Tesi sul tema "Entropic criterion"

Entropy is a measure of the randomness of a system state. This quantity gives us a measure of uncertainty that is associated with each particular observation belonging to a specific cluster. We examine this property and its potential use in analyzing high dimension datasets. Entropy proves most interesting in identifying possible dimensions that do not contribute meaningful classification to the clusters present. We can remove the dimension(s) found which are the least important and generalize this idea to a procedure. After identifying all the dimensions that should be eliminated from the dataset, we then compare its ability in recovering the true classification of the observations versus the estimated classification of the data. From the results obtained and shown in this paper, it is clear that entropy is a good candidate for a criterion in variable reduction.

Cette thèse a pour sujet l'étude de structures sans propriété de diffusion. Nous nous intéressons à deux classes de telles structures.Le premier sujet traite du calcul de Malliavin pour les variables aléatoires conditionnellement indépendantes qui est un cas de calcul de Malliavin discret. Il généralise aussi celui théorisé sur des produits dénombrables d'espaces de probabilité, pour les variables aléatoires indépendantes. Dans notre cas, l'intérêt d'un tel calcul est de venir compléter des résultats d'analyse stochastique avec des preuves d'inégalités fonctionnelles (inégalité de Poincaré, inégalité de McDiarmid) et de théorèmes limites. Une des applications phares est la détermination de la vitesse de convergence de théorèmes centraux limites via la méthode de Stein. En combinant le calcul de Malliavin avec la structure de Dirichlet sous-jacente aux variables aléatoires, nous obtenons une formule d'intégration par parties cruciale pour déterminer des bornes supérieures sur les vitesses de convergence. Nous montrons des théorèmes limites quantitatifs, dont un théorème de quatrième moment avec reste. En particulier, nous discutons d'une application à la normalité asymptotique du comptage de motifs dans des hypergraphes aléatoires échangeables.Le deuxième sujet étudie les fonctionnelles d'une mesure de Poisson en utilisant la notion d'inversibilité de transformations de cette mesure sur l'espace échantillon des mesures aléatoires. Nous utilisons l'identification de ces mesures et des processus ponctuels marqués associés. Les transformations inversibles sont obtenues via le théorème de Girsanov, en respectant l'absolue continuité par rapport à la mesure de référence. Il en résulte un critère entropique pour l'inversibilité des transformations. Enfin, nous faisons le lien avec les équations différentielles stochastiques dirigées par des mesures de Poisson
This thesis is concerned with the study of non-diffusive structures. We focus on two classes of such structures.The first subject deals with Malliavin calculus for conditionally independent random variables, which is a special case of discrete Malliavin calculus. It also generalizes the calculus that has been developed for countable products of probability spaces, for independent random variables.In our case, the interest of such a calculus is to complement results in stochastic analysis with proofs of functional inequalities (Poincaré inequality, McDiarmid's inequality) and limit theorems. One of the main applications is the determination of the convergence rate of central limit theorems via the Stein method.By combining Malliavin calculus with the underlying Dirichlet structure of the random variables, we obtain an integration by parts formula which is key to the derivations of so-called Stein bounds of the rates of convergence. We show quantitative limit theorems, including a fourth moment theorem with remainder. In particular, we discuss an application to the asymptotic normality of motif counting in exchangeable random hypergraphs.The second subject studies functionals of a Poisson measure using the notion of invertibility of transformations of that measure on the sample space of random measures. We use the identification of these measures and the associated marked point processes. Invertible transformations are obtained via the Girsanov's theorem, respecting absolute continuity with respect to the reference measure. This results in an entropy criterion for the invertibility of transformations. Finally, we make the connection with stochastic differential equations driven by Poisson measures

