Entropy, first introduced in thermodynamics, is used in a wide range of fields. Chapter 1 discusses some important theoretical and practical aspects of entropy: what is entropy, is it subjective or objective, and how to properly apply it to living organisms. Chapter 2 presents applications of entropy to evolution. Chapter 3 shows how cellulosic biofuel production can be improved. Chapter 4 shows how lattice vacancies influence the thermodynamic properties of materials. To determine the nature of thermodynamic entropy, Chapters 1 and 2 describe the roots, the conceptual history of entropy, as well as its path of development and application. From the viewpoint of physics, thermal entropy is a measure of useless energy stored in a system resulting from thermal motion of particles. Thermal entropy is a non-negative objective property. The negentropy concept, while mathematically correct, is physically misleading. This dissertation hypothesizes that concepts from thermodynamics and statistical mechanics can be used to define statistical measurements, similar to thermodynamic entropy, to summarize the convergence of processes driven by random inputs subject to deterministic constraints. A primary example discussed here is evolution in biological systems. As discussed in this dissertation, the first and second laws of thermodynamics do not translate directly into parallel laws for the biome. But, the fundamental principles on which thermodynamic entropy is based are also true for information. Based on these principles, it is shown that adaptation and evolution are stochastically deterministic. Chapter 3 discusses the hydrolysis of cellulose to glucose, which is a key reaction in renewable energy from biomass and in mineralization of soil organic matter to CO2. Conditional thermodynamic parameters, ΔhydG', ΔhydH', and ΔhydS', and equilibrium glucose concentrations are reported for the reaction C6H10O5(cellulose) + H2O(l) ⇄ C6H12O6(aq) as functions of temperature from 0 to 100°C. Activity coefficients of aqueous glucose solution were determined as a function of temperature. The results suggest that producing cellulosic biofuels at higher temperatures will result in higher conversion. Chapter 4 presents the data and a theory relating the linear term in the low temperature heat capacity to lattice vacancy concentration. The theory gives a quantitative result for disordered vacancies, but overestimates the contribution from ordered vacancies because ordering leads to a decreased influence of vacancies on heat capacity.

Previous research has identified linear boundaries within a normalized unit square for specific paired strategies within the iterated prisoner's dilemma schema. In this work, general methods of capturing linear boundaries are developed and demonstrated on a wider variety of paired strategies. The method is also tested using an alternate scoring method. An application of Burnside's Lemma simplifies the number of neighbourhood configurations to be considered. In addition, Shannon entropy is used as a means of evaluating diversity of agents evolved with different payoff matrices, by which one might locate a game that is as balanced as possible.

In this work it is address the question of how certain climatic variables may be significant related to alterations of avian biodiversity in a semi-agricultural Natura wetland side in Northern Greece. Particularly, the current research highlights the effects of climate and land cover intensity on the Thermaikos gulf bird biodiversity and its importance for healthy ecosystem functioning. Also, the maintenance of a good state of conservation in the Thermaikos gulf has direct impacts on a larger scale since it benefits the rest of the Natura wetlands network considering the connectivity related to migratory birds. Furthermore, the methodology which is used is essential to help inform the science-based management of environments that support threatened and endangered wildlife and can be further applied to other wetlands in the Mediterranean with similar weather conditions and agricultural land use. The alteration in compositional diversity of bird abundances has been studied at the species level from 2012 to 2017 in one of the most important wetland Natura sites in Northern Greece and by using different biodiversity indices. Shannon Entropy was lower during 2012 (DH = 1.509) albeit remained in similar levels from 2013 and afterwards. The highest values of Shannon Entropy were recorded in 2014 (DH = 2.927) and 2016 (DH = 2.888) suggesting that there is a higher diversity compared to the other observation years and especially 2012. The yearly trends of the Simpson dominance index and the Gini-Simpson Index had quite similar patterns. The Berger-Parker index, DD, which represents the maximum proportion of any species estimated in the sample assemblage, had its highest values in 2012 (DD = 0.58) and 2017 (DD = 0.39) and its lowest in 2014 (DD = 0.13) and 2016 (DD = 0.15). A complete characterization of diversity was possible through the projection of Hill numbers and the Rényi entropy, parameterized by the order q in terms of an empirical curve. According to the Hills numbers pooled over the years, the