This thesis explores motion trajectory-based approaches to recognize human actions in real-world, unconstrained videos. Recognizing actions is an important task in applications such as video retrieval, surveillance, human-robot interactions, analysis of sports videos, summarization of videos, behaviour monitoring, etc. There has been a considerable amount of research done in this regard. Earlier work used to be on videos captured by static cameras where it was relatively easy to recognise the actions. With more videos being captured by moving cameras, recognition of actions in such videos with irregular camera motion is still a challenge in unconstrained settings with variations in scale, view, illumination, occlusion and unrelated motions in the background. With the increase in videos being captured from wearable or head-mounted cameras, recognizing actions in egocentric videos is also explored in this thesis. At first, an effective motion segmentation method to identify the camera motion in videos captured by moving cameras is explored. Next, action recognition in videos captured in normal third-person view (perspective) is discussed. Further, the action recognition approaches for first-person (egocentric) views are investigated. First-person videos are often associated with frequent unintended camera motion. This is due to the motion of the head resulting in the motion of the head-mounted cameras (wearable cameras). This is followed by recognition of actions in egocentric videos in a multicamera setting. And lastly, novel feature encoding and subvolume sampling (for “deep” approaches) techniques are explored in the context of action recognition in videos. The first part of the thesis explores two effective segmentation approaches to identify the motion due to camera. The first approach is based on curve fitting of the motion trajectories and finding the model which best fits the camera motion model. The curve fitting approach works when the trajectories generated are smooth enough. To overcome this drawback and segment trajectories under non-smooth conditions, a second approach based on trajectory scoring and grouping is proposed. By identifying the instantaneous dominant background motion and accordingly aggregating the scores (denoting the “foregroundness”) along the trajectory, the motion that is associated with the camera can be separated from the motion due to foreground objects. Additionally, the segmentation result has been used to align videos from moving cameras, resulting in videos that seem to be captured by nearly-static cameras. In the second part of the thesis, recognising actions in normal videos captured from third-person cameras is investigated. To this end, two kinds of descriptors are explored. The first descriptor is the covariance descriptor adapted for the motion trajectories. The covariance descriptor for a trajectory encodes the co-variations of different features along the trajectory’s length. Covariance, being a second-order encoding, encodes information of the trajectory that is different from that of the first-order encoding. The second descriptor is based on Granger causality. The novel causality descriptor encodes the “cause and effect” relationships between the motion trajectories of the actions. This type of interaction descriptors captures the causal inter-dependencies among the motion trajectories and encodes complimentary information different from those descriptors based on the occurrence of features. The causal dependencies are traditionally computed on time-varying signals. We extend it further to capture dependencies between spatiotemporal signals and compute generalised causality descriptors which perform better than their traditional counterparts. An egocentric or first-person video is captured from the perspective of the personof-interest (POI). The POI wears a camera and moves around doing his/her activities. This camera records the events and activities as seen by him/her. The POI who is performing actions or activities is not seen by the camera worn by him/her. Activities performed by the POI are called first-person actions and third-person actions are those done by others and observed by the POI. The third part of the thesis explores action recognition in egocentric videos. Differentiating first-person and third-person actions is important when summarising/analysing the behaviour of the POI. Thus, the goal is to recognise the action and the perspective from which it is being observed. Trajectory descriptors are adapted to recognise actions along with the motion trajectory ranking method of segmentation as pre-processing step to identify the camera motion. The motion segmentation step is necessary to remove unintended head motion (camera motion) during video capture. To recognise actions and corresponding perspectives in a multi-camera setup, a novel inter-view causality descriptor based on the causal dependencies between trajectories in different views is explored. Since this is a new problem being addressed, two first-person datasets are created with eight actions in third-person and first-person perspectives. The first dataset is a single camera dataset with action instances from first-person and third-person views. The second dataset is a multi-camera dataset with each action instance having multiple first-person and third-person views. In the final part of the thesis, a feature encoding scheme and a subvolume sampling scheme for recognising actions in videos is proposed. The proposed Hyper-Fisher Vector feature encoding is based on embedding the Bag-of-Words encoding into the Fisher Vector encoding. The resulting encoding is simple, effective and improves the classification performance over the state-of-the-art techniques. This encoding can be used in place of the traditional Fisher Vector encoding in other recognition approaches. The proposed subvolume sampling scheme, used to generate second layer features in “deep” approaches for action recognition in videos, is based on iteratively increasing the size of the valid subvolumes in the temporal direction to generate newer subvolumes. The proposed sampling requires lesser number of subvolumes to be generated to “better represent” the actions and thus, is less computationally intensive compared to the original sampling scheme. The techniques are evaluated on large-scale, challenging, publicly available datasets. The Hyper-Fisher Vector combined with the proposed sampling scheme perform better than the state-of-the-art techniques for action classification in videos.

