One of the differentiating features of PARAFAC decompositions is that, under certain conditions, unique solutions are possible. The search for uniqueness conditions for the PARAFAC Decomposition has a limited past, spanning only three decades. The complex structure of the problem and the need for tensor algebras or other similarly abstract characterizations provided a roadblock to the development of uniqueness conditions. Theoretically, the PARAFAC decomposition surpasses its bilinear counterparts in that it is possible to obtain solutions that do not suffer from the rotational problem. However, not all PARAFAC solutions will be constrained sufficiently so that the resulting decomposition is unique. The work of Kruskal, 1977, provides the most in depth investigation into the conditions for uniqueness, so much so that many have assumed, without formal proof, that his sufficient conditions were also necessary. Aided by the introduction of Khatri-Rao products to represent the PARAFAC decomposition, ten Berge and Sidiropoulos (2002) used the column spaces of Khatri-Rao products to provide the first evidence for countering the claim of necessity, identifying PARAFAC decompositions that were unique when Kruskals condition was not met. Moreover, ten Berge and Sidiropoulos conjectured that, with additional k-rank restrictions, a class of decompositions could be formed where Kruskals condition would be necessary and sufficient. Unfortunately, the column space argument of ten Berge and Sidiropoulos was limited in its application and failed to provide an explanation of why uniqueness occurred. On the other hand, the use of orthogonal complement spaces provided an alternative approach to evaluate uniqueness that would provide a much richer return than the use of column spaces for the investigation of uniqueness. The Orthogonal Complement Space Approach (OCSA), adopted here, would provide: (1) the answers to lingering questions about the occurrence of uniqueness, (2) evidence that necessity would require more than a restriction on k-rank, and (3) an approach that could be extended to cases beyond those investigated by ten Berge and Sidiropoulos.

Mass customization (MC) constitutes a promising strategy for companies which aim to provide products which are better adapted to individual customers' aesthetic and functional preferences. Drawing on commodity theory, we argue that the perceived uniqueness of a self-designed product is a second driver of utility in MC. We find that in addition to the significant effect of aesthetic and functional fit, the perceived uniqueness of a self-designed product (1) contributes independently to the utility a customer experiences, and (2) that this effect is moderated by the consumer's need for uniqueness. In product categories which can serve this counterconformity motive for consumers, this suggests that MC toolkits should be constructed with the objective of facilitating the creation of unique products as well as providing affirmative feedback that this uniqueness has been achieved. (authors' abstract)

A satisfactory account of human cognitive evolution will explain not only the psychological mechanisms that make our species unique, but also how, when, and why these traits evolved. To date, researchers have made substantial progress toward defining uniquely human aspects of cognition, but considerably less effort has been devoted to questions about the evolutionary processes through which these traits have arisen. In this article, I aim to link these complementary aims by synthesizing recent advances in our understanding of what makes human cognition unique, with theory and data regarding the processes of cognitive evolution. I review evidence that uniquely human cognition depends on synergism between both representational and motivational factors and is unlikely to be accounted for by changes to any singular cognitive system. I argue that, whereas no nonhuman animal possesses the full constellation of traits that define the human mind, homologies and analogies of critical aspects of human psychology can be found in diverse nonhuman taxa. I suggest that phylogenetic approaches to the study of animal cognition-which can address questions about the selective pressures and proximate mechanisms driving cognitive change-have the potential to yield important insights regarding the processes through which the human cognitive phenotype evolved.

In a transferable utility context, Choo and Siow (2006) introduced a competitive model of the marriage market with gumbel distributed stochastic part, and derived its equilibrium output, a marriage match- ing function. The marriage matching function defines the gains generated by a marriage between agents of prescribed types in terms of the observed frequency of such marriages within the population, relative to the number of unmarried individuals of the same types. Left open in their work is the issue of existence and uniqueness of equilibrium. We resolve this question in the affirmative, assuming the norm of the gains matrix (viewed as an operator) to be less than two. Our method adapts a strategy called the continuity method,more commonly used to solve elliptic partial differen- tial equations, to the new setting of isolating positive roots of polynomial systems. Finally, the data estimated in [4] falls within the scope of our results.

In a transferable utility context, Choo and Siow (2006) introduced a competitive model of the marriage market with gumbel distributed stochastic part, and derived its equilibrium output, a marriage match- ing function. The marriage matching function defines the gains generated by a marriage between agents of prescribed types in terms of the observed frequency of such marriages within the population, relative to the number of unmarried individuals of the same types. Left open in their work is the issue of existence and uniqueness of equilibrium. We resolve this question in the affirmative, assuming the norm of the gains matrix (viewed as an operator) to be less than two. Our method adapts a strategy called the continuity method,more commonly used to solve elliptic partial differen- tial equations, to the new setting of isolating positive roots of polynomial systems. Finally, the data estimated in [4] falls within the scope of our results.

