Functor homology over an additive category

We uncover several general phenomenas governing functor homology over additive categories. In particular, we generalize the strong comparison theorem of Franjou Friedlander Scorichenko and Suslin to the setting of Fp-linear additive categories. Our results have a strong impact in terms of explicit computations of functor homology, and they open the way to new applications to stable homology of groups or to K-theory. As an illustration, we prove comparison theorems between cohomologies of classical algebraic groups over infinite perfect fields, in the spirit of a celebrated result of Cline, Parshall, Scott et van der Kallen for finite fields

Approximate Membership for Regular Languages modulo the Edit Distance

International audienceWe present a probabilistic algorithm for testing approximate membership of words to regular languages modulo the edit distance. The time complexity of our algorithm, which is independent of the size of the input word, is polynomial in the size of the input automaton and the inverse error precision. All previous property testing algorithms for regular languages, whether they consider approximations modulo the Hamming distance or the edit distance with moves, run in exponential time if not fixing one of these parameters

An Investigation into the Use of Artificial Intelligence Techniques for the Analysis and Control of Instrumental Timbre and Timbral Combinations

Researchers have investigated harnessing computers as a tool to aid in the composition of music for over 70 years. In major part, such research has focused on creating algorithms to work with pitches and rhythm, which has resulted in a selection of sophisticated systems. Although the musical possibilities of these systems are vast, they are not directly considering another important characteristic of sound. Timbre can be defined as all the sound attributes, except pitch, loudness and duration, which allow us to distinguish and recognize that two sounds are dissimilar. This feature plays an essential role in combining instruments as it involves mixing instrumental properties to create unique textures conveying specific sonic qualities. Within this thesis, we explore harnessing techniques for the analysis and control of instrumental timbre and timbral combinations. This thesis begins with investigating the link between musical timbre, auditory perception and psychoacoustics for sounds emerging from instrument mixtures. It resulted in choosing to use verbal descriptors of timbral qualities to represent auditory perception of instrument combination sounds. Therefore, this thesis reports on the developments of methods and tools designed to automatically retrieve and identify perceptual qualities of timbre within audio files, using specific musical acoustic features and artificial intelligence algorithms. Different perceptual experiments have been conducted to evaluate the correlation between selected acoustics cues and humans' perception. Results of these evaluations confirmed the potential and suitability of the presented approaches. Finally, these developments have helped to design a perceptually-orientated generative system harnessing aspects of artificial intelligence to combine sampled instrument notes. The findings of this exploration demonstrate that an artificial intelligence approach can help to harness the perceptual aspect of instrumental timbre and timbral combinations. This investigation suggests that established methods of measuring timbral qualities, based on a diverse selection of sounds, also work for sounds created by combining instrument notes. The development of tools designed to automatically retrieve and identify perceptual qualities of timbre also helped in designing a comparative scale that goes towards standardising metrics for comparing timbral attributes. Finally, this research demonstrates that perceptual characteristics of timbral qualities, using verbal descriptors as a representation, can be implemented in an intelligent computing system designed to combine sampled instrument notes conveying specific perceptual qualities.Arts and Humanities Research Council funded 3D3 Centre for Doctoral Trainin

Predicción de demanda y producción de energía eléctrica mediante redes neuronales y validación de los resultados mediante ensayos realizados en el laboratorio de recursos energéticos distribuidos de la UPV

[ES] El objetivo de este TFM es aplicar una metodología para predecir la producción y generación de energía de la microrred del Laboratorio de Recursos Energéticos Distribuidos de la UPV (LabDER) usando redes neuronales artificiales. Esta metodología se puede extrapolar a otras microrredes. Se dispone la potencia generada en tiempo real para cada una de las fuentes: solar fotovoltaica, eólica y baterías. Además, se dispone de datos meteorológicos tales como irradiación, velocidad de viento, temperatura ambiente entre otros. Con esta información se pretende predecir las curvas de demanda y de generación global de cada componente para optimizar la gestión de la energía. El tratamiento de los datos y la predicción se realizará mediante el lenguaje Python y usando la herramienta tensorflow. Tensorflow es una herramienta que permite generar diferentes tipos de redes neuronales como es el caso del clásico ¿perceptrón¿, redes convolucionales o redes recurrentes. Con el fin de obtener mejores resultados, esta herramienta permite crear redes neuronales artificiales con diferentes algoritmos de optimización para su entrenamiento. La primera parte de este trabajo consistirá en adaptar los datos de entrada (datos de la red y datos meteorológicos) para que pueden ser utilizados como inputs en la red neuronal. Posteriormente se seleccionarán los diferentes tipos de redes neuronales según lo que se decida predecir. Por ejemplo, para la producción global diaria, se podrían obtener resultados óptimos mediante un perceptrón clásico, mientras que para obtener la curva de producción sería mejor trabajar con redes neuronales recurrentes. Finalmente, mediante Tensorflow se puede definir una red neuronal con sus diferentes capas, el ritmo de aprendizaje y el algoritmo de entrenamiento entre otros. Esta herramienta permite crear una red a medida para obtener resultados adaptando los diferentes parámetros para así conseguir un mejor entrenamiento. Este tipo de redes implica un alto coste computacional.Martinez, AA. (2021). Predicción de demanda y producción de energía eléctrica mediante redes neuronales y validación de los resultados mediante ensayos realizados en el laboratorio de recursos energéticos distribuidos de la UPV. Universitat Politècnica de València. http://hdl.handle.net/10251/164734TFG

Homological finiteness of functors and applications

We give sufficient conditions which ensure that a functor of finite length from an additive category to finite-dimensional vector spaces has a projective resolution whose terms are finitely generated. For polynomial functors, we study also a weaker homological finiteness property, which applies to twisted homological stability for matrix monoids. This is inspired by works by Schwartz and Betley-Pirashvili, which are generalised; this also uses decompositions {\`a} la Steinberg over an additive category that we recently got with Vespa. We show also, as an application, a finiteness property for stable homology of linear groups on suitable rings.Comment: in French languag

A HLLC Riemann solver to compute shallow water equations with topography and friction

We consider the resolution, by a finite-volume method, of the two-dimensional model of the shallow water equations with topography and friction. Thanks to the property of invariance per rotation of the flux of shallow water equations, we show that the study of the 2D case rises from the good resolution of the monodimensional system of the shallow water equations. The numerical implementation is carried out by a finite volume scheme of Godunov type using an Riemann approximate solver of the type HLLC which preserves the positivity height of water and which is well adapted for the treatment of the shock waves. Lastly, numercal examples on academic problems are presented as well as a real case : application of the model to the phenomenon of flood of the town of Cotonou (BENIN) by the risings of the lagoon of Cotonou

Un schema de volumes-finis decentre pour la resolution des equations d'Euler en axisymetrique

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