156 research outputs found

    Sampling theorems with derivatives in shift-invariant spaces generated by periodic exponential B-splines

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    We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a new notion of measuring the gap between consecutive samples. These conditions are near optimal, and, in particular, they imply the existence of sampling sets with lower Beurling density arbitrarily close to the necessary density.Comment: 40 pages, 3 figure

    CONTEXT EFFECTS ON THE NEURAL CORRELATES OF EMOTION

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    Human emotions are inextricably linked to the context in which they occur, yet neuroscience research on emotion often overlooks the role of context in shaping the neural correlates of human emotions. This dissertation, through three studies, begins to address this gap. Study 1 (Chapter 2) investigated how language as a form of context influences the brain’s response to facial expressions of anger and disgust, showing distinct differences in neural activity related to disgust perception between Chinese Asian and White American participants. Language was found to play a significant role in shaping the neural correlates of emotion perception, particularly in the context of disgust for Chinese Asian participants. Study 2 (Chapter 3) examined the influence of social and cultural contexts on the neural correlates of fear and sadness, demonstrating that both cultural group membership and cultural attitudes are related to the brain’s processing of negative emotional experiences. Study 3 (Chapter 4) focused on individual and group level variation in emotion-related functional connectivity, finding both idiographic and nomothetic patterns of connectivity related to negative emotional experiences. It further highlighted the influence of cultural attitudes on the neural correlates of emotion. Overall, these studies illustrate the importance of considering diverse contextual variables in studying the neural basis of emotion. They show that social and cultural contexts influence how the human brain processes and represents emotions.Doctor of Philosoph

    Statistical Analysis of Audio Signals using Time-Frequency Analysis

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    In this thesis, we provide nonparametric estimation of signals corrupted by stationary noise in the white noise model. We derive adaptive and rate-optimal estimators of signals in modulation spaces by thresholding the coefficients obtained from the Gabor expansion. The rates obtained using the classical oracle inequalities of Donoho and Johnstone (1994) exhibit new features that reflect the inclusion of both time and frequency. The scope of our results is extended to alpha-modulation spaces in the one-dimensional setting, allowing a comparison with Sobolev and Besov spaces. To confirm the practical applicability of our methods, we perform extensive simulations. These simulations evaluate the performance of our methods in comparison to state-of-the-art methods over a range of scenarios

    Essentially translation invariant pseudodifferential operators on manifolds with cylindrical ends

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    We study two classes (or calculi) of pseudodifferential operators defined on manifolds with cylindrical ends: the class of pseudodifferential operators that are ``translation invariant at infinity'' and the class of ``essentially translation invariant operators'' that have appeared in the study of layer potential operators on manifolds with straight cylindrical ends. Both classes are close to the bb-calculus considered by Melrose and Schulze and to the cc-calculus considered by Melrose and Mazzeo-Melrose. Our calculi, however, are different and, while some of their properties follow from those of the bb- or cc-calculi, many of their properties do not. In particular, the ``essentially translation invariant calculus'' is spectrally invariant, a property not enjoyed by the ``translation invariant at infinity'' calculus or the bb-calculus. For our calculi, we provide easy, intuitive proofs of the usual properties: stability for products and adjoints, mapping and boundedness properties for operators acting between Sobolev spaces, regularity properties, existence of a quantization map and topological properties of our algebras, the Fredholm property. Since our applications will be to the Stokes operator, we systematically work in the setting of Agmon-Douglis-Nirenberg-elliptic operators.Comment: 39 page

