Academic literature on the topic 'Wald Entropy'

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.<br>Includes bibliographical references (leaves 81-86).<br>Graphical models provide a powerful formalism for statistical signal processing. Due to their sophisticated modeling capabilities, they have found applications in a variety of fields such as computer vision, image processing, and distributed sensor networks. In this thesis we study two central signal processing problems involving Gaussian graphical models, namely modeling and estimation. The modeling problem involves learning a sparse graphical model approximation to a specified distribution. The estimation problem in turn exploits this graph structure to solve high-dimensional estimation problems very efficiently. We propose a new approach for learning a thin graphical model approximation to a specified multivariate probability distribution (e.g., the empirical distribution from sample data). The selection of sparse graph structure arises naturally in our approach through the solution of a convex optimization problem, which differentiates our procedure from standard combinatorial methods. In our approach, we seek the maximum entropy relaxation (MER) within an exponential family, which maximizes entropy subject to constraints that marginal distributions on small subsets of variables are close to the prescribed marginals in relative entropy. We also present a primal-dual interior point method that is scalable and tractable provided the level of relaxation is sufficient to obtain a thin graph. A crucial element of this algorithm is that we exploit sparsity of the Fisher information matrix in models defined on chordal graphs. The merits of this approach are investigated by recovering the graphical structure of some simple graphical models from sample data. Next, we present a general class of algorithms for estimation in Gaussian graphical models with arbitrary structure.<br>(cont.) These algorithms involve a sequence of inference problems on tractable subgraphs over subsets of variables. This framework includes parallel iterations such as Embedded Trees, serial iterations such as block Gauss-Seidel, and hybrid versions of these iterations. We also discuss a method that uses local memory at each node to overcome temporary communication failures that may arise in distributed sensor network applications. We analyze these algorithms based on the recently developed walk-sum interpretation of Gaussian inference. We describe the walks "computed" by the algorithms using walk-sum diagrams, and show that for non-stationary iterations based on a very large and flexible set of sequences of subgraphs, convergence is achieved in walk-summable models. Consequently, we are free to choose spanning trees and subsets of variables adaptively at each iteration. This leads to efficient methods for optimizing the next iteration step to achieve maximum reduction in error. Simulation results demonstrate that these non-stationary algorithms provide a significant speedup in convergence over traditional one-tree and two-tree iterations.<br>by Venkat Chandrasekaran.<br>S.M.

Thesis (M.S.)--University of Missouri-Columbia, 2005.<br>The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (January 23, 2007) Includes bibliographical references.

Ground penetrating radar (GPR) has been extensively utilized as a highly efficient and non-destructive testing method for infrastructure evaluation, such as highway rebar detection, bridge decks inspection, asphalt pavement monitoring, underground pipe leakage detection, railroad ballast assessment, etc. The focus of this dissertation is to investigate the key techniques to tackle with GPR signal processing from three perspectives: (1) Removing or suppressing the radar clutter signal; (2) Detecting the underground target or the region of interest (RoI) in the GPR image; (3) Imaging the underground target to eliminate or alleviate the feature distortion and reconstructing the shape of the target with good fidelity. In the first part of this dissertation, a low-rank and sparse representation based approach is designed to remove the clutter produced by rough ground surface reflection for impulse radar. In the second part, Hilbert Transform and 2-D Renyi entropy based statistical analysis is explored to improve RoI detection efficiency and to reduce the computational cost for more sophisticated data post-processing. In the third part, a back-projection imaging algorithm is designed for both ground-coupled and air-coupled multistatic GPR configurations. Since the refraction phenomenon at the air-ground interface is considered and the spatial offsets between the transceiver antennas are compensated in this algorithm, the data points collected by receiver antennas in time domain can be accurately mapped back to the spatial domain and the targets can be imaged in the scene space under testing. Experimental results validate that the proposed three-stage cascade signal processing methodologies can improve the performance of GPR system.

