Stochastic variability of output levels in a pulp mill

Quite often, in the construction of a pulp mill involves establishing the size of tanks which will accommodate the material from the various processes in which case estimating the right tank size a priori would be vital. Hence, simulation of the whole production process would be worthwhile. Therefore, there is need to develop mathematical models that would mimic the behavior of the output from the various production units of the pulp mill to work as simulators. Markov chain models, Autoregressive moving average (ARMA) model, Mean reversion models with ensemble interaction together with Markov regime switching models are proposed for that purpose.

Non-Linear Unsteady Aerodynamic Response Approximation Using Multi-Layer Functionals

Non-linear functional representation of the aerodynamic response provides a convenient mathematical model for motion-induced unsteady transonic aerodynamic loads response, that accounts for both complex non-linearities and time-history effects. A recent development, based on functional approximation theory, has established a novel functional form; namely, the multi-layer functional. For a large class of non-linear dynamic systems, such multi-layer functional representations can be realised via finite impulse response (FIR) neural networks. Identification of an appropriate FIR neural network model is facilitated by means of a supervised training process in which a limited sample of system input-output data sets is presented to the temporal neural network. The present work describes a procedure for the systematic identification of parameterised neural network models of motion-induced unsteady transonic aerodynamic loads response. The training process is based on a conventional genetic algorithm to optimise the network architecture, combined with a simplified random search algorithm to update weight and bias values. Application of the scheme to representative transonic aerodynamic loads response data for a bidimensional airfoil executing finite-amplitude motion in transonic flow is used to demonstrate the feasibility of the approach. The approach is shown to furnish a satisfactory generalisation property to different motion histories over a range of Mach numbers in the transonic regime.

Modelagem da distribuição geográfica de espécies lenhosas de cerrado no Estado de São Paulo

Atualmente vêm sendo desenvolvidas e utilizadas várias técnicas de modelagem de distribuição geográfica de espécies com os mais variados objetivos. Algumas dessas técnicas envolvem modelagem baseada em análise ambiental, nas quais os algoritmos procuram por condições ambientais semelhantes àquelas onde as espécies foram encontradas, resultando em áreas potenciais onde as condições ambientais seriam propícias ao desenvolvimento dessas espécies. O presente estudo trata do uso da modelagem preditiva de distribuição geográfica de espécies nativas, através da utilização de algoritmo genético, como ferramenta para auxiliar o entendimento dos padrões de distribuição do bioma cerrado no Estado de São Paulo. A metodologia empregada e os resultados obtidos foram considerados satisfatórios para a geração de modelos de distribuição geográfica de espécies vegetais, baseados em dados abióticos, para as regiões de estudo. A eficácia do modelo em predizer a ocorrência de espécies do cerrado é maior se forem utilizados apenas pontos de amostragem com fisionomias de cerrado, excluindo-se áreas de transição. Para minimizar problemas decorrentes da falta de convergência do algoritmo utilizado GARP ("Genetic Algorithm for Rule Set Production"), foram gerados 100 modelos para cada espécie modelada. O uso de modelagem pode auxiliar no entendimento dos padrões de distribuição de um bioma ou ecossistema em uma análise regional.

