Development of unsupervised learning methods with applications to life sciences data

Machine Learning makes computers capable of performing tasks typically requiring human intelligence. A domain where it is having a considerable impact is the life sciences, allowing to devise new biological analysis protocols, develop patients’ treatments efficiently and faster, and reduce healthcare costs. This Thesis work presents new Machine Learning methods and pipelines for the life sciences focusing on the unsupervised field. At a methodological level, two methods are presented. The first is an “Ab Initio Local Principal Path” and it is a revised and improved version of a pre-existing algorithm in the manifold learning realm. The second contribution is an improvement over the Import Vector Domain Description (one-class learning) through the Kullback-Leibler divergence. It hybridizes kernel methods to Deep Learning obtaining a scalable solution, an improved probabilistic model, and state-of-the-art performances. Both methods are tested through several experiments, with a central focus on their relevance in life sciences. Results show that they improve the performances achieved by their previous versions. At the applicative level, two pipelines are presented. The first one is for the analysis of RNA-Seq datasets, both transcriptomic and single-cell data, and is aimed at identifying genes that may be involved in biological processes (e.g., the transition of tissues from normal to cancer). In this project, an R package is released on CRAN to make the pipeline accessible to the bioinformatic Community through high-level APIs. The second pipeline is in the drug discovery domain and is useful for identifying druggable pockets, namely regions of a protein with a high probability of accepting a small molecule (a drug). Both these pipelines achieve remarkable results. Lastly, a detour application is developed to identify the strengths/limitations of the “Principal Path” algorithm by analyzing Convolutional Neural Networks induced vector spaces. This application is conducted in the music and visual arts domains.

The combinatorics of Hilbert-Poincaré series of matroids

In this thesis we explore the combinatorial properties of several polynomials arising in matroid theory. Our main motivation comes from the problem of computing them in an efficient way and from a collection of conjectures, mainly the real-rootedness and the monotonicity of their coefficients with respect to weak maps. Most of these polynomials can be interpreted as Hilbert--Poincaré series of graded vector spaces associated to a matroid and thus some combinatorial properties can be inferred via combinatorial algebraic geometry (non-negativity, palindromicity, unimodality); one of our goals is also to provide purely combinatorial interpretations of these properties, for example by redefining these polynomials as poset invariants (via the incidence algebra of the lattice of flats); moreover, by exploiting the bases polytopes and the valuativity of these invariants with respect to matroid decompositions, we are able to produce efficient closed formulas for every paving matroid, a class that is conjectured to be predominant among all matroids. One last goal is to extend part of our results to a higher categorical level, by proving analogous results on the original graded vector spaces via abelian categorification or on equivariant versions of these polynomials.

Power sharing e controllo modulare di macchine elettriche multi-trifase

La costante ricerca e lo sviluppo nel campo degli azionamenti e dei motori elettrici hanno portato ad una loro sempre maggiore applicazione ed utilizzo. Tuttavia, la crescente esigenza di sistemi ad alta potenza sempre più performanti da una parte ha evidenziato i limiti di certe soluzioni, dall’altra l’affermarsi di altre. In questi sistemi, infatti, la macchina elettrica trifase non rappresenta più l’unica soluzione possibile: negli ultimi anni si è assistito ad una sempre maggiore diffusione di macchine elettriche multifase. Grazie alle maggiori potenzialità che sono in grado di offrire, per quanto alcune di queste siano ancora sconosciute, risultano già essere una valida alternativa rispetto alla tradizionale controparte trifase. Sicuramente però, fra le varie architetture multifase, quelle multi-trifase (ovvero quelle con un numero di fasi multiplo di tre) rappresentano una soluzione particolarmente vantaggiosa in ambito industriale. Infatti, se impiegate all’interno di architetture multifase, la profonda conoscenza dei tradizionali sistemi trifase consente di ridurre i costi ed i tempi legati alla loro progettazione. In questo elaborato la macchina elettrica multi-trifase analizzata è una macchina sincrona esafase con rotore a magneti permanenti superficiali. Questa particolare tipologia di macchina elettrica può essere modellizzata attraverso due approcci completamente differenti: uno esafase ed uno doppio trifase. Queste possibilità hanno portato molti ricercatori alla ricerca della migliore strategia di controllo per questa macchina. L’obiettivo di questa tesi è di effettuare un’analisi comparativa tra tre diverse strategie di controllo applicate alla stessa macchina elettrica multi-trifase, analizzandone la risposta dinamica in diverse condizioni di funzionamento.

