Academic literature on the topic 'Interaction functionals'

This thesis is a contribution to the mathematical theory of Hyperbolic Conservation Laws. Three are the main results which we collect in this work. The first and the second result (denoted in the thesis by Theorem A and Theorem B respectively) deal with the following problem. The most comprehensive result about existence, uniqueness and stability of the solution to the Cauchy problem \begin{equation}\tag{$\mathcal C$} \label{E:abstract} \begin{cases} u_t + F(u)_x = 0, \\u(0, x) = \bar u(x), \end{cases} \end{equation} where $F: \R^N \to \R^N$ is strictly hyperbolic, $u = u(t,x) \in \R^N$, $t \geq 0$, $x \in \R$, $\TV(\bar u) \ll 1$, can be found in [Bianchini, Bressan 2005], where the well-posedness of \eqref{E:abstract} is proved by means of vanishing viscosity approximations. After the paper [Bianchini, Bressan 2005], however, it seemed worthwhile to develop a \emph{purely hyperbolic} theory (based, as in the genuinely nonlinear case, on Glimm or wavefront tracking approximations, and not on vanishing viscosity parabolic approximations) to prove existence, uniqueness and stability results. The reason of this interest can be mainly found in the fact that hyperbolic approximate solutions are much easier to study and to visualize than parabolic ones. Theorems A and B in this thesis are a contribution to this line of research. In particular, Theorem A proves an estimate on the change of the speed of the wavefronts present in a Glimm approximate solution when two of them interact; Theorem B proves the convergence of the Glimm approximate solutions to the weak admissible solution of \eqref{E:abstract} and provides also an estimate on the rate of convergence. Both theorems are proved in the most general setting when no assumption on $F$ is made except the strict hyperbolicity. The third result of the thesis, denoted by Theorem C, deals with the Lagrangian structure of the solution to \eqref{E:abstract}. The notion of Lagrangian flow is a well-established concept in the theory of the transport equation and in the study of some particular system of conservation laws, like the Euler equation. However, as far as we know, the general system of conservations laws \eqref{E:abstract} has never been studied from a Lagrangian point of view. This is exactly the subject of Theorem C, where a Lagrangian representation for the solution to the system \eqref{E:abstract} is explicitly constructed. The main reasons which led us to look for a Lagrangian representation of the solution of \eqref{E:abstract} are two: on one side, this Lagrangian representation provides the continuous counterpart in the exact solution of \eqref{E:abstract} to the well established theory of wavefront approximations; on the other side, it can lead to a deeper understanding of the behavior of the solutions in the general setting, when the characteristic field are not genuinely nonlinear or linearly degenerate.

The emergence of genomics as a discrete field of biology has changed humanity’s understanding of our relationship with bacteria. Sequencing the genome of each newly-discovered bacterial species can reveal novel gene sequences, though the genome may contain genes coding for hundreds or thousands of proteins of unknown function (PUFs). In some cases, these coding sequences appear to be conserved across nearly all bacteria. Exploring the functional roles of these cases ideally requires an integrative, cross-species approach involving not only gene sequences but knowledge of interactions among their products. Protein interactions, studied at genome scale, extend genomics into the field of interactomics. I have employed novel computational methods to provide context for bacterial PUFs and to leverage the rich genomic, proteomic, and interactomic data available for hundreds of bacterial species. The methods employed in this study began with sets of protein complexes. I initially hypothesized that, if protein interactions reveal protein functions and interactions are frequently conserved through protein complexes, then conserved protein functions should be revealed through the extent of conservation of protein complexes and their components. The subsequent analyses revealed how partial protein complex conservation may, unexpectedly, be the rule rather than the exception. Next, I expanded the analysis by combining sets of thousands of experimental protein-protein interactions. Progressing beyond the scope of protein complexes into interactions across full proteomes revealed novel evolutionary consistencies across bacteria but also exposed deficiencies among interactomics-based approaches. I have concluded this study with an expansion beyond bacterial protein interactions and into those involving bacteriophage-encoded proteins. This work concerns emergent evolutionary properties among bacterial proteins. It is primarily intended to serve as a resource for microbiologists but is relevant to any research into evolutionary biology. As microbiomes and their occupants become increasingly critical to human health, similar approaches may become increasingly necessary.