Mathematical modeling and optimal control of malaria

Malaria continues to infect millions and kill hundreds of thousands of people worldwide each year, despite over a century of research and attempts to control and eliminate this infectious disease. Challenges such as the development and spread of drug resistant malaria parasites, insecticide resistance to mosquitoes, climate change, the presence of individuals with subpatent malaria infections which normally are asymptomatic and behavioral plasticity in the mosquito hinder the prospects of malaria control and elimination. In this thesis, mathematical models of malaria transmission and control that address the role of drug resistance, immunity, iron supplementation and anemia, immigration and visitation, and the presence of asymptomatic carriers in malaria transmission are developed. A within-host mathematical model of severe Plasmodium falciparum malaria is also developed. First, a deterministic mathematical model for transmission of antimalarial drug resistance parasites with superinfection is developed and analyzed. The possibility of increase in the risk of superinfection due to iron supplementation and fortification in malaria endemic areas is discussed. The model results calls upon stakeholders to weigh the pros and cons of iron supplementation to individuals living in malaria endemic regions. Second, a deterministic model of transmission of drug resistant malaria parasites, including the inflow of infective immigrants, is presented and analyzed. The optimal control theory is applied to this model to study the impact of various malaria and vector control strategies, such as screening of immigrants, treatment of drug-sensitive infections, treatment of drug-resistant infections, and the use of insecticide-treated bed nets and indoor spraying of mosquitoes. The results of the model emphasize the importance of using a combination of all four controls tools for effective malaria intervention. Next, a two-age-class mathematical model for malaria transmission with asymptomatic carriers is developed and analyzed. In development of this model, four possible control measures are analyzed: the use of long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic, and screening and treatment of asymptomatic individuals. The numerical results show that a disease-free equilibrium can be attained if all four control measures are used. A common pitfall for most epidemiological models is the absence of real data; model-based conclusions have to be drawn based on uncertain parameter values. In this thesis, an approach to study the robustness of optimal control solutions under such parameter uncertainty is presented. Numerical analysis of the optimal control problem in the presence of parameter uncertainty demonstrate the robustness of the optimal control approach that: when a comprehensive control strategy is used the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the design of cost-effective strategies for disease control with multiple interventions, even under considerable uncertainty of model parameters. Finally, a separate work modeling the within-host Plasmodium falciparum infection in humans is presented. The developed model allows re-infection of already-infected red blood cells. The model hypothesizes that in severe malaria due to parasite quest for survival and rapid multiplication, the Plasmodium falciparum can be absorbed in the already-infected red blood cells which accelerates the rupture rate and consequently cause anemia. Analysis of the model and parameter identifiability using Markov chain Monte Carlo methods is presented.

Parameter identification in time series models

Time series analysis can be categorized into three different approaches: classical, Box-Jenkins, and State space. Classical approach makes a basement for the analysis and Box-Jenkins approach is an improvement of the classical approach and deals with stationary time series. State space approach allows time variant factors and covers up a broader area of time series analysis. This thesis focuses on parameter identifiablity of different parameter estimation methods such as LSQ, Yule-Walker, MLE which are used in the above time series analysis approaches. Also the Kalman filter method and smoothing techniques are integrated with the state space approach and MLE method to estimate parameters allowing them to change over time. Parameter estimation is carried out by repeating estimation and integrating with MCMC and inspect how well different estimation methods can identify the optimal model parameters. Identification is performed in probabilistic and general senses and compare the results in order to study and represent identifiability more informative way.

Inverting ionospheric D-region electron density pro-file from riometer measurement

The aim of this work is to invert the ionospheric electron density profile from Riometer (Relative Ionospheric opacity meter) measurement. The newly Riometer instrument KAIRA (Kilpisjärvi Atmospheric Imaging Receiver Array) is used to measure the cosmic HF radio noise absorption that taking place in the D-region ionosphere between 50 to 90 km. In order to invert the electron density profile synthetic data is used to feed the unknown parameter Neq using spline height method, which works by taking electron density profile at different altitude. Moreover, smoothing prior method also used to sample from the posterior distribution by truncating the prior covariance matrix. The smoothing profile approach makes the problem easier to find the posterior using MCMC (Markov Chain Monte Carlo) method.

Kalman filter for computational market dynamics

Kalman filter is a recursive mathematical power tool that plays an increasingly vital role in innumerable fields of study. The filter has been put to service in a multitude of studies involving both time series modelling and financial time series modelling. Modelling time series data in Computational Market Dynamics (CMD) can be accomplished using the Jablonska-Capasso-Morale (JCM) model. Maximum likelihood approach has always been utilised to estimate the parameters of the JCM model. The purpose of this study is to discover if the Kalman filter can be effectively utilized in CMD. Ensemble Kalman filter (EnKF), with 50 ensemble members, applied to US sugar prices spanning the period of January, 1960 to February, 2012 was employed for this work. The real data and Kalman filter trajectories showed no significant discrepancies, hence indicating satisfactory performance of the technique. Since only US sugar prices were utilized, it would be interesting to discover the nature of results if other data sets are employed.

Initialization of Continuous Nonlinear Models Using Extended Kalman Filter

The two main objectives of Bayesian inference are to estimate parameters and states. In this thesis, we are interested in how this can be done in the framework of state-space models when there is a complete or partial lack of knowledge of the initial state of a continuous nonlinear dynamical system. In literature, similar problems have been referred to as diffuse initialization problems. This is achieved first by extending the previously developed diffuse initialization Kalman filtering techniques for discrete systems to continuous systems. The second objective is to estimate parameters using MCMC methods with a likelihood function obtained from the diffuse filtering. These methods are tried on the data collected from the 1995 Ebola outbreak in Kikwit, DRC in order to estimate the parameters of the system.

