot spiral, radial or echo-planar trajectories do. Previously, it was shown that second-order cone optimization problems can be defined for each arc independent of the others, that nulling of zeroth and higher moments can be encoded as constraints, and that individual arcs can be optimized in seconds. For use in steady-state imaging, sampling duty cycles are predicted to exceed 95 percent. Using such pseudorandom trajectories, aliasing caused by under-sampling manifests itself as incoherent noise. In this paper, a genetic algorithm (GA) is formulated and numerically evaluated. A large set of arcs is designed using previous methods, and the GA choses particular fit subsets of a given size, corresponding to a desired acquisition time. Numerical simulations of 1 second acquisitions show good detail and acceptable noise for large-volume imaging with 32 coils. PMID:18604305
A stochastic learning algorithm for layered neural networks
Bartlett, E.B.; Uhrig, R.E.
1992-12-31
The random optimization method typically uses a Gaussian probability density function (PDF) to generate a random search vector. In this paper the random search technique is applied to the neural network training problem and is modified to dynamically seek out the optimal probability density function (OPDF) from which to select the search vector. The dynamic OPDF search process, combined with an auto-adaptive stratified sampling technique and a dynamic node architecture (DNA) learning scheme, completes the modifications of the basic method. The DNA technique determines the appropriate number of hidden nodes needed for a given training problem. By using DNA, researchers do not have to set the neural network architectures before training is initiated. The approach is applied to networks of generalized, fully interconnected, continuous perceptions. Computer simulation results are given.
A stochastic learning algorithm for layered neural networks
Bartlett, E.B. . Dept. of Mechanical Engineering); Uhrig, R.E. . Dept. of Nuclear Engineering)
1992-01-01
The random optimization method typically uses a Gaussian probability density function (PDF) to generate a random search vector. In this paper the random search technique is applied to the neural network training problem and is modified to dynamically seek out the optimal probability density function (OPDF) from which to select the search vector. The dynamic OPDF search process, combined with an auto-adaptive stratified sampling technique and a dynamic node architecture (DNA) learning scheme, completes the modifications of the basic method. The DNA technique determines the appropriate number of hidden nodes needed for a given training problem. By using DNA, researchers do not have to set the neural network architectures before training is initiated. The approach is applied to networks of generalized, fully interconnected, continuous perceptions. Computer simulation results are given.
Binomial tau-leap spatial stochastic simulation algorithm for applications in chemical kinetics.
Marquez-Lago, Tatiana T; Burrage, Kevin
2007-09-14
In cell biology, cell signaling pathway problems are often tackled with deterministic temporal models, well mixed stochastic simulators, and/or hybrid methods. But, in fact, three dimensional stochastic spatial modeling of reactions happening inside the cell is needed in order to fully understand these cell signaling pathways. This is because noise effects, low molecular concentrations, and spatial heterogeneity can all affect the cellular dynamics. However, there are ways in which important effects can be accounted without going to the extent of using highly resolved spatial simulators (such as single-particle software), hence reducing the overall computation time significantly. We present a new coarse grained modified version of the next subvolume method that allows the user to consider both diffusion and reaction events in relatively long simulation time spans as compared with the original method and other commonly used fully stochastic computational methods. Benchmarking of the simulation algorithm was performed through comparison with the next subvolume method and well mixed models (MATLAB), as well as stochastic particle reaction and transport simulations (CHEMCELL, Sandia National Laboratories). Additionally, we construct a model based on a set of chemical reactions in the epidermal growth factor receptor pathway. For this particular application and a bistable chemical system example, we analyze and outline the advantages of our presented binomial tau-leap spatial stochastic simulation algorithm, in terms of efficiency and accuracy, in scenarios of both molecular homogeneity and heterogeneity. PMID:17867731
Webster, Clayton G; Tran, Hoang A; Trenchea, Catalin S
2013-01-01
n this paper we show how stochastic collocation method (SCM) could fail to con- verge for nonlinear differential equations with random coefficients. First, we consider Navier-Stokes equation with uncertain viscosity and derive error estimates for stochastic collocation discretization. Our analysis gives some indicators on how the nonlinearity negatively affects the accuracy of the method. The stochastic collocation method is then applied to noisy Lorenz system. Simulation re- sults demonstrate that the solution of a nonlinear equation could be highly irregular on the random data and in such cases, stochastic collocation method cannot capture the correct solution.
Discrete Randomness in Discrete Time Quantum Walk: Study Via Stochastic Averaging
NASA Astrophysics Data System (ADS)
Ellinas, D.; Bracken, A. J.; Smyrnakis, I.
2012-10-01
The role of classical noise in quantum walks (QW) on integers is investigated in the form of discrete dichotomic random variable affecting its reshuffling matrix parametrized as a SU2)/U (1) coset element. Analysis in terms of quantum statistical moments and generating functions, derived by the completely positive trace preserving (CPTP) map governing evolution, reveals a pronounced eventual transition in walk's diffusion mode, from a quantum ballistic regime with rate O(t) to a classical diffusive regime with rate O(√{t}), when condition (strength of noise parameter)2 × (number of steps) = 1, is satisfied. The role of classical randomness is studied showing that the randomized QW, when treated on the stochastic average level by means of an appropriate CPTP averaging map, turns out to be equivalent to a novel quantized classical walk without randomness. This result emphasizes the dual role of quantization/randomization in the context of classical random walk.
NASA Astrophysics Data System (ADS)
Sabelfeld, K. K.
2015-09-01
A stochastic algorithm for simulation of fluctuation-induced kinetics of H2 formation on grain surfaces is suggested as a generalization of the technique developed in our recent studies [1] where this method was developed to describe the annihilation of spatially separate electrons and holes in a disordered semiconductor. The stochastic model is based on the spatially inhomogeneous, nonlinear integro-differential Smoluchowski equations with random source term. In this paper we derive the general system of Smoluchowski type equations for the formation of H2 from two hydrogen atoms on the surface of interstellar dust grains with physisorption and chemisorption sites. We focus in this study on the spatial distribution, and numerically investigate the segregation in the case of a source with a continuous generation in time and randomly distributed in space. The stochastic particle method presented is based on a probabilistic interpretation of the underlying process as a stochastic Markov process of interacting particle system in discrete but randomly progressed time instances. The segregation is analyzed through the correlation analysis of the vector random field of concentrations which appears to be isotropic in space and stationary in time.
NASA Astrophysics Data System (ADS)
Zhao, Xiangrong; Xu, Wei; Yang, Yongge; Wang, Xiying
2016-06-01
This paper deals with the stochastic responses of a viscoelastic-impact system under additive and multiplicative random excitations. The viscoelastic force is replaced by a combination of stiffness and damping terms. The non-smooth transformation of the state variables is utilized to transform the original system to a new system without the impact term. The stochastic averaging method is applied to yield the stationary probability density functions. The validity of the analytical method is verified by comparing the analytical results with the numerical results. It is invaluable to note that the restitution coefficient, the viscoelastic parameters and the damping coefficients can induce the occurrence of stochastic P-bifurcation. Furthermore, the joint stationary probability density functions with three peaks are explored.
Cycles, randomness, and transport from chaotic dynamics to stochastic processes.
Gaspard, Pierre
2015-09-01
An overview of advances at the frontier between dynamical systems theory and nonequilibrium statistical mechanics is given. Sensitivity to initial conditions is a mechanism at the origin of dynamical randomness-alias temporal disorder-in deterministic dynamical systems. In spatially extended systems, sustaining transport processes, such as diffusion, relationships can be established between the characteristic quantities of dynamical chaos and the transport coefficients, bringing new insight into the second law of thermodynamics. With methods from dynamical systems theory, the microscopic time-reversal symmetry can be shown to be broken at the statistical level of description in nonequilibrium systems. In this way, the thermodynamic entropy production turns out to be related to temporal disorder and its time asymmetry away from equilibrium. PMID:26428559
Zhijie Xu
2014-07-01
We present a new stochastic analysis for steady and transient one-dimensional heat conduction problem based on the homogenization approach. Thermal conductivity is assumed to be a random field K consisting of random variables of a total number N. Both steady and transient solutions T are expressed in terms of the homogenized solution (symbol) and its spatial derivatives (equation), where homogenized solution (symbol) is obtained by solving the homogenized equation with effective thermal conductivity. Both mean and variance of stochastic solutions can be obtained analytically for K field consisting of independent identically distributed (i.i.d) random variables. The mean and variance of T are shown to be dependent only on the mean and variance of these i.i.d variables, not the particular form of probability distribution function of i.i.d variables. Variance of temperature field T can be separated into two contributions: the ensemble contribution (through the homogenized temperature (symbol)); and the configurational contribution (through the random variable Ln(x)Ln(x)). The configurational contribution is shown to be proportional to the local gradient of (symbol). Large uncertainty of T field was found at locations with large gradient of (symbol) due to the significant configurational contributions at these locations. Numerical simulations were implemented based on a direct Monte Carlo method and good agreement is obtained between numerical Monte Carlo results and the proposed stochastic analysis.
Simple-random-sampling-based multiclass text classification algorithm.
Liu, Wuying; Wang, Lin; Yi, Mianzhu
2014-01-01
Multiclass text classification (MTC) is a challenging issue and the corresponding MTC algorithms can be used in many applications. The space-time overhead of the algorithms must be concerned about the era of big data. Through the investigation of the token frequency distribution in a Chinese web document collection, this paper reexamines the power law and proposes a simple-random-sampling-based MTC (SRSMTC) algorithm. Supported by a token level memory to store labeled documents, the SRSMTC algorithm uses a text retrieval approach to solve text classification problems. The experimental results on the TanCorp data set show that SRSMTC algorithm can achieve the state-of-the-art performance at greatly reduced space-time requirements. PMID:24778587
Simple-Random-Sampling-Based Multiclass Text Classification Algorithm
Liu, Wuying; Wang, Lin; Yi, Mianzhu
2014-01-01
Multiclass text classification (MTC) is a challenging issue and the corresponding MTC algorithms can be used in many applications. The space-time overhead of the algorithms must be concerned about the era of big data. Through the investigation of the token frequency distribution in a Chinese web document collection, this paper reexamines the power law and proposes a simple-random-sampling-based MTC (SRSMTC) algorithm. Supported by a token level memory to store labeled documents, the SRSMTC algorithm uses a text retrieval approach to solve text classification problems. The experimental results on the TanCorp data set show that SRSMTC algorithm can achieve the state-of-the-art performance at greatly reduced space-time requirements. PMID:24778587
NASA Astrophysics Data System (ADS)
Li, Yangrong; Gu, Anhui; Li, Jia
2015-01-01
A concept of a bi-spatial random attractor for a random dynamical system is introduced. A unified result about existence and upper semi-continuity for a family of bi-spatial random attractors is obtained if a family of random systems is convergent, uniformly absorbing in an initial space and uniformly omega-compact in both initial and terminate spaces. The upper semi-continuity result improves all existing results even for single-spatial attractors. As an application of the abstract result, it is shown that every semilinear Laplacian equation on the entire space perturbed by a multiplicative and stochastic noise possesses an (L2, Lq)-random attractor with q > 2. Moreover, it is proved that the family of obtained attractors is upper semi-continuous at any density of noises and the family of attractors for the corresponding compact systems is both upper and lower semi-continuous at infinity under the topology of both spaces.
Chavanis, P H; Delfini, L
2014-03-01
We study random transitions between two metastable states that appear below a critical temperature in a one-dimensional self-gravitating Brownian gas with a modified Poisson equation experiencing a second order phase transition from a homogeneous phase to an inhomogeneous phase [P. H. Chavanis and L. Delfini, Phys. Rev. E 81, 051103 (2010)]. We numerically solve the N-body Langevin equations and the stochastic Smoluchowski-Poisson system, which takes fluctuations (finite N effects) into account. The system switches back and forth between the two metastable states (bistability) and the particles accumulate successively at the center or at the boundary of the domain. We explicitly show that these random transitions exhibit the phenomenology of the ordinary Kramers problem for a Brownian particle in a double-well potential. The distribution of the residence time is Poissonian and the average lifetime of a metastable state is given by the Arrhenius law; i.e., it is proportional to the exponential of the barrier of free energy ΔF divided by the energy of thermal excitation kBT. Since the free energy is proportional to the number of particles N for a system with long-range interactions, the lifetime of metastable states scales as eN and is considerable for N≫1. As a result, in many applications, metastable states of systems with long-range interactions can be considered as stable states. However, for moderate values of N, or close to a critical point, the lifetime of the metastable states is reduced since the barrier of free energy decreases. In that case, the fluctuations become important and the mean field approximation is no more valid. This is the situation considered in this paper. By an appropriate change of notations, our results also apply to bacterial populations experiencing chemotaxis in biology. Their dynamics can be described by a stochastic Keller-Segel model that takes fluctuations into account and goes beyond the usual mean field approximation. PMID
Random vibration of nonlinear beams by the new stochastic linearization technique
NASA Technical Reports Server (NTRS)
Fang, J.
1994-01-01
In this paper, the beam under general time dependent stationary random excitation is investigated, when exact solution is unavailable. Numerical simulations are carried out to compare its results with those yielded by the conventional linearization techniques. It is found that the modified version of the stochastic linearization technique yields considerably more accurate results for the mean square displacement of the beam than the conventional equivalent linearization technique, especially in the case of large nonlinearity.
Quadruped Robot Locomotion using a Global Optimization Stochastic Algorithm
NASA Astrophysics Data System (ADS)
Oliveira, Miguel; Santos, Cristina; Costa, Lino; Ferreira, Manuel
2011-09-01
The problem of tuning nonlinear dynamical systems parameters, such that the attained results are considered good ones, is a relevant one. This article describes the development of a gait optimization system that allows a fast but stable robot quadruped crawl gait. We combine bio-inspired Central Patterns Generators (CPGs) and Genetic Algorithms (GA). CPGs are modelled as autonomous differential equations, that generate the necessar y limb movement to perform the required walking gait. The GA finds parameterizations of the CPGs parameters which attain good gaits in terms of speed, vibration and stability. Moreover, two constraint handling techniques based on tournament selection and repairing mechanism are embedded in the GA to solve the proposed constrained optimization problem and make the search more efficient. The experimental results, performed on a simulated Aibo robot, demonstrate that our approach allows low vibration with a high velocity and wide stability margin for a quadruped slow crawl gait.
Nuclear space-valued stochastic differential equations driven by Poisson random measures
Xiong, J.
1992-01-01
The thesis is devoted primarily to the study of stochastic differential equations on duals of nuclear spaces driven by Poisson random measures. The existence of a weak solution is obtained by the Galerkin method and the uniqueness is established by implementing the Yamada-Watanabe argument in the present setup. When the magnitudes of the driving terms are small enough and the Poisson streams occur frequently enough, it is proved that the stochastic differential equations mentioned above can be approximated by diffusion equations. Finally, the author considers a system of interacting stochastic differential equations driven by Poisson random measures. Let (X[sup n][sub i](t), [center dot][center dot][center dot], X[sup n][sub n](t)) be the solution of this system and consider the empirical measures [zeta]n([omega],B) [identical to] (1/n) (sum of j=1 to n) [delta]x[sup n][sub j]([center dot],[omega])(B) (n[>=]1). It is provided that [zeta][sub n] converges in distribution to a non-random measure which is the unique solution of a McKean-Vlasov equation. The above problems are motivated by applications to neurophysiology, in particular, to the fluctuation of voltage potentials of spatially distributed neurons and to the study of asymptotic behavior of large systems of interacting neurons.
The stochastic evolution of a protocell: the Gillespie algorithm in a dynamically varying volume.
Carletti, T; Filisetti, A
2012-01-01
We propose an improvement of the Gillespie algorithm allowing us to study the time evolution of an ensemble of chemical reactions occurring in a varying volume, whose growth is directly related to the amount of some specific molecules, belonging to the reactions set. This allows us to study the stochastic evolution of a protocell, whose volume increases because of the production of container molecules. Several protocell models are considered and compared with the deterministic models. PMID:22536297
Witteveen, Jeroen A.S. Bijl, Hester
2009-10-01
The Unsteady Adaptive Stochastic Finite Elements (UASFE) method resolves the effect of randomness in numerical simulations of single-mode aeroelastic responses with a constant accuracy in time for a constant number of samples. In this paper, the UASFE framework is extended to multi-frequency responses and continuous structures by employing a wavelet decomposition pre-processing step to decompose the sampled multi-frequency signals into single-frequency components. The effect of the randomness on the multi-frequency response is then obtained by summing the results of the UASFE interpolation at constant phase for the different frequency components. Results for multi-frequency responses and continuous structures show a three orders of magnitude reduction of computational costs compared to crude Monte Carlo simulations in a harmonically forced oscillator, a flutter panel problem, and the three-dimensional transonic AGARD 445.6 wing aeroelastic benchmark subject to random fields and random parameters with various probability distributions.
Genetic Algorithm and Tabu Search for Vehicle Routing Problems with Stochastic Demand
NASA Astrophysics Data System (ADS)
Ismail, Zuhaimy; Irhamah
2010-11-01
This paper presents a problem of designing solid waste collection routes, involving scheduling of vehicles where each vehicle begins at the depot, visits customers and ends at the depot. It is modeled as a Vehicle Routing Problem with Stochastic Demands (VRPSD). A data set from a real world problem (a case) is used in this research. We developed Genetic Algorithm (GA) and Tabu Search (TS) procedure and these has produced the best possible result. The problem data are inspired by real case of VRPSD in waste collection. Results from the experiment show the advantages of the proposed algorithm that are its robustness and better solution qualities.