mean species abundance (q = 0) was estimated at 31 species, the mean biodiversity (q = 1) was 13 species and the most dominant species (q = 2) were 8 species. The quantification of bird biodiversity in the particular research area patterns is a fundamental task to evaluate current management actions, improve conservation and design future management strategies. Moreover, the interplay between temperature, relative humidity and three different bird biodiversity indexes, including Shannon Entropy, Simpson’s dominance (evenness) index and the Berger-Parker index has been also examined. By using different modeling approaches, parametric and non- parametric multivariate models, we make effort to get a consensus on the interrelationships between climate and avian biodiversity. In particular, it is been shown that in most cases nonlinear models and surface-plot analysis methodology, are able to capture the relation of a considerable increase in the estimated biodiversity indexes with increased temperatures and rain levels. Thus, biodiversity is to a significant extent affected by the aforementioned climate factors at a proximate level involving synergies between the different climate factors. Finally, the combined effect of climate variables and remote sensing land cover indicators on bird richness has been also explored to detect any influence on bird diversity due to agricultural intensification. In particular the association between bird richness and environmental drivers, as well as remote sensed land cover indices was explored for seven successive seasons using correlation analysis and a Cox-Box transformed multivariate linear model. Three climate variables were tested: mean temperature, rain level and mean relative humidity and three land cover indices: the Normalized Difference Vegetation Index (NDVI), the Atmospheric Resistance Vegetation Index (ARVI) and an Agricultural Band Combination Index (ABCI). Among the environmental drivers explored, temperature, rain levels and ABCI were significantly correlated to bird richness in contrast to NDVI and ARVI which showed a lower correlation, while relative humidity displayed the poorest correlation. Additionally, the multivariable linear model indicates that temperature, rain levels and ABCI have a statistically significant effect (p<0.05) on bird species richness accounting for 73,02% of data variability. Based on the overall model results and the related 3D contour plot model simulations, we conclude that bird species richness increases with an increase in temperature and rain levels, as well as with a decrease in agricultural intensity (ABCI). Concluding, in most cases temperature, rain levels and agricultural intensity significantly influenced bird richness in a combined manner. Furthermore, agricultural intensification has resulted in most cases in the loss of bird richness. Understanding the factors that can affect the biodiversity is of great importance for rational land use planning and conservation management of semi-Natural areas. Agriculture is the main driving force that influences the topographic and biological diversity of Europe, shaping the natural landscape of the European countryside for thousands of years. Revealing potential interrelationship between biodiversity, climate drivers and landscape indicators, although is a complex—even though challenging—task, contributing to our understanding of the mechanisms connecting climate change with ecosystem functioning. Moreover, a better understanding of biodiversity functioning in relation to human activities in natural protected areas as well as climate is essential for biodiversity awareness and the design of effective biodiversity-related conservation management policies.

We investigate the extraction of cryptographic keying material from nano-scale variations of digital circuit outputs by using nested polar codes and neural leakage estimators. A runtime-efficient algorithm is developed to simulate such a system. A certain family of digital circuit outputs are known to be a source of randomness that can be used as a unique identifier for each output. By generating secret keys from these unique outputs, one can apply cryptographic methods by using the secret keys as the seed. One is required to store extra helper data generated first time the outputs are measured, since there is noise in digital circuit outputs, to be able to reconstruct the same key from every measurement of the same digital circuit. The generation of the secret keys and helper data follow a nested polar code construction, and they are generated in this thesis to estimate the Shannon entropy of the secret key and secrecy leakage to a passive attacker using neural networks. The estimators used illustrate, for the first time, that the system generates secret keys of almost maximum entropy and negligible secrecy leakage for practical cryptographic systems if the digital circuit outputs can be preprocessed to obtain almost independent and identically distributed (i.i.d.) random outputs distributed according to a binary uniform distribution. The algorithm design is evaluated and improvements for lower runtime are suggested. Ideas for future research are presented.

