An algebraic operator approach to the analysis of Gerber-Shiu functions

We introduce an algebraic operator framework to study discounted penalty functions in renewal risk models. For inter-arrival and claim size distributions with rational Laplace transform, the usual integral equation is transformed into a boundary value problem, which is solved by symbolic techniques. The factorization of the differential operator can be lifted to the level of boundary value problems, amounting to iteratively solving first-order problems. This leads to an explicit expression for the Gerber-Shiu function in terms of the penalty function.

INTERMED predicts non-return to work in an occupational rehabilitation setting for individuals with orthopaedic trauma-Part I

Introduction.- Knowledge of predictors of an unfavourable outcome, e.g. non-return to work after an injury enables to identify patients at risk and to target interventions for modifiable predictors. It has been recently shown that INTERMED; a tool to measure biopsychosocial complexity in four domains (biologic, psychologic, social and care, with a score between 0-60 points) can be useful in this context. The aim of this study was to set up a predictive model for non-return to work using INTERMED in patients in vocational rehabilitation after orthopaedic injury.Patients and methods.- In this longitudinal prospective study, the cohort consisted of 2156 consecutively included inpatients with orthopaedic trauma attending a rehabilitation hospital after a work, traffic or sport related injury. Two years after discharge, a questionnaire regarding return to work was sent (1502 returned their questionnaires). In addition to INTERMED, 18 predictors known at baseline of the rehabilitation were selected based on previous research. A multivariable logistic regression was performed.Results.- In the multivariate model, not-returning to work at 2 years was significantly predicted by the INTERMED: odds-ratio (OR) 1.08 (95% confidence interval, CI [1.06; 1.11]) for a one point increase in scale; by qualified work-status before the injury OR = 0.74, CI (0.54; 0.99), by using French as preferred language OR = 0.60, CI (0.45; 0.80), by upper-extremity injury OR = 1.37, CI (1.03; 1.81), by higher education (> 9 years) OR = 0.74, CI (0.55; 1.00), and by a 10 year increase in age OR = 1.15, CI (1.02; 1.29). The area under the receiver-operator-characteristics curve (ROC)-curve was 0.733 for the full model (INTERMED plus 18 variables).Discussion.- These results confirm that the total score of the INTERMED is a significant predictor for return to work. The full model with 18 predictors combined with the total score of INTERMED has good predictive value. However, the number of variables (19) to measure is high for the use as screening tool in a clinic.

Enhanced pulse propagation in non-linear arrays of oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

INTERMED predicts non-return to work in an occupational rehabilitation setting for individuals with orthopaedic trauma-part 2

Introduction.- The model presented in part I (19 predictors) had good predictive values for non-return to work 2 years after vocational rehabilitation for orthopaedic trauma. However, the number of predictors is high for the detection of patients at risk in a clinic. For example, the INTERMED for itself consists of 20 questions and needs 20 minutes to be filled in. For this reason, the aim of this study was to compare the predictive value of different models for the prediction of non-return to work.Patients and methods.- In this longitudinal prospective study, the cohort consisted of 2156 included inpatients with orthopaedic trauma attending a rehabilitation hospital after a work, traffic, sport or leisure related injury. Two years after discharge, 1502 patients returned a questionnaire regarding return to work. We compared the area under the receiver-operator-characteristics curve (ROC) between different models: INTERMED total score, the 4 partial INTERMED scores, the items of the most predictive partial score; with or without confounders.Results.- The ROC for the total score of the INTERMED plus the five confounders of the of the part one (qualified work, speaking French, lesion of upper extremity, education and age) was 0.72. The sole partial INTERMED score to predict return to work was the social sub score. The ROC for the five items of the latter sub score of the INTERMED was 0.69. The ROC for the five items of the social subscale of the INTERMED combined with five predictors was 0.73. This was significantly better than the use of only the five items from INTERMED alone (delta 0.034; 95% CI 0.017 to .050). The model presented in part I (INTERMED total score plus 18 predictors) was not significantly better than the five items INTERMED social score plus five confounders.Discussion.- The use of a model with ten variables (INTERMED social five items plus five confounders) has good predictive value to detect patients not returning to work after vocational rehabilitation after orthopaedic trauma. The parsimony of this model facilitates its use in a clinic for the detection of patients at risk.

Non-Markovian dynamics and quantum information probes

This Thesis discusses the phenomenology of the dynamics of open quantum systems marked by non-Markovian memory effects. Non-Markovian open quantum systems are the focal point of a flurry of recent research aiming to answer, e.g., the following questions: What is the characteristic trait of non-Markovian dynamical processes that discriminates it from forgetful Markovian dynamics? What is the microscopic origin of memory in quantum dynamics, and how can it be controlled? Does the existence of memory effects open new avenues and enable accomplishments that cannot be achieved with Markovian processes? These questions are addressed in the publications forming the core of this Thesis with case studies of both prototypical and more exotic models of open quantum systems. In the first part of the Thesis several ways of characterizing and quantifying non-Markovian phenomena are introduced. Their differences are then explored using a driven, dissipative qubit model. The second part of the Thesis focuses on the dynamics of a purely dephasing qubit model, which is used to unveil the origin of non-Markovianity for a wide class of dynamical models. The emergence of memory is shown to be strongly intertwined with the structure of the spectral density function, as further demonstrated in a physical realization of the dephasing model using ultracold quantum gases. Finally, as an application of memory effects, it is shown that non- Markovian dynamical processes facilitate a novel phenomenon of timeinvariant discord, where the total quantum correlations of a system are frozen to their initial value. Non-Markovianity can also be exploited in the detection of phase transitions using quantum information probes, as shown using the physically interesting models of the Ising chain in a transverse field and a Coulomb chain undergoing a structural phase transition.