The uncertainty principle lies at the heart of quantum physics. It exhibits one of the key divergences between a classical and a quantum system: it is impossible to define a quantum state for which the values of two observables that do not commute are simultaneously specified with infinite precision. A paradigmatic example is given by Heisenberg’s original formulation of the uncertainty principle expressed in terms of variances of two canonically-conjugate variables, such as position x and momentum p, which was later generalized to a symplectic-invariant form by Schrödinger and Robertson. A different kind of uncertainty relations, originated by Białynicki-Birula and Mycielski, again for canonically-conjugate variables, relies on Shannon entropy instead of variances as a measure of uncertainty. In this thesis, we suggest several improvements of these entropic uncertainty relations and highlight the fact that they are better formulated in terms of entropy power, a notion borrowed from the information theory of real-valued signals. Our first novel entropic uncertainty relation takes x-p correlations into account and is consequently saturated by all pure Gaussian states in an arbitrary number of modes, improving on the original formulation by Białynicki-Birula and Mycielski. Our second main result is the derivation of an entropic uncertainty relation that holds for any n-tuples of not-necessarily canonically conjugate variables based on the matrix of their commutators. We then define a general form of the entropic uncertainty principle that combines both previous results. It expresses the incompatibility between two arbitrary variable n-uples and is saturated by all pure Gaussian states. Interestingly, we can also deduce from it the most general form of the Robertson uncertainty relation based on the covariance matrix of n variables.This line of research underlines the interest of defining an entropic uncertainty relation that is intrinsically invariant under symplectic transformations. Then, as a first attempt to reach this goal, we conjecture a symplectic-invariant uncertainty relation that is based on the joint differential entropy of the Wigner function. This conjecture is, however, only legitimate for states with a non-negative Wigner function. We also suggest a complex extension of this so-called Wigner entropy, which could provide the way towards an extension (and proof) of the above conjecture for all states. As a second attempt, we introduce the notion of multi-copy uncertainty observables, exploiting a connection with the algebra of angular momenta. Expressing the positivity of the variance of our multi-copy observable coincides with the Schrödinger-Robertson uncertainty relation, which suggests that the discrete Shannon entropy of such an uncertainty observable provides a new symplectic-invariant measure of uncertainty.Currently available separability criteria for continuous-variable systems imply a necessary and sufficient condition for a two-mode Gaussian state to be separable, but leave many entangled non-Gaussian states undetected. In this thesis, we introduce two improved separability criteria that enable a stronger entanglement detection. The first improved condition is based on the knowledge of an additional parameter, namely the degree of Gaussianity, and exploits a connection with Gaussianity-bounded uncertainty relations by Mandilara and Cerf. We exhibit families of non- Gaussian entangled states whose entanglement remains undetected by the Duan- Simon criterion. The second improved separability criterion is based on our improved entropic uncertainty relation that takes x-p correlations into account, and has the main advantage over the one proposed by Walborn et al. that it does not require any optimization procedure.
Le principe d’incertitude se situe au cœur de la physique quantique. Il représente l’une des différences majeures entre des systèmes classiques et quantiques, soit qu’il est impossible de définir un état quantique pour lequel deux observables qui ne commutent pas auraient des valeurs spécifiées simultanément et avec une précision infinie. La formulation originale du principe d’incertitude est due à Heisenberg et est exprimée en termes des variances de deux variables canoniquement conjuguées, telles que la position x et l’impulsion p. Cela fut par la suite généralisé par Schrödinger et Robertson qui ont donné au principe d’incertitude une forme invariante sous transformations symplectiques. Si l’incertitude est mesurée à l’aide de l’entropie différentielle de Shannon plutôt que des variances, il est alors possible de définir d’autres types de relations d’incertitude. Originellement introduites par Białynicki-Birula et Mycielski, elles expriment également l’incompatibilité entre deux variables canoniquement conjuguées. Dans cette thèse, nous proposons différentes améliorations de ces relations d’incertitude entropiques et mettons particulièrement l’accent sur le fait qu’elles s’expriment mieux sous forme de puissances entropiques, une notion empruntée à la théorie de l’information. En premier lieu, nous introduisons une nouvelle relation d’incertitude entropique qui tient compte des corrélations x-p et qui est par conséquent saturée par tous les états purs Gaussiens, ce qui représente une amélioration par rapport à la formulation originale de Białynicki- Birula et Mycielski. En second lieu, nous dérivons une relation d’incertitude entropique valide pour tous les n-uplets de variables non nécessairement canoniquement conjuguées et basée sur la matrice de leurs commutateurs. Nous définissons ensuite une forme plus générale du principe d’incertitude entropique qui combine les deux résultats précédents. Il exprime l’incompatibilité entre deux n-uplets arbitraires de variables et est saturé par tous les états purs Gaussiens. Notons que de ce principe d’incertitude entropique, nous pouvons déduire la forme la plus générale de la relation d’incertitude de Robertson, basée sur la matrice de covariance de n variables. Les résultats précédents soulignent un des points essentiels de notre axe de recherche: définir une relation d’incertitude entropique intrinsèquement invariante sous trans- formations symplectiques. Afin d’atteindre cet objectif, notre première tentative est de conjecturer une relation d’incertitude — invariante sous transformations symplectiques — basée sur l’entropie différentielle jointe de la fonction de Wigner. Cette conjecture n’est cependant légitime que pour des états décrits par une fonction de Wigner non-négative. Nous proposons aussi une extension complexe de cette en- tropie dite entropie de Wigner, qui pourrait ouvrir la voie vers une extension (et une preuve) de la conjecture proposée ci-dessus qui serait alors valide pour tous les états quantiques. Comme seconde tentative, en exploitant une connexion avec l’algèbre des moments angulaires, nous introduisons la notion d’observables d’incertitude agissant sur plusieurs copies d’un état. Exprimer la positivité de la variance de notre observable coïncide avec la relation d’incertitude de Schrödinger-Robertson, ce qui suggère que l’entropie discrète de Shannon d’une telle observable fournit une nouvelle mesure de l’incertitude. Cette relation d’incertitude est invariante sous transformations symplectiques.Les critères de séparabilité actuellement disponibles pour les variables continues donnent une condition nécessaire et suffisante afin qu’un état Gaussien bimodal soit séparable, mais laissent de nombreux états intriqués non-Gaussiens non détectés. Dans cette thèse, nous introduisons deux nouveaux critères de séparabilité qui permettent une meilleure détection de l’intrication. La première nouvelle condition est basée sur la connaissance d’un paramètre supplémentaire, à savoir le degré de Gaussianité de l’état, et exploite une connexion avec les relations d’incertitude de Mandilara et Cerf bornées par ce degré de Gaussianité. En particulier, nous donnons l’exemple de familles d’états intriqués non Gaussiens dont l’intrication est détectée par notre critère, mais pas par celui de Duan-Simon. Le second critère de séparabil- ité entropique que nous proposons est basé sur notre nouvelle relation d’incertitude entropique qui tient compte des corrélations x-p. Son principal avantage par rapport au critère de Walborn et al. est de ne nécessiter aucune procédure d’optimisation.
Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished

