A Molecular-scale Programmable Stochastic Process Based On Resonance Energy Transfer Networks: Modeling And Applications

While molecular and cellular processes are often modeled as stochastic processes, such as Brownian motion, chemical reaction networks and gene regulatory networks, there are few attempts to program a molecular-scale process to physically implement stochastic processes. DNA has been used as a substrate for programming molecular interactions, but its applications are restricted to deterministic functions and unfavorable properties such as slow processing, thermal annealing, aqueous solvents and difficult readout limit them to proof-of-concept purposes. To date, whether there exists a molecular process that can be programmed to implement stochastic processes for practical applications remains unknown.

In this dissertation, a fully specified Resonance Energy Transfer (RET) network between chromophores is accurately fabricated via DNA self-assembly, and the exciton dynamics in the RET network physically implement a stochastic process, specifically a continuous-time Markov chain (CTMC), which has a direct mapping to the physical geometry of the chromophore network. Excited by a light source, a RET network generates random samples in the temporal domain in the form of fluorescence photons which can be detected by a photon detector. The intrinsic sampling distribution of a RET network is derived as a phase-type distribution configured by its CTMC model. The conclusion is that the exciton dynamics in a RET network implement a general and important class of stochastic processes that can be directly and accurately programmed and used for practical applications of photonics and optoelectronics. Different approaches to using RET networks exist with vast potential applications. As an entropy source that can directly generate samples from virtually arbitrary distributions, RET networks can benefit applications that rely on generating random samples such as 1) fluorescent taggants and 2) stochastic computing.

By using RET networks between chromophores to implement fluorescent taggants with temporally coded signatures, the taggant design is not constrained by resolvable dyes and has a significantly larger coding capacity than spectrally or lifetime coded fluorescent taggants. Meanwhile, the taggant detection process becomes highly efficient, and the Maximum Likelihood Estimation (MLE) based taggant identification guarantees high accuracy even with only a few hundred detected photons.

Meanwhile, RET-based sampling units (RSU) can be constructed to accelerate probabilistic algorithms for wide applications in machine learning and data analytics. Because probabilistic algorithms often rely on iteratively sampling from parameterized distributions, they can be inefficient in practice on the deterministic hardware traditional computers use, especially for high-dimensional and complex problems. As an efficient universal sampling unit, the proposed RSU can be integrated into a processor / GPU as specialized functional units or organized as a discrete accelerator to bring substantial speedups and power savings.

Zero miss distance guidance using feedforward and periodic control

There have been attempts at obtaining robust guidance laws to ensure zero miss distance (ZMD) for interceptors with parametric uncertainties. All these laws require the plant to be of minimum phase type to enable the overall guidance loop transfer function to satisfy strict positive realness (SPR). The SPR property implies absolute stability of the closed loop system, and has been shown in the literature to lead to ZMD because it avoids saturation of lateral acceleration. In these works higher order interceptors are reduced to lower order equivalent models for which control laws are designed to ensure ZMD. However, it has also been shown that when the original system with right half plane (RHP) zeros is considered, the resulting miss distances, using such strategies, can be quite high. In this paper, an alternative approach using the circle criterion establishes the conditions for absolute stability of the guidance loop and relaxes the conservative nature of some earlier results arising from assumption of in�nite engagement time. Further, a feedforward scheme in conjunction with a lead-lag compensator is used as one control strategy while a generalized sampled hold function is used as a second strategy, to shift the RHP transmission zeros, thereby achieving ZMD. It is observed that merely shifting the RHP zero(s) to the left half plane reduces miss distances signi�cantly even when no additional controllers are used to ensure SPR conditions.

Analysis of optical systems with extended depth of field using the Wigner distribution function

We describe the use of a Wigner distribution function approach for exploring the problem of extending the depth of field in a hybrid imaging system. The Wigner distribution function, in connection with the phase-space curve that formulates a joint phase-space description of an optical field, is employed as a tool to display and characterize the evolving behavior of the amplitude point spread function as a wave propagating along the optical axis. It provides a comprehensive exhibition of the characteristics for the hybrid imaging system in extending the depth of field from both wave optics and geometrical optics. We use it to analyze several well-known optical designs in extending the depth of field from a new viewpoint. The relationships between this approach and the earlier ambiguity function approach are also briefly investigated. (c) 2006 Optical Society of America.