Comparison of non-HDL cholesterol and waist circumference vs. triglyceride levels and waist circumference in predicting coronary heart disease risk

BACKGROUND: Dyslipidemia is recognized as a major cause of coronary heart disease (CHD). Emerged evidence suggests that the combination of triglycerides (TG) and waist circumference can be used to predict the risk of CHD. However, considering the known limitations of TG, non-high-density lipoprotein (non-HDL = Total cholesterol - HDL cholesterol) cholesterol and waist circumference model may be a better predictor of CHD. PURPOSE: The Framingham Offspring Study data were used to determine if combined non-HDL cholesterol and waist circumference is equivalent to or better than TG and waist circumference (hypertriglyceridemic waist phenotype) in predicting risk of CHD. METHODS: A total of3,196 individuals from Framingham Offspring Study, aged ~ 40 years old, who fasted overnight for ~ 9 hours, and had no missing information on nonHDL cholesterol, TG levels, and waist circumference measurements, were included in the analysis. Receiver Operator Characteristic Curve (ROC) Area Under the Curve (AUC) was used to compare the predictive ability of non-HDL cholesterol and waist circumference and TG and waist circumference. Cox proportional-hazards models were used to examine the association between the joint distributions of non-HDL cholesterol, waist circumference, and non-fatal CHD; TG, waist circumference, and non-fatal CHD; and the joint distribution of non-HDL cholesterol and TG by waist circumference strata, after adjusting for age, gender, smoking, alcohol consumption, diabetes, and hypertension status. RESULTS: The ROC AUC associated with non-HDL cholesterol and waist circumference and TG and waist circumference are 0.6428 (CI: 0.6183, 0.6673) and 0.6299 (CI: 0.6049, 0.6548) respectively. The difference in the ROC AVC is 1.29%. The p-value testing if the difference in the ROC AVCs between the two models is zero is 0.10. There was a strong positive association between non-HDL cholesterol and the risk for non-fatal CHD within each TO levels than that for TO levels within each level of nonHDL cholesterol, especially in individuals with high waist circumference status. CONCLUSION: The results suggest that the model including non-HDL cholesterol and waist circumference may be superior at predicting CHD compared to the model including TO and waist circumference.

The Fast Regulation of Photosynthesis in Diatoms: an inquiry into the physiological and physical origins of non-photochemical chlorophyll fluorescence quenching.

Diatoms are renowned for their robust ability to perform NPQ (Non-Photochemical Quenching of chlorophyll fluorescence) as a dissipative response to heightened light stress on photosystem II, plausibly explaining their dominance over other algal groups in turbulent light environs. Their NPQ mechanism has been principally attributed to a xanthophyll cycle involving the lumenal pH regulated reversible de-epoxidation of diadinoxanthin. The principal goal of this dissertation is to reveal the physiological and physical origins and consequences of the NPQ response in diatoms during short-term transitions to excessive irradiation. The investigation involves diatom species from different originating light environs to highlight the diversity of diatom NPQ and to facilitate the detection of core mechanisms common among the diatoms as a group. A chiefly spectroscopic approach was used to investigate NPQ in diatom cells. Prime methodologies include: the real time monitoring of PSII excitation and de-excitation pathways via PAM fluorometry and pigment interconversion via transient absorbance measurements, the collection of cryogenic absorbance spectra to measure pigment energy levels, and the collection of cryogenic fluorescence spectra and room temperature picosecond time resolved fluorescence decay spectra to study excitation energy transfer and dissipation. Chemical inhibitors that target the trans-thylakoid pH gradient, the enzyme responsible for diadinoxanthin de-epoxidation, and photosynthetic electron flow were additionally used to experimentally manipulate the NPQ response. Multifaceted analyses of the NPQ responses from two previously un-photosynthetically characterised species, Nitzschia curvilineata and Navicula sp., were used to identify an excitation pressure relief ‘strategy’ for each species. Three key areas of NPQ were examined: (i) the NPQ activation/deactivation processes, (ii) how NPQ affects the collection, dissipation, and usage of absorbed light energy, and (iii) the interdependence of NPQ and photosynthetic electron flow. It was found that Nitzschia cells regulate excitation pressure via performing a high amplitude, reversible antenna based quenching which is dependent on the de-epoxidation of diadinoxanthin. In Navicula cells excitation pressure could be effectively regulated solely within the PSII reaction centre, whilst antenna based, diadinoxanthin de-epoxidation dependent quenching was implicated to be used as a supplemental, long-lasting source of excitation energy dissipation. These strategies for excitation balance were discussed in the context of resource partitioning under these species’ originating light climates. A more detailed investigation of the NPQ response in Nitzschia was used to develop a comprehensive model describing the mechanism for antenna centred non-photochemical quenching in this species. The experimental evidence was strongly supportive of a mechanism whereby: an acidic lumen triggers the diadinoxanthin de-epoxidation and protonation mediated aggregation of light harvesting complexes leading to the formation of quencher chlorophyll a-chlorophyll a dimers with short-lived excited states; quenching relaxes when a rise in lumen pH triggers the dispersal of light harvesting complex aggregates via deprotonation events and the input of diadinoxanthin. This model may also be applicable for describing antenna based NPQ in other diatom species.

