A Numerical method for the semilinear stochastic transport equation

Trabalho apresentado no XXXV CNMAC, Natal-RN, 2014.

Non-asymptotic confidence bounds for the optimal value of a stochastic program

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds for the optimal value of the problem which are essentially better than the quality of the corresponding optimal solutions. At the same time, such bounds are more reliable than “standard” confidence bounds obtained through the asymptotic approach. We also discuss bounding the optimal value of MinMax Stochastic Optimization and stochastically constrained problems. We conclude with a small simulation study illustrating the numerical behavior of the proposed bounds.

Langevin simulation of scalar fields: Additive and multiplicative noises and lattice renormalization

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Numerical simulation of Ginzburg-Landau-Langevin equations

This work is concerned with non-equilibrium phenomena, with focus on the numerical simulation of the relaxation of non-conserved order parameters described by stochastic kinetic equations known as Ginzburg-Landau-Langevin (GLL) equations. We propose methods for solving numerically these type of equations, with additive and multiplicative noises. Illustrative applications of the methods are presented for different GLL equations, with emphasis on equations incorporating memory effects.

Estimation of population profiles of two strains of the fly Megaselia scalaris (Diptera: Phoridae) by bootstrap simulation

A partir de perfis populacionais experimentais de linhagens do díptero forídeo Megaselia scalaris, foi determinado o número mínimo de perfis amostrais que devem ser repetidos, via processo de simulação bootstrap, para se ter uma estimativa confiável do perfil médio populacional e apresentar estimativas do erro-padrão como medida da precisão das simulações realizadas. Os dados originais são provenientes de populações experimentais fundadas com as linhagens SR e R4, com três réplicas cada, e que foram mantidas por 33 semanas pela técnica da transferência seriada em câmara de temperatura constante (25 ± 1,0ºC). A variável usada foi tamanho populacional e o modelo adotado para cada perfíl foi o de um processo estocástico estacionário. Por meio das simulações, os perfis de três populações experimentais foram amplificados, determinando-se, dessa forma, o tamanho mínimo de amostra. Fixado o tamanho de amostra, simulações bootstrap foram realizadas para construção de intervalos de confiança e comparação dos perfis médios populacionais das duas linhagens. Os resultados mostram que com o tamanho de amostra igual a 50 inicia-se o processo de estabilização dos valores médios.

Optimal reactive power dispatch using stochastic chance-constrained programming

Deterministic Optimal Reactive Power Dispatch problem has been extensively studied, such that the demand power and the availability of shunt reactive power compensators are known and fixed. Give this background, a two-stage stochastic optimization model is first formulated under the presumption that the load demand can be modeled as specified random parameters. A second stochastic chance-constrained model is presented considering uncertainty on the demand and the equivalent availability of shunt reactive power compensators. Simulations on six-bus and 30-bus test systems are used to illustrate the validity and essential features of the proposed models. This simulations shows that the proposed models can prevent to the power system operator about of the deficit of reactive power in the power system and suggest that shunt reactive sourses must be dispatched against the unavailability of any reactive source. © 2012 IEEE.

Cooperative RNA Polymerase Molecules Behavior on a Stochastic Sequence-Dependent Model for Transcription Elongation

The transcription process is crucial to life and the enzyme RNA polymerase (RNAP) is the major component of the transcription machinery. The development of single-molecule techniques, such as magnetic and optical tweezers, atomic-force microscopy and single-molecule fluorescence, increased our understanding of the transcription process and complements traditional biochemical studies. Based on these studies, theoretical models have been proposed to explain and predict the kinetics of the RNAP during the polymerization, highlighting the results achieved by models based on the thermodynamic stability of the transcription elongation complex. However, experiments showed that if more than one RNAP initiates from the same promoter, the transcription behavior slightly changes and new phenomenona are observed. We proposed and implemented a theoretical model that considers collisions between RNAPs and predicts their cooperative behavior during multi-round transcription generalizing the Bai et al. stochastic sequence-dependent model. In our approach, collisions between elongating enzymes modify their transcription rate values. We performed the simulations in Mathematica® and compared the results of the single and the multiple-molecule transcription with experimental results and other theoretical models. Our multi-round approach can recover several expected behaviors, showing that the transcription process for the studied sequences can be accelerated up to 48% when collisions are allowed: the dwell times on pause sites are reduced as well as the distance that the RNAPs backtracked from backtracking sites. © 2013 Costa et al.

