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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
261

Sorção de lantanídeos em meio aquoso visando ao estudo de rejeitos nucleares

Belline, Jean de Brito January 2009 (has links)
O problema de rejeitos radioativos é uma preocupação de âmbito mundial, uma vez que não há, ainda, um local definido para a construção de um repositório para rejeitos radioativos de alto nível. Uma das etapas preliminares para a escolha do local mais apropriado é o estudo geológico associado a estudos experimentais de adsorção das espécies químicas envolvidas nos processo. Neste trabalho foi utilizado uma amostra de rocha basáltica, da região sul da Formação Serra Geral, coletada em Frederico Westphalen (RS), que servirá como candidata à rocha hospedeira para locação de rejeitos radioativos. Foram realizados dois experimentos, a saber: "Batch Test" e percolação, ambos sob pressão atmosférica, à temperatura ambiente de 25°C, com a finalidade de estudar a capacidade de sorção dos elementos terras raras - ETR. Os ETR são utilizados neste trabalho em função de sua analogia com os actinídeos, visando a investigar o comportamento geoquímico e a especiações dos mesmos em águas naturais, buscando a possibilidade de armazenamento geológico de rejeitos radioativos, uma vez que a adsorção dos ETR depende de variáveis do ambiente como pH, força iônica, temperatura e presença de ligantes, como carbonatos e constituintes de superfícies dos minerais. Foi realizado experimento de percolação dos ETR, a 100ppb, no basalto (com granulometria 80 mesh) em soluções com força iônica I= 0,025 M e I=0,5 M de NaCl. O pH foi controlado em uma faixa de 5,6 a 7,6 com adição de HNO3. As concentrações foram analisadas por ICP-MS. O "Batch Test" é uma eficiente forma de se obter isotermas de sorção/dessorção, além de valores da razão entre as distribuições sólido/solução e estimar a solubilidade. O experimento de percolação, foi realizado sob pH controlado em torno de 6, e permitiu verificar a "preferência" dos ETR pesados em relação aos ETR leves. / The problem of radioactive wastes is a concern of world-wide scope, a time that does not still have a defined local for the construction of a repository for radioactive wastes of high level. One of the preliminary stages for the choice of the place more appropriate is the geologic study associated to the experimental studies of adsorprtion of the involved chemical species in the process. In this work, a sample of basaltic rock was used, of the South Region of the Formation Serra Geral, collected in Frederico Westphalen Town (RS), that it will be probably a candidate to the rock hostess for location of radioactive wastes. Two experiments have been carried out through, namely: "Test Batch" and Percolating, both under atmospheric pressure, at the ambient temperature of 25°C, with the purpose to study the capacity of sorption of the rare earth elements - REE. The REE are used in this work in function of its analogy with the actinídes, aiming at to investigate the chemistry behavior and the speciations of the same in natural waters, searching the possibility of geologic storage of radioactive wastes, a time that the adsorption of the REE depends on variables of the environment as pH, ionic strengh, temperature and presence of ligants, as carbonates and constituent of surfaces of minerals. Experiment of percolating of the REE was carried through, 100ppb, in the basalt (with 80 mesh) in solutions with ionic strengh I= 0,025 M and I=0,5 M of NaCl. pH was controlled in a range of 5,6 the 7,6 with HNO3 addition. The concentrations were analyzed by ICP-MS. The "Batch Test" is an efficient form of studing sorption/dessorption isotherms, beyond values of the reason between the distributions solid/solution and estimation of the solubility. The percolating experiment, was carried through under pH controlled around 6, and allowed to verify the behaviour of heavy REE in comparison with the light REE.
262

"Estudo da influência do coeficiente de partição de metais no solo de Figueira, Paraná, no cálculo de risco à saúde humana, utilizando o modelo C-Soil" / STUDY OF THE INFLUENCE OF THE METAL PARTITION COEFFICIENT ON THE HUMAN HEALTH RISK EVALUATION, APPLIED TO FIGUEIRA (PR) SOIL REGION, USING C-SOIL MODEL

