946 research outputs found

    Geometric Data Analysis: Advancements of the Statistical Methodology and Applications

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    Data analysis has become fundamental to our society and comes in multiple facets and approaches. Nevertheless, in research and applications, the focus was primarily on data from Euclidean vector spaces. Consequently, the majority of methods that are applied today are not suited for more general data types. Driven by needs from fields like image processing, (medical) shape analysis, and network analysis, more and more attention has recently been given to data from non-Euclidean spaces–particularly (curved) manifolds. It has led to the field of geometric data analysis whose methods explicitly take the structure (for example, the topology and geometry) of the underlying space into account. This thesis contributes to the methodology of geometric data analysis by generalizing several fundamental notions from multivariate statistics to manifolds. We thereby focus on two different viewpoints. First, we use Riemannian structures to derive a novel regression scheme for general manifolds that relies on splines of generalized Bézier curves. It can accurately model non-geodesic relationships, for example, time-dependent trends with saturation effects or cyclic trends. Since Bézier curves can be evaluated with the constructive de Casteljau algorithm, working with data from manifolds of high dimensions (for example, a hundred thousand or more) is feasible. Relying on the regression, we further develop a hierarchical statistical model for an adequate analysis of longitudinal data in manifolds, and a method to control for confounding variables. We secondly focus on data that is not only manifold- but even Lie group-valued, which is frequently the case in applications. We can only achieve this by endowing the group with an affine connection structure that is generally not Riemannian. Utilizing it, we derive generalizations of several well-known dissimilarity measures between data distributions that can be used for various tasks, including hypothesis testing. Invariance under data translations is proven, and a connection to continuous distributions is given for one measure. A further central contribution of this thesis is that it shows use cases for all notions in real-world applications, particularly in problems from shape analysis in medical imaging and archaeology. We can replicate or further quantify several known findings for shape changes of the femur and the right hippocampus under osteoarthritis and Alzheimer's, respectively. Furthermore, in an archaeological application, we obtain new insights into the construction principles of ancient sundials. Last but not least, we use the geometric structure underlying human brain connectomes to predict cognitive scores. Utilizing a sample selection procedure, we obtain state-of-the-art results

    Graphonomics and your Brain on Art, Creativity and Innovation : Proceedings of the 19th International Graphonomics Conference (IGS 2019 – Your Brain on Art)

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    [Italiano]: “Grafonomia e cervello su arte, creatività e innovazione”. Un forum internazionale per discutere sui recenti progressi nell'interazione tra arti creative, neuroscienze, ingegneria, comunicazione, tecnologia, industria, istruzione, design, applicazioni forensi e mediche. I contributi hanno esaminato lo stato dell'arte, identificando sfide e opportunità, e hanno delineato le possibili linee di sviluppo di questo settore di ricerca. I temi affrontati includono: strategie integrate per la comprensione dei sistemi neurali, affettivi e cognitivi in ambienti realistici e complessi; individualità e differenziazione dal punto di vista neurale e comportamentale; neuroaesthetics (uso delle neuroscienze per spiegare e comprendere le esperienze estetiche a livello neurologico); creatività e innovazione; neuro-ingegneria e arte ispirata dal cervello, creatività e uso di dispositivi di mobile brain-body imaging (MoBI) indossabili; terapia basata su arte creativa; apprendimento informale; formazione; applicazioni forensi. / [English]: “Graphonomics and your brain on art, creativity and innovation”. A single track, international forum for discussion on recent advances at the intersection of the creative arts, neuroscience, engineering, media, technology, industry, education, design, forensics, and medicine. The contributions reviewed the state of the art, identified challenges and opportunities and created a roadmap for the field of graphonomics and your brain on art. The topics addressed include: integrative strategies for understanding neural, affective and cognitive systems in realistic, complex environments; neural and behavioral individuality and variation; neuroaesthetics (the use of neuroscience to explain and understand the aesthetic experiences at the neurological level); creativity and innovation; neuroengineering and brain-inspired art, creative concepts and wearable mobile brain-body imaging (MoBI) designs; creative art therapy; informal learning; education; forensics

