Extremal properties of certain risk models

Cette thèse s'intéresse à étudier les propriétés extrémales de certains modèles de risque d'intérêt dans diverses applications de l'assurance, de la finance et des statistiques. Cette thèse se développe selon deux axes principaux, à savoir: Dans la première partie, nous nous concentrons sur deux modèles de risques univariés, c'est-à- dire, un modèle de risque de déflation et un modèle de risque de réassurance. Nous étudions le développement des queues de distribution sous certaines conditions des risques commun¬s. Les principaux résultats sont ainsi illustrés par des exemples typiques et des simulations numériques. Enfin, les résultats sont appliqués aux domaines des assurances, par exemple, les approximations de Value-at-Risk, d'espérance conditionnelle unilatérale etc. La deuxième partie de cette thèse est consacrée à trois modèles à deux variables: Le premier modèle concerne la censure à deux variables des événements extrême. Pour ce modèle, nous proposons tout d'abord une classe d'estimateurs pour les coefficients de dépendance et la probabilité des queues de distributions. Ces estimateurs sont flexibles en raison d'un paramètre de réglage. Leurs distributions asymptotiques sont obtenues sous certaines condi¬tions lentes bivariées de second ordre. Ensuite, nous donnons quelques exemples et présentons une petite étude de simulations de Monte Carlo, suivie par une application sur un ensemble de données réelles d'assurance. L'objectif de notre deuxième modèle de risque à deux variables est l'étude de coefficients de dépendance des queues de distributions obliques et asymétriques à deux variables. Ces distri¬butions obliques et asymétriques sont largement utiles dans les applications statistiques. Elles sont générées principalement par le mélange moyenne-variance de lois normales et le mélange de lois normales asymétriques d'échelles, qui distinguent la structure de dépendance de queue comme indiqué par nos principaux résultats. Le troisième modèle de risque à deux variables concerne le rapprochement des maxima de séries triangulaires elliptiques obliques. Les résultats théoriques sont fondés sur certaines hypothèses concernant le périmètre aléatoire sous-jacent des queues de distributions. -- This thesis aims to investigate the extremal properties of certain risk models of interest in vari¬ous applications from insurance, finance and statistics. This thesis develops along two principal lines, namely: In the first part, we focus on two univariate risk models, i.e., deflated risk and reinsurance risk models. Therein we investigate their tail expansions under certain tail conditions of the common risks. Our main results are illustrated by some typical examples and numerical simu¬lations as well. Finally, the findings are formulated into some applications in insurance fields, for instance, the approximations of Value-at-Risk, conditional tail expectations etc. The second part of this thesis is devoted to the following three bivariate models: The first model is concerned with bivariate censoring of extreme events. For this model, we first propose a class of estimators for both tail dependence coefficient and tail probability. These estimators are flexible due to a tuning parameter and their asymptotic distributions are obtained under some second order bivariate slowly varying conditions of the model. Then, we give some examples and present a small Monte Carlo simulation study followed by an application on a real-data set from insurance. The objective of our second bivariate risk model is the investigation of tail dependence coefficient of bivariate skew slash distributions. Such skew slash distributions are extensively useful in statistical applications and they are generated mainly by normal mean-variance mixture and scaled skew-normal mixture, which distinguish the tail dependence structure as shown by our principle results. The third bivariate risk model is concerned with the approximation of the component-wise maxima of skew elliptical triangular arrays. The theoretical results are based on certain tail assumptions on the underlying random radius.

Dissociation of allocentric and egocentric orientation: Effect on hippocampal place cells and place navigation

Navigation by means of cognitive maps appears to require the hippocampus; hippocampal place cells (PCs) appear to store spatial memories because their discharge is confined to cell-specific places called firing fields (FFs). Experiments with rats manipulated idiothetic and landmark-related information to understand the relationship between PC activity and spatial rotation. Rotating a circular arena in the caused a discrepancy between these cuse. This discrepancy caused most FFs to disappear in both the arena and room reference frames. However, FFs persisted in the rotating arena frame when the discrepancy was reduced by darkness or by a card in the arena. The discrepancy was increased by "field clamping" the rat in a room-defined FF location by rotations that countered its locomotion. Most FFs disspared and reappeared an hour or more after the clamp. Place-avoidance experiments showed that navigation uses independent idiothetic and exteroceptive memories. Rats learned to avoid the unmarked footshock region within a circular arena. When acquired on the stable arena in the light, the location of the punishment was learned by using both room and idiothetic cues; extinction in the dark transferred to the following session in the light. If, however, extinction occured during rotation, only the arena-frame avoidance was extinguished in darkness; the room-defined location was avoided when the light were turned back on. Idiothetic memory of room-defined avoidance was not formed during rotation in light; regardless of rotation with a randomly dispersed pellet. The resulting behaviour alternated between random pellet searching and target-directed navigation, making it possible to examine PC correlates of these two classes of spatial behaviour. The independence of idiothetic and exteroceptive spatial memories and the disruption of PC firing during rotation suggest that PCs may not be necessary for spatial cognition; this idea can be tested by recording during place-avoidance and preference tasks.