Iara Maria Carneiro de Camargo 11 November 2005 (has links)
Estudos de coeficiente de partição mostram que o valor de Kp do metal pode variar ordens de grandeza conforme as características físico-químicas do solo. Portanto, o Kp é um parâmetro sensível no modelo de avaliação de risco à saúde humana, e normalmente é um valor nominal adotado por agências ambientais que pode não representar adequadamente o solo em estudo e implicar erros no cálculo do risco. Este trabalho tem como objetivos: avaliar a contaminação do solo adjacente à usina termoelétrica de Figueira por metais tóxicos; determinar o Kp dos metais As, Cd, Co, Cr, Cu, Mo, Ni, Pb e Zn no solo pela razão entre a concentração do metal obtida por digestão com HNO3 concentrado e a concentração do metal obtida por extração com EDTA 0,05 mol L-1 (KpEDTA) ou Ca(NO3)2 0,1 mol L-1 (KpCa(NO3)2); e avaliar a influência do uso dos diferentes valores de Kp no modelo de avaliação de risco à saúde humana C-Soil no cálculo do risco. As principais conclusões foram: os metais contaminantes do solo de Figueira foram As, Cd, Mo, Pb e Zn, e o As foi o elemento mais crítico; tanto o valor de KpCa(NO3)2 quanto o de KpEDTA poderiam ser utilizados no cálculo do risco à saúde humana, no caso de Figueira, exceto para o Pb, mas o KpEDTA seria mais recomendado, por apresentar valores com menor dispersão; os valores nominais de KpCSoil dos metais poderiam ser utilizados para o cálculo de risco à saúde humana no caso de Figueira, ou seja, não teria necessidade de se determinar valores de Kp locais (KpEDTA e KpCa(NO3)2), exceto para o Pb. / Studies of partition coefficient show that Kp values of metals can vary orders of magnitude according to the soil physical-chemistry characteristics. Therefore, the Kp is a sensible parameter in human health risk assessment model. In general, a default value is adopted by environmental agencies and often it is not represent suitably the soil studied and can cause errors in the risk calculation. The objectives of this work are: evaluate the heavy metals soil contamination around the Figueira coal-fired power plant; determine the metal Kp of As, Cd, Co, Cr, Cu, Mo, Ni, Pb and Zn in soil by the ratio between the metal concentration obtained by concentrate HNO3 digestion and the metal concentration obtained by extraction with EDTA 0,05 mol L-1 (KpEDTA) or Ca(NO3)2 0,1 mol L-1 (KpCa(NO3)2); and evaluate the influence of the application of different Kp values in human health risk assessment C-Soil model in risk calculation. The main conclusions of the present study were: As, Cd, Mo, Pb e Zn were the Figueira soil metal contaminants, being As the pollunt of major human health concern; either KpCa(NO3)2 or KpEDTA values could be used for human health risk calculation, in Figueira case, except for Pb, and the KpEDTA values were preferably recommended due to the less dispersion of their values; the KpCSoil metals default values could be applied for the human health risk calculation in Figueira case, in other words, it would not have necessity to determine Kp values of region (KpEDTA and KpCa(NO3)2), except to Pb.
263

Modelagem do coeficiente de sorção do solo de poluentes orgânicos persistentes no meio ambiente / Modeling of soil sorption coefficient from persistent organic pollutants in the environment

