Spatio-temporal data have become increasingly prevalent and important for both science and enterprises. Such data are typically embedded in a grid with a resolution larger than the true dimensionality of the underlying system. One major task is to identify the distinct semi-autonomous functional components of the spatio-temporal system and to infer their interconnections. In this thesis, we propose two methods that identify the functional components of a spatio-temporal system. Next, an edge inference process identifies the possibly lagged and weighted connections between the system’s components. The weight of an edge accounts for the magnitude of the interaction between two components; the lag associated with each edge accounts for the temporal ordering of these interactions. The first method, geo-Cluster, infers the spatial components as “areas”; spatially contiguous, non-overlapping, sets of grid cells satisfying a homogeneity constraint in terms of their average pair-wise cross-correlation. However, in real physical systems the underlying physical components might overlap. To this end we also propose δ-MAPS, a method that first identifies the epicenters of activity of the functional components of the system and then creates domains – spatially contiguous, possibly overlapping, sets of grid cells that satisfy the same homogeneity constraint. The proposed framework is applied in climate science and neuroscience. We show how these methods can be used to evaluate cutting edge climate models and identify lagged relationships between different climate regions. In the context of neuroscience, the method successfully identifies well-known “resting state networks” as well as a few areas forming the backbone of the functional cortical network. Finally, we contrast the proposed methods to dimensionality reduction techniques (e.g., clustering PCA/ICA) and show their limitations.

Network science has provided useful answers to research questions in many fields, from biology to social science, from ecology to urban science. The first analyses of networked systems focused on binary networks, where only the topology of the connections were considered. Soon network scientists started considering weighted networks, to represent interactions with different strength, cost, or distance in space and time. Also, connections are not fixed but change over time. This is why in more recent years, a lot of attention has been devoted to temporal or time-varying networks. We now entered the era of multi-layer networks, or multiplex networks, relational systems whose units are connected by different relationships, with links of distinct types embedded in different layers. Multiplexity has been observed in many contexts, from social network analysis to economics, medicine and ecology. The new challenge consists in applying the new tools of multiplex theory to unveil the richness associated to this novel level of complexity. How do agents organise their interactions across layers? How does this affect the dynamics of the system? In the first part of the thesis, we provide a mathematical framework to deal with multiplex networks. We suggest metrics to unveil multiplexity from basic node, layer and edge properties to more complicated structure at the micro- and meso-scale, such as motifs, communities and cores. Measures are validated through the analysis of real-world systems such as social and collaboration networks, transportation systems and the human brain. In the second part of the thesis we focus on dynamical processes taking place on top of multiplex networks, namely biased random walks, opinion dynamics, cultural dynamics and evolutionary game theory. All these examples show how multiplexity is crucial to determine the emergence of unexpected and instrinsically multiplex collective behavior, opening novel perspectives for the field of non-linear dynamics on networks.

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This book, then, starts with a general statement: that regulators should try, wherever possible, to use the physical methodological tools presently available in order to draft better legislation. While such an assertion may be applied to the law in general, this work will concentrate on the much narrower area of Internet regulation and the science of complex networks The Internet is the subject of this book not only because it is my main area of research, but also because –without over-emphasising the importance of the Internet to everyday life– one cannot deny that the growth and popularisation of the global communications network has had a tremendous impact on the way in which we interact with one another. The Internet is, however, just one of many interactive networks. One way of looking at the complex and chaotic nature of society is to see it as a collection of different nodes of interaction. Humans are constantly surrounded by networks: the social network, the financial network, the transport network, the telecommunications network and even the network of our own bodies. Understanding how these systems operate and interact with one another has been the realm of physicists, economists, biologists and mathematicians. Until recently, the study of networks has been mainly theoretical and academic, because it is difficult to gather data about large and complex systems that is sufficiently reliable to support proper empirical application. In recent years, though, the Internet has given researchers the opportunity to study and test the mathematical descriptions of these vast complex systems. The growth rate and structure of cyberspace has allowed researchers to map and test several previously unproven theories about how links and hubs within networks interact with one another. The Web now provides the means with which to test the organisational structures, architecture and growth of networks, and even permits some limited prediction about their behaviour, strengths and vulnerabilities. The main objective of this book is first and foremost to serve as an introduction to the wider legal audience to some of the theories of complexity and networks. The second objective is more ambitious. By looking at the application of complexity theory and network science in various areas of Internet regulation, it is hoped that there will be enough evidence to postulate a theory of Internet regulation based on network science. To achieve these two goals, Chapter 2 will look in detail at the science of complex networks to set the stage for the legal and regulatory arguments to follow. With the increase in reliability of the descriptive (and sometimes predictive) nature of network science, a logical next step for legal scholars is to look at the legal implications of the characteristics of networks. Chapter 3 highlights the efforts of academics and practitioners who have started to find potential uses for network science tools. Chapter 4 takes this idea further, and explores how network theory can shape Internet regulation. The following chapters will analyse the potential for application of the tools described in the previous chapters, applying complexity theory to specific areas of study related to Internet Law. Chapter 5 deals with the subject of copyright in the digital world. Chapter 6 explores the issue of peer-production and user-generated content using network science as an analytical framework. Chapter 7 finishes the evidence section of the work by studying the impact of network architecture in the field of cybercrime, and asks whether the existing architecture hinders or assists efforts to tackle those problems. It is clear that these are very disparate areas of study. It is not the intention of this book to be overreaching in its scope, although I am mindful that it covers a lot of ground and attempts to study and describe some disciplines that fall outside of my intellectual comfort zone. While the focus of the work is the Internet, its applications may extend beyond mere electronic bits. Without trying to be over-ambitious, it is my strong belief that legal scholarship has been neglectful in that it has been slow to respond to the wealth of research into complexity. That is not to say that there has been no legal research on the topic, but it would seem that lawyers, legislators and policy-makers are reluctant to consider technical solutions to legal problems. It is hoped then that this work will serve as a stepping stone that will lead to new interest in some of the theories that I describe.

