Simulation methods with extended stability for stiff biochemical kinetics

Background: With increasing computer power, simulating the dynamics of complex systems in chemistry and biology is becoming increasingly routine. The modelling of individual reactions in (bio)chemical systems involves a large number of random events that can be simulated by the stochastic simulation algorithm (SSA). The key quantity is the step size, or waiting time, τ, whose value inversely depends on the size of the propensities of the different channel reactions and which needs to be re-evaluated after every firing event. Such a discrete event simulation may be extremely expensive, in particular for stiff systems where τ can be very short due to the fast kinetics of some of the channel reactions. Several alternative methods have been put forward to increase the integration step size. The so-called τ-leap approach takes a larger step size by allowing all the reactions to fire, from a Poisson or Binomial distribution, within that step. Although the expected value for the different species in the reactive system is maintained with respect to more precise methods, the variance at steady state can suffer from large errors as τ grows. Results: In this paper we extend Poisson τ-leap methods to a general class of Runge-Kutta (RK) τ-leap methods. We show that with the proper selection of the coefficients, the variance of the extended τ-leap can be well-behaved, leading to significantly larger step sizes.Conclusions: The benefit of adapting the extended method to the use of RK frameworks is clear in terms of speed of calculation, as the number of evaluations of the Poisson distribution is still one set per time step, as in the original τ-leap method. The approach paves the way to explore new multiscale methods to simulate (bio)chemical systems.

Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

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

Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

Stochastic methods based on time-series modeling combined with geostatistics can be useful tools to describe the variability of water-table levels in time and space and to account for uncertainty. Monitoring water-level networks can give information about the dynamic of the aquifer domain in both dimensions. Time-series modeling is an elegant way to treat monitoring data without the complexity of physical mechanistic models. Time-series model predictions can be interpolated spatially, with the spatial differences in water-table dynamics determined by the spatial variation in the system properties and the temporal variation driven by the dynamics of the inputs into the system. An integration of stochastic methods is presented, based on time-series modeling and geostatistics as a framework to predict water levels for decision making in groundwater management and land-use planning. The methodology is applied in a case study in a Guarani Aquifer System (GAS) outcrop area located in the southeastern part of Brazil. Communication of results in a clear and understandable form, via simulated scenarios, is discussed as an alternative, when translating scientific knowledge into applications of stochastic hydrogeology in large aquifers with limited monitoring network coverage like the GAS.

Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

Stochastic methods based on time-series modeling combined with geostatistics can be useful tools to describe the variability of water-table levels in time and space and to account for uncertainty. Monitoring water-level networks can give information about the dynamic of the aquifer domain in both dimensions. Time-series modeling is an elegant way to treat monitoring data without the complexity of physical mechanistic models. Time-series model predictions can be interpolated spatially, with the spatial differences in water-table dynamics determined by the spatial variation in the system properties and the temporal variation driven by the dynamics of the inputs into the system. An integration of stochastic methods is presented, based on time-series modeling and geostatistics as a framework to predict water levels for decision making in groundwater management and land-use planning. The methodology is applied in a case study in a Guarani Aquifer System (GAS) outcrop area located in the southeastern part of Brazil. Communication of results in a clear and understandable form, via simulated scenarios, is discussed as an alternative, when translating scientific knowledge into applications of stochastic hydrogeology in large aquifers with limited monitoring network coverage like the GAS.

A few what-ifs on using statistical analysis of stochastic simulation runs to extract timeliness properties

Modern real-time systems, with a more flexible and adaptive nature, demand approaches for timeliness evaluation based on probabilistic measures of meeting deadlines. In this context, simulation can emerge as an adequate solution to understand and analyze the timing behaviour of actual systems. However, care must be taken with the obtained outputs under the penalty of obtaining results with lack of credibility. Particularly important is to consider that we are more interested in values from the tail of a probability distribution (near worst-case probabilities), instead of deriving confidence on mean values. We approach this subject by considering the random nature of simulation output data. We will start by discussing well known approaches for estimating distributions out of simulation output, and the confidence which can be applied to its mean values. This is the basis for a discussion on the applicability of such approaches to derive confidence on the tail of distributions, where the worst-case is expected to be.

