Simulation using the Monte Carlo method

Photocopy. Springfield, Va., Distributed by Clearinghouse for Federal Scientific and Technical Information [1969]

Binomial leap methods for simulating stochastic chemical kinetics

This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the tau-leap and midpoint tau-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches. (C) 2004 American Institute of Physics.

Analysis and simulation of computer controlled cellular mobile radio systems

Cellular mobile radio systems will be of increasing importance in the future. This thesis describes research work concerned with the teletraffic capacity and the canputer control requirements of such systems. The work involves theoretical analysis and experimental investigations using digital computer simulation. New formulas are derived for the congestion in single-cell systems in which there are both land-to-mobile and mobile-to-mobile calls and in which mobile-to-mobile calls go via the base station. Two approaches are used, the first yields modified forms of the familiar Erlang and Engset formulas, while the second gives more complicated but more accurate formulas. The results of computer simulations to establish the accuracy of the formulas are described. New teletraffic formulas are also derived for the congestion in multi -cell systems. Fixed, dynamic and hybrid channel assignments are considered. The formulas agree with previously published simulation results. Simulation programs are described for the evaluation of the speech traffic of mobiles and for the investigation of a possible computer network for the control of the speech traffic. The programs were developed according to the structured progranming approach leading to programs of modular construction. Two simulation methods are used for the speech traffic: the roulette method and the time-true method. The first is economical but has some restriction, while the second is expensive but gives comprehensive answers. The proposed control network operates at three hierarchical levels performing various control functions which include: the setting-up and clearing-down of calls, the hand-over of calls between cells and the address-changing of mobiles travelling between cities. The results demonstrate the feasibility of the control netwvork and indicate that small mini -computers inter-connected via voice grade data channels would be capable of providing satisfactory control

Concepts and methods of quantitative assessment of risk to groundwater resources

This work presents a two-dimensional approach of risk assessment method based on the quantification of the probability of the occurrence of contaminant source terms, as well as the assessment of the resultant impacts. The risk is calculated using Monte Carlo simulation methods whereby synthetic contaminant source terms were generated to the same distribution as historically occurring pollution events or a priori potential probability distribution. The spatial and temporal distributions of the generated contaminant concentrations at pre-defined monitoring points within the aquifer were then simulated from repeated realisations using integrated mathematical models. The number of times when user defined ranges of concentration magnitudes were exceeded is quantified as risk. The utilities of the method were demonstrated using hypothetical scenarios, and the risk of pollution from a number of sources all occurring by chance together was evaluated. The results are presented in the form of charts and spatial maps. The generated risk maps show the risk of pollution at each observation borehole, as well as the trends within the study area. This capability to generate synthetic pollution events from numerous potential sources of pollution based on historical frequency of their occurrence proved to be a great asset to the method, and a large benefit over the contemporary methods.

Selection of simulation tools for improving supply chain performance

Simulation is an effective method for improving supply chain performance. However, there is limited advice available to assist practitioners in selecting the most appropriate method for a given problem. Much of the advice that does exist relies on custom and practice rather than a rigorous conceptual or empirical analysis. An analysis of the different modelling techniques applied in the supply chain domain was conducted, and the three main approaches to simulation used were identified; these are System Dynamics (SD), Discrete Event Simulation (DES) and Agent Based Modelling (ABM). This research has examined these approaches in two stages. Firstly, a first principles analysis was carried out in order to challenge the received wisdom about their strengths and weaknesses and a series of propositions were developed from this initial analysis. The second stage was to use the case study approach to test these propositions and to provide further empirical evidence to support their comparison. The contributions of this research are both in terms of knowledge and practice. In terms of knowledge, this research is the first holistic cross paradigm comparison of the three main approaches in the supply chain domain. Case studies have involved building ‘back to back’ models of the same supply chain problem using SD and a discrete approach (either DES or ABM). This has led to contributions concerning the limitations of applying SD to operational problem types. SD has also been found to have risks when applied to strategic and policy problems. Discrete methods have been found to have potential for exploring strategic problem types. It has been found that discrete simulation methods can model material and information feedback successfully. Further insights have been gained into the relationship between modelling purpose and modelling approach. In terms of practice, the findings have been summarised in the form of a framework linking modelling purpose, problem characteristics and simulation approach.

The challenges of representing human behaviour in simulation models:some case examples from supply chain, evacuation modelling and rail disruption

As more of the economy moves from traditional manufacturing to the service sector, the nature of work is becoming less tangible and thus, the representation of human behaviour in models is becoming more important. Representing human behaviour and decision making in models is challenging, both in terms of capturing the essence of the processes, and also the way that those behaviours and decisions are or can be represented in the models themselves. In order to advance understanding in this area, a useful first step is to evaluate and start to classify the various types of behaviour and decision making that are required to be modelled. This talk will attempt to set out and provide an initial classification of the different types of behaviour and decision making that a modeller might want to represent in a model. Then, it will be useful to start to assess the main methods of simulation in terms of their capability in representing these various aspects. The three main simulation methods, System Dynamics, Agent Based Modelling and Discrete Event Simulation all achieve this to varying degrees. There is some evidence that all three methods can, within limits, represent the key aspects of the system being modelled. The three simulation approaches are then assessed for their suitability in modelling these various aspects. Illustration of behavioural modelling will be provided from cases in supply chain management, evacuation modelling and rail disruption.