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The main idea of this thesis is to define and formulate the role of cognitive control in cognitive dynamic systems and complex networks in order to control the directed flow of information. A cognitive dynamic system is based on Fuster's principles of cognition, the most basic of which is the so-called global perception-action cycle, that the other three build on. Cognitive control, by definition, completes the executive part of this important cycle. In this thesis, we first provide the rationales for defining cognitive control in a way that it suits engineering requirements. To this end, the novel idea of entropic state and thereby the two-state model is first described. Next, on the sole basis of entropic state and the concept of directed information flow, we formulate the learning algorithm as the first process of cognitive control. Most importantly, we show that the derived algorithm is indeed a special case of the celebrated Bellman's dynamic programming. Another significant key point is that cognitive control intrinsically differs from the generic dynamic programming and its approximations (commonly known as reinforcement learning) in that it is stateless by definition. As a result, the main two desired characteristics of the derived algorithm are described as follows: a) it is convergent to optimal policy, and b) it is free of curse of dimensionality. Next, the predictive planning is described as the second process of cognitive control. The planning process is on the basis of shunt cycles (called mutually composite cycles herein) to bypass the environment and facilitate the prediction of future global perception-action cycles. Our results demonstrate predictive planning to have a very significant improvement to the functionality of cognitive control. We also deploy the explore/exploit strategy in order to apply a simplistic form of executive attention. The thesis is then expanded by applying cognitive control into two different applications of practical importance. The first one involves cognitive tracking radar, which is based on a benchmark example and provides the means for testing the theory. In order to have a frame of reference, the results are compared to other cognitive controllers, which use traditional Q-learning and the method of dynamic optimization. In both cases, the new algorithm demonstrates considerable improvement with less computational load. For the second application, the problem of observability in stochastic complex networks has been picked due to its importance in many practical situations. Having known cognitive control theory and its significant performance, the idea here is to view the network as the environment of a cognitive dynamic system; thereby, cognitive dynamic system with the cognitive controller plays a supervisory role over the network. The proposed methodology differs from the state-of-the-art in the literature in two accounts: 1) stochasticity both in modelling as well as monitoring processes, and 2) complexity in terms of edge density. We present several examples to demonstrate the information processing power of cognitive control in this context too. The thesis will finish by drawing line for future research in three main directions. / Thesis / Doctor of Philosophy (PhD)