Made available in DSpace on 2014-06-12T17:42:30Z (GMT). No. of bitstreams: 2 arquivo7476_1.pdf: 1049109 bytes, checksum: 9d7b0f2a4e925f496b0e83f04553ddeb (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2005 / Esta dissertação propõe-se a ser um estudo avaliativo e comparativo do ensinoaprendizagem da Matemática nas 4ª séries do Ensino Fundamental das Escolas Municipais e Estaduais do Recife: estudo de caso do Ibura. O objetivo principal é verificar e analisar as causas do baixo rendimento escolar do ensino-aprendizagem da Matemática das escolas municipais e estaduais. A pesquisa foi conduzida através de entrevistas, com questionário aplicado aos professores para identificar a proposta de trabalho que está sendo vivenciada em cada sala de aula. Verificou-se, porém, que muitas vezes, essas propostas que fazem o ensino acontecer ainda não estão sendo utilizadas devidamente. Além disso, foi aplicado um teste avaliativo sobre o uso e a aplicação das quatro operações básicas, aos alunos, realizadas em 10 salas de aula das escolas estudadas. Logo, observou-se que muitas vezes a Matemática ensinada é uma arrumação de regras prontas, exigindo em determinados momentos, uma grande quantidade de memorização para armazenar dados, regras, textos e formulários. Mediante essas considerações, aplicou-se o teste de FISHER ao resultado dos valores do Enfoque Pedagógico e identificou-se que os professores ainda utilizam indevidamente as propostas do Ensino-Aprendizagem Tradicional da Matemática, não incorporando totalmente as vantagens da Nova Proposta do ensino Aprendizagem da Matemática. Então, o autor deseja que este trabalho possa contribuir na formação dos Educadores e Educandos e que os conduzam a pensar, refletir, resumir, analisar e aplicar suas sugestões de proposta Ensino-aprendizagem, porém, de modo que possa somar valores a projetos educativos

This thesis takes its cue from Roy Fisher's comment, in 1971, that his poems are 'to do with getting around in the mind'. This getting around, however, is not quite the simple process of 'propositions or explorations in aesthetic ideas', which Fisher suggests. This thesis discusses the relationship between Fisher's poetry and the empirical reality which his poems actually do describe and engage with. The thesis suggests that this engagement is of a mystical nature, in which Fisher's sense of linguistic play is allied to an acute awareness of instabilities in both the self and the empirical world. Such play in language and content makes Fisher's poetry a unique site, in contemporary poetry, for his further engagement with a mystery which is ineffable. Yet, this ineffability is held and controlled by Fisher so that it does not have a theological teleology. Fisher's poetry does not point towards a mystery which finds its manifestation and exploration in ways which are recognised within a contemporary religious framework. The thesis is organised into four chapters. The first chapter outlines some of the history and context of Roy Fisher's writing. It outlines the early critical reception of Fisher's first substantial publication, City, and his publications in the nineteen sixties. It then discusses some of the interviews that Fisher has given. These interviews are placed in the context of the critical reception of Fisher's work, during this time, that aligned Fisher with the avant-garde and 'Linguistically-Innovative' poetry of the period. In the second chapter, the thesis examines Fisher's relationship with the 'self' in his poetry. In the light of a sense of instability perceived in the self in Fisher's writing, the idea of the 'mystical' is introduced and defined. This is particularly relevant in the light of Fisher's tussles with the empirical world. A further exploration of the 'other' in Fisher's poetry is undertaken in the third chapter, which examines Fisher's relationship with the urban, the abject and the woman. In the final chapter, Fisher's long poem from 1986, A Furnace is discussed in the light of the foregoing, to highlight its own exploration of mysticism. The second half of the thesis consists of a portfolio of original poetry

