Fault identification through the combination of symbolic conflict recognition and Markov Chain-aided belief revision

F. Smith and Q. Shen. Fault identification through the combination of symbolic conflict recognition and Markov Chain-aided belief revision. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 34(5):649-663, 2004.

Quantum behavior in mesoscopic systems

In this thesis I present the work done during my PhD. The Thesis is divided into two parts; in the first one I present the study of mesoscopic quantum systems whereas in the second one I address the problem of the definition of Markov regime for quantum system dynamics. The first work presented is the study of vortex patterns in (quasi) two dimensional rotating Bose Einstein condensates (BECs). I consider the case of an anisotropy trapping potential and I shall show that the ground state of the system hosts vortex patterns that are unstable. In a second work I designed an experimental scheme to transfer entanglement from two entangled photons to two BECs. This work is meant to propose a feasible experimental set up to bring entanglement from microscopic to macroscopic systems for both the study of fundamental questions (quantum to classical transition) and technological applications. In the last work of the first part another experimental scheme is presented in order to detect coherences of a mechanical oscillator which is assumed to have been previously cooled down to the quantum regime. In this regime in fact the system can rapidly undergo decoherence so that new techniques have to be employed in order to detect and manipulate their states. In the scheme I propose a micro-mechanical oscillator is coupled to a BEC and the detection is performed by monitoring the BEC with a negligible back-action on the cantilever. In the second part of the thesis I give a definition of Markov regime for open quantum dynamics. The importance of such definition comes from both the mathematical description of the system dynamics and from the understanding of the role played by the environment in the evolution of an open system. In the Markov regime the mathematical description can be simplified and the role of the environment is a passive one.

Regularity of invariant densities for 1D systems with random switching

© 2015 IOP Publishing Ltd & London Mathematical Society.This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove the smoothness of the invariant densities away from critical points and describe the asymptotics of the invariant densities at critical points.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Positive dilations of piecewise monotonic Markov maps

We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems.

The Effects of Anti-Hypertensive Drugs Evaluated Using Markov Modelling for Northern Ireland Chronic Kidney Disease Patients

The aim of this paper is to use Markov modelling to
investigate survival for particular types of kidney patients
in relation to their exposure to anti-hypertensive treatment
drugs. In order to monitor kidney function an intuitive three
point assessment is proposed through the collection of blood
samples in relation to Chronic Kidney Disease for Northern
Ireland patients. A five state Markov Model was devised
using specific transition probabilities for males and
females over all age groups. These transition probabilities
were then adjusted appropriately using relative risk scores
for the event death for different subgroups of patients. The
model was built using TreeAge software package in order to
explore the effects of anti-hypertensive drugs on patients.

Algorithms for Hidden Markov Models With Imprecisely Specified Parameters

Hidden Markov models (HMMs) are widely used models for sequential data. As with other probabilistic graphical models, they require the specification of precise probability values, which can be too restrictive for some domains, especially when data are scarce or costly to acquire. We present a generalized version of HMMs, whose quantification can be done by sets of, instead of single, probability distributions. Our models have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. Efficient inference algorithms are developed to address standard HMM usage such as the computation of likelihoods and most probable explanations. Experiments with real data show that the use of imprecise probabilities leads to more reliable inferences without compromising efficiency.

A Continuous Time Markov Chain Based Sequential Analytical Approach for Composite Power System Reliability Assessment

This paper proposes a continuous time Markov chain (CTMC) based sequential analytical approach for composite generation and transmission systems reliability assessment. The basic idea is to construct a CTMC model for the composite system. Based on this model, sequential analyses are performed. Various kinds of reliability indices can be obtained, including expectation, variance, frequency, duration and probability distribution. In order to reduce the dimension of the state space, traditional CTMC modeling approach is modified by merging all high order contingencies into a single state, which can be calculated by Monte Carlo simulation (MCS). Then a state mergence technique is developed to integrate all normal states to further reduce the dimension of the CTMC model. Moreover, a time discretization method is presented for the CTMC model calculation. Case studies are performed on the RBTS and a modified IEEE 300-bus test system. The results indicate that sequential reliability assessment can be performed by the proposed approach. Comparing with the traditional sequential Monte Carlo simulation method, the proposed method is more efficient, especially in small scale or very reliable power systems.

Arc exchange systems and renormalization

We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.

Stochastic processes and their applications semi-markov analysis of some inventory and queuing problems

This thesis analyses certain problems in Inventories and Queues. There are many situations in real-life where we encounter models as described in this thesis. It analyses in depth various models which can be applied to production, storag¢, telephone traffic, road traffic, economics, business administration, serving of customers, operations of particle counters and others. Certain models described here is not a complete representation of the true situation in all its complexity, but a simplified version amenable to analysis. While discussing the models, we show how a dependence structure can be suitably introduced in some problems of Inventories and Queues. Continuous review, single commodity inventory systems with Markov dependence structure introduced in the demand quantities, replenishment quantities and reordering levels are considered separately. Lead time is assumed to be zero in these models. An inventory model involving random lead time is also considered (Chapter-4). Further finite capacity single server queueing systems with single/bulk arrival, single/bulk services are also discussed. In some models the server is assumed to go on vacation (Chapters 7 and 8). In chapters 5 and 6 a sort of dependence is introduced in the service pattern in some queuing models.

Investigations on Stochastic Storage Systems with Positive Service Time

In this thesis the queueing-inventory models considered are analyzed as continuous time Markov chains in which we use the tools such as matrix analytic methods. We obtain the steady-state distributions of various queueing-inventory models in product form under the assumption that no customer joins the system when the inventory level is zero. This is despite the strong correlation between the number of customers joining the system and the inventory level during lead time. The resulting quasi-birth-anddeath (QBD) processes are solved explicitly by matrix geometric methods

Markov Process Modeling of A System Under WIPLOAD Control

This paper analyzes a proposed release controlmethodology, WIPLOAD Control (WIPLCtrl), using a transfer line case modeled by Markov process modeling methodology. The performance of WIPLCtrl is compared with that of CONWIP under 13 system configurations in terms of throughput, average inventory level, as well as average cycle time. As a supplement to the analytical model, a simulation model of the transfer line is used to observe the performance of the release control methodologies on the standard deviation of cycle time. From the analysis, we identify the system configurations in which the advantages of WIPLCtrl could be observed.

Modeling and Analysis of Two-Part Type Manufacturing Systems

This paper presents a model and analysis of a synchronous tandem flow line that produces different part types on unreliable machines. The machines operate according to a static priority rule, operating on the highest priority part whenever possible, and operating on lower priority parts only when unable to produce those with higher priorities. We develop a new decomposition method to analyze the behavior of the manufacturing system by decomposing the long production line into small analytically tractable components. As a first step in modeling a production line with more than one part type, we restrict ourselves to the case where there are two part types. Detailed modeling and derivations are presented with a small two-part-type production line that consists of two processing machines and two demand machines. Then, a generalized longer flow line is analyzed. Furthermore, estimates for performance measures, such as average buffer levels and production rates, are presented and compared to extensive discrete event simulation. The quantitative behavior of the two-part type processing line under different demand scenarios is also provided.