    A Combined Numerical and Experimental Approach for Rolling Bearing Modelling and Prognostics

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    Rolling-element bearings are widely employed components which cover a major role in the NVH behaviour of the mechanical systems in which they are inserted. Therefore, it is crucial to thoroughly understand their fundamental properties and accurately quantify their most relevant parameters. Moreover, their inevitable failure due to contact fatigue leads to the necessity of correctly describing their dynamic behaviour. In fact, they permit to develop diagnostic and prognostic schemes, which are heavily requested in the nowadays industrial scenario due to their increasingly important role in the development of efficient maintenance strategies. As a result, throughout the years several techniques have been developed by researchers to address different challenges related to the modelling of these components. Within this context, this thesis aims at improving the available methods and at proposing novel approaches to tackle the modelling of rolling-element bearings both in case of static and dynamic simulations. In particular, the dissertation is divided in three major topics related to this field, i.e. the estimation of bearing radial stiffness trough the finite-element method, the lumped-parameter modelling of defective bearings and the development of physics-based prognostic models. The first part of the thesis deals with the finite-element simulations of rolling-element bearings. In particular, the investigation aims at providing an efficient procedure for the generation of load-dependent meshes. The method is developed with the primary objective of determining the radial stiffness of the examined components. In this regard, the main contribution to the subject is the definition of mesh element dimensions on the basis of analytical formulae and in the proposed methodology for the estimation of bearing stiffness. Then, the second part describes a multi-objective optimization technique for the estimation of unknown parameters in lumped parameter models of defective bearings. In fact, it was observed that several parameters which are commonly inserted in these models are hardly measurable or rather denoted by a high degree of uncertainty. On this basis, an optimization procedure aimed at minimizing the difference between experimental and numerical results is proposed. The novelty of the technique lies in the approach developed to tackle the problem and its peculiar implementation in the context of bearing lumped-parameter models. Lastly, the final part of the dissertation is devoted to the development of physics-based prognostic models. Specifically, two models are detailed, both based on a novel degradation-related parameter, i.e. the Equivalent Damaged Volume (EDV). An algorithm capable of extracting this quantity from experimental data is detailed. Then, EDV values are used as input parameters for two prognostic models. The first one aims at predicting the bearing vibration under different operative conditions with respect to a given reference deterioration history. On the other hand, the objective of the second model is to predict the time until a certain threshold on the equivalent damaged volume is crossed, regardless of the applied load and the shaft rotation speed. Therefore, the original aspect of this latter part is the development of prognostic models based on a novel indicator specifically introduced in this work. Results obtained from all proposed models are validated through analytical methods retrieved from the literature and by comparison with data acquired on a dedicated test bench. To this end, a test rig which was set-up at the Engineering Department of the University of Ferrara was employed to perform two type of tests, i.e. stationary tests on bearings with artificial defects and run-to-failure tests on initially healthy