Quasi-reaction systems are often modelled with stochastic differential equations in order to capture the inherent randomness of their dynamics. The traditional local linear approximation methods for the estimation of the reaction rates face significant challenges in certain conditions. When the system is observed at short intervals, high correlations between successive observations result in numerical instability, while measurements at wider intervals lead to biased estimates of the parameters. This thesis addresses these issues with the development of novel inferential procedures. First, we introduce a latent event history model, by formalizing a latent space of unobserved reactions and their connection with the observed states. Under this framework, the system parameters can be estimated via a modified Expectation-Maximisation algorithm, with an extended Kalman filter at the E-step for reconstructing the underlying latent states. The approach is shown to be more accurate than existing methods, particularly for observations measured at short time intervals. In order to model more complex scenarios, the method is further extended to account for external time-varying factors that may affect the reaction rates of the system. As a second inferential approach, we concentrate on the mean of the dynamics and propose a novel mean-field approximation method. The method exploits the analytical solution of the ordinary differential equations in the case of unitary systems to propose an approximate solution for a generic quasi-reaction system. Besides a high computational efficiency, the resulting approach is found to perform particularly well when the measurements of the system are taken at wide time intervals. Finally, we provide an illustration of the proposed inferential procedures on the modelling of COVID-19 transmission and cell differentiation.

The theory of partial differential equations constitutes today one of the most important topics of scientific understanding. A standard approach for solving a time-dependent partial differential equation consists in discretizing the spatial variables by finite differences or finite elements. This results in a huge system of (stiff) ordinary differential equations that has to be integrated in time. Exponential integrators constitute an interesting class of numerical methods for the time integration of stiff systems of differential equations. Their efficient implementation heavily relies on the fast computation of the action of certain matrix functions; among those, the matrix exponential is the most prominent one. In this manuscript, we go through the steps that led to the development of backward error accurate routines for computing the action of the matrix exponential.

La leptospirose est considérée comme la zoonose la plus répandue au monde mais les incidences sont les plus élevées dans les régions tropicales et en particulier sur les îles. Les îles du Sud-Ouest de l'Océan Indien ne dérogent pas à la règle puisque la maladie y représente un problème de santé humaine majeur sur plusieurs îles, notamment aux Seychelles qui enregistrent un des plus fort taux d'incidence humaine au monde. Sur la base des données disponibles, l'épidémiologie humaine apparait contrastée à l'échelle de la région : les cas cliniques sur Mayotte résultent d'infections par quatre espèces de leptospires distinctes alors qu'à La Réunion ou aux Seychelles, une seule espèce est à l'origine de la grande majorité des cas cliniques. L'objectif général de cette thèse est d'identifier certains des déterminants de cette épidémiologie singulière. Nous avons dans un premier temps complété les informations humaines en investiguant la leptospirose en Union des Comores, pays n'ayant jamais rapporté de transmission autochtone. Nos résultats indiquent que les populations humaines y sont exposées à des antigènes de leptospires comparables à ceux retrouvés sur l'île voisine de Mayotte. Ce résultat suggére que l'absence de leptospirose sur certaines îles est le résultat d'un déficit de surveillance. Nous avons ensuite caractérisé la diversité génétique des leptospires au sein de la faune de certaines îles, caractérisées par des niveaux d'endémisme élevés à même d'être en partie à l'origine de cette épidémiologie contrastée. Nous décrivons d'une part une importante diversité des leptospires pathogènes chez les chauves-souris (Chiroptères) malgaches. Nous montrons d'autre part que cette diversité de leptospires n'est pas structurée géographiquement mais présente au contraire une importante spécificité d'hôte, résultant de différents processus évolutifs incluant co-spéciation et host-switch. Nous avons exploité cette spécificité d'hôte pour éclairer l'épidémiologie de la leptospirose à Mayotte, où nous montrons que l'importante diversité bactérienne impliquée dans les cas cliniques résulte de la présence de nombreux réservoirs, dont certains originaires de Madagascar. Ainsi, il apparaît que l'épidémiologie humaine de la leptospirose dans le SOOI est le reflet d'assemblages distincts de leptospires cosmopolites et autochtones/endémiques maintenus et excrétés par des réservoirs animaux particuliers. / Leptospirosis is considered as the most widespread zoonosis worldwide but the incidence levels are higher in tropical regions and particularly on islands. The South-Western Indian Ocean islands are no exception and the disease is of major medical concern in several islands notably in Seychelles, displaying some of the highest human incidence ever reported. Based on available data, the human epidemiology appears contrasted in the region: on Mayotte, human cases result from the infection with four distinct Leptospira species whereas on Reunion Island or Seychelles, a single species causes the majority of clinical cases. The main objective of this thesis is to identify some of the drivers of this singular epidemiology. We first completed the information available on this human disease in the region by investigating the leptospirosis situation in the Union of the Comoros, a country where no autochthonous transmission has been reported so far. Our results indicate that Comorian populations are exposed to Leptospira, which are antigenically comparable to those detected in the neighbouring island of Mayotte. This finding suggests that the apparent absence of leptospirosis in some islands rather reflects a lack of surveillance. We then investigated the genetic diversity of Leptospira on distinct islands home to distinct endemic animal species that may shed distinct Leptospira lineages and thus at least in part explain the contrasted epidemiology of leptospirosis in the region. Specifically, we describe a high diversity of pathogenic Leptospira within Malagasy bats (Chiroptera) and further show that Leptospira diversity is not structured by geography. Instead, we show that these Leptospira display a strong specificity towards their hosts, which may result from different evolutionary processes including co-speciation and host switching. Using this tight host specificity, we investigated the leptospirosis epidemiology on Mayotte, where we show that the important bacterial diversity reported in clinical cases is due of the presence of several distinct animal species acting as reservoirs, some of which introduced from the neighbouring Madagascar. Altogether, results presented herein combined to data produced by our lab suggest that the epidemiology of leptospirosis in the SWOI results from distinct assemblages of cosmopolitan and autochthonous/endemic Leptospira. Keywords : Leptospirosis, Leptospira, Chiroptera, small mammals, hosts-parasites associations, MAT, MLST, co-phylogeny, Madagascar, Mayotte, Union of Comoros, South-Western Indian Ocean.