High-entropy alloys (HEAs) represent a special group of solid solutions containing five or more principal elements. The new design strategy has attracted extensive attention from the materials science community. The design and development of HEAs with desired properties have become an important subject in materials science and technology. For understanding the basic properties of HEAs, here we investigate the magnetic properties, Curie temperatures, electronic structures, phase stabilities, and elastic properties of paramagnetic (PM) body-centered cubic (bcc) and face-centered cubic (fcc) AlxCrMnFeCoNi (0 ≤ x ≤ 5, in molar fraction) HEAs using the first-principles exact muffin-tin orbitals (EMTO) method in combination with the coherent potential approximation (CPA) for dealing with the chemical and magnetic disorder. Whenever possible, we compare the theoretical predictions to the available experimental data in order to verify our methodology. In addition, we make use of the previous theoretical investigations carried out on AlxCrFeCoNi HEAs to reveal and understand the role of Mn in the present HEAs. The theoretical lattice constants are found to increase with increasing x, which is in good agreement with the available experimental data. The magnetic transition temperature for the bcc structure strongly decreases with x, whereas that for the fcc structure shows a weak composition dependence. Within their own stability fields, both structures are predicted to be PM at ambient conditions. Upon Al addition, the crystal structure changes from fcc to bcc with a broad two-phase field region, in line with the observations. Bain path calculations suggest that within the duplex region both phases are dynamically stable. Comparison with available experimental data demonstrates that the employed approach describes accurately the elastic moduli of the present HEAs. The elastic parameters exhibit complex composition dependences, although the predicted lattice constants increase monotonously with Al addition. The elastic anisotropy is unusually high for both phases. The brittle/ductile transitions formulated in terms of Cauchy pressure and Pugh ratio become consistent only when the strong elastic anisotropy is accounted for. The negative Cauchy pressure of CrMnFeCoNi is found to be due to the relatively low bulk modulus and C12 elastic constant, which in turn are consistent with the relatively low cohesive energy. Our findings in combination with the experimental data suggest anomalous metallic character for the present HEAs system. The work and results presented in this thesis give a good background to go further and study the plasticity of AlxCrMnFeCoNi type of HEAs as a function of chemistry and temperature. This is a very challenging task and only a very careful pre-study concerning the phase stability, magnetism and elasticity can provide enough information to turn my plan regarding ab initio description of the thermo-plastic deformation mechanisms in AlxCrMnFeCoNi HEAs into a successful research.

Criticality calculations are often performed in MCNP5 using the Shannon entropy as an indicator of source convergence for the given neutron transport problem. The Shannon entropy is a concept that comes from information theory. The Shannon entropy is calculated for each batch in MCNP5, and it has been shown that the Shannon entropy tends to converge to a single value as the source distribution converges. MCNP5 has its own criteria for when the Shannon entropy has converged and recommends a number for how many batches should be skipped; however, this value for how many batches should be skipped is often not very accurate and has room for improvement. This work will investigate an approach for using the Shannon entropy source distribution convergence information obtained in a shorter simulation to predict the required number of generations skipped in the reference case with desired statistical precision. In several test cases, it has been found that running a lesser number of particles per batch produces a similar Shannon entropy graph when compared to running more particles per batch. Then, by appropriate adjustment through a synthetic model, one is able to determine when the Shannon entropy will converge by running fewer particles, finding the point where it converges and then using this value to determine how many batches one should skip for a given problem. This reduces computational time and any "guessing" involved when deciding how many batches to skip. Thus, the purpose of this research is to develop a model showing how one can use this concept and produce a streamlined approach for applying this concept to a criticality problem.

Aquest treball està enmarcat en el context de gràfics per computador partint de la intersecció de tres camps: rendering, teoria de la informació, i complexitat.

Inicialment, el concepte de complexitat d'una escena es analitzat considerant tres perspectives des d'un punt de vista de la visibilitat geomètrica: complexitat en un punt interior, complexitat d'una animació, i complexitat d'una regió. L'enfoc principal d'aquesta tesi és l'exploració i desenvolupament de nous criteris de refinament pel problema de la il·luminació global. Mesures de la teoria de la informació basades en la entropia de Shannon i en la entropia generalitzada de Harvda-Charvát-Tsallis, conjuntament amb les f-divergències, són analitzades com a nuclis del refinement. Mostrem com ens aporten una rica varietat d'eficients i altament discriminatòries mesures que són aplicables al rendering en els seus enfocs de pixel-driven (ray-tracing) i object-space (radiositat jeràrquica).

Primerament, basat en la entropia de Shannon, es defineixen un conjunt de mesures de qualitat i contrast del pixel. S'apliquen al supersampling en ray-tracing com a criteris de refinement, obtenint un algorisme nou de sampleig adaptatiu basat en entropia, amb un alt rati de qualitat versus cost. En segon lloc, basat en la entropia generalitzada de Harvda-Charvát-Tsallis, i en la informació mutua generalitzada, es defineixen tres nous criteris de refinament per la radiositat jeràrquica. En correspondencia amb tres enfocs clàssics, es presenten els oracles basats en la informació transportada, el suavitzat de la informació, i la informació mutua, amb resultats molt significatius per aquest darrer. Finalment, tres membres de la familia de les f-divergències de Csiszár's (divergències de Kullback-Leibler, chi-square, and Hellinger) son analitzats com a criteris de refinament mostrant bons resultats tant pel ray-tracing com per la radiositat jeràrquica.
This work is framed within the context of computer graphics starting out from the intersection of three fields: rendering, information theory, and complexity.

Initially, the concept of scene complexity is analysed considering three perspectives from a geometric visibility point of view: complexity at an interior point, complexity of an animation, and complexity of a region. The main focus of this dissertation is the exploration and development of new refinement criteria for the global illumination problem. Information-theoretic measures based on Shannon entropy and Harvda-Charvát-Tsallis generalised entropy, together with f-divergences, are analysed as kernels of refinement. We show how they give us a rich variety of efficient and highly discriminative measures which are applicable to rendering in its pixel-driven (ray-tracing) and object-space (hierarchical radiosity) approaches.