Olguín, Carlos José Maria 17 February 2017 (has links)
Submitted by Edineia Teixeira (edineia.teixeira@unioeste.br) on 2017-09-04T17:30:26Z No. of bitstreams: 2 Carlos_Olguin2017.pdf: 2821259 bytes, checksum: 4f44c019ceff1c4613be9b0b525a188e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-09-04T17:30:26Z (GMT). No. of bitstreams: 2 Carlos_Olguin2017.pdf: 2821259 bytes, checksum: 4f44c019ceff1c4613be9b0b525a188e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-02-17 / The soil sorption coefficient normalized for organic carbon content (Koc) is a physicochemical parameter used in environmental risk assessments to determine the final destination of chemicals released in the environment. So, in oreder to predict this parameter, several models were proposed based on the relationship between LogKoc and LogP. The difficulty and cost to obtain experimental values of LogP have drawn to the algorithms development to calculate those values. Thus, in the first paper of this thesis, several free algorithms were considered to calculate LogP, and it was concluded that the best QSPR models to predict soil sorption coefficient of organic nonionic compounds were obtained using ALOGPs, KOWWIN and XLOGP3 algorithms. This study demonstrated the importance and usefulness of the statistical equivalence test used, since it allowed us to state that the models obtained from the considered algorithms are statistically equivalent. In this study, the both importance and usefulness of the statistical equivalence test were proved. These data allowed us to state that the models that have been obtained from the algorithms are statistically equivalent. Thus, in the impossibility of obtaining LogP values based on one of the algorithms, values obtained by another one of them can be used. It was also observed that the models presented in this study presented statistical quality and predictive capacity compatible with more complex models recently published in the area. In addition, it is a well accepted practice in the area the requirement to validate the prediction of a QSPR model from a data set that was not used in the model generation. In this context, some studies have explored the impact that several sizes of training sets would have on the predictive capacity of the generated QSPR models, consequently not reaching conclusive results. Thus, the second paper has been shown that, from not so large training sets, statistically equivalent QSPR models can be developed and that these models have similar predictive capacity to those ones created from a larger training set. Therefore, models were generated considering LogP values of the total training set, calculated with the ALOGPs algorithm and also with subsets of itself (i.e., halves, quarters and eighths). This study, just like the previous one, has confirmed the importance of using the statistical equivalence test since it was ascertained that, following the adopted procedures, the models obtained with subsets of the training set are statistically equivalent / O coeficiente de sorção do solo normalizado para o conteúdo de carbono orgânico (Koc) é um parâmetro físico-químico utilizado em avaliações de risco ambiental e na determinação do destino final das substâncias químicas lançadas na natureza. Vários modelos para prever este parâmetro foram propostos com base na relação entre LogKoc e LogP. A dificuldade e o custo para a obtenção de valores experimentais de LogP levaram ao desenvolvimento de algoritmos para calculá-los. Assim, no primeiro artigo desta tese foram considerados diversos algoritmos gratuitos para cálculo de LogP, e concluiu-se que os melhores modelos QSPR para predizer o coeficiente de sorção do solo de compostos orgânicos não iónicos foram obtidos usando os algoritmos ALOGPs, KOWWIN e XLOGP3. Neste estudo, foram demonstradas a importância e a utilidade do teste de equivalência estatística utilizado, dados que nos permitiram afirmar que os modelos obtidos dos algoritmos considerados são estatisticamente equivalentes. Assim, na impossibilidade de obterem-se valores de LogP a partir de um dos algoritmos, valores obtidos por outro podem ser usados. Verificou-se ainda que os modelos apresentados neste estudo possuem qualidade estatística e capacidade de predição compatíveis à de modelos mais complexos, publicados recentemente na área. Adicionalmente, a necessidade de se realizar a validação da predição de um modelo QSPR a partir de um conjunto de dados que não foi utilizado na geração do modelo é uma prática bem aceita na área. Nesse contexto, alguns trabalhos exploraram o impacto que diversos tamanhos de conjuntos de treinamento teriam na capacidade de predição dos modelos QSPR gerados, não chegando a resultados conclusivos. Assim, no segundo artigo desta tese, foi mostrado que, a partir de conjuntos de treinamento não tão grandes, modelos QSPR estatisticamente equivalentes podem ser desenvolvidos e que tais modelos têm capacidade de predição similar daqueles criados a partir de um conjunto de treinamento maior. Para isto, modelos foram gerados considerando valores de LogP do conjunto de treinamento total, calculados com o algoritmo ALOGPs e também com subconjuntos do mesmo (i.e., metades, quartos e oitavos). Este estudo, assim como o anterior, confirmou a importância do uso do teste de equivalência estatística utilizado nesta tese já que foi verificado que, seguindo os procedimentos adotados, os modelos obtidos com subconjuntos do conjunto de treinamento são estatisticamente equivalentes.
264

Techniques for Automatic Generation of Tests from Programs and Specifications

Edvardsson, Jon January 2006 (has links)
Software testing is complex and time consuming. One way to reduce the effort associated with testing is to generate test data automatically. This thesis is divided into three parts. In the first part a mixed-integer constraint solver developed by Gupta et. al is studied. The solver, referred to as the Unified Numerical Approach (una), is an important part of their generator and it is responsible for solving equation systems that correspond to the program path currently under test. In this thesis it is shown that, in contrast to traditional optimization methods, the una is not bounded by the size of the solved equation system. Instead, it depends on how the system is composed. That is, even for very simple systems consisting of one variable we can easily get more than a thousand iterations. It is also shown that the una is not complete, that is, it does not always find a mixed-integer solution when there is one. It is found that a better approach is to use a traditional optimization method, like the simplex method in combination with branch-and-bound and/or a cutting-plane algorithm as a constraint solver. The second part explores a specification-based approach for generating tests developed by Meudec. Tests are generated by partitioning the specification input domain into a set of subdomains using a rule-based automatic partitioning strategy. An important step of Meudec’s method is to reduce the number of generated subdomains and find a minimal partition. This thesis shows that Meudec’s minimal partition algorithm is incorrect. Furthermore, two new efficient alternative algorithms are developed. In addition, an algorithm for finding the upper and lower bound on the number of subdomains in a partition is also presented. Finally, in the third part, two different designs of automatic testing tools are studied. The first tool uses a specification as an oracle. The second tool, on the other hand, uses a reference program. The fault-detection effectiveness of the tools is evaluated using both randomly and systematically generated inputs.
265

