Gravity beyond general relativity : theory and phenomenology

Despite the notorious achievements of General Relativity, Einstein's theory is under scrutiny due to the lack of a suitable scheme to quantize gravity as well as for the puzzling features it shows both at strong (early universe, black holes) and weak (Dark Energy problem) regime. The proposal to extend the classical theory of gravity harbours the intriguing goals to cure some of these inconsistencies. A large class of modi cations of General Relativity (GR) has been widely explored in the past; in principle, the main motivation for such early e orts was to solve the problem of non-renormalizability by providing a new framework in which (thanks to higher order corrections in the gravitational action) gravity could be quantized. The analysis of the cosmological implications of such models also showed a number of peculiar features that justi ed further developments. The ultraviolet modi cations that naturally arise at high energy in the context of quantum gravity have been taken into account for their impact on the phenomenology of the very early universe. Furthermore, it was recently argued that alternative infrared extensions of the Einstein-Hilbert (EH) action could be invoked to presumably alleviate the Dark Sector problem

Contributions to Time Series Classification: Meta-Learning and Explainability

141 p.La presente tesis incluye 3 contribuciones de diferentes tipos al área de la clasificación supervisada de series temporales, un campo en auge por la cantidad de series temporales recolectadas día a día en una gran variedad en ámbitos. En este contexto, la cantidad de métodos disponibles para clasificar series temporales es cada vez más grande, siendo los clasificadores cada vez más competitivos y variados. De esta manera, la primera contribución de la tesis consiste en proponer una taxonomía de los clasificadores de series temporales basados en distancias, donde se hace una revisión exhaustiva de los métodos existentes y sus costes computacionales. Además, desde el punto de vista de un/a usuario/a no experto/a (incluso desde la de un/a experto/a), elegir un clasificador adecuado para un problema concreto es una tarea difícil. En la segunda contribución, por tanto, se aborda la recomendación de clasificadores de series temporales, para lo que usaremos un enfoque basado en el meta-aprendizaje. Por último, la tercera contribución consiste en proponer un método para explicar la predicción de los clasificadores de series temporales, en el que calculamos la relevancia de cada región de una serie en la predicción. Este método de explicación está basado en perturbaciones, para lo que consideraremos transformaciones específicas y realistas para las series temporales

Contributions to Time Series Classification: Meta-Learning and Explainability

This thesis includes 3 contributions of different types to the area of supervised time series classification, a growing field of research due to the amount of time series collected daily in a wide variety of domains. In this context, the number of methods available for classifying time series is increasing, and the classifiers are becoming more and more competitive and varied. Thus, the first contribution of the thesis consists of proposing a taxonomy of distance-based time series classifiers, where an exhaustive review of the existing methods and their computational costs is made. Moreover, from the point of view of a non-expert user (even from that of an expert), choosing a suitable classifier for a given problem is a difficult task. The second contribution, therefore, deals with the recommendation of time series classifiers, for which we will use a meta-learning approach. Finally, the third contribution consists of proposing a method to explain the prediction of time series classifiers, in which we calculate the relevance of each region of a series in the prediction. This method of explanation is based on perturbations, for which we will consider specific and realistic transformations for the time series.BES-2016-07689

Community detection for correlation matrices

A challenging problem in the study of complex systems is that of resolving, without prior information, the emergent, mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are not explicitly oriented towards identifying such modules and can suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, this approach has focused predominantly on replacing network data with correlation matrices, a procedure that tends to be intrinsically biased due to its inconsistency with the null hypotheses underlying the existing algorithms. Here we introduce, via a consistent redefinition of null models based on random matrix theory, the appropriate correlation-based counterparts of the most popular community detection techniques. Our methods can filter out both unit-specific noise and system-wide dependencies, and the resulting communities are internally correlated and mutually anti-correlated. We also implement multiresolution and multifrequency approaches revealing hierarchically nested sub-communities with `hard' cores and `soft' peripheries. We apply our techniques to several financial time series and identify mesoscopic groups of stocks which are irreducible to a standard, sectorial taxonomy, detect `soft stocks' that alternate between communities, and discuss implications for portfolio optimization and risk management.Comment: Final version, accepted for publication on PR

Paving the way for transitions --- a case for Weyl geometry

This paper presents three aspects by which the Weyl geometric generalization of Riemannian geometry, and of Einstein gravity, sheds light on actual questions of physics and its philosophical reflection. After introducing the theory's principles, it explains how Weyl geometric gravity relates to Jordan-Brans-Dicke theory. We then discuss the link between gravity and the electroweak sector of elementary particle physics, as it looks from the Weyl geometric perspective. Weyl's hypothesis of a preferred scale gauge, setting Weyl scalar curvature to a constant, gets new support from the interplay of the gravitational scalar field and the electroweak one (the Higgs field). This has surprising consequences for cosmological models. In particular it leads to a static (Weyl geometric) spacetime with "inbuilt" cosmological redshift. This may be used for putting central features of the present cosmological model into a wider perspective.Comment: 54 pp, 2 figs. To appear in D. Lehmkuhl (ed.) "Towards a Theory of Spacetime Theories", Einstein Studies, Basel: Birkhaeuser), revised version June 201

Material Theories

The subject of this meeting was mathematical modeling of strongly interacting multi-particle systems that can be interpreted as advanced materials. The main emphasis was placed on contributions attempting to bridge the gap between discrete and continuum approaches, focusing on the multi-scale nature of physical phenomena and bringing new and nontrivial mathematics. The mathematical debates concentrated on nonlinear PDE, stochastic dynamical systems, optimal transportation, calculus of variations and large deviations theory

Hadron models and related New Energy issues

The present book covers a wide-range of issues from alternative hadron models to their likely implications in New Energy research, including alternative interpretation of lowenergy reaction (coldfusion) phenomena. The authors explored some new approaches to describe novel phenomena in particle physics. M Pitkanen introduces his nuclear string hypothesis derived from his Topological Geometrodynamics theory, while E. Goldfain discusses a number of nonlinear dynamics methods, including bifurcation, pattern formation (complex GinzburgLandau equation) to describe elementary particle masses. Fu Yuhua discusses a plausible method for prediction of phenomena related to New Energy development. F. Smarandache discusses his unmatter hypothesis, and A. Yefremov et al. discuss Yang-Mills field from Quaternion Space Geometry. Diego Rapoport discusses theoretical link between Torsion fields and Hadronic Mechanic. A.H. Phillips discusses semiconductor nanodevices, while V. and A. Boju discuss Digital Discrete and Combinatorial methods and their likely implications in New Energy research. Pavel Pintr et al. describe planetary orbit distance from modified Schrödinger equation, and M. Pereira discusses his new Hypergeometrical description of Standard Model of elementary particles. The present volume will be suitable for researchers interested in New Energy issues, in particular their link with alternative hadron models and interpretation