An optimal dividend problem with investment opportunities, taking into consideration a source of strategic risk is being considered, as well as the effect of market frictions on the decision process of the financial entities. It concerns the problem of determining an optimal control of the dividend under debt constraints and investment opportunities in an economy with business cycles. It is assumed that the company is to be allowed to accept or reject investment opportunities arriving at random times with random sizes, by changing its outstanding indebtedness, which would impact its capital structure and risk profile. This work mainly focuses on the strategic risk faced by the companies; and, in particular, it focuses on the manager's problem of setting appropriate priorities to deploy the limited resources available. This component is taken into account by introducing frictions in the capital structure modification process. The problem is formulated as a bi-dimensional singular control problem under regime switching in presence of jumps. An explicit condition is obtained in order to ensure that the value function is finite. A viscosity solution approach is used to get qualitative descriptions of the solution. Moreover, a lending scheme for a system of interconnected banks with probabilistic constraints of failure is being considered. The problem arises from the fact that financial institutions cannot possibly carry enough capital to withstand counterparty failures or systemic risk. In such situations, the central bank or the government becomes effectively the risk manager of last resort or, in extreme cases, the lender of last resort. If, on the one hand, the health of the whole financial system depends on government intervention, on the other hand, guaranteeing a high probability of salvage may result in increasing the moral hazard of the banks in the financial network. A closed form solution for an optimal control problem related to interbank lending schemes has been derived, subject to terminal probability constraints on the failure of banks which are interconnected through a financial network. The derived solution applies to real bank networks by obtaining a general solution when the aforementioned probability constraints are assumed for all the banks. We also present a direct method to compute the systemic relevance parameter for each bank within the network. Finally, a possible computation technique for the Default Risk Charge under to regulatory risk measurement processes is being considered. We focus on the Default Risk Charge measure as an effective alternative to the Incremental Risk Charge one, proposing its implementation by a quasi exhaustive-heuristic algorithm to determine the minimum capital requested to a bank facing the market risk associated to portfolios based on assets emitted by several financial agents. While most of the banks use the Monte Carlo simulation approach and the empirical quantile to estimate this risk measure, we provide new computational approaches, exhaustive or heuristic, currently becoming feasible, because of both new regulation and the high speed - low cost technology available nowadays.