Glacier surges are periods of dynamic instabilities which result in semi-regular alternating periods of slow flow, termed the quiescent phase, and fast flow, termed the active phase. This study uses remotely sensed imagery, digital elevation models, glacier velocity datasets, and in situ oblique photographs to reconstruct the surge history and dynamics of Fisher Glacier to better characterize surging in the southwest Yukon and assess the risk posed by this glacier’s surges on surrounding regions. Fisher Glacier has previously been identified as a surge-type glacier but, until now, it had not been the focus of any detailed studies. We find evidence that Fisher Glacier underwent two surges during the study period from 1948 to 2022. Visual analysis of characteristic surge features on the glacier surface show that the glacier was in quiescence from <1948 to at least 1963. In 1972, an advanced terminus position, intense surface crevassing, and high point velocities suggest that a surge had recently terminated, corroborating a previous report of a surge occurring around 1970. This was followed by a 40-year quiescent phase from ~1973-2013 during which the terminus underwent consistent retreat, totaling a terminus-wide average of 2058 ± 8 m (up to 3567 ± 8 m in certain sections). Velocities during the quiescent phase were low (generally <50 m yr⁻¹), but underwent a slow multidecadal increase starting around 1985, spreading from the center of the glacier towards the head and the terminus. A pre-surge buildup phase beginning in ~2008-2010 resulted in velocities of up to ~200 m yr⁻¹. The active phase of the surge initiated in winter 2013/14 and was characterised by a velocity increase to ~1500 m yr⁻¹ that propagated both up- and down-glacier from the surge nucleus in the mid-region (~22 km upglacier from the terminus). Velocities peaked at >2100 m yr⁻¹ in the winter/early spring of 2016 at ~12 km from the terminus. The surge resulted in a mean terminus-wide advance of 868 ± 8 m, intense surface crevassing and a downglacier transfer of mass from the reservoir zone to the receiving zone. The terminus area increased in elevation by a mean of ~80 m. In July 2016, the surge rapidly terminated within a period of ~1 month, although velocities at the head and the terminus took a few more months to slow to quiescent values. Since then, average annual velocities along the centerline have been lower than pre-surge velocities, the crevasses have closed up, and the rate of ice surface elevation change has been negative across the entire glacier. Fisher Glacier’s surge dynamics suggest predominantly hydrologically controlled surging, but with some aspects more representative of thermally controlled surging. Thus, we propose that more than one mechanism might be at play in controlling its surges, although further research is required to confirm this. Under current climate conditions, it is unlikely that Fisher Glacier could dam the nearby Alsek River and cause a glacier lake outburst flood.

Une part importante de l’activité en calcul scientifique et analyse numérique est consacrée aux problèmes de transport d’une quantité par un champ donné (ou lui-même calculé numériquement). Les questions de conservations étant essentielles dans ce domaine, on formule en général le problème de façon eulérienne sous la forme d’un bilan au niveau de chaque cellule élémentaire du maillage, et l’on gère l’évolution en suivant les valeurs moyennes dans ces cellules au cours du temps. Une autre approche consiste à suivre les caractéristiques du champ et à transporter les valeurs ponctuelles le long de ces caractéristiques. Cette approche est délicate à mettre en oeuvre, n’assure pas en général une parfaite conservation de la matière transportée, mais peut permettre dans certaines situations de transporter des quantités non régulières avec une grande précision, et sur des temps très longs (sans conditions restrictives sur le pas de temps comme dans le cas des méthodes eulériennes). Les travaux de thèse présentés ici partent de l’idée suivante : dans le cadre des méthodes utilisant un suivi de caractéristiques, transporter une quantité supplémentaire géométrique apportant plus d’informations sur le problème (on peut penser à un tenseur des contraintes dans le contexte de la mécanique des fluides, une métrique sous-jacente lors de l’adaptation de maillage, etc. ). Un premier pan du travail est la formulation théorique d’une méthode de transport de telles quantités. Elle repose sur le principe suivant : utiliser la différentielle du champ de transport pour calculer la différentielle du flot, nous donnant une information sur la déformation locale du domaine nous permettant de modifier nos quantités géométriques. Cette une approche a été explorée dans dans le contexte des méthodes particulaires plus particulièrement dans le domaine de la physique des plasmas. Ces premiers travaux amènent à travailler sur des densités paramétrées par un couple point/tenseur, comme les gaussiennes par exemple, qui sont un contexte d’applications assez naturelles de la méthode. En effet, on peut par la formulation établie transporter le point et le tenseur. La question qui se pose alors et qui constitue le second axe de notre travail est celle du choix d’une distance sur des espaces de densités, permettant par exemple d’étudier l’erreur commise entre la densité transportée et son approximation en fonction de la « concentration » au voisinage