Kullback-Leibler relative-entropy or KL-entropy of P with respect to R defined as ∫xlnddPRdP , where P and R are probability measures on a measurable space (X, ), plays a basic role in the definitions of classical information measures. It overcomes a shortcoming of Shannon entropy – discrete case definition of which cannot be extended to nondiscrete case naturally. Further, entropy and other classical information measures can be expressed in terms of KL-entropy and hence properties of their measure-theoretic analogs will follow from those of measure-theoretic KL-entropy. An important theorem in this respect is the Gelfand-Yaglom-Perez (GYP) Theorem which equips KL-entropy with a fundamental definition and can be stated as: measure-theoretic KL-entropy equals the supremum of KL-entropies over all measurable partitions of X . In this thesis we provide the measure-theoretic formulations for ‘generalized’ information measures, and state and prove the corresponding GYP-theorem – the ‘generalizations’ being in the sense of R ´enyi and nonextensive, both of which are explained below. Kolmogorov-Nagumo average or quasilinear mean of a vector x = (x1, . . . , xn) with respect to a pmf p= (p1, . . . , pn)is defined ashxiψ=ψ−1nk=1pkψ(xk), whereψis an arbitrarycontinuous and strictly monotone function. Replacing linear averaging in Shannon entropy with Kolmogorov-Nagumo averages (KN-averages) and further imposing the additivity constraint – a characteristic property of underlying information associated with single event, which is logarithmic – leads to the definition of α-entropy or R ´enyi entropy. This is the first formal well-known generalization of Shannon entropy. Using this recipe of R´enyi’s generalization, one can prepare only two information measures: Shannon and R´enyi entropy. Indeed, using this formalism R´enyi characterized these additive entropies in terms of axioms of KN-averages. On the other hand, if one generalizes the information of a single event in the definition of Shannon entropy, by replacing the logarithm with the so called q-logarithm, which is defined as lnqx =x1− 1 −1 −q , one gets what is known as Tsallis entropy. Tsallis entropy is also a generalization of Shannon entropy but it does not satisfy the additivity property. Instead, it satisfies pseudo-additivity of the form x ⊕qy = x + y + (1 − q)xy, and hence it is also known as nonextensive entropy. One can apply R´enyi’s recipe in the nonextensive case by replacing the linear averaging in Tsallis entropy with KN-averages and thereby imposing the constraint of pseudo-additivity. A natural question that arises is what are the various pseudo-additive information measures that can be prepared with this recipe? We prove that Tsallis entropy is the only one. Here, we mention that one of the important characteristics of this generalized entropy is that while canonical distributions resulting from ‘maximization’ of Shannon entropy are exponential in nature, in the Tsallis case they result in power-law distributions. The concept of maximum entropy (ME), originally from physics, has been promoted to a general principle of inference primarily by the works of Jaynes and (later on) Kullback. This connects information theory and statistical mechanics via the principle: the states of thermodynamic equi- librium are states of maximum entropy, and further connects to statistical inference via select the probability distribution that maximizes the entropy. The two fundamental principles related to the concept of maximum entropy are Jaynes maximum entropy principle, which involves maximizing Shannon entropy and the Kullback minimum entropy principle that involves minimizing relative-entropy, with respect to appropriate moment constraints. Though relative-entropy is not a metric, in cases involving distributions resulting from relative-entropy minimization, one can bring forth certain geometrical formulations. These are reminiscent of squared Euclidean distance and satisfy an analogue of the Pythagoras’ theorem. This property is referred to as Pythagoras’ theorem of relative-entropy minimization or triangle equality and plays a fundamental role in geometrical approaches to statistical estimation theory like information geometry. In this thesis we state and prove the equivalent of Pythagoras’ theorem in the nonextensive formalism. For this