Champs de densité d'énergie pour la vibroacoustique basse et moyenne fréquence des structures complexes utilisant un modèle numérique stochastique : application à la partition structurale des automobiles / Energy-density field for low- and medium- frequency vibroacoustics of complex structures using a stochastic numerical model : application to the structural partitioning of automotive vehicles

Kassem, Morad 10 December 2009 (has links)
Ce travail de recherche s’inscrit dans le cadre de l’analyse vibroacoustique des structures complexes. Il propose une nouvelle approche énergétique utilisant le champ de densité d’énergie afin de simplifier une telle analyse. Cette approche est basée sur un modèle numérique stochastique construit à l’aide de l’approche probabiliste non paramétrique des incertitudes de modélisation et de paramètres. L’approche énergétique stochastique développée correspond à une nouvelle représentation du système vibroacoustique en terme des grandeurs énergétiques aléatoires. Un modèle vibroacoustique énergétique moyen est alors construit en prenant la moyenne statistique des grandeurs énergétiques. On dispose alors d’un modèle énergétique moyen pour analyser la vibroacoustique des systèmes complexes dans la bande des basses et des moyennes fréquences alors que la méthode SEA ne permet pas d’analyser cette bande de fréquence. L’analyse des propriétés des grandeurs énergétiques moyennes utilisées pour la construction du modèle vibroacoustique énergétique permet de construire une version simplifiée conduisant à un modèle énergétique simplifié pour lequel une méthodologie de partition structurale par zone est établie. Une application de cette approche énergétique et de la méthodologie de partition structurale par zone est présentée pour une voiture constituée d’une structure automobile couplée avec sa cavité acoustique interne / This research lies in the domain of the vibroacoustic analysis of complex structures. It proposes a new energy approach using the energy-density field in order to simplify such an analysis. This approach is based on a stochastic computational model constructed using the nonparametric probabilistic approach of modeling and parameters uncertainties. The stochastic energy approach developed corresponds to a new representation of the vibroacoustic system in terms of random energy quantities. A mean vibroacoustic energy model is thus constructed using a statistical averaging of the random energy quantities. This mean energy model provides a tool to perform a vibroacoustic analysis of complex structures in the low and medium frequency range while the SEA is not adapted to this frequency band. The analysis of the properties of the mean energy quantities used for the construction of the vibroacoustic energy model allows the construction of a simplified model to be obtained and yields a simplified energy model for which a structural partitioning methodology is then established. An application of the energy approach ant of the structural partitioning methodology is done on an automotive vehicle structure coupled with its internal acoustic cavity
266

Non-Uniformly Partitioned Block Convolution on Graphics Processing Units

Sadreddini, Maryam January 2013 (has links)
Real time convolution has many applications among others simulating room reverberation in audio processing. Non-uniformly partitioning filters could satisfy the both desired features of having a low latency and less computational complexity for an efficient convolution. However, distributing the computation to have an uniform demand on Central Processing Unit (CPU) is still challenging. Moreover, computational cost for very long filters is still not acceptable. In this thesis, a new algorithm is presented by taking advantage of the broad memory on Graphics Processing Units (GPU). Performing the computations of a non-uniformly partitioned block convolution on GPU could solve the problem of work load on CPU. It is shown that the computational time in this algorithm reduces for the filters with long length.
267

Amélioration instrumentale de la chromatographie de partage centrifuge en vue de la purification de molécules très polaires / Centrifugal partition chromatography : an improved instrument for highly polar molecule purification

