Network theory is finding applications in the life and social sciences for ecology, epidemiology, finance and social-ecological systems. While there are methods to generate specific types of networks, the broad literature is focused on generating unweighted networks. In this paper, we present a framework for generating weighted networks that satisfy user- defined criteria. Each criterion hierarchically defines a feature of the network and, in doing so, complements existing algorithms in the literature. We use a general example of ecological species dispersal to illustrate the method and provide open- source code for academic purposes.

This paper studies the topological properties of the International Trade Network (ITN) among world countries using a network analysis. We explore the distribu- tions of the most important network statistics measuring connectivity, assortativ- ity and clustering. We show that the topological properties of the weighted rep- resentation of the ITN are very different from those obtained by a binary network approach. In particular, we find that: (i) the majority of countries are character- ized by weak trade relationships, (ii) well connected countries tend to trade with poorly connected partners and (iii) countries holding more intense trade relation- ships are more clustered. Finally, we display that all structural properties of the ITN have remained remarkably stable over time.

This dissertation focuses on studying various network formation games in Economics. We explore a different model in each chapter to capture various aspects of networks. Chapter 1provides an overview of this dissertation. Chapter 2 studies the possible Nash equilibrium configurations in a model of signed network formation as proposed by Hiller (2017). We specify the Nash equilibria in the case of heterogeneous agents. We find 3 possible Nash equilibrium configurations: Utopia network, positive assortative matching, and disassortative matching. We derive the specific conditions under which they arise in a Nash equilibrium. In Chapter 3, we study a generalized model of signed network formation game where the players can choose not only positive and negative links but also neutral links. We check whether the results of the signed network formation model in the literature still hold in our generalized framework using the notion of pairwise Nash equilibrium. Chapter 4 studies inequality in a weighted network formation model using the notion of Nash equilibrium. As a factor of inequality, there are two types of players: Rich players and poor players. We show that both rich and poor players designate other rich players as their best friends. As a result, We present that nested split graphs are drawn from survey data because researchers tend to ask respondents to list only a few friends. / Doctor of Philosophy / This dissertation focuses on studying various network formation games in Economics. We explore a different model in each chapter to capture various aspects of networks. Chapter 1 provides an overview of this dissertation. Chapter 2 studies the possible singed network configurations in equilibrium. In the signed network, players can choose a positive (+) relationship or a negative (-) relationship toward each other player. We study the case that the players are heterogeneous. We find 3 possible categories of networks in equilibrium: Utopia network, positive assortative matching, and disassortative matching. We derive the specific conditions under which they arise in equilibrium. In Chapter 3, we study a generalized model of signed network formation game where the players can choose not only positive and negative links but also neutral links. We check whether the results of the signed network formation model in the literature still hold in our generalized framework. Chapter 4 studies inequality in a weighted network formation model using the notion of Nash equilibrium. In this weighted network model, each player can choose the level of relationship. As a factor of inequality, there are two types of players: rich players and poor players. We show that both rich and poor players choose other rich players as their best friends. As a result, we present that nested split graphs are drawn from survey data because these social network data are censored due to the limit of the number of responses.