purpose we study relative-entropy minimization in detail and present some results. Finally, we demonstrate the use of power-law distributions, resulting from ME-rescriptions of Tsallis entropy, in evolutionary algorithms. This work is motivated by the recently proposed generalized simulated annealing algorithm based on Tsallis statistics. To sum up, in light of their well-known axiomatic and operational justifications, this thesis establishes some results pertaining to the mathematical significance of generalized measures of information. We believe that these results represent an important contribution towards the ongoing research on understanding the phenomina of information. (For formulas pl see the original document) ii

[EN] In this thesis, we consider two problems: we first explore the application of visibility graphs for describing the orbits of a discrete dynamical system that is governed by a fractional version of the logistic equation. We also study how to use this type of graphs to study response time series from the perspective of psychology. The preliminaries and introduction of these visibility graphs are presented in Chapter 1, where we revisit some basic facts from network science related to them. In the first part of this thesis, we analyze a phenomenon of mathematical nature. Wu and Baleanu introduced a fractional discrete dynamical system inspired by the fractional difference logistic equation. In order to study the trajectories of this model under this perspective of network science, in Chapter 2, we first review the most used fractional derivatives (Riemann-Liouville, Caputo, and Gründwald-Letnikov). Later, we show how to consider discrete fractional derivatives. Within our work, we present an alternative way of deducing the governing equation with respect to the one shown by Wu and Baleanu. We revisit the Wu-Baleanu equation in Chapter 3, focused on the visibility graphs of trajectories generated under different values of the scaling factor and the fractional exponent. We also study the existing connections between these parameters and the fitting with the degree distribution of the corresponding visibility graphs. When chaos is present, we link them with the exponent obtained when fitting the degree distribution to a power-law of the form x^(¿¿). With this approach, we provide an integrated vision of the dynamics of a family of fractional discrete dynamical systems that cannot be obtained from single Feigenbaum diagrams computed for each scaling factor and fractional exponent. We also connect the power-law exponent of the degree distribution fitting with the Shannon entropy of the visibility graphs degree distribution. In the second part, we analyze the response times of students to a binary decision task from the perspective of network science. We analyze the properties of the natural visibility graphs associated with their reaction time series. We observe that the degree distribution of these graphs usually fits a power-law distribution p(x) = x^(¿¿). We study the range in which parameter ¿ occurs and the changes of this exponent with respect to the age and gender of the students. Besides, we also study the links between the parameter ¿ and the ex-Gaussian distribution parameters that best fits each subject's response times. Finally, we outline some conclusions and perspectives of future research in both parts in Chapter 6. / [ES] En esta tesis, hemos considerado dos problemas: primero exploramos la aplicación de los grafos de visibilidad para describir las órbitas de un sistema dinámico discreto que está gobernado por una versión fraccionaria de la ecuación logística. Además, también estudiamos cómo usar este tipo de grafos para estudiar series temporales de tiempos de respuesta desde una perspectiva psicológica. Los preliminares, así como una introducción a estos grafos de visibilidad, se presentan en el Capítulo 1, donde revisitamos algunos hechos básicos de la ciencia de redes relacionados con dichos grafos. En la primera parte de esta tesis, analizamos un fenómeno de naturaleza matemática. Wu y Baleanu introdujeron un sistema dinámico discreto fraccionario inspirado en la ecuación logística con derivadas fraccionarias. Con el propósito de estudiar las trayectorias de este modelo desde la perspectiva de la ciencia de redes, en el Capítulo 2, primero revisamos las