<p dir="ltr">Topological Data Analysis (TDA) with its roots embedded in the field of algebraic topology has successfully found its applications in computational biology, drug discovery, machine learning and in many diverse areas of science. One of its cornerstones, persistent homology, captures topological features latent in the data. Recent progress in TDA allows us to integrate these finer topological features into traditional machine learning and deep learning pipelines. However, the utilization of topological methods within a conventional deep learning framework remains relatively uncharted. This thesis presents four scenarios where computational topology tools are employed to advance machine learning.</p><p dir="ltr">The first one involves integrating persistent homology to explore high-dimensional cytometry data. The second one incorporates Extended persistence in a supervised graph classification framework and demonstrates leveraging TDA in cases where data naturally aligns with higher-order elements by extending graph neural networks to higher-order networks, applied specifically in non-manifold mesh classification. The third and fourth scenarios delve into enhancing graph neural networks through multiparameter persistence.</p>

L’amélioration des performances de reproduction des poissons d’élevage nécessite de déterminer les facteurs intrinsèques et extrinsèques influençant la qualité des gamètes d’une part, et de définir des paramètres fiables permettant de prédire les performances de reproduction d’autre part. Notre objectif est donc de comprendre le déterminisme multifactoriel de la reproduction chez la perche commune, Perca fluviatilis. Quatre facteurs nutritionnels (type d’aliment et taux de rationnement distribués lors des phases d’induction et de vernalisation) et 3 facteurs populationnels (poids initial, origine géographique, niveau de domestication) ont été testés. Une différence de réponse entre les sexes a été observée. Le type d’aliment distribué en vernalisation et le poids initial ont modifié l’état général des femelles. Les mâles ont plutôt été sensibles aux taux de rationnement et à l’origine géographique. L’étude des performances de reproduction a montré que le taux de ponte était sous l’influence de l’interaction entre le type d’aliment distribué en induction et en vernalisation, tandis que l’origine géographique a modulé la date de ponte. La régulation des performances de reproduction est donc un mécanisme complexe sous l’influence simultanée de plusieurs facteurs. La seconde partie de ce travail concerne la recherche de marqueurs prédictifs de la qualité des ovules. Nous avons d’abord montré que peu de paramètres morpho-anatomiques des pontes ou ovules sont des prédicateurs fiables. Cependant, l’analyse protéomique a permis de mettre en évidence plusieurs protéines exprimées différemment selon la qualité des pontes, pouvant jouer le rôle de biomarqueurs de qualité des ovules / Improving fish reproduction in breeding conditions implies to understand intrinsic and extrinsic factors influencing gametes quality on the one hand and to define relevant parameters allowing the prediction of fish reproductive performance on the other hand. Our goal was thus to understand the multifactorial determinism of the common perch (Perca fluviatilis) reproduction. Four nutritional factors (type of food and rate of rationing used either during the induction or vernalization phases) and 3 populational factors (initial weight, geographic origin and domestication level of breeders) have been tested. Data show different responses between females and males. type of food during wintering phase and initial broodstock weigh modified female condition. Males have been sensitive to rationing during wintering phase as well as geographical origin. Data show also that spawning rate was under the influence of interaction between kind of food during wintering phase and induction whereas geographical origin modulated the spawning date. The regulation of the performance reproduction is also a complex mechanism influenced by several factors. The second part of this work consisted on the research of parameters potentially predictive of ova quality. Firstly, our work shows that morphometric parameters measured before the fertilization are poorly relevant to predict reproductive performance. However, the proteomic analysis of several spawn allowed us to highlight proteins differently expressed according to the spawn quality, such proteins could be ova quality biomarkers

