So called discrete models have been successfully used in engineering and computational systems biology. This thesis discusses algebraic methods for modeling and analysis of gene regulatory networks within the discrete modeling context. The first chapter gives a background for discrete models and put in context some of the main research problems that have been pursued in this field for the last fifty years. It also outlines the content of each subsequent chapter. The second chapter focuses on the problem of inferring dynamics from the structure (topology) of the network. It also discusses the characterization of the attractor structure of a network when a particular class of functions control the nodes of the network. Chapters~3 and 4 focus on the study of multi-state nested canalyzing functions as biologically inspired functions and the characterization of their dynamics. Chapter 5 focuses on stochastic methods, specifically on the development of a stochastic modeling framework for discrete models. Stochastic discrete modeling is an alternative approach from the well-known mathematical formalizations such as stochastic differential equations and Gillespie algorithm simulations. Within the discrete setting, a framework that incorporates propensity probabilities for activation and degradation is presented. This approach allows a finer analysis of discrete models and provides a natural setup for cell population simulations. Finally, Chapter 6 discusses future research directions inspired by the work presented here. / Ph. D.

One goal of systems biology is to predict and modify the behavior of biological networks by accurately monitoring and modeling their responses to certain types of perturbations. The construction of mathematical models based on observation of these responses, referred to as reverse engineering, is an important step in elucidating the structure and dynamics of such networks. Continuous models, described by systems of differential equations, have been used to reverse engineer biochemical networks. Of increasing interest is the use of discrete models, which may provide a conceptual description of the network. In this dissertation we introduce a discrete modeling approach, rooted in computational algebra, to reverse-engineer networks from experimental time series data. The algebraic method uses algorithmic tools, including Groebner-basis techniques, to build the set of all discrete models that fit time series data and to select minimal models from this set. The models used in this work are discrete-time finite dynamical systems, which, when defined over a finite field, are described by systems of polynomial functions. We present novel reverse-engineering algorithms for discrete models, where each algorithm is suitable for different amounts and types of data. We demonstrate the effectiveness of the algorithms on simulated networks and conclude with a description of an ongoing project to reverse-engineer a real gene regulatory network in yeast. / Ph. D.

Submitted by Celso Magalhaes (celsomagalhaes@ufrrj.br) on 2017-09-18T11:33:32Z No. of bitstreams: 1 2016 - Jo?o M?rcio Sutana Alvim.pdf: 4276113 bytes, checksum: 115487153abb7bab43e2a012959a64e4 (MD5) / Made available in DSpace on 2017-09-18T11:33:34Z (GMT). No. of bitstreams: 1 2016 - Jo?o M?rcio Sutana Alvim.pdf: 4276113 bytes, checksum: 115487153abb7bab43e2a012959a64e4 (MD5) Previous issue date: 2016-12-21 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior - CAPES / In the classic set of unit operations of solid-liquid separation, sedimentation and filtration techniques stand out as critical processing steps for a broad spectrum of industrial activities. In this context, the proper knowledge of the properties and characteristics of the particulate systems directly involved represents an important aspect for the safe and efficient design of equipment and processes. Over the past 20 years, several methodologies were developed to study such phenomena, resulting in a huge library of sedimentation and filtration models available in the literature. This work presents a study based on the use of a particle-scale numerical simulation technique called Discrete Element Method (DEM), to describe the deposition of particulate solids in liquids. Tridimensional simulations of the sedimentation and filtration processes were carried out in a previously known flow field, as a way to test the applicability of the code and its capacity to virtually describe such processes. Cake properties, such as thickness, porosity and permeability were quantified over time and compared qualitatively and quantitatively with literature data. The effects of operational conditions, solids and liquid properties on the particulate model?s response were also investigated through a series of controlled numerical tests. The packing fraction values obtained in this work for the sedimentation process, when compared to the values found in the literature on similar conditions, showed a satisfactory agreement, with deviations smaller than 12% for all the points assessed / Dentro do conjunto cl?ssico das opera??es unit?rias de separa??o s?lido?l?quido, as t?cnicas de sedimenta??o e filtra??o se destacam como etapas de processamento cruciais para um amplo espectro de atividades da ind?stria. Neste contexto, o conhecimento adequado das propriedades e caracter?sticas dos sistemas particulados diretamente envolvidos representa um aspecto importante para o projeto seguro e eficiente de equipamentos e processos. Ao longo dos ?ltimos 20 anos, diversas metodologias foram desenvolvidas para estudar tais fen?menos, resultando em uma ampla biblioteca de modelos de sedimenta??o e filtra??o dispon?vel na literatura. O presente trabalho apresenta um estudo baseado no uso da simula??o num?rica em escala de part?cula, atrav?s do M?todo de Elementos Discretos ou DEM (do ingl?s ?Discrete Element Method?), para descrever a deposi??o de s?lidos particulados em suspens?es. Foram realizadas simula??es da sedimenta??o e filtra??o em tr?s dimens?es como forma de testar o funcionamento do c?digo e a sua capacidade de reproduzir virtualmente tais processos. As propriedades da torta, tais como espessura, porosidade e permeabilidade foram quantificadas ao longo do tempo e comparadas qualitativa e quantitativamente com dados da literatura. A sensibilidade do modelo desenvolvido a varia??es nas condi??es operacionais de simula??o e nas propriedades f?sicas do s?lido e do l?quido tamb?m foi analisada. Os dados de fra??o de s?lidos obtidos nas simula??es da sedimenta??o apresentaram uma concord?ncia satisfat?ria, quando comparados aos valores encontrados na literatura em condi??es similares, apresentando desvios menores do que 12% para todos os pontos avaliados.