Extremal problems on sum-free sets and coverings in tridimensional spaces

Given a prime power q, define c (q) as the minimum cardinality of a subset H of F 3 q which satisfies the following property: every vector in this space di ff ers in at most 1 coordinate from a multiple of a vector in H. In this work, we introduce two extremal problems in combinatorial number theory aiming to discuss a known connection between the corresponding coverings and sum-free sets. Also, we provide several bounds on these maps which yield new classes of coverings, improving the previous upper bound on c (q)

Topological entropy of catalytic sets: Hypercycles revisited

The dynamics of catalytic networks have been widely studied over the last decades because of their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One of the most studied mathematical bodies for catalytic networks was initially formulated in the context of prebiotic evolution, by means of the hypercycle theory. The hypercycle is a set of self-replicating species able to catalyze other replicator species within a cyclic architecture. Hypercyclic organization might arise from a quasispecies as a way to increase the informational containt surpassing the so-called error threshold. The catalytic coupling between replicators makes all the species to behave like a single and coherent evolutionary multimolecular unit. The inherent nonlinearities of catalytic interactions are responsible for the emergence of several types of dynamics, among them, chaos. In this article we begin with a brief review of the hypercycle theory focusing on its evolutionary implications as well as on different dynamics associated to different types of small catalytic networks. Then we study the properties of chaotic hypercycles with error-prone replication with symbolic dynamics theory, characterizing, by means of the theory of topological Markov chains, the topological entropy and the periods of the orbits of unimodal-like iterated maps obtained from the strange attractor. We will focus our study on some key parameters responsible for the structure of the catalytic network: mutation rates, autocatalytic and cross-catalytic interactions.

Extraction of topological structures in 2D and 3D vector fields

feature extraction, feature tracking, vector field visualization

Biological rhythms and vector insects

The adjustment of all species, animals and plants, to the Earth’s cyclic environments is ensured by their temporal organisation. The relationships between parasites, vectors and hosts rely greatly upon the synchronisation of their biological rhythms, especially circadian rhythms. In this short note, parasitic infections by Protozoa and by microfilariae have been chosen as examples of the dependence of successful transmission mechanisms on temporal components.

Interruption of vector transmission by native vectors and “the art of the possible”

In a recent article in the Reader’s Opinion, advantages and disadvantages of the certification processes of interrupted Chagas disease transmission (American trypanosomiasis) by native vector were discussed. Such concept, accepted by those authors for the case of endemic situations with introduced vectors, has been built on a long and laborious process by endemic countries and Subregional Initiatives for Prevention, Control and Treatment of Chagas, with Technical Secretariat of the Pan American Health Organization/World Health Organization, to create a horizon target and goal to concentrate priorities and resource allocation and actions. With varying degrees of sucess, which are not replaceable for a certificate of good practice, has allowed during 23 years to safeguard the effective control of transmission of Trypanosoma cruzi not to hundreds of thousands, but millions of people at risk conditions, truly “the art of the possible.”

