On the inverse parabolicity of pdf equations in turbulent flows

The focus of the present work is the well-known feature of the probability density function (PDF) transport equations in turbulent flows-the inverse parabolicity of the equations. While it is quite common in fluid mechanics to interpret equations with direct (forward-time) parabolicity as diffusive (or as a combination of diffusion, convection and reaction), the possibility of a similar interpretation for equations with inverse parabolicity is not clear. According to Einstein's point of view, a diffusion process is associated with the random walk of some physical or imaginary particles, which can be modelled by a Markov diffusion process. In the present paper it is shown that the Markov diffusion process directly associated with the PDF equation represents a reasonable model for dealing with the PDFs of scalars but it significantly underestimates the diffusion rate required to simulate turbulent dispersion when the velocity components are considered.

Typical case behaviour of spin systems in random graph and composite ensembles

This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm. The algorithm can be formulated in the large system limit as a branching process, for which critical properties can be analysed. Far from the critical point a set of differential equations may be used to model the process, and these are solved by numerical integration and exact bounding methods. The multi-access channel problem is formulated as an equilibrium statistical physics problem for the case of bit transmission on a channel with power control and synchronisation. A sparse code division multiple access method is considered and the optimal detection properties are examined in typical case by use of the replica method, and compared to detection performance achieved by interactive decoding methods. These codes are found to have phenomena closely resembling the well-understood dense codes. The composite model is introduced as an abstraction of canonical sparse and dense disordered spin models. The model includes couplings due to both dense and sparse topologies simultaneously. The new type of codes are shown to outperform sparse and dense codes in some regimes both in optimal performance, and in performance achieved by iterative detection methods in finite systems.

A methodological framework for modeling pavement maintenance costs for projects with performance-based contracts

Performance-based maintenance contracts differ significantly from material and method-based contracts that have been traditionally used to maintain roads. Road agencies around the world have moved towards a performance-based contract approach because it offers several advantages like cost saving, better budgeting certainty, better customer satisfaction with better road services and conditions. Payments for the maintenance of road are explicitly linked to the contractor successfully meeting certain clearly defined minimum performance indicators in these contracts. Quantitative evaluation of the cost of performance-based contracts has several difficulties due to the complexity of the pavement deterioration process. Based on a probabilistic analysis of failures of achieving multiple performance criteria over the length of the contract period, an effort has been made to develop a model that is capable of estimating the cost of these performance-based contracts. One of the essential functions of such model is to predict performance of the pavement as accurately as possible. Prediction of future degradation of pavement is done using Markov Chain Process, which requires estimating transition probabilities from previous deterioration rate for similar pavements. Transition probabilities were derived using historical pavement condition rating data, both for predicting pavement deterioration when there is no maintenance, and for predicting pavement improvement when maintenance activities are performed. A methodological framework has been developed to estimate the cost of maintaining road based on multiple performance criteria such as crack, rut and, roughness. The application of the developed model has been demonstrated via a real case study of Miami Dade Expressways (MDX) using pavement condition rating data from Florida Department of Transportation (FDOT) for a typical performance-based asphalt pavement maintenance contract. Results indicated that the pavement performance model developed could predict the pavement deterioration quite accurately. Sensitivity analysis performed shows that the model is very responsive to even slight changes in pavement deterioration rate and performance constraints. It is expected that the use of this model will assist the highway agencies and contractors in arriving at a fair contract value for executing long term performance-based pavement maintenance works.

A decision support framework for infrastructure maintenance investment decision-making

Infrastructure management agencies are facing multiple challenges, including aging infrastructure, reduction in capacity of existing infrastructure, and availability of limited funds. Therefore, decision makers are required to think innovatively and develop inventive ways of using available funds. Maintenance investment decisions are generally made based on physical condition only. It is important to understand that spending money on public infrastructure is synonymous with spending money on people themselves. This also requires consideration of decision parameters, in addition to physical condition, such as strategic importance, socioeconomic contribution and infrastructure utilization. Consideration of multiple decision parameters for infrastructure maintenance investments can be beneficial in case of limited funding. Given this motivation, this dissertation presents a prototype decision support framework to evaluate trade-off, among competing infrastructures, that are candidates for infrastructure maintenance, repair and rehabilitation investments. Decision parameters' performances measured through various factors are combined to determine the integrated state of an infrastructure using Multi-Attribute Utility Theory (MAUT). The integrated state, cost and benefit estimates of probable maintenance actions are utilized alongside expert opinion to develop transition probability and reward matrices for each probable maintenance action for a particular candidate infrastructure. These matrices are then used as an input to the Markov Decision Process (MDP) for the finite-stage dynamic programming model to perform project (candidate)-level analysis to determine optimized maintenance strategies based on reward maximization. The outcomes of project (candidate)-level analysis are then utilized to perform network-level analysis taking the portfolio management approach to determine a suitable portfolio under budgetary constraints. The major decision support outcomes of the prototype framework include performance trend curves, decision logic maps, and a network-level maintenance investment plan for the upcoming years. The framework has been implemented with a set of bridges considered as a network with the assistance of the Pima County DOT, AZ. It is expected that the concept of this prototype framework can help infrastructure management agencies better manage their available funds for maintenance.