Firstly, based on Shannon entropy, a set of pixel quality and pixel contrast measures are defined. They are applied to supersampling in ray-tracing as refinement criteria, obtaining a new entropy-based adaptive sampling algorithm with a high rate quality versus cost. Secondly, based on Harvda-Charvát-Tsallis generalised entropy, and generalised mutual information, three new refinement criteria are defined for hierarchical radiosity. In correspondence with three classic approaches, oracles based on transported information, information smoothness, and mutual information are presented, with very significant results for the latter. And finally, three members of the family of Csiszár's f-divergences (Kullback-Leibler, chi-square, and Hellinger divergences) are analysed as refinement criteria showing good results for both ray-tracing and hierarchical radiosity.

Measurement of visual quality is crucial for various image and video processing applications.

The goal of objective image quality assessment is to introduce a computational quality metric that can predict image or video quality. Many methods have been proposed in the past decades. Traditionally, measurements convert the spatial data into some other feature domains, such as the Fourier domain, and detect the similarity, such as mean square distance or Minkowsky distance, between the test data and the reference or perfect data, however only limited success has been achieved. None of the complicated metrics show any great advantage over other existing metrics.

The common idea shared among many proposed objective quality metrics is that human visual error sensitivities vary in different spatial and temporal frequency and directional channels. In this thesis, image quality assessment is approached by proposing a novel framework to compute the lost information in each channel not the similarities as used in previous methods. Based on natural scene statistics and several image models, an information theoretic framework is designed to compute the perceptual information contained in images and evaluate image quality in the form of entropy.

The thesis is organized as follows. Chapter I give a general introduction about previous work in this research area and a brief description of the human visual system. In Chapter II statistical models for natural scenes are reviewed. Chapter III proposes the core ideas about the computation of the perceptual information contained in the images. In Chapter IV, information theoretic criteria for image quality assessment are defined. Chapter V presents the simulation results in detail. In the last chapter, future direction and improvements of this research are discussed.

In questo eleborato viene presentato uno studio focalizzato sull’ottimizzazione della geometria dei microcanali di un dissipatore di calore, con lo scopo di fornire una serie di relazioni operative e quindi direttamente utilizzabili per la progettazione di tali dispositivi. Alla definizione delle tradizionali funzioni obiettivo, legate ai Performance Evaluation Criteria (PEC), è stata aggiunta un’analisi dal punto di vista del secondo principio della termodinamica, per valutare l’entropia generata da un flusso fluido in un canale. Normalizzando l’entropia generata si è passati all’utilizzo di un numero di generazione entropica adimensionale e quindi più adatto alla valutazione delle prestazioni. Dopo una prima fase di analisi dal punto di vista fisico, il modello è stato applicato a casi concreti, in cui funzione obiettivo e numero di generazione entropica sono stati espressi in dipendenza dell’incognita geometrica da valutare. Inoltre, è stato approfondito anche il caso in cui non siano trascurabili gli effetti di dissipazione viscosa, che possono effettivamente incidere in modo determinante sullo scambio termico, soprattutto alle microscale.

Due to their great importance, both from the fundamental and from the practical points of view, it is imperative that the various facets of the concepts of information and entanglement are explored systematically in connection with diverse physical systems and processes. These concepts are at the core of the emerging field of the Physics of Information. In this Thesis I investigate some aspects of the dynamics of information in both classical and quantum mechanical systems and then move on to explore entanglement in fermion systems by searching for novel ways to classify and quantify entanglement in fermionic systems. In Chapter 1 a brief review of the different information and entropic measures as well as of the main evolution equations of classical dynamical and quantum mechanical systems is given. The conservation of information as a fundamental principle both at the classical and quantum levels, and the implications of Landauer's theorem are discussed in brief. An alternative and more intuitive proof of the no-broadcasting theorem is also provided. Chapter 2 is a background chapter on quantum entanglement, where the differences between the concept of entanglement in systems consisting of distinguishable subsystems and the corresponding concept in systems of identical fermions are emphasized. Different measures of entanglement and relevant techniques such as majorization, are introduced. To illustrate some of the concepts reviewed here I discuss the entanglement properties of an exactly soluble many-body model which was studied in paper (E) of the publication list corresponding to the present Thesis. An alternative approach to the characterization of quantum correlations, based on perturbations under local measurements, is also briefly reviewed. The use of uncertainty relations as entanglement indicators in composite systems having distinguishable subsystems is then examined in some detail. Chapter 3 is based on papers (A) and (B) of the list of publications. Extended Landauer-like principles are developed, based amongst others on the conservation of information of divergenceless dynamical systems. Conservation of information within the framework of general probabilistic theories, which include the classical and quantum mechanical probabilities as particular instances, is explored. Furthermore, Zurek's information transfer theorem and the no-deleting theorem are generalized. Chapter 4 is based on articles (C) and (D) mentioned in the publication list, and investigates several separability criteria for fermions. Criteria for the detection of entanglement are developed based either on the violation of appropriate uncertainty relations or on inequalities involving entropic measures. Chapter 5 introduces an approach for the characterization of quantum correlations (going beyond entanglement) in fermion systems based upon the state disturbances generated by the measurement of local observables. Chapter 6 summarizes the conclusions drawn in the previous chapters. The work leading up to this Thesis has resulted in five publications in peer reviewed science research journals.
Thesis (PhD)--University of Pretoria, 2012.
Physics
unrestricted

In recent years the greater emphasis is placed on the renewable energy sources that are environmentally friendly. Demand for renewable energy sources is supported by government incentives, which leads to an increasing pace of investment in this sector. Prices for electricity from renewable energies are far higher than the prices of conventional electricity. If the current trend continues, it is only a matter of time before they meet. According to this fact, PRE Company decided to invest in hydropower. This thesis deals with identifying of potential investment opportunities in small hydropower plants from the PRE point of view and the subsequent evaluation of these variants on the basis of multi-criteria decision making.

