A Parallel Algorithm for Efficient Solution of Stochastic Collection Equation

The sine cosine algorithm’s main idea is the sine and cosine-based vacillation outwards or towards the best solution. The first main contribution of this paper proposes an enhanced version of the SCA algorithm called as ESCA algorithm. The supremacy of the proposed algorithm over a set of state-of-the-art algorithms in terms of solution accuracy and convergence speed will be demonstrated by experimental tests. When these algorithms are transferred to the business sector, they must meet time requirements dependent on the industrial process. If these temporal requirements are not met, an efficient solution is to speed them up by designing parallel algorithms. The second major contribution of this work is the design of several parallel algorithms for efficiently exploiting current multicore processor architectures. First, one-level synchronous and asynchronous parallel ESCA algorithms are designed. They have two favors; retain the proposed algorithm’s behavior and provide excellent parallel performance by combining coarse-grained parallelism with fine-grained parallelism. Moreover, the parallel scalability of the proposed algorithms is further improved by employing a two-level parallel strategy. Indeed, the experimental results suggest that the one-level parallel ESCA algorithms reduce the computing time, on average, by 87.4% and 90.8%, respectively, using 12 physical processing cores. The two-level parallel algorithms provide extra reductions of the computing time by 91.4%, 93.1%, and 94.5% with 16, 20, and 24 processing cores, including physical and logical cores. Comparison analysis is carried out on 30 unconstrained benchmark functions and three challenging engineering design problems. The experimental outcomes show that the proposed ESCA algorithm behaves outstandingly well in terms of exploration and exploitation behaviors, local optima avoidance, and convergence speed toward the optimum. The overall performance of the proposed algorithm is statistically validated using three non-parametric statistical tests, namely Friedman, Friedman aligned, and Quade tests.

To improve the modeling of warm rain initiation, a two-moment bulk parameterization of the drop collection growth in warm clouds is developed by two steps: (i) its prototype is first derived based on the analytic solution of the stochastic collection equation (SCE) with the Golovin kernel, and (ii) the prototype is then revamped empirically to fit the numerical solution of SCE with the real hydrodynamic collection kernel, reaching the final version of the parameterization. Since the final version represents the self-collection of cloud drops explicitly, it replicates warm rain initiation well even when liquid water content (cloud-drop number concentration) is very low (high). It also replicates the autoconversion threshold and time delay of rain initiation via a small autoconversion rate.

In this paper we present a new result on an analytical study of stochastic logistic equations of Richards-type for population growth. First, we introduce the Richards equation as a generalization of the classical Verhulst equation which allows a flexibility in the sigmoid shape of the solution curve. Next, the stochastic equation is formed by adding a multiplicative white noise in the corresponding deterministic Richards equation. Our goal is to solve the stochastic Richards equation and investigate some of the qualitative properties of the solution. As a main result, an exact expression for the solution of the stochastic Richards equation is obtained by using tools from the Itô calculus. Some qualitative aspects of the solution, such as long time behavior and noise-induced transition, will be also discussed within the framework of diffusion processes theory. We also give a simulation of the solution of the stochastic Richards equation to illustrate the role of the so-called allometric parameter.

