Starting from the observation that substances and reactions are the central entities of chemistry, I have structured chemical knowledge into a formal space called a directed hypergraph, which arises when substances are connected by their reactions. I call this hypernet chemical space. In this thesis, I explore different levels of description of this space: its evolution over time, its curvature, and categorical models of its compositionality. The vast majority of the chemical literature focuses on investigations of particular aspects of some substances or reactions, which have been systematically recorded in comprehensive databases such as Reaxys for the last 200 years. While complexity science has made important advances in physics, biology, economics, and many other fields, it has somewhat neglected chemistry. In this work, I propose to take a global view of chemistry and to combine complexity science tools, modern data analysis techniques, and geometric and compositional theories to explore chemical space. This provides a novel view of chemistry, its history, and its current status. We argue that a large directed hypergraph, that is, a model of directed relations between sets, underlies chemical space and that a systematic study of this structure is a major challenge for chemistry. Using the Reaxys database as a proxy for chemical space, we search for large-scale changes in a directed hypergraph model of chemical knowledge and present a data-driven approach to navigate through its history and evolution. These investigations focus on the mechanistic features by which this space has been expanding: the role of synthesis and extraction in the production of new substances, patterns in the selection of starting materials, and the frequency with which reactions reach new regions of chemical space. Large-scale patterns that emerged in the last two centuries of chemical history are detected, in particular, in the growth of chemical knowledge, the use of reagents, and the synthesis of products, which reveal both conservatism and sharp transitions in the exploration of the space. Furthermore, since chemical similarity of substances arises from affinity patterns in chemical reactions, we quantify the impact of changes in the diversity of the space on the formulation of the system of chemical elements. In addition, we develop formal tools to probe the local geometry of the resulting directed hypergraph and introduce the Forman-Ricci curvature for directed and undirected hypergraphs. This notion of curvature is characterized by applying it to social and chemical networks with higher order interactions, and then used for the investigation of the structure and dynamics of chemical space. The network model of chemistry is strongly motivated by the observation that the compositional nature of chemical reactions must be captured in order to build a model of chemical reasoning. A step forward towards categorical chemistry, that is, a formalization of all the flavors of compositionality in chemistry, is taken by the construction of a categorical model of directed hypergraphs. We lifted the structure from a lineale (a poset version of a symmetric monoidal closed category) to a category of Petri nets, whose wiring is a bipartite directed graph equivalent to a directed hypergraph. The resulting construction, based on the Dialectica categories introduced by Valeria De Paiva, is a symmetric monoidal closed category with finite products and coproducts, which provides a formal way of composing smaller networks into larger in such a way that the algebraic properties of the components are preserved in the resulting network. Several sets of labels, often used in empirical data modeling, can be given the structure of a lineale, including: stoichiometric coefficients in chemical reaction networks, reaction rates, inhibitor arcs, Boolean interactions, unknown or incomplete data, and probabilities. Therefore, a wide range of empirical data types for chemical substances and reactions can be included in our model.

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This research paper focuses on fraud detection in the financial industry using Generative Adversarial Networks (GANs) in conjunction with Uni and Multi Variate Bayesian Model with Shrinkage Priors (BMSP). The problem addressed is the need for accurate and advanced fraud detection techniques due to the increasing sophistication of fraudulent activities. The methodology involves the implementation of GANs and the application of BMSP for variable selection to generate synthetic fraud samples for fraud detection using the augmented dataset. Experimental results demonstrate the effectiveness of the BMSP GAN approach in detecting fraud with improved performance compared to other methods. The conclusions drawn highlight the potential of GANs and BMSP for enhancing fraud detection capabilities and suggest future research directions for further improvements in the field.