Cost-effective analysis of different algorithms for the diagnosis of hepatitis C virus infection

We compared the cost-benefit of two algorithms, recently proposed by the Centers for Disease Control and Prevention, USA, with the conventional one, the most appropriate for the diagnosis of hepatitis C virus (HCV) infection in the Brazilian population. Serum samples were obtained from 517 ELISA-positive or -inconclusive blood donors who had returned to Fundação Pró-Sangue/Hemocentro de São Paulo to confirm previous results. Algorithm A was based on signal-to-cut-off (s/co) ratio of ELISA anti-HCV samples that show s/co ratio ³95% concordance with immunoblot (IB) positivity. For algorithm B, reflex nucleic acid amplification testing by PCR was required for ELISA-positive or -inconclusive samples and IB for PCR-negative samples. For algorithm C, all positive or inconclusive ELISA samples were submitted to IB. We observed a similar rate of positive results with the three algorithms: 287, 287, and 285 for A, B, and C, respectively, and 283 were concordant with one another. Indeterminate results from algorithms A and C were elucidated by PCR (expanded algorithm) which detected two more positive samples. The estimated cost of algorithms A and B was US$21,299.39 and US$32,397.40, respectively, which were 43.5 and 14.0% more economic than C (US$37,673.79). The cost can vary according to the technique used. We conclude that both algorithms A and B are suitable for diagnosing HCV infection in the Brazilian population. Furthermore, algorithm A is the more practical and economical one since it requires supplemental tests for only 54% of the samples. Algorithm B provides early information about the presence of viremia.

Bayesian analysis of SEIR epidemic models

This thesis concerns the analysis of epidemic models. We adopt the Bayesian paradigm and develop suitable Markov Chain Monte Carlo (MCMC) algorithms. This is done by considering an Ebola outbreak in the Democratic Republic of Congo, former Zaïre, 1995 as a case of SEIR epidemic models. We model the Ebola epidemic deterministically using ODEs and stochastically through SDEs to take into account a possible bias in each compartment. Since the model has unknown parameters, we use different methods to estimate them such as least squares, maximum likelihood and MCMC. The motivation behind choosing MCMC over other existing methods in this thesis is that it has the ability to tackle complicated nonlinear problems with large number of parameters. First, in a deterministic Ebola model, we compute the likelihood function by sum of square of residuals method and estimate parameters using the LSQ and MCMC methods. We sample parameters and then use them to calculate the basic reproduction number and to study the disease-free equilibrium. From the sampled chain from the posterior, we test the convergence diagnostic and confirm the viability of the model. The results show that the Ebola model fits the observed onset data with high precision, and all the unknown model parameters are well identified. Second, we convert the ODE model into a SDE Ebola model. We compute the likelihood function using extended Kalman filter (EKF) and estimate parameters again. The motivation of using the SDE formulation here is to consider the impact of modelling errors. Moreover, the EKF approach allows us to formulate a filtered likelihood for the parameters of such a stochastic model. We use the MCMC procedure to attain the posterior distributions of the parameters of the SDE Ebola model drift and diffusion parts. In this thesis, we analyse two cases: (1) the model error covariance matrix of the dynamic noise is close to zero , i.e. only small stochasticity added into the model. The results are then similar to the ones got from deterministic Ebola model, even if methods of computing the likelihood function are different (2) the model error covariance matrix is different from zero, i.e. a considerable stochasticity is introduced into the Ebola model. This accounts for the situation where we would know that the model is not exact. As a results, we obtain parameter posteriors with larger variances. Consequently, the model predictions then show larger uncertainties, in accordance with the assumption of an incomplete model.