bearings. The characteristics of acceleration signals acquired during both tests are extensively discussed.I cuscinetti a rotolamento sono componenti meccanici che influenzano in maniera considerevole il comportamento dinamico dei sistemi all’interno dei quali sono montati. Pertanto, è di fondamentale importanza possedere strumenti atti alla stima dei loro parametri più rilevanti e avere a disposizione modelli dedicati allo studio delle loro caratteristiche dinamiche. Questo aspetto è di estrema importanza soprattutto nell’ottica dello sviluppo di schemi di diagnostica e prognostica, i quali sono sempre più richiesti all’interno dello scenario industriale odierno. In questo contesto, questa tesi si propone di migliorare le tecniche numeriche già esistenti e di fornire nuovi approcci per la modellazione dei cuscinetti a rotolamento sia nel caso di problemi statici che dinamici. Nello specifico, il lavoro tratta in maniera dettagliata tre diversi argomenti relativi a questo tema, ossia la stima della rigidezza radiale tramite il metodo agli elementi finiti, la modellazione a parametri concentrati di cuscinetti con difetti e lo sviluppo di modelli di prognostica physics-based. La prima parte della tesi concerne la simulazione di cuscinetti a rotolamento tramite il metodo ad elementi finiti. In particolare, lo studio si propone di fornire una procedura per la generazione di griglie le cui dimensioni dipendano dal carico applicato. Il metodo è sviluppato con l’obbiettivo di stimare in maniera computazionalmente efficace la rigidezza radiale del componente in esame. Pertanto, il contributo principale sul tema dato da questa prima parte riguarda il metodo analitico che permette di definire a priori le dimensioni degli elementi che costituiscono la mesh e la metodologia utilizzata per la stima della rigidezza. La seconda parte descrive una procedura di ottimizzazione multi obbiettivo per la stima dei parametri incogniti all’interno dei modelli a parametri concentrati di cuscinetti con difetti. Questa esigenza nasce dall’osservazione che numerosi parametri tipicamente inseriti in questa tipologia di modelli sono difficilmente misurabili oppure caratterizzati da un alto grado di incertezza. Perciò, nella seconda parte viene introdotta una tecnica innovativa che consente di stimare i parametri di modello che minimizzano la differenza fra risultati numerici e sperimentali in diverse condizioni di funzionamento. Infine, l’ultima parte è dedicata allo sviluppo di modelli di prognostica physics-based. A tal riguardo, vengono dettagliati due modelli basati su un nuovo indicatore di degrado del cuscinetto, denominato Equivalent Damaged Volume (EDV). Questo indicatore viene calcolato durante il funzionamento del cuscinetto tramite un algoritmo dedicato. I valori così ottenuti sono poi utilizzati come dati di input per i due modelli prognostici. Il primo mira a predire la vibrazione del cuscinetto in condizioni operative diverse rispetto ad una storia di degrado di riferimento. Diversamente, il secondo modello permette di prevedere il tempo rimanente prima del superamento di una soglia critica di volume equivalente danneggiato, indipendentemente da carico applicato e velocità di rotazione. Dunque, l’aspetto originale di quest’ultima parte ricade nello sviluppo di tecniche prognostiche basate su un nuovo indicatore introdotto ad-hoc in questo lavoro. I risultati ottenuti da tutti i modelli proposti sono validati grazie a metodi analitici di letteratura e a dati acquisiti in laboratorio per mezzo di un banco prova installato presso il Dipartimento di Ingegneria dell’Università di Ferrara. Il banco prova è stato utilizzato per realizzare due tipologie di prove, ossia test stazionari su cuscinetti che presentano difetti artificiali e prove di tipo run-to-failure su cuscinetti inizialmente sani. Le caratteristiche dei segnali di accelerazione acquisiti in entrambe le prove sono discussi in maniera esaustiva