Previous article Next article A Simple Proof of the Existence of a Solution of Itô’s Equation with Monotone CoefficientsN. V. KrylovN. V. Krylovhttps://doi.org/10.1137/1135082PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] N. V. Krylov and , B. L. Rozovskii, Stochastic evolution equationsCurrent problems in mathematics, Vol. 14 (Russian), Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 1979, 71–147, 256 81m:60116 Google Scholar[2] I. Gyongy and , N. V. Krylov, On stochastic equations with respect to semimartingales. I, Stochastics, 4 (1980/81), 1–21 82j:60104 CrossrefGoogle Scholar[3] N. V. Krylov, Extremal properties of solutions of stochastic equations, Theory Probab. Appl., 29 (1984), 205–217 10.1137/1129033 0557.60042 LinkGoogle Scholar[4] L. A. Alyushina, Euler polygonal lines for Itô equations with monotone coefficients, Theory Probab. Appl., 32 (1987), 340–346 10.1137/1132046 0663.60049 LinkGoogle Scholar[5] Gisirō Maruyama, Continuous Markov processes and stochastic equations, Rend. Circ. Mat. Palermo (2), 4 (1955), 48–90 17,166f 0053.40901 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A splitting method for SDEs with locally Lipschitz drift: Illustration on the FitzHugh-Nagumo modelApplied Numerical Mathematics | 1 Apr 2022 Cross Ref Approximation of BSDEs with super-linearly growing generators by Euler’s polygonal line method: A simple proof of the existenceSystems & Control Letters, Vol. 153 | 1 Jul 2021 Cross Ref Fractional Stochastic Active Scalar Equations Generalizing the Multi-Dimensional Quasi-Geostrophic & 2D-Navier–Stokes Equations: The General CaseJournal of Mathematical Fluid Mechanics, Vol. 22, No. 4 | 4 September 2020 Cross Ref A note on strong convergence of implicit scheme for SDEs under local one-sided Lipschitz conditionsInternational Journal of Computer Mathematics, Vol. 5 | 9 March 2020 Cross Ref Strong Convergence Rates for Euler Approximations to a Class of Stochastic Path-Dependent Volatility ModelsAndrei Cozma and Christoph ReisingerSIAM Journal on Numerical Analysis, Vol. 56, No. 6 | 11 December 2018AbstractPDF (1095 KB)Well-Posedness of the Multidimensional Fractional Stochastic Navier–Stokes Equations on the Torus and on Bounded DomainsJournal of Mathematical Fluid Mechanics, Vol. 18, No. 1 | 22 October 2015 Cross Ref An Explicit Euler Scheme with Strong Rate of Convergence for Financial SDEs with Non-Lipschitz CoefficientsJean-François Chassagneux, Antoine Jacquier, and Ivo MihaylovSIAM Journal on Financial Mathematics, Vol. 7, No. 1 | 14 December 2016AbstractPDF (602 KB)A New Type of Stability Theorem for Stochastic Systems With Application to Stochastic StabilizationIEEE Transactions on Automatic Control, Vol. 61, No. 1 | 1 Jan 2016 Cross Ref Loss of regularity for Kolmogorov equationsThe Annals of Probability, Vol. 43, No. 2 | 1 Mar 2015 Cross Ref Strong Convergence of Euler Approximations of Stochastic Differential Equations with Delay Under Local Lipschitz ConditionStochastic Analysis and Applications, Vol. 32, No. 2 | 28 February 2014 Cross Ref A Note on Euler Approximations for Stochastic Differential Equations with DelayApplied Mathematics & Optimization, Vol. 68, No. 3 | 24 August 2013 Cross Ref Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equationsThe Annals of Applied Probability, Vol. 23, No. 5 | 1 Oct 2013 Cross Ref Rate of convergence of Euler’s approximations for SDEs with non-Lipschitz coefficientsActa Mathematica Sinica, English Series, Vol. 29, No. 8 | 15 July 2013 Cross Ref Stochastic Itô inclusion with upper separated multifunctionsJournal of Mathematical Analysis and Applications, Vol. 400, No. 2 | 1 Apr 2013 Cross Ref Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficientsThe Annals of Applied Probability, Vol. 22, No. 4 | 1 Aug 2012 Cross Ref Stochastic 3D tamed Navier–Stokes equations: Existence, uniqueness and small time large deviation principlesJournal of Differential Equations, Vol. 252, No. 1 | 1 Jan 2012 Cross Ref On the Strong Solution for the 3D Stochastic Leray-Alpha ModelBoundary Value Problems, Vol. 2010, No. 1 | 1 Jan 2010 Cross Ref ON STOCHASTIC EVOLUTION EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTSStochastics and Dynamics, Vol. 09, No. 04 | 21 November 2011 Cross Ref Stochastic tamed 3D Navier–Stokes equations: existence, uniqueness and ergodicityProbability Theory and Related Fields, Vol. 145, No. 1-2 | 19 July 2008 Cross Ref Large deviations in the Langevin dynamics of a random field Ising modelStochastic Processes and their Applications, Vol. 105, No. 2 | 1 Jun 2003 Cross Ref Viable solutions of set-valued stochastic equationOptimization, Vol. 48, No. 2 | 1 Jan 2000 Cross Ref Volume 35, Issue 3| 1991Theory of Probability & Its Applications411-623 History Submitted:05 September 1988Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1135082Article page range:pp. 583-587ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Recurrence solution of a block tridiagonal matrix equation with Neumann, Dirichlet, mixed or periodic boundary conditions