A Multi-Stage Stochastic Non-Linear Model for Reactive Power Planning Under Contingencies

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

Transport and dynamical properties for a bouncing ball model with regular and stochastic perturbations

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

Permutation-based stochastic ordering using pairwise comparisons

The topic of this work concerns nonparametric permutation-based methods aiming to find a ranking (stochastic ordering) of a given set of groups (populations), gathering together information from multiple variables under more than one experimental designs. The problem of ranking populations arises in several fields of science from the need of comparing G>2 given groups or treatments when the main goal is to find an order while taking into account several aspects. As it can be imagined, this problem is not only of theoretical interest but it also has a recognised relevance in several fields, such as industrial experiments or behavioural sciences, and this is reflected by the vast literature on the topic, although sometimes the problem is associated with different keywords such as: "stochastic ordering", "ranking", "construction of composite indices" etc., or even "ranking probabilities" outside of the strictly-speaking statistical literature. The properties of the proposed method are empirically evaluated by means of an extensive simulation study, where several aspects of interest are let to vary within a reasonable practical range. These aspects comprise: sample size, number of variables, number of groups, and distribution of noise/error. The flexibility of the approach lies mainly in the several available choices for the test-statistic and in the different types of experimental design that can be analysed. This render the method able to be tailored to the specific problem and the to nature of the data at hand. To perform the analyses an R package called SOUP (Stochastic Ordering Using Permutations) has been written and it is available on CRAN.

Pricing in stochastic-local volatility models with default

In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a consistent way, one needs to develop a quantitative model. We have studied analytical approximation formulas and numerical methods such as Monte Carlo method in order to calculate the price of a bond. We have illustrated how to obtain fast and accurate pricing approximations by expanding the drift and diffusion as a Taylor series and we have compared the second and third order approximation of the Bond and Call price with an accurate Monte Carlo simulation. We have analysed JDCEV model with constant or stochastic interest rate. We have provided numerical examples that illustrate the effectiveness and versatility of our methods. We have used Wolfram Mathematica and Matlab.

Simulation of Smart Materials

The aim of this thesis is the elucidation of structure-properties relationship of molecular semiconductors for electronic devices. This involves the use of a comprehensive set of simulation techniques, ranging from quantum-mechanical to numerical stochastic methods, and also the development of ad-hoc computational tools. In more detail, the research activity regarded two main topics: the study of electronic properties and structural behaviour of liquid crystalline (LC) materials based on functionalised oligo(p-phenyleneethynylene) (OPE), and the investigation on the electric field effect associated to OFET operation on pentacene thin film stability. In this dissertation, a novel family of substituted OPE liquid crystals with applications in stimuli-responsive materials is presented. In more detail, simulations can not only provide evidence for the characterization of the liquid crystalline phases of different OPEs, but elucidate the role of charge transfer states in donor-acceptor LCs containing an endohedral metallofullerene moiety. Such systems can be regarded as promising candidates for organic photovoltaics. Furthermore, exciton dynamics simulations are performed as a way to obtain additional information about the degree of order in OPE columnar phases. Finally, ab initio and molecular mechanics simulations are used to investigate the influence of an applied electric field on pentacene reactivity and stability. The reaction path of pentacene thermal dimerization in the presence of an external electric field is investigated; the results can be related to the fatigue effect observed in OFETs, that show significant performance degradation even in the absence of external agents. In addition to this, the effect of the gate voltage on a pentacene monolayer are simulated, and the results are then compared to X-ray diffraction measurements performed for the first time on operating OFETs.

