Cette thèse présente des méthodes d’imagerie pour l’analyse du mouvement cardiaque afin de permettre des statistiques groupées, un diagnostic automatique et une étude longitudinale. Ceci est réalisé en combinant des méthodes d’apprentissage et de modélisation statistique. En premier lieu, une méthode automatique de segmentation du myocarde est définie. Pour ce faire, nous développons une méthode de recalage très rapide basée sur des réseaux neuronaux convolutifs qui sont entrainés à apprendre le recalage cardiaque inter-sujet. Ensuite, nous intégrons cette méthode de recalage dans une pipeline de segmentation multi-atlas. Ensuite, nous améliorons des méthodes de suivi du mouvement cardiaque afin de définir des représentations à faible dimension. Deux méthodes différentes sont développées, l’une s’appuyant sur des sous-espaces barycentriques construits sur des frames de référence de la séquence et une autre basée sur une représentation d’ordre réduit du mouvement avec des transformations polyaffine. Enfin, nous appliquons la représentation précédemment définie au problème du diagnostic et de l’analyse longitudinale. Nous montrons que ces représentations en- codent des caractéristiques pertinentes permettant le diagnostic des patients atteint d’infarct et de Tétralogie de Fallot ainsi que l’analyse de l’évolution dans le temps du mouvement cardiaque des patients atteints de cardiomyopathies ou d’obésité. Ces trois axes forment un cadre pour l’étude du mouvement cardiaque de bout en bout de l’acquisition des images médicales jusqu’à leur analyse automatique afin d’améliorer la prise de décision clinique grâce à un traitement personnalisé assisté par ordinateur. / This thesis presents image-based methods for the analysis of cardiac motion to enable group-wise statistics, automatic diagnosis and longitudinal study. This is achieved by combining advanced medical image processing with machine learning methods and statistical modelling. The first axis of this work is to define an automatic method for the segmentation of the myocardium. We develop a very-fast registration method based on convolutional neural networks that is trained to learn inter-subject heart registration. Then, we embed this registration method into a multi-atlas segmentation pipeline. The second axis of this work is focused on the improvement of cardiac motion tracking methods in order to define relevant low-dimensional representations. Two different methods are developed, one relying on Barycentric Subspaces built on ref- erences frames of the sequence, and another based on a reduced order representation of the motion from polyaffine transformations. Finally, in the last axis, we apply the previously defined representation to the problem of diagnosis and longitudinal analysis. We show that these representations encode relevant features allowing the diagnosis of infarcted patients and Tetralogy of Fallot versus controls and the analysis of the evolution through time of the cardiac motion of patients with either cardiomyopathies or obesity. These three axes form an end to end framework for the study of cardiac motion starting from the acquisition of the medical images to their automatic analysis. Such a framework could be used for diagonis and therapy planning in order to improve the clinical decision making with a more personalised computer-aided medicine.

Title: Photon strength functions in Gd isotopes studied from resonance neutron capture Author: RNDr. Jiří Kroll Department: Intitute of particle and nuclear physics Supervisor: doc. Mgr. Milan Krtička, Ph.D., Intitute of particle and nuclear physics Abstract: Photon strength functions have been studied for more than sixty years. A number of theoretical models was proposed to describe experimental data during that time. However, the correctness of these models is still very questionable and its verification is the subject of very intensive experimental and theoretical activity at present time. In this thesis the analysis of spectra of γ rays following the radiative capture of neutrons on isolated neutron resonances of 152,154−158 Gd nuclei is used to study photon strength functions. Experimental data were measured using segmented DANCE calorimeter that is installed at Los Alamos Neutron Scattering Center in New Mexico, USA. Experimental spectra are then compared with the outputs of Monte Carlo simulation of nuclear elec- tromagnetic decay, performed by DICEBOX code, that is based on the validity of the so-called Extreme Statistical Model. The response of the detector system to generated γ cascades was subsequently calculated using the Geant4 code. An analysis of the data clearly indicates that magnetic...