Bilateral sequential nonarteritic anterior ischemic optic neuropathy: a comparison of visual outcomes in fellow eyes using quantitative analysis of goldmann visual fields.

OBJECTIVE To better define the concordance of visual loss in patients with nonarteritic anterior ischemic optic neuropathy (NAION). METHODS The medical records of 86 patients with bilateral sequential NAION were reviewed retrospectively, and visual function was assessed using visual acuity, Goldmann visual fields, color vision, and relative afferent papillary defect. A quantitative total visual field score and score per quadrant were analyzed for each eye using the numerical Goldmann visual field scoring method. RESULTS Outcome measures were visual acuity, visual field, color vision, and relative afferent papillary defect. A statistically significant correlation was found between fellow eyes for multiple parameters, including logMAR visual acuity (P = .01), global visual field (P < .001), superior visual field (P < .001), and inferior visual field (P < .001). The mean deviation of total (P < .001) and pattern (P < .001) deviation analyses was significantly less between fellow eyes than between first and second eyes of different patients. CONCLUSIONS Visual function between fellow eyes showed a fair to moderate correlation that was statistically significant. The pattern of vision loss was also more similar in fellow eyes than between eyes of different patients. These results may help allow better prediction of visual outcome for the second eye in patients with NAION.

The average inter-crossing number of equilateral random walks and polygons

In this paper, we study the average inter-crossing number between two random walks and two random polygons in the three-dimensional space. The random walks and polygons in this paper are the so-called equilateral random walks and polygons in which each segment of the walk or polygon is of unit length. We show that the mean average inter-crossing number ICN between two equilateral random walks of the same length n is approximately linear in terms of n and we were able to determine the prefactor of the linear term, which is a = (3 In 2)/(8) approximate to 0.2599. In the case of two random polygons of length n, the mean average inter-crossing number ICN is also linear, but the prefactor of the linear term is different from that of the random walks. These approximations apply when the starting points of the random walks and polygons are of a distance p apart and p is small compared to n. We propose a fitting model that would capture the theoretical asymptotic behaviour of the mean average ICN for large values of p. Our simulation result shows that the model in fact works very well for the entire range of p. We also study the mean ICN between two equilateral random walks and polygons of different lengths. An interesting result is that even if one random walk (polygon) has a fixed length, the mean average ICN between the two random walks (polygons) would still approach infinity if the length of the other random walk (polygon) approached infinity. The data provided by our simulations match our theoretical predictions very well.

Subknots in ideal knots, random knots, and knotted proteins.

We introduce disk matrices which encode the knotting of all subchains in circular knot configurations. The disk matrices allow us to dissect circular knots into their subknots, i.e. knot types formed by subchains of the global knot. The identification of subknots is based on the study of linear chains in which a knot type is associated to the chain by means of a spatially robust closure protocol. We characterize the sets of observed subknot types in global knots taking energy-minimized shapes such as KnotPlot configurations and ideal geometric configurations. We compare the sets of observed subknots to knot types obtained by changing crossings in the classical prime knot diagrams. Building upon this analysis, we study the sets of subknots in random configurations of corresponding knot types. In many of the knot types we analyzed, the sets of subknots from the ideal geometric configurations are found in each of the hundreds of random configurations of the same global knot type. We also compare the sets of subknots observed in open protein knots with the subknots observed in the ideal configurations of the corresponding knot type. This comparison enables us to explain the specific dispositions of subknots in the analyzed protein knots.

Tightness of random knotting.

Long polymers in solution frequently adopt knotted configurations. To understand the physical properties of knotted polymers, it is important to find out whether the knots formed at thermodynamic equilibrium are spread over the whole polymer chain or rather are localized as tight knots. We present here a method to analyze the knottedness of short linear portions of simulated random chains. Using this method, we observe that knot-determining domains are usually very tight, so that, for example, the preferred size of the trefoil-determining portions of knotted polymer chains corresponds to just seven freely jointed segments.

Predicting optimal lengths of random knots

In a thermally fluctuating long linear polymeric chain in a solution, the ends, from time to time, approach each other. At such an instance, the chain can be regarded as closed and thus will form a knot or rather a virtual knot. Several earlier studies of random knotting demonstrated that simpler knots show a higher occurrence for shorter random walks than do more complex knots. However, up to now there have been no rules that could be used to predict the optimal length of a random walk, i.e. the length for which a given knot reaches its highest occurrence. Using numerical simulations, we show here that a power law accurately describes the relation between the optimal lengths of random walks leading to the formation of different knots and the previously characterized lengths of ideal knots of a corresponding type.