Cette thèse traite de l'optimisation de modèles markoviens dédiés à la reconnaissance de textes manuscrits, dans le cas particulier d'une application à vocabulaire réduit : la lecture des montants littéraux de chèques. Le premier chapitre décrit brièvement les techniques utilisées pour la reconnaissance de l'écrit. Nous présentons également les descriptions des mots que nous avons utilisées. Le second chapitre présente les modèles de Markov cache. Nous présentons notamment les différents niveaux de représentation du problème de la lecture de l'écrit dans le cas de modélisations markoviennes : les niveaux phrase, mot et lettre. Finalement, nous présentons les algorithmes couramment utilisés pour exploiter des modèles de Markov : les algorithmes de Viterbi et de Baum-welch, avec des variantes que nous avons adaptées à nos besoins. Dans le troisième chapitre, nous traitons du problème d'une optimisation des descriptions des mots. Nous donnons trois méthodes de représentation des mots. Nous présentons ensuite une méthode de recherche de l'ordre optimal d'un processus de Markov basée sur la minimisation de critères d'information de type Akaike soit AIC, BIC etc. Finalement, nous comparons les résultats des trois alphabets pour les ordres de 1 à 3. Ceci nous permet de valider le choix de la description des mots et de l'ordre du modèle de Markov correspondant. Nous réutilisons ces résultats au chapitre 4. Dans ce chapitre, trois approches sont proposées pour la reconnaissance des mots : la première est une approche globale qui par définition ne s'attache pas à l'identification des lettres, la seconde est une approche analytique basée sur une modélisation complètement explicitée, la troisième méthode est une approche pseudo-analytique intermédiaire entre les deux approches précédentes. Elle modélise le mot de manière analytique en utilisant des modèles globaux de lettres. Finalement, les résultats de ces trois méthodes sont ensuite fusionnés : chapitre 5. Ce chapitre traite de l'identification des montants littéraux de chèques. La stratégie développée se décompose en trois parties : validation de la segmentation des mots, identification des mots et reconstitution de la phrase. A chaque partie correspond une modélisation markovienne adaptée.

Network and system management has always been of concern for telecommunication and computer system operators. The need for standardization was recognised already 20 years ago, hence several standards for network management exist today. However, the ever-increasing number of units connected to networks and the ever-increasing number of services being provided results in significant increased complexity of average network environments. This challenges current management systems. In addition to the general increase in complexity the trend among network owners and operators of merging several single service networks into larger, heterogeneous and complex full service networks challenges current management systems even further. The full service networks will require management systems more powerful than what is possible to realize basing systems purely on todays management standards. This thesis presents a distributed stochastic optimization algorithm which enables implementations of highly robust and efficient management tools. These tools may be integrated into management systems and potentially make the systems more powerful and better prepared for management of full service networks.

Emergent behavior is common in nature and easily observable in colonies of social insects and animals. Even an old oak tree can be viewed as an emergent system with its collection of interacting cells. Characteristic for any emergent system is how the overall behavior of the system emerge from many relatively simple, restricted behaviors interacting, e.g. a thousand ants building a trail, a flock of birds flying south or millions of cells making a tree grow. No centralized control exist, i.e. no single unit is in charge making global decisions. Despite distributed control, high work redundancy and stochastic behavior components, emergent systems tend to be very efficient problem solvers. In fact emergent systems tend to be both efficient, adaptive and robust which are three properties indeed desirable for a network management system. The algorithm presented in this thesis relates to a class of emergent behavior based systems known as swarm intelligence systems, i.e. the algorithm is potentially efficient, adaptive and robust.

On the contrary to other related swarm intelligence algorithms, the algorithm presented has a thorough formal foundation. This enables a better understanding of the algorithm’s potentials and limitations, and hence enables better adaptation of the algorithm to new problem areas without loss of efficiency, adaptability or robustness. The formal foundations are based on work by Reuven Rubinstein on cross entropy driven optimization. The transition from Ruinstein’s centralized and synchronous algorithm to a distributed and asynchronous algorithm is described, and the distributed algorithm’s ability to solve complex problems (NP-complete) efficiently is demonstrated.

Four examples of how the distributed algorithm may be applied in a network management context are presented. A system for finding near optimal patterns of primary/backup paths together with a system for finding cyclic protection paths in mesh networks demonstrate the algorithm’s ability to act as a tool helping management system to ensure quality of service. The algorithm’s potential as a management policy implementation mechanism is also demonstrated. The algorithm’s adaptability is shown to enable resolution of policy conflicts in a soft manner causing as little loss as possible. Finally, the algorithm’s ability to find near optimal paths (i.e. sequences) of resources in networks of large scale is demonstrated.