Structures quantiques de certaines sous-variétés lagrangiennes non-monotones

Soit (M,ω) un variété symplectique fermée et connexe.On considère des sous-variétés lagrangiennes α : L → (M,ω). Si α est monotone, c.- à-d. s’il existe η > 0 tel que ημ = ω, Paul Biran et Octav Conea ont défini une version relative de l’homologie quantique. Dans ce contexte ils ont déformé l’opérateur de bord du complexe de Morse ainsi que le produit d’intersection à l’aide de disques pseudo-holomorphes. On note (QH(L), ∗), l’homologie quantique de L munie du produit quantique. Le principal objectif de cette dissertation est de généraliser leur construction à un classe plus large d’espaces. Plus précisément on considère soit des sous-variétés presque monotone, c.-à-d. α est C1-proche d’un plongement lagrangian monotone ; soit les fibres toriques de variétés toriques Fano. Dans ces cas non nécessairement monotones, QH(L) va dépendre de certains choix, mais cela sera irrelevant pour les applications présentées ici. Dans le cas presque monotone, on s’intéresse principalement à des questions de déplaçabilité, d’uniréglage et d’estimation d’énergie de difféomorphismes hamiltoniens. Enfin nous terminons par une application combinant les deux approches, concernant la dynamique d’un hamiltonien déplaçant toutes les fibres toriques non-monotones dans CPn.

Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

Non-destruct|ve testing of non-metallic materials using microwaves

The motivatitni for" the present work is from .a project sanctioned by TSRO. The work involved the development of a quick and reliable test procedure using microwaves, for tflue inspection of cured propellant samples and a method to monitor the curing conditions of propellant mix undergoing the curing process.Normal testing CHE the propellant samples involvecuttimg a piece from each carton and testing it for their tensile strength. The values are then compared with standard ones and based on this result the sample isaccepted or rejected. The tensile strength is a measure ofdegree of cure of the propellant mix. But this measurementis a destructive procedure as it involves cutting of the sample. Moreover, it does not guarantee against nonuniform curing due to power failure, hot air-line failure,operator error etc. This necessitated the need for the development of a quick and reliable non-destructive test procedure.

Dissociated Dipoles: Image representation via non-local comparisons

A fundamental question in visual neuroscience is how to represent image structure. The most common representational schemes rely on differential operators that compare adjacent image regions. While well-suited to encoding local relationships, such operators have significant drawbacks. Specifically, each filter's span is confounded with the size of its sub-fields, making it difficult to compare small regions across large distances. We find that such long-distance comparisons are more tolerant to common image transformations than purely local ones, suggesting they may provide a useful vocabulary for image encoding. . We introduce the "Dissociated Dipole," or "Sticks" operator, for encoding non-local image relationships. This operator de-couples filter span from sub-field size, enabling parametric movement between edge and region-based representation modes. We report on the perceptual plausibility of the operator, and the computational advantages of non-local encoding. Our results suggest that non-local encoding may be an effective scheme for representing image structure.

Non-commutative symbolic coding

We give a non-commutative generalization of classical symbolic coding in the presence of a synchronizing word. This is done by a scattering theoretical approach. Classically, the existence of a synchronizing word turns out to be equivalent to asymptotic completeness of the corresponding Markov process. A criterion for asymptotic completeness in general is provided by the regularity of an associated extended transition operator. Commutative and non-commutative examples are analysed.

On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities

We prove that all the eigenvalues of a certain highly non-self-adjoint Sturm–Liouville differential operator are real. The results presented are motivated by and extend those recently found by various authors (Benilov et al. (2003) [3], Davies (2007) [7] and Weir (2008) [18]) on the stability of a model describing small oscillations of a thin layer of fluid inside a rotating cylinder.

Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

A study of anticipatory non-autonomous systems

Rhythms are manifested ubiquitously in dynamical biological processes. These fundamental processes which are necessary for the survival of living organisms include metabolism, breathing, heart beat, and, above all, the circadian rhythm coupled to the diurnal cycle. Thus, in mathematical biology, biological processes are often represented as linear or nonlinear oscillators. In the framework of nonlinear and dissipative systems (ie. the flow of energy, substances, or sensory information), they generate stable internal oscillations as a response to environmental input and, in turn, utilise such output as a means of coupling with the environment.