    Smart models to improve agrometeorological estimations and predictions

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    La población mundial, en continuo crecimiento, alcanzará de forma estimada los 9,7 mil millones de habitantes en el 2050. Este incremento, combinado con el aumento en los estándares de vida y la situación de emergencia climática (aumento de la temperatura, intensificación del ciclo del agua, etc.) nos enfrentan al enorme desafío de gestionar de forma sostenible los cada vez más escasos recursos disponibles. El sector agrícola tiene que afrontar retos tan importantes como la mejora en la gestión de los recursos naturales, la reducción de la degradación medioambiental o la seguridad alimentaria y nutricional. Todo ello condicionado por la escasez de agua y las condiciones de aridez: factores limitantes en la producción de cultivos. Para garantizar una producción agrícola sostenible bajo estas condiciones, es necesario que todas las decisiones que se tomen estén basadas en el conocimiento, la innovación y la digitalización de la agricultura de forma que se garantice la resiliencia de los agroecosistemas, especialmente en entornos áridos, semi-áridos y secos sub-húmedos en los que el déficit de agua es estructural. Por todo esto, el presente trabajo se centra en la mejora de la precisión de los actuales modelos agrometeorológicos, aplicando técnicas de inteligencia artificial. Estos modelos pueden proporcionar estimaciones y predicciones precisas de variables clave como la precipitación, la radiación solar y la evapotranspiración de referencia. A partir de ellas, es posible favorecer estrategias agrícolas más sostenibles, gracias a la posibilidad de reducir el consumo de agua y energía, por ejemplo. Además, se han reducido el número de mediciones requeridas como parámetros de entrada para estos modelos, haciéndolos más accesibles y aplicables en áreas rurales y países en desarrollo que no pueden permitirse el alto costo de la instalación, calibración y mantenimiento de estaciones meteorológicas automáticas completas. Este enfoque puede ayudar a proporcionar información valiosa a los técnicos, agricultores, gestores y responsables políticos de la planificación hídrica y agraria en zonas clave. Esta tesis doctoral ha desarrollado y validado nuevas metodologías basadas en inteligencia artificial que han ser vido para mejorar la precision de variables cruciales en al ámbito agrometeorológico: precipitación, radiación solar y evapotranspiración de referencia. En particular, se han modelado sistemas de predicción y rellenado de huecos de precipitación a diferentes escalas utilizando redes neuronales. También se han desarrollado modelos de estimación de radiación solar utilizando exclusivamente parámetros térmicos y validados en zonas con características climáticas similares a lugar de entrenamiento, sin necesidad de estar geográficamente en la misma región o país. Analógamente, se han desarrollado modelos de estimación y predicción de evapotranspiración de referencia a nivel local y regional utilizando también solamente datos de temperatura para todo el proceso: regionalización, entrenamiento y validación. Y finalmente, se ha creado una librería de Python de código abierto a nivel internacional (AgroML) que facilita el proceso de desarrollo y aplicación de modelos de inteligencia artificial, no solo enfocadas al sector agrometeorológico, sino también a cualquier modelo supervisado que mejore la toma de decisiones en otras áreas de interés.The world population, which is constantly growing, is estimated to reach 9.7 billion people in 2050. This increase, combined with the rise in living standards and the climate emergency situation (increase in temperature, intensification of the water cycle, etc.), presents us with the enormous challenge of managing increasingly scarce resources in a sustainable way. The agricultural sector must face important challenges such as improving natural resource management, reducing environmental degradation, and ensuring food and nutritional security. All of this is conditioned by water scarcity and aridity, limiting factors in crop production. To guarantee sustainable agricultural production under these conditions, it is necessary to based all the decision made on knowledge, innovation, and the digitization of agriculture to ensure the resilience of agroecosystems, especially in arid, semi-arid, and sub-humid dry environments where water deficit is structural. Therefore, this work focuses on improving the precision of current agrometeorological models by applying artificial intelligence techniques. These models can provide accurate estimates and predictions of key variables such as precipitation, solar radiation, and reference evapotranspiration. This way, it is possible to promote more sustainable agricultural strategies by reducing water and energy consumption, for example. In addition, the number of measurements required as input parameters for these models has been reduced, making them more accessible and applicable in rural areas and developing countries that cannot afford the high cost of installing, calibrating, and maintaining complete automatic weather stations. This approach can help provide valuable information to technicians, farmers, managers, and policy makers in key wáter and agricultural planning areas. This doctoral thesis has developed and validated new methodologies based on artificial intelligence that have been used to improve the precision of crucial variables in the agrometeorological field: precipitation, solar radiation, and reference evapotranspiration. Specifically, prediction systems and gap-filling models for precipitation at different scales have been modeled using neural networks. Models for estimating solar radiation using only thermal parameters have also been developed and validated in areas with similar climatic characteristics to the training location, without the need to be geographically in the same region or country. Similarly, models for estimating and predicting reference evapotranspiration at the local and regional level have been developed using only temperature data for the entire process: regionalization, training, and validation. Finally, an internationally open-source Python library (AgroML) has been created to facilitate the development and application of artificial intelligence models, not only focused on the agrometeorological sector but also on any supervised model that improves decision-making in other areas of interest

    Filter-Based Probabilistic Markov Random Field Image Priors: Learning, Evaluation, and Image Analysis