Threat management of water distribution systems is essential for protecting consumers. In a contamination event, different strategies may be implemented to protect public health, including flushing the system through opening hydrants or isolating the contaminant by manipulating valves. To select the most effective options for responding to a contamination threat, the location and loading profile of the source of the contaminant should be considered. These characteristics can be identified by utilizing water quality data from sensors that have been strategically placed in a water distribution system. A simulation-optimization approach is described here to solve the inverse problem of source characterization, by coupling an evolutionary computation-based search with a water distribution system model. The solution of this problem may reveal, however, that a set of non-unique sources exists, where sources with significantly different locations and loading patterns produce similar concentration profiles at sensors. The problem of non-uniqueness should be addressed to prevent the misidentification of a contaminant source and improve response planning. This paper aims to address the problem of non-uniqueness through the use of Niched Co-Evolution Strategies (NCES). NCES is an evolutionary algorithm designed to identify a specified number of alternative solutions that are maximally different in their decision vectors, which are source characteristics for the water distribution problem. NCES is applied to determine the extent of non-uniqueness in source characterization for a virtual city, Mesopolis, with a population of approximately 150,000 residents. Results indicate that NCES successfully identifies non-uniqueness in source characterization and provides alternative sources of contamination. The solutions found by NCES assist in making decisions about response actions. Once alternative sources are identified, each source can be modeled to determine where the vulnerable areas of the system are, indicating the areas where response actions should be implemented.

Mass customization (MC) constitutes a promising strategy for companies which aim to provide products which are better adapted to individual customers' aesthetic and functional preferences. Drawing on commodity theory, we argue that the perceived uniqueness of a self-designed product is a second driver of utility in MC. We find that in addition to the significant effect of aesthetic and functional fit, the perceived uniqueness of a self-designed product (1) contributes independently to the utility a customer experiences, and (2) that this effect is moderated by the consumer's need for uniqueness. In product categories which can serve this counterconformity motive for onsumers, this suggests that MC toolkits should be constructed with the objective of facilitating the creation of unique products as well as providing affirmative feedback that this uniqueness has been achieved. (authors' abstract)

In recent decades, significant interest, based on physics and engineering applications, has developed on so-called anomalous diffusion processes that possess different spread functions with classical ones. The resulting differential equation whose fundamental solution matches this decay process is best modeled by an equation containing a fractional order derivative. This dissertation mainly focuses on some inverse problems for fractional diffusion equations. After some background introductions and preliminaries in Section 1 and 2, in the third section we consider our first inverse boundary problem. This is where an unknown boundary condition is to be determined from overposed data in a time- fractional diffusion equation. Based upon the fundamental solution in free space, we derive a representation for the unknown parameters as the solution of a nonlinear Volterra integral equation of second kind with a weakly singular kernel. We are able to make physically reasonable assumptions on our constraining functions (initial and given boundary values) to be able to prove a uniqueness and reconstruction result. This is achieved by an iterative process and is an immediate result of applying a certain fixed point theorem. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method. In the fourth section a reaction-diffusion problem with an unknown nonlinear source function, which has to be determined from overposed data, is considered. A uniqueness result is proved and a numerical algorithm including convergence analysis under some physically reasonable assumptions is presented in the one-dimensional case. To show effectiveness of the proposed method, some results of numerical simulations are presented. In Section 5, we also attempted to reconstruct a nonlinear source in a heat equation from a number of known input sources. This represents a new research even for the case of classical diffusion and would be the first step in a solution method for the fractional diffusion case. While analytic work is still in progress on this problem, Newton and Quasi-Newton method are applied to show the feasibility of numerical reconstructions. In conclusion, the fractional diffusion equations have some different properties with the classical ones but there are some similarities between them. The classical tools like integral equations and fixed point theory still hold under slightly different assumptions. Inverse problems for fractional diffusion equations have applications in many engineering and physics areas such as material design, porous media. They are trickier than classical ones but there are also some advantages due to the mildly ill-conditioned singularity caused by the new kernel functions.