The fidelity of biological processes and reactions, inspite of the widespread diversity, is programmed by highly specific physico-chemical principles. This underlines our basic understanding of different interesting phenomena of biological relevance, ranging from enzyme specificity to allosteric communication, from selection of fold to structural organization / states of oligomerization, from half-sites-reactivity to reshuffling of the conformational free energy landscape, encompassing the dogma of sequence-structure dynamics-function of macromolecules. The role of striking an optimal balance between rigidity and flexibility in macromolecular 3D structural organisation is yet another concept that needs attention from the functional perspective. Needless to say that the variety of protein structures and conformations naturally leads to the diversity of their function and consequently many other biological functions in general. Classical models of allostery like the ‘MWC model’ or the ‘KNF model’ and the more recently proposed ‘population shift model’ have advanced our understanding of the underlying principles of long range signal transfer in macromolecules. Extensive studies have also reported the importance of the fold selection and 3D structural organisation in the context of macromolecular function. Also ligand induced conformational changes in macromolecules, both subtle and drastic, forms the basis for controlling several biological processes in an ordered manner by re-organizing the free energy landscape. The above mentioned biological phenomena have been observed from several different biochemical and biophysical approaches. Although these processes may often seem independent of each other and are associated with regulation of specialized functions in macromolecules, it is worthwhile to investigate if they share any commonality or interdependence at the detailed atomic level of the 3D structural organisation. So the nagging question is, do these diverse biological processes have a unifying theme, when probed at a level that takes into account even subtle re-orchestrations of the interactions and energetics at the protein/nucleic acid side-chain level. This is a complex problem to address and here we have made attempts to examine this problem using computational tools. Two methods have been extensively applied: Molecular Dynamics (MD) simulations and network theory and related parameters. Network theory has been extensively used in the past in several studies, ranging from analysis of social networks to systems level networks in biology (e.g., metabolic networks) and have also found applications in the varied fields of physics, economics, cartography and psychology. More recently, this concept has been applied to study the intricate details of the structural organisation in proteins, providing a local view of molecular interactions from a global perspective. On the other hand, MD simulations capture the dynamics of interactions and the conformational space associated with a given state (e.g., different ligand-bound states) of the macromolecule. The unison of these two methods enables the detection and investigation of the energetic and geometric re-arrangements of the 3D structural organisation of macromolecule/macromolecular complexes from a dynamical or ensemble perspective and this has been one of the thrust areas of the current study. So we not only correlate structure and functions in terms of subtle changes in interactions but also bring in conformational dynamics into the picture by studying such changes along the MD ensemble. The focus was to identify the subtle rearrangements of interactions between non-covalently interacting partners in proteins and the interacting nucleic acids. We propose that these rearrangements in interactions between residues (amino acids in proteins, nucleic acids in RNA/DNA) form the common basis for different biological phenomena which regulates several apparently unrelated processes in biology. Broadly, the major goal of this work is to elucidate the physico-chemical principles underlying some of the important biological phenomena, such as allosteric communication, ligand induced modulation of rigidity/flexibility, half-sites-reactivity and so on, in molecular details. We have investigated several proteins, protein-RNA/DNA complexes to formulate general methodologies to address these questions from a molecular perspective. In the process we have also specifically illuminated upon the mechanistic aspects of the aminoacylation reaction by aminoacyl-tRNA synthetases like tryptophanyl and pyrrolysyl tRNA synthetase, structural details related to an enzyme catalyzed reaction that influences the process of quorum sensing in bacteria. Further, we have also examined the ‘dynamic allosterism’ that manipulates the activity of MutS, a prominent component of the DNA bp ‘mismatch repair’ machinery. Additionally, our protein structure network (PSN) based studies on a dataset of Rossmann fold containing proteins have provided insights into the structural signatures that drive the adoption of a fold from a repertoire of diverse sequences. Ligand induced percolations distant from the active sites, which may be of functional relevance have also been probed, in the context of the S1A family of serine proteases. In the course of our investigation, we have borrowed several concepts of network parameters from social network analysis and have developed new concepts. The Introduction (Chapter-1) summarizes the relevant literature and lays down a suitable background for the subsequent chapters in the thesis. The major questions addressed and the main goal of this thesis are described to set an appropriate stage for the detailed discussions. The methodologies involved are discussed in Chapter-2. Chapter-3 deals with a protein, LuxS that is involved in the bacterial quorum sensing; the first part of the chapter describes the application of network analysis on the static structures of several LuxS proteins from different organisms and the second part of this chapter describes the application of a dynamic network approach to analyze the MD trajectories of H.pylori LuxS. Chapter-4 focuses on the investigation of human tryptophanyl-tRNA synthetase (hTrpRS), with an emphasis to identify ligand induced subtle conformational changes in terms of the alternation of rigidity/flexibility at different sites and the re-organisation of the free energy landscape. Chapter-5 presents a novel application of a quantum clustering (QC) technique, popular in the fields of pattern recognition, to objectively cluster the conformations, sampled by molecular dynamics simulations performed on different ligand bound structures of the protein. The protein structure network (PSN) in the earlier studies were constituted on the basis of geometric interactions. In Chapters 6 and 7, we describe the networks (proteins+nucleic acids) using interaction energy as edges, thus incorporating the detailed chemistry in terms of an energy-weighted complex network. Chapter-6 describes an application of the energy weighted network formalism to probe allosteric communication in D.hafniense pyrrolysyl-tRNA synthetase. The methodology developed for in-depth study of ligand induced changes in DhPylRS has been adopted to the protein MutS, the first ‘check-point protein’ for DNA base pair (bp) mismatch repair. In Chapter-7, we describe the network analysis and the biological insights derived from this study (the work is done in collaboration with Prof. David Beveridge and Dr. Susan Pieniazek). Chapter-8 describes the application of a network approach to capture the ligand-induced subtle global changes in protein structures, using a dataset of high resolution structures from the S1A family of serine proteases. Chapter-9 deals with probing the structural rationale behind diverse sequences adopting the same fold with the NAD(P)-binding Rossmann fold as a case study. Future directions are discussed in the final chapter of the thesis (Chapter-10).