Made available in DSpace on 2016-12-12T20:15:51Z (GMT). No. of bitstreams: 1 Marsal Eduardo Bento.pdf: 1108751 bytes, checksum: c5c36b13c56d8d4fadcee9ddc5a9098e (MD5) Previous issue date: 2014-12-16<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>The development of Density Functional Theory (DFT) has been focused primarily on two main pillars: (1) the pursuit of more accurate exchange-correlation (XC) density functionals; (2) the feasibility of computational implementation when dealing with many-body systems. In this context, this work is aimed on using one-dimensional quantum systems as theoretical laboratories to investigate the implementation of orbital functionals (OFs) of density. By definition, OFs are those which depend only implicitly on the density, via an explicit formulation in terms of Kohn-Sham orbitals. Typical examples are the XC functionals arising from the Perdew-Zunger self-interaction correction (PZSIC). Formally, via Kohn-Sham equations, the implementation of OFs must be performed by means of the optimized effective potential method (OEP), which is known by requiring an excessive computational effort even when dealing with few electrons systems (N &#820; 10). Here, we proceed a systematical investigation aiming to simplify or avoid the OEP procedure, taking as reference the implementation of the PZSIC correction applied to one-dimensional Hubbard chains.<br>O desenvolvimento da Teoria do Funcional da Densidade (DFT) tem se concentrado, sobretudo, em dois pilares fundamentais: (1) a busca por funcionais de troca e correlação (XC) mais precisos; (2) a viabilidade de implementação computacional diante de sistemas com muitos elétrons. Nesse contexto, o objetivo principal deste trabalho consiste em utilizar sistemas quânticos unidimensionais, mais simples de serem tratados numericamente, como laboratórios teóricos para o desenvolvimento de alternativas de implementação numérica de funcionais orbitais (OFs) da densidade. Por definição, OFs são todos aqueles que dependem apenas implicitamente da densidade, via formulação explícita em termos dos orbitais Kohn-Sham. Exemplos típicos são os funcionais XC advindos da correção de auto-interação de Perdew e Zunger (PZSIC). Formalmente, via equações de Kohn-Sham, a implementação de OFs deve ser procedida por meio do método do potencial efetivo otimizado (OEP) que, no contexto computacional, é conhecido por se tornar demasiadamente custoso, inclusive para sistemas com poucos elétrons (N &#820; 10). Sendo assim, investigamos, de forma sistemática, alternativas de simplificar ou evitar o procedimento OEP, tomando como referência a implementação da correção PZSIC aplicada a cadeias de Hubbard unidimensionais.

Protein-protein interaction networks provide important information about what the biological function of proteins whose roles are unknown might be in a cell. These interaction networks were analyzed by a variety of approaches by running them on a single computer and the roles of the proteins identified were used to predict the function of the proteins unidentified. The functional flow is an approach that takes the network connectivity, distance effect, topology of the network with local and global views into account. With these advantages, that the functional flow produces more accurate results on the prediction of protein functions was presented by the previos conducted researches. However, the application implemented for this approach could not be practically applied on the large and complex network produced for the complex species because of memory limitation. The purpose of this thesis is to provide a new application be implemented on the high computing performance where the application can be scaled on the large data sets. Therefore, Hadoop, one of the open source map/reduce environments, was installed on 18 hosts each of which has eight cores. Method<br>the first map/reduce job distributes the protein interaction network as a format which allows parallel distributed computing to all the worker nodes, the other map/reduce job generates flows for each known protein function and the role of the proteins unidentified are predicted by accumulating all of these generated flows. It has been observed in the experiments we performed that the application requiring high performance computing can be decomposed into worker nodes efficiently and the application can provide better performance as the resources increase.

We propose a new kind of execution environment where applications can be debugged and re-programmed while they are being used. We call our overall concept interactive programming. We develop some of the key components of interactive programming in the setting of a pure, call-by-value functional language. We illustrate our ideas via a proof-of-concept implementation called lambdaCalc, but leave several important components of the overall vision, including efficient incremental update and scaling to large programs, for future work. Our specific achievements are as follows. First, we show how to reify the execution of a program into a live document which can be interactively decomposed into both sequential steps and parallel slices. We give a novel characterisation of forward and backward dynamic slicing and show that for a fixed computation the two problems describe a Galois connection. Second, we introduce a novel execution indexing scheme which derives execution differences from program differences. Our scheme supports the wholesale reorganisation of a computation via operations such as moves and splices. The programmer is able to see the consequences of edits on the intensional structure of the execution. Where possible, node identity is preserved, allowing an edit to be made whilst an execution is being explored and the changes to be reflected in the user's current view of the execution.