A new method to retrieve aerosol optical thickness from satellite images on a parallel system

Biomedical Engineering, usually known as Bioengineering, is among the fastest developing and one of most important interdisciplinary fields today. It connects natural and technical sciences, for all of which biological and medical phenomena, computation, and data management play important roles in science and industry. Distributed computing and parallel algorithms have proved to be effective in solving the problem with high computational complexity in a wide range of domains, including areas of computational bioengineering. This special edition collects high-quality research papers in the field of application of distributed computing systems in bioengineering applications. This issue is the achievement of the developments of modern computer and biomedical technology. Most bioengineering or bioinformatics methods need to access and analyses large amounts of data. For that it is necessary to achieve an effective way that from Big data creates knowledge and useful applications. The nature of such scientific data/information/knowledge demands the use of a powerful computing and intelligent database management systems. Areas of current and future research include advanced topics in this special issue. The paper from Juhasz et al. present a novel, GPU-based streaming architecture that has the potential for drastically reducing execution times and at the same time providing simultaneous 2D and 3D visualization facilities. The system uses a highly-optimised and re-configurable pipeline of CPU and GPU cores that attempts to exploit the tremendous computing power whenever possible. The system can process live data arriving from an EEG device or data stored in EEG data files. The computer drives a large display wall system of four 46 monitors that provides a 4K-resolution drawing surface for visualizing raw EEG data, potential maps and various 3D views of the patient's head. Authors from the group of M. Gusev presents the scalable balancer in Cloud computing extended to Dew Computing level. Given a successful implementation of scalable low level load balancer, implemented on the network layer. The scalability is proved with series of experiments. The experiments showed that it adds small latency of several milliseconds and thus it slightly reduces the performance when the distributed system is underutilized. Rybicki et al. demonstrate how to realize a Software-as-a-Service solution for a variety of science software using container technologies. The presented solution utilized DARIAH-DE research infrastructure based on OpenStack and UNICORE grid to deliver an extensible solution for the digital humanities domain. The paper from authors Forer et al. describe the extension of Cloudflow to support ApacheSpark without any adaptions to already implemented pipelines. The described performance evaluation demonstrates that Spark can bring an additional boost for analyzing next generation sequencing(NGS) data to the eld of genetics. The Cloudflow framework is open source and freely available at https://github.com/genepi/cloudflow . The paper by Memon et al. describes an approach for executing computational jobs across HPC and HTC resources while operating on geographically dispersed data via a global federated file system. The solution is realized as a new framework that integrates UNICORE and GFFS to provide a standards-based environment to support large scale data intensive computations frequent in today's biomedical analyses. The paper Parallel algorithm for the state space exploration, authored by L. Allal et al., proposes a new automatic verification technique based on model checking that determines whether a given system satisfies its specification. Such a technique suffers from the state explosion problem when traversing all possible states of systems. A new synchronized parallel algorithm (SPA) of exploration is proposed based on a fixed number of threads. Exhaustive comparative studies between the standard parallel exploration algorithm in SPIN and the new SPA show that the SPA performs slightly better regarding the execution time and memory complexity. Smart systems in telemedicine frequently use intelligent sensor devices at large scale. Practitioners can monitor non-stop the vital parameters of hundreds of patients in real-time. The most important pillars of remote patient monitoring services are communication and data processing. Large scale data processing is done mainly using workflows. In the paper Eszter et al. give a brief overview of the different check pointing techniques and propose two new provenance based check pointing algorithms which uses the information stored in the workflow structure to dynamically change the frequency of check pointing and can be efficiently used for dynamic health care smart systems.

In this paper we study the parallel solution of the discrete-time Lyapunov equation. Two parallel fine and medium grain algorithms for solving dense and large order equations [Formula: see text] on a shared memory multiprocessor are presented. They are based on Hammarling’s method and directly obtain the Cholesky factor of the solution. The parallel algorithms work following an antidiagonal wavefront. In order to improve the performance, column-block-oriented and wrap-around algorithms are used. Finally, combined fine and medium grain parallel algorithms are presented.