Encapsulated membrane proteins:a simplified system for molecular simulation

Over the past 50 years there has been considerable progress in our understanding of biomolecular interactions at an atomic level. This in turn has allowed molecular simulation methods employing full atomistic modeling at ever larger scales to develop. However, some challenging areas still remain where there is either a lack of atomic resolution structures or where the simulation system is inherently complex. An area where both challenges are present is that of membranes containing membrane proteins. In this review we analyse a new practical approach to membrane protein study that offers a potential new route to high resolution structures and the possibility to simplify simulations. These new approaches collectively recognise that preservation of the interaction between the membrane protein and the lipid bilayer is often essential to maintain structure and function. The new methods preserve these interactions by producing nano-scale disc shaped particles that include bilayer and the chosen protein. Currently two approaches lead in this area: the MSP system that relies on peptides to stabilise the discs, and SMALPs where an amphipathic styrene maleic acid copolymer is used. Both methods greatly enable protein production and hence have the potential to accelerate atomic resolution structure determination as well as providing a simplified format for simulations of membrane protein dynamics.

Bioactive sol-gel glasses at the atomic scale:the complementary use of advanced probe and computer modeling methods

Sol-gel-synthesized bioactive glasses may be formed via a hydrolysis condensation reaction, silica being introduced in the form of tetraethyl orthosilicate (TEOS), and calcium is typically added in the form of calcium nitrate. The synthesis reaction proceeds in an aqueous environment; the resultant gel is dried, before stabilization by heat treatment. These materials, being amorphous, are complex at the level of their atomic-scale structure, but their bulk properties may only be properly understood on the basis of that structural insight. Thus, a full understanding of their structure-property relationship may only be achieved through the application of a coherent suite of leading-edge experimental probes, coupled with the cogent use of advanced computer simulation methods. Using as an exemplar a calcia-silica sol-gel glass of the kind developed by Larry Hench, in the memory of whom this paper is dedicated, we illustrate the successful use of high-energy X-ray and neutron scattering (diffraction) methods, magic-angle spinning solid-state NMR, and molecular dynamics simulation as components to a powerful methodology for the study of amorphous materials.

I. Quantal effects in biochemical cooperativity and a proposed mechanism for the differentiation of calcium signaling in synaptic plasticity. II. Evolutionary algorithms for the optimization of methods in computational chemistry

In Part 1 of this thesis, we propose that biochemical cooperativity is a fundamentally non-ideal process. We show quantal effects underlying biochemical cooperativity and highlight apparent ergodic breaking at small volumes. The apparent ergodic breaking manifests itself in a divergence of deterministic and stochastic models. We further predict that this divergence of deterministic and stochastic results is a failure of the deterministic methods rather than an issue of stochastic simulations.

Ergodic breaking at small volumes may allow these molecular complexes to function as switches to a greater degree than has previously been shown. We propose that this ergodic breaking is a phenomenon that the synapse might exploit to differentiate Ca$^{2+}$ signaling that would lead to either the strengthening or weakening of a synapse. Techniques such as lattice-based statistics and rule-based modeling are tools that allow us to directly confront this non-ideality. A natural next step to understanding the chemical physics that underlies these processes is to consider \textit{in silico} specifically atomistic simulation methods that might augment our modeling efforts.

In the second part of this thesis, we use evolutionary algorithms to optimize \textit{in silico} methods that might be used to describe biochemical processes at the subcellular and molecular levels. While we have applied evolutionary algorithms to several methods, this thesis will focus on the optimization of charge equilibration methods. Accurate charges are essential to understanding the electrostatic interactions that are involved in ligand binding, as frequently discussed in the first part of this thesis.

Collaborative Web-Based Simulation Platform for Construction Project Planning

Part 13: Virtual Reality and Simulation

Hybrid Method to Assess Sensitive Process Interruption Costs Due to Faults in Electric Power Distribution Networks

This paper shows a new hybrid method for risk assessment regarding interruptions in sensitive processes due to faults in electric power distribution systems. This method determines indices related to long duration interruptions and short duration voltage variations (SDVV), such as voltage sags and swells in each customer supplied by the distribution network. Frequency of such occurrences and their impact on customer processes are determined for each bus and classified according to their corresponding magnitude and duration. The method is based on information regarding network configuration, system parameters and protective devices. It randomly generates a number of fault scenarios in order to assess risk areas regarding long duration interruptions and voltage sags and swells in an especially inventive way, including frequency of events according to their magnitude and duration. Based on sensitivity curves, the method determines frequency indices regarding disruption in customer processes that represent equipment malfunction and possible process interruptions due to voltage sags and swells. Such approach allows for the assessment of the annual costs associated with each one of the evaluated power quality indices.