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In the environmental licensing of hydroelectric plants are prescribed streamflow should be maintained downstream of the dam, but these flows often cannot ensure the maintenance of water quality for the stretch. The aim of this study is to present a robust and expeditious strategy of water quality monitoring. This strategy is developed for supporting the stipulation of flow regime in reduced flow reach (RFR) by dams. The Hydropower plant Passo São João (HPP PSJ) in Rio Ijuí-RS was used as study case. This Hydropower is a power plant without storage capacity presenting a RFR of 4 km. The monitoring for collecting water quality data is made by using a multiparameter probe and laboratory analysis. It is used ten monitoring points along the Rio Ijuí, two of them located in the RFR. Correlations between data obtained with a multiparameter probe and data determined in the laboratory are made to evaluate the application of the probe. Complementing the study, the HPP PSJ is contextualized according to the impact on water quality in the Rio Ijuí, tracing a longitudinal profile of dissolved oxygen (DO) along with the evaluation of the direct contribution by RFR comparison of flows. Moreover, the variability of DO concentrations in sections monitoring RFR is evaluated considering the determinations along the section. Those sections are associated with flow velocity profiles that were determined by the Acoustic Doppler Current Profiler (ADCP). The correlations between the curves of monitoring data and curves from the extraction of data - at different frequencies - are developed for determining the optimal monitoring frequency. The comparison between measurements with the probe and measurements in the laboratory are satisfactory, presenting similar values for most parameters. The layout of the longitudinal profile of the DO concentrations demonstrates the strong influence of the HPP PSJ structures in dam downstream DO level, reinforcing the need for a monitoring strategy. However the effect of reducing inflow in the dilution charges has not been noted in view of the minimum incremental area flow. Near riverbank measurements were representative, since the variability of measurements along the section generally was less than 2% on average. Finally the ideal frequency obtained with the correlation curves for different frequencies is four days for both points of RFR. The overall conclusion of this study is to propose a monitoring strategy based on using a multiparameter probe in which the operator formulates the determinations near the riverbank with a monitoring frequency of four days, taking as basis the representative parameter the dissolved oxygen for this case. / Quando do licenciamento ambiental de usinas hidrelétricas, são prescritas vazões a serem mantidas a jusante do barramento, que muitas vezes podem não garantir a manutenção da qualidade da água para o trecho. O objetivo deste estudo foi propor uma estratégia expedita de monitoramento da qualidade da água em suporte a prescrição de regime de vazões remanescentes em trechos de vazão reduzida (TVR) por barramentos. Para tanto foi utilizado como caso de estudo a UHE Passo do São João (UHE PSJ) no Rio Ijuí-RS, que opera a fio d água e possui um TVR de 4 km. Como base do estudo foi feito um monitoramento para levantamento de dados de qualidade da água com a utilização de sonda multiparâmetro e análises em laboratório. Foram utilizados 10 pontos de monitoramento ao longo do Rio Ijuí, sendo 2 deles, os principais no estudo, localizados no TVR. Foram feitas correlações entre os dados obtidos com a sonda multiparâmetro e determinados em laboratórios para avaliação do uso da sonda. Complementando o estudo, foi feita uma contextualização da UHE PSJ no que se refere ao impacto na qualidade da água no Rio Ijuí, traçando um perfil longitudinal de concentração de oxigênio dissolvido (OD), juntamente com a avaliação do aporte direto ao TVR por meio da comparação de vazões. Ainda foi realizada uma avaliação da variabilidade das concentrações de OD nas seções de monitoramento do TVR, com determinações ao longo da seção, associadas aos perfis de velocidade do escoamento determinados com o uso de Acoustic Doppler Current Profiler (ADCP). Por fim foram realizadas correlações entre as curvas dos dados do monitoramento e curvas resultantes da extração de dados com diferentes frequências, para a determinação da frequência ideal de monitoramento. A comparação entre as determinações com a sonda e no laboratório foi satisfatória, mostrando valores próximos para a maioria dos parâmetros. O traçado do perfil longitudinal das concentrações de OD mostrou a forte influência das estruturas da UHE PSJ nos níveis de OD a jusante do barramento no TVR, reforçando a demanda por uma estratégia de monitoramento. Porém o efeito da redução das vazões na diluição de cargas não foi notado, tendo em vista a insignificância das vazões da área incremental ao TVR. As medições próximas a margem foram representativas, pois a variabilidade das determinações ao longo da seção em geral foi menor que 2% em relação a média. Por fim a frequência ideal obtida com a correlação das curvas de diferentes frequências foi de 4 dias para os dois pontos do TVR. Como conclusão geral deste estudo, fica a proposição de uma estratégia de monitoramento, baseada na utilização de uma sonda multiparâmetro, onde o operador fará as determinações próximas a margem do rio, com uma frequência de monitoramento de 4 dias, tendo como base um parâmetro representativo, no caso o oxigênio dissolvido.