Les questions d'anonymat surgissent dans de nombreux contextes et tout particulièrement dans celui des transactions électroniques. Il est souvent souhaitable de protéger l'identité des participants afin d'éviter la constitution de profils de consommateurs ou de bases de données de renseignements commerciaux. De nombreuses solutions cryptographiques ont été apportées afin de renforcer la confiance des utilisateurs dans ces applications. Une nouvelle approche dans l'élaboration de mécanismes d'anonymat sûrs et performants s'appuie sur des applications bilinéaires (couplages de Weil et de Tate sur les courbes elliptiques). Dans cette thèse nous présentons tout d'abord un état de l'art des différentes signatures utilisées pour l'anonymat en cryptographie, en particulier les signatures de groupe, les signa- tures aveugles et les signatures d'anneau. Dans ce contexte nous décrivons un nouveau protocole d'authentification et montrons comment il peut être converti en signature d'anneau. Notre étude porte ensuite sur les signatures aveugles à anonymat révocable. Il s'agit de signatures aveugles dont l'anonymat et l'intraçabilité peuvent être révoqués par une autorité. Nous proposons le pre- mier véritable modèle de sécurité pour ces signatures, ainsi qu'une nouvelle construction basée sur les couplages dont nous prouvons la sécurité dans ce modèle. Nos derniers travaux portent sur les systèmes de multi-coupons et de monnaie électronique. L'utilisation des couplages nous permet d'introduire de nouvelles propriétés destinées à faciliter leur usage. Pour chacun de ces systèmes nous proposons un modèle de sécurité, puis décrivons un schéma dont nous prouvons la sécurité dans ce modèle.

Symbiosis brought important evolutionary novelties to life on Earth. Lichens, the symbiotic entities formed by fungi, photosynthetic organisms and bacteria, represent an example of a successful adaptation in surviving hostile environments. Yet many aspects of the lichen symbiosis remain unexplored. This thesis aims at bringing insights into lichen biology and the importance of symbiosis in adaptation. I am using as model system a successful colonizer of tundra and alpine environments, the worm lichens Thamnolia, which seem to only reproduce vegetatively through symbiotic propagules. When the genetic architecture of the mating locus of the symbiotic fungal partner was analyzed with genomic and transcriptomic data, a sexual self-incompatible life style was revealed. However, a screen of the mating types ratios across natural populations detected only one of the mating types, suggesting that Thamnolia has no potential for sexual reproduction because of lack of mating partners. Genetic data based on molecular markers revealed the existence of three morphologically cryptic Thamnolia lineages. One lineage had a clear recombination structure and was found in the tundra region of Siberia, shorelines of Scandinavia, and Aleutian Islands. The other lineage was allopatric with the previous, and was highly clonal; only two haplotypes were found across the alpine region of central and southeastern Europe. However, the third lineage was sympatric with the other two, had a worldwide distribution, and although highly clonal, showed a recombinant population structure. Our data could not reveal whether the signs of recombination resulted from rare recombination events due to the extreme low frequency of the other mating type or ancestral variation before the loss of sexual reproduction. However, investigation of Thamnolia’s green algal population showed that in different localities, different algal genotypes were associated with the same fungal genotype. Furthermore, data suggest that Thamnolia carried several algal genotypes within its thalli and shared them with other distantly related but ecologically similar fungal species.

Opiatberoende är ett allvarligt och svårt tillstånd och narkotikadödligheten i Sverige är mycket hög. Syftet med denna studie är att skaffa kunskap om och belysa hur missbrukshandläggare inom socialtjänsten i Dalarna ser på sitt arbete med personer med opiatberoende i relation till att behandlingsformen LARO ligger hos en annan huvudman. En kvalitativ studie har genomförts där missbrukshandläggare från fem olika kommuner i Dalarna har intervjuats. Det empiriska materialet har sedan analyserats i relation till tidigare forskning inom området samt teorier om domäner och professioner. Slutsatsen av studien visar att missbrukshandläggare i Dalarna upplever en del svårigheter i sitt arbete med opiatberoende klienter utifrån att det är två aktörer inblandade i att hjälpa dessa. Bland annat är långa köer till LARO samt svårigheter att få igenom tvångsvård för klienter som står i kö till eller är inskrivna på LARO problem som kan innebära en risk för klienternas liv. / Opiate addiction is a serious and difficult condition and drug mortality in Sweden is very high. The purpose of this study is to acquire knowledge and illustrate how staff working with drug addiction in social services in Dalarna look at their work with people with opiate addiction in relation to the fact that MAT lies with another operator. A qualitative study has been carried out where social workers who works with drug addiction from five different municipalities in Dalarna have been interviewed. The empirical data were analyzed in relation to previous research on the area and the theories of domains and professions. The conclusion of the study shows that the social workers in Dalarna experiencing some obstacles in their work with clients with opioid dependence since it is two operators involved. For example, the long queues to MAT and difficulties to get through forced addiction care were issues that may be a risk for clients lives.

