In this thesis, we present symbolic implementation techniques for model checking probabilistic timed automata as models for systems, for example, communication networks and randomised distributed algorithms. Given a system model as probabilistic timed automata and a specification, such as, “a leader will be elected within 5 time units with probability 0.999” and “the message can be successfully...

Prospective pregnancy studies are a valuable source of longitudinal data on menstrual cycle length. However, care is needed when making inferences of such renewal processes. For example, accounting for the sampling plan is necessary for unbiased estimation of the menstrual cycle length distribution for the study population. If couples can enroll when they learn of the study as opposed to waitin...

A backward biorthogonalization approach is proposed, which modifies biorthogonal functions so as to generate orthogonal projections onto a reduced subspace. The technique is relevant to problems amenable to be represented by a general linear model. In particular, problems of data compression, noise reduction and sparse representations may be tackled by the proposed approach.

Within a Markovian complete financial market, we consider the problem of hedging a Bermudan option with a given probability. Using stochastic target and duality arguments, we derive a backward algorithm for the Fenchel transform of the pricing function. This algorithm is similar to the usual American backward induction, except that it requires two additional Fenchel transformations at each exer...

We present a connectionist model of false memories called the Associative Self-Organizing Network (ASON) model. Four mechanisms underlying the Constructive Memory Framework (CMF) guide the design of the ASON model, a connectionist operationalisation of the CMF. Simulation studies of experiments in the DRM paradigm reveal the ASON model to exhibit false memories. In addition, the effects of Mean...

We apply the optimization algorithm Adaptive Simulated Annealing (ASA) to the problem of analyzing data on a large population and selecting the best model to predict the probability that an individual with various traits will have a particular disease. We compare ASA with traditional forward and backward regression on computer simulated data. We find that the traditional methods of modeling are...

We develop an analytic model for finding the statistics of polarization-dependent gain (PDG) in fiber-based Raman amplifiers. We use it to find an analytic form for the probability distribution of PDG and study how the mean PDG and the variance of PDG fluctuations depend on the PMD parameter. We show that mean PDG as well as PDG fluctuations are reduced by approximately a factor of 30 in the ca...

A mixed-framework adaptive arithmetic coding technique is introduced in which the probability estimation process dynamically switches among a set of allowed models; the sequence of model choices is determined jointly with the relative data segmen-tation to yield the optimal coding performance for the given set of predictors. A speciic application is detailed in which the arithmetic coder can sw...

OF THE DISSERTATION Two-Stage Portfolio Optimization with Higher-Order Conditional Measures of Risk by Sıtkı Gülten Dissertation Director: Dr. Andrzej Ruszczyński In this study, an application of novel risk modeling and optimization techniques to daily portfolio management will be described. In the first part, I develop and compare specialized methods for scenario generation and scenario tree c...

This paper presents a new prediction model for predicting when an online customer leaves a current page and which next Web page the customer will visit. The model can forecast the total number of visits of a given Web page by all incoming users at the same time. The prediction technique can be used as a component for many Web based applications . The prediction model regards a Web browsing sess...