Existence, stability and bifurcation of random complete and periodic solutions of stochastic parabolic equations

A digital electromagnetic model of electric power system is suggested. The parallel and the sequential algorithms to solve the equation set are described. Implementation of the parallel algorithm on k processors provides more then k times speedup.

The paper proposes a mathematical model aimed at calculating the effective elastic moduli of a micro-inhomogeneous two-component isotropic composite material, which components are connected randomly depending on the level of their relative volumetric contents. A stochastic equation is formulated for the connectivity parameter of the constituent components, according to which, with an increase in the volumetric content of the filler, individual inclusions build the structures of the matrix mixture in the form of interpenetrating frameworks, and then turn into a new binding matrix with individual inclusions from the material of the rest of the old matrix. The algorithm for the numerical solution of this stochastic differential equation is constructed in accordance with the Euler-Maruyama method. For each implementation of this algorithm, the corresponding stochastic trajectories are constructed for the random connectivity function of the constituent components of the composite material. A variant of the method aimed at calculating the mathematical expectation of a random connectivity function of the constituent components has been developed and the corresponding differential equation has been obtained for it. It is shown that the numerical solution of this equation and the average value of the production factor function calculated for all realizations of stochastic trajectories give close numerical values. New macroscopic constitutive relations are found for microinhomogeneous materials with a variable microstructure and their effective elastic moduli are calculated. It is noted that the formulas for these effective elastic moduli generalize the known results for isotropic composite materials. The values of the effective elastic moduli, constructed according to the expressions obtained in the paper, lie within the Khashin-Shtrikman range for the lower and upper bounds of the effective elastic moduli of the composite materials. The numerical analysis of the developed models showed a good agreement with the known experimental data.

Fractional Brownian Motions, Fractional Noises and Applications

The speedup of element-by-element FEM algorithms depends not only on peak processor performance but also on access time to shared mesh data. Eliminating memory boundness would significantly speed up unstructured mesh computations on hybrid multi-core architectures, where the gap between processor and memory performance continues to grow. The speedup can be achieved by ordering unknowns so that only those elements are processed in parallel which do not have common nodes. Therefore, memory conflicts are minimized. FEM assembly is performed with respect to the ordering, which defines how to compose vectors. Mesh can be partitioned into disjoint subdomains by using different layer-by-layer schemes. In this work, we evaluated several partitioning schemes (block, odd, even, and their modifications) on multi-core platforms, using Gunther's Universal Law of Computational Scalability. We performed numerical experiments with element-by-element matrix-vector multiplication on unstructured meshes on multi-core processors accelerated by MIC and GPU. With ordering, we achieved 5-times speedup on CPU, 40-times speedup on MIC, and 200- times speedup on GPU.

We propose a parallel decoding algorithm based on error checking and correcting to improve the performance of the short polar codes. In order to enhance the error-correcting capacity of the decoding algorithm, we first derive the error-checking equations generated on the basis of the frozen nodes, and then we introduce the method to check the errors in the input nodes of the decoder by the solutions of these equations. In order to further correct those checked errors, we adopt the method of modifying the probability messages of the error nodes with constant values according to the maximization principle. Due to the existence of multiple solutions of the error-checking equations, we formulate a CRC-aided optimization problem of finding the optimal solution with three different target functions, so as to improve the accuracy of error checking. Besides, in order to increase the throughput of decoding, we use a parallel method based on the decoding tree to calculate probability messages of all the nodes in the decoder. Numerical results show that the proposed decoding algorithm achieves better performance than that of some existing decoding algorithms with the same code length.

We shall give a fairly selfcontained account of some results on waves in random media and related problems that we have considered in the past few years [l]–[6]. These results rcly upon properties of solutions of differential equations with random coefficients, i.e., stochastic equations. We restrict attention to one-dimensional problems so that we are dealing with stochastic ordinary differential equations. There are a few results, at present, dealing with multidimensional problems at [cf. 12} but we shall not discuss these here.