derivadas fraccionarias más utilizadas (Riemann-Liouville, Caputo y Gründwald-Letnikov). Posteriormente, mostramos cómo considerar derivadas fraccionarias discretas. En nuestro trabajo, presentamos una forma alternativa de deducir la ecuación gobernante con respecto a la presentada por Wu y Baleanu. Revisitamos la ecuación de Wu-Baleanu en el Capítulo 3, centrado en los grafos de visibilidad de trayectorias generadas a partir de distintos valores del factor de escala y del exponente fraccionario. También estudiamos la existencia de conexiones entre estos parámetros y el ajuste de la distribución de los grados de los correspondientes grafos de visibilidad. Cuando el caos está presente, los enlazamos con el exponente obtenido al ajustar la distribución de los grados a una ley de potencias de la forma x^(¿¿). A través de este enfoque, proporcionamos una visión integrada de la dinámica de una familia de sistemas dinámicos discretos fraccionarios que no se pueden obtener a partir de diagramas de Feigenbaum individuales calculados para cada factor de escala y exponente fraccionario. Además, relacionamos el exponente de la ley de potencias del ajuste de la distribución de grados con la entropía de Shannon de la distribución de grados de los grafos de visibilidad. En la segunda parte, analizamos el tiempo de respuesta de un grupo de estudiantes que realizaron una tarea de decisión binaria desde la perspectiva de la ciencia de redes. Estudiamos las propiedades de los grafos de visibilidad natural asociados con sus correspondientes series de tiempos de respuesta. Observamos que la distribución de los grados de estos grafos normalmente sigue una distribución ley de potencias p(x) = x^(¿¿). Analizamos el rango en el cual el parámetro ¿ se mueve y los cambios de este exponente con respecto a la edad y el sexo de los estudiantes. Por otro lado, también estudiamos la relación entre el parámetro ¿ y los parámetros de la distribución ex-Gaussiana que mejor se ajusta al tiempo de respuesta de cada sujeto. Finalmente, destacamos algunas conclusiones y perspectivas de investigación futura en ambas líneas de trabajo en el Capítulo 6. / [CAT] En aquesta tesi, hem considerat dos problemes: primer explorem l'aplicació dels grafs de visibilitat per a descriure les òrbites d'un sistema dinàmic discret que està governat per una versió fraccionària de l'equació logística. A més a més, també estudiem com emprar aquest tipus de grafs per a analitzar sèries temporals de temps de resposta des d'una perspectiva psicològica. Els preliminars, així com una introducció a aquests grafs de visibilitat, es presenten al Capítol 1, on revisitem alguns fets bàsics de la ciència de xarxes relacionats amb ells. En la primera part d'aquesta tesi, analitzem un fenomen de naturalesa matemàtica. Wu i Baleanu van introduir un sistema dinàmic discret fraccionari inspirat en l'equació logística amb derivades fraccionàries. Amb el fi d'estudiar les trajectòries d'aquest model des d'una perspectiva de la ciència de xarxes, en el Capítol 2, primer revisem les derivades fraccionàries més utilitzades (Riemann-Liouville, Caputo i Gründwald-Letnikov). Posteriorment, mostrem com considerar derivades fraccionàries discretes. Al nostre treball, presentem una forma alternativa de deduir l'equació governant respecte a la presentada per Wu i Baleanu. Revisitem l'equació de Wu-Baleanu al Capítol 3, focalitzat en els grafs de visibilitat de trajectòries generades a partir de valors diferents del factor d'escala i de l'exponent fraccionari. També estudiem l'existència de connexions entre aquests paràmetres i l'ajust de la distribució dels graus dels corresponents grafs de visibilitat. Quan el caos hi és, els enllacem amb l'exponent que hem obtés en ajustar la distribució dels graus a una llei de potències de la forma x^(¿¿). Des d'aquesta perspectiva, proporcionem una visió integrada de la dinàmica d'una família de sistemes dinàmics discrets fraccionaris que no es poden obtenir a partir de diagrames de Feigenbaum individuals calculats per a cada factor d'escala i exponent fraccionari. A més a més, relacionem l'exponent de la llei de potències de l'ajust de la distribució de graus amb l'entropia de Shannon de la distribució de graus dels grafs de visibilitat. A la segona part, analitzem el temps de resposta d'un grup d'estudiants que realitzaren una tasca de decisió