Bouiche, Feriel 25 January 2018 (has links)
L'objectif de cette thèse est de développer un nouvel instrument de chromatographie de partage centrifuge (CPC) dédié à la purification de molécules très polaires. La CPC est une technique préparative permettant la séparation des molécules grâce à l'utilisation d'un système solvant constitué de deux liquides non miscibles. Ce manuscrit expose dans un premier temps les différentes techniques de purification de protéines utilisées dans le cas d'un procédé industriel de production. Un focus est réalisé sur l'utilisation de systèmes biphasiques aqueux pour la purification des biomolécules, qui représente un réel avenir dans l'industrie du fait de son faible coût, de sa facilité de montée en échelle et surtout de l'environnement favorable qu'il fournit aux biomolécules. Ainsi en se basant sur les avantages de ces systèmes solvants dits Aqueous Two Phase Systems (ATPS), la CPC pourrait apporter une efficacité supplémentaire permettant de purifier les protéines à moindre coût. Pour pouvoir répondre à cet enjeu industriel, il est nécessaire de développer à la fois des méthodes chromatographiques innovantes et de nouveaux instruments dédiés. En effet, les instruments de CPC actuels ne sont pas compatibles avec les Bonne Pratique de Fabrication du fait de la présence de joints téflons qui empêche la possibilité de stériliser les instruments. La fabrication d'un nouvel instrument monobloc entièrement en titane a été réalisée grâce à la technologie de l'impression 3D pour répondre à cette problématique. L'objet de cette thèse est l'évaluation poussée des performances de cette nouvelle colonne afin de déterminer son applicabilité à la purification des biomolécules. Un focus sera également apporté à l'injection de volumes très faibles d'échantillon afin de faciliter le développement de méthodes / The aim of this thesis is to develop a new centrifugal partition chromatography (CPC) instrument in order to purify highly polar molecules. CPC is a preparative technique for the separation of molecules using a solvent system composed of two immiscible liquids. This manuscript describes the different protein purification techniques used in industrial production process. A focus is made on the use of aqueous biphasic systems for the purification of biomolecules, which represents a real trend in the industry thanks to its low cost, scaling simplicity and especially the favorable environment that it provides to biomolecules. Thus, based on the advantages of these solvent systems known as Aqueous Two Phase Systems (ATPS), CPC could provide additional performances to purify proteins at lower cost. To respond to this industrial challenge, it is necessary to develop both innovative chromatographic methods and new devoted instruments. Indeed, current CPC instruments are not compatible with Good Manufacturing Practices due to the presence of Teflon seals which prevents the possibility of sterilizing the instruments. The manufacture of a new monobloc instrument entirely made of titanium was achieved thanks to the 3D printing technology. The purpose of this thesis is the evaluation of this new column performance in order to determine its applicability to biomolecules purification. A special attention is also provided to the injection of very small sample volumes in order to facilitate method development
268

Un bruit pieux. La musique des bandas à la fête de Santa Maria Mater Gratiae à Zabbar (Malte) / A pious noise. Bandas’ music at the Santa Maria Mater Gratiae festival in Zabbar (Malta)

Iacovazzi, Giovanna 10 July 2009 (has links)
À Zabbar, un village maltais du Nord-Est, la banda Maria Mater Gratiae et la banda San Mikiel, rivales depuis leur fondation, en 1883, sont intégrées dans la vie villageoise et animent la fête patronale de Santa Maria Mater Gratiae, tous les ans, le 8 septembre. La musique des bandas – des marches – est une musique populaire, festive, religieuse et écrite. Elle ne joue pas seulement un rôle décoratif ou d’utilité ni de stricte nécessité sociale, elle constitue un véritable fait social total. Elle s’inscrit dans une pratique collective du quotidien et produit des sociabilités multiples, des échanges, des univers sonores, un imaginaire musical riche en mouvement. La première partie de cette thèse, d’un caractère ethnographique, décrit le contexte musical du village, en mettant l’accent sur les bandas, leur siège – le kazin –, leur histoire, leur rôle dans le contexte musical maltais. Dans une deuxième partie, la musique des bandas se révèle être au centre d’échanges - des musiciens et des partitions – et de rivalités dans l’espace villageois et de l’île. Enfin, après une description de la musique dans la fête et une étude comparée qui montre l’origine même de ces formations dans la double histoire des orchestres de cuivre et d’harmonie, une dernière partie est consacrée à l’analyse musicale et a pour but de découvrir la logique de ces musiques paraliturgiques / In Zabbar, a village in north-east Malta, two bandas, Maria Mater Gratiae and San Mikiel, have been rivals since they were founded in 1883. They are part and parcel of village life and bring life to the Santa Maria Mater Gratiae village festival each year, on the 8th of September. The music of bandas, of marches, is a popular, festive, religious, written music. Its role is neither decorative nor utilitarian, nor is it a strict social necessity, it is an actual complete social fact. It is part of a collective pratice in daily life and produces multiple sociabilities, exchanges, musical worlds, an imaginary musical universe full of movement. The first part of this thesis, which is ethnographic, describes the musical context of the village, drawing attention to the bandas, their seats (or kazin), their history, the role they play in the Maltese musical context. In the second part, banda music is discovered to be central to exchanges (musicians and music scores) and rivalries within the village space and the island itself. Then comes a description of the music within the festival and a comparative study meant to show how the bandas found their origins in the history of brass bands and orchestras. Finally, a last part is dedicated to musical analysis and aims at discovering the logic within those paraliturgical musics.
269