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Nicolai maps in supersymmetric Yang-Mills theories

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    This dissertation presents new results for the Nicolai map formalism. Integrating out all the fermionic variables of any supersymmetric field theory, one obtains a non-local theory of the remaining bosonic fields. In 1979, Hermann Nicolai proved the existence of a nonlocal and nonlinear transformation of the bosonic fields, that enables the evaluation of quantum correlators using only a free, purely bosonic functional measure. They agree with the bosonic correlators of the original supersymmetric field theory and thus the formalism provides an entirely distinct understanding of supersymmetry. In this classical construction, a lot of information about quantum correlators is shifted to the construction of the Nicolai map. A central result of this work is a new universal formula for the Nicolai map in terms of a path-ordered exponential of the so-called coupling flow differential operator. From this, the map can be constructed perturbatively whenever supersymmetry is realized off-shell. Moreover, in gauge theories, this can be achieved in any gauge. A second recurrent theme is the broad ambiguity of the Nicolai map. Next to the known gauge dependence, there are at least two more ambiguities: An integration-path dependence for theories with multiple couplings and an R-symmetry ambiguity for theories with extended supersymmetry. Despite any ambiguities, correlators obtained by the Nicolai map formalism are always unique. This allows one to fine-tune the map for finding the most simple avenues towards physical observables. A particularly useful observation is that incorporating topological terms in the action can be interpreted as adding a special kind of coupling that provides significant simplifications in the formalism. In this thesis, starting with a general overview, we next study the Nicolai map in supersymmetric quantum mechanics, as it allows us to understand many properties in a relatively simple ‘toy’ model. We then move on to N = 1 supersymmetric Yang–Mills theories, predominantly in four space- time dimensions. Combining the Landau gauge with the fine-tuning of a topological term, we develop a much simpler Nicolai map expansion com- pared to previous constructions. Lastly, we turn to N = 4 supersymmetric Yang–Mills theory and develop a framework for its R-covariant coupling flow operator.Diese Dissertation präsentiert neue Ergebnisse für den „Nicolai map“ Formalismus. Integriert man alle fermionischen Variablen einer beliebigen supersymmetrischen Feldtheorie aus, erhält man eine nichtlokale Theorie der verbleibenden bosonischen Felder. 1979 bewies Hermann Nicolai die Ex- istenz einer nichtlokalen und nichtlinearen Transformation der bosonischen Felder, die es ermöglicht, Quantenkorrelatoren nur mit einem freien, rein bosonischen Funktionsmaß zu berechnen. Sie stimmen mit den bosonischen Korrelatoren der ursprünglichen supersymmetrischen Feldtheorie überein und somit ermöglicht der Formalismus ein völlig anderes Verständnis der Supersymmetrie. In dieser klassischen Konstruktion werden viele Informa- tionen über Quantenkorrelatoren in die Konstruktion der Nicolai-Abbildung verlagert. Ein zentrales Ergebnis dieser Arbeit ist eine neue universelle Formel für die Nicolai-Abbildung in Form eines pfadgeordneten Exponentials des sogenannten „coupling flow“-Differentialoperators. Daraus kann die Ab- bildung störungstheoretisch konstruiert werden, wenn die Supersymmetrie „off-shell“ realisiert ist. Außerdem kann dies in Eichtheorien für beliebige Eichungen erreicht werden. Ein zweites wiederkehrendes Thema ist die weitgehende Mehrdeutigkeit der Nicolai-Abbildung. Neben der bekannten Eichabhängigkeit gibt es mindestens zwei weitere Mehrdeutigkeiten: Eine Integrationspfad- Abhängigkeit für Theorien mit mehr als einer Kopplung und eine R- Symmetrie-Ambiguität für Theorien mit erweiterter Supersymmetrie. Trotz dieser Mehrdeutigkeiten sind die Korrelatoren, die mit der Nicolai- Abbildung erhalten werden, immer eindeutig. Dies ermöglicht eine Feinabstimmung der Abbildung, um möglichst einfach, physikalische Observablen zu bestimmen. Eine besonders nützliche Beobachtung ist, dass die Einbeziehung topologischer Terme in die Wirkung als Hinzufügen einer speziellen Art von Kopplung interpretiert werden kann, die den Formalismus erheblich vereinfacht. In dieser Arbeit untersuchen wir, beginnend mit einem allgemeinen Überblick, als Nächstes die Nicolai-Abbildung in der supersymmetrischen Quantenmechanik, da sie uns erlaubt, viele Eigenschaften in einem relativ einfachen „Spielzeug“-Modell zu verstehen. Anschließend befassen wir uns mit N = 1 supersymmetrischen Yang–Mills-Theorien, vorwiegend in vier Raumzeitdimensionen. Durch die Kombination der Landau-Eichung mit der Feinabstimmung eines topologischen Terms entwickeln wir eine im Vergleich zu früheren Konstruktionen wesentlich einfachere Entwicklung der Nicolai-Abbildung. Schließlich wenden wir uns der N = 4 supersym- metrischen Yang–Mills-Theorie zu und entwickeln ein Verständnis für ihren R-kovarianten Kopplungsflussoperator