du point. On verra que les distances Lp montrent des limites par rapport au phénomène que nous souhaitons étudier. Cette étude repose principalement sur deux outils, les distances de Wasserstein, tirées de la théorie du transport optimal, et la distance de Fisher, au carrefour des statistiques et de la géométrie différentielle. / In applied mathematics, question of moving quantities by vector is an important question : fluid mechanics, kinetic theory… Using particle methods, we're going to move an additional quantity giving more information on the problem. First part of the work is the theorical formulation for this kind of transport. It's going to use the differential in space of the vector field to compute the differential of the flow. An immediate and natural application is density who are parametrized by and point and a tensor, like gaussians. We're going to move such densities by moving point and tensor. Natural question is now the accuracy of such approximation. It's second part of our work , which discuss of distance to estimate such type of densities.

A Síndrome de Guillain-Barré (SGB) é uma neuropatia periférica inflamatória aguda que tem sido definida pelo achado ou história de tetraparesia flácida arreflexa ascendente. Apresentações atípicas podem ser mais frequentes do que tem sido referido na literatura, particularmente na faixa etária infantil. Objetivo: Avaliar dados epidemiológicos e a prevalência de assimetria no exame neurológico em crianças com SGB. Métodos: Foram revisados 40 prontuários de crianças de 0 a 15 anos de idade com o diagnóstico de SGB, atendidas entre janeiro de 2000 e agosto de 2016. Avaliouse a presença de assimetrias no exame neurológico na admissão hospitalar, os desfechos clínicos e as características demográficas e clinico-laboratoriais. Resultados: Dois pacientes apresentaram assimetria no exame neurológico na admissão hospitalar e três pacientes admitidos com tetraparesia simétrica apresentaram um quadro motor assimétrico antes da internação. Uma criança evoluiu para assimetria após ter sido admitida com quadro simétrico. Outros oito casos tinham fraqueza segmentar. A presença de assimetria motora ou fraqueza segmentar se correlacionou com a progressão estática dos sintomas (p=0,004) e observou-se uma tendência desses pacientes serem mais jovens, mas essa diferença não foi significativa (p=0,08). Onze pacientes apresentavam reflexos miotáticos preservados e um paciente exibia hiperreflexia na admissão hospitalar. A maioria dos pacientes foi admitida sem conseguir deambular e, na alta, a maioria deambulava com ou sem apoio. Cinco crianças necessitaram de suporte ventilatório e nenhuma foi a óbito. Conclusão: Uma proporção significativa dos pacientes apresentava quadro motor assimétrico ou segmentar e reflexos miotáticos preservados. Os resultados obtidos delineiam aspectos clínicos atípicos na SGB em crianças e podem ajudar na definição diagnóstica e instituição de tratamento precoce. / Guillain-Barré syndrome (GBS) is an acute, inflammatory, peripheral neuropathy that has been being defined as an ascending flaccid tetraparesis. Atypical presentations can be frequent, particularly in children, leading to greater challenges in the diagnosis. Objectives: To analyze the epidemiological data and the prevalence of motor asymmetries in the neurological examination of children with GBS. Methods: A total of 40 medical records were analyzed, of children aged 0 to 15 years old diagnosed with GBS, admitted from January 2000 to August 2016. We evaluated the presence of motor asymmetries at the hospital admission, the clinical outcomes and the demographic and clinic-laboratorial characteristics. Results: Two patients had motor asymmetries at hospital admission and three patients admitted with symmetric tetraparesis had an initial motor asymmetry before admission. One patient progressed to asymmetric tetraparesis after being initially admitted with symmetric weakness. Eight other cases had segmental weakness at admission. Motor asymmetry and segmental weakness correlated with a static progression of symptoms (p=0.004) and these patients tended to be younger, but this difference was not significant (p=0.08). Eleven patients had preserved deep tendon reflexes and one exhibited hyperreflexia at the hospital admission. Most patients were admitted on wheel-chair or bedridden, and at discharge the majority could walk with or without help. Five children required mechanical ventilation and no patient died. Conclusion: A significant proportion of patients had asymmetric or segmental weakness and preserved deep tendon reflexes. Those results show that the so-called atypical clinical findings in children with GBS are not uncommon, and needs to be kept in mind to allow an earlier diagnosis and treatment.