Exactly averaged stochastic equations for flow and transport in random media
Shvidler, Mark; Karasaki, Kenzi
2001-11-30
It is well known that exact averaging of the equations of flow and transport in random porous media are at present realized only for a small number of special, occasionally exotic, fields. On the other hand, the properties of approximate averaging methods are not yet fully understood. For example, the convergence behavior and the accuracy of truncated perturbation series are not well known. Furthermore, the calculation of the high-order perturbations is very complicated. These problems for a long time have stimulated attempts to find the answer for the question: Are there in existence some exact general and sufficiently universal forms of averaged equations? If the answer is positive, there arises the problem of the construction of these equations and analyzing them. There exist many publications related to these problems and oriented on different applications: hydrodynamics, flow and transport in porous media, theory of elasticity, acoustic and electromagnetic waves in random fields, etc. We present a method of finding some general forms of exactly averaged equations for flow and transport in random fields by using (1) an assumption of the existence of Green's functions for appropriate stochastic problems, (2 ) some general properties of the Green's functions, and (3) the some basic information about the random fields of the conductivity, porosity and flow velocity. We present some general forms of the exactly averaged non-local equations for the following cases. 1. Steady-state flow with sources in porous media with random conductivity. 2. Transient flow with sources in compressible media with random conductivity and porosity. 3. Non-reactive solute transport in random porous media. We discuss the problem of uniqueness and the properties of the non-local averaged equations, for the cases with some types of symmetry (isotropic, transversal isotropic, orthotropic) and we analyze the hypothesis of the structure of non-local equations in a general case of
Jenny, Patrick Torrilhon, Manuel; Heinz, Stefan
2010-02-20
In this paper, a stochastic model is presented to simulate the flow of gases, which are not in thermodynamic equilibrium, like in rarefied or micro situations. For the interaction of a particle with others, statistical moments of the local ensemble have to be evaluated, but unlike in molecular dynamics simulations or DSMC, no collisions between computational particles are considered. In addition, a novel integration technique allows for time steps independent of the stochastic time scale. The stochastic model represents a Fokker-Planck equation in the kinetic description, which can be viewed as an approximation to the Boltzmann equation. This allows for a rigorous investigation of the relation between the new model and classical fluid and kinetic equations. The fluid dynamic equations of Navier-Stokes and Fourier are fully recovered for small relaxation times, while for larger values the new model extents into the kinetic regime. Numerical studies demonstrate that the stochastic model is consistent with Navier-Stokes in that limit, but also that the results become significantly different, if the conditions for equilibrium are invalid. The application to the Knudsen paradox demonstrates the correctness and relevance of this development, and comparisons with existing kinetic equations and standard solution algorithms reveal its advantages. Moreover, results of a test case with geometrically complex boundaries are presented.
Monotonic continuous-time random walks with drift and stochastic reset events
NASA Astrophysics Data System (ADS)
Montero, Miquel; Villarroel, Javier
2013-01-01
In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.
Generalized stochastic resonance in a linear fractional system with a random delay
NASA Astrophysics Data System (ADS)
Gao, Shi-Long
2012-12-01
The generalized stochastic resonance (GSR) phenomena in a linear fractional random-delayed system driven by a weak periodic signal and an additive noise are considered in this paper. A random delay is considered for a linear fractional Langevin equation to describe the intercellular signal transmission and material exchange processes in ion channels. By virtue of the small delay approximation and Laplace transformation, the analytical expression for the amplitude of the first-order steady state moment is obtained. The simulation results show that the amplitude curves as functions of different system parameters behave non-monotonically and exhibit typical characteristics of GSR phenomena. Furthermore, a physical explanation for all the GSR phenomena is given and the cooperative effects of random delay and the fractional memory are also discussed.
An iterative curvelet thresholding algorithm for seismic random noise attenuation
NASA Astrophysics Data System (ADS)
Wang, De-Li; Tong, Zhong-Fei; Tang, Chen; Zhu, Heng
2010-12-01
In this paper, we explore the use of iterative curvelet thresholding for seismic random noise attenuation. A new method for combining the curvelet transform with iterative thresholding to suppress random noise is demonstrated and the issue is described as a linear inverse optimal problem using the L1 norm. Random noise suppression in seismic data is transformed into an L1 norm optimization problem based on the curvelet sparsity transform. Compared to the conventional methods such as median filter algorithm, FX deconvolution, and wavelet thresholding, the results of synthetic and field data processing show that the iterative curvelet thresholding proposed in this paper can sufficiently improve signal to noise radio (SNR) and give higher signal fidelity at the same time. Furthermore, to make better use of the curvelet transform such as multiple scales and multiple directions, we control the curvelet direction of the result after iterative curvelet thresholding to further improve the SNR.
NASA Astrophysics Data System (ADS)
Vrettas, Michail D.; Opper, Manfred; Cornford, Dan
2015-01-01
This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.
An adaptive algorithm for simulation of stochastic reaction-diffusion processes
Ferm, Lars Hellander, Andreas Loetstedt, Per
2010-01-20
We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction-diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie's stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the timesteps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.
Empirical Analysis of Stochastic Volatility Model by Hybrid Monte Carlo Algorithm
NASA Astrophysics Data System (ADS)
Takaishi, Tetsuya
2013-04-01
The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is superior to other Markov Chain Monte Carlo methods in sampling volatility variables. We perform the HMC simulations of the SV model for two liquid stock returns traded on the Tokyo Stock Exchange and measure the volatilities of those stock returns. Then we calculate the accuracy of the volatility measurement using the realized volatility as a proxy of the true volatility and compare the SV model with the GARCH model which is one of other volatility models. Using the accuracy calculated with the realized volatility we find that empirically the SV model performs better than the GARCH model.
NASA Astrophysics Data System (ADS)
Sochi, Taha
2016-09-01
Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder-Mead, Quasi-Newton and global) are investigated in conjunction with energy minimization principle to resolve the pressure and volumetric flow rate fields in single ducts and networks of interconnected ducts. The algorithms are tested with seven types of fluid: Newtonian, power law, Bingham, Herschel-Bulkley, Ellis, Ree-Eyring and Casson. The results obtained from all those algorithms for all these types of fluid agree very well with the analytically derived solutions as obtained from the traditional methods which are based on the conservation principles and fluid constitutive relations. The results confirm and generalize the findings of our previous investigations that the energy minimization principle is at the heart of the flow dynamics systems. The investigation also enriches the methods of computational fluid dynamics for solving the flow fields in tubes and networks for various types of Newtonian and non-Newtonian fluids.
Dynamic phasing of multichannel cw laser radiation by means of a stochastic gradient algorithm
Volkov, V A; Volkov, M V; Garanin, S G; Dolgopolov, Yu V; Kopalkin, A V; Kulikov, S M; Starikov, F A; Sukharev, S A; Tyutin, S V; Khokhlov, S V; Chaparin, D A
2013-09-30
The phasing of a multichannel laser beam by means of an iterative stochastic parallel gradient (SPG) algorithm has been numerically and experimentally investigated. The operation of the SPG algorithm is simulated, the acceptable range of amplitudes of probe phase shifts is found, and the algorithm parameters at which the desired Strehl number can be obtained with a minimum number of iterations are determined. An experimental bench with phase modulators based on lithium niobate, which are controlled by a multichannel electronic unit with a real-time microcontroller, has been designed. Phasing of 16 cw laser beams at a system response bandwidth of 3.7 kHz and phase thermal distortions in a frequency band of about 10 Hz is experimentally demonstrated. The experimental data are in complete agreement with the calculation results. (control of laser radiation parameters)
R-leaping: Accelerating the stochastic simulation algorithm by reaction leaps
NASA Astrophysics Data System (ADS)
Auger, Anne; Chatelain, Philippe; Koumoutsakos, Petros
2006-08-01
A novel algorithm is proposed for the acceleration of the exact stochastic simulation algorithm by a predefined number of reaction firings (R-leaping) that may occur across several reaction channels. In the present approach, the numbers of reaction firings are correlated binomial distributions and the sampling procedure is independent of any permutation of the reaction channels. This enables the algorithm to efficiently handle large systems with disparate rates, providing substantial computational savings in certain cases. Several mechanisms for controlling the accuracy and the appearance of negative species are described. The advantages and drawbacks of R-leaping are assessed by simulations on a number of benchmark problems and the results are discussed in comparison with established methods.
Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media
Tong Zhisong; Korotkova, Olga
2010-09-15
The theory of scattering of scalar stochastic fields from deterministic and random media is generalized to the electromagnetic domain under the first-order Born approximation. The analysis allows for determining the changes in spectrum, coherence, and polarization of electromagnetic fields produced on their propagation from the source to the scattering volume, interaction with the scatterer, and propagation from the scatterer to the far field. An example of scattering of a field produced by a {delta}-correlated partially polarized source and scattered from a {delta}-correlated medium is provided.
Combinatorial approximation algorithms for MAXCUT using random walks.
Seshadhri, Comandur; Kale, Satyen
2010-11-01
We give the first combinatorial approximation algorithm for MaxCut that beats the trivial 0.5 factor by a constant. The main partitioning procedure is very intuitive, natural, and easily described. It essentially performs a number of random walks and aggregates the information to provide the partition. We can control the running time to get an approximation factor-running time tradeoff. We show that for any constant b > 1.5, there is an {tilde O}(n{sup b}) algorithm that outputs a (0.5 + {delta})-approximation for MaxCut, where {delta} = {delta}(b) is some positive constant. One of the components of our algorithm is a weak local graph partitioning procedure that may be of independent interest. Given a starting vertex i and a conductance parameter {phi}, unless a random walk of length {ell} = O(log n) starting from i mixes rapidly (in terms of {phi} and {ell}), we can find a cut of conductance at most {phi} close to the vertex. The work done per vertex found in the cut is sublinear in n.
Random Matrix Approach to Quantum Adiabatic Evolution Algorithms
NASA Technical Reports Server (NTRS)
Boulatov, Alexei; Smelyanskiy, Vadier N.
2004-01-01
We analyze the power of quantum adiabatic evolution algorithms (Q-QA) for solving random NP-hard optimization problems within a theoretical framework based on the random matrix theory (RMT). We present two types of the driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that the failure mechanism of the QAA is due to the interaction of the ground state with the "cloud" formed by all the excited states, confirming that in the driven RMT models. the Landau-Zener mechanism of dissipation is not important. We show that the QAEA has a finite probability of success in a certain range of parameters. implying the polynomial complexity of the algorithm. The second model corresponds to the standard QAEA with the problem Hamiltonian taken from the Gaussian Unitary RMT ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. However, the driven RMT model always leads to the exponential complexity of the algorithm due to the presence of the long-range intertemporal correlations of the eigenvalues. Our results indicate that the weakness of effective transitions is the leading effect that can make the Markovian type QAEA successful.
Algorithmic randomness, physical entropy, measurements, and the second law
Zurek, W.H.
1989-01-01
Algorithmic information content is equal to the size -- in the number of bits -- of the shortest program for a universal Turing machine which can reproduce a state of a physical system. In contrast to the statistical Boltzmann-Gibbs-Shannon entropy, which measures ignorance, the algorithmic information content is a measure of the available information. It is defined without a recourse to probabilities and can be regarded as a measure of randomness of a definite microstate. I suggest that the physical entropy S -- that is, the quantity which determines the amount of the work {Delta}W which can be extracted in the cyclic isothermal expansion process through the equation {Delta}W = k{sub B}T{Delta}S -- is a sum of two contributions: the mission information measured by the usual statistical entropy and the known randomness measured by the algorithmic information content. The sum of these two contributions is a constant of motion'' in the process of a dissipation less measurement on an equilibrium ensemble. This conservation under a measurement, which can be traced back to the noiseless coding theorem of Shannon, is necessary to rule out existence of a successful Maxwell's demon. 17 refs., 3 figs.
NASA Astrophysics Data System (ADS)
Lu, B.; Darmon, M.; Leymarie, N.; Chatillon, S.; Potel, C.
2012-05-01
In-service inspection of Sodium-Cooled Fast Reactors (SFR) requires the development of non-destructive techniques adapted to the harsh environment conditions and the examination complexity. From past experiences, ultrasonic techniques are considered as suitable candidates. The ultrasonic telemetry is a technique used to constantly insure the safe functioning of reactor inner components by determining their exact position: it consists in measuring the time of flight of the ultrasonic response obtained after propagation of a pulse emitted by a transducer and its interaction with the targets. While in-service the sodium flow creates turbulences that lead to temperature inhomogeneities, which translates into ultrasonic velocity inhomogeneities. These velocity variations could directly impact the accuracy of the target locating by introducing time of flight variations. A stochastic simulation model has been developed to calculate the propagation of ultrasonic waves in such an inhomogeneous medium. Using this approach, the travel time is randomly generated by a stochastic process whose inputs are the statistical moments of travel times known analytically. The stochastic model predicts beam deviations due to velocity inhomogeneities, which are similar to those provided by a determinist method, such as the ray method.
Lu, B.; Darmon, M.; Leymarie, N.; Chatillon, S.; Potel, C.
2012-05-17
In-service inspection of Sodium-Cooled Fast Reactors (SFR) requires the development of non-destructive techniques adapted to the harsh environment conditions and the examination complexity. From past experiences, ultrasonic techniques are considered as suitable candidates. The ultrasonic telemetry is a technique used to constantly insure the safe functioning of reactor inner components by determining their exact position: it consists in measuring the time of flight of the ultrasonic response obtained after propagation of a pulse emitted by a transducer and its interaction with the targets. While in-service the sodium flow creates turbulences that lead to temperature inhomogeneities, which translates into ultrasonic velocity inhomogeneities. These velocity variations could directly impact the accuracy of the target locating by introducing time of flight variations. A stochastic simulation model has been developed to calculate the propagation of ultrasonic waves in such an inhomogeneous medium. Using this approach, the travel time is randomly generated by a stochastic process whose inputs are the statistical moments of travel times known analytically. The stochastic model predicts beam deviations due to velocity inhomogeneities, which are similar to those provided by a determinist method, such as the ray method.
NASA Astrophysics Data System (ADS)
Alfonso, Lester; Zamora, Jose; Cruz, Pedro
2015-04-01
The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.
Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm.
Chang, Joshua; Paydarfar, David
2014-12-01
Inducing a switch in neuronal state using energy optimal stimuli is relevant to a variety of problems in neuroscience. Analytical techniques from optimal control theory can identify such stimuli; however, solutions to the optimization problem using indirect variational approaches can be elusive in models that describe neuronal behavior. Here we develop and apply a direct gradient-based optimization algorithm to find stimulus waveforms that elicit a change in neuronal state while minimizing energy usage. We analyze standard models of neuronal behavior, the Hodgkin-Huxley and FitzHugh-Nagumo models, to show that the gradient-based algorithm: (1) enables automated exploration of a wide solution space, using stochastically generated initial waveforms that converge to multiple locally optimal solutions; and (2) finds optimal stimulus waveforms that achieve a physiological outcome condition, without a priori knowledge of the optimal terminal condition of all state variables. Analysis of biological systems using stochastically-seeded gradient methods can reveal salient dynamical mechanisms underlying the optimal control of system behavior. The gradient algorithm may also have practical applications in future work, for example, finding energy optimal waveforms for therapeutic neural stimulation that minimizes power usage and diminishes off-target effects and damage to neighboring tissue. PMID:25145955
Application of stochastic weighted algorithms to a multidimensional silica particle model
Menz, William J.; Patterson, Robert I.A.; Wagner, Wolfgang; Kraft, Markus
2013-09-01
Highlights: •Stochastic weighted algorithms (SWAs) are developed for a detailed silica model. •An implementation of SWAs with the transition kernel is presented. •The SWAs’ solutions converge to the direct simulation algorithm’s (DSA) solution. •The efficiency of SWAs is evaluated for this multidimensional particle model. •It is shown that SWAs can be used for coagulation problems in industrial systems. -- Abstract: This paper presents a detailed study of the numerical behaviour of stochastic weighted algorithms (SWAs) using the transition regime coagulation kernel and a multidimensional silica particle model. The implementation in the SWAs of the transition regime coagulation kernel and associated majorant rates is described. The silica particle model of Shekar et al. [S. Shekar, A.J. Smith, W.J. Menz, M. Sander, M. Kraft, A multidimensional population balance model to describe the aerosol synthesis of silica nanoparticles, Journal of Aerosol Science 44 (2012) 83–98] was used in conjunction with this coagulation kernel to study the convergence properties of SWAs with a multidimensional particle model. High precision solutions were calculated with two SWAs and also with the established direct simulation algorithm. These solutions, which were generated using large number of computational particles, showed close agreement. It was thus demonstrated that SWAs can be successfully used with complex coagulation kernels and high dimensional particle models to simulate real-world systems.
Parasuraman, Ramviyas; Fabry, Thomas; Molinari, Luca; Kershaw, Keith; Di Castro, Mario; Masi, Alessandro; Ferre, Manuel
2014-01-01
The reliability of wireless communication in a network of mobile wireless robot nodes depends on the received radio signal strength (RSS). When the robot nodes are deployed in hostile environments with ionizing radiations (such as in some scientific facilities), there is a possibility that some electronic components may fail randomly (due to radiation effects), which causes problems in wireless connectivity. The objective of this paper is to maximize robot mission capabilities by maximizing the wireless network capacity and to reduce the risk of communication failure. Thus, in this paper, we consider a multi-node wireless tethering structure called the "server-relay-client" framework that uses (multiple) relay nodes in between a server and a client node. We propose a robust stochastic optimization (RSO) algorithm using a multi-sensor-based RSS sampling method at the relay nodes to efficiently improve and balance the RSS between the source and client nodes to improve the network capacity and to provide redundant networking abilities. We use pre-processing techniques, such as exponential moving averaging and spatial averaging filters on the RSS data for smoothing. We apply a receiver spatial diversity concept and employ a position controller on the relay node using a stochastic gradient ascent method for self-positioning the relay node to achieve the RSS balancing task. The effectiveness of the proposed solution is validated by extensive simulations and field experiments in CERN facilities. For the field trials, we used a youBot mobile robot platform as the relay node, and two stand-alone Raspberry Pi computers as the client and server nodes. The algorithm has been proven to be robust to noise in the radio signals and to work effectively even under non-line-of-sight conditions. PMID:25615734
Parasuraman, Ramviyas; Fabry, Thomas; Molinari, Luca; Kershaw, Keith; Di Castro, Mario; Masi, Alessandro; Ferre, Manuel
2014-01-01
The reliability of wireless communication in a network of mobile wireless robot nodes depends on the received radio signal strength (RSS). When the robot nodes are deployed in hostile environments with ionizing radiations (such as in some scientific facilities), there is a possibility that some electronic components may fail randomly (due to radiation effects), which causes problems in wireless connectivity. The objective of this paper is to maximize robot mission capabilities by maximizing the wireless network capacity and to reduce the risk of communication failure. Thus, in this paper, we consider a multi-node wireless tethering structure called the “server-relay-client” framework that uses (multiple) relay nodes in between a server and a client node. We propose a robust stochastic optimization (RSO) algorithm using a multi-sensor-based RSS sampling method at the relay nodes to efficiently improve and balance the RSS between the source and client nodes to improve the network capacity and to provide redundant networking abilities. We use pre-processing techniques, such as exponential moving averaging and spatial averaging filters on the RSS data for smoothing. We apply a receiver spatial diversity concept and employ a position controller on the relay node using a stochastic gradient ascent method for self-positioning the relay node to achieve the RSS balancing task. The effectiveness of the proposed solution is validated by extensive simulations and field experiments in CERN facilities. For the field trials, we used a youBot mobile robot platform as the relay node, and two stand-alone Raspberry Pi computers as the client and server nodes. The algorithm has been proven to be robust to noise in the radio signals and to work effectively even under non-line-of-sight conditions. PMID:25615734
NASA Astrophysics Data System (ADS)
Rakkiyappan, R.; Chandrasekar, A.; Lakshmanan, S.