    Zooming in on the Universe: In Search of Quantum Spacetime

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    This thesis investigates low-dimensional models of nonperturbative quantum gravity, with a special focus on Causal Dynamical Triangulations (CDT). We define the so-called curvature profile, a new quantum gravitational observable based on the quantum Ricci curvature. We subsequently study its coarse-graining capabilities on a class of regular, two-dimensional polygons with isolated curvature singularities, and we determine the curvature profile of (1+1)-dimensional CDT with toroidal topology. Next, we focus on CDT in 2+1 dimensions, intvestigating the behavior of the two-dimensional spatial slice geometries. We then turn our attention to matrix models, exploring a differential reformulation of the integrals over one- and two-matrix ensembles. Finally, we provide a hands-on introduction to computer simulations of CDT quantum gravity.Comment: Ph.D. thesi

    Elements of Ion Linear Accelerators, Calm in The Resonances, Other_Tales

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    The main part of this book, Elements of Linear Accelerators, outlines in Part 1 a framework for non-relativistic linear accelerator focusing and accelerating channel design, simulation, optimization and analysis where space charge is an important factor. Part 1 is the most important part of the book; grasping the framework is essential to fully understand and appreciate the elements within it, and the myriad application details of the following Parts. The treatment concentrates on all linacs, large or small, intended for high-intensity, very low beam loss, factory-type application. The Radio-Frequency-Quadrupole (RFQ) is especially developed as a representative and the most complicated linac form (from dc to bunched and accelerated beam), extending to practical design of long, high energy linacs, including space charge resonances and beam halo formation, and some challenges for future work. Also a practical method is presented for designing Alternating-Phase- Focused (APF) linacs with long sequences and high energy gain. Full open-source software is available. The following part, Calm in the Resonances and Other Tales, contains eyewitness accounts of nearly 60 years of participation in accelerator technology. (September 2023) The LINACS codes are released at no cost and, as always,with fully open-source coding. (p.2 & Ch 19.10)Comment: 652 pages. Some hundreds of figures - all images, there is no data in the figures. (September 2023) The LINACS codes are released at no cost and, as always,with fully open-source coding. (p.2 & Ch 19.10

    Neurogeometry of reaching

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    The purpose of the thesis is to develop a model for the functional behaviour of neurons in the primary motor cortex (M1) responsible for arm reaching movements. From Georgopoulos neurophysiological data, we provide a first bundle structure compatible with the hypercolumnar organization and with the position-direction selectivity of motor cortical cells. We then extend this model to encode the direction of arm movement which varies in time, as experimentally measured by Hatsopoulos by introducing the notion of movement fragments. We provide a sub-Riemannian model which describes the time-dependent directional selectivity of cells though integral curves of the geometric structure we set up. The sub-Riemannian distance we define allows to implement a grouping algorithm able to detect a set of hand motor trajectories. These paths, identified by using a kernel defined in terms of kinematic variables, are compatible with the motor primitives obtained from neurophysiological results by spectral analysis applied directly on cortical variables. In a second part of the work, we propose geodesics in this space as an alternative model of models for arm movement trajectories. We define a special class of curves, called admissible, on which to study the geodesics problem: we provide a connectivity property in terms of admissible paths and the existence of normal length minimizers. Admissible geodesics are used as a model of reaching paths, finding a first validation through Flash and Hogan minimizing trajectories

    Quantum Features of the Cosmological Horizon

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    Self-supervised Learning of Primitive-based Robotic Manipulation

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