Laminar Cortical Dynamics of Cognitive and Motor Working Memory, Sequence Learning and Performance: Toward a Unified Theory of How the Cerebral Cortex Works

How do the layered circuits of prefrontal and motor cortex carry out working memory storage, sequence learning, and voluntary sequential item selection and performance? A neural model called LIST PARSE is presented to explain and quantitatively simulate cognitive data about both immediate serial recall and free recall, including bowing of the serial position performance curves, error-type distributions, temporal limitations upon recall, and list length effects. The model also qualitatively explains cognitive effects related to attentional modulation, temporal grouping, variable presentation rates, phonemic similarity, presentation of non-words, word frequency/item familiarity and list strength, distracters and modality effects. In addition, the model quantitatively simulates neurophysiological data from the macaque prefrontal cortex obtained during sequential sensory-motor imitation and planned performance. The article further develops a theory concerning how the cerebral cortex works by showing how variations of the laminar circuits that have previously clarified how the visual cortex sees can also support cognitive processing of sequentially organized behaviors.

Addressing Bed Costs for the Elderly: A New Methodology for Modelling Patient Outcomes and Length of Stay

The proportion of elderly in the population has dramatically increased and will continue to do so for at least the next 50 years. Medical resources throughout the world are feeling the added strain of the increasing proportion of elderly in the population. The effective care of elderly patients in hospitals may be enhanced by accurately modelling the length of stay of the patients in hospital and the associated costs involved. This paper examines previously developed models for patient length of stay in hospital and describes the recently developed conditional phase-type distribution (C-Ph) to model patient duration of stay in relation to explanatory patient variables. The Clinics data set was used to demonstrate the C-Ph methodology. The resulting model highlighted a strong relationship between Barthel grade, patient outcome and length of stay showing various groups of patient behaviour. The patients who stay in hospital for a very long time are usually those that consume the largest amount of hospital resources. These have been identified as the patients whose resulting outcome is transfer. Overall, the majority of transfer patients spend a considerably longer period of time in hospital compared to patients who die or are discharged home. The C-Ph model has the potential for considering costs where different costs are attached to the various phases or subgroups of patients and the anticipated cost of care estimated in advance. It is hoped that such a method will lead to the successful identification of the most cost effective case-mix management of the hospital ward.

Rheological, mechanical and membrane penetration properties of novel dual drug systems for percutaneous delivery

In this study it has been demonstrated that mixtures of two solid drugs, ibuprofen and methyl nicotinate, with different but complementary pharmacological activities and which exist as a single liquid phase over a wide composition range at skin temperature, can be formulated as o/w emulsions without the use of an additional hydrophobic carrier. These novel dual drug systems provided significantly enhanced in vitro penetration rates through a model lipophilic barrier membrane compared to conventional individual formulations of each active. Thus, for ibuprofen, drug penetration flux enhancements of three- and 10-fold were observed when compared to an aqueous ibuprofen suspension and a commercial alcohol-based ibuprofen formulation, respectively. Methyl nicotinate penetration rates were shown to be similar for aqueous gels and emulsified systems. Mechanisms explaining these observations are proposed. Novel dual drug formulations of ibuprofen and methyl nicotinate, formulated within the liquid range at skin temperature, were investigated by oscillatory rheology and texture profile analysis. demonstrating the effects of drug and viscosity enhancer concentrations, and disperse phase type upon the rheological, mechanical and drug penetration properties of these systems. (C) 2000 Elsevier Science B.V. All rights reserved.

Using the hidden Markov model to capture quality of care in Lombardy geriatric wards

Quality of care is an important aspect of healthcare monitoring, which is used to ensure that the healthcare system is delivering care of the highest standard. With populations growing older there is an increased urgency in making sure that the healthcare delivered is of the highest standard. Healthcare providers are under increased pressure to ensure that this is the case with public and government demand expecting a healthcare system of the highest quality. Modelling quality of care is difficult to measure due to the many ways of defining it. This paper introduces a potential model which could be used to take quality of care into account when modelling length of stay. The Coxian phase-type distribution is used to model length of stay and the associated quality of care incorporated into the Coxian using a Hidden Markov model. Covariates are also introduced to determine their impact on the hidden level to find out what potentially can affect quality of care. This model is applied to geriatic patient data from the Lombardy region of Italy. The results obtained highlighted that bed numbers and the type of hospital (public or private) can have an effect on the quality of care delivered.