Comparativecost-effectivenessanalyses of cardiacmagneticresonanceimaging versus invasive coronary angiography combined with fractional flow reserve testing to diagnose ischemia in coronary artery disease

Introduction: According to guidelines, patients with coronary artery disease (CAD) should undergo revascularization if myocardial ischemia is present. While coronary angiography (CXA) allows the morphological assessment of CAD, the fractional flow reserve (FFR) has proved to be a complementary invasive test to assess the functional significance of CAD, i.e. to detect ischemia. Perfusion Cardiac Magnetic Resonance (CMR) has turned out to be a robust non-invasive technique to assess myocardial ischemia. The objective: is to compare the cost-effectiveness ratio - defined as the costs per patient correctly diagnosed - of two algorithms used to diagnose hemodynamically significant CAD in relation to the pretest likelihood of CAD: 1) aCMRto assess ischemia before referring positive patients to CXA (CMR + CXA), 2) a CXA in all patients combined with a FFR test in patients with angiographically positive stenoses (CXA + FFR). Methods: The costs, evaluated from the health care system perspective in the Swiss, German, the United Kingdom (UK) and the United States (US) contexts, included public prices of the different tests considered as outpatient procedures, complications' costs and costs induced by diagnosis errors (false negative). The effectiveness criterion wasthe ability to accurately identify apatient with significantCAD.Test performancesused in the model were based on the clinical literature. Using a mathematical model, we compared the cost-effectiveness ratio for both algorithms for hypothetical patient cohorts with different pretest likelihood of CAD. Results: The cost-effectiveness ratio decreased hyperbolically with increasing pretest likelihood of CAD for both strategies. CMR + CXA and CXA + FFR were equally costeffective at a pretest likelihood of CAD of 62% in Switzerland, 67% in Germany, 83% in the UK and 84% in the US with costs of CHF 5'794, Euros 1'472, £ 2'685 and $ 2'126 per patient correctly diagnosed. Below these thresholds, CMR + CXA showed lower costs per patient correctly diagnosed than CXA + FFR. Implications for the health care system/professionals/patients/society These results facilitate decision making for the clinical use of new generations of imaging procedures to detect ischemia. They show to what extent the cost-effectiveness to diagnose CAD depends on the prevalence of the disease.

Evolutionary history and its relevance in understanding and conserving southern African biodiversity

