Influence has been studied across many different domains including sociology, statistics, marketing, network theory, psychology, social media, politics, and web search. In each of these domains, being able to measure and rank various degrees of influence has useful applications. For example, measuring influence in web search allows internet users to discover useful content more quickly. However, many of these algorithms measure influence across networks and graphs that are mathematically static. This project explores influence measurement within the context of linear time invariant (LTI) systems. While dynamical networks do have mathematical models for quantifying influence on a node-to-node basis, to the best of our knowledge, there are no proposed mathematical formulations that measure aggregate level influence across an entire dynamical network. The dynamics associated with each link, which can differ from one link to another, add additional complexity to the problem. Because of this complexity, many of the static-graph approaches used in web search do not achieve the desired outcome for dynamical networks. In this work we build upon concepts from PageRank and systems theory introduce two new methods for measuring influence within dynamical networks: 1) Dynamical Responsive Page Rank (DRPR) and 2) Aggregated Targeted Reachability (ATR). We then compare and analyze and compare results with these new methods.

Cette thèse propose une méthode pour construire des réseaux de régulations causales réalistes, qui a un taux de faux positifs inférieur aux méthodes traditionnelles. Cette approche consiste à intégrer des informations hétérogènes à partir de deux types de prédictions de réseau pour déterminer une explication causale des gènes co-exprimés. Ce processus d'intégration se modélise par un problème d'optimisation combinatoire, de complexité NP-difficile. Nous proposons une approche heuristique pour déterminer une solution approchée en un temps d'exécution raisonnable. Nos expérimentations montrent que, pour l'espèce modèle E. coli, le réseau de régulation résultant de l'application de cette méthode a une précision supérieure à celle construite avec des outils traditionnels. La bactérie Acidithiobacillus ferrooxidans présente des défis importants pour la détermination expérimentale de son réseau de régulation. En utilisant les outils que nous avons développés, nous proposons un réseau de régulation putatif et analysons la pertinence de ses régulateurs centraux. Dans une deuxième partie de cette thèse, nous explorons la façon dont ces relations de régulation se manifestent, en développant une méthode pour compléter un réseau de régulation lié à la maladie d'Alzheimer. Enfin, nous abordons le problème mathématique de la conception de la sonde de puces à ADN. Nous concluons que, pour prévoir pleinement les dynamiques d'hybridation, nous avons besoin d'une fonction d'énergie modifiée pour les structures secondaires des molécules d'ADN attachées en surface et proposons un schéma pour la détermination de cette fonction. / This thesis proposes a method to build realistic causal regulatory networks hat has lower false positive rate than traditional methods. The first contribution of this thesis is to integrate heterogeneous information from two types of network predictions to determine a causal explanation of the observed gene co-expression. The second contribution is to model this integration as a combinatorial optimization problem. We demonstrate that this problem belongs to the NP-hard complexity class. The third contribution is the proposition of a heuristic approach to have an approximate solution in a practical execution time. Our evaluation shows that the E.coli regulatory network resulting from the application of this method has a higher accuracy than the putative one built with traditional tools. The bacterium Acidithiobacillus ferrooxidans is particularly challenging for the experimental determination of its regulatory network. Using the tools we developed, we propose a putative regulatory network and analyze it to rank the relevance of central regulators. In a second part of this thesis we explore how these regulatory relationships are manifested in a case linked to human health, developing a method to complete a linked to Alzheimer 's disease network. As an addendum we address the mathematical problem of microarray probe design. We conclude that, to fully predict the hybridization dynamics, we need a modified energy function for secondary structures of surface-attached DNA molecules and propose a scheme for determining such function.

Passive network reconstruction is the process of learning a structured (networked) representation of a dynamic system through the use of known information about the structure of the system as well as data collected by observing the inputs into a system along with the resultant outputs. This work demonstrates an improvement on an existing network reconstruction algorithm so that the algorithm is capable of consistently and perfectly reconstructing a network when system inputs and outputs are measured without error. This work then extends the improved network reconstruction algorithm so that it functions even in the presence of noise as well as the situation where inputs into the system are unknown. Furthermore, this work demonstrates the capability of the new extended algorithms by reconstructing financial networks from stock market data, and then performing an analysis to understand the vulnerabilities of the reconstructed network to destabilization through localized attacks. The creation of these improved and extended algorithms has opened many theoretical questions, paving the way for future research into network reconstruction.