A Síndrome de Guillain-Barré (SGB) é uma neuropatia periférica inflamatória aguda que tem sido definida pelo achado ou história de tetraparesia flácida arreflexa ascendente. Apresentações atípicas podem ser mais frequentes do que tem sido referido na literatura, particularmente na faixa etária infantil. Objetivo: Avaliar dados epidemiológicos e a prevalência de assimetria no exame neurológico em crianças com SGB. Métodos: Foram revisados 40 prontuários de crianças de 0 a 15 anos de idade com o diagnóstico de SGB, atendidas entre janeiro de 2000 e agosto de 2016. Avaliouse a presença de assimetrias no exame neurológico na admissão hospitalar, os desfechos clínicos e as características demográficas e clinico-laboratoriais. Resultados: Dois pacientes apresentaram assimetria no exame neurológico na admissão hospitalar e três pacientes admitidos com tetraparesia simétrica apresentaram um quadro motor assimétrico antes da internação. Uma criança evoluiu para assimetria após ter sido admitida com quadro simétrico. Outros oito casos tinham fraqueza segmentar. A presença de assimetria motora ou fraqueza segmentar se correlacionou com a progressão estática dos sintomas (p=0,004) e observou-se uma tendência desses pacientes serem mais jovens, mas essa diferença não foi significativa (p=0,08). Onze pacientes apresentavam reflexos miotáticos preservados e um paciente exibia hiperreflexia na admissão hospitalar. A maioria dos pacientes foi admitida sem conseguir deambular e, na alta, a maioria deambulava com ou sem apoio. Cinco crianças necessitaram de suporte ventilatório e nenhuma foi a óbito. Conclusão: Uma proporção significativa dos pacientes apresentava quadro motor assimétrico ou segmentar e reflexos miotáticos preservados. Os resultados obtidos delineiam aspectos clínicos atípicos na SGB em crianças e podem ajudar na definição diagnóstica e instituição de tratamento precoce. / Guillain-Barré syndrome (GBS) is an acute, inflammatory, peripheral neuropathy that has been being defined as an ascending flaccid tetraparesis. Atypical presentations can be frequent, particularly in children, leading to greater challenges in the diagnosis. Objectives: To analyze the epidemiological data and the prevalence of motor asymmetries in the neurological examination of children with GBS. Methods: A total of 40 medical records were analyzed, of children aged 0 to 15 years old diagnosed with GBS, admitted from January 2000 to August 2016. We evaluated the presence of motor asymmetries at the hospital admission, the clinical outcomes and the demographic and clinic-laboratorial characteristics. Results: Two patients had motor asymmetries at hospital admission and three patients admitted with symmetric tetraparesis had an initial motor asymmetry before admission. One patient progressed to asymmetric tetraparesis after being initially admitted with symmetric weakness. Eight other cases had segmental weakness at admission. Motor asymmetry and segmental weakness correlated with a static progression of symptoms (p=0.004) and these patients tended to be younger, but this difference was not significant (p=0.08). Eleven patients had preserved deep tendon reflexes and one exhibited hyperreflexia at the hospital admission. Most patients were admitted on wheel-chair or bedridden, and at discharge the majority could walk with or without help. Five children required mechanical ventilation and no patient died. Conclusion: A significant proportion of patients had asymmetric or segmental weakness and preserved deep tendon reflexes. Those results show that the so-called atypical clinical findings in children with GBS are not uncommon, and needs to be kept in mind to allow an earlier diagnosis and treatment.