Cette thèse porte essentiellement sur l'étude des solutions stationnaires, en dimension 1 d'espace, d'unmodèle de champs de phase cristallin introduit par Elder en 2002. Ainsi, nous prouvons, par la méthode deréduction de Lyapunov-Schmidt et la technique des multiparamètres, l'existence de courbes de solutionsbifurquantes stationnaires lorsque le noyau de l'opérateur linéarisé, au voisinage de la solution triviale estde dimension 2. Une parenthèse est ouverte pour la comparaison de l'énergie de la solution bifurquantepar rapport à celle la solution triviale. Aussi, grâce au principe de la stabilité réduite, nous fournissonsdes ensembles précis de valeurs des paramètres de bifurcation pour lesquelles les solutions obtenues sontstables ou instables. Ces résultats théoriques sont corroborés par plusieurs tests numériques.Par ailleurs, dans le cas classique du noyau unidimensionel, nous établissons des diagrammes de phasespermettant de comprendre les différentes orientations de courbes de solutions non triviales au voisinage dechaque point de bifurcation. / This thesis is devoted to the study of stationary solutions of a Phase Field Crystal model, in one spacedimension, introduced by Elder in 2002. Thus, we prove by the Lyapunov-Schmidt method of reductionand the multiparameter technique, the existence of the curves of bifurcating stationary solutions whenthe kernel of the linearized operator near to trivial solution is of two dimension. A parenthesis is open forcomparing the energies of the bifurcating solution and the trivial solution. Also, thanks to the principle ofreduced stability, we provide specific sets of parameter values for wich the obtained solutions are stable orunstable. These theoretical results are confirmed by several numerical tests.Moreover, in the classical case of a one dimensional kernel, we establish the phase diagrams allowing tounderstand the different orientations of non-trivial solutions curves near to of each bifurcation point.

Le radar géologique est une méthode d'investigation géophysique basée sur la propagation d'ondes électromagnétiques dans le sous-sol. Avec des fréquences allant de 5 MHz à quelques GHz et une forte sensibilité aux propriétés électriques, le géoradar fournit des images de réflectivité dans des contextes et à des échelles très variés : génie civil, géologie, hydrogéologie, glaciologie, archéologie. Cependant, dans certains cas, la compréhension fine des processus étudiés dans la subsurface nécessite une quantification des paramètres physiques du sous-sol. Dans ce but, l'inversion des formes d'ondes complètes, méthode initialement développée pour l'exploration sismique qui exploite l'ensemble des signaux enregistrés, pourrait s'avérer efficace. Dans cette thèse, je propose ainsi des développements méthodologiques par une approche d'inversion multiparamètres (permittivité diélectrique et conductivité), pour des configurations en transmission, en deux dimensions.Ces développements sont ensuite appliqués à un jeu de données réelles acquises entre forages.Dans une première partie, je présente tout d'abord la méthode numérique utilisée pour modéliser la propagation des ondes électromagnétiques dans un milieu 2D hétérogène, élément indispensable pour mener à bien le processus d'imagerie. Ensuite, j’introduis puis étudie le potentiel des méthodes d’optimisation locale standards (gradient conjugué non linéaire, l-BFGS, Newton tronqué dans ses versions Gauss-Newton et Exact-Newton) pour découpler la permittivité diélectrique et la conductivité électrique. Je montre notamment qu’un découplage effectif n’est possible qu’avec un modèle initial suffisamment précis et la méthode la plus sophistiquée (Newton tronqué). Comme dans le cas général, ce modèle initial n’est pas disponible, il s’avère nécessaire d'introduire un facteur d'échelle qui répartit le poids relatif de chaque classe de paramètres dans l'inversion. Dans un milieu réaliste avec une acquisition entre puits, je montre que les différentes méthodes d'optimisation donnent des résultats similaires en matière de découplage de paramètres. C'est finalement la méthode l-BFGS qui est retenue pour l'application aux données réelles, en raison de coûts de calcul plus faibles.Dans une deuxième partie, j'applique cette méthodologie