2016-07-01
This paper is concerned with the stochastic sampled data robust stabilisation of T-S fuzzy neutral systems with randomly occurring uncertainties and time-varying delays. The sampling period is assumed to be m in number, whose occurrence probabilities are given constants and satisfy Bernoulli distribution. By introducing an improved Lyapunov-Krasovskii functional with new triple integral terms and by combining both the convex combination technique and reciprocal convex technique, delay-dependent robust stability criteria are obtained in terms of linear matrix inequalities. These linear matrix inequalities can be easily solved by using standard convex optimisation algorithms. The designed stochastic sampled data fuzzy controller gain can be obtained. Finally, three numerical examples are given to illustrate the effectiveness of the proposed methods.
Hermann, Philipp; Mrkvička, Tomáš; Mattfeldt, Torsten; Minárová, Mária; Helisová, Kateřina; Nicolis, Orietta; Wartner, Fabian; Stehlík, Milan
2015-08-15
Fractals are models of natural processes with many applications in medicine. The recent studies in medicine show that fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Inspired by Sierpinski carpet, we introduce a flexible parametric model of random carpets. Randomization is introduced by usage of binomial random variables. We provide an algorithm for estimation of parameters of the model and illustrate theoretical and practical issues in generation of Sierpinski gaskets and Hausdorff measure calculations. Stochastic geometry models can also serve as models for binary cancer images. Recently, a Boolean model was applied on the 200 images of mammary cancer tissue and 200 images of mastopathic tissue. Here, we describe the Quermass-interaction process, which can handle much more variations in the cancer data, and we apply it to the images. It was found out that mastopathic tissue deviates significantly stronger from Quermass-interaction process, which describes interactions among particles, than mammary cancer tissue does. The Quermass-interaction process serves as a model describing the tissue, which structure is broken to a certain level. However, random fractal model fits well for mastopathic tissue. We provide a novel discrimination method between mastopathic and mammary cancer tissue on the basis of complex wavelet-based self-similarity measure with classification rates more than 80%. Such similarity measure relates to Hurst exponent and fractional Brownian motions. The R package FractalParameterEstimation is developed and introduced in the paper. PMID:25847279
Roberts, William M; Augustine, Steven B; Lawton, Kristy J; Lindsay, Theodore H; Thiele, Tod R; Izquierdo, Eduardo J; Faumont, Serge; Lindsay, Rebecca A; Britton, Matthew Cale; Pokala, Navin; Bargmann, Cornelia I; Lockery, Shawn R
2016-01-01
Random search is a behavioral strategy used by organisms from bacteria to humans to locate food that is randomly distributed and undetectable at a distance. We investigated this behavior in the nematode Caenorhabditis elegans, an organism with a small, well-described nervous system. Here we formulate a mathematical model of random search abstracted from the C. elegans connectome and fit to a large-scale kinematic analysis of C. elegans behavior at submicron resolution. The model predicts behavioral effects of neuronal ablations and genetic perturbations, as well as unexpected aspects of wild type behavior. The predictive success of the model indicates that random search in C. elegans can be understood in terms of a neuronal flip-flop circuit involving reciprocal inhibition between two populations of stochastic neurons. Our findings establish a unified theoretical framework for understanding C. elegans locomotion and a testable neuronal model of random search that can be applied to other organisms. DOI: http://dx.doi.org/10.7554/eLife.12572.001 PMID:26824391
NASA Astrophysics Data System (ADS)
Wu, Zhizhang; Huang, Zhongyi
2016-07-01
In this paper, we consider the numerical solution of the one-dimensional Schrödinger equation with a periodic lattice potential and a random external potential. This is an important model in solid state physics where the randomness results from complicated phenomena that are not exactly known. Here we generalize the Bloch decomposition-based time-splitting pseudospectral method to the stochastic setting using the generalized polynomial chaos with a Galerkin procedure so that the main effects of dispersion and periodic potential are still computed together. We prove that our method is unconditionally stable and numerical examples show that it has other nice properties and is more efficient than the traditional method. Finally, we give some numerical evidence for the well-known phenomenon of Anderson localization.
NASA Astrophysics Data System (ADS)
French, O. E.
2009-06-01
A random walk model with a negative binomially fluctuating number of steps is considered in the case where the mean of the number fluctuations, \\bar{N} , is finite. The asymptotic behaviour of the resultant statistics in the large \\bar{N} limit is derived and shown to give the K distribution. The equivalence of this model to the hitherto unrelated doubly stochastic representation of the K distribution is also demonstrated. The convergence to the K distribution of the probability density function generated by a random walk with a finite mean number of steps is examined along with the moments, and the non-Gaussian statistics are shown to be a direct result of discreteness and bunching effects.
Polynomial iterative algorithms for coloring and analyzing random graphs.
Braunstein, A; Mulet, R; Pagnani, A; Weigt, M; Zecchina, R
2003-09-01
We study the graph coloring problem over random graphs of finite average connectivity c. Given a number q of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable. Depending on q, we find with a one-step replica-symmetry breaking approximation the precise value of the critical average connectivity c(q). Moreover, we show that below c(q) there exists a clustering phase c in [c(d),c(q)] in which ground states spontaneously divide into an exponential number of clusters. Furthermore, we extended our considerations to the case of single instances showing consistent results. This leads us to propose a different algorithm that is able to color in polynomial time random graphs in the hard but colorable region, i.e., when c in [c(d),c(q)]. PMID:14524921
Using genetic algorithm to solve a new multi-period stochastic optimization model
NASA Astrophysics Data System (ADS)
Zhang, Xin-Li; Zhang, Ke-Cun
2009-09-01
This paper presents a new asset allocation model based on the CVaR risk measure and transaction costs. Institutional investors manage their strategic asset mix over time to achieve favorable returns subject to various uncertainties, policy and legal constraints, and other requirements. One may use a multi-period portfolio optimization model in order to determine an optimal asset mix. Recently, an alternative stochastic programming model with simulated paths was proposed by Hibiki [N. Hibiki, A hybrid simulation/tree multi-period stochastic programming model for optimal asset allocation, in: H. Takahashi, (Ed.) The Japanese Association of Financial Econometrics and Engineering, JAFFE Journal (2001) 89-119 (in Japanese); N. Hibiki A hybrid simulation/tree stochastic optimization model for dynamic asset allocation, in: B. Scherer (Ed.), Asset and Liability Management Tools: A Handbook for Best Practice, Risk Books, 2003, pp. 269-294], which was called a hybrid model. However, the transaction costs weren't considered in that paper. In this paper, we improve Hibiki's model in the following aspects: (1) The risk measure CVaR is introduced to control the wealth loss risk while maximizing the expected utility; (2) Typical market imperfections such as short sale constraints, proportional transaction costs are considered simultaneously. (3) Applying a genetic algorithm to solve the resulting model is discussed in detail. Numerical results show the suitability and feasibility of our methodology.
NASA Astrophysics Data System (ADS)
Tompson, A. F. B.; Mellors, R. J.; Dyer, K.; Yang, X.; Chen, M.; Trainor Guitton, W.; Wagoner, J. L.; Ramirez, A. L.
2014-12-01
A stochastic joint inverse algorithm is used to analyze diverse geophysical and hydrologic data associated with a geothermal prospect. The approach uses a Markov Chain Monte Carlo (MCMC) global search algorithm to develop an ensemble of hydrothermal groundwater flow models that are most consistent with the observations. The algorithm utilizes an initial conceptual model descriptive of structural (geology), parametric (permeability) and hydrothermal (saturation, temperature) characteristics of the geologic system. Initial (a-priori) estimates of uncertainty in these characteristics are used to drive simulations of hydrothermal fluid flow and related geophysical processes in a large number of random realizations of the conceptual geothermal system spanning these uncertainties. The process seeks to improve the conceptual model by developing a ranked subset of model realizations that best match all available data within a specified norm or tolerance. Statistical (posterior) characteristics of these solutions reflect reductions in the a-priori uncertainties. The algorithm has been tested on a geothermal prospect located at Superstition Mountain, California and has been successful in creating a suite of models compatible with available temperature, surface resistivity, and magnetotelluric (MT) data. Although the MCMC method is highly flexible and capable of accommodating multiple and diverse datasets, a typical inversion may require the evaluation of thousands of possible model runs whose sophistication and complexity may evolve with the magnitude of data considered. As a result, we are testing the use of sensitivity analyses to better identify critical uncertain variables, lower order surrogate models to streamline computational costs, and value of information analyses to better assess optimal use of related data. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL
Stochastic models: theory and simulation.
Field, Richard V., Jr.
2008-03-01
Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.
Decelle, Aurelien; Krzakala, Florent; Moore, Cristopher; Zdeborová, Lenka
2011-12-01
In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network. We use the cavity method of statistical physics to obtain an asymptotically exact analysis of the phase diagram. We describe in detail properties of the detectability-undetectability phase transition and the easy-hard phase transition for the community detection problem. Our analysis translates naturally into a belief propagation algorithm for inferring the group memberships of the nodes in an optimal way, i.e., that maximizes the overlap with the underlying group memberships, and learning the underlying parameters of the block model. Finally, we apply the algorithm to two examples of real-world networks and discuss its performance. PMID:22304154
NASA Astrophysics Data System (ADS)
Decelle, Aurelien; Krzakala, Florent; Moore, Cristopher; Zdeborová, Lenka
2011-12-01
In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network. We use the cavity method of statistical physics to obtain an asymptotically exact analysis of the phase diagram. We describe in detail properties of the detectability-undetectability phase transition and the easy-hard phase transition for the community detection problem. Our analysis translates naturally into a belief propagation algorithm for inferring the group memberships of the nodes in an optimal way, i.e., that maximizes the overlap with the underlying group memberships, and learning the underlying parameters of the block model. Finally, we apply the algorithm to two examples of real-world networks and discuss its performance.
2D stochastic-integral models for characterizing random grain noise in titanium alloys
Sabbagh, Harold A.; Murphy, R. Kim; Sabbagh, Elias H.; Cherry, Matthew; Pilchak, Adam; Knopp, Jeremy S.; Blodgett, Mark P.
2014-02-18
We extend our previous work, in which we applied high-dimensional model representation (HDMR) and analysis of variance (ANOVA) concepts to the characterization of a metallic surface that has undergone a shot-peening treatment to reduce residual stresses, and has, therefore, become a random conductivity field. That example was treated as a onedimensional problem, because those were the only data available. In this study, we develop a more rigorous two-dimensional model for characterizing random, anisotropic grain noise in titanium alloys. Such a model is necessary if we are to accurately capture the 'clumping' of crystallites into long chains that appear during the processing of the metal into a finished product. The mathematical model starts with an application of the Karhunen-Loève (K-L) expansion for the random Euler angles, θ and φ, that characterize the orientation of each crystallite in the sample. The random orientation of each crystallite then defines the stochastic nature of the electrical conductivity tensor of the metal. We study two possible covariances, Gaussian and double-exponential, which are the kernel of the K-L integral equation, and find that the double-exponential appears to satisfy measurements more closely of the two. Results based on data from a Ti-7Al sample will be given, and further applications of HDMR and ANOVA will be discussed.
NASA Astrophysics Data System (ADS)
Jiang, Daqing; Shi, Ningzhong; Li, Xiaoyue
2008-04-01
This paper discusses a randomized non-autonomous logistic equation , where B(t) is a 1-dimensional standard Brownian motion. In [D.Q. Jiang, N.Z. Shi, A note on non-autonomous logistic equation with random perturbation, J. Math. Anal. Appl. 303 (2005) 164-172], the authors show that E[1/N(t)] has a unique positive T-periodic solution E[1/Np(t)] provided a(t), b(t) and [alpha](t) are continuous T-periodic functions, a(t)>0, b(t)>0 and . We show that this equation is stochastically permanent and the solution Np(t) is globally attractive provided a(t), b(t) and [alpha](t) are continuous T-periodic functions, a(t)>0, b(t)>0 and mint[set membership, variant][0,T]a(t)>maxt[set membership, variant][0,T][alpha]2(t). By the way, the similar results of a generalized non-autonomous logistic equation with random perturbation are yielded.
Random Process Simulation for stochastic fatigue analysis. Ph.D. Thesis - Rice Univ., Houston, Tex.
NASA Technical Reports Server (NTRS)
Larsen, Curtis E.
1988-01-01
A simulation technique is described which directly synthesizes the extrema of a random process and is more efficient than the Gaussian simulation method. Such a technique is particularly useful in stochastic fatigue analysis because the required stress range moment E(R sup m), is a function only of the extrema of the random stress process. The family of autoregressive moving average (ARMA) models is reviewed and an autoregressive model is presented for modeling the extrema of any random process which has a unimodal power spectral density (psd). The proposed autoregressive technique is found to produce rainflow stress range moments which compare favorably with those computed by the Gaussian technique and to average 11.7 times faster than the Gaussian technique. The autoregressive technique is also adapted for processes having bimodal psd's. The adaptation involves using two autoregressive processes to simulate the extrema due to each mode and the superposition of these two extrema sequences. The proposed autoregressive superposition technique is 9 to 13 times faster than the Gaussian technique and produces comparable values for E(R sup m) for bimodal psd's having the frequency of one mode at least 2.5 times that of the other mode.
Stochastic Seismic Response of an Algiers Site with Random Depth to Bedrock
NASA Astrophysics Data System (ADS)
Badaoui, M.; Berrah, M. K.; Mébarki, A.
2010-05-01
Among the important effects of the Boumerdes earthquake (Algeria, May 21st 2003) was that, within the same zone, the destructions in certain parts were more important than in others. This phenomenon is due to site effects which alter the characteristics of seismic motions and cause concentration of damage during earthquakes. Local site effects such as thickness and mechanical properties of soil layers have important effects on the surface ground motions. This paper deals with the effect of the randomness aspect of the depth to bedrock (soil layers heights) which is assumed to be a random variable with lognormal distribution. This distribution is suitable for strictly non-negative random variables with large values of the coefficient of variation. In this case, Monte Carlo simulations are combined with the stiffness matrix method, used herein as a deterministic method, for evaluating the effect of the depth to bedrock uncertainty on the seismic response of a multilayered soil. This study considers a P and SV wave propagation pattern using input accelerations collected at Keddara station, located at 20 km from the epicenter, as it is located directly on the bedrock. A parametric study is conducted do derive the stochastic behavior of the peak ground acceleration and its response spectrum, the transfer function and the amplification factors. It is found that the soil height heterogeneity causes a widening of the frequency content and an increase in the fundamental frequency of the soil profile, indicating that the resonance phenomenon concerns a larger number of structures.
Stochastic Seismic Response of an Algiers Site with Random Depth to Bedrock
Badaoui, M.; Mebarki, A.; Berrah, M. K.
2010-05-21
Among the important effects of the Boumerdes earthquake (Algeria, May 21{sup st} 2003) was that, within the same zone, the destructions in certain parts were more important than in others. This phenomenon is due to site effects which alter the characteristics of seismic motions and cause concentration of damage during earthquakes. Local site effects such as thickness and mechanical properties of soil layers have important effects on the surface ground motions.This paper deals with the effect of the randomness aspect of the depth to bedrock (soil layers heights) which is assumed to be a random variable with lognormal distribution. This distribution is suitable for strictly non-negative random variables with large values of the coefficient of variation. In this case, Monte Carlo simulations are combined with the stiffness matrix method, used herein as a deterministic method, for evaluating the effect of the depth to bedrock uncertainty on the seismic response of a multilayered soil. This study considers a P and SV wave propagation pattern using input accelerations collected at Keddara station, located at 20 km from the epicenter, as it is located directly on the bedrock.A parametric study is conducted do derive the stochastic behavior of the peak ground acceleration and its response spectrum, the transfer function and the amplification factors. It is found that the soil height heterogeneity causes a widening of the frequency content and an increase in the fundamental frequency of the soil profile, indicating that the resonance phenomenon concerns a larger number of structures.
A stochastic control approach to Slotted-ALOHA random access protocol
NASA Astrophysics Data System (ADS)
Pietrabissa, Antonio
2013-12-01
ALOHA random access protocols are distributed protocols based on transmission probabilities, that is, each node decides upon packet transmissions according to a transmission probability value. In the literature, ALOHA protocols are analysed by giving necessary and sufficient conditions for the stability of the queues of the node buffers under a control vector (whose elements are the transmission probabilities assigned to the nodes), given an arrival rate vector (whose elements represent the rates of the packets arriving in the node buffers). The innovation of this work is that, given an arrival rate vector, it computes the optimal control vector by defining and solving a stochastic control problem aimed at maximising the overall transmission efficiency, while keeping a grade of fairness among the nodes. Furthermore, a more general case in which the arrival rate vector changes in time is considered. The increased efficiency of the proposed solution with respect to the standard ALOHA approach is evaluated by means of numerical simulations.
Randomized tree construction algorithm to explore energy landscapes.
Jaillet, Léonard; Corcho, Francesc J; Pérez, Juan-Jesús; Cortés, Juan
2011-12-01
In this work, a new method for exploring conformational energy landscapes is described. The method, called transition-rapidly exploring random tree (T-RRT), combines ideas from statistical physics and robot path planning algorithms. A search tree is constructed on the conformational space starting from a given state. The tree expansion is driven by a double strategy: on the one hand, it is naturally biased toward yet unexplored regions of the space; on the other, a Monte Carlo-like transition test guides the expansion toward energetically favorable regions. The balance between these two strategies is automatically achieved due to a self-tuning mechanism. The method is able to efficiently find both energy minima and transition paths between them. As a proof of concept, the method is applied to two academic benchmarks and the alanine dipeptide. PMID:21919017
NASA Astrophysics Data System (ADS)
Salah, Ahmad M.; Nelson, E. James; Williams, Gustavious P.