The use of stochastic dynamic programming in optimal landscape reconstruction for metapopulations

A decision theory framework can be a powerful technique to derive optimal management decisions for endangered species. We built a spatially realistic stochastic metapopulation model for the Mount Lofty Ranges Southern Emu-wren (Stipiturus malachurus intermedius), a critically endangered Australian bird. Using diserete-time Markov,chains to describe the dynamics of a metapopulation and stochastic dynamic programming (SDP) to find optimal solutions, we evaluated the following different management decisions: enlarging existing patches, linking patches via corridors, and creating a new patch. This is the first application of SDP to optimal landscape reconstruction and one of the few times that landscape reconstruction dynamics have been integrated with population dynamics. SDP is a powerful tool that has advantages over standard Monte Carlo simulation methods because it can give the exact optimal strategy for every landscape configuration (combination of patch areas and presence of corridors) and pattern of metapopulation occupancy, as well as a trajectory of strategies. It is useful when a sequence of management actions can be performed over a given time horizon, as is the case for many endangered species recovery programs, where only fixed amounts of resources are available in each time step. However, it is generally limited by computational constraints to rather small networks of patches. The model shows that optimal metapopulation, management decisions depend greatly on the current state of the metapopulation,. and there is no strategy that is universally the best. The extinction probability over 30 yr for the optimal state-dependent management actions is 50-80% better than no management, whereas the best fixed state-independent sets of strategies are only 30% better than no management. This highlights the advantages of using a decision theory tool to investigate conservation strategies for metapopulations. It is clear from these results that the sequence of management actions is critical, and this can only be effectively derived from stochastic dynamic programming. The model illustrates the underlying difficulty in determining simple rules of thumb for the sequence of management actions for a metapopulation. This use of a decision theory framework extends the capacity of population viability analysis (PVA) to manage threatened species.

Avaliação da dose absorvida na tiróide, em cintigrafias com 123I e Na99mTcO4 utilizando modelos biocinéticos e métodos de Monte Carlo

Mestrado em Radiações Aplicadas às Tecnologias da Saúde. Área de especialização: Protecção contra Radiações

Population pharmacokinetic study of gentamicin: A retrospective analysis in a large cohort of neonate patients

Objectives: Gentamicin is one of the most commonly prescribed antibiotics for suspected or proven infection in newborns. Because of age-associated (pre- and post- natal) changes in body composition and organ function, large interindividual variability in gentamicin drug levels exists, thus requiring a close monitoring of this drug due to its narrow therapeutic index. We aimed to investigate clinical and demographic factors influencing gentamicin pharmacokinetics (PK) in a large cohort of unselected newborns and to explore optimal regimen based on simulation. Methods: All gentamicin concentration data from newborns treated at the University Hospital Center of Lausanne between December 2006 and October 2011 were retrieved. Gentamicin concentrations were measured within the frame of a routine therapeutic drug monitoring program, in which 2 concentrations (at 1h and 12h) are systematically collected after the first administered dose, and a few additional concentrations are sampled along the treatment course. A population PK analysis was performed by comparing various structural models, and the effect of clinical and demographic factors on gentamicin disposition was explored using NONMEM®. Results: A total of 3039 concentrations collected in 994 preterm (median gestational age 32.3 weeks, range 24.2-36.5 weeks) and 455 term newborns were used in the analysis. Most of the data (86%) were sampled after the first dose (C1 h and C12 h). A two-compartment model best characterized gentamicin PK. Average clearance (CL) was 0.044 L/h/kg (CV 25%), central volume of distribution (Vc) 0.442 L/kg (CV 18%), intercompartmental clearance (Q) 0.040 L/h/kg and peripheral volume of distribution (Vp) 0.122 L/kg. Body weight, gestational age and postnatal age positively influenced CL. The use of both gestational age and postnatal age better predicted CL than postmenstrual age alone. CL was affected by dopamine and furosemide administration and non-significantly by indometacin. Body weight, gestational age and dopamine coadminstration significantly influenced Vc. Model based simulation confirms that preterm infants need higher dose, superior to 4 mg/kg, and extended interval dosage regimen to achieve adequate concentration. Conclusions: This study, performed on a very large cohort of neonates, identified important factors influencing gentamicin PK. The model will serve to elaborate a Bayesian tool for dosage individualization based on a single measurement.

An ATM distributed simulator for network management research

Due to the high cost of a large ATM network working up to full strength to apply our ideas about network management, i.e., dynamic virtual path (VP) management and fault restoration, we developed a distributed simulation platform for performing our experiments. This platform also had to be capable of other sorts of tests, such as connection admission control (CAC) algorithms, routing algorithms, and accounting and charging methods. The platform was posed as a very simple, event-oriented and scalable simulation. The main goal was the simulation of a working ATM backbone network with a potentially large number of nodes (hundreds). As research into control algorithms and low-level, or rather cell-level methods, was beyond the scope of this study, the simulation took place at a connection level, i.e., there was no real traffic of cells. The simulated network behaved like a real network accepting and rejecting SNMP ones, or experimental tools using the API node