The present thesis is located within the context of the diffusion approximation of Wright–Fisher models and the Kolmogorov equations describing their evolution. On the one hand, a full account of recombinational Wright–Fisher model is developed as well as their enhancement by other evolutionary mechanisms, including some information geometrical analysis. On the other hand, the thesis addresses several issues arising in the context of analytical solution schemes for such Kolmogorov equations, namely the inclusion of the entire boundary of the state space. For this, a hierarchical extension scheme is developed, both for the forward and the backward evolution, and the uniqueness of such extensions is proven. First, a systematic approach to the diffusion approximation of recombinational two- or more loci Wright–Fisher models is presented. As a point of departure a specific Kolmogorov backward equation for the diffusion approximation of a recombinational two-loci Wright–Fisher model is chosen, to which – with the help of some information geometrical methods, i. e. by calculating the sectional curvatures of the corresponding statistical manifold (which is the domain equipped with the corresponding Fisher metric) – one succeeds to identify the underlying Wright–Fisher model. Accompanying this, for all methods and tools involved a suitable introduction is presented. Furthermore, the considerations span a separate analysis for the two most common underlying models (RUZ and RUG) as well as a comparison of the two models. Finally, transferring corresponding results for a simpler model described by Antonelli and Strobeck, solutions of the Kolmogorov equations are contrasted with Brownian motion in the same domain. Furthermore, the perspective of the diffusion approximation of recombinational Wright–Fisher models is widened as the model underlying the Ohta–Kimura formula is subsequently extended by an integration of the concepts of natural fitness and mutation. Simultaneously, the corresponding extensions of the Ohta–Kimura formula are stated. Crucial for this is the development of a suitable fitness scheme, which is accomplished by a multiplicative aggregation of fitness values for pairs of gametes/zygotes. Furthermore, the model is generalised to have an arbitrary number of alleles and – in the following step – an arbitrary number of loci respectively. The latter involves an increased number of recombination modes, for which the concept of recombination masks is also implemented into the model. Another generalisation in terms of coarse-graining is performed via an application of schemata; this also affects the previously introduced concepts, specifically mask recombination, which are adapted accordingly. Eventually, a geometric analysis of linkage equilibrium states of the multi-loci Wright–Fisher models is carried out, relating to the concept of hierarchical probability distributions in information geometry, which concludes the considerations of recombinational Wright–Fisher models and their extensions. Subsequently, the discussion of analytical solution schemes for the Kolmogorov equations corresponding to the diffusion approximation of Wright–Fisher models is ushered in, which represents the second part of the thesis. This is started with the simplest setting of a 1-dimensional Wright–Fisher model, for which the solution strategy for the corresponding Kolmogorov forward equation given by M. Kimura is recalled. From this, one may construct a unique extended solution which also accounts for the dynamics of the model on lower-dimensional entities of the state space, i. e. configurations of the model where one of the alleles no longer exists in the population, utilising the concept of (boundary) flux of a solution; a discussion of the moments of the distribution confirms the findings. A similar treatment is then carried out for the corresponding Kolmogorov backward equation, yielding analogous results of existence and uniqueness for an extended solution. For the latter in particular, a corresponding account of the configuration on the boundary turns out to be crucial, which is also reflected in the probabilistic interpretation of the backward solution. Additionally, the long-term behaviour of solutions is analysed, and a comparison between such solutions of the forward and the backward equation is made. Next, it is basically aimed to transfer the results obtained in the previous chapter to the subsequent increasingly complicated setting of a Wright–Fisher model with 1 locus and an arbitrary number of alleles: With solution schemes for the interior of the state space (i. e. not encompassing the boundary) already existing in the literature, an extension scheme for a successive determination of the solution on lower-dimensional entities of the domain is developed. This scheme, again, makes use of the concept of the (boundary) flux of solutions, and one may therefore show that this extended solution fulfils additional properties regarding the completeness of the diffusion approximation with respect to the