Η παρούσα διπλωματική εργασία ασχολείται με πολυδιάστατα κατηγορικά δεδομένα όπως αυτά προκύπτουν από συλλογή μέσω ερωτηματολογίων. Για να αναλυθεί όμως ένα ερωτηματολόγιο το οποίο περιλαμβάνει πλήθος ερωτήσεων-μεταβλητών και να εξάγουμε ορισμένα χρήσιμα συμπεράσματα θα πρέπει, πρώτα από όλα να γίνει η κατάλληλη κωδικοποίηση των δεδομένων. Χρησιμοποιώντας στατιστικές τεχνικές και μεθόδους κατάλληλες για κατηγορικά δεδομένα μπορούμε πιο εύκολα να μελετήσουμε τις σχέσεις μεταξύ των μεταβλητών. Για τον σκοπό αυτό, παρουσιάζουμε και αναλύουμε τη θεωρία της Παραγοντικής Ανάλυσης των Αντιστοιχιών και της Πολλαπλής Παραγοντικής Ανάλυσης των Αντιστοιχιών. Ύστερα, αναλύουμε τα αποτελέσματα που δίνουν οι μέθοδοι όταν τις χρησιμοποιήσουμε για την ανάλυση του ερωτηματολογίου. Τα συμπεράσματα που προκύπτουν έχουν ιδιαίτερο ενδιαφέρον. Η δυναμικότητα των μοντέλων αυτών παρουσιάζεται μέσα από μία εφαρμογή από τον χώρο των κοινωνικών επιστημών σε θέματα που αφορούν τα σχολεία και τους μαθητές της Πρωτοβάθμιας εκπαίδευσης. Στις μεθόδους αυτές δίνεται έμφαση κυρίως στα γραφικά αποτελέσματα αλλά και στις εκτιμήσεις των σκορ των κατηγοριών των μεταβλητών. Όλα τα παραπάνω τα συγκρίνουμε κριτικά μεταξύ τους στη θεωρία και στη πράξη έτσι ώστε ο ενδιαφερόμενος αναγνώστης να κατανοήσει περισσότερο τις μεθόδους αυτές και να αποκομίσει όσο το δυνατόν περισσότερες πληροφορίες που θα τον βοηθήσουν για την εφαρμογή τους. / This dissertation deals with multivariate categorical data of a raw data set produced by a questionnaire designed for a research purpose. However, in order to analyze a questionnaire and extract some fruitful results, that includes a great number of questions-variables, we must first impose a structure on it especially on situations this specific structure is missing. Whenever the structure is imposed, by using statistical techniques and methods designed for categorical data, we can then study more efficiently the relations among the variables in concern for further analyses. The capacity of these models is presented through an application from the social sciences on issues concerning schools and pupils in primary education. The analysis on a smaller subset is further explored by describing the issues of Correspondence Analysis, and Multiple Correspondence Analysis. With these methods, we focus on the interpretation of the results on the graphical displays of the data but also on the estimated category scores of the variables. The above methods described in this dissertation and the results after implementing them are all critically compared with each other at each chapter. This gives to the interesting reader the possibility to fully understand them and to obtain additional information on their implementation.

Le modèle computo-fonctionnel de la vision de haut niveau de Kosslyn et Koenig (1992) repose sur la dissociation entre la reconnaissance et le traitement spatial de la scène visuelle. En 1987, Kosslyn postula l’existence de deux processus pour le traitement des relations spatiales : un processus catégoriel qui calcule les positions relatives des objets et un processus coordonné qui calcule la distance entre les objets. Des études utilisant le paradigme de présentation en champ visuel divisé ont mis en évidence que l’hémisphère gauche sous-tendrait un traitement catégoriel ; l’hémisphère droit sous-tendrait un traitement coordonné. Cette interaction semblerait valider la dichotomie des deux types de processus.Une revue de la littérature pluridisciplinaire a été menée afin de savoir si ce fait est suffisant pour rejeter l’hypothèse d’un processus unique pour les traitements catégoriels et coordonnés. Entre autres, plusieurs études ont observé un effet de pratique au cours de la réalisation de jugements coordonnés : une diminution de l’intervention de l’hémisphère droit au profit d’une prise en charge progressive de l’hémisphère gauche. De plus, l’avantage de l’hémisphère gauche pour le traitement catégoriel a été rarement observé.Une série de cinq expériences comportementales ont été conduites pour vérifier certains biais expérimentaux qui pourraient expliquer les différences hémisphériques et l’effet de pratique observés. Nos résultats nous ont permis d’avancer des hypothèses axées sur la communication entre les hémisphères et sur un lien entre les processus catégoriels et coordonnés. Une critique du paradigme de présentation en champ visuel divisé et différents modèles d’interaction hémisphérique ont été présentés. Trois expériences ont été menées, afin d’évaluer l’impact des communications hémisphériques dans le traitement des relations spatiales. A la lumière de nos résultats, la dichotomie des processus catégoriels et coordonnés a été discutée. / The computational-functional conception of high-level processing of vision in Kosslyn and Koenig (1992) relies on dissociation between object recognition and spatial processing. In 1987, Kosslyn postulated that two different processes compute spatial-relations: categorical process computes relative position of objects and coordinate process computes the distance between objects. Some studies indicate a left-hemisphere advantage for processing categorical spatial relations and a right-hemisphere advantage for processing coordinate spatial relations. This hemispheric difference is interpreted as an evidence of a dichotomy between these two processes. A pluridisciplinary review was conducted to assure that single process hypothesis is dismissed out. Some studies showed, in a coordinate task, that practice resulted in a decreased right-hemisphere involvement and a concurrent increase in left-hemisphere involvement (i.e., practice effect). Furthermore, the left-hemisphere advantage in categorical was seldom observed. The theoretical aim of the thesis was based on two questions: (1) Are there single or several processes encoding visual spatial relations? (2) How can we interpret this practice effect ?Five experiments were run to verify possible bias which might explain observed hemispheric differences and practice effect. Our results suggested that hemispheric communication might be an important factor in spatial-relation processing.An theoretical investigation of divided visual field paradigm was led and several interhemispheric models were described. Three experiments were conducted to estimate hemispheric communication in spatial-relation process. In the light of our results, separate categorical-coordinate processes hypothesis were discussed.