The parallel tracks of Partition, India-Pakistan 1947 : histories, geographies, cartographies

Fitzpatrick, Hannah January 2016 (has links)
On 15 August 1947, the British government withdrew from India and partitioned the subcontinent to create two new nation-states: India and Pakistan. The Partition of India and Pakistan has been studied chiefly as a historical phenomenon with legacies that reach into the present. Questions of geography and space are crucial to this history, yet have hitherto received scant attention. This dissertation is a historical geography of Partition that probes the interplay of temporality and spatiality, and the historical and geographical layering, at work in the making of India and Pakistan. It treats Partition as both an event and a process, examining how the 1947 borders were rooted in a set of imaginative geographies and material geographical practices that were fashioned for and applied to the purpose of refashioning territory as part of a transfer of colonial power to independent postcolonial states and the making of new (national, religious) identities. The dissertation teases out the constitutive role of ideals and practices of territorial and cultural imagining, classification, mapping and boundary-making in this historical geography, but also highlights their contingent and contested qualities. It critically analyses and reframes Partition historiography using a range of theoretical literatures (especially critical geographical work on empire and strands of postcolonial and subaltern theory) that foster a sensitivity to the entanglements of power, knowledge, geography, expertise in the context of Partition, and draws on an eclectic range of primary sources, including the hitherto unused papers of the geographer Oskar Spate. Parts I and II trace strands of geographical and cartographic representations of ‘India' and ‘Pakistan' before 1947. Part III examines the geographies and spaces of the Punjab Boundary Commission of July 1947, in which Spate participated as an advisor to the Muslim League. Part IV points to the continued relevance of these geographies of Partition and their critical framing in this dissertation as lines of power.
270

Normal Factor Graphs

Al-Bashabsheh, Ali January 2014 (has links)
This thesis introduces normal factor graphs under a new semantics, namely, the exterior function semantics. Initially, this work was motivated by two distinct lines of research. One line is ``holographic algorithms,'' a powerful approach introduced by Valiant for solving various counting problems in computer science; the other is ``normal graphs,'' an elegant framework proposed by Forney for representing codes defined on graphs. The nonrestrictive normality constraint enables the notion of holographic transformations for normal factor graphs. We establish a theorem, called the generalized Holant theorem, which relates a normal factor graph to its holographic transformation. We show that the generalized Holant theorem on one hand underlies the principle of holographic algorithms, and on the other reduces to a general duality theorem for normal factor graphs, a special case of which was first proved by Forney. As an application beyond Forney's duality, we show that the normal factor graphs duality facilitates the approximation of the partition function for the two-dimensional nearest-neighbor Potts model. In the course of our development, we formalize a new semantics for normal factor graphs, which highlights various linear algebraic properties that enables the use of normal factor graphs as a linear algebraic tool. Indeed, we demonstrate the ability of normal factor graphs to encode several concepts from linear algebra and present normal factor graphs as a generalization of ``trace diagrams.'' We illustrate, with examples, the workings of this framework and how several identities from linear algebra may be obtained using a simple graphical manipulation procedure called ``vertex merging/splitting.'' We also discuss translation association schemes with the aid of normal factor graphs, which we believe provides a simple approach to understanding the subject. Further, under the new semantics, normal factor graphs provide a probabilistic model that unifies several graphical models such as factor graphs, convolutional factor graphs, and cumulative distribution networks.

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