2010-04-01
We present algorithms and tools we developed to automatically link an overland flow model to a hydrodynamic water quality model with different spatial and temporal discretizations. These tools run the linked models which provide a stochastic simulation frame. We also briefly present the tools and algorithms we developed to facilitate and analyze stochastic simulations of the linked models. We demonstrate the algorithms by linking the Gridded Surface Subsurface Hydrologic Analysis (GSSHA) model for overland flow with the CE-QUAL-W2 model for water quality and reservoir hydrodynamics. GSSHA uses a two-dimensional horizontal grid while CE-QUAL-W2 uses a two-dimensional vertical grid. We implemented the algorithms and tools in the Watershed Modeling System (WMS) which allows modelers to easily create and use models. The algorithms are general and could be used for other models. Our tools create and analyze stochastic simulations to help understand uncertainty in the model application. While a number of examples of linked models exist, the ability to perform automatic, unassisted linking is a step forward and provides the framework to easily implement stochastic modeling studies.
Caballero-Águila, Raquel; Hermoso-Carazo, Aurora; Linares-Pérez, Josefa
2016-01-01
This paper is concerned with the distributed and centralized fusion filtering problems in sensor networked systems with random one-step delays in transmissions. The delays are described by Bernoulli variables correlated at consecutive sampling times, with different characteristics at each sensor. The measured outputs are subject to uncertainties modeled by random parameter matrices, thus providing a unified framework to describe a wide variety of network-induced phenomena; moreover, the additive noises are assumed to be one-step autocorrelated and cross-correlated. Under these conditions, without requiring the knowledge of the signal evolution model, but using only the first and second order moments of the processes involved in the observation model, recursive algorithms for the optimal linear distributed and centralized filters under the least-squares criterion are derived by an innovation approach. Firstly, local estimators based on the measurements received from each sensor are obtained and, after that, the distributed fusion filter is generated as the least-squares matrix-weighted linear combination of the local estimators. Also, a recursive algorithm for the optimal linear centralized filter is proposed. In order to compare the estimators performance, recursive formulas for the error covariance matrices are derived in all the algorithms. The effects of the delays in the filters accuracy are analyzed in a numerical example which also illustrates how some usual network-induced uncertainties can be dealt with using the current observation model described by random matrices. PMID:27338387
Caballero-Águila, Raquel; Hermoso-Carazo, Aurora; Linares-Pérez, Josefa
2016-01-01
This paper is concerned with the distributed and centralized fusion filtering problems in sensor networked systems with random one-step delays in transmissions. The delays are described by Bernoulli variables correlated at consecutive sampling times, with different characteristics at each sensor. The measured outputs are subject to uncertainties modeled by random parameter matrices, thus providing a unified framework to describe a wide variety of network-induced phenomena; moreover, the additive noises are assumed to be one-step autocorrelated and cross-correlated. Under these conditions, without requiring the knowledge of the signal evolution model, but using only the first and second order moments of the processes involved in the observation model, recursive algorithms for the optimal linear distributed and centralized filters under the least-squares criterion are derived by an innovation approach. Firstly, local estimators based on the measurements received from each sensor are obtained and, after that, the distributed fusion filter is generated as the least-squares matrix-weighted linear combination of the local estimators. Also, a recursive algorithm for the optimal linear centralized filter is proposed. In order to compare the estimators performance, recursive formulas for the error covariance matrices are derived in all the algorithms. The effects of the delays in the filters accuracy are analyzed in a numerical example which also illustrates how some usual network-induced uncertainties can be dealt with using the current observation model described by random matrices. PMID:27338387
Random matrix approach to quantum adiabatic evolution algorithms
Boulatov, A.; Smelyanskiy, V.N.
2005-05-15
We analyze the power of the quantum adiabatic evolution algorithm (QAA) for solving random computationally hard optimization problems within a theoretical framework based on random matrix theory (RMT). We present two types of driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that nonadiabatic corrections in the QAA are due to the interaction of the ground state with the 'cloud' formed by most of the excited states, confirming that in driven RMT models, the Landau-Zener scenario of pairwise level repulsions is not relevant for the description of nonadiabatic corrections. We show that the QAA has a finite probability of success in a certain range of parameters, implying a polynomial complexity of the algorithm. The second model corresponds to the standard QAA with the problem Hamiltonian taken from the RMT Gaussian unitary ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. For this reason, the driven GUE model can also lead to polynomial complexity of the QAA. The main contribution to the failure probability of the QAA comes from the nonadiabatic corrections to the eigenstates, which only depend on the absolute values of the transition amplitudes. Due to the mapping between the two models, these absolute values are the same in both cases. Our results indicate that this 'phase irrelevance' is the leading effect that can make both the Markovian- and GUE-type QAAs successful.
NASA Astrophysics Data System (ADS)
Tsai, C.; Hung, R. J.
2015-12-01
This study attempts to apply queueing theory to develop a stochastic framework that could account for the random-sized batch arrivals of incoming sediment particles into receiving waters. Sediment particles, control volume, mechanics of sediment transport (such as mechanics of suspension, deposition and resuspension) are treated as the customers, service facility and the server respectively in queueing theory. In the framework, the stochastic diffusion particle tracking model (SD-PTM) and resuspension of particles are included to simulate the random transport trajectories of suspended particles. The most distinguished characteristic of queueing theory is that customers come to the service facility in a random manner. In analogy to sediment transport, this characteristic is adopted to model the random-sized batch arrival process of sediment particles including the random occurrences and random magnitude of incoming sediment particles. The random occurrences of arrivals are simulated by Poisson process while the number of sediment particles in each arrival can be simulated by a binominal distribution. Simulations of random arrivals and random magnitude are proposed individually to compare with the random-sized batch arrival simulations. Simulation results are a probabilistic description for discrete sediment transport through ensemble statistics (i.e. ensemble means and ensemble variances) of sediment concentrations and transport rates. Results reveal the different mechanisms of incoming particles will result in differences in the ensemble variances of concentrations and transport rates under the same mean incoming rate of sediment particles.
Inner Random Restart Genetic Algorithm for Practical Delivery Schedule Optimization
NASA Astrophysics Data System (ADS)
Sakurai, Yoshitaka; Takada, Kouhei; Onoyama, Takashi; Tsukamoto, Natsuki; Tsuruta, Setsuo
A delivery route optimization that improves the efficiency of real time delivery or a distribution network requires solving several tens to hundreds but less than 2 thousands cities Traveling Salesman Problems (TSP) within interactive response time (less than about 3 second), with expert-level accuracy (less than about 3% of error rate). Further, to make things more difficult, the optimization is subjects to special requirements or preferences of each various delivery sites, persons, or societies. To meet these requirements, an Inner Random Restart Genetic Algorithm (Irr-GA) is proposed and developed. This method combines meta-heuristics such as random restart and GA having different types of simple heuristics. Such simple heuristics are 2-opt and NI (Nearest Insertion) methods, each applied for gene operations. The proposed method is hierarchical structured, integrating meta-heuristics and heuristics both of which are multiple but simple. This method is elaborated so that field experts as well as field engineers can easily understand to make the solution or method easily customized and extended according to customers' needs or taste. Comparison based on the experimental results and consideration proved that the method meets the above requirements more than other methods judging from not only optimality but also simplicity, flexibility, and expandability in order for this method to be practically used.
A new algorithm for calculating the curvature perturbations in stochastic inflation
Fujita, Tomohiro; Kawasaki, Masahiro; Tada, Yuichiro; Takesako, Tomohiro E-mail: kawasaki@icrr.u-tokyo.ac.jp E-mail: takesako@icrr.u-tokyo.ac.jp
2013-12-01
We propose a new approach for calculating the curvature perturbations produced during inflation in the stochastic formalism. In our formalism, the fluctuations of the e-foldings are directly calculated without perturbatively expanding the inflaton field and they are connected to the curvature perturbations by the δN formalism. The result automatically includes the contributions of the higher order perturbations because we solve the equation of motion non-perturbatively. In this paper, we analytically prove that our result (the power spectrum and the nonlinearity parameter) is consistent with the standard result in single field slow-roll inflation. We also describe the algorithm for numerical calculations of the curvature perturbations in more general inflation models.
Stochastic generation of explicit pore structures by thresholding Gaussian random fields
Hyman, Jeffrey D.; Winter, C. Larrabee
2014-11-15
We provide a description and computational investigation of an efficient method to stochastically generate realistic pore structures. Smolarkiewicz and Winter introduced this specific method in pores resolving simulation of Darcy flows (Smolarkiewicz and Winter, 2010 [1]) without giving a complete formal description or analysis of the method, or indicating how to control the parameterization of the ensemble. We address both issues in this paper. The method consists of two steps. First, a realization of a correlated Gaussian field, or topography, is produced by convolving a prescribed kernel with an initial field of independent, identically distributed random variables. The intrinsic length scales of the kernel determine the correlation structure of the topography. Next, a sample pore space is generated by applying a level threshold to the Gaussian field realization: points are assigned to the void phase or the solid phase depending on whether the topography over them is above or below the threshold. Hence, the topology and geometry of the pore space depend on the form of the kernel and the level threshold. Manipulating these two user prescribed quantities allows good control of pore space observables, in particular the Minkowski functionals. Extensions of the method to generate media with multiple pore structures and preferential flow directions are also discussed. To demonstrate its usefulness, the method is used to generate a pore space with physical and hydrological properties similar to a sample of Berea sandstone. -- Graphical abstract: -- Highlights: •An efficient method to stochastically generate realistic pore structures is provided. •Samples are generated by applying a level threshold to a Gaussian field realization. •Two user prescribed quantities determine the topology and geometry of the pore space. •Multiple pore structures and preferential flow directions can be produced. •A pore space based on Berea sandstone is generated.
Xiang, Bingren; Wu, Xiaohong; Liu, Dan
2014-01-01
Simultaneous determination of multiple weak chromatographic peaks via stochastic resonance algorithm attracts much attention in recent years. However, the optimization of the parameters is complicated and time consuming, although the single-well potential stochastic resonance algorithm (SSRA) has already reduced the number of parameters to only one and simplified the process significantly. Even worse, it is often difficult to keep amplified peaks with beautiful peak shape. Therefore, multiobjective genetic algorithm was employed to optimize the parameter of SSRA for multiple optimization objectives (i.e., S/N and peak shape) and multiple chromatographic peaks. The applicability of the proposed method was evaluated with an experimental data set of Sudan dyes, and the results showed an excellent quantitative relationship between different concentrations and responses. PMID:24526920
A matrix product algorithm for stochastic dynamics on locally tree-like graphs
NASA Astrophysics Data System (ADS)
Barthel, Thomas; de Bacco, Caterina; Franz, Silvio
In this talk, I describe a novel algorithm for the efficient simulation of generic stochastic dynamics of classical degrees of freedom defined on the vertices of locally tree-like graphs. Such models correspond for example to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon the cavity method and ideas from quantum many-body theory, the algorithm is based on a matrix product approximation of the so-called edge messages - conditional probabilities of vertex variable trajectories. The matrix product edge messages (MPEM) are constructed recursively. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the MPEM in truncations. In contrast to Monte Carlo simulations, the approach has a better error scaling and works for both, single instances as well as the thermodynamic limit. Due to the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations with unprecedented accuracy. The method is demonstrated for the prototypical non-equilibrium Glauber dynamics of an Ising spin system. Reference: arXiv:1508.03295.
An efficient algorithm for the stochastic simulation of the hybridization of DNA to microarrays
2009-01-01
Background Although oligonucleotide microarray technology is ubiquitous in genomic research, reproducibility and standardization of expression measurements still concern many researchers. Cross-hybridization between microarray probes and non-target ssDNA has been implicated as a primary factor in sensitivity and selectivity loss. Since hybridization is a chemical process, it may be modeled at a population-level using a combination of material balance equations and thermodynamics. However, the hybridization reaction network may be exceptionally large for commercial arrays, which often possess at least one reporter per transcript. Quantification of the kinetics and equilibrium of exceptionally large chemical systems of this type is numerically infeasible with customary approaches. Results In this paper, we present a robust and computationally efficient algorithm for the simulation of hybridization processes underlying microarray assays. Our method may be utilized to identify the extent to which nucleic acid targets (e.g. cDNA) will cross-hybridize with probes, and by extension, characterize probe robustnessusing the information specified by MAGE-TAB. Using this algorithm, we characterize cross-hybridization in a modified commercial microarray assay. Conclusions By integrating stochastic simulation with thermodynamic prediction tools for DNA hybridization, one may robustly and rapidly characterize of the selectivity of a proposed microarray design at the probe and "system" levels. Our code is available at http://www.laurenzi.net. PMID:20003312
Random finite set multi-target trackers: stochastic geometry for space situational awareness
NASA Astrophysics Data System (ADS)
Vo, Ba-Ngu; Vo, Ba-Tuong
2015-05-01
This paper describes the recent development in the random finite set RFS paradigm in multi-target tracking. Over the last decade the Probability Hypothesis Density filter has become synonymous with the RFS approach. As result the PHD filter is often wrongly used as a performance benchmark for the RFS approach. Since there is a suite of RFS-based multi-target tracking algorithms, benchmarking tracking performance of the RFS approach by using the PHD filter, the cheapest of these, is misleading. Such benchmarking should be performed with more sophisticated RFS algorithms. In this paper we outline the high-performance RFS-based multi-target trackers such that the Generalized Labled Multi-Bernoulli filter, and a number of efficient approximations and discuss extensions and applications of these filters. Applications to space situational awareness are discussed.
Berco, Dan Tseng, Tseung-Yuen
2015-12-21
This study presents an evaluation method for resistive random access memory retention reliability based on the Metropolis Monte Carlo algorithm and Gibbs free energy. The method, which does not rely on a time evolution, provides an extremely efficient way to compare the relative retention properties of metal-insulator-metal structures. It requires a small number of iterations and may be used for statistical analysis. The presented approach is used to compare the relative robustness of a single layer ZrO{sub 2} device with a double layer ZnO/ZrO{sub 2} one, and obtain results which are in good agreement with experimental data.
NASA Astrophysics Data System (ADS)
Berco, Dan; Tseng, Tseung-Yuen
2015-12-01
This study presents an evaluation method for resistive random access memory retention reliability based on the Metropolis Monte Carlo algorithm and Gibbs free energy. The method, which does not rely on a time evolution, provides an extremely efficient way to compare the relative retention properties of metal-insulator-metal structures. It requires a small number of iterations and may be used for statistical analysis. The presented approach is used to compare the relative robustness of a single layer ZrO2 device with a double layer ZnO/ZrO2 one, and obtain results which are in good agreement with experimental data.
Ariyawansa, K.A.
1991-04-01
A benchmark parallel implementation of the Van Slyke and Wets algorithm for stochastic linear programs, and the results of a carefully designed numerical experiment on the Sequent/Balance using the implementation are presented. An important use of this implementation is as a benchmark to assess the performance of approximation algorithms for stochastic linear programs. These approximation algorithms are best suited for implementation on parallel vector processes like the Alliant FX/8. Therefore, the performance of the benchmark implementation on the Alliant FX/8 is of interest. In this paper, we present results observed when a portion of the numerical experiment is performed on the Alliant FX/8. These results indicate that the implementation makes satisfactory use of the concurrency capabilities of the Alliant FX/8. They also indicate that the vectorization capabilities of the Alliant FX/8 are not satisfactorily utilized by the implementation. 9 refs., 9 tabs.
Genetic Algorithm Based Framework for Automation of Stochastic Modeling of Multi-Season Streamflows
NASA Astrophysics Data System (ADS)
Srivastav, R. K.; Srinivasan, K.; Sudheer, K.
2009-05-01
bootstrap (MABB) ) based on the explicit objective functions of minimizing the relative bias and relative root mean square error in estimating the storage capacity of the reservoir. The optimal parameter set of the hybrid model is obtained based on the search over a multi- dimensional parameter space (involving simultaneous exploration of the parametric (PAR(1)) as well as the non-parametric (MABB) components). This is achieved using the efficient evolutionary search based optimization tool namely, non-dominated sorting genetic algorithm - II (NSGA-II). This approach helps in reducing the drudgery involved in the process of manual selection of the hybrid model, in addition to predicting the basic summary statistics dependence structure, marginal distribution and water-use characteristics accurately. The proposed optimization framework is used to model the multi-season streamflows of River Beaver and River Weber of USA. In case of both the rivers, the proposed GA-based hybrid model yields a much better prediction of the storage capacity (where simultaneous exploration of both parametric and non-parametric components is done) when compared with the MLE-based hybrid models (where the hybrid model selection is done in two stages, thus probably resulting in a sub-optimal model). This framework can be further extended to include different linear/non-linear hybrid stochastic models at other temporal and spatial scales as well.
Di Pierro, Michele; Elber, Ron; Leimkuhler, Benedict
2015-12-01
We present an algorithm termed COMPEL (COnstant Molecular Pressure with Ewald sum for Long range forces) to conduct simulations in the NPT ensemble. The algorithm combines novel features recently proposed in the literature to obtain a highly efficient and accurate numerical integrator. COMPEL exploits the concepts of molecular pressure, rapid stochastic relaxation to equilibrium, exact calculation of the contribution to the pressure of long-range nonbonded forces with Ewald summation, and the use of Trotter expansion to generate a robust, highly stable, symmetric, and accurate algorithm. Explicit implementation in the MOIL program and illustrative numerical examples are discussed. PMID:26616351
Stochastic generation of explicit pore structures by thresholding Gaussian random fields
NASA Astrophysics Data System (ADS)
Hyman, Jeffrey D.; Winter, C. Larrabee
2014-11-01
We provide a description and computational investigation of an efficient method to stochastically generate realistic pore structures. Smolarkiewicz and Winter introduced this specific method in pores resolving simulation of Darcy flows (Smolarkiewicz and Winter, 2010 [1]) without giving a complete formal description or analysis of the method, or indicating how to control the parameterization of the ensemble. We address both issues in this paper. The method consists of two steps. First, a realization of a correlated Gaussian field, or topography, is produced by convolving a prescribed kernel with an initial field of independent, identically distributed random variables. The intrinsic length scales of the kernel determine the correlation structure of the topography. Next, a sample pore space is generated by applying a level threshold to the Gaussian field realization: points are assigned to the void phase or the solid phase depending on whether the topography over them is above or below the threshold. Hence, the topology and geometry of the pore space depend on the form of the kernel and the level threshold. Manipulating these two user prescribed quantities allows good control of pore space observables, in particular the Minkowski functionals. Extensions of the method to generate media with multiple pore structures and preferential flow directions are also discussed. To demonstrate its usefulness, the method is used to generate a pore space with physical and hydrological properties similar to a sample of Berea sandstone.