This thesis proposes a method to build realistic causal regulatory networks hat has lower false positive rate than traditional methods. The first contribution of this thesis is to integrate heterogeneous information from two types of network predictions to determine a causal explanation of the observed gene co-expression. The second contribution is to model this integration as a combinatorial optimization problem. We demonstrate that this problem belongs to the NP-hard complexity class. The third contribution is the proposition of a heuristic approach to have an approximate solution in a practical execution time. Our evaluation shows that the E.coli regulatory network resulting from the application of this method has a higher accuracy than the putative one built with traditional tools. The bacterium Acidithiobacillus ferrooxidans is particularly challenging for the experimental determination of its regulatory network. Using the tools we developed, we propose a putative regulatory network and analyze it to rank the relevance of central regulators. In a second part of this thesis we explore how these regulatory relationships are manifested in a case linked to human health, developing a method to complete a linked to Alzheimer 's disease network. As an addendum we address the mathematical problem of microarray probe design. We conclude that, to fully predict the hybridization dynamics, we need a modified energy function for secondary structures of surface-attached DNA molecules and propose a scheme for determining such function.

In the past years, several network reconstruction methods modeled as Gaussian Graphical Model in high dimensional settings where proposed. In this work we will analyze three different methods, the Graphical Lasso (GLasso), Graphical Ridge (GGMridge) and a novel method called LPC, or Local Partial Correlation. The evaluation will be performed in high dimensional data generated from different simulated random graph structures (Erdos-Renyi, Barabasi-Albert, Watts-Strogatz ), using Receiver Operating Characteristic or ROC curve. We will also apply the methods in the reconstruction of genetic co-expression network for the differentially expressed genes in cervical cancer tumors. / Vários métodos tem sido propostos para a reconstrução de redes em alta dimensão, que e tratada como um Modelo Gráfico Gaussiano. Neste trabalho vamos analisar três métodos diferentes, o método Graphical Lasso (GLasso), Graphical Ridge (GGMridge) e um novo método chamado LPC, ou Correlação Parcial Local. A avaliação será realizada em dados de alta dimensão, gerados a partir de grafos aleatórios (Erdos-Renyi, Barabasi-Albert, Watts-Strogatz ), usando Receptor de Operação Característica, ou curva ROC. Aplicaremos também os metidos apresentados, na reconstrução da rede de co-expressão gênica para tumores de câncer cervical.

In the past years, several network reconstruction methods modeled as Gaussian Graphical Model in high dimensional settings where proposed. In this work we will analyze three different methods, the Graphical Lasso (GLasso), Graphical Ridge (GGMridge) and a novel method called LPC, or Local Partial Correlation. The evaluation will be performed in high dimensional data generated from different simulated random graph structures (Erdos-Renyi, Barabasi-Albert, Watts-Strogatz ), using Receiver Operating Characteristic or ROC curve. We will also apply the methods in the reconstruction of genetic co-expression network for the differentially expressed genes in cervical cancer tumors. / Vários métodos tem sido propostos para a reconstrução de redes em alta dimensão, que e tratada como um Modelo Gráfico Gaussiano. Neste trabalho vamos analisar três métodos diferentes, o método Graphical Lasso (GLasso), Graphical Ridge (GGMridge) e um novo método chamado LPC, ou Correlação Parcial Local. A avaliação será realizada em dados de alta dimensão, gerados a partir de grafos aleatórios (Erdos-Renyi, Barabasi-Albert, Watts-Strogatz ), usando Receptor de Operação Característica, ou curva ROC. Aplicaremos também os metidos apresentados, na reconstrução da rede de co-expressão gênica para tumores de câncer cervical.

One of the most powerful properties of mathematical systems theory is the fact that interconnecting systems yields composites that are themselves systems. This property allows for the engineering of complex systems by aggregating simpler systems into intricate patterns. We call these interconnection patterns the "structure" of the system. Similarly, this property also enables the understanding of complex systems by decomposing them into simpler parts. We likewise call the relationship between these parts the "structure" of the system. At first glance, these may appear to represent identical views of structure of a system. However, further investigation invites the question: are these two notions of structure of a system the same? This dissertation answers this question by developing a theory of dynamical structure. The work begins be distinguishing notions of structure from their associated mathematical representations, or models, of a system. Focusing on linear time invariant (LTI) systems, the key technical contributions begin by extending the definition of the dynamical structure function to all LTI systems and proving essential invariance properties as well as extending necessary and sufficient conditions for the reconstruction of the dynamical structure function from data. Given these extensions, we then develop a framework for analyzing the structures associated with different representations of the same system and use this framework to show that interconnection (or subsystem) structures are not necessarily the same as decomposition (or signal) structures. We also show necessary and sufficient conditions for the reconstruction of the interconnection (or subsystem) structure for a class of systems. In addition to theoretical contributions, this work also makes key contributions to specific applications. In particular, network reconstruction algorithms are developed that extend the applicability of existing methods to general LTI systems while improving the computational complexity. Also, a passive reconstruction method was developed that enables reconstruction without actively probing the system. Finally, the structural theory developed here is used to analyze the vulnerability of a system to simultaneous attacks (coordinated or uncoordinated), enabling a novel approach to the security of cyber-physical-human systems.

