A multi-scaled approach for simulating chemical reaction systems

In 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.

Evolving noisy oscillatory dynamics in genetic regulatory networks

We introduce a genetic programming (GP) approach for evolving genetic networks that demonstrate desired dynamics when simulated as a discrete stochastic process. Our representation of genetic networks is based on a biochemical reaction model including key elements such as transcription, translation and post-translational modifications. The stochastic, reaction-based GP system is similar but not identical with algorithmic chemistries. We evolved genetic networks with noisy oscillatory dynamics. The results show the practicality of evolving particular dynamics in gene regulatory networks when modelled with intrinsic noise.

GIS linked environmental process models

In recent years there has been a great effort to combine the technologies and techniques of GIS and process models. This project examines the issues of linking a standard current generation 2½d GIS with several existing model codes. The focus for the project has been the Shropshire Groundwater Scheme, which is being developed to augment flow in the River Severn during drought periods by pumping water from the Shropshire Aquifer. Previous authors have demonstrated that under certain circumstances pumping could reduce the soil moisture available for crops. This project follows earlier work at Aston in which the effects of drawdown were delineated and quantified through the development of a software package that implemented a technique which brought together the significant spatially varying parameters. This technique is repeated here, but using a standard GIS called GRASS. The GIS proved adequate for the task and the added functionality provided by the general purpose GIS - the data capture, manipulation and visualisation facilities - were of great benefit. The bulk of the project is concerned with examining the issues of the linkage of GIS and environmental process models. To this end a groundwater model (Modflow) and a soil moisture model (SWMS2D) were linked to the GIS and a crop model was implemented within the GIS. A loose-linked approach was adopted and secondary and surrogate data were used wherever possible. The implications of which relate to; justification of a loose-linked versus a closely integrated approach; how, technically, to achieve the linkage; how to reconcile the different data models used by the GIS and the process models; control of the movement of data between models of environmental subsystems, to model the total system; the advantages and disadvantages of using a current generation GIS as a medium for linking environmental process models; generation of input data, including the use of geostatistic, stochastic simulation, remote sensing, regression equations and mapped data; issues of accuracy, uncertainty and simply providing adequate data for the complex models; how such a modelling system fits into an organisational framework.

Evaluation and development of drainage and pipeline construction processes

In 1974 Dr D M Bramwell published his research work at the University of Aston a part of which was the establishment of an elemental work study data base covering drainage construction. The Transport and Road Research Laboratory decided to, extend that work as part of their continuing research programme into the design and construction of buried pipelines by placing a research contract with Bryant Construction. This research may be considered under two broad categories. In the first, site studies were undertaken to validate and extend the data base. The studies showed good agreement with the existing data with the exception of the excavation trench shoring and pipelaying data which was amended to incorporate new construction plant and methods. An inter-active on-line computer system for drainage estimating was developed. This system stores the elemental data, synthesizes the standard time of each drainage operation and is used to determine the required resources and construction method of the total drainage activity. The remainder of the research was into the general topic of construction efficiency. An on-line command driven computer system was produced. This system uses a stochastic simulation technique, based on distributions of site efficiency measurements to evaluate the effects of varying performance levels. The analysis of this performance data quantities the variability inherent in construction and demonstrates how some of this variability can be reconciled by considering the characteristics of a contract. A long term trend of decreasing efficiency with contract duration was also identified. The results obtained from the simulation suite were compared to site records collected from current contracts. This showed that this approach will give comparable answers, but these are greatly affected by the site performance parameters.