à des données réelles acquises entre deux forages localisés dans des formations carbonatées, à Rustrel (France, 84). Cette inversion est réalisée en parallèle d'une approche synthétique à l'aide d'un modèle représentatif du site étudié et des configurations d'acquisition similaires. Ceci permet de pouvoir comprendre, contrôler et valider les observations et conclusions obtenues sur les données réelles. Cette démarche montre que la reconstruction de la permittivité est très robuste. A contrario, l'estimation de la conductivité souffre de deux couplages majeurs, avec la permittivité diélectrique, d'une part, et avec l'amplitude de la source estimée, d'autre part. Les résultats obtenus sont confrontés avec succès à des données indépendantes (géophysique depuis la surface, analyse sur échantillons de roche), et permet de bénéficier d'une image haute-résolution des formations géologiques. Enfin, une analyse 3D confirme que les structures 3D à fort contraste de propriétés, telles que la galerie enfouie sur notre site, nécessiteraient une approche de modélisation 3D, notamment pour mieux expliquer les amplitudes observées. / Ground Penetrating Radar (GPR) is a geophysical investigation method based on electromagnetic waves propagation in the underground. With frequencies ranging from 5 MHz to a few GHz and a high sensitivity to electrical properties, GPR provides reflectivity images in a wide variety of contexts and scales: civil engineering, geology, hydrogeology, glaciology, archeology. However, in some cases, a better understanding of some subsurface processes requires a quantification of the physical parameters of the subsoil. For this purpose, inversion of full waveforms, a method initially developed for seismic exploration that exploits all the recorded signals, could prove effective. In this thesis, I propose methodological developments using a multiparameter inversion approach (dielectric permittivity and conductivity), for two-dimensional transmission configurations. These developments are then applied to a real data set acquired between boreholes.In a first part, I present the numerical method used to model the propagation of electromagnetic waves in a heterogeneous 2D environment, a much-needed element to carry out the process of imaging. Then, I introduce and study the potential of standard local optimization methods (nonlinear conjugate gradient, l-BFGS, Newton truncated in its Gauss-Newton and Exact-Newton versions) to fight the trade-off effects related to the dielectric permittivity and to the electrical conductivity. In particular, I show that effective decoupling is possible only with a sufficiently accurate initial model and the most sophisticated method (truncated Newton). As in the general case, this initial model is not available, it is necessary to introduce a scaling factor which distributes the relative weight of each parameter class in the inversion. In a realistic medium and for a cross-hole acquisition configuration, I show that the different optimization methods give similar results in terms of parameters decoupling. It is eventually the l-BFGS method that is used for the application to the real data, because of lower computation costs.In a second part, I applied the developed Full waveform inversion methodology to a set of real data acquired between two boreholes located in carbonate formations, in Rustrel (France, 84). This inversion is carried out together with a synthetic approach using a model representative of the studied site and with a similar acquisition configuration. This approach enables us to monitor and validate the observations and conclusions derived from data inversion. It shows that reconstruction of dielectrical permittivity is very robust. Conversely, conductivity estimation suffers from two major couplings: the permittivity and the amplitude of the estimated source. The derived results are successfully compared with independent data (surface geophysics and rock analysis on plugs) and provides a high resolution image of the geological formation. On the other hand, a 3D analysis confirms that 3D structures presenting high properties contrasts, such as the buried gallery present in our site, would require a 3D approach, notably to better explain the observed amplitudes.