Bounds on edit metric codes with combinatorial DNA constraints

The design of a large and reliable DNA codeword library is a key problem in DNA based computing. DNA codes, namely sets of fixed length edit metric codewords over the alphabet {A, C, G, T}, satisfy certain combinatorial constraints with respect to biological and chemical restrictions of DNA strands. The primary constraints that we consider are the reverse--complement constraint and the fixed GC--content constraint, as well as the basic edit distance constraint between codewords. We focus on exploring the theory underlying DNA codes and discuss several approaches to searching for optimal DNA codes. We use Conway's lexicode algorithm and an exhaustive search algorithm to produce provably optimal DNA codes for codes with small parameter values. And a genetic algorithm is proposed to search for some sub--optimal DNA codes with relatively large parameter values, where we can consider their sizes as reasonable lower bounds of DNA codes. Furthermore, we provide tables of bounds on sizes of DNA codes with length from 1 to 9 and minimum distance from 1 to 9.

GA approach for finding Rough Set decision rules based on bireducts

Feature selection plays an important role in knowledge discovery and data mining nowadays. In traditional rough set theory, feature selection using reduct - the minimal discerning set of attributes - is an important area. Nevertheless, the original definition of a reduct is restrictive, so in one of the previous research it was proposed to take into account not only the horizontal reduction of information by feature selection, but also a vertical reduction considering suitable subsets of the original set of objects. Following the work mentioned above, a new approach to generate bireducts using a multi--objective genetic algorithm was proposed. Although the genetic algorithms were used to calculate reduct in some previous works, we did not find any work where genetic algorithms were adopted to calculate bireducts. Compared to the works done before in this area, the proposed method has less randomness in generating bireducts. The genetic algorithm system estimated a quality of each bireduct by values of two objective functions as evolution progresses, so consequently a set of bireducts with optimized values of these objectives was obtained. Different fitness evaluation methods and genetic operators, such as crossover and mutation, were applied and the prediction accuracies were compared. Five datasets were used to test the proposed method and two datasets were used to perform a comparison study. Statistical analysis using the one-way ANOVA test was performed to determine the significant difference between the results. The experiment showed that the proposed method was able to reduce the number of bireducts necessary in order to receive a good prediction accuracy. Also, the influence of different genetic operators and fitness evaluation strategies on the prediction accuracy was analyzed. It was shown that the prediction accuracies of the proposed method are comparable with the best results in machine learning literature, and some of them outperformed it.

Explaining the Transition Between Exchange Rate Regimes

This paper studies the transition between exchange rate regimes using a Markov chain model with time-varying transition probabilities. The probabilities are parameterized as nonlinear functions of variables suggested by the currency crisis and optimal currency area literature. Results using annual data indicate that inflation, and to a lesser extent, output growth and trade openness help explain the exchange rate regime transition dynamics.

A maximum likelihood framework for protein design

Affiliation: Claudia Kleinman, Nicolas Rodrigue & Hervé Philippe : Département de biochimie, Faculté de médecine, Université de Montréal

Modélisation de l’observance et détermination de son impact biopharmaceutique

L’observance, qui décrit à quel degré le patient suit la prescription, est un facteur essentiel pour que le traitement réussisse. Les observances des patients varient beaucoup et l’efficacité du médicament varie parallèlement. Par conséquent, il faut avoir des paramètres sensibles et fiables pour mesurer l’observance. Dans la littérature, on trouve beaucoup de paramètres pour évaluer l’observance mais leurs avantages, limites et inconvénients, en ce qui concerne l’évaluation de l’impact de l’observance sur les effets des médicaments n’ont pas encore été étudiés en profondeur. L’évaluation de ces paramètres nécessite de les tester dans différentes situations. Comme les données disponibles sur l’observance ne concernent pas un ensemble exhaustif de situations, le recours à la simulation, en s’inspirant des cas réels ou plausibles, est très pertinent. On a ainsi réussi à développer un modèle dont les paramètres sont simples et compréhensibles et qui est pratique et flexible pour simuler les différents cas et même les cas extrêmes de l’observance. On a proposé de nouveaux paramètres pour mesurer l’impact biopharmaceutique de l’observance. Ensuite, on a comparé la performance, en termes de sensibilité et la fiabilité, des paramètres proposés et celles de paramètres déjà utilisés. En conclusion, on peut souligner qu’il n’y a pas de paramètre parfait étant donné que chacun a ses propres limites. Par exemple, pour les médicaments dont les effets sont directement liés aux leurs concentrations plasmatiques, le pourcentage des doses prises, qui est le paramètre le plus utilisé, offre la pire performance; par contre, le pourcentage des doses correctes nettes qui est un nouveau paramètre possède une bonne performance et des avantages prometteurs.