boundary. These properties may be formulated in terms of the moments of the distribution, and their connection to the underlying Wright–Fisher model is illustrated. Altogether, stipulating such a moments condition, existence and uniqueness of an extended solution on the entire domain are shown. Furthermore, the corresponding Kolmogorov backward equation is examined, for which similarly a (backward) extension scheme is presented, which allows extending a solution in a domain (perceived as a boundary instance of a larger domain) to all adjacent higher-dimensional entities of the larger domain along a certain path. This generalises the integration of boundary data observed in the previous chapter; in total, the existence of a solution of the Kolmogorov backward equation in the entire domain is shown for arbitrary boundary data. Of particular interest to the discussion are stationary solutions of the Kolmogorov backward equation as they describe eventual hit probabilities for a certain target set of the model (in accordance with the probabilistic interpretation of solutions of the backward equation). The presented backward extension scheme allows the construction of solutions for all relevant cases, reconfirming some results by R. A. Littler for the stationary case, but now providing a previously missing systematic derivation. Eventually, the hitherto missing uniqueness assertion for this type of solutions is established by means of a specific iterated transformation which resolves the critical incompatibilities of solutions by a successive blow-up while the domain is converted from a simplex into a cube. Then – under certain additional assumptions on the regularity of the transformed solution – the uniqueness directly follows from general principles. Lastly, several other aspects of the blow-up scheme are discussed; in particular, it is illustrated in what way the required extra regularity relates to reasonable additional properties of the underlying Wright–Fisher model.

Thesis (M.A.)--West Virginia University, 2005. / Title from document title page. Document formatted into pages; contains iii, 90 p. Includes abstract. Includes bibliographical references (p. 88-90).

L'objectif de la thèse est d'étudier le modèle du look-down avec sélection dans le cas d'une population composée seulement de deux types génétiques, l'un deux bénéficiant d'un avantage sélectif. Dans cette thèse, cette sélection est modélisée par un taux de mort pour les individus non avantagés. Tout d'abord, nous nous intéressons dans le cas d'une population de taille infinie. Nous montrons que le modèle est bien défini. Nous montrons aussi que dans la limite d'une population de taille infinie, la proportion d'individu d'un type donné suit la diffusion de Wright-Fisher avec sélection. Ensuite nous étudions ce modèle dans le cas d'une population de taille finie et fixée. Nous proposons deux méthodes de convergence de ce modèle fini vers la diffusion deWright-Fisher avec sélection. Enfin, une autre approche est considérée. Nous étudions le modèle de look-down dans le cas d'une population de taille infinie en remplaçant le modèle de reproduction dual du coalescent de Kingman par le modèle de reproduction dual du Lambda-coalescent. Nous montrons d'abord que le modèle est bien défini. Ensuite nous montrons que la proportion de l'un des types converge en probabilité, quand la taille N de la population tend vers l'infini, vers un processus qui est solution d'une équation différentielle stochastique dirigée par processus ponctuel de Poisson. Pour finir, nous montrons que si Lambda-coalescent descend de l'infini alors l'un des types se fixe en temps fini. / The purpose of the dissertation is to study the look-down model with selection in the case of a population composed only two alleles, one of them has a selective advantage. In this thesis, this selective advantage is modelled by a death rate for the wild-type allele. In the first part, we are interested in the case of a population of infinite size. We show the model is well defined. We show convergence in probability, as the population size tends to infinity, towards the Wright-Fisher diffusion with selection. In the second part we study a variant of the simplest look-down with selection where the size of the population is finite and fixed. We propose two methods of convergence of this finite model towards the Wright-Fisher diffusion with selection. Finally, another approach is considered. We study the look-down model with selection when we replace the usual reproduction model, which is dual to Kingman's coalescent by a population model dual to the Lambda-coalescent in the case of a population of infinite size. We first show this model is well defined. We show that the proportion of one of the two types converges in probability, as the population size N tends to infinity, towards the solution of a stochastic differential equation driven by a Poisson point process. Finally, we show that one of the two types fixate in finite time if and only if the Lambda-coalescent comes down from infinity.