Bei Verdacht auf Vorliegen einer systemischen Autoimmunerkrankung wird für die serologische Routinediagnostik ein Zwei-Stufen-Verfahren empfohlen. Zuerst werden Autoantikörpern (AAK) mittels sensitiver zellbasierter indirekter Immunfluoreszenz (IIF)-Teste bestimmt. Ein positives Ergebnis muss aufgrund der Möglichkeit von falsch-positiven Ergebnissen mit einem weiteren, spezifischen Test bestätigt werden. Dieses sukzessive Vorgehen ist notwendig, da zurzeit keine Assaytechnik die notwendigen Anforderungen an ein einstufiges Verfahren hinsichtlich Sensitivität und Spezifität erfüllt. Im Sinne einer effektiven AAK-Diagnostik kann heute schon eine simultane Bestimmung von mehreren AAK mittels multiparametrischer Bestätigungstests die Diagnosefindung im Vergleich zu konventionellen, monoparametrischen Tests wesentlich verkürzen. Jedoch erlauben die verfügbaren multiparametrischen AAK-Nachweismethoden nicht die Kombination von Screening- und Bestätigungstesten. Deshalb wurde basierend auf der digitalen Fluoreszenz mit der hier vorgestellten CytoBead Technologie ein neuer Ansatz entwickelt. Ziel war die Kombination der empfohlenen Stufendiagnostik bestehend aus sensitivem Screening und spezifischer Bestätigungsdiagnostik in einer Reaktionsumgebung und darüber hinaus die Möglichkeit der Adaption auf die serologische Diagnostik mehrerer Autoimmunerkrankungen. Durch a) die Nutzung von Standardglasobjektträgern, b) die Kombination von nativen zellulären oder Gewebesubstraten mit antigenbeladenen fluoreszierenden Mikropartikeln (Beads) in einer Reaktionsumgebung, c) die Möglichkeit der manuellen und automatischen Auswertung mittels IIF und d) die Erhebung von quantitativen Fluoreszenzmessergebnissen konnten die Nachteile der bisher bestehenden Testsysteme überwunden werden. Das neue Prinzip ist auf verschiedene multiparametrische AAK-Nachweise wie zum Beispiel die Bestimmung von antinukleären Antikörpern und AAK gegen entsprechende nukleäre und zytoplasmatische autoantigene Zielstrukturen anwendbar. Damit wurde weiterhin die Basis für die simultane AAK-Multiparameterbestimmung für die Serologie der Zöliakie und von ANCA-assoziierten systemischen Vaskulitiden geschaffen.

This thesis is focused on shape optimization of Venturi´s nozzle with optimization method called response surface method. The first part of this work is concerned with the description of this method as well as explaining the basic principle. Furthermore, there is an explanation of the application of this method in synchronicity with CFD and its operating algorithm. The second part of this thesis is then focused on simple example with plane wing and simplified optimization of Venturi´s nozzle in which this method was tested. In the third part there is described full multiparameter shape optimalization of the nozzle for two geometries.

<p>The only datasets used in my thesis work are from TUDatasets, <a href="https://chrsmrrs.github.io/datasets/">TUDataset | TUD Benchmark datasets (chrsmrrs.github.io)</a>, a collection of public benchmark datasets for graph classification and regression.</p><p><br></p>

<p>Osnovni doprinos ove doktorske disertacije je razvoj algortima i sistema za objektivnu procenu vizuelnog kvaliteta slike uzimajući u obzir najvažnija moguća oštećenja kao što su zamućenje ivica (oštrina) i poremećaj prirodnog izgleda teksture objekata na slici sa jedne strane i uticaj sadržaja slike (procenta ivica u slici) na procenu kvaliteta sa druge strane. Dakle, hipoteza izneta u ovom radu je da je potreban multiparametarski pristup da bi se dobila objektivna procena kvaliteta slike koja je što približnija subjektivnoj proceni.</p>