The growing importance of emerging markets in the global economy leads many multinationals (MNEs) to explore and expand into them. Saturation and slow growth in home markets, coupled with rising incomes in emerging markets, has also accelerated retail internationalisation. These markets are generally unfamiliar to the predominantly western firms, and they come with intractable social problems, where resultant stakeholder activism abounds.The purpose of this study was to investigate stakeholder management during entry of a retailer, Wal-Mart, into an emerging market, South Africa, in order to draw lessons that could be of use to other MNEs seeking to enter similar emerging markets. The method used for the study was a qualitative archival analysis that relied on publicly available sources, namely the regulatory bodies, parliament, press releases and the print media.The research found that the key stakeholders during the entry of Wal-Mart into South Africa were the government and trade unions. Government and trade unions were concerned that Wal-Mart’s entry would lead to an increase in imports and displace local producers, in turn worsening South Africa’s unemployment crisis. It was also feared that Wal-Mart would seek to change the existing labour regime in order to marginalise trade unions and lower labour standards. The research found that stakeholder management was poor and highlights the importance of integrating stakeholder management strategy into the broader entry strategy into developing markets.<br>Dissertation (MBA)--University of Pretoria, 2012.<br>Gordon Institute of Business Science (GIBS)<br>unrestricted

Con il testo presente, si intende mostrare come i gradi di libertà associati all'entropia di un buco nero possano essere ricercati in parte fruttuosamente nell'interazione dei campi quantistici con la struttura causale e geometrica esibita da un buco nero. Nel Capitolo 1, si affrontano le principali caratteristiche dei buchi neri alla luce della teoria classica di Relatività Generale: sono analizzate la soluzione di Schwarzschild e la struttura causale nello spazio-tempo conseguente, discutendo le definizioni di orizzonte e di singolarità e il rapporto che le lega, con riferimento ai risultati di Penrose e Hawking. Introdotto, all'inizio del Capitolo 2, il concetto di gravità superficiale e la metrica di Kerr-Newman, si studia il significato delle Quattro Leggi dei buchi neri, valide per soluzioni stazionarie. Il Capitolo 3 espone quali motivazioni spingano a proporre una caratterizzazione termodinamica dei buchi neri, attribuendovi una temperatura e un'entropia (detta “di Bekenstein-Hawking”) di natura geometrica, dipendente dall'area dell'orizzonte; si trattano qui i problemi che si incontrano nel costruire una corrispondente Meccanica Statistica. Si descrive dunque in quali termini il processo di radiazione di Hawking riesca a dare una spiegazione fisica della temperatura, e si rileva la presenza, secondo osservatori statici, di un'atmosfera termica nei pressi dell’orizzonte. Infine, si esamina la possibilità di attribuire alla radiazione di Hawking i gradi di libertà relativi all'entropia di Bekenstein-Hawking. In particolare, si illustra il modello a muro di mattoni di 't Hooft, che lega i gradi di libertà all'atmosfera termica. Considerando infine la deformazione dell'orizzonte dovuta a fluttuazioni quantistiche, si giunge alla conclusione che l'entropia dell'atmosfera termica rappresenta non un'interpretazione dell'entropia di Bekenstein-Hawking, bensì una sua correzione al secondo ordine.

This thesis began as an exploration of the idea of home, a study that revealed the importance of place. Seeking to understand what makes a successful place, I studied neighborhoods with which I was familiar, identifying characteristics of both the vital and the lifeless. As a foundation for architectural exploration, this study helped me to recognize the dynamic qualities of denser, more urban neighborhoods, and to establish rowhousing as the vehicle through which to undertake my exploration of urban living. While providing the genesis for the project and further defining certain elements as worthy of further study, this initial exploration was nonetheless lacking. I had to do more than just speak of the conditions I hoped to achieve and of the characteristics of the elements with which to make the conditions manifest. I had to make the conditions, make the elements. It was essential for me to establish a clear order, so that these conditions could be brought together to form a cohesive whole. I was able to arrive at a fully conceived expression of the project by structuring the conditions that I identified through the application of three dimensional grids. The interrelationships among the grids helped structure the relationships among various conditions, ensuring that they enhanced one another, and were, in fact, stronger together than separately. Working with the grids taught me that in order for them to be effective regulators the grids had to be intelligible while still being flexible; that they should help define but never dictate. It exposed the tension between the regulating devices we, as architects, utilize as tools for design and the three-dimensional material with which the designs are constructed, as well as the obligation of reconciling the two. Not only must the device accommodate the material and the material reveal the device, but indeed all facets of the design must be considered in relation to one another and to the whole. When philosopy, device, and material work in service of one another the possibility for architectural expression rather than simple building is created. One does not revere great architects solely for their philosophies of design, the functionality of the spaces they create, the materials with which they construct them, or the regulating devices they employ, but rather for the complexity with which these elements are brought together to form a whole so well designed that it seems that it could have been done no other way.<br>Master of Architecture

