118,027 research outputs found
Parallel implementation of stochastic simulation for large-scale cellular processes
No full textExperimental and theoretical studies have shown the importance of stochastic processes in genetic regulatory networks and cellular processes. Cellular networks and genetic circuits often involve small numbers of key proteins such as transcriptional factors and signaling proteins. In recent years stochastic models have been used successfully for studying noise in biological pathways, and stochastic modelling of biological systems has become a very important research field in computational biology. One of the challenge problems in this field is the reduction of the huge computing time in stochastic simulations. Based on the system of the mitogen-activated protein kinase cascade that is activated by epidermal growth factor, this work give a parallel implementation by using OpenMP and parallelism across the simulation. Special attention is paid to the independence of the generated random numbers in parallel computing, that is a key criterion for the success of stochastic simulations. Numerical results indicate that parallel computers can be used as an efficient tool for simulating the dynamics of large-scale genetic regulatory networks and cellular processes
Adams-type methods for the numerical solution of stochastic ordinary differential equations
No full textThe modelling of many real life phenomena for which either the parameter estimation is difficult, or which are subject to random noisy perturbations, is often carried out by using stochastic ordinary differential equations (SODEs). For this reason, in recent years much attention has been devoted to deriving numerical methods for approximating their solution. In particular, in this paper we consider the use of linear multistep formulae (LMF). Strong order convergence conditions up to order 1 are stated, for both commutative and non-commutative problems. The case of additive noise is further investigated, in order to obtain order improvements. The implementation of the methods is also considered, leading to a predictor-corrector approach. Some numerical tests on problems taken from the literature are also included
A Spectrally Accurate Step-by-Step Method for the Numerical Solution of Fractional Differential Equations
No full textIn this paper we consider the numerical solution of fractional differential equations. In particular, we study a step-by-step procedure, defined over a graded mesh, which is based on a truncated expansion of the vector field along the orthonormal Jacobi polynomial basis. Under mild hypotheses, the proposed procedure is capable of getting spectral accuracy. A few numerical examples are reported to confirm the theoretical findings
A spectral method for time-fractional diffusion systems
No full textThe time fractional derivative of a function y(t) depends on the past history of the function
y(t), and so time fractional differential systems are naturally suitable to describe evolutionary processes with memory. Fractional models are increasingly used in many modelling situations including, for example, viscoelastic materials in mechanics, anomalous diffusion in transport dynamics of complex systems and some biological processes in rheology. Here we consider a time-fractional reaction diusion problem [2]. This is a non-local model and as the solution depends on all its past history, numerical step-by-step methods are computationally expensive. We propose a mixed method, which consists of a finite difference scheme through space and a spectral collocation method through time. The spectral method considerably reduces the computational cost with respect to step-by-step methods and is exponentially convergent [3]. Some classes of spectral bases are considered, which exhibit different convergence rates and some numerical results based on time diffusion reaction diffusion equations are given [1].
References
[1] Burrage, K., Cardone, A., D'Ambrosio, R. and Paternoster, B. 2017 Numerical solution of time fractional diffusion systems. Appl. Numer. Math. 116 8294.
[2] Gafiychuk, V., Datsko, B. and Meleshko, V. 2008 Mathematical modeling of time fractional reaction-diffusion systems. J. Comput. Appl. Math. 220(1-2) 215225.
[3] Zayernouri, M. and Karniadakis, G. Em 2014 Fractional spectral collocation method. SIAM J. Sci. Comput. 36(1) A40A62
Effective simulation techniques for biological systems
No full textIn this paper we give an overview of some very recent work on the stochastic simulation of systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge-Kutta methods and the Balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and discuss how novel computing implementations can enhance the performance of these simulations
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Square Dancing with the Stars to Enhance Dynamic Hirschman Linkages?
No full textIn this Presidential Address, the author takes the reader on a reconnaissance of his life and time as a regional scientist. He points out scenery he found scintillating along the way, hoping that some may pick up the banner and chew on a few of the ideas for a while. He suggests a revisit to Albert O. Hirschman’s notion of key sectors and more empirical analysis related to Marcus Berliant’s and Masahisa Fujita’s notion of knowledge creation and transfer.Presidential Address, San Antonio, Texas, March 29, 2014 (53rd Meetings of the Southern Regional Science Association
Appropriate Similarity Measures for Author Cocitation Analysis
No full textWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
A multi-scaled approach for simulating chemical reaction systems
No full textIn this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge–Kutta methods and the balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and present a new approach which couples the three regimes mentioned above. We then apply this approach to a biologically inspired problem involving the expression and activity of LacZ and LacY proteins in E. coli, and conclude with a discussion on the significance of this work
- …