The structural effects of divalent cations and insulin on phospholipid model membranes /

It is well accepted that structural studies with model membranes are of considerable value in understanding the structure of biological membranes. Many studies with models of pure phospholipids have been done; but the effects of divalent cations and protein on these models would make these studies more applicable to intact membrane. The present study, performed with above view, is a structural analysis of divalent io~cardio1ipin complexes using the technique of x-ray diffraction. Cardiolipin, precipitated from dilute solution by divalent ionscalcium, magnesium and barium, contains little water and the structure formed is similar to the structure of pure cardiolipin with low water content. The calcium-cardiolipin complex forms a pure hexagonal type II phase that exists from 40 to 400 C. The molar ratio of calcium and cardiolipin in the complex is 1 : 1. Cardiolipin, precipitated with magnesium and barium forms two co-existing phases, lamellar and hexagonal, the relative quantity of the two phases being dependent on temperature. The hexagonal phase type II consisting of water filled channels formed by adding calcium to cardiolipin may have a remarkable permeability property in intact membrane. Pure cardiolipin and insulin at pH 3.0 and 4.0 precipitate but form no organised structure. Lecithin/cardiolipin and insulin precipitated at pH 3.0 give a pure lamellar phase. As the lecithin/cardiolipin molar ratio changes from 93/7 to SO/50, (a) the repeat distance of the lamellar changes from 72.8 X to 68.2 A; (b) the amount of protein bound increases in such a way that cardiolipin/insulin molar ratio in the complex reaches a maximum constant value at lecithin/cardiolipin molar ratio 70/30. A structural model based on these data shows that the molecular arrangement of lipid and protein is a lipid bilayer coated with protein molecules. The lipid-protein interaction is chiefly electrostatic and little, if any, hydrophobic bonding occurs in this particular system. So, the proposed model is essentially the same as Davson-Daniellifs model of biological membrane.

Some Applications of Markov Additive Processes as Models in Insurance and Financial Mathematics

Cette thèse est principalement constituée de trois articles traitant des processus markoviens additifs, des processus de Lévy et d'applications en finance et en assurance. Le premier chapitre est une introduction aux processus markoviens additifs (PMA), et une présentation du problème de ruine et de notions fondamentales des mathématiques financières. Le deuxième chapitre est essentiellement l'article "Lévy Systems and the Time Value of Ruin for Markov Additive Processes" écrit en collaboration avec Manuel Morales et publié dans la revue European Actuarial Journal. Cet article étudie le problème de ruine pour un processus de risque markovien additif. Une identification de systèmes de Lévy est obtenue et utilisée pour donner une expression de l'espérance de la fonction de pénalité actualisée lorsque le PMA est un processus de Lévy avec changement de régimes. Celle-ci est une généralisation des résultats existant dans la littérature pour les processus de risque de Lévy et les processus de risque markoviens additifs avec sauts "phase-type". Le troisième chapitre contient l'article "On a Generalization of the Expected Discounted Penalty Function to Include Deficits at and Beyond Ruin" qui est soumis pour publication. Cet article présente une extension de l'espérance de la fonction de pénalité actualisée pour un processus subordinateur de risque perturbé par un mouvement brownien. Cette extension contient une série de fonctions escomptée éspérée des minima successives dus aux sauts du processus de risque après la ruine. Celle-ci a des applications importantes en gestion de risque et est utilisée pour déterminer la valeur espérée du capital d'injection actualisé. Finallement, le quatrième chapitre contient l'article "The Minimal entropy martingale measure (MEMM) for a Markov-modulated exponential Lévy model" écrit en collaboration avec Romuald Hervé Momeya et publié dans la revue Asia-Pacific Financial Market. Cet article présente de nouveaux résultats en lien avec le problème de l'incomplétude dans un marché financier où le processus de prix de l'actif risqué est décrit par un modèle exponentiel markovien additif. Ces résultats consistent à charactériser la mesure martingale satisfaisant le critère de l'entropie. Cette mesure est utilisée pour calculer le prix d'une option, ainsi que des portefeuilles de couverture dans un modèle exponentiel de Lévy avec changement de régimes.

Stochastic Modelling Using Markov Chains

Department of Statistics, Cochin University of Science and Technology

On Queues with Interruptions and Repeat or Resumption of Service

This thesis entitled' On Queues with Interruptions and Repeat or Resumption of Service' introduces several new concepts into queues with service interruption. It is divided into Seven chapters including an introductory chapter. The following are keywords that we use in this thesis: Phase type (PH) distribution, Markovian Arrival Process (MAP), Geometric Distribution, Service Interruption, First in First out (FIFO), threshold random variable and Super threshold random variable. In the second chapter we introduce a new concept called the 'threshold random variable' which competes with interruption time to decide whether to repeat or resume the interrupted service after removal of interruptions. This notion generalizes the work reported so far in queues with service interruptions. In chapter 3 we introduce the concept of what is called 'Super threshold clock' (a random variable) which keeps track of the total interruption time of a customer during his service except when it is realized before completion of interruption in some cases to be discussed in this thesis and in other cases it exactly measures the duration of all interruptions put together. The Super threshold clock is OIl whenever the service is interrupted and is deactivated when service is rendered. Throughout this thesis the first in first out service discipline is followed except for priority queues.