On Chaos and Fractals in General Topological Spaces

The present study on chaos and fractals in general topological spaces. Chaos theory originated with the work of Edward Lorenz. The phenomenon which changes order into disorder is known as chaos. Theory of fractals has its origin with the frame work of Benoit Mandelbrot in 1977. Fractals are irregular objects. In this study different properties of topological entropy in chaos spaces are studied, which also include hyper spaces. Topological entropy is a measures to determine the complexity of the space, and compare different chaos spaces. The concept of fractals can’t be extended to general topological space fast it involves Hausdorff dimensions. The relations between hausdorff dimension and packing dimension. Regular sets in Metric spaces using packing measures, regular sets were defined in IR” using Hausdorff measures. In this study some properties of self similar sets and partial self similar sets. We can associate a directed graph to each partial selfsimilar set. Dimension properties of partial self similar sets are studied using this graph. Introduce superself similar sets as a generalization of self similar sets and also prove that chaotic self similar self are dense in hyper space. The study concludes some relationships between different kinds of dimension and fractals. By defining regular sets through packing dimension in the same way as regular sets defined by K. Falconer through Hausdorff dimension, and different properties of regular sets also.

Box Products in Fuzzy Topological Spaces and Related Topics

The topology as the product set with a base chosen as all products of open sets in the individual spaces. This topology is known as box topology. The main objective of this study is to extend the concept of box products to fuzzy box products and to obtain some results regarding them. Owing to the fact that box products have plenty of applications in uniform and covering properties, here made an attempt to explore some inter relations of fuzzy uniform properties and fuzzy covering properties in fuzzy box products. Even though the main focus is on fuzzy box products, some brief sketches regarding hereditarily fuzzy normal spaces and fuzzy nabla product is also provided. The main results obtained include characterization of fuzzy Hausdroffness and fuzzy regularity of box products of fuzzy topological spaces. The investigation of the completeness of fuzzy uniformities in fuzzy box products proved that a fuzzy box product of spaces is fuzzy topologically complete if each co-ordinate space is fuzzy topologically complete. The thesis also prove that the fuzzy box product of a family of fuzzy α-paracompact spaces is fuzzy topologically complete. In Fuzzy box product of hereditarily fuzzy normal spaces, the main result obtained is that if a fuzzy box product of spaces is hereditarily fuzzy normal ,then every countable subset of it is fuzzy closed. It also deals with the notion of fuzzy nabla product of spaces which is a quotient of fuzzy box product. Here the study deals the relation connecting fuzzy box product and fuzzy nabla product

Reproducing kernel Hilbert spaces associated with kernels on topological spaces

We analyze reproducing kernel Hilbert spaces of positive definite kernels on a topological space X being either first countable or locally compact. The results include versions of Mercer's theorem and theorems on the embedding of these spaces into spaces of continuous and square integrable functions.

Administration of helper-dependent adenoviral vectors and sequential delivery of different vector serotype for long-term liver-directed gene transfer in baboons

The efficiency of first-generation adenoviral vectors as gene delivery tools is often limited by the short duration of transgene expression, which can be related to immune responses and to toxic effects of viral proteins. In addition, readministration is usually ineffective unless the animals are immunocompromised or a different adenovirus serotype is used. Recently, adenoviral vectors devoid of all viral coding sequences (helper-dependent or gutless vectors) have been developed to avoid expression of viral proteins. In mice, liver-directed gene transfer with AdSTK109, a helper-dependent adenoviral (Ad) vector containing the human α1-antitrypsin (hAAT) gene, resulted in sustained expression for longer than 10 months with negligible toxicity to the liver. In the present report, we have examined the duration of expression of AdSTK109 in the liver of baboons and compared it to first-generation vectors expressing hAAT. Transgene expression was limited to approximately 3–5 months with the first-generation vectors. In contrast, administration of AdSTK109 resulted in transgene expression for longer than a year in two of three baboons. We have also investigated the feasibility of circumventing the humoral response to the virus by sequential administration of vectors of different serotypes. We found that the ineffectiveness of readministration due to the humoral response to an Ad5 first-generation vector was overcome by use of an Ad2-based vector expressing hAAT. These data suggest that long-term expression of transgenes should be possible by combining the reduced immunogenicity and toxicity of helper-dependent vectors with sequential delivery of vectors of different serotypes.

New lower bounds for the topological complexity of aspherical spaces

Date of Acceptance: 5/04/2015 15 pages, 4 figures