binària des del punt de vista de la ciència de xarxes. Estudiem les propietats dels grafs de visibilitat natural associats amb les seues corresponents sèries temporals de temps de resposta. Observem que la distribució dels graus d'aquests grafs normalment segueix una distribució llei de potències p(x) = x^(¿¿). Analitzem el rang en què el paràmetre ¿ es mou i els canvis d'aquest exponent respecte a l'edat i el sexe dels estudiants. D'altra banda, també estudiem la relació entre el paràmetre ¿ i els paràmetres de la distribució ex-Gaussiana que millor fita el temps de resposta de cada subjecte. Finalment, destaquem algunes conclusions i perspectives d'investigació futura en ambdues línies de treball en el Capítol 6. / Mira Iglesias, A. (2021). Applications of Visibility Graphs for the representation of Time Series [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/176012 / TESIS

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Le point de départ de ce travail est la thèse réalisée par Pascal Vrignat sur la modélisation de niveaux de dégradation d’un système dynamique à l’aide de Modèles de Markov Cachés (MMC), pour une application en maintenance industrielle. Quatre niveaux ont été définis : S1 pour un arrêt de production et S2 à S4 pour des dégradations graduelles. Recueillant un certain nombre d’observations sur le terrain dans divers entreprises de la région, nous avons réalisé un modèle de synthèse à base de MMC afin de simuler les différents niveaux de dégradation d’un système réel. Dans un premier temps, nous identifions la pertinence des différentes observations ou symboles utilisés dans la modélisation d’un processus industriel. Nous introduisons ainsi le filtre entropique. Ensuite, dans un but d’amélioration du modèle, nous essayons de répondre aux questions : Quel est l’échantillonnage le plus pertinent et combien de symboles sont ils nécessaires pour évaluer au mieux le modèle ? Nous étudions ensuite les caractéristiques de plusieurs modélisations possibles d’un processus industriel afin d’en déduire la meilleure architecture. Nous utilisons des critères de test comme les critères de l’entropie de Shannon, d’Akaike ainsi que des tests statistiques. Enfin, nous confrontons les résultats issus du modèle de synthèse avec ceux issus d’applications industrielles. Nous proposons un réajustement du modèle pour être plus proche de la réalité de terrain. / As part of preventive maintenance, many companies are trying to improve the decision support of their experts. This thesis aims to assist our industrial partners in improving their maintenance operations (production of pastries, aluminum smelter and glass manufacturing plant). To model industrial processes, different topologies of Hidden Markov Models have been used, with a view to finding the best topology by studying the relevance of the model outputs (also called signatures). This thesis should make it possible to select a model framework (a framework includes : a topology, a learning & decoding algorithm and a distribution) by assessing the signature given by different synthetic models. To evaluate this « signature », the following widely-used criteria have been applied : Shannon Entropy, Maximum likelihood, Akaike Information Criterion, Bayesian Information Criterion and Statistical tests.

Made available in DSpace on 2016-06-02T20:19:17Z (GMT). No. of bitstreams: 1 4130.pdf: 7746703 bytes, checksum: 425a15aa93496be6f1802d7a31fd28d2 (MD5) Previous issue date: 2012-02-29 / Financiadora de Estudos e Projetos / OBJECTIVE Evaluate the heart rate variability (HRV) of individuals with Type 2 diabetes, in the supine and in response to active postural maneuver from the supine to orthostatic position, by means of linear and non linear analysis and correlate these data. RESEARCH DESIGN AND METHODS Sixteen men with type 2 diabetes (DM) and sixteen control subjects (CG), age-range from 40 to 65 year were studied. The R-R intervals were recorded with a Polar RS800CX for 10 minutes in supine and 10 minutes in the orthostatic position. We assessed HRV using spectral (LFnu, HFnu and LF/HF), symbolic (0V%, 1V%, 2LV% and 2ULV%) analysis, Shannon (SE) and conditional entropy (complexity Index - CI and Normalized Complexity Index- NCI). RESULTS The DM presented higher sympathetic modulation (LFnu) in the supine position than the CG. In active