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    Markov random fields (MRF) based on linear filter responses are one of the most popular forms for modeling image priors due to their rigorous probabilistic interpretations and versatility in various applications. In this dissertation, we propose an application-independent method to quantitatively evaluate MRF image priors using model samples. To this end, we developed an efficient auxiliary-variable Gibbs samplers for a general class of MRFs with flexible potentials. We found that the popular pairwise and high-order MRF priors capture image statistics quite roughly and exhibit poor generative properties. We further developed new learning strategies and obtained high-order MRFs that well capture the statistics of the inbuilt features, thus being real maximum-entropy models, and other important statistical properties of natural images, outlining the capabilities of MRFs. We suggest a multi-modal extension of MRF potentials which not only allows to train more expressive priors, but also helps to reveal more insights of MRF variants, based on which we are able to train compact, fully-convolutional restricted Boltzmann machines (RBM) that can model visual repetitive textures even better than more complex and deep models. The learned high-order MRFs allow us to develop new methods for various real-world image analysis problems. For denoising of natural images and deconvolution of microscopy images, the MRF priors are employed in a pure generative setting. We propose efficient sampling-based methods to infer Bayesian minimum mean squared error (MMSE) estimates, which substantially outperform maximum a-posteriori (MAP) estimates and can compete with state-of-the-art discriminative methods. For non-rigid registration of live cell nuclei in time-lapse microscopy images, we propose a global optical flow-based method. The statistics of noise in fluorescence microscopy images are studied to derive an adaptive weighting scheme for increasing model robustness. High-order MRFs are also employed to train image filters for extracting important features of cell nuclei and the deformation of nuclei are then estimated in the learned feature spaces. The developed method outperforms previous approaches in terms of both registration accuracy and computational efficiency

    Data science for buildings, a multi-scale approach bridging occupants to smart-city energy planning

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    In a context of global carbon emission reduction goals, buildings have been identified to detain valuable energy-saving abilities. With the exponential increase of smart, connected building automation systems, massive amounts of data are now accessible for analysis. These coupled with powerful data science methods and machine learning algorithms present a unique opportunity to identify untapped energy-saving potentials from field information, and effectively turn buildings into active assets of the built energy infrastructure.However, the diversity of building occupants, infrastructures, and the disparities in collected information has produced disjointed scales of analytics that make it tedious for approaches to scale and generalize over the building stock.This coupled with the lack of standards in the sector has hindered the broader adoption of data science practices in the field, and engendered the following questioning:How can data science facilitate the scaling of approaches and bridge disconnected spatiotemporal scales of the built environment to deliver enhanced energy-saving strategies?This thesis focuses on addressing this interrogation by investigating data-driven, scalable, interpretable, and multi-scale approaches across varying types of analytical classes. The work particularly explores descriptive, predictive, and prescriptive analytics to connect occupants, buildings, and urban energy planning together for improved energy performances.First, a novel multi-dimensional data-mining framework is developed, producing distinct dimensional outlines supporting systematic methodological approaches and refined knowledge discovery. Second, an automated building heat dynamics identification method is put forward, supporting large-scale thermal performance examination of buildings in a non-intrusive manner. The method produced 64\% of good quality model fits, against 14\% close, and 22\% poor ones out of 225 Dutch residential buildings. %, which were open-sourced in the interest of developing benchmarks. Third, a pioneering hierarchical forecasting method was designed, bridging individual and aggregated building load predictions in a coherent, data-efficient fashion. The approach was evaluated over hierarchies of 37, 140, and 383 nodal elements and showcased improved accuracy and coherency performances against disjointed prediction systems.Finally, building occupants and urban energy planning strategies are investigated under the prism of uncertainty. In a neighborhood of 41 Dutch residential buildings, occupants were determined to significantly impact optimal energy community designs in the context of weather and economic uncertainties.Overall, the thesis demonstrated the added value of multi-scale approaches in all analytical classes while fostering best data-science practices in the sector from benchmarks and open-source implementations

    Data science for buildings, a multi-scale approach bridging occupants to smart-city energy planning

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    On the encoding of natural music in computational models and human brains

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    This article discusses recent developments and advances in the neuroscience of music to understand the nature of musical emotion. In particular, it highlights how system identification techniques and computational models of music have advanced our understanding of how the human brain processes the textures and structures of music and how the processed information evokes emotions. Musical models relate physical properties of stimuli to internal representations called features, and predictive models relate features to neural or behavioral responses and test their predictions against independent unseen data. The new frameworks do not require orthogonalized stimuli in controlled experiments to establish reproducible knowledge, which has opened up a new wave of naturalistic neuroscience. The current review focuses on how this trend has transformed the domain of the neuroscience of music

    Fractional Calculus and the Future of Science

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    Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding
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