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / The short film All San Francisco, 14 minutes, directed by young Cearà Charliane de Oliveira is the starting point for this research. Recounts personal stories of a family who lives in Morro de Santa Terezinha from their testimonies and pictures of the daily lives of these characters. Was chosen as the site for being a relevant video from the latest audiovisual production in the city of Fortaleza, having been recognized and awarded nationally in relevant festivals like Kinoforum (SP-2010). From a film analysis of the video there is an immersion in the daily work of young people from the outskirts of Fortaleza involved with training and audiovisual productions. The focus of attention is on the relationship of young videographers with photographic and audiovisual production and the becoming of this contact. The strength of audiovisual images and their relationship to the process of meeting with the singularity, with the aid of theoretical reflections of Walter Benjamin, Felix Guattari, Roland Barthes, Giorgio Agamben, Georges Didi-Huberman, among others, form the subject of this investigation . Among the forwards, the audiovisual images that assist in the formation of a critical consciousness and meeting with the uniqueness of each involved. / O curta-metragem Todos SÃo Francisco, de 14 minutos, dirigido pela jovem cearense Charliane de Oliveira à o ponto de partida para este trabalho de pesquisa. Relata histÃrias pessoais de uma famÃlia moradora no Morro de Santa Terezinha a partir de seus depoimentos e imagens do cotidiano desses personagens. Foi escolhido como objeto por ter sido um vÃdeo relevante entre a produÃÃo audiovisual recente na cidade de Fortaleza, tendo sido reconhecido e premiado nacionalmente em festivais relevantes como o KinofÃrum (SP-2010). A partir de uma anÃlise fÃlmica do vÃdeo hà um trabalho de imersÃo no cotidiano de jovens da periferia de Fortaleza envolvidos com formaÃÃes e produÃÃes audiovisuais. O foco da atenÃÃo à para a relaÃÃo dos jovens videomakers com a produÃÃo fotogrÃfica e audiovisual e o devir desse contato. A forÃa das imagens audiovisuais e a relaÃÃo delas com o processo de encontro com a singularidade, com o auxÃlio das reflexÃes teÃricas de Walter Benjamin, Felix Guattari, Roland Barthes, Giorgio Agamben, Georges Didi-Huberman, entre outros, compÃem o objeto desta investigaÃÃo. Entre os encaminhamentos, o de que as imagens audiovisuais auxiliam na formaÃÃo de uma consciÃncia crÃtica e no encontro com a singularidade de cada envolvido.

For many years, accounting discourse has been concerned with the measurement of attributes of accounting events. The concept of measurement forms one of the central pillars on which the preparation of financial statements is based. For example, financial statements can only be prepared if economic events meet the definition of an element of the financial statements and have a cost or value that can be measured with reliability. This has created the belief that accounting practices are practices of measurement. The principles of measurement require that every process of measurement be based on an appropriate theory of measurement. Given the belief in the accounting discipline that accounting practices are synonymous with practices of measurement, it is to be assumed that acceptable theories of measurement exist in the discipline. However, over the decades, researchers in this field have been unsuccessful in creating an acceptable theory of accounting measurement. This suggests that there is a gap between the accounting concept of measurement and the scientific principles of measurement. The main goals of this thesis are to determine whether the concept of measurement in accounting is in harmony with the principles of the representational theory of measurement and to develop a conceptual model of the accounting measurement problem. Representational theory establishes measurement in the social sciences. Accounting is regarded as a social science. This study applies the principles of the representational theory of measurement to determine the nature of the gap between the accounting concept of measurement and the principles of this theory. The very fact of referring to accounting as a measurement discipline implies the presence of an established and well-known theory of measurement in that discipline: a discipline cannot be referred to as a measurement discipline without the existence of such a theory. Therefore, the lack of success of researchers in creating a theory of accounting measurement suggests that accounting is not a measurement discipline and that accountants are currently unaware of this. To test this hypothesis: 1. A critical literature analysis was conducted, investigating whether the accounting concept of measurement is in harmony with the principles of the representational theory of measurement. The results of this analysis indicated that the accounting concept of measurement is not in harmony with the principles of the representational theory of measurement. 2. A questionnaire was sent to accountants, testing whether they were familiar with the principles of the representational theory of measurement and their application to the accounting discipline. The results of the survey indicated that accountants are not familiar with the principles of the representational theory of measurement or their application to the accounting discipline. The main contributions of this study lie in the fact that it reveals that current accounting practices are not in harmony with the principles of representational measurement. Accountants should be educated in the purpose of the principles of measurement in the social sciences in order to ensure their proper application during accounting measurement. / Thesis (DCom)--University of Pretoria, 2009. / Financial Management / unrestricted