Spatial and temporal patterns of true bug assemblages extracted with Berlese funnels (Data to the knowledge on the ground-living Heteroptera of Hungary, No. 2)

A rich material of Heteroptera extracted with Berlese funnels by Dr. I. Loksa between 1953–1974 in Hungary, has been examined. Altogether 157 true bug species have been identified. The ground-living heteropteran assemblages collected in different plant communities, substrata, phytogeographical provinces and seasons have been compared with multivariate methods. Because of the unequal number of samples, the objects have been standardized with stochastic simulation. There are several true bug species, which have been collected in almost all of the plant communities. However, characteristic ground-living heteropteran assemblages have been found in numerous Hungarian plant community types. Leaf litter and debris seem to have characteristic bug assemblages. Some differences have also been recognised between the bug fauna of mosses growing on different surfaces. Most of the species have been found in all of the great phytogeographical provinces of Hungary. Most high-dominance species, which have been collected, can be found at the ground-level almost throughout the year. Specimens of many other species have been collected with Berlese funnels in spring, autumn and/or winter. The diversities of the ground-living heteropteran assemblages of the examined objects have also been compared.

A hybrid algorithm combining metaheuristic with Monte Carlo simulation for solving the Stochastic Flow Shop problem

In this paper, a hybrid simulation-based algorithm is proposed for the StochasticFlow Shop Problem. The main idea of the methodology is to transform the stochastic problem into a deterministic problem and then apply simulation to the latter. In order to achieve this goal, we rely on Monte Carlo Simulation and an adapted version of a deterministic heuristic. This approach aims to provide flexibility and simplicity due to the fact that it is not constrained by any previous assumption and relies in well-tested heuristics.

A hybrid algorithm combining metaheuristic with Monte Carlo simulation for solving the Stochastic Flow Shop problem

In this paper, a hybrid simulation-based algorithm is proposed for the StochasticFlow Shop Problem. The main idea of the methodology is to transform the stochastic problem into a deterministic problem and then apply simulation to the latter. In order to achieve this goal, we rely on Monte Carlo Simulation and an adapted version of a deterministic heuristic. This approach aims to provide flexibility and simplicity due to the fact that it is not constrained by any previous assumption and relies in well-tested heuristics.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

Simulation-based smoothing and filtering in factor stochastic volatility models : two econometric applications

In this article we use factor models to describe a certain class of covariance structure for financiaI time series models. More specifical1y, we concentrate on situations where the factor variances are modeled by a multivariate stochastic volatility structure. We build on previous work by allowing the factor loadings, in the factor mo deI structure, to have a time-varying structure and to capture changes in asset weights over time motivated by applications with multi pIe time series of daily exchange rates. We explore and discuss potential extensions to the models exposed here in the prediction area. This discussion leads to open issues on real time implementation and natural model comparisons.

Simulation -based smoothing and filtering in factor stochastic volatility models : two econometric applications (July-2001)

The past decade has wítenessed a series of (well accepted and defined) financial crises periods in the world economy. Most of these events aI,"e country specific and eventually spreaded out across neighbor countries, with the concept of vicinity extrapolating the geographic maps and entering the contagion maps. Unfortunately, what contagion represents and how to measure it are still unanswered questions. In this article we measure the transmission of shocks by cross-market correlation\ coefficients following Forbes and Rigobon's (2000) notion of shift-contagion,. Our main contribution relies upon the use of traditional factor model techniques combined with stochastic volatility mo deIs to study the dependence among Latin American stock price indexes and the North American indexo More specifically, we concentrate on situations where the factor variances are modeled by a multivariate stochastic volatility structure. From a theoretical perspective, we improve currently available methodology by allowing the factor loadings, in the factor model structure, to have a time-varying structure and to capture changes in the series' weights over time. By doing this, we believe that changes and interventions experienced by those five countries are well accommodated by our models which learns and adapts reasonably fast to those economic and idiosyncratic shocks. We empirically show that the time varying covariance structure can be modeled by one or two common factors and that some sort of contagion is present in most of the series' covariances during periods of economical instability, or crisis. Open issues on real time implementation and natural model comparisons are thoroughly discussed.

Computer simulation of the stochastic transport equation

Trabalho apresentado no 37th Conference on Stochastic Processes and their Applications - July 28 - August 01, 2014 -Universidad de Buenos Aires

Economic viability and selection of irrigation systems using simulation and stochastic dominance

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)