Title Sensorimotor response to the audiovisual impulse of young school age children. The aim of the work The aim of the work was quantification of sensorimotor response to the audiovisual impulse of young school age girls. Method Pilot study - experimental research, indirect measurement. Results Investigation showed that the group of girls who do coordination-aesthetic sports reached better results of sensorimotor response to the audiovisual impulse in the tests of gross and fine coordination than the group of girls who do not or have not been doing coordination-aesthetic sports in the past. Key words Sensomotor, Coordination-aesthetic sports, Dance mat, Dance Dance Revolution (DDR), Exergames

Frente ao treinamento físico, o organismo está sujeito a alterações anatomofisiológicas em vários sistemas, especialmente o sistema músculo-esquelético. Pretendeu-se, descrever alterações no trofismo muscular do sóleo e das propriedades mecânicas das tíbias de ratos submetidos a treinamento físico em esteira rolante (TFER), bem como analisar estas relações com o tempo de treinamento. Utilizou-se de 40 ratos (20 treinados e 20 controles) da linhagem Wistar, treinados 60 min/dia, 5 dias por semana, durante 3, 6, 9 e 12 semanas, totalizando 8 grupos de 5 ratos cada. Os grupos controles foram submetidos aos mesmos procedimentos experimentais, com exceção da aplicação do treinamento físico. Após o sacrifício, o tecido muscular foi retirado unilateralmente, congelado e, posteriormente foram corados pela técnica de Hematoxilina e Eosina, para análise das áreas das fibras musculares. Para análise das propriedades mecânicas, 80 tíbias (direita e esquerda) foram medidas e pesadas e, posteriormente, realizados os ensaios de flexão em três pontos para obtenção das propriedades de carga máxima e rigidez. Após aplicação do teste ANOVA, quando comparados os grupos treinados (T) e não treinados (NT) encontramos que o TFER altera, significantemente (p < 0,05), e de maneira crescente com o tempo de treinamento, as características de hipertrofia muscular e as propriedades mecânicas de flexão das tíbias dos ratos treinados / Facing the physical training, the agency is subject of alterations anatomophysiological in several systems, specially the muscle and bone system. It is intended, to describe alterations of muscle trophy of the soleus and of the mechanical properties of the rat tibia submitted to physical training in rolling mat (PTRM), as well as like analyze these relations with the time of training. It was used 40 rats (20 training and 20 controls) of the lineage Wistar, coached 60 min/day, 5 days/week, during 3, 6, 9 and 12 weeks, totalling up to 8 groups of 5 each rats. The groups controls were submitted to the same experimental procedures, with exception of the application of the physical training. After the sacrifice, the muscle weave was withdrawn unilaterally, frozen and, subsequently were paintting by the technical one of Hematoxilina and Eosina, for analysis of the areas of the muscle fibers. For the analysis of the mechanical properties, 80 tibia (right and left) were measured and weighted and, subsequently, carried out the attempt of inflection in three points bending to obtain of the properties of maximum load and module of Young. After application of the test ANOVA, when compared the groups training (T) and controls (C) we found that the PTRM alters, significantly (p < 0,05), and going up with the time of training, the characteristics of muscle hypertrophy and the mechanical properties of inflection of the tibia of the rats training

The aim of this thesis is to identify differences among Mathematics textbooks and to find out how they work in real education process. This research will provide information whether such textbooks are actually used by Maths teachers, and if so, then in what manner and how effectively. This will be viewed from the perspective of a teacher-beginner who searches for the most appropriate textbook for Mathematics lessons. Another goal is to introduce the offer of various Maths textbooks for the 2nd stage of basic schools. Also, there is a research performed that could compare these books, especially books published by Prometheus, Fraus and H-mat. Results of the research will be then used for lesson plans of a beginning teacher.