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The current investigation is aimed at the reconstruction and analysis of genome-scale metabolic models. Specifically, it is focused on the use of mathematical-computational simulations to predict the cellular metabolism behavior towards bio-products production. The photosynthetic cyanobacterium Synechococcus elongatus PCC7942 was studied as biological system. This prokaryotic has been used in several studies as a biological platform for the synthesis of several substances for industrial interest. These studies are based on the advantage of autotrophic systems, which basically requires light and CO2 for growth. The main objective of this thesis is the integration of different types of biological information, whose interaction can be extract applicable knowledge for economic interests. To this end, our study was addressed to the use of methods for modeling, analyzing and predicting the behavior of metabolic phenotypes of cyanobacterium. The work has been divided into chapters organized sequentially, where the starting point was the in silico metabolic reconstruction network. This process intent to join in a metabolic model of all chemical reactions codified in genome. The stoichiometric coefficients of each reactions, can be arranged into a sparse matrix (stoichiometric matrix), where the columns corresponds to reactions and rows to metabolites. As a result of this process the first model was obtained (iSyf646) than later was updated to another (iSyf714). Both were generated from data ¿omics published in databases, scientific reviews as well as textbooks. To validate them, each one of the stoichiometric matrix together with relevant constraints were used by simulation techniques based on linear programming. These reconstructions have to be flexible enough to allow autotrophic growth under which the organism grows in nature. Once the reconstructions were validated, environmental variations can be simulated and we were able to study its effects through changes in outline system parameters. Subsequently, synthetic capabilities were evaluated from the in silico models in order to design metabolic engineering strategies. To do this a genetic variation was simulated in reactions network, where the disturbed stoichiometric matrix was the object of the quadratic optimization methods. As a results sets of optimal solutions were generated to enhanced production of various metabolites of energetic interest such as: ethanol, n-butanol isomers, lipids and hydrogen, as well as lactic acid as the compound which is an interest to the industry. Furthermore, functionally coupled reactions have been studied and have been weighted to the importance in the production of metabolites. Finally, genome-scale metabolic models allow us to establish criteria to integrate different types of data to help of find important points of regulation that may be subject to genetic modification. These regulatory centers have been investigated under drastic changes of illumination and have been inferred operational principles of cyanobacterium metabolism. In general, this thesis presents the metabolic capabilities of photosynthetic cyanobacterium Synechococcus elongatus PCC7942 to produce substances of interest, being a potential biological platform for clean and sustainable production. / Triana Dopico, J. (2014). Model-based analysis and metabolic design of a cyanobacterium for bio-products synthesis [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/39351 / TESIS

For precise measurement of new TeV-scale physics and precision studies of the Higgs Boson, a new lepton collider is required. To enable meaningful analysis, a centre of mass energy of 500GeV and luminosity of 10³⁴cm^-2s^-1 is needed. The planned 31km long International Linear Collider is capable of meeting these targets, requiring a final emittance of 10 micro-radians horizontally and 35nmrad vertically. To achieve these demanding emittance values, the accelerator components in the main linacs must be aligned against an accurately mapped network of reference markers along the entire tunnel. An automated system could map this tunnel network quickly, accurately, safely and repeatedly; the Linear Collider Alignment and Survey (LiCAS) Rapid Tunnel Reference Surveyor (RTRS) is a working prototype of such a system. The LiCAS RTRS is a train of measurement units that accurately locate regularly spaced retro-reflector markers using Frequency Scanning Interferometry (FSI). The unit locations with respect to each other are precisely reconstructed using a Laser Straightness Monitor (LSM) and tilt sensor system, along with a system of internal FSI lines. The design, commissioning, practical usage, calibration, and reconstruction performance of the LSM is addressed in this work. The commissioned RTRS is described and the properties of the LSM components are investigated in detail. A method of finding the position of laser beam spots on the LSM cameras is developed, along with a process of combining individual spot positions into a more robust measurement compatible with the data from other sub-systems. Laser beam propagation along the LSM is modelled and a robust method of reconstructing CCD beam spot position measurements into positions and orientations of the LSM units is described. A method of calibrating LSM units using an external witness system is presented, along with a way of using the overdetermined nature of the LSM to improve calibration constant errors by including data taken from unwitnessed runs. The reconstruction uncertainty, inclusive of both statistical and systematic effects, of the LSM system is found to be of 5.8 microns × 5.3 microns in lateral translations and 27.6 microradians × 34.1 microradians in rotations perpendicular to the beam, with an uncertainty of 51.1 microradians in rotations around the beam coming from a tilt-sensor arrangement.