Le présent travail traite l’optimisation des paramètres des amortisseurs à masses accordées (AMA) accrochés sur des structures, linéaires. Les AMAs sont des dispositifs de contrôle passif utilisés pour atténuer les vibrations induites par des chargements dynamiques (en particulier stochastiques) appliqués sur des structures. L’efficacité de tels dispositifs est étroitement liée aux caractéristiques dynamiques qu’on doit imposer à ces systèmes. Dans ce cadre, plusieurs stratégies d’optimisation peuvent être utilisées dans des contextes déterministes et non déterministes, où les paramètres de la structure à contrôler sont incertains. Parmi les différentes approches qu’on peut trouver dans la littérature, l’optimisation structurale stochastique (OSS) et l’optimisation basée sur la fiabilité (OBF) étaient particulièrement traitées dans le présent travail.Dans la première partie de ce travail, en plus de la nature stochastique des chargements extérieurs appliqués à la structure linéaire à contrôler, la présence de paramètres structuraux de type incertains mais bornés (IMB) est prise en considération et les bornes optimales des paramètres AMA ont été calculées. Le calcul de ces bornes a été fait en utilisant une technique basée sur un développement de Taylor suivi d’une extension aux intervalles. La technique, permettant l’obtention d’une approximation des bornes optimales, a été appliquée dans les cas d’un système à un degré de liberté (1DDL) et un autre à plusieurs degrés de libertés (nDDL). Les résultats obtenus ont montrés que la technique utilisée était bien adaptée pour la stratégie OSS et elle l’est moins pour l’approche OBF.Comme suite logique aux résultats de la première partie, la seconde partie de la présente dissertation est consacrée à la présentation de deux méthodes permettant l’obtention des bornes exactes et des bornes approximées des paramètres optimaux de l’AMA et ce, en présence de paramètres structuraux de type IMB. La première méthode est celle de la boucle d’optimisation continue imbriquée, la seconde est celle des extensions aux intervalles basées sur la monotonie. Les méthodes présentées, qui ont été appliquées avec l’approche OBF, sont valables pour n’importe quel problème d’optimisation faisant intervenir des paramètres de type IMB. Mis à part le calcul de bornes optimisées du dispositif AMA, la question de la robustesse, vis-à-vis des incertitudes structurales, a été également traitée et il a été prouvé que la solution optimale correspondante au contexte déterministe était la plus robuste.L’introduction d’une nouvelle stratégie OBF des paramètres AMA a fait l’objet de la troisième partie de cette dissertation. En effet, un problème OBF est toujours relié à un mode de défaillance caractérisé par le franchissement d’une certaine réponse, de la structure à contrôler, d’un certain seuil limite pendant une certaine durée de temps. Le nouveau mode de défaillance, correspondant à la nouvelle stratégie OBF, consiste à considérer qu’une défaillance ait lieu lorsque la puissance dissipée au niveau de la structure à contrôler, pendant une période de temps, excède une certaine valeur. Faisant intervenir l’approche par franchissement ainsi que la formule de Rice, la nouvelle stratégie a été appliquée dans le cas d’un système 1DDL et l’expression exacte de la probabilité de défaillance est calculée. En se basant sur une approximation mettant en œuvre la technique du minimum d’entropie croisé, la nouvelle stratégie a été, également, appliquée dans le cas d’un système à nDDL et les résultats obtenus ont montrés la supériorité de cette stratégie par rapports à deux autres tirées de la bibliographie
The present work deals with the parameters optimization of tuned mass dampers (TMD) used in the control of vibrating linear structures under stochastic loadings. The performance of the TMD device is deeply affected by its parameters that should be carefully chosen. In this context, several optimization strategies can be found in the literature and among them the stochastic structural optimization (SSO) and the reliability based optimization (RBO) are particularly addressed in this dissertation.The first part of this work in dedicated to the calculation of the optimal bounds solutions of the TMD parameters in presence of uncertain but bounded (UBB) structural parameters. The bounds of the optimal TMD parameters are obtained using an approximation technique based on Taylor expansion followed by interval extension. The numerical investigations applied with one degree of freedom (1DOF) and with multi-degree of freedom (multi-DOF) systems showed that the studied technique is suitable for the SSO strategy and that it’s less appropriate for the RBO strategy.As immediate consequence of the obtained results in the first part of this work, in the second part a method, called the continuous-optimization nested loop method (CONLM), providing the exact range of the optimal TMD parameters is presented and validated. The numerical studies demonstrated that the CONLM is time consuming and to overcome this disadvantage, a second method is also presented. The second method is called the monotonicity based extension method (MBEM) with box splitting. Both methods have been applied in the context of the RBO strategy with 1DOF and multi-DOF systems. The issue of effectiveness and robustness of the presented optimum bounds of the TMD parameters is also addressed and it has been demonstrated that the optimum solution corresponding to the deterministic context (deterministic structural parameters) provide good effectiveness and robustness.Another aspect of RBO approach is dealt in the third part of the present work. Indeed, a new RBO strategy of TMD parameters based on energetic criterion is presented and validated. The new RBO approach is linked to a new failure mode characterized by the exceedance of the power dissipated into the controlled structure over a certain threshold during some interval time. Based on the outcrossing approach and the Rice’s formula, the new strategy is firstly applied to 1DOF system and exact expression of the failure probability is calculated. After that, a multi-DOF system is considered and the minimum cross entropy method has been used providing an approximation to the failure probability and then the optimization is carried out. The numerical investigations showed the superiority of the presented strategy when compared with other from the literature

碩士
國立臺灣大學
電信工程學研究所
106
Target identification has drawn lots of attentions in remote sensing and radar applications. Among various algorithms, the polarimetric entropy is a powerful means to discriminate between different targets. This thesis begins with a brief review of the statistical entropy, the polarimetric radar and scattering matrix, and the formulation of polarimetric entropy and its physical interpretation. Then, the formulas are discussed qualitatively, and based on the discussion, a criterion for radar antenna design is proposed to enhance the target-identifying efficacy. Next, an exemplary scenario is considered, in which the radar antenna is designed following the proposed criterion. After performing full-wave scattering simulations on the scenario, the polarimetric entropies can readily be calculated, and the results outperform those in the conventional paradigm. Additionally, an experiment in anechoic chamber is designed and performed to demonstrate the feasibility and performance of this algorithm in realistic environment. Besides, some invariance properties of polarimetric radar are also introduced to be used in conjunction with polarimetric entropy to enlighten prospective works in the field of radar target identification. To this end, the support vector machine (SVM), well known in machine learning, is adopted. Preliminary simulations are conducted to demonstrate the effectiveness of the concept. Finally, a brief conclusion of this work and some potential future works are given at the end of this thesis. We hope that they can inspire those who are interested in radar target identification.