Innovation is defined as the introduction of new things or methods. In the history of human society, progress and cultural evolution occurred as a consequence of innovation processes. Typically changes proposed by a restricted number of peoples became widely adopted innovations as soon as a broad consensus formed around their adoption. In this thesis, we explore the role of innovators as potentially influential individuals in our society. Studying their behaviour is crucial to understand what are the factors that drove their decision in the process of becoming influential. In particular, here we uncover the importance of cultural attractors as cities where strong akin communities are present. Our approach involves the use of Wikipedia as a source for historical mobility data to model the migration patterns of globally relevant innovators. While here we study mobility on a broad range of different disciplines where different innovators gave their contributions, we also focus on a smaller and more modern system. Historical innovators are easily identified and discerned from uninfluential ones thanks to the wisdom of the time. However, due to the scarce availability of individual historical data, we point our attention to more recent versions of innovators: code developer. The flourishment of the digital era made code developers at the very centre of our global economy. We study this coupled system as a representative example of the interaction between innovators and the economy. Indeed, a significant, non-trivial interaction is found among the two worlds. More in general, in this thesis we highlight the relevance of innovators in shaping human collective responses. Our results reveal that innovators play a major role both individually and collectively at different scales. We provide measures of these effects (i) by looking at how innovator communities construct the attractiveness of a city and (ii) by studying how individual contributions in the innovation domain can dramatically affect financial behaviour also at short time scales. Our result expands the evidence of the need for a new research dimension, where human behaviour is studied as a complex system moving over an intricate network of intertwined interactions.

The advent of advanced high-throughput biological technologies provides opportunities to measure the whole genome at different molecular levels in biological systems, which produces different types of omic data such as genome, epigenome, transcriptome, translatome, proteome, metabolome and interactome. Biological systems are highly dynamic and complex mechanisms which involve not only the within-level functionality but also the between-level regulation. In order to uncover the complexity of biological systems, it is desirable to integrate multi-omic data to transform the multiple level data into biological knowledge about the underlying mechanisms. Due to the heterogeneity and high-dimension of multi-omic data, it is necessary to develop effective and efficient methods for multi-omic data integration. This thesis aims to develop efficient approaches for multi-omic data integration using machine learning methods and network theory. We assume that a biological system can be represented by a network with nodes denoting molecules and edges indicating functional links between molecules, in which multi-omic data can be integrated as attributes of nodes and edges. We propose four network-based approaches for multi-omic data integration using machine learning methods. Firstly, we propose an approach for gene module detection by integrating multi-condition transcriptome data and interactome data using network overlapping module detection method. We apply the approach to study the transcriptome data of human pre-implantation embryos across multiple development stages, and identify several stage-specific dynamic functional modules and genes which provide interesting biological insights. We evaluate the reproducibility of the modules by comparing with some other widely used methods and show that the intra-module genes are significantly overlapped between the different methods. Secondly, we propose an approach for gene module detection by integrating transcriptome, translatome, and interactome data using multilayer network. We apply the approach to study the ribosome profiling data of mTOR perturbed human prostate cancer cells and mine several translation efficiency regulated modules associated with mTOR perturbation. We develop an R package, TERM, for implementation of the proposed approach which offers a useful tool for the research field. Next, we propose an approach for feature selection by integrating transcriptome and interactome data using network-constrained regression. We develop a more efficient network-constrained regression method eGBL. We evaluate its performance in term of variable selection and prediction, and show that eGBL outperforms the other related regression methods. With application on the transcriptome data of human blastocysts, we select several interested genes associated with time-lapse parameters. Finally, we propose an approach for classification by integrating epigenome and transcriptome data using neural networks. We introduce a superlayer neural network (SNN) model which learns DNA methylation and gene expression data parallelly in superlayers but with cross-connections allowing crosstalks between them. We evaluate its performance on human breast cancer classification. The SNN provides superior performances and outperforms several other common machine learning methods. The approaches proposed in this thesis offer effective and efficient solutions for integration of heterogeneous high-dimensional datasets, which can be easily applied to other datasets presenting the similar structures. They are therefore applicable to many fields including but not limited to Bioinformatics and Computer Science.

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (leaves [285]-291).

<div>This study explores historical syntactic changes within a complex network framework focusing on the development of the German verb <i>werden</i> (to become) and the emergence of the related passive and future periphrases. The data are collected from a corpus of Middle and Early New High German texts and the analysis of the instances is carried out in two different stages. The first stage focuses on the frequency of the verb <i>werden</i> and the elements that co-occurred with it throughout Middle and Early New High German. The second stage investigates the same instances through a complex network framework by applying descriptive statistics to uncover the features of the Middle and Early New High German networks that have been created with the occurrences of<i> werden</i> found in the corpus.</div><div><br></div><div><div>The results of the analysis show that <i>werden</i> experienced an increase in the type of connections it was able to establish throughout the centuries. Such a process is known in the literature as preferential attachment. This suggests that linguistic networks, and specifically, syntactic networks, are also subjected to processes that are common among non-linguistic networks.</div></div>