Systems biology aims at system-level understanding of biological systems, in particular cellular networks. The milestones of this understanding are knowledge of the structure of the system, understanding of its dynamics, effective control methods, and powerful prediction capability. The complexity of biological systems makes it inevitable to consider mathematical modeling in order to achieve these goals. The enormous accumulation of experimental data representing the activities of the living cell has triggered an increasing interest in the reverse engineering of biological networks from data. In particular, construction of discrete models for reverse engineering of biological networks is receiving attention, with the goal of providing a coarse-grained description of such networks. In this dissertation we consider the modeling framework of polynomial dynamical systems over finite fields constructed from experimental data. We present and propose solutions to two problems inherent in this modeling method: the necessity of appropriate discretization of the data and the selection of a particular polynomial model from the set of all models that fit the data. Data discretization, also known as binning, is a crucial issue for the construction of discrete models of biological networks. Experimental data are however usually continuous, or, at least, represented by computer floating point numbers. A major challenge in discretizing biological data, such as those collected through microarray experiments, is the typically small samples size. Many methods for discretization are not applicable due to the insufficient amount of data. The method proposed in this work is a first attempt to develop a discretization tool that takes into consideration the issues and limitations that are inherent in short data time courses. Our focus is on the two characteristics that any discretization method should possess in order to be used for dynamic modeling: preservation of dynamics and information content and inhibition of noise. Given a set of data points, of particular importance in the construction of polynomial models for the reverse engineering of biological networks is the collection of all polynomials that vanish on this set of points, the so-called ideal of points. Polynomial ideals can be represented through a special finite generating set, known as Gröbner basis, that possesses some desirable properties. For a given ideal, however, the Gröbner basis may not be unique since its computation depends on the choice of leading terms for the multivariate polynomials in the ideal. The correspondence between data points and uniqueness of Gröbner bases is studied in this dissertation. More specifically, an algorithm is developed for finding all minimal sets of points that, added to the given set, have a corresponding ideal of points with a unique Gröbner basis. This question is of interest in itself but the main motivation for studying it was its relevance to the construction of polynomial dynamical systems. This research has been partially supported by NIH Grant Nr. RO1GM068947-01. / Ph. D.

Computer based simulation models have often been used to study the multimodal freight transportation system. But these studies have not been able to dynamically couple the various modes into one model; therefore, they are limited in their ability to inform on dynamic system level interactions. This research thesis is motivated by the need to dynamically couple the multimodal freight transportation system to operate at multiple spatial and temporal scales. It is part of a larger research program to develop a systems modeling framework applicable to freight transportation. This larger research program attempts to dynamically couple railroad, seaport, and highway freight transportation models. The focus of this thesis is the development of the coupled railroad and seaport models. A separate volume (Wall 2010) on the development of the highway model has been completed. The model railroad and seaport was developed using Arena® simulation software and it comprises of the Ports of Savannah, GA, Charleston, NC, Jacksonville, FL, their adjacent CSX rail terminal, and connecting CSX railroads in the southeastern U.S. However, only the simulation outputs for the Port of Savannah are discussed in this paper. It should be mentioned that the modeled port layout is only conceptual; therefore, any inferences drawn from the model's outputs do not represent actual port performance. The model was run for 26 continuous simulation days, generating 141 containership calls, 147 highway truck deliveries of containers, 900 trains, and a throughput of 28,738 containers at the Port of Savannah, GA. An analysis of each train's trajectory from origin to destination shows that trains spend between 24 - 67 percent of their travel time idle on the tracks waiting for permission to move. Train parking demand analysis on the adjacent shunting area at the multimodal terminal seems to indicate that there aren't enough containers coming from the port because the demand is due to only trains waiting to load. The simulation also shows that on average it takes containerships calling at the Port of Savannah about 3.2 days to find an available dock to berth and unload containers. The observed mean turnaround time for containerships was 4.5 days. This experiment also shows that container residence time within the port and adjacent multimodal rail terminal varies widely. Residence times within the port range from about 0.2 hours to 9 hours with a mean of 1 hour. The average residence time inside the rail terminal is about 20 minutes but observations varied from as little as 2 minutes to a high of 2.5 hours. In addition, about 85 percent of container residence time in the port is spent idle. This research thesis demonstrates that it is possible to dynamically couple the different sub-models of the multimodal freight transportation system. However, there are challenges that need to be addressed by future research. The principal challenge is the development of a more efficient train movement algorithm that can incorporate the actual Direct Traffic Control (DTC) and / or Automatic Block Signal (ABS) track segmentation. Such an algorithm would likely improve the capacity estimates of the railroad network. In addition, future research should seek to reduce the high computational cost imposed by a discrete process modeling methodology and the adoption of single container resolution level for terminal operations. A methodology combining both discrete and continuous process modeling as proposed in this study could lessen computational costs and lower computer system requirements at a cost of some of the feedback capabilities of the model This tradeoff must be carefully examined.