Abstract : Understanding how biodiversity is distributed is central to any conservation effort and has traditionally been based on niche modeling and the causal relationship between spatial distribution of organisms and their environment. More recently, the study of species' evolutionary history and relatedness has permeated the fields of ecology and conservation and, coupled with spatial predictions, provides useful insights to the origin of current biodiversity patterns, community structuring and potential vulnerability to extinction. This thesis explores several key ecological questions by combining the fields of niche modeling and phylogenetics and using important components of southern African biodiversity. The aims of this thesis are to provide comparisons of biodiversity measures, to assess how climate change will affect evolutionary history loss, to ask whether there is a clear link between evolutionary history and morphology and to investigate the potential role of relatedness in macro-climatic niche structuring. The first part of my thesis provides a fine scale comparison and spatial overlap quantification of species richness and phylogenetic diversity predictions for one of the most diverse plant families in the Cape Floristic Region (CFR), the Proteaceae. In several of the measures used, patterns do not match sufficiently to argue that species relatedness information is implicit in species richness patterns. The second part of my thesis predicts how climate change may affect threat and potential extinction of southern African animal and plant taxa. I compare present and future niche models to assess whether predicted species extinction will result in higher or lower V phylogenetic diversity survival than what would be experienced under random extinction processes. l find that predicted extinction will result in lower phylogenetic diversity survival but that this non-random pattern will be detected only after a substantial proportion of the taxa in each group has been lost. The third part of my thesis explores the relationship between phylogenetic and morphological distance in southern African bats to assess whether long evolutionary histories correspond to equally high levels of morphological variation, as predicted by a neutral model of character evolution. I find no such evidence; on the contrary weak negative trends are detected for this group, as well as in simulations of both neutral and convergent character evolution. Finally, I ask whether spatial and climatic niche occupancy in southern African bats is influenced by evolutionary history or not. I relate divergence time between species pairs to climatic niche and range overlap and find no evidence for clear phylogenetic structuring. I argue that this may be due to particularly high levels of micro-niche partitioning. Résumé : Comprendre la distribution de la biodiversité représente un enjeu majeur pour la conservation de la nature. Les analyses se basent le plus souvent sur la modélisation de la niche écologique à travers l'étude des relations causales entre la distribution spatiale des organismes et leur environnement. Depuis peu, l'étude de l'histoire évolutive des organismes est également utilisée dans les domaines de l'écologie et de la conservation. En combinaison avec la modélisation de la distribution spatiale des organismes, cette nouvelle approche fournit des informations pertinentes pour mieux comprendre l'origine des patterns de biodiversité actuels, de la structuration des communautés et des risques potentiels d'extinction. Cette thèse explore plusieurs grandes questions écologiques, en combinant les domaines de la modélisation de la niche et de la phylogénétique. Elle s'applique aux composants importants de la biodiversité de l'Afrique australe. Les objectifs de cette thèse ont été l) de comparer différentes mesures de la biodiversité, 2) d'évaluer l'impact des changements climatiques à venir sur la perte de diversité phylogénétique, 3) d'analyser le lien potentiel entre diversité phylogénétique et diversité morphologique et 4) d'étudier le rôle potentiel de la phylogénie sur la structuration des niches macro-climatiques des espèces. La première partie de cette thèse fournit une comparaison spatiale, et une quantification du chevauchement, entre des prévisions de richesse spécifique et des prédictions de la diversité phylogénétique pour l'une des familles de plantes les plus riches en espèces de la région floristique du Cap (CFR), les Proteaceae. Il résulte des analyses que plusieurs mesures de diversité phylogénétique montraient des distributions spatiales différentes de la richesse spécifique, habituellement utilisée pour édicter des mesures de conservation. La deuxième partie évalue les effets potentiels des changements climatiques attendus sur les taux d'extinction d'animaux et de plantes de l'Afrique australe. Pour cela, des modèles de distribution d'espèces actuels et futurs ont permis de déterminer si l'extinction des espèces se traduira par une plus grande ou une plus petite perte de diversité phylogénétique en comparaison à un processus d'extinction aléatoire. Les résultats ont effectivement montré que l'extinction des espèces liées aux changements climatiques pourrait entraîner une perte plus grande de diversité phylogénétique. Cependant, cette perte ne serait plus grande que celle liée à un processus d'extinction aléatoire qu'à partir d'une forte perte de taxons dans chaque groupe. La troisième partie de cette thèse explore la relation entre distances phylogénétiques et morphologiques d'espèces de chauves-souris de l'Afrique australe. ll s'agit plus précisément de déterminer si une longue histoire évolutive correspond également à des variations morphologiques plus grandes dans ce groupe. Cette relation est en fait prédite par un modèle neutre d'évolution de caractères. Aucune évidence de cette relation n'a émergé des analyses. Au contraire, des tendances négatives ont été détectées, ce qui représenterait la conséquence d'une évolution convergente entre clades et des niveaux élevés de cloisonnement pour chaque clade. Enfin, la dernière partie présente une étude sur la répartition de la niche climatique des chauves-souris de l'Afrique australe. Dans cette étude je rapporte temps de divergence évolutive (ou deux espèces ont divergé depuis un ancêtre commun) au niveau de chevauchement de leurs niches climatiques. Les résultats n'ont pas pu mettre en évidence de lien entre ces deux paramètres. Les résultats soutiennent plutôt l'idée que cela pourrait être I dû à des niveaux particulièrement élevés de répartition de la niche à échelle fine.

Non-random fertilization in mice correlates with the MHC and something else

One evolutionary explanation for the success of sexual reproduction assumes that sex is an advantage in the coevolutionary arms race between pathogens and hosts. Accordingly, an important criterion in mate choice and maternal selection thereafter could be the allelic specificity at polymorphic loci involved in parasite-host interactions, e.g. the MHC (major histocompatibility complex). The MHC has been found to influence mate choice and selective abortions in mice and humans. However, it could also influence the fertilization process itself, i.e. (i) the oocyte's choice for the fertilizing sperm, and (ii) the outcome of the second meiotic division after the sperm has entered the egg. We tested both hypotheses in an in vitro fertilization experiment with two inbred mouse strains congenic for their MHC. The genotypes of the resulting blastocysts were determined by polymerase chain reaction. We found nonrandom MHC combinations in the blastocysts which may result from both possible choice mechanisms. The outcome changed significantly over time, indicating that a choice for MHC combinations during fertilization may be influenced by one or several external factors.

Error and attack tolerance of layered complex networks.

Many complex systems may be described by not one but a number of complex networks mapped on each other in a multi-layer structure. Because of the interactions and dependencies between these layers, the state of a single layer does not necessarily reflect well the state of the entire system. In this paper we study the robustness of five examples of two-layer complex systems: three real-life data sets in the fields of communication (the Internet), transportation (the European railway system), and biology (the human brain), and two models based on random graphs. In order to cover the whole range of features specific to these systems, we focus on two extreme policies of system's response to failures, no rerouting and full rerouting. Our main finding is that multi-layer systems are much more vulnerable to errors and intentional attacks than they appear from a single layer perspective.