This thesis makes an original contribution to knowledge in the fi eld of data objects' comparison where the objects are described by attributes of fuzzy or heterogeneous (numeric and symbolic) data types. Many real world database systems and applications require information management components that provide support for managing such imperfect and heterogeneous data objects. For example, with new online information made available from various sources, in semi-structured, structured or unstructured representations, new information usage and search algorithms must consider where such data collections may contain objects/records with di fferent types of data: fuzzy, numerical and categorical for the same attributes. New approaches of similarity have been presented in this research to support such data comparison. A generalisation of both geometric and set theoretical similarity models has enabled propose new similarity measures presented in this thesis, to handle the vagueness (fuzzy data type) within data objects. A framework of new and unif ied similarity measures for comparing heterogeneous objects described by numerical, categorical and fuzzy attributes has also been introduced. Examples are used to illustrate, compare and discuss the applications and e fficiency of the proposed approaches to heterogeneous data comparison.

Dans Dialectique de la Raison, Adorno et Horkheimer tentent d’esquisser le pourquoi et le comment de ce retour à la barbarie qu’a connu la civilisation européenne, lors du troisième Reich. Quelles sont ces conditions qui ont rendu possibles les massacres administrés sous le régime nazi? La résolution de cette énigme qui se solde sur l’échec de l’Auflkärung nous dévoile une nécessité, celle d’une transformation radicale à la fois de l’éthique et de la métaphysique dans sa conception de la vérité. Celle-ci se présente à nous sous la forme d’une norme morale : « Dans leur état de non-liberté, Hitler a imposé aux hommes un nouvel impératif catégorique; penser et agir en sorte qu’Auschwitz ne se répète pas ». Quelles modalités de penser et d’agir nous exhortent ce nouvel impératif catégorique? La philosophie d’Adorno, critiqué pour n’avoir été que négative dans son entreprise, est-elle en mesure de nous fournir des prescriptions normatives capables de réorienter le penser théorétique et l’éthique? / In Dialectic of Enlightenment, Adorno and Horkheimer try to explain the reasons for why and how, European civilization committed barbaric crimes during the third Reich. What conditions that made possible the massacres administered under the Nazi regime? The failure of the Enlightenment is the answer to this question and requires a radical transformationof ethics and metaphysics. This necessity takes the form of a new categorical imperative: “A new categorical imperative has been imposed by Hitler upon human beings in the state of their unfreedom: to arrange theirs thoughts and actions so that Auschwitz will not repeat itself, so that nothing similar will happen”. Is Adorno’s philosophy, often accused of being too negative, is it able to provide normative prescriptions able to give a new direction to the theoretical thinking and ethics?

Diploma thesis "Kant's Categorical Imperative and Its Critique by Nineteenth Century Philosophers" deals with a question of Kant's fundamental principle known as the Categorical Imperative or Moral Law. The aim of this work is at first to discuss two other moral principles because of their great impact on Kant seeking the moral principle. These are Hume's moral code called Moral sense and Rousseau' moral views relating to the freedom of individuals. Secondly, to find out how both moral theories did inspire Immanuel Kant. It is necessary to explain strengths of Kant's Formula of the Categorical Imperative especially to emphasise its objectivity and universality. Then the purpose is to show Kant's influence on moral thinking in the nineteenth century. It is necessary to mention philosophers such as Johan Gottlieb Fichte and Bernard Bolzano who focused on critique of the Categorical Imperative.

The importance of simultaneous consideration of forms and functions in youth measures of aggressive behavior is well established. Competing models have presented these highly interrelated constructs as either independent (e.g., reactive or overt) or paired factors (e.g., reactive and overt). The current study examines these models in the context of assessing the viability of a new self-report measure, the Peer Conflict Scale – 20 Item Version. Confirmatory factor analyses were conducted on PCS 20 responses from 1,048 school-age youth living in the Gulf Coast region. Both models significantly improved upon one or two-factor alternatives, and demonstrated partial invariance across gender and grade. The models showed comparable levels of fit to the data, though some loadings for the independent factors model were non-significant. Results encourage use of the PCS 20 across research settings and developmental contexts, while also demonstrating the viability of a paired factors model of aggression.