A Methodological Framework for Modeling Pavement Maintenance Costs for Projects with Performance-based Contracts

Performance-based maintenance contracts differ significantly from material and method-based contracts that have been traditionally used to maintain roads. Road agencies around the world have moved towards a performance-based contract approach because it offers several advantages like cost saving, better budgeting certainty, better customer satisfaction with better road services and conditions. Payments for the maintenance of road are explicitly linked to the contractor successfully meeting certain clearly defined minimum performance indicators in these contracts. Quantitative evaluation of the cost of performance-based contracts has several difficulties due to the complexity of the pavement deterioration process. Based on a probabilistic analysis of failures of achieving multiple performance criteria over the length of the contract period, an effort has been made to develop a model that is capable of estimating the cost of these performance-based contracts. One of the essential functions of such model is to predict performance of the pavement as accurately as possible. Prediction of future degradation of pavement is done using Markov Chain Process, which requires estimating transition probabilities from previous deterioration rate for similar pavements. Transition probabilities were derived using historical pavement condition rating data, both for predicting pavement deterioration when there is no maintenance, and for predicting pavement improvement when maintenance activities are performed. A methodological framework has been developed to estimate the cost of maintaining road based on multiple performance criteria such as crack, rut and, roughness. The application of the developed model has been demonstrated via a real case study of Miami Dade Expressways (MDX) using pavement condition rating data from Florida Department of Transportation (FDOT) for a typical performance-based asphalt pavement maintenance contract. Results indicated that the pavement performance model developed could predict the pavement deterioration quite accurately. Sensitivity analysis performed shows that the model is very responsive to even slight changes in pavement deterioration rate and performance constraints. It is expected that the use of this model will assist the highway agencies and contractors in arriving at a fair contract value for executing long term performance-based pavement maintenance works.

Systems of exchange values as tools for multi-agent organizations

This paper introduces systems of exchange values as tools for the organization of multi-agent systems. Systems of exchange values are defined on the basis of the theory of social exchanges, developed by Piaget and Homans. A model of social organization is proposed, where social relations are construed as social exchanges and exchange values are put into use in the support of the continuity of the performance of social exchanges. The dynamics of social organizations is formulated in terms of the regulation of exchanges of values, so that social equilibrium is connected to the continuity of the interactions. The concept of supervisor of social equilibrium is introduced as a centralized mechanism for solving the problem of the equilibrium of the organization The equilibrium supervisor solves such problem making use of a qualitative Markov Decision Process that uses numerical intervals for the representation of exchange values.

Exact Solution of Bayes and Minimax Change-Detection Problems

The challenge of detecting a change in the distribution of data is a sequential decision problem that is relevant to many engineering solutions, including quality control and machine and process monitoring. This dissertation develops techniques for exact solution of change-detection problems with discrete time and discrete observations. Change-detection problems are classified as Bayes or minimax based on the availability of information on the change-time distribution. A Bayes optimal solution uses prior information about the distribution of the change time to minimize the expected cost, whereas a minimax optimal solution minimizes the cost under the worst-case change-time distribution. Both types of problems are addressed. The most important result of the dissertation is the development of a polynomial-time algorithm for the solution of important classes of Markov Bayes change-detection problems. Existing techniques for epsilon-exact solution of partially observable Markov decision processes have complexity exponential in the number of observation symbols. A new algorithm, called constellation induction, exploits the concavity and Lipschitz continuity of the value function, and has complexity polynomial in the number of observation symbols. It is shown that change-detection problems with a geometric change-time distribution and identically- and independently-distributed observations before and after the change are solvable in polynomial time. Also, change-detection problems on hidden Markov models with a fixed number of recurrent states are solvable in polynomial time. A detailed implementation and analysis of the constellation-induction algorithm are provided. Exact solution methods are also established for several types of minimax change-detection problems. Finite-horizon problems with arbitrary observation distributions are modeled as extensive-form games and solved using linear programs. Infinite-horizon problems with linear penalty for detection delay and identically- and independently-distributed observations can be solved in polynomial time via epsilon-optimal parameterization of a cumulative-sum procedure. Finally, the properties of policies for change-detection problems are described and analyzed. Simple classes of formal languages are shown to be sufficient for epsilon-exact solution of change-detection problems, and methods for finding minimally sized policy representations are described.