Stochastic knock detection model for spark ignited engines

This report presents the development of a Stochastic Knock Detection (SKD) method for combustion knock detection in a spark-ignition engine using a model based design approach. Knock Signal Simulator (KSS) was developed as the plant model for the engine. The KSS as the plant model for the engine generates cycle-to-cycle accelerometer knock intensities following a stochastic approach with intensities that are generated using a Monte Carlo method from a lognormal distribution whose parameters have been predetermined from engine tests and dependent upon spark-timing, engine speed and load. The lognormal distribution has been shown to be a good approximation to the distribution of measured knock intensities over a range of engine conditions and spark-timings for multiple engines in previous studies. The SKD method is implemented in Knock Detection Module (KDM) which processes the knock intensities generated by KSS with a stochastic distribution estimation algorithm and outputs estimates of high and low knock intensity levels which characterize knock and reference level respectively. These estimates are then used to determine a knock factor which provides quantitative measure of knock level and can be used as a feedback signal to control engine knock. The knock factor is analyzed and compared with a traditional knock detection method to detect engine knock under various engine operating conditions. To verify the effectiveness of the SKD method, a knock controller was also developed and tested in a model-in-loop (MIL) system. The objective of the knock controller is to allow the engine to operate as close as possible to its border-line spark-timing without significant engine knock. The controller parameters were tuned to minimize the cycle-to-cycle variation in spark timing and the settling time of the controller in responding to step increase in spark advance resulting in the onset of engine knock. The simulation results showed that the combined system can be used adequately to model engine knock and evaluated knock control strategies for a wide range of engine operating conditions.

STOCHASTIC CHARGE TRANSPORT IN MULTI-ISLAND SINGLE-ELECTRON TUNNELING DEVICES

The physics of the operation of singe-electron tunneling devices (SEDs) and singe-electron tunneling transistors (SETs), especially of those with multiple nanometer-sized islands, has remained poorly understood in spite of some intensive experimental and theoretical research. This computational study examines the current-voltage (IV) characteristics of multi-island single-electron devices using a newly developed multi-island transport simulator (MITS) that is based on semi-classical tunneling theory and kinetic Monte Carlo simulation. The dependence of device characteristics on physical device parameters is explored, and the physical mechanisms that lead to the Coulomb blockade (CB) and Coulomb staircase (CS) characteristics are proposed. Simulations using MITS demonstrate that the overall IV characteristics in a device with a random distribution of islands are a result of a complex interplay among those factors that affect the tunneling rates that are fixed a priori (e.g. island sizes, island separations, temperature, gate bias, etc.), and the evolving charge state of the system, which changes as the source-drain bias (VSD) is changed. With increasing VSD, a multi-island device has to overcome multiple discrete energy barriers (up-steps) before it reaches the threshold voltage (Vth). Beyond Vth, current flow is rate-limited by slow junctions, which leads to the CS structures in the IV characteristic. Each step in the CS is characterized by a unique distribution of island charges with an associated distribution of tunneling probabilities. MITS simulation studies done on one-dimensional (1D) disordered chains show that longer chains are better suited for switching applications as Vth increases with increasing chain length. They are also able to retain CS structures at higher temperatures better than shorter chains. In sufficiently disordered 2D systems, we demonstrate that there may exist a dominant conducting path (DCP) for conduction, which makes the 2D device behave as a quasi-1D device. The existence of a DCP is sensitive to the device structure, but is robust with respect to changes in temperature, gate bias, and VSD. A side gate in 1D and 2D systems can effectively control Vth. We argue that devices with smaller island sizes and narrower junctions may be better suited for practical applications, especially at room temperature.

Technical throughput of material flow systems required to achieve design flow – determined by simulation with aniteration algorithm

This article deals with complex material flow systems and series connections of conveyor and op-erating elements. These can be characterised by a specific availability. The thus resultant overall availabil-ity of necessary “technical throughput” of the individual elements for the achievement of a specified throughput. When the conveyor and operating elements are subjected to a stochastic distribution, the interposition of buffers is necessary but these can also lead to a reduction of the necessary throughput due faults. The system behaviour of complex installations can only be investigated by simulation. The parame-ter changes required in order to achieve specific target values can also be determined by simulation runs in iteration loops.