The key objective of this thesis is the outline of an alternative capital market modeling framework, the Volatility Asset Pricing Model, VAPM, inspired by the innovative dual approach of Mandelbrot and Hudson using the method based on synthesis of two seemingly antagonistic factors -- the volatility of market prices and their serial dependence determining the capital markets' dynamics. The pilot tests of this model in various periods using the market index as well as a portfolio of selected securities delivered generally satisfactory results. Firstly, the work delivers a brief recapitulation regarding the concepts of a consumer/investor choice under general conditions of hypothetical certainty. Secondly, this outline is then followed by a description of the "classical" methodologies in the risky environment of uncertainty, with assessment of their corresponding key models, i.e. the CAPM, SIM, MIM, APTM, etc., notwithstanding results of the related testing approaches. Thirdly, this assessment is based on evaluation of the underlying doctrine of Efficient Market Hypothesis in relation to the so called Random Walk Model. Fourthly, in this context the work also offers a brief exposure to a few selected tests of these contraversial concepts. Fifthly, the main points of conteporary approaches such as the Fractal Dimension and the Hurst Exponent in the dynamic framework of information entropy are subsequently described as the theoretical tools leading to development of the abovementioned model VAPM. The major contribution of this thesis is considered its attempt to apply the abovementioned concepts in practice, with the intention to possibly inspire a further analytical research.

thresh-old noun `thresh-`hold, `thre-`shold _the sill of a doorway _the entrance to a house or building _any place or point of entering or beginning A threshold can be understood as the visible or invisible division and demarcation of space. It is an age-old concept tracing back even to the first notions of urban space. The largest scaled gestures of thresholds are those lines and walls that divide nations and territories. All complexities of past and current geopolitical tensions simply derive from the interpretations and implementation of the walls and geopolitical lines or lineaments. It is therefore crucial to comprehend the concept of lineaments on every scale, as it is the base idea that permeates all design. It is design in its purest form. The following architectural argument will explore Leon Battista Albert's theory of lineaments, particularly the wall as an architectural element, as he spells out in his architectural treatise On the Art of Building in Ten Books. A closer look at Alberti's treatise and the idea of lineaments will help to better refine the definition and implementation of international borders and treatises. Reconsideration of a lineament in the slightest form has the potential to drastically change the execution and enforcement of a lineament in tangible materials and their assembly during construction. The chosen design proposes a new U.S.-Mexico Joint Land Port of Entry along the border of Columbus, New Mexico, United State of America, and Puerto Palomas, Chihuahua, Mexico<br>Master of Architecture

In dieser Arbeit werden verschieden Ansätze diskutiert, die zum Verständnis und zur Beschreibung anomalen Diffusionsverhaltens beitragen, wobei insbesondere zwei unterschiedliche Aspekte hervorgehoben werden. Zum einen wird das Entropieproduktions-Paradoxon beschrieben, welches bei der Analyse der Entropieproduktion bei der anomalen Diffusion, beschrieben durch fraktionale Diffusionsgleichungen auftritt. Andererseits wird ein detaillierter Vergleich zwischen Lösungen verallgemeinerter Diffusionsgleichungen mit numerischen Daten präsentiert, die durch Iteration der Mastergleichung auf verschiedenen Fraktalen produziert worden sind. Die Entropieproduktionsrate für superdiffusive Prozesse wird berechnet und zeigt einen unerwarteten Anstieg beim Übergang von dissipativer Diffusion zur reversiblen Wellenausbreitung. Dieses Entropieproduktions-Paradoxon ist die direkte Konsequenz einer anwachsenden intrinsischen Rate bei Prozessen mit zunehmendem Wellencharakter. Nach Berücksichtigung dieser Rate zeigt die Entropie den erwarteten monotonen Abfall. Diese Überlegungen werden für generalisierte Entropiedefinitionen, wie die Tsallis- und Renyi-Entropien, fortgeführt. Der zweite Aspekt bezieht sich auf die anomale Diffusion auf Fraktalen, im Besonderen auf Sierpinski-Dreiecke und -Teppiche. Die entsprechenden Mastergleichungen werden iteriert und die auf diese Weise numerisch gewonnenen Wahrscheinlichkeitsverteilungen werden mit den Lösungen vier verschiedener verallgemeinerter Diffusionsgleichungen verglichen.