Queues with Customer Induced Interruption

In this thesis we have introduced and studied the notion of self interruption of service by customers. Service interruption in queueing systems have been extensively discussed in literature (see, Krishnamoorthy, Pramod and Chakravarthy [38]) for the most recent survey. So far all work reported deal with cases in which service interruptions are generated by sources other than customers. However, there are situations where interruptions are due to the customers rather than the system. Such situations are especially arise at doctors clinic, banks, reservation counter etc. Our attempt is to quantify a few of such problems. Systematically we have proceed from single server queue (in Chapter 2) to multi-server queues (Chapter 3). In Chapte 4, we have studied a very general multiserver queueing model with service interruption and protection of service phases. We also introduced customer interruption in a retrial setup (in Chapter 5). All models (from Chapter 2 to Chapter 4) that were analyzed involve 'non-preemptive priority' for interrupted customers where as in the model discussed in Chapter 5 interruption of service by customers is not encouraged. So the interrupted customers cannot access the server as long as there are primary customers in the system. In Chapter 5 we have obtained an explicit expression for the stability condition of the system. In all models analyzed in this thesis, we have assumed that no more than one interruption is allowed for a customer while in service. Since the models are not analytically tractable, a large number of numerical illustrations were given in each chapter it illustrate the working of the systems. We can extend the models discussed in this thesis to several directions. For example some of the models can be analyzed with both server induced and customer induced interruptions the results for which are not available till date. Another possible extension of work is to the case where there is no bound on the number of interruptions a customer is permitted to have before service completion. More complex is the case where a customer is permitted to have a nite number (K ≥ 2) of We can extend the models discussed in this thesis to several directions.

Analysis of some Stochastic models in inventories and Queues

The thesis entitled Analysis of Some Stochastic Models in Inventories and Queues. This thesis is devoted to the study of some stochastic models in Inventories and Queues which are physically realizable, though complex. It contains a detailed analysis of the basic stochastic processes underlying these models. In this thesis, (s,S) inventory systems with nonidentically distributed interarrival demand times and random lead times, state dependent demands, varying ordering levels and perishable commodities with exponential life times have been studied. The queueing system of the type Ek/Ga,b/l with server vacations, service systems with single and batch services, queueing system with phase type arrival and service processes and finite capacity M/G/l queue when server going for vacation after serving a random number of customers are also analysed. The analogy between the queueing systems and inventory systems could be exploited in solving certain models. In vacation models, one important result is the stochastic decomposition property of the system size or waiting time. One can think of extending this to the transient case. In inventory theory, one can extend the present study to the case of multi-item, multi-echelon problems. The study of perishable inventory problem when the commodities have a general life time distribution would be a quite interesting problem. The analogy between the queueing systems and inventory systems could be exploited in solving certain models.

Epsilon Birnbaum-Saunders distribution family: properties and inference

In this paper we introduce a new extension for the Birnbaum-Saunder distribution based on the family of the epsilon-skew-symmetric distributions studied in Arellano-Valle et al. (J Stat Plan Inference 128(2):427-443, 2005). The extension allows generating Birnbaun-Saunders type distributions able to deal with extreme or outlying observations (Dupuis and Mills, IEEE Trans Reliab 47:88-95, 1998). Basic properties such as moments and Fisher information matrix are also studied. Results of a real data application are reported illustrating good fitting properties of the proposed model.

Estrógenos em água: otimização da extração em fase sólida utilizando ferramentas quimiométricas

Muitos métodos analíticos estão sendo desenvolvidos visando à determinação de contaminantes orgânicos, especialmente alteradores endócrinos. Tais métodos baseiam-se geralmente na extração em fase sólida (SPE) seguida por determinação cromatográfica (CG ou HPLC). No presente trabalho utilizou-se ferramentas quimiométricas no processo de SPE para avaliar os principais fatores que influenciam tal processo e as interações entre os mesmos. Foram analisadas matrizes de água subterrânea fortificada com hormônios (17 b estradiol, estrona e 17 b etinilestradiol) e a determinação analítica foi feita por HPLC/Fluorescência. Um planejamento fatorial completo foi utilizado. Os fatores escolhidos incluíram: condicionamento da fase sólida, concentração dos analitos, volume da amostra e solvente de eluição. As melhores condições obtidas foram: 500 mL da amostra, condicionamento da fase sólida (C18) com acetona (4mL), metanol (6 mL) e água pH 3(10 mL), e eluição dos analitos com 4 mL de acetona.