碩士
國立中山大學
通訊工程研究所
99
This thesis considers the use of the tone reservation (TR) technique in orthogonal frequency division multiplexing (OFDM) systems. The nonlinear distortion is usually introduces by the high power amplifiers (HPA) used in wireless communications systems. It orders to reduce the inter-modulation distortion (IMD) in OFDM systems. In addition to the original peak-to-average power ratio (PAPR)-reduction criterion, we propose signal-to-distortion plus noise power ratio (SDNR) criterion and distortion power plus inverse of signal power (DIS) criterion. Based on these criteria, the cross-entropy (CE) algorithm is introduced to determine desired values of the peak reduction carriers (PRCs) to improve the bit error rate (BER) of nonlinearly distorted. Computational complexity is always the major concern of PAPR technique. Therefore, the real-valued PRCs and the modified transform decomposition (MTD) method are introduced here to dramatically decrease complexity of inverse fast Fourier transform (IFFT) operation with slightly performance loss. The simulation results show that the proposed criteria provide a better BER performance and a lower computational complexity.

L’obiettivo del presente studio è quello di sviluppare un approccio in grado di integrare, per il contesto progettuale relativo all’uso delle aree urbane da riservare o già adibite a parcheggi, le innumerevoli opportunità offerte nel campo della progettazione, con il ricorso alle pratiche scientifiche dal punto di vista degli economisti dei trasporti e della mobilità. Il risultato atteso dall’analisi è lo sviluppo di un nuovo modello econometrico, come utile supporto per il decisore dei progetti, che tenga conto e analizzi che cosa determina la domanda di trasporto in un contesto di sostenibilità e stimi dei parametri relativi agli attributi qualitativi del servizio (per esempio: il valore del tempo, la teoria dei bisogni , gli obiettivi, le strategie, le azioni) rispetto al consumo del territorio, per diverse tipologie di utenti dei parcheggi urbani. Una puntuale analisi della domanda diventa, perciò, lo strumento di un’attenta programmazione e pianificazione dell’attività economica di qualsiasi nuova iniziativa “imprenditoriale” pubblica. In tal senso, ogni piano economico che contempli l’analisi della domanda, può essere definito come l’anello di congiunzione tra la “strategia” e la “gestione operativa” ossia, in altri termini, lo strumento, o in un’accezione molto più restrittiva lo studio, che consenta e assicuri un’affidabile formalizzazione degli indirizzi strategici dell’attività economica e l’indirizzo, per la verifica dei risultati della gestione operativa, attraverso il controllo di gestione . Abbiamo anche dimostrato, metodologicamente e con mera enfatizzazione, come si possa costruire un modello logit multidimensionale entropizzato e ottimizzato, in grado di prevedere, con maggiore precisione, nelle fasi minimum minimorum, maximum maximorum e best estimate, le produttività tecniche e le redditività delle infrastrutture di sosta.
The objective of this study, is to develop an approach of integrating, for the design context on the use of urban areas to be reserved or already used for parking, the countless opportunities in the field of planning, with the use of scientific practices from the point of view of transport and mobility economists. The expected result of the analysis, is to develop a new econometric model, as a useful support for the decision maker of the projects, taking into account and analyze what determines the demand for transportation in a context of sustainability and esteem of the parameters relating to the quality attributes of service (for example: the value of time, the theory of needs, goals, strategies, actions) with respect to the use of land for different types of users of urban parks. A detailed analysis of the question becomes, therefore, the instrument for careful planning and economic planning of any new public "entrepreneurial" initiative. In this sense, any economic plan, which addresses the demand analysis, can be defined as the link between the "strategy" and "operating" or, in other words, the instrument, or in a sense very more restrictive the study, which allows reliable and ensure formalization of strategic economic activity and address, for verification of results from operations, through the control of management.

Yes
In this paper, a novel control algorithm is presented to enhance the performance of the tracking property for a class of nonlinear and dynamic stochastic systems subjected to non-Gaussian noises. Although the existing standard PI controller can be used to obtain the basic tracking of the systems, the desired tracking performance of the stochastic systems is difficult to achieve due to the random noises. To improve the tracking performance, an enhanced performance loop is constructed using the EKF-based state estimates without changing the existing closed loop with a PI controller. Meanwhile, the gain of the enhanced performance loop can be obtained based upon the entropy optimization of the tracking error. In addition, the stability of the closed loop system is analyzed in the mean-square sense. The simulation results are given to illustrate the effectiveness of the proposed control algorithm.
This work was supported in part by the PNNL Control of Complex Systems Initiative and in part by the National Natural Science Foundation of China under Grants 61621004,61573022 and 61333007.

碩士
朝陽科技大學
資訊管理系碩士班
99
Generally speaking, we have to consider the effect of many factors when making a decision. The recommended system can help user to analyze needs and give suggestions with complex information. Our research focuses on the assistance of medical suggestion for doctors. According to the statistics of Department of Health, diabetes was one of the top ten causes of death in Taiwan in 2009. Therefore, developing an effective treatment for diabetes is very important. The fact is that the amount of diabetes specialists is not enough and not all diabetic patients can be treated by specialists. We present this recommender system to help treatment. The purpose is to develop a recommender system to assist the general practitioner (GP) to make more appropriate decision in selecting anti-diabetic medicines. First, we built up the ontology of diabetic knowledge, and then multiples criteria decision making method (MCDM) was applied to compute for medication. Entropy was used to compute data of patients’ profile. With medicine knowledge ontology, the results of calculation will list appropriate medications. Finally, the system will show the preference of medications to doctors.