The present study explores the use of interactions for a communicative purpose, when it comes to communicate banking brand values through a website. By establishing important banking values, trust, sincerity and transparency this study investigates how interaction can be used to communicate those values, through the theory of interaction attributes. Using interaction attributes to communicate emotions as well as brand values has been previously investigated. However, not in the setting of banking. Through designing and exploring interactions this study established some important qualities to consider when designing for banking, with the goal of communicating trust, sincerity and transparency. Attributes consistency, expectedness and apparent are favourable, whilst pliability is found to have a negative effect. In addition to these attributes established by previous work, the findings suggest the importance of a new quality, to design interactions that animate slowly over time, as a way to guide the user through the interaction.

Neste trabalho utilizamos sistemas modelos no desenvolvimento, implementação e análise de funcionais orbitais da densidade, focando, em particular, nas correções de autointeração de Perdew-Zunger (PZSIC) e Lundin-Eriksson (LESIC). Aplicamos as correções de auto-interação ao funcional local (LDA) do modelo de Hubbard e de poços quânticos semicondutores, ambos unidimensionais, no caso estático e dependente do tempo, respectivamente. Para o modelo de Hubbard unidimensional, comparamos a LDA, LDA+PZSIC e LDA+LESIC, identificando o desempenho para energias e densidades do estado fundamental, com e sem impurezas locais, além do gap fundamental de energia. Em adição, averiguamos o desempenho diante de cargas fracionárias, estabelecendo conexões com o erro de delocalização da LDA. Mostramos a possibilidade da correta descrição das freqüências das oscilações de Friedel no modelo de Hubbard, além de investigar como a falha da LDA em reproduzir esse aspecto pode estar relacionada com os erros de auto-interação e delocalização. Investigamos ainda as diferentes possibilidades de implementação autoconsistente de qualquer funcional orbital da densidade, analisando a relação entre funcionais aproximados e suas implementações aproximadas. Nos poços quânticos, sob o enfoque dependente do tempo, analisamos a descontinuidade do potencial de troca e correlação ao variarmos o número de partículas, em dois processos distintos: a ionização eletrônica em um poço simples e dissociação de um poço duplo assimétrico. No último caso, avaliamos os efeitos da descontinuidade no número total de partículas em cada poço, revelando os mecanismos que resgatam a neutralidade elétrica durante processos de dissociação, com a correta carga final inteira.<br>In this work we use model systems to develop, implement and analyse orbital-dependent density functionals, focusing, specifically, on the self-interaction corrections (SICs) of Perdew and Zunger (PZSIC) and of Lundin and Eriksson (LESIC). These self-interaction corrections are applied to the local-density approximation (LDA) for the one-dimensional Hubbard model and for semiconductor quantum wells, in one-dimensional static and time-dependent situations. For the one-dimensional Hubbard model we compare LDA, LDA+PZSIC and LDA+LESIC, and investigate the performance of these approaches for ground-state energies, densities and energy gaps, with and without impurities in the system. We also consider the case of fractional charges, where a connection to the delocalization error of the LDA can be made. We show that in principle a correct description of the frequences of Friedel oscillations in the Hubbard model can be obtained from DFT, and investigate how the failure of the LDA in reproducing this is related to the selfinteraction and delocalization errors. Moreover, we investigate different procedures for the selfconsistent implementation of any orbital-dependent functional, and analyse the question of the interplay between an approximate functional and its approximate implementation. For quantum wells sytems we analyse, in a time-dependent framework, the discontinuity of the exchange-correlation potential under variation of the particle number in two different processes: the ionization of a simple quantum well and the dissociation of an asymmetric double well. In the latter case, we also consider the effect of changes in the particle number in each subwell, thus revealing the mechanism that restores electric neutrality during dissociation, with correct final charge.