postural maneuver for the variables LFnu and HFnu, DM showed no significant responses. Irrespective of position DM presented lower complexity than CG for SE. The same did not occur with conditional entropy, however, in both groups a reduction in values of entropies was observed with postural change. The reduction in complexity observed by SE was related to an increase in sympathetic modulation (0V%). CONCLUSION Our study showed that DM had higher sympathetic modulation in the supine position, which may be related to less complexity of HRV in this population. In addition, DM did not present the expected response of the autonomic nervous system to active postural maneuver for the variables LFnu and HFnu. / OBJETIVO Avaliar a variabilidade da frequência cardíaca (VFC) de indivíduos com diabetes mellitus tipo 2, na posição supina e em resposta a manobra postural ativa de supino para ortostático, por meio de análise linear e não linear e correlacioná-las. MÉTODOS Foram avaliados dezesseis homens com diabetes mellitus tipo 2 (DM) e dezesseis sujeitos controle (GC), na faixa etária de 40 a 65 anos. Os intervalos R-R (iRR) foram captados por um Polar RS800CX durante 10 minutos na posição supina e 10 minutos na posição ortostática. Avaliou-se a VFC utilizando análises espectral (BFun, AFun e BF/AF), simbólica (0V%, 1V%, 2LV% e 2ULV%), entropia de Shannon (ES) e condicional (índice de complexidade - IC e índice de complexidade normalizado - ICN). RESULTADOS O DM apresentou maior modulação simpática (BFun) na posição supina do que o GC. Na manobra postural ativa para as variáveis BFun e AFun o DM não mostrou resposta significativa. Independentemente da posição DM apresentou menor complexidade (menor ES) do que o GC. O mesmo não ocorreu com a entropia condicional, entretanto em ambos os grupos foi observada redução nos valores das entropias com a mudança postural. A redução da complexidade observada pela ES foi relacionada ao aumento da modulação simpática (0V%). CONCLUSÃO Nosso estudo mostrou que DM apresentou maior modulação simpática na posição supina, a qual pode estar relacionada com a menor complexidade da VFC nessa população. Além disso, DM não apresentou resposta esperada do sistema nervoso autonômico à manobra postural ativa para as variáveis BFun e AFun.

Cette thèse s’intéresse à la création de nouvelles approches algorithmiques pour la résolution du problème inverse en biophysiques. Dans un premier temps, on vise l’application RMN de type DOSY: une nouvelle approche de régularisation hybride a été proposée avec un nouvel algorithme PALMA (http://palma.labo.igbmc.fr/). Cet algorithme permet d’analyser des données réelles DOSY avec une précision importante quelque soit leur type. Dans un deuxième temps, notre intérêt s’est tourné vers l’application de spectrométrie de masse. Nous avons proposé une nouvelle approche par dictionnaire dédiée à l’analyse protéomique en utilisant le modèle averagine et une stratégie de minimisation sous contraintes d'une pénalité de parcimonie. Afin d’améliorer la précision de l’information obtenue, nous avons proposé une nouvelle méthode SPOQ, basée sur une nouvelle fonction de pénalisation, résolue par un nouvel algorithme Forward-Backward à métrique variable localement ajustée. Tous nos algorithmes bénéficient de garanties théoriques de convergence, et ont été validés expérimentalement sur des spectres synthétisés et des données réelles / This thesis aims at proposing new approaches to solve the inverse problem in biophysics. Firstly, we study the DOSY NMR experiment: a new hybrid regularization approach has been proposed with a novel PALMA algorithm (http://palma.labo.igbmc.fr/). This algorithm ensures the efficient analysis of real DOSY data with a high precision for all different type. In a second time, we study the mass spectrometry application. We have proposed a new dictionary based approach dedicated to proteomic analysis using the averagine model and the constrained minimization approach associated with a sparsity inducing penalty. In order to improve the accuracy of the information, we proposed a new SPOQ method based on a new penalization, solved with a new Forward-Backward algorithm with a variable metric locally adjusted. All our algorithms benefit from sounded convergence guarantees, and have been validated experimentally on synthetics and real data.