Biased Randomized Algorithm for Fast Model-Based Diagnosis
NASA Technical Reports Server (NTRS)
Williams, Colin; Vartan, Farrokh
2005-01-01
A biased randomized algorithm has been developed to enable the rapid computational solution of a propositional- satisfiability (SAT) problem equivalent to a diagnosis problem. The closest competing methods of automated diagnosis are described in the preceding article "Fast Algorithms for Model-Based Diagnosis" and "Two Methods of Efficient Solution of the Hitting-Set Problem" (NPO-30584), which appears elsewhere in this issue. It is necessary to recapitulate some of the information from the cited articles as a prerequisite to a description of the present method. As used here, "diagnosis" signifies, more precisely, a type of model-based diagnosis in which one explores any logical inconsistencies between the observed and expected behaviors of an engineering system. The function of each component and the interconnections among all the components of the engineering system are represented as a logical system. Hence, the expected behavior of the engineering system is represented as a set of logical consequences. Faulty components lead to inconsistency between the observed and expected behaviors of the system, represented by logical inconsistencies. Diagnosis - the task of finding the faulty components - reduces to finding the components, the abnormalities of which could explain all the logical inconsistencies. One seeks a minimal set of faulty components (denoted a minimal diagnosis), because the trivial solution, in which all components are deemed to be faulty, always explains all inconsistencies. In the methods of the cited articles, the minimal-diagnosis problem is treated as equivalent to a minimal-hitting-set problem, which is translated from a combinatorial to a computational problem by mapping it onto the Boolean-satisfiability and integer-programming problems. The integer-programming approach taken in one of the prior methods is complete (in the sense that it is guaranteed to find a solution if one exists) and slow and yields a lower bound on the size of the
Webster, Clayton; Tempone, Raul; Nobile, Fabio
2007-12-01
This work describes the convergence analysis of a Smolyak-type sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations with random coefficients and forcing terms (input data of the model). To compute solution statistics, the sparse grid stochastic collocation method uses approximate solutions, produced here by finite elements, corresponding to a deterministic set of points in the random input space. This naturally requires solving uncoupled deterministic problems and, as such, the derived strong error estimates for the fully discrete solution are used to compare the computational efficiency of the proposed method with the Monte Carlo method. Numerical examples illustrate the theoretical results and are used to compare this approach with several others, including the standard Monte Carlo.
Albert, Jaroslav
2016-01-01
Modeling stochastic behavior of chemical reaction networks is an important endeavor in many aspects of chemistry and systems biology. The chemical master equation (CME) and the Gillespie algorithm (GA) are the two most fundamental approaches to such modeling; however, each of them has its own limitations: the GA may require long computing times, while the CME may demand unrealistic memory storage capacity. We propose a method that combines the CME and the GA that allows one to simulate stochastically a part of a reaction network. First, a reaction network is divided into two parts. The first part is simulated via the GA, while the solution of the CME for the second part is fed into the GA in order to update its propensities. The advantage of this method is that it avoids the need to solve the CME or stochastically simulate the entire network, which makes it highly efficient. One of its drawbacks, however, is that most of the information about the second part of the network is lost in the process. Therefore, this method is most useful when only partial information about a reaction network is needed. We tested this method against the GA on two systems of interest in biology - the gene switch and the Griffith model of a genetic oscillator—and have shown it to be highly accurate. Comparing this method to four different stochastic algorithms revealed it to be at least an order of magnitude faster than the fastest among them. PMID:26930199
MULTILEVEL ACCELERATION OF STOCHASTIC COLLOCATION METHODS FOR PDE WITH RANDOM INPUT DATA
Webster, Clayton G; Jantsch, Peter A; Teckentrup, Aretha L; Gunzburger, Max D
2013-01-01
Stochastic Collocation (SC) methods for stochastic partial differential equa- tions (SPDEs) suffer from the curse of dimensionality, whereby increases in the stochastic dimension cause an explosion of computational effort. To combat these challenges, multilevel approximation methods seek to decrease computational complexity by balancing spatial and stochastic discretization errors. As a form of variance reduction, multilevel techniques have been successfully applied to Monte Carlo (MC) methods, but may be extended to accelerate other methods for SPDEs in which the stochastic and spatial degrees of freedom are de- coupled. This article presents general convergence and computational complexity analysis of a multilevel method for SPDEs, demonstrating its advantages with regard to standard, single level approximation. The numerical results will highlight conditions under which multilevel sparse grid SC is preferable to the more traditional MC and SC approaches.
Volkov, M V; Garanin, S G; Dolgopolov, Yu V; Kopalkin, A V; Kulikov, S M; Sinyavin, D N; Starikov, F A; Sukharev, S A; Tyutin, S V; Khokhlov, S V; Chaparin, D A
2014-11-30
A seven-channel fibre laser system operated by the master oscillator – multichannel power amplifier scheme is the phase locked using a stochastic parallel gradient algorithm. The phase modulators on lithium niobate crystals are controlled by a multichannel electronic unit with the microcontroller processing signals in real time. The dynamic phase locking of the laser system with the bandwidth of 14 kHz is demonstrated, the time of phasing is 3 – 4 ms. (fibre and integrated-optical structures)
Orio, Patricio; Soudry, Daniel
2012-01-01
Background The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects that channel noise can have on neural dynamics are generally studied using numerical simulations of stochastic models. Algorithms based on discrete Markov Chains (MC) seem to be the most reliable and trustworthy, but even optimized algorithms come with a non-negligible computational cost. Diffusion Approximation (DA) methods use Stochastic Differential Equations (SDE) to approximate the behavior of a number of MCs, considerably speeding up simulation times. However, model comparisons have suggested that DA methods did not lead to the same results as in MC modeling in terms of channel noise statistics and effects on excitability. Recently, it was shown that the difference arose because MCs were modeled with coupled gating particles, while the DA was modeled using uncoupled gating particles. Implementations of DA with coupled particles, in the context of a specific kinetic scheme, yielded similar results to MC. However, it remained unclear how to generalize these implementations to different kinetic schemes, or whether they were faster than MC algorithms. Additionally, a steady state approximation was used for the stochastic terms, which, as we show here, can introduce significant inaccuracies. Main Contributions We derived the SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable – allowing an easy, transparent and efficient DA implementation, avoiding unnecessary approximations. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods, except when
A novel quantum random number generation algorithm used by smartphone camera
NASA Astrophysics Data System (ADS)
Wu, Nan; Wang, Kun; Hu, Haixing; Song, Fangmin; Li, Xiangdong
2015-05-01
We study an efficient algorithm to extract quantum random numbers (QRN) from the raw data obtained by charge-coupled device (CCD) or complementary metal-oxide semiconductor (CMOS) based sensors, like a camera used in a commercial smartphone. Based on NIST statistical test for random number generators, the proposed algorithm has a high QRN generation rate and high statistical randomness. This algorithm provides a kind of simple, low-priced and reliable devices as a QRN generator for quantum key distribution (QKD) or other cryptographic applications.
Haron, Zaiton; Bakar, Suhaimi Abu; Dimon, Mohamad Ngasri
2015-01-01
Strategic noise mapping provides important information for noise impact assessment and noise abatement. However, producing reliable strategic noise mapping in a dynamic, complex working environment is difficult. This study proposes the implementation of the random walk approach as a new stochastic technique to simulate noise mapping and to predict the noise exposure level in a workplace. A stochastic simulation framework and software, namely RW-eNMS, were developed to facilitate the random walk approach in noise mapping prediction. This framework considers the randomness and complexity of machinery operation and noise emission levels. Also, it assesses the impact of noise on the workers and the surrounding environment. For data validation, three case studies were conducted to check the accuracy of the prediction data and to determine the efficiency and effectiveness of this approach. The results showed high accuracy of prediction results together with a majority of absolute differences of less than 2 dBA; also, the predicted noise doses were mostly in the range of measurement. Therefore, the random walk approach was effective in dealing with environmental noises. It could predict strategic noise mapping to facilitate noise monitoring and noise control in the workplaces. PMID:25875019
Han, Lim Ming; Haron, Zaiton; Yahya, Khairulzan; Bakar, Suhaimi Abu; Dimon, Mohamad Ngasri
2015-01-01
Strategic noise mapping provides important information for noise impact assessment and noise abatement. However, producing reliable strategic noise mapping in a dynamic, complex working environment is difficult. This study proposes the implementation of the random walk approach as a new stochastic technique to simulate noise mapping and to predict the noise exposure level in a workplace. A stochastic simulation framework and software, namely RW-eNMS, were developed to facilitate the random walk approach in noise mapping prediction. This framework considers the randomness and complexity of machinery operation and noise emission levels. Also, it assesses the impact of noise on the workers and the surrounding environment. For data validation, three case studies were conducted to check the accuracy of the prediction data and to determine the efficiency and effectiveness of this approach. The results showed high accuracy of prediction results together with a majority of absolute differences of less than 2 dBA; also, the predicted noise doses were mostly in the range of measurement. Therefore, the random walk approach was effective in dealing with environmental noises. It could predict strategic noise mapping to facilitate noise monitoring and noise control in the workplaces. PMID:25875019
NASA Astrophysics Data System (ADS)
Mohamed, Majeed; Narayan Kar, Indra
2015-11-01
This paper focuses on a stochastic version of contraction theory to construct observer-controller structure for a flight dynamic system with noisy velocity measurement. A nonlinear stochastic observer is designed to estimate the pitch rate, the pitch angle, and the velocity of an aircraft example model using stochastic contraction theory. Estimated states are used to compute feedback control for solving a tracking problem. The structure and gain selection of the observer is carried out using Itô's stochastic differential equations and the contraction theory. The contraction property of integrated observer-controller structure is derived to ensure the exponential convergence of the trajectories of closed-loop nonlinear system. The upper bound of the state estimation error is explicitly derived and the efficacy of the proposed observer-controller structure has been shown through the numerical simulations.
NASA Astrophysics Data System (ADS)
Huang, Zhehao; Liu, Zhengrong
2016-07-01
In this paper, we study the influences of dually environmental noises on the traveling wave which develops from the deterministic KPP equation. We prove that if the strengths of noises satisfy some condition, the solution of the stochastic KPP equation with Heaviside initial condition develops a random traveling wave, whose wave speed is deterministic and depends on the strengths of noises. If the strengths of noises satisfy some other conditions, the solution tends to zero as time tends to infinity. Therefore, there exist bifurcations of asymptotic behaviors of solution induced by the strengths of dual noises.
Diffusion and stochastic island generation in the magnetic field line random walk
Vlad, M.; Spineanu, F.
2014-08-10
The cross-field diffusion of field lines in stochastic magnetic fields described by the 2D+slab model is studied using a semi-analytic statistical approach, the decorrelation trajectory method. We show that field line trapping and the associated stochastic magnetic islands strongly influence the diffusion coefficients, leading to dependences on the parameters that are different from the quasilinear and Bohm regimes. A strong amplification of the diffusion is produced by a small slab field in the presence of trapping. The diffusion regimes are determined and the corresponding physical processes are identified.
Hermes, Matthew R; Hirata, So
2014-12-28
A stochastic algorithm based on Metropolis Monte Carlo (MC) is presented for the size-extensive vibrational self-consistent field methods (XVSCF(n) and XVSCF[n]) for anharmonic molecular vibrations. The new MC-XVSCF methods substitute stochastic evaluations of a small number of high-dimensional integrals of functions of the potential energy surface (PES), which is sampled on demand, for diagrammatic equations involving high-order anharmonic force constants. This algorithm obviates the need to evaluate and store any high-dimensional partial derivatives of the potential and can be applied to the fully anharmonic PES without any Taylor-series approximation in an intrinsically parallelizable algorithm. The MC-XVSCF methods reproduce deterministic XVSCF calculations on the same Taylor-series PES in all energies, frequencies, and geometries. Calculations using the fully anharmonic PES evaluated on the fly with electronic structure methods report anharmonic effects on frequencies and geometries of much greater magnitude than deterministic XVSCF calculations, reflecting an underestimation of anharmonic effects in a Taylor-series approximation to the PES. PMID:25554137
Hermes, Matthew R.; Hirata, So
2014-12-28
A stochastic algorithm based on Metropolis Monte Carlo (MC) is presented for the size-extensive vibrational self-consistent field methods (XVSCF(n) and XVSCF[n]) for anharmonic molecular vibrations. The new MC-XVSCF methods substitute stochastic evaluations of a small number of high-dimensional integrals of functions of the potential energy surface (PES), which is sampled on demand, for diagrammatic equations involving high-order anharmonic force constants. This algorithm obviates the need to evaluate and store any high-dimensional partial derivatives of the potential and can be applied to the fully anharmonic PES without any Taylor-series approximation in an intrinsically parallelizable algorithm. The MC-XVSCF methods reproduce deterministic XVSCF calculations on the same Taylor-series PES in all energies, frequencies, and geometries. Calculations using the fully anharmonic PES evaluated on the fly with electronic structure methods report anharmonic effects on frequencies and geometries of much greater magnitude than deterministic XVSCF calculations, reflecting an underestimation of anharmonic effects in a Taylor-series approximation to the PES.
NASA Astrophysics Data System (ADS)
Tavakkoli-Moghaddam, Reza; Alinaghian, Mehdi; Salamat-Bakhsh, Alireza; Norouzi, Narges
2012-05-01
A vehicle routing problem is a significant problem that has attracted great attention from researchers in recent years. The main objectives of the vehicle routing problem are to minimize the traveled distance, total traveling time, number of vehicles and cost function of transportation. Reducing these variables leads to decreasing the total cost and increasing the driver's satisfaction level. On the other hand, this satisfaction, which will decrease by increasing the service time, is considered as an important logistic problem for a company. The stochastic time dominated by a probability variable leads to variation of the service time, while it is ignored in classical routing problems. This paper investigates the problem of the increasing service time by using the stochastic time for each tour such that the total traveling time of the vehicles is limited to a specific limit based on a defined probability. Since exact solutions of the vehicle routing problem that belong to the category of NP-hard problems are not practical in a large scale, a hybrid algorithm based on simulated annealing with genetic operators was proposed to obtain an efficient solution with reasonable computational cost and time. Finally, for some small cases, the related results of the proposed algorithm were compared with results obtained by the Lingo 8 software. The obtained results indicate the efficiency of the proposed hybrid simulated annealing algorithm.
Stochastic nonlinear wave equation with memory driven by compensated Poisson random measures
Liang, Fei; Department of Mathematics, Xi An University of Science and Technology, Xi An 710054 ; Gao, Hongjun
2014-03-15
In this paper, we study a class of stochastic nonlinear wave equation with memory driven by Lévy noise. We first show the existence and uniqueness of global mild solutions using a suitable energy function. Second, under some additional assumptions we prove the exponential stability of the solutions.
Li, Tong; Gu, YuanTong
2014-04-15
As all-atom molecular dynamics method is limited by its enormous computational cost, various coarse-grained strategies have been developed to extend the length scale of soft matters in the modeling of mechanical behaviors. However, the classical thermostat algorithm in highly coarse-grained molecular dynamics method would underestimate the thermodynamic behaviors of soft matters (e.g. microfilaments in cells), which can weaken the ability of materials to overcome local energy traps in granular modeling. Based on all-atom molecular dynamics modeling of microfilament fragments (G-actin clusters), a new stochastic thermostat algorithm is developed to retain the representation of thermodynamic properties of microfilaments at extra coarse-grained level. The accuracy of this stochastic thermostat algorithm is validated by all-atom MD simulation. This new stochastic thermostat algorithm provides an efficient way to investigate the thermomechanical properties of large-scale soft matters.
Space resection model calculation based on Random Sample Consensus algorithm
NASA Astrophysics Data System (ADS)
Liu, Xinzhu; Kang, Zhizhong
2016-03-01
Resection has been one of the most important content in photogrammetry. It aims at the position and attitude information of camera at the shooting point. However in some cases, the observed values for calculating are with gross errors. This paper presents a robust algorithm that using RANSAC method with DLT model can effectually avoiding the difficulties to determine initial values when using co-linear equation. The results also show that our strategies can exclude crude handicap and lead to an accurate and efficient way to gain elements of exterior orientation.
NASA Astrophysics Data System (ADS)
Che, Yan; Shu, Huisheng; Yang, Hua; Ding, Derui
2013-07-01
In this article, the H ∞ filtering problem is investigated for a class of nonlinear stochastic systems with incomplete measurements. The considered incomplete measurements include both the missing measurements and the randomly occurring communication delays. By using a set of Kronecker delta functions, a unified measurement model is employed to describe the phenomena of random communication delays and missing measurements. The purpose of the problem addressed is to design an H ∞ filter such that, for all nonlinearities, incomplete measurements and external disturbances, the filtering error dynamics is exponentially mean-square stable and the H ∞-norm requirement is satisfied. A sufficient condition for the existence of the desired filter is established in terms of certain linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed filter scheme.
Mignon, David; Simonson, Thomas
2016-07-15
Computational protein design depends on an energy function and an algorithm to search the sequence/conformation space. We compare three stochastic search algorithms: a heuristic, Monte Carlo (MC), and a Replica Exchange Monte Carlo method (REMC). The heuristic performs a steepest-descent minimization starting from thousands of random starting points. The methods are applied to nine test proteins from three structural families, with a fixed backbone structure, a molecular mechanics energy function, and with 1, 5, 10, 20, 30, or all amino acids allowed to mutate. Results are compared to an exact, "Cost Function Network" method that identifies the global minimum energy conformation (GMEC) in favorable cases. The designed sequences accurately reproduce experimental sequences in the hydrophobic core. The heuristic and REMC agree closely and reproduce the GMEC when it is known, with a few exceptions. Plain MC performs well for most cases, occasionally departing from the GMEC by 3-4 kcal/mol. With REMC, the diversity of the sequences sampled agrees with exact enumeration where the latter is possible: up to 2 kcal/mol above the GMEC. Beyond, room temperature replicas sample sequences up to 10 kcal/mol above the GMEC, providing thermal averages and a solution to the inverse protein folding problem. © 2016 Wiley Periodicals, Inc. PMID:27197555
NASA Astrophysics Data System (ADS)
Franke, Brian C.; Kensek, Ronald P.; Prinja, Anil K.
2014-06-01
Stochastic-media simulations require numerous boundary crossings. We consider two Monte Carlo electron transport approaches and evaluate accuracy with numerous material boundaries. In the condensed-history method, approximations are made based on infinite-medium solutions for multiple scattering over some track length. Typically, further approximations are employed for material-boundary crossings where infinite-medium solutions become invalid. We have previously explored an alternative "condensed transport" formulation, a Generalized Boltzmann-Fokker-Planck GBFP method, which requires no special boundary treatment but instead uses approximations to the electron-scattering cross sections. Some limited capabilities for analog transport and a GBFP method have been implemented in the Integrated Tiger Series (ITS) codes. Improvements have been made to the condensed history algorithm. The performance of the ITS condensed-history and condensed-transport algorithms are assessed for material-boundary crossings. These assessments are made both by introducing artificial material boundaries and by comparison to analog Monte Carlo simulations.