Extremum estimators and stochastic optimization methods

Submitted in partial fulfillment for the Requirements for the Degree of PhD in Mathematics, in the Speciality of Statistics in the Faculdade de Ciências e Tecnologia

Stochastic simulation of the morphology of fluvial sand channels reservoirs

Dissertação para obtenção do Grau de Mestre em Engenharia Geológica (Georrecursos)

Comparing simulation methods for modelling the errors of stand inventory data

Abstract

INCLUDING RISK IN ECONOMIC FEASIBILITY ANALYSIS:A STOCHASTIC SIMULATION MODEL FOR BLUEBERRY INVESTMENT DECISIONS IN CHILE

ABSTRACT The traditional method of net present value (NPV) to analyze the economic profitability of an investment (based on a deterministic approach) does not adequately represent the implicit risk associated with different but correlated input variables. Using a stochastic simulation approach for evaluating the profitability of blueberry (Vaccinium corymbosum L.) production in Chile, the objective of this study is to illustrate the complexity of including risk in economic feasibility analysis when the project is subject to several but correlated risks. The results of the simulation analysis suggest that the non-inclusion of the intratemporal correlation between input variables underestimate the risk associated with investment decisions. The methodological contribution of this study illustrates the complexity of the interrelationships between uncertain variables and their impact on the convenience of carrying out this type of business in Chile. The steps for the analysis of economic viability were: First, adjusted probability distributions for stochastic input variables (SIV) were simulated and validated. Second, the random values of SIV were used to calculate random values of variables such as production, revenues, costs, depreciation, taxes and net cash flows. Third, the complete stochastic model was simulated with 10,000 iterations using random values for SIV. This result gave information to estimate the probability distributions of the stochastic output variables (SOV) such as the net present value, internal rate of return, value at risk, average cost of production, contribution margin and return on capital. Fourth, the complete stochastic model simulation results were used to analyze alternative scenarios and provide the results to decision makers in the form of probabilities, probability distributions, and for the SOV probabilistic forecasts. The main conclusion shown that this project is a profitable alternative investment in fruit trees in Chile.

Simulation methods in the modelling of bioaffinity assays

Computational model-based simulation methods were developed for the modelling of bioaffinity assays. Bioaffinity-based methods are widely used to quantify a biological substance in biological research, development and in routine clinical in vitro diagnostics. Bioaffinity assays are based on the high affinity and structural specificity between the binding biomolecules. The simulation methods developed are based on the mechanistic assay model, which relies on the chemical reaction kinetics and describes the forming of a bound component as a function of time from the initial binding interaction. The simulation methods were focused on studying the behaviour and the reliability of bioaffinity assay and the possibilities the modelling methods of binding reaction kinetics provide, such as predicting assay results even before the binding reaction has reached equilibrium. For example, a rapid quantitative result from a clinical bioaffinity assay sample can be very significant, e.g. even the smallest elevation of a heart muscle marker reveals a cardiac injury. The simulation methods were used to identify critical error factors in rapid bioaffinity assays. A new kinetic calibration method was developed to calibrate a measurement system by kinetic measurement data utilizing only one standard concentration. A nodebased method was developed to model multi-component binding reactions, which have been a challenge to traditional numerical methods. The node-method was also used to model protein adsorption as an example of nonspecific binding of biomolecules. These methods have been compared with the experimental data from practice and can be utilized in in vitro diagnostics, drug discovery and in medical imaging.

Stochastic approximation methods in stochastic optimization

Stochastic approximation methods for stochastic optimization are considered. Reviewed the main methods of stochastic approximation: stochastic quasi-gradient algorithm, Kiefer-Wolfowitz algorithm and adaptive rules for them, simultaneous perturbation stochastic approximation (SPSA) algorithm. Suggested the model and the solution of the retailer's profit optimization problem and considered an application of the SQG-algorithm for the optimization problems with objective functions given in the form of ordinary differential equation.

Stochastic simulation to improve land-cover estimates derived from coarse spatial resolution satellite imagery = La simulation stochastique pour améliorer les estimations de la couverture des sols à partir d'images satellitales à résolution spatiale grossière

Thèse diffusée initialement dans le cadre d'un projet pilote des Presses de l'Université de Montréal/Centre d'édition numérique UdeM (1997-2008) avec l'autorisation de l'auteur.

Learning in neural networks and stochastic approximation methods with averaging

The problem of adjusting the weights (learning) in multilayer feedforward neural networks (NN) is known to be of a high importance when utilizing NN techniques in various practical applications. The learning procedure is to be performed as fast as possible and in a simple computational fashion, the two requirements which are usually not satisfied practically by the methods developed so far. Moreover, the presence of random inaccuracies are usually not taken into account. In view of these three issues, an alternative stochastic approximation approach discussed in the paper, seems to be very promising.