SEQUENTIAL DECISIONS AND PREDICTIONS IN NATURAL LANGUAGE PROCESSING

Natural language processing has achieved great success in a wide range of ap- plications, producing both commercial language services and open-source language tools. However, most methods take a static or batch approach, assuming that the model has all information it needs and makes a one-time prediction. In this disser- tation, we study dynamic problems where the input comes in a sequence instead of all at once, and the output must be produced while the input is arriving. In these problems, predictions are often made based only on partial information. We see this dynamic setting in many real-time, interactive applications. These problems usually involve a trade-off between the amount of input received (cost) and the quality of the output prediction (accuracy). Therefore, the evaluation considers both objectives (e.g., plotting a Pareto curve). Our goal is to develop a formal understanding of sequential prediction and decision-making problems in natural language processing and to propose efficient solutions. Toward this end, we present meta-algorithms that take an existent batch model and produce a dynamic model to handle sequential inputs and outputs. Webuild our framework upon theories of Markov Decision Process (MDP), which allows learning to trade off competing objectives in a principled way. The main machine learning techniques we use are from imitation learning and reinforcement learning, and we advance current techniques to tackle problems arising in our settings. We evaluate our algorithm on a variety of applications, including dependency parsing, machine translation, and question answering. We show that our approach achieves a better cost-accuracy trade-off than the batch approach and heuristic-based decision- making approaches. We first propose a general framework for cost-sensitive prediction, where dif- ferent parts of the input come at different costs. We formulate a decision-making process that selects pieces of the input sequentially, and the selection is adaptive to each instance. Our approach is evaluated on both standard classification tasks and a structured prediction task (dependency parsing). We show that it achieves similar prediction quality to methods that use all input, while inducing a much smaller cost. Next, we extend the framework to problems where the input is revealed incremen- tally in a fixed order. We study two applications: simultaneous machine translation and quiz bowl (incremental text classification). We discuss challenges in this set- ting and show that adding domain knowledge eases the decision-making problem. A central theme throughout the chapters is an MDP formulation of a challenging problem with sequential input/output and trade-off decisions, accompanied by a learning algorithm that solves the MDP.

Threshold behaviour and final outcome of an epidemic on a random network with household structure

This paper considers a stochastic SIR (susceptible-infective-removed) epidemic model in which individuals may make infectious contacts in two ways, both within 'households' (which for ease of exposition are assumed to have equal size) and along the edges of a random graph describing additional social contacts. Heuristically-motivated branching process approximations are described, which lead to a threshold parameter for the model and methods for calculating the probability of a major outbreak, given few initial infectives, and the expected proportion of the population who are ultimately infected by such a major outbreak. These approximate results are shown to be exact as the number of households tends to infinity by proving associated limit theorems. Moreover, simulation studies indicate that these asymptotic results provide good approximations for modestly-sized finite populations. The extension to unequal sized households is discussed briefly.

Critical age-dependent branching Markov processes and their scaling limits

This paper studies:(i)the long-time behaviour of the empirical distribution of age and normalized position of an age-dependent critical branching Markov process conditioned on non-extinction;and (ii) the super-process limit of a sequence of age-dependent critical branching Brownian motions.

Supercritical age-dependent branching Markov processes and their scaling limits

This paper studies the long-time behavior of the empirical distribution of age and normalized position of an age-dependent supercritical branching Markov process. The motion of each individual during its life is a random function of its age. It is shown that the empirical distribution of the age and the normalized position of all individuals alive at time t converges as t -> infinity to a deterministic product measure.