Can stochastic, dissipative wave fields be treated as random walk generators
NASA Technical Reports Server (NTRS)
Weinstock, J.
1986-01-01
A suggestion by Meek et al. (1985) that the gravity wave field be viewed as stochastic, with significant nonlinearities, is applied to calculate diffusivities. The purpose here is to calculate the diffusivity for stochastic wave model and compare it with previous diffusivity estimates. The researchers do this for an idealized case in which the wind velocity changes but slowly, and for which saturation is the principal mechanism by which wave energy is lost. A related calculation was given in a very brief way (Weinstock, 1976), but the approximations were not fully justified, nor were the physical pre-suppositions clearly explained. The observations of Meek et al. (1985) have clarified the pre-suppositions for the researchers and provided a rationalization and improvement of the approximations employed.
Exact Mapping of the Stochastic Field Theory for Manna Sandpiles to Interfaces in Random Media
NASA Astrophysics Data System (ADS)
Le Doussal, Pierre; Wiese, Kay Jörg
2015-03-01
We show that the stochastic field theory for directed percolation in the presence of an additional conservation law [the conserved directed-percolation (C-DP) class] can be mapped exactly to the continuum theory for the depinning of an elastic interface in short-range correlated quenched disorder. Along one line of the parameters commonly studied, this mapping leads to the simplest overdamped dynamics. Away from this line, an additional memory term arises in the interface dynamics; we argue that this does not change the universality class. Since C-DP is believed to describe the Manna class of self-organized criticality, this shows that Manna stochastic sandpiles and disordered elastic interfaces (i.e., the quenched Edwards-Wilkinson model) share the same universal large-scale behavior.
Exact mapping of the stochastic field theory for Manna sandpiles to interfaces in random media.
Le Doussal, Pierre; Wiese, Kay Jörg
2015-03-20
We show that the stochastic field theory for directed percolation in the presence of an additional conservation law [the conserved directed-percolation (C-DP) class] can be mapped exactly to the continuum theory for the depinning of an elastic interface in short-range correlated quenched disorder. Along one line of the parameters commonly studied, this mapping leads to the simplest overdamped dynamics. Away from this line, an additional memory term arises in the interface dynamics; we argue that this does not change the universality class. Since C-DP is believed to describe the Manna class of self-organized criticality, this shows that Manna stochastic sandpiles and disordered elastic interfaces (i.e., the quenched Edwards-Wilkinson model) share the same universal large-scale behavior. PMID:25839253
ERIC Educational Resources Information Center
Argoti, A.; Fan, L. T.; Cruz, J.; Chou, S. T.
2008-01-01
The stochastic simulation of chemical reactions, specifically, a simple reversible chemical reaction obeying the first-order, i.e., linear, rate law, has been presented by Martinez-Urreaga and his collaborators in this journal. The current contribution is intended to complement and augment their work in two aspects. First, the simple reversible…
Fault detection of aircraft system with random forest algorithm and similarity measure.
Lee, Sanghyuk; Park, Wookje; Jung, Sikhang
2014-01-01
Research on fault detection algorithm was developed with the similarity measure and random forest algorithm. The organized algorithm was applied to unmanned aircraft vehicle (UAV) that was readied by us. Similarity measure was designed by the help of distance information, and its usefulness was also verified by proof. Fault decision was carried out by calculation of weighted similarity measure. Twelve available coefficients among healthy and faulty status data group were used to determine the decision. Similarity measure weighting was done and obtained through random forest algorithm (RFA); RF provides data priority. In order to get a fast response of decision, a limited number of coefficients was also considered. Relation of detection rate and amount of feature data were analyzed and illustrated. By repeated trial of similarity calculation, useful data amount was obtained. PMID:25057508
An efficient algorithm for generating random number pairs drawn from a bivariate normal distribution
NASA Technical Reports Server (NTRS)
Campbell, C. W.
1983-01-01
An efficient algorithm for generating random number pairs from a bivariate normal distribution was developed. Any desired value of the two means, two standard deviations, and correlation coefficient can be selected. Theoretically the technique is exact and in practice its accuracy is limited only by the quality of the uniform distribution random number generator, inaccuracies in computer function evaluation, and arithmetic. A FORTRAN routine was written to check the algorithm and good accuracy was obtained. Some small errors in the correlation coefficient were observed to vary in a surprisingly regular manner. A simple model was developed which explained the qualities aspects of the errors.
NASA Astrophysics Data System (ADS)
Lu, Dawei; Zhu, Jing; Zou, Ping; Peng, Xinhua; Yu, Yihua; Zhang, Shanmin; Chen, Qun; Du, Jiangfeng
2010-02-01
An important quantum search algorithm based on the quantum random walk performs an oracle search on a database of N items with O(phN) calls, yielding a speedup similar to the Grover quantum search algorithm. The algorithm was implemented on a quantum information processor of three-qubit liquid-crystal nuclear magnetic resonance (NMR) in the case of finding 1 out of 4, and the diagonal elements’ tomography of all the final density matrices was completed with comprehensible one-dimensional NMR spectra. The experimental results agree well with the theoretical predictions.
Lu Dawei; Peng Xinhua; Du Jiangfeng; Zhu Jing; Zou Ping; Yu Yihua; Zhang Shanmin; Chen Qun
2010-02-15
An important quantum search algorithm based on the quantum random walk performs an oracle search on a database of N items with O({radical}(phN)) calls, yielding a speedup similar to the Grover quantum search algorithm. The algorithm was implemented on a quantum information processor of three-qubit liquid-crystal nuclear magnetic resonance (NMR) in the case of finding 1 out of 4, and the diagonal elements' tomography of all the final density matrices was completed with comprehensible one-dimensional NMR spectra. The experimental results agree well with the theoretical predictions.
Study on 2D random medium inversion algorithm based on Fuzzy C-means Clustering theory
NASA Astrophysics Data System (ADS)
Xu, Z.; Zhu, P.; Gu, Y.; Yang, X.; Jiang, J.
2015-12-01
Abstract: In seismic exploration for metal deposits, the traditional seismic inversion method based on layered homogeneous medium theory seems difficult to inverse small scale inhomogeneity and spatial variation of the actual medium. The reason is that physical properties of actual medium are more likely random distribution rather than layered. Thus, it is necessary to investigate a random medium inversion algorithm. The velocity of 2D random medium can be described as a function of five parameters: the background velocity (V0), the standard deviation of velocity (σ), the horizontal and vertical autocorrelation lengths (A and B), and the autocorrelation angle (θ). In this study, we propose an inversion algorithm for random medium based on the Fuzzy C-means Clustering (FCM) theory, whose basic idea is that FCM is used to control the inversion process to move forward to the direction we desired by clustering the estimated parameters into groups. Our method can be divided into three steps: firstly, the three parameters (A, B, θ) are estimated from 2D post-stack seismic data using the non-stationary random medium parameter estimation method, and then the estimated parameters are clustered to different groups according to FCM; secondly, the initial random medium model is constructed with clustered groups and the rest two parameters (V0 and σ) obtained from the well logging data; at last, inversion of the random medium are conducted to obtain velocity, impedance and random medium parameters using the Conjugate Gradient Method. The inversion experiments of synthetic seismic data show that the velocity models inverted by our algorithm are close to the real velocity distribution and the boundary of different media can be distinguished clearly.Key words: random medium, inversion, FCM, parameter estimation
Polan, Daniel F; Brady, Samuel L; Kaufman, Robert A
2016-09-01
There is a need for robust, fully automated whole body organ segmentation for diagnostic CT. This study investigates and optimizes a Random Forest algorithm for automated organ segmentation; explores the limitations of a Random Forest algorithm applied to the CT environment; and demonstrates segmentation accuracy in a feasibility study of pediatric and adult patients. To the best of our knowledge, this is the first study to investigate a trainable Weka segmentation (TWS) implementation using Random Forest machine-learning as a means to develop a fully automated tissue segmentation tool developed specifically for pediatric and adult examinations in a diagnostic CT environment. Current innovation in computed tomography (CT) is focused on radiomics, patient-specific radiation dose calculation, and image quality improvement using iterative reconstruction, all of which require specific knowledge of tissue and organ systems within a CT image. The purpose of this study was to develop a fully automated Random Forest classifier algorithm for segmentation of neck-chest-abdomen-pelvis CT examinations based on pediatric and adult CT protocols. Seven materials were classified: background, lung/internal air or gas, fat, muscle, solid organ parenchyma, blood/contrast enhanced fluid, and bone tissue using Matlab and the TWS plugin of FIJI. The following classifier feature filters of TWS were investigated: minimum, maximum, mean, and variance evaluated over a voxel radius of 2 (n) , (n from 0 to 4), along with noise reduction and edge preserving filters: Gaussian, bilateral, Kuwahara, and anisotropic diffusion. The Random Forest algorithm used 200 trees with 2 features randomly selected per node. The optimized auto-segmentation algorithm resulted in 16 image features including features derived from maximum, mean, variance Gaussian and Kuwahara filters. Dice similarity coefficient (DSC) calculations between manually segmented and Random Forest algorithm segmented images from 21
Botet, Robert; Kuratsuji, Hiroshi
2010-03-15
We present a framework for the stochastic features of the polarization state of an electromagnetic wave propagating through the optical medium with both deterministic (controlled) and disordered birefringence. In this case, the Stokes parameters obey a Langevin-type equation on the Poincare sphere. The functional integral method provides for a natural tool to derive the Fokker-Planck equation for the probability distribution of the Stokes parameters. We solve the Fokker-Planck equation in the case of a random anisotropic active medium submitted to a homogeneous electromagnetic field. The possible dissipation and relaxation phenomena are studied in general and in various cases, and we give hints about how to validate experimentally the corresponding phenomenological equations.
NASA Astrophysics Data System (ADS)
Zhao, Guo-Zhong; Chen, Gang; Kang, Zhan
2012-04-01
This paper analyzes the random response of structural-acoustic coupled systems. Most existing works on coupled structural-acoustic analysis are limited to systems under deterministic excitations due to high computational cost required by a random response analysis. To reduce the computational burden involved in the coupled random analysis, an iterative procedure based on the Pseudo excitation method has been developed. It is found that this algorithm has an overwhelming advantage in computing efficiency over traditional methods, as demonstrated by some numerical examples given in this paper.
NASA Technical Reports Server (NTRS)
Boussalis, Dhemetrios; Wang, Shyh J.
1992-01-01
This paper presents a method for utilizing artificial neural networks for direct adaptive control of dynamic systems with poorly known dynamics. The neural network weights (controller gains) are adapted in real time using state measurements and a random search optimization algorithm. The results are demonstrated via simulation using two highly nonlinear systems.
NASA Technical Reports Server (NTRS)
Deavours, Daniel D.; Qureshi, M. Akber; Sanders, William H.
1997-01-01
Modeling tools and technologies are important for aerospace development. At the University of Illinois, we have worked on advancing the state of the art in modeling by Markov reward models in two important areas: reducing the memory necessary to numerically solve systems represented as stochastic activity networks and other stochastic Petri net extensions while still obtaining solutions in a reasonable amount of time, and finding numerically stable and memory-efficient methods to solve for the reward accumulated during a finite mission time. A long standing problem when modeling with high level formalisms such as stochastic activity networks is the so-called state space explosion, where the number of states increases exponentially with size of the high level model. Thus, the corresponding Markov model becomes prohibitively large and solution is constrained by the the size of primary memory. To reduce the memory necessary to numerically solve complex systems, we propose new methods that can tolerate such large state spaces that do not require any special structure in the model (as many other techniques do). First, we develop methods that generate row and columns of the state transition-rate-matrix on-the-fly, eliminating the need to explicitly store the matrix at all. Next, we introduce a new iterative solution method, called modified adaptive Gauss-Seidel, that exhibits locality in its use of data from the state transition-rate-matrix, permitting us to cache portions of the matrix and hence reduce the solution time. Finally, we develop a new memory and computationally efficient technique for Gauss-Seidel based solvers that avoids the need for generating rows of A in order to solve Ax = b. This is a significant performance improvement for on-the-fly methods as well as other recent solution techniques based on Kronecker operators. Taken together, these new results show that one can solve very large models without any special structure.
Beyond the random coil: stochastic conformational switching in intrinsically disordered proteins.
Choi, Ucheor B; McCann, James J; Weninger, Keith R; Bowen, Mark E
2011-04-13
Intrinsically disordered proteins (IDPs) participate in critical cellular functions that exploit the flexibility and rapid conformational fluctuations of their native state. Limited information about the native state of IDPs can be gained by the averaging over many heterogeneous molecules that is unavoidable in ensemble approaches. We used single molecule fluorescence to characterize native state conformational dynamics in five synaptic proteins confirmed to be disordered by other techniques. For three of the proteins, SNAP-25, synaptobrevin and complexin, their conformational dynamics could be described with a simple semiflexible polymer model. Surprisingly, two proteins, neuroligin and the NMDAR-2B glutamate receptor, were observed to stochastically switch among distinct conformational states despite the fact that they appeared intrinsically disordered by other measures. The hop-like intramolecular diffusion found in these proteins is suggested to define a class of functionality previously unrecognized for IDPs. PMID:21481779
Sidje, R B; Vo, H D
2015-11-01
The mathematical framework of the chemical master equation (CME) uses a Markov chain to model the biochemical reactions that are taking place within a biological cell. Computing the transient probability distribution of this Markov chain allows us to track the composition of molecules inside the cell over time, with important practical applications in a number of areas such as molecular biology or medicine. However the CME is typically difficult to solve, since the state space involved can be very large or even countably infinite. We present a novel way of using the stochastic simulation algorithm (SSA) to reduce the size of the finite state projection (FSP) method. Numerical experiments that demonstrate the effectiveness of the reduction are included. PMID:26319118
Koh, Wonryull; Blackwell, Kim T.
2011-01-01
Stochastic simulation of reaction–diffusion systems enables the investigation of stochastic events arising from the small numbers and heterogeneous distribution of molecular species in biological cells. Stochastic variations in intracellular microdomains and in diffusional gradients play a significant part in the spatiotemporal activity and behavior of cells. Although an exact stochastic simulation that simulates every individual reaction and diffusion event gives a most accurate trajectory of the system's state over time, it can be too slow for many practical applications. We present an accelerated algorithm for discrete stochastic simulation of reaction–diffusion systems designed to improve the speed of simulation by reducing the number of time-steps required to complete a simulation run. This method is unique in that it employs two strategies that have not been incorporated in existing spatial stochastic simulation algorithms. First, diffusive transfers between neighboring subvolumes are based on concentration gradients. This treatment necessitates sampling of only the net or observed diffusion events from higher to lower concentration gradients rather than sampling all diffusion events regardless of local concentration gradients. Second, we extend the non-negative Poisson tau-leaping method that was originally developed for speeding up nonspatial or homogeneous stochastic simulation algorithms. This method calculates each leap time in a unified step for both reaction and diffusion processes while satisfying the leap condition that the propensities do not change appreciably during the leap and ensuring that leaping does not cause molecular populations to become negative. Numerical results are presented that illustrate the improvement in simulation speed achieved by incorporating these two new strategies. PMID:21513371
High-resolution climate data over conterminous US using random forest algorithm
NASA Astrophysics Data System (ADS)
Hashimoto, H.; Nemani, R. R.; Wang, W.
2014-12-01
We developed a new methodology to create high-resolution precipitation data using the random forest algorithm. We have used two approaches: physical downscaling from GCM data using a regional climate model, and interpolation from ground observation data. Physical downscaling method can be applied only for a small region because it is computationally expensive and complex to deploy. On the other hand, interpolation schemes from ground observations do not consider physical processes. In this study, we utilized the random forest algorithm to integrate atmospheric reanalysis data, satellite data, topography data, and ground observation data. First we considered situations where precipitation is same across the domain, largely dominated by storm like systems. We then picked several points to train random forest algorithm. The random forest algorithm estimates out-of-bag errors spatially, and produces the relative importance of each of the input variable.This methodology has the following advantages. (1) The methodology can ingest any spatial dataset to improve downscaling. Even non-precipitation datasets can be ingested such as satellite cloud cover data, radar reflectivity image, or modeled convective available potential energy. (2) The methodology is purely statistical so that physical assumptions are not required. Meanwhile, most of interpolation schemes assume empirical relationship between precipitation and elevation for orographic precipitation. (3) Low quality value in ingested data does not cause critical bias in the results because of the ensemble feature of random forest. Therefore, users do not need to pay a special attention to quality control of input data compared to other interpolation methodologies. (4) Same methodology can be applied to produce other high-resolution climate datasets, such as wind and cloud cover. Those variables are usually hard to be interpolated by conventional algorithms. In conclusion, the proposed methodology can produce reasonable
Magnetic localization and orientation of the capsule endoscope based on a random complex algorithm
He, Xiaoqi; Zheng, Zizhao; Hu, Chao
2015-01-01
The development of the capsule endoscope has made possible the examination of the whole gastrointestinal tract without much pain. However, there are still some important problems to be solved, among which, one important problem is the localization of the capsule. Currently, magnetic positioning technology is a suitable method for capsule localization, and this depends on a reliable system and algorithm. In this paper, based on the magnetic dipole model as well as magnetic sensor array, we propose nonlinear optimization algorithms using a random complex algorithm, applied to the optimization calculation for the nonlinear function of the dipole, to determine the three-dimensional position parameters and two-dimensional direction parameters. The stability and the antinoise ability of the algorithm is compared with the Levenberg–Marquart algorithm. The simulation and experiment results show that in terms of the error level of the initial guess of magnet location, the random complex algorithm is more accurate, more stable, and has a higher “denoise” capacity, with a larger range for initial guess values. PMID:25914561
Prados-Privado, María; Prados-Frutos, Juan Carlos; Calvo-Guirado, José Luis; Bea, José Antonio
2016-11-01
To measure fatigue in dental implants and in its components, it is necessary to use a probabilistic analysis since the randomness in the output depends on a number of parameters (such as fatigue properties of titanium and applied loads, unknown beforehand as they depend on mastication habits). The purpose is to apply a probabilistic approximation in order to predict fatigue life, taking into account the randomness of variables. More accuracy on the results has been obtained by taking into account different load blocks with different amplitudes, as happens with bite forces during the day and allowing us to know how effects have different type of bruxism on the piece analysed. PMID:27073012
Lessor, K.S.