The γ decay of highly excited nuclear levels can be described within the statistical model of nucleus in terms of the level density and a set of photon strength functions. The knowledge of these quantities enables more accurate calculations of reaction rates in many different reactions which are important especially in nuclear astrophysics and in the development of advanced nuclear reactors. Despite the fact that the photon strength functi- ons have been studied for decades, there are still contradicting experimental results regarding the low energy behavior of dipole strength. One of these ca- ses is the shape of electric dipole photon strength function and the strength of the scissors mode in well-deformed rare-earth nuclei. In this thesis the ana- lyses of γ-ray spectra measured by two different experimental setups are pre- sented. The two-step γ cascades measurements with odd gadolinium targets were performed at the research reactor LVR-15 at the Research Centre Řež. In the multi-step γ cascades experiments the γ rays following resonance ne- utron capture on 161−163 Dy targets were measured with the highly-segmented γ-ray calorimeter Detector for Advanced Neutron Capture Experiments in the Los Alamos Neutron Science Center at Los Alamos National Labora- tory. Experimental spectra were compared...

In the thesis "On Boundaries of Statistical Models" problems related to a description of probability distributions with zeros, lying in the boundary of a statistical model, are treated. The distributions considered are joint distributions of finite collections of finite discrete random variables. Owing to this restriction, statistical models are subsets of finite dimensional real vector spaces. The support set problem for exponential families, the main class of models considered in the thesis, is to characterize the possible supports of distributions in the boundaries of these statistical models. It is shown that this problem is equivalent to a characterization of the face lattice of a convex polytope, called the convex support. The main tool for treating questions related to the boundary are implicit representations. Exponential families are shown to be sets of solutions of binomial equations, connected to an underlying combinatorial structure, called oriented matroid. Under an additional assumption these equations are polynomial and one is placed in the setting of commutative algebra and algebraic geometry. In this case one recovers results from algebraic statistics. The combinatorial theory of exponential families using oriented matroids makes the established connection between an exponential family and its convex support completely natural: Both are derived from the same oriented matroid. The second part of the thesis deals with hierarchical models, which are a special class of exponential families constructed from simplicial complexes. The main technical tool for their treatment in this thesis are so called elementary circuits. After their introduction, they are used to derive properties of the implicit representations of hierarchical models. Each elementary circuit gives an equation holding on the hierarchical model, and these equations are shown to be the "simplest", in the sense that the smallest degree among the equations corresponding to elementary circuits gives a lower bound on the degree of all equations characterizing the model. Translating this result back to polyhedral geometry yields a neighborliness property of marginal polytopes, the convex supports of hierarchical models. Elementary circuits of small support are related to independence statements holding between the random variables whose joint distributions the hierarchical model describes. Models for which the complete set of circuits consists of elementary circuits are shown to be described by totally unimodular matrices. The thesis also contains an analysis of the case of binary random variables. In this special situation, marginal polytopes can be represented as the convex hulls of linear codes. Among the results here is a classification of full-dimensional linear code polytopes in terms of their subgroups. If represented by polynomial equations, exponential families are the varieties of binomial prime ideals. The third part of the thesis describes tools to treat models defined by not necessarily prime binomial ideals. It follows from Eisenbud and Sturmfels'' results on binomial ideals that these models are unions of exponential families, and apart from solving the support set problem for each of these, one is faced with finding the decomposition. The thesis discusses algorithms for specialized treatment of binomial ideals, exploiting their combinatorial nature. The provided software package Binomials.m2 is shown to be able to compute very large primary decompositions, yielding a counterexample to a recent conjecture in algebraic statistics.