Ergodicity and regularity of invariant measure for branching Markov processes with immigration

In this thesis we consider systems of finitely many particles moving on paths given by a strong Markov process and undergoing branching and reproduction at random times. The branching rate of a particle, its number of offspring and their spatial distribution are allowed to depend on the particle's position and possibly on the configuration of coexisting particles. In addition there is immigration of new particles, with the rate of immigration and the distribution of immigrants possibly depending on the configuration of pre-existing particles as well. In the first two chapters of this work, we concentrate on the case that the joint motion of particles is governed by a diffusion with interacting components. The resulting process of particle configurations was studied by E. Löcherbach (2002, 2004) and is known as a branching diffusion with immigration (BDI). Chapter 1 contains a detailed introduction of the basic model assumptions, in particular an assumption of ergodicity which guarantees that the BDI process is positive Harris recurrent with finite invariant measure on the configuration space. This object and a closely related quantity, namely the invariant occupation measure on the single-particle space, are investigated in Chapter 2 where we study the problem of the existence of Lebesgue-densities with nice regularity properties. For example, it turns out that the existence of a continuous density for the invariant measure depends on the mechanism by which newborn particles are distributed in space, namely whether branching particles reproduce at their death position or their offspring are distributed according to an absolutely continuous transition kernel. In Chapter 3, we assume that the quantities defining the model depend only on the spatial position but not on the configuration of coexisting particles. In this framework (which was considered by Höpfner and Löcherbach (2005) in the special case that branching particles reproduce at their death position), the particle motions are independent, and we can allow for more general Markov processes instead of diffusions. The resulting configuration process is a branching Markov process in the sense introduced by Ikeda, Nagasawa and Watanabe (1968), complemented by an immigration mechanism. Generalizing results obtained by Höpfner and Löcherbach (2005), we give sufficient conditions for ergodicity in the sense of positive recurrence of the configuration process and finiteness of the invariant occupation measure in the case of general particle motions and offspring distributions.

Multivariate Markov Process Models for the transmission of methicillin-resistant Staphylococcus Aureus in a hospital ward

Methicillin-resistant Staphylococcus Aureus (MRSA) is a pathogen that continues to be of major concern in hospitals. We develop models and computational schemes based on observed weekly incidence data to estimate MRSA transmission parameters. We extend the deterministic model of McBryde, Pettitt, and McElwain (2007, Journal of Theoretical Biology 245, 470–481) involving an underlying population of MRSA colonized patients and health-care workers that describes, among other processes, transmission between uncolonized patients and colonized health-care workers and vice versa. We develop new bivariate and trivariate Markov models to include incidence so that estimated transmission rates can be based directly on new colonizations rather than indirectly on prevalence. Imperfect sensitivity of pathogen detection is modeled using a hidden Markov process. The advantages of our approach include (i) a discrete valued assumption for the number of colonized health-care workers, (ii) two transmission parameters can be incorporated into the likelihood, (iii) the likelihood depends on the number of new cases to improve precision of inference, (iv) individual patient records are not required, and (v) the possibility of imperfect detection of colonization is incorporated. We compare our approach with that used by McBryde et al. (2007) based on an approximation that eliminates the health-care workers from the model, uses Markov chain Monte Carlo and individual patient data. We apply these models to MRSA colonization data collected in a small intensive care unit at the Princess Alexandra Hospital, Brisbane, Australia.

A Bayesian‐Markov process for reliability prediction

Accurate reliability prediction for large-scale, long lived engineering is a crucial foundation for effective asset risk management and optimal maintenance decision making. However, a lack of failure data for assets that fail infrequently, and changing operational conditions over long periods of time, make accurate reliability prediction for such assets very challenging. To address this issue, we present a Bayesian-Marko best approach to reliability prediction using prior knowledge and condition monitoring data. In this approach, the Bayesian theory is used to incorporate prior information about failure probabilities and current information about asset health to make statistical inferences, while Markov chains are used to update and predict the health of assets based on condition monitoring data. The prior information can be supplied by domain experts, extracted from previous comparable cases or derived from basic engineering principles. Our approach differs from existing hybrid Bayesian models which are normally used to update the parameter estimation of a given distribution such as the Weibull-Bayesian distribution or the transition probabilities of a Markov chain. Instead, our new approach can be used to update predictions of failure probabilities when failure data are sparse or nonexistent, as is often the case for large-scale long-lived engineering assets.