博士
中原大學
應用數學研究所
107
Distance, similarity and entropy play an indispensable role in almost every field of our daily life settings. Distance and similarity measures are widely used to differentiate between two sets or objects. While entropy measures the fuzziness in a fuzzy set. Different distance and similarity measures have been proposed for hesitant fuzzy sets (HFSs) in the literature, but either they are in sufficient or not reflect desirable results. In this manuscript, the construction of new distance and similarity measures between HFSs based on Hausdorff metric is proposed. We first present a novel and simple method for calculating a distance between HFSs based on Hasudorff metric in a suitable and intuitive way. Two main features of the proposed approach are: (1) not necessary to add a minimum value, a maximum value or any value to the shorter one of hesitant fuzzy elements (HFEs) for extending it to the larger one of HFEs; and (2) no need to arrange HFEs either in ascending or descending order. This is because adding such values and arrangements of elements will not put any impact on final results. We then extend distance to similarity measure between HFSs. Next, measuring uncertainty for an HFS is computed by an amount of distinction between an HFS and its complement. Hausdorff metric is used to calculate a distance between an HFS and its complement which assists us to construct novel entropy of HFSs. An axiomatic definition of entropy measure for HFSs is also given in this dissertation. The proposed entropy is proved to satisfy all axioms. Furthermore, more generalizations of the proposed entropy allow us to onstruct different entropy measures of HFSs which reflect that the closer of an HFS to its complement shows less distinction between them and produces the larger entropy measure of the HFS, and also the more distinction between them gives smaller amount of uncertainty. Furthermore, we claim some properties and also several examples are presented to compare our proposed distance, similarity and entropy measures with existing methods. We apply the proposed distance of HFSs to multi-criteria decision making and the similarity measure of HFSs to clustering. The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method is used to construct hesitant fuzzy (TOPSIS) based on the proposed entropy measure to solve multicriteria decision making problems. Finally, expository examples are utilized to manifest simplicity, practicability and effectiveness of our proposed distance, similarity and entropies as compared to existing methods. The comparison results demonstrate that the proposed distance, similarity and entropy measures are much simpler, intuitive and better than most existing methods.

Die vorliegende Arbeit befasst sich mit einer Vermutung von Sarnak aus dem Jahre 2010 über die Orthogonalität von durch deterministische dynamische Systeme induzierte Folgen zur Möbiusschen μ-Funktion. Ihre Hauptresultate sind zum einen der Ergodensatz mit Möbiusgewichten, welcher eine maßtheoretische (schwächere) Version von Sarnaks Vermutung darstellt, und zum anderen die bereits gesicherte Gültigkeit der genannten Vermutung in Spezialfällen, wobei hier exemplarisch unter anderem der Thue–Morse Shift und Schiefprodukterweiterungen von rationalen Rotationen auf dem Kreis gewählt worden sind. Zum Zwecke der Motivation zeigen wir, dass eine gewisse Wachstumsabschätzung für die Mertensfunktion äquivalent ist zum Primzahlsatz und skizzieren ein Resultat, welches die Äquivalenz einer weiteren solchen Abschätzung zur Riemannschen Vermutung liefert, um auf diese Weise die Bedeutung der Möbiusfunktion für die Zahlentheorie herauszustellen. Da sie für das Verständnis von Sarnaks Vermutung unerlässlich ist, geben wir eine Einführung in die Theorie der Entropie dynamischer Systeme auf Grundlage der Definitionen von Adler–Konheim–McAndrew, Bowen–Dinaburg und Kolmogorov–Sinai. Ferner berechnen wir die topologische Entropie des Thue–Morse Shifts und von Schiefprodukterweiterungen von Rotatione auf dem Kreis. Wir studieren die ergodische Zerlegung T-invarianter Maße auf kompakten metrischen Räumen mit stetiger Transformation T, welche wir für den Beweis des Ergodensatzes mit Möbiusgewichten benötigen. Sodann beweisen wir den genannten gewichteten Ergodensatz. Wir geben eine hinreichende Bedingung an für das Erfülltsein von Sarnaks Vermutung in einem gegebenen dynamischen System, welche im anschließenden Kapitel Anwendung findet. So wird nachgewiesen, dass Sarnaks Vermutung im Falle des Thue–Morse Shifts und von Schiefprodukterweiterungen von rationalen Rotationen auf dem Kreis erfüllt ist. Abschließend wird gezeigt, dass Sarnaks Vermutung sich als Konsequenz aus einer Vermutung von Chowla ergibt.
The thesis in hand deals with a conjecture of Sarnak from 2010 about the orthogonality of sequences induced by deterministic dynamical systems to the Möbius μ-function. Its main results are the ergodic theorem with Möbius weights, which is a measure theoretic (weaker) version of Sarnak’s conjecture, and the already assured validity of Sarnak’s conjecture in special cases, where we have exemplarily chosen the Thue–Morse shift and skew product extensions of rational rotations on the significance of the Möbius function for number theory. Since it is essential for the understanding of Sarnak’s conjecture we give an introduction to the theory of entropy of dynamical systems based on the definitions of Adler–Konheim–McAndrew, Bowen–Dinaburg and Kolmogorov–Sinai. Furthermore, we calculate the topological entropy of the Thue–Morse shift and of skew product extensions of rotations on the circle. We study the ergodic decomposition for T-invariant measures on compact metric spaces with continuous transformations T, which we will need for the proof of the ergodic theorem with Möbius weights. Thereafter, we prove the namely weighted ergodic theorem. We give a sufficient condition for Sarnak’s conjecture to hold for a given dynamical system, which we make use of in the following chapter. Thereupon, it is varified that Sarnak’s conjecture holds for the Thue–Morse shift and for skew product extensions of rational rotations on the circle. Lastly, it is shown that Sarnak’s conjecture from one of Chowla.