While operating in online markets offers opportunities for expanded assortment and convenience, it also poses challenges such as increased competition and the need to build personal relationships with customers. Customer retention be- comes crucial in maintaining a successful business, emphasizing the importance of understanding customer behavior. Traditionally, customer behavior analysis has focused on transactional behavior, such as purchase frequency and spending amounts. However, there has been a shift towards non-transactional behavior, driven by the popularity of loyalty programs that reward customers beyond trans- actions and aim to make customers feel appreciated and included, regardless of their spending power. This study is conducted at a global retailer with the aim of enhancing the under- standing of how non-transactional customer behavior influences customer churn. The approach in this study is to understand such behavior by developing a statis- tical model and to analyze statistical approaches of feature importance. Two types of approaches for statistical modeling, each with four variations, are assessed: (1) Random forest; and (2) Logistic regression. Furthermore, three different feature importance methods are considered; (1) Gini importance; (2) Permutation impor- tance and (3) Coefficient importance. The results showed that this approach can be used to analyze customer behavior and gain a better understanding of the driving factors for churn. Furthermore, the results showed that random forest approaches outperform logistic regression. With the definition of churn constructed in this study, the most important factors that affect the probability of churn are the customer’s number of sessions and inter session interval. / Att bedriva e-handel erbjuder inte enbart möjligheter för utökat sortiment och bekvämlighet, utan leder även till ökad konkurrens och ett ökat behov av att bygga relationer med kunder. Kundlojalitet är därmed avgörande för att upprätthålla en framgångsrik verksamhet, och betonar vikten av att förstå kundernas beteende. Traditionellt har analyser av kundbeteende främst bedrivits med fokus på transak- tionellt beteende, såsom frekvens eller totalbelopp för köp. På senare tid har allt mer fokus lagts på icke-transaktionellt beteende, på grund av införandet av lo- jalitetsprogram som belönar kunder bortom transaktioner, med målet att kunder ska känna sig uppskattade och inkluderade, oavsett köpkraft. Denna studie genomförs hos ett globalt detaljhandelsföretag med målet att utöka förståelsen för hur icke-transaktionellt kundbeteende påverkar kundbortfall. För att uppnå detta konstrueras en statistisk modell som utnyttjas för att med hjälp av statistiska metoder analysera signifikans hos variabler. Två kategorier av statis- tiska modeller undersöks; (1) Random forest och (2) Logistisk regression. Utöver detta används tre olika metoder för att analysera signifikans hos variabler; (1) Gini-betydelse; (2) Permutationsbetydelse; och (3) Koefficientbetydelse. Resultatet visar att studiens tillvägagångssätt kan användas för att analysera kund- beteende och nå ökad förståelse för vad som driver kundbortfall. Vidare visar re- sultatet att random forest-modeller överträffar modeller baserade på logistisk re- gression. Baserat på den definition av kundbortfall som definierats i denna studie är de viktigaste faktorerna som påverkar sannolikheten för kundbortfall, kundens antal sessioner och intervallet mellan kundens sessioner.

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With the prevalence of technology and computer systems in today’s society, it is crucial to ensure that the systems we use are secure. The fields that study these issues, cybersecurity and cybersafety, use the formal verification technique of modelchecking. This paper tackles one aspect of the work needed to develop model-checking methods as we try to improve the efficiency and the reliability of model-checking techniques using the Time Petri Net model. Formal methods based on Time Petri Nets are not exempt from the state-explosion problem, and we study here different approaches to circumvent this problem. In particular, we show that limiting the exploration of such a model to runs with integer dates maintains the integrity of the model-checking result. We also show that it is possible to set a limit on the number of runs that can be explored while maintaining the probability that the observation is correct above a certain threshold. / Med tanke på hur vanligt det är med teknik och datorsystem i dagens samhälle är det viktigt att se till att de system vi använder är säkra. De områden som studerar dessa frågor, cybersäkerhet och cybersafety, använder den formella verifieringstekniken modellkontroll. Denna artikel tar upp en aspekt av det arbete som krävs för att utveckla metoder för modellkontroll, eftersom vi försöker förbättra effektiviteten och tillförlitligheten hos metoder för modellkontroll med hjälp av Time Petri Netmodellen. Formella metoder baserade på Time Petri Nets är inte undantagna från problemet med tillståndsexplosion, och vi studerar här olika tillvägagångssätt för att kringgå detta problem. I synnerhet visar vi att om man begränsar utforskningen av en sådan modell till körningar med heltalsdatum bibehålls integriteten hos resultatet av modellkontrollen. Vi visar också att det är möjligt att sätta en gräns för antalet körningar som kan utforskas samtidigt som sannolikheten för att observationen är korrekt hålls över ett visst tröskelvärde.

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