1988-08-26
The parallel algorithm of Ariyawansa, Sorensen, and Wets for approximating the values and subgradients of the recourse function in a stochastic program with complete recourse is implemented and timing results are reported for limited experimental trials. 14 refs., 6 figs., 8 tabs.
Dulikravich, George S.; Sikka, Vinod K.; Muralidharan, G.
2006-06-01
The goal of this project was to adapt and use an advanced semi-stochastic algorithm for constrained multiobjective optimization and combine it with experimental testing and verification to determine optimum concentrations of alloying elements in heat-resistant and corrosion-resistant H-series stainless steel alloys that will simultaneously maximize a number of alloy's mechanical and corrosion properties.
Biased Random-Key Genetic Algorithms for the Winner Determination Problem in Combinatorial Auctions.
de Andrade, Carlos Eduardo; Toso, Rodrigo Franco; Resende, Mauricio G C; Miyazawa, Flávio Keidi
2015-01-01
In this paper we address the problem of picking a subset of bids in a general combinatorial auction so as to maximize the overall profit using the first-price model. This winner determination problem assumes that a single bidding round is held to determine both the winners and prices to be paid. We introduce six variants of biased random-key genetic algorithms for this problem. Three of them use a novel initialization technique that makes use of solutions of intermediate linear programming relaxations of an exact mixed integer linear programming model as initial chromosomes of the population. An experimental evaluation compares the effectiveness of the proposed algorithms with the standard mixed linear integer programming formulation, a specialized exact algorithm, and the best-performing heuristics proposed for this problem. The proposed algorithms are competitive and offer strong results, mainly for large-scale auctions. PMID:25299242
Wang, Rui; Zhou, Yongquan; Zhao, Chengyan; Wu, Haizhou
2015-01-01
Multi-threshold image segmentation is a powerful image processing technique that is used for the preprocessing of pattern recognition and computer vision. However, traditional multilevel thresholding methods are computationally expensive because they involve exhaustively searching the optimal thresholds to optimize the objective functions. To overcome this drawback, this paper proposes a flower pollination algorithm with a randomized location modification. The proposed algorithm is used to find optimal threshold values for maximizing Otsu's objective functions with regard to eight medical grayscale images. When benchmarked against other state-of-the-art evolutionary algorithms, the new algorithm proves itself to be robust and effective through numerical experimental results including Otsu's objective values and standard deviations. PMID:26405895
Autoclassification of the Variable 3XMM Sources Using the Random Forest Machine Learning Algorithm
NASA Astrophysics Data System (ADS)
Farrell, Sean A.; Murphy, Tara; Lo, Kitty K.
2015-11-01
In the current era of large surveys and massive data sets, autoclassification of astrophysical sources using intelligent algorithms is becoming increasingly important. In this paper we present the catalog of variable sources in the Third XMM-Newton Serendipitous Source catalog (3XMM) autoclassified using the Random Forest machine learning algorithm. We used a sample of manually classified variable sources from the second data release of the XMM-Newton catalogs (2XMMi-DR2) to train the classifier, obtaining an accuracy of ∼92%. We also evaluated the effectiveness of identifying spurious detections using a sample of spurious sources, achieving an accuracy of ∼95%. Manual investigation of a random sample of classified sources confirmed these accuracy levels and showed that the Random Forest machine learning algorithm is highly effective at automatically classifying 3XMM sources. Here we present the catalog of classified 3XMM variable sources. We also present three previously unidentified unusual sources that were flagged as outlier sources by the algorithm: a new candidate supergiant fast X-ray transient, a 400 s X-ray pulsar, and an eclipsing 5 hr binary system coincident with a known Cepheid.
NASA Astrophysics Data System (ADS)
Atanassov, E.; Dimitrov, D.; Gurov, T.
2015-10-01
The recent developments in the area of high-performance computing are driven not only by the desire for ever higher performance but also by the rising costs of electricity. The use of various types of accelerators like GPUs, Intel Xeon Phi has become mainstream and many algorithms and applications have been ported to make use of them where available. In Financial Mathematics the question of optimal use of computational resources should also take into account the limitations on space, because in many use cases the servers are deployed close to the exchanges. In this work we evaluate various algorithms for option pricing that we have implemented for different target architectures in terms of their energy and space efficiency. Since it has been established that low-discrepancy sequences may be better than pseudorandom numbers for these types of algorithms, we also test the Sobol and Halton sequences. We present the raw results, the computed metrics and conclusions from our tests.
Atanassov, E.; Dimitrov, D. E-mail: emanouil@parallel.bas.bg Gurov, T.
2015-10-28
The recent developments in the area of high-performance computing are driven not only by the desire for ever higher performance but also by the rising costs of electricity. The use of various types of accelerators like GPUs, Intel Xeon Phi has become mainstream and many algorithms and applications have been ported to make use of them where available. In Financial Mathematics the question of optimal use of computational resources should also take into account the limitations on space, because in many use cases the servers are deployed close to the exchanges. In this work we evaluate various algorithms for option pricing that we have implemented for different target architectures in terms of their energy and space efficiency. Since it has been established that low-discrepancy sequences may be better than pseudorandom numbers for these types of algorithms, we also test the Sobol and Halton sequences. We present the raw results, the computed metrics and conclusions from our tests.
Effect of the driving algorithm on the turbulence generated by a random jet array
NASA Astrophysics Data System (ADS)
Pérez-Alvarado, Alejandro; Mydlarski, Laurent; Gaskin, Susan
2016-02-01
Different driving algorithms for a large random jet array (RJA) were tested and their performance characterized by comparing the statistics of the turbulence generated downstream of the RJA. Of particular interest was the spatial configuration of the jets operating at any given instant (an aspect that has not been documented in previous RJAs studies), as well as the statistics of their respective on/off times. All algorithms generated flows with nonzero skewnesses of the velocity fluctuation normal to the plane of the RJA (identified as an inherent limitation of the system resulting from the unidirectional forcing imposed from only one side of the RJA), and slightly super-Gaussian kurtoses of the velocity fluctuations in all directions. It was observed that algorithms imposing spatial configurations generated the most isotropic flows; however, they suffered from high mean flows and low turbulent kinetic energies. The algorithm identified as RANDOM (also referred to as the "sunbathing algorithm") generated the flow that, on an overall basis, most closely approximated zero-mean-flow homogeneous isotropic turbulence, with variations in horizontal and vertical homogeneities of RMS velocities of no more than ±6 %, deviations from isotropy ( w RMS/ u RMS) in the range of 0.62-0.77, and mean flows on the order of 7 % of the RMS velocities (determined by averaging their absolute values over the three velocity components and three downstream distances). A relatively high turbulent Reynolds number ( Re T = u T ℓ/ ν = 2360, where ℓ is the integral length scale of the flow and u T is a characteristic RMS velocity) was achieved using the RANDOM algorithm and the integral length scale ( ℓ = 11.5 cm) is the largest reported to date. The quality of the turbulence in our large facility demonstrates the ability of RJAs to be scaled-up and to be the laboratory system most capable of generating the largest quasi-homogeneous isotropic turbulent regions with zero mean flow.
Fast randomized Hough transformation track initiation algorithm based on multi-scale clustering
NASA Astrophysics Data System (ADS)
Wan, Minjie; Gu, Guohua; Chen, Qian; Qian, Weixian; Wang, Pengcheng
2015-10-01
A fast randomized Hough transformation track initiation algorithm based on multi-scale clustering is proposed to overcome existing problems in traditional infrared search and track system(IRST) which cannot provide movement information of the initial target and select the threshold value of correlation automatically by a two-dimensional track association algorithm based on bearing-only information . Movements of all the targets are presumed to be uniform rectilinear motion throughout this new algorithm. Concepts of space random sampling, parameter space dynamic linking table and convergent mapping of image to parameter space are developed on the basis of fast randomized Hough transformation. Considering the phenomenon of peak value clustering due to shortcomings of peak detection itself which is built on threshold value method, accuracy can only be ensured on condition that parameter space has an obvious peak value. A multi-scale idea is added to the above-mentioned algorithm. Firstly, a primary association is conducted to select several alternative tracks by a low-threshold .Then, alternative tracks are processed by multi-scale clustering methods , through which accurate numbers and parameters of tracks are figured out automatically by means of transforming scale parameters. The first three frames are processed by this algorithm in order to get the first three targets of the track , and then two slightly different gate radius are worked out , mean value of which is used to be the global threshold value of correlation. Moreover, a new model for curvilinear equation correction is applied to the above-mentioned track initiation algorithm for purpose of solving the problem of shape distortion when a space three-dimensional curve is mapped to a two-dimensional bearing-only space. Using sideways-flying, launch and landing as examples to build models and simulate, the application of the proposed approach in simulation proves its effectiveness , accuracy , and adaptivity
Nonconvergence of the Wang-Landau algorithms with multiple random walkers
NASA Astrophysics Data System (ADS)
Belardinelli, R. E.; Pereyra, V. D.
2016-05-01
This paper discusses some convergence properties in the entropic sampling Monte Carlo methods with multiple random walkers, particularly in the Wang-Landau (WL) and 1 /t algorithms. The classical algorithms are modified by the use of m -independent random walkers in the energy landscape to calculate the density of states (DOS). The Ising model is used to show the convergence properties in the calculation of the DOS, as well as the critical temperature, while the calculation of the number π by multiple dimensional integration is used in the continuum approximation. In each case, the error is obtained separately for each walker at a fixed time, t ; then, the average over m walkers is performed. It is observed that the error goes as 1 /√{m } . However, if the number of walkers increases above a certain critical value m >mx , the error reaches a constant value (i.e., it saturates). This occurs for both algorithms; however, it is shown that for a given system, the 1 /t algorithm is more efficient and accurate than the similar version of the WL algorithm. It follows that it makes no sense to increase the number of walkers above a critical value mx, since it does not reduce the error in the calculation. Therefore, the number of walkers does not guarantee convergence.
NASA Astrophysics Data System (ADS)
Ivanova, Violeta M.; Sousa, Rita; Murrihy, Brian; Einstein, Herbert H.
2014-06-01
This paper presents results from research conducted at MIT during 2010-2012 on modeling of natural rock fracture systems with the GEOFRAC three-dimensional stochastic model. Following a background summary of discrete fracture network models and a brief introduction of GEOFRAC, the paper provides a thorough description of the newly developed mathematical and computer algorithms for fracture intensity, aperture, and intersection representation, which have been implemented in MATLAB. The new methods optimize, in particular, the representation of fracture intensity in terms of cumulative fracture area per unit volume, P32, via the Poisson-Voronoi Tessellation of planes into polygonal fracture shapes. In addition, fracture apertures now can be represented probabilistically or deterministically whereas the newly implemented intersection algorithms allow for computing discrete pathways of interconnected fractures. In conclusion, results from a statistical parametric study, which was conducted with the enhanced GEOFRAC model and the new MATLAB-based Monte Carlo simulation program FRACSIM, demonstrate how fracture intensity, size, and orientations influence fracture connectivity.
Margul, Daniel T; Tuckerman, Mark E
2016-05-10
Molecular dynamics remains one of the most widely used computational tools in the theoretical molecular sciences to sample an equilibrium ensemble distribution and/or to study the dynamical properties of a system. The efficiency of a molecular dynamics calculation is limited by the size of the time step that can be employed, which is dictated by the highest frequencies in the system. However, many properties of interest are connected to low-frequency, long time-scale phenomena, requiring many small time steps to capture. This ubiquitous problem can be ameliorated by employing multiple time-step algorithms, which assign different time steps to forces acting on different time scales. In such a scheme, fast forces are evaluated more frequently than slow forces, and as the former are often computationally much cheaper to evaluate, the savings can be significant. Standard multiple time-step approaches are limited, however, by resonance phenomena, wherein motion on the fastest time scales limits the step sizes that can be chosen for the slower time scales. In atomistic models of biomolecular systems, for example, the largest time step is typically limited to around 5 fs. Previously, we introduced an isokinetic extended phase-space algorithm (Minary et al. Phys. Rev. Lett. 2004, 93, 150201) and its stochastic analog (Leimkuhler et al. Mol. Phys. 2013, 111, 3579) that eliminate resonance phenomena through a set of kinetic energy constraints. In simulations of a fixed-charge flexible model of liquid water, for example, the time step that could be assigned to the slow forces approached 100 fs. In this paper, we develop a stochastic isokinetic algorithm for multiple time-step molecular dynamics calculations using a polarizable model based on fluctuating dipoles. The scheme developed here employs two sets of induced dipole moments, specifically, those associated with short-range interactions and those associated with a full set of interactions. The scheme is demonstrated on
A Stochastic Algorithm for Generating Realistic Virtual Interstitial Cell of Cajal Networks.
Gao, Jerry; Sathar, Shameer; O'Grady, Gregory; Archer, Rosalind; Cheng, Leo K
2015-08-01
Interstitial cells of Cajal (ICC) play a central role in coordinating normal gastrointestinal (GI) motility. Depletion of ICC numbers and network integrity contributes to major functional GI motility disorders. However, the mechanisms relating ICC structure to GI function and dysfunction remains unclear, partly because there is a lack of large-scale ICC network imaging data across a spectrum of depletion levels to guide models. Experimental imaging of these large-scale networks remains challenging because of technical constraints, and hence, we propose the generation of realistic virtual ICC networks in silico using the single normal equation simulation (SNESIM) algorithm. ICC network imaging data obtained from wild-type (normal) and 5-HT2B serotonin receptor knockout (depleted ICC) mice were used to inform the algorithm, and the virtual networks generated were assessed using ICC network structural metrics and biophysically-based computational modeling. When the virtual networks were compared to the original networks, there was less than 10% error for four out of five structural metrics and all four functional measures. The SNESIM algorithm was then modified to enable the generation of ICC networks across a spectrum of depletion levels, and as a proof-of-concept, virtual networks were successfully generated with a range of structural and functional properties. The SNESIM and modified SNESIM algorithms, therefore, offer an alternative strategy for obtaining the large-scale ICC network imaging data across a spectrum of depletion levels. These models can be applied to accurately inform the physiological consequences of ICC depletion. PMID:25781477
Parrallel Implementation of Fast Randomized Algorithms for Low Rank Matrix Decomposition
Lucas, Andrew J.; Stalizer, Mark; Feo, John T.
2014-03-01
We analyze the parallel performance of randomized interpolative decomposition by de- composing low rank complex-valued Gaussian random matrices larger than 100 GB. We chose a Cray XMT supercomputer as it provides an almost ideal PRAM model permitting quick investigation of parallel algorithms without obfuscation from hardware idiosyncrasies. We obtain that on non-square matrices performance scales almost linearly with runtime about 100 times faster on 128 processors. We also verify that numerically discovered error bounds still hold on matrices two orders of magnitude larger than those previously tested.
NASA Technical Reports Server (NTRS)
Molusis, J. A.
1982-01-01
An on line technique is presented for the identification of rotor blade modal damping and frequency from rotorcraft random response test data. The identification technique is based upon a recursive maximum likelihood (RML) algorithm, which is demonstrated to have excellent convergence characteristics in the presence of random measurement noise and random excitation. The RML technique requires virtually no user interaction, provides accurate confidence bands on the parameter estimates, and can be used for continuous monitoring of modal damping during wind tunnel or flight testing. Results are presented from simulation random response data which quantify the identified parameter convergence behavior for various levels of random excitation. The data length required for acceptable parameter accuracy is shown to depend upon the amplitude of random response and the modal damping level. Random response amplitudes of 1.25 degrees to .05 degrees are investigated. The RML technique is applied to hingeless rotor test data. The inplane lag regressing mode is identified at different rotor speeds. The identification from the test data is compared with the simulation results and with other available estimates of frequency and damping.
Bad News Comes in Threes: Stochastic Structure in Random Events (Invited)
NASA Astrophysics Data System (ADS)
Newman, W. I.; Turcotte, D. L.; Malamud, B. D.
2013-12-01
Plots of random numbers have been known for nearly a century to show repetitive peak-to-peak sequences with an average length of 3. Geophysical examples include events such as earthquakes, geyser eruptions, and magnetic substorms. We consider a classic model in statistical physics, the Langevin equation x[n+1] = α*x[n] + η[n], where x[n] is the nth value of a measured quantity and η[n] is a random number, commonly a Gaussian white noise. Here, α is a parameter that ranges from 0, corresponding to independent random data, to 1, corresponding to Brownian motion which preserves memory of past steps. We show that, for α = 0, the mean peak-to-peak sequence length is 3 while, for α = 1, the mean sequence length is 4. We obtain the physical and mathematical properties of this model, including the distribution of peak-to-peak sequence lengths that can be expected. We compare the theory with observations of earthquake magnitudes emerging from large events, observations of the auroral electrojet index as a measure of global electrojet activity, and time intervals observed between successive eruptions of Old Faithful Geyser in Yellowstone National Park. We demonstrate that the largest earthquake events as described by their magnitudes are consistent with our theory for α = 0, thereby confronting the aphorism (and our analytic theory) that "bad news comes in threes." Electrojet activity, on the other hand, demonstrates some memory effects, consistent with the intuitive picture of the magnetosphere presenting a capacitor-plate like system that preserves memory. Old Faithful Geyser, finally, shows strong antipersistence effects between successive events, i.e. long-time intervals are followed by short ones, and vice versa. As an additional application, we apply our theory to the observed 3-4 year mammalian population cycles.
Enhancing network robustness against targeted and random attacks using a memetic algorithm
NASA Astrophysics Data System (ADS)
Tang, Xianglong; Liu, Jing; Zhou, Mingxing
2015-08-01
In the past decades, there has been much interest in the elasticity of infrastructures to targeted and random attacks. In the recent work by Schneider C. M. et al., Proc. Natl. Acad. Sci. U.S.A., 108 (2011) 3838, the authors proposed an effective measure (namely R, here we label it as R t to represent the measure for targeted attacks) to evaluate network robustness against targeted node attacks. Using a greedy algorithm, they found that the optimal structure is an onion-like one. However, real systems are often under threats of both targeted attacks and random failures. So, enhancing networks robustness against both targeted and random attacks is of great importance. In this paper, we first design a random-robustness index (Rr) . We find that the onion-like networks destroyed the original strong ability of BA networks in resisting random attacks. Moreover, the structure of an R r -optimized network is found to be different from that of an onion-like network. To design robust scale-free networks (RSF) which are resistant to both targeted and random attacks (TRA) without changing the degree distribution, a memetic algorithm (MA) is proposed, labeled as \\textit{MA-RSF}\\textit{TRA} . In the experiments, both synthetic scale-free networks and real-world networks are used to validate the performance of \\textit{MA-RSF}\\textit{TRA} . The results show that \\textit{MA-RSF} \\textit{TRA} has a great ability in searching for the most robust network structure that is resistant to both targeted and random attacks.
IQ-TREE: A Fast and Effective Stochastic Algorithm for Estimating Maximum-Likelihood Phylogenies
Nguyen, Lam-Tung; Schmidt, Heiko A.; von Haeseler, Arndt; Minh, Bui Quang
2015-01-01
Large phylogenomics data sets require fast tree inference methods, especially for maximum-likelihood (ML) phylogenies. Fast programs exist, but due to inherent heuristics to find optimal trees, it is not clear whether the best tree is found. Thus, there is need for additional approaches that employ different search strategies to find ML trees and that are at the same time as fast as currently available ML programs. We show that a combination of hill-climbing approaches and a stochastic perturbation method can be time-efficiently implemented. If we allow the same CPU time as RAxML and PhyML, then our software IQ-TREE found higher likelihoods between 62.2% and 87.1% of the studied alignments, thus efficiently exploring the tree-space. If we use the IQ-TREE stopping rule, RAxML and PhyML are faster in 75.7% and 47.1% of the DNA alignments and 42.2% and 100% of the protein alignments, respectively. However, the range of obtaining higher likelihoods with IQ-TREE improves to 73.3–97.1%. IQ-TREE is freely available at http://www.cibiv.at/software/iqtree. PMID:25371430
González-Recio, O; Jiménez-Montero, J A; Alenda, R
2013-01-01
In the next few years, with the advent of high-density single nucleotide polymorphism (SNP) arrays and genome sequencing, genomic evaluation methods will need to deal with a large number of genetic variants and an increasing sample size. The boosting algorithm is a machine-learning technique that may alleviate the drawbacks of dealing with such large data sets. This algorithm combines different predictors in a sequential manner with some shrinkage on them; each predictor is applied consecutively to the residuals from the committee formed by the previous ones to form a final prediction based on a subset of covariates. Here, a detailed description is provided and examples using a toy data set are included. A modification of the algorithm called "random boosting" was proposed to increase predictive ability and decrease computation time of genome-assisted evaluation in large data sets. Random boosting uses a random selection of markers to add a subsequent weak learner to the predictive model. These modifications were applied to a real data set composed of 1,797 bulls genotyped for 39,714 SNP. Deregressed proofs of 4 yield traits and 1 type trait from January 2009 routine evaluations were used as dependent variables. A 2-fold cross-validation scenario was implemented. Sires born before 2005 were used as a training sample (1,576 and 1,562 for production and type traits, respectively), whereas younger sires were used as a testing sample to evaluate predictive ability of the algorithm on yet-to-be-observed phenotypes. Comparison with the original algorithm was provided. The predictive ability of the algorithm was measured as Pearson correlations between observed and predicted responses. Further, estimated bias was computed as the average difference between observed and predicted phenotypes. The results showed that the modification of the original boosting algorithm could be run in 1% of the time used with the original algorithm and with negligible differences in accuracy
Representation of high frequency Space Shuttle data by ARMA algorithms and random response spectra
NASA Technical Reports Server (NTRS)
Spanos, P. D.; Mushung, L. J.
1990-01-01
High frequency Space Shuttle lift-off data are treated by autoregressive (AR) and autoregressive-moving-average (ARMA) digital algorithms. These algorithms provide useful information on the spectral densities of the data. Further, they yield spectral models which lend themselves to incorporation to the concept of the random response spectrum. This concept yields a reasonably smooth power spectrum for the design of structural and mechanical systems when the available data bank is limited. Due to the non-stationarity of the lift-off event, the pertinent data are split into three slices. Each of the slices is associated with a rather distinguishable phase of the lift-off event, where stationarity can be expected. The presented results are rather preliminary in nature; it is aimed to call attention to the availability of the discussed digital algorithms and to the need to augment the Space Shuttle data bank as more flights are completed.
Browning, Lauren M.; Lee, Kerry J.; Huang, Tao; Nallathamby, Prakash D.; Lowman, Jill E.; Xu, Xiao-Hong Nancy
2010-01-01
We have synthesized and characterized stable (non-aggregation, non-photobleaching and non-blinking), nearly monodisperse and highly-purified Au nanoparticles, and used them to probe transport of cleavage-stage zebrafish embryos and to study their effects on embryonic development in real time. We found that single Au nanoparticles (11.6 ± 0.9 nm in diameter) passively diffused into chorionic space of the embryos via their chorionic-pore-canals and continued their random-walk through chorionic space and into inner mass of embryos. Diffusion coefficients of single nanoparticles vary dramatically (2.8×10-11 to 1.3×10-8 cm2/s) as nanoparticles diffuse through various parts of embryos, suggesting highly diverse transport barriers and viscosity gradients of embryos. The amount of Au nanoparticles accumulated in embryos increase with its concentration. Interestingly, their effects on embryonic development are not proportionally related to the concentration. Majority of embryos (74% on average) incubated chronically with 0.025-1.2 nM Au nanoparticles for 120 h developed to normal zebrafish, with some (24%) being dead and few (2%) deformed. We developed a new approach to image and characterize individual Au nanoparticles embedded in tissues using histology sample preparation methods and LSRP spectra of single nanoparticles. We found that Au nanoparticles in various parts of normally developed and deformed zebrafish, suggesting that random-walk of nanoparticles in embryos during their development might have led to stochastic effects on embryonic development. These results show that Au nanoparticles are much more biocompatible (less toxic) to the embryos than Ag nanoparticles that we reported previously, suggesting that they are better suited as biocompatible probes for imaging embryos in vivo. The results provide powerful evidences that biocompatibility and toxicity of nanoparticles highly depend on their chemical properties, and the embryos can serve as effective in
Gholami-Boroujeny, Shiva; Bolic, Miodrag
2016-04-01
Fitting the measured bioimpedance spectroscopy (BIS) data to the Cole model and then extracting the Cole parameters is a common practice in BIS applications. The extracted Cole parameters then can be analysed as descriptors of tissue electrical properties. To have a better evaluation of physiological or pathological properties of biological tissue, accurate extraction of Cole parameters is of great importance. This paper proposes an improved Cole parameter extraction based on bacterial foraging optimization (BFO) algorithm. We employed simulated datasets to test the performance of the BFO fitting method regarding parameter extraction accuracy and noise sensitivity, and we compared the results with those of a least squares (LS) fitting method. The BFO method showed better robustness to the noise and higher accuracy in terms of extracted parameters. In addition, we applied our method to experimental data where bioimpedance measurements were obtained from forearm in three different positions of the arm. The goal of the experiment was to explore how robust Cole parameters are in classifying position of the arm for different people, and measured at different times. The extracted Cole parameters obtained by LS and BFO methods were applied to different classifiers. Two other evolutionary algorithms, GA and PSO were also used for comparison purpose. We showed that when the classifiers are fed with the extracted feature sets by BFO fitting method, higher accuracy is obtained both when applying on training data and test data. PMID:26215520
Enhanced cancer recognition system based on random forests feature elimination algorithm.
Ozcift, Akin
2012-08-01
Accurate classifiers are vital to design precise computer aided diagnosis (CADx) systems. Classification performances of machine learning algorithms are sensitive to the characteristics of data. In this aspect, determining the relevant and discriminative features is a key step to improve performance of CADx. There are various feature extraction methods in the literature. However, there is no universal variable selection algorithm that performs well in every data analysis scheme. Random Forests (RF), an ensemble of trees, is used in classification studies successfully. The success of RF algorithm makes it eligible to be used as kernel of a wrapper feature subset evaluator. We used best first search RF wrapper algorithm to select optimal features of four medical datasets: colon cancer, leukemia cancer, breast cancer and lung cancer. We compared accuracies of 15 widely used classifiers trained with all features versus to extracted features of each dataset. The experimental results demonstrated the efficiency of proposed feature extraction strategy with the increase in most of the classification accuracies of the algorithms. PMID:21567124
Jaeger, Sébastien; Fernandez, Bastien; Ferrier, Pierre
2013-06-01
To perform their specific functional role, B and T lymphocytes, cells of the adaptive immune system of jawed vertebrates, need to express one (and, preferably, only one) form of antigen receptor, i.e. the immunoglobulin or T-cell receptor (TCR), respectively. This end goal depends initially on a series of DNA cis-rearrangement events between randomly chosen units from separate clusters of V, D (at some immunoglobulin and TCR loci) and J gene segments, a biomolecular process collectively referred to as V(D)J recombination. V(D)J recombination takes place in immature T and B cells and relies on the so-called RAG nuclease, a site-specific DNA cleavage apparatus that corresponds to the lymphoid-specific moiety of the VDJ recombinase. At the genome level, this recombinase's mission presents substantial biochemical challenges. These relate to the huge distance between (some of) the gene segments that it eventually rearranges and the need to achieve cell-lineage-restricted and developmentally ordered routines with at times, mono-allelic versus bi-allelic discrimination. The entire process must be completed without any recombination errors, instigators of chromosome instability, translocation and, potentially, tumorigenesis. As expected, such a precisely choreographed and yet potentially risky process demands sophisticated controls; epigenetics demonstrates what is possible when calling upon its many facets. In this vignette, we will recall the evidence that almost from the start appeared to link the two topics, V(D)J recombination and epigenetics, before reviewing the latest advances in our knowledge of this joint venture. PMID:23278765
NASA Astrophysics Data System (ADS)
Rebora, N.; Silvestro, F.; Rudari, R.; Herold, C.; Ferraris, L.
2016-06-01
Downscaling methods are used to derive stream flow at a high temporal resolution from a data series that has a coarser time resolution. These algorithms are useful for many applications, such as water management and statistical analysis, because in many cases stream flow time series are available with coarse temporal steps (monthly), especially when considering historical data; however, in many cases, data that have a finer temporal resolution are needed (daily). In this study, we considered a simple but efficient stochastic auto-regressive model that is able to downscale the available stream flow data from monthly to daily time resolution and applied it to a large dataset that covered the entire North and Central American continent. Basins with different drainage areas and different hydro-climatic characteristics were considered, and the results show the general good ability of the analysed model to downscale monthly stream flows to daily stream flows, especially regarding the reproduction of the annual maxima. If the performance in terms of the reproduction of hydrographs and duration curves is considered, better results are obtained for those cases in which the hydrologic regime is such that the annual maxima stream flow show low or medium variability, which means that they have a low or medium coefficient of variation; however, when the variability increases, the performance of the model decreases.
NASA Astrophysics Data System (ADS)
Huang, Wen-Cheng; Yuan, Lun-Chin; Lee, Chi-Ming
2002-12-01
The objective of this paper is to present a genetic algorithm-based stochastic dynamic programming (GA-based SDP) to cope with the dimensionality problem of a multiple-reservoir system. The joint long-term operation of a parallel reservoir system in the Feitsui and Shihmen reservoirs in northern Taiwan demonstrates the successful application of the proposed GA-based SDP model. Within the case study system it is believed that GA is a useful technique in supporting optimization. Though the employment of GA-based SDP may be time consuming as it proceeds through generation by generation, the model can overcome the "dimensionality curse" in searching solutions. Simulation results show Feitsui's surplus water can be utilized efficiently to fill Shihmen's deficit water without affecting Feitsui's main purpose as Taipei city's water supply. The optimal joint operation suggests that Feitsui, on average, can provide 650,000 m3/day and 920,000 m3/day to Shihmen during the wet season and dry season, respectively.
NASA Astrophysics Data System (ADS)
Sun, Xu; Yang, Lina; Gao, Lianru; Zhang, Bing; Li, Shanshan; Li, Jun
2015-01-01
Center-oriented hyperspectral image clustering methods have been widely applied to hyperspectral remote sensing image processing; however, the drawbacks are obvious, including the over-simplicity of computing models and underutilized spatial information. In recent years, some studies have been conducted trying to improve this situation. We introduce the artificial bee colony (ABC) and Markov random field (MRF) algorithms to propose an ABC-MRF-cluster model to solve the problems mentioned above. In this model, a typical ABC algorithm framework is adopted in which cluster centers and iteration conditional model algorithm's results are considered as feasible solutions and objective functions separately, and MRF is modified to be capable of dealing with the clustering problem. Finally, four datasets and two indices are used to show that the application of ABC-cluster and ABC-MRF-cluster methods could help to obtain better image accuracy than conventional methods. Specifically, the ABC-cluster method is superior when used for a higher power of spectral discrimination, whereas the ABC-MRF-cluster method can provide better results when used for an adjusted random index. In experiments on simulated images with different signal-to-noise ratios, ABC-cluster and ABC-MRF-cluster showed good stability.
Personalized PageRank Clustering: A graph clustering algorithm based on random walks
NASA Astrophysics Data System (ADS)
A. Tabrizi, Shayan; Shakery, Azadeh; Asadpour, Masoud; Abbasi, Maziar; Tavallaie, Mohammad Ali
2013-11-01
Graph clustering has been an essential part in many methods and thus its accuracy has a significant effect on many applications. In addition, exponential growth of real-world graphs such as social networks, biological networks and electrical circuits demands clustering algorithms with nearly-linear time and space complexity. In this paper we propose Personalized PageRank Clustering (PPC) that employs the inherent cluster exploratory property of random walks to reveal the clusters of a given graph. We combine random walks and modularity to precisely and efficiently reveal the clusters of a graph. PPC is a top-down algorithm so it can reveal inherent clusters of a graph more accurately than other nearly-linear approaches that are mainly bottom-up. It also gives a hierarchy of clusters that is useful in many applications. PPC has a linear time and space complexity and has been superior to most of the available clustering algorithms on many datasets. Furthermore, its top-down approach makes it a flexible solution for clustering problems with different requirements.
Fuzzy stochastic elements method. Spectral approach
NASA Astrophysics Data System (ADS)
Sniady, Pawel; Mazur-Sniady, Krystyna; Sieniawska, Roza; Zukowski, Stanislaw
2013-05-01
We study a complex dynamic problem, which concerns a structure with uncertain parameters subjected to a stochastic excitation. Formulation of such a problem introduces fuzzy random variables for parameters of the structure and fuzzy stochastic processes for the load process. The uncertainty has two sources, namely the randomness of structural parameters such as geometry characteristics, material and damping properties, load process and imprecision of the theoretical model and incomplete information or uncertain data. All of these have a great influence on the response of the structure. By analyzing such problems we describe the random variability using the probability theory and the imprecision by use of fuzzy sets. Due to the fact that it is difficult to find an analytic expression for the inversion of the stochastic operator in the stochastic differential equation, a number of approximate methods have been proposed in the literature which can be connected to the finite element method. To evaluate the effects of excitation in the frequency domain we use the spectral density function. The spectral analysis is widely used in stochastic dynamics field of linear systems for stationary random excitation. The concept of the evolutionary spectral density is used in the case of non-stationary random excitation. We solve the considered problem using fuzzy stochastic finite element method. The solution is based on the idea of a fuzzy random frequency response vector for stationary input excitation and a transient fuzzy random frequency response vector for the fuzzy non-stationary one. We use the fuzzy random frequency response vector and the transient fuzzy random frequency response vector in the context of spectral analysis in order to determine the influence of structural uncertainty on the fuzzy random response of the structure. We study a linear system with random parameters subjected to two particular cases of stochastic excitation in a frequency domain. The first one
Analysis of (1+1) evolutionary algorithm and randomized local search with memory.
Sung, Chi Wan; Yuen, Shiu Yin
2011-01-01
This paper considers the scenario of the (1+1) evolutionary algorithm (EA) and randomized local search (RLS) with memory. Previously explored solutions are stored in memory until an improvement in fitness is obtained; then the stored information is discarded. This results in two new algorithms: (1+1) EA-m (with a raw list and hash table option) and RLS-m+ (and RLS-m if the function is a priori known to be unimodal). These two algorithms can be regarded as very simple forms of tabu search. Rigorous theoretical analysis of the expected time to find the globally optimal solutions for these algorithms is conducted for both unimodal and multimodal functions. A unified mathematical framework, involving the new concept of spatially invariant neighborhood, is proposed. Under this framework, both (1+1) EA with standard uniform mutation and RLS can be considered as particular instances and in the most general cases, all functions can be considered to be unimodal. Under this framework, it is found that for unimodal functions, the improvement by memory assistance is always positive but at most by one half. For multimodal functions, the improvement is significant; for functions with gaps and another hard function, the order of growth is reduced; for at least one example function, the order can change from exponential to polynomial. Empirical results, with a reasonable fitness evaluation time assumption, verify that (1+1) EA-m and RLS-m+ are superior to their conventional counterparts. Both new algorithms are promising for use in a memetic algorithm. In particular, RLS-m+ makes the previously impractical RLS practical, and surprisingly, does not require any extra memory in actual implementation. PMID:20868262
Early Seizure Detection Algorithm Based on Intracranial EEG and Random Forest Classification.
Donos, Cristian; Dümpelmann, Matthias; Schulze-Bonhage, Andreas
2015-08-01
The goal of this study is to provide a seizure detection algorithm that is relatively simple to implement on a microcontroller, so it can be used for an implantable closed loop stimulation device. We propose a set of 11 simple time domain and power bands features, computed from one intracranial EEG contact located in the seizure onset zone. The classification of the features is performed using a random forest classifier. Depending on the training datasets and the optimization preferences, the performance of the algorithm were: 93.84% mean sensitivity (100% median sensitivity), 3.03 s mean (1.75 s median) detection delays and 0.33/h mean (0.07/h median) false detections per hour. PMID:26022388
Random Search Algorithm for Solving the Nonlinear Fredholm Integral Equations of the Second Kind
Hong, Zhimin; Yan, Zaizai; Yan, Jiao
2014-01-01
In this paper, a randomized numerical approach is used to obtain approximate solutions for a class of nonlinear Fredholm integral equations of the second kind. The proposed approach contains two steps: at first, we define a discretized form of the integral equation by quadrature formula methods and solution of this discretized form converges to the exact solution of the integral equation by considering some conditions on the kernel of the integral equation. And then we convert the problem to an optimal control problem by introducing an artificial control function. Following that, in the next step, solution of the discretized form is approximated by a kind of Monte Carlo (MC) random search algorithm. Finally, some examples are given to show the efficiency of the proposed approach. PMID:25072373