Community Detection in Quantum Complex Networks

Determining community structure is a central topic in the study of complex networks, be it technological, social, biological or chemical, in static or interacting systems. In this paper, we extend the concept of community detection from classical to quantum systems---a crucial missing component of a theory of complex networks based on quantum mechanics. We demonstrate that certain quantum mechanical effects cannot be captured using current classical complex network tools and provide new methods that overcome these problems. Our approaches are based on defining closeness measures between nodes, and then maximizing modularity with hierarchical clustering. Our closeness functions are based on quantum transport probability and state fidelity, two important quantities in quantum information theory. To illustrate the effectiveness of our approach in detecting community structure in quantum systems, we provide several examples, including a naturally occurring light-harvesting complex, LHCII. The prediction of our simplest algorithm, semiclassical in nature, mostly agrees with a proposed partitioning for the LHCII found in quantum chemistry literature, whereas our fully quantum treatment of the problem uncovers a new, consistent, and appropriately quantum community structure.Comment: 16 pages, 4 figures, 1 tabl

Structured iterative alternating sparse matrix decomposition for thermal imaging diagnostic system

In this paper, we propose a structured iterative alternating sparse matrix decomposition to efficiently decompose the input multidimensional data from active thermography into the sum of a low-rank matrix, a sparse matrix, and a noise matrix. In particular, the sparse matrix is further factorized into a pattern constructed dictionary matrix and a coefficient matrix. The estimation of the dictionary matrix and coefficient matrix is based on integrating the vertex component analysis with the framework of the alternating direction method of multipliers. In addition, the joint structure sparsity and nonnegative constraint are emphasized as part of the learning strategy. In order to verify the effectiveness and robustness of the proposed method, experimental studies have been carried out by applying the proposed method to thermal imaging diagnostic system for carbon fiber reinforced plastics (CFRP) defects detections. The validation study has been conducted by comparing the proposed method with the current state-of-the-art algorithms. The results indicate that the proposed method significantly improves the contrast ratio between the defective regions and the non-defective regions

Dissémination de l’information et dynamique des opinions dans les réseaux sociaux

Our aim in this Ph. D. thesis is to study the diffusion of information as well as the opinion dynamics of users in social networks. Information diffusion models explore the paths taken by information being transmitted through a social network in order to understand and analyze the relationships between users in such network, leading to a better comprehension of human relations and dynamics. This thesis is based on both sides of information diffusion: first by developing mathematical theories and models to study the relationships between people and information, and in a second time by creating tools to better exploit the hidden patterns in these relationships. The theoretical tools developed in this thesis are opinion dynamics models and information diffusion models, where we study the information flow from users in social networks, and the practical tools developed in this thesis are a novel community detection algorithm and a novel trend detection algorithm. We start by introducing an opinion dynamics model in which agents interact with each other about several distinct opinions/contents. In our framework, agents do not exchange all their opinions with each other, they communicate about randomly chosen opinions at each time. We show, using stochastic approximation algorithms, that under mild assumptions this opinion dynamics algorithm converges as time increases, whose behavior is ruled by how users choose the opinions to broadcast at each time. We develop next a community detection algorithm which is a direct application of this opinion dynamics model: when agents broadcast the content they appreciate the most. Communities are thus formed, where they are defined as groups of users that appreciate mostly the same content. This algorithm, which is distributed by nature, has the remarkable property that the discovered communities can be studied from a solid mathematical standpoint. In addition to the theoretical advantage over heuristic community detection methods, the presented algorithm is able to accommodate weighted networks, parametric and nonparametric versions, with the discovery of overlapping communities a byproduct with no mathematical overhead. In a second part, we define a general framework to model information diffusion in social networks. The proposed framework takes into consideration not only the hidden interactions between users, but as well the interactions between contents and multiple social networks. It also accommodates dynamic networks and various temporal effects of the diffusion. This framework can be combined with topic modeling, for which several estimation techniques are derived, which are based on nonnegative tensor factorization techniques. Together with a dimensionality reduction argument, this techniques discover, in addition, the latent community structure of the users in the social networks. At last, we use one instance of the previous framework to develop a trend detection algorithm designed to find trendy topics in a social network. We take into consideration the interaction between users and topics, we formally define trendiness and derive trend indices for each topic being disseminated in the social network. These indices take into consideration the distance between the real broadcast intensity and the maximum expected broadcast intensity and the social network topology. The proposed trend detection algorithm uses stochastic control techniques in order calculate the trend indices, is fast and aggregates all the information of the broadcasts into a simple one-dimensional process, thus reducing its complexity and the quantity of necessary data to the detection. To the best of our knowledge, this is the first trend detection algorithm that is based solely on the individual performances of topicsLa dissémination d'information explore les chemins pris par l'information qui est transmise dans un réseau social, afin de comprendre et modéliser les relations entre les utilisateurs de ce réseau, ce qui permet une meilleur compréhension des relations humaines et leurs dynamique. Même si la priorité de ce travail soit théorique, en envisageant des aspects psychologiques et sociologiques des réseaux sociaux, les modèles de dissémination d'information sont aussi à la base de plusieurs applications concrètes, comme la maximisation d'influence, la prédication de liens, la découverte des noeuds influents, la détection des communautés, la détection des tendances, etc. Cette thèse est donc basée sur ces deux facettes de la dissémination d'information: nous développons d'abord des cadres théoriques mathématiquement solides pour étudier les relations entre les personnes et l'information, et dans un deuxième moment nous créons des outils responsables pour une exploration plus cohérente des liens cachés dans ces relations. Les outils théoriques développés ici sont les modèles de dynamique d'opinions et de dissémination d'information, où nous étudions le flot d'informations des utilisateurs dans les réseaux sociaux, et les outils pratiques développés ici sont un nouveau algorithme de détection de communautés et un nouveau algorithme de détection de tendances dans les réseaux sociau

Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure

Mining Time-aware Actor-level Evolution Similarity for Link Prediction in Dynamic Network

Topological evolution over time in a dynamic network triggers both the addition and deletion of actors and the links among them. A dynamic network can be represented as a time series of network snapshots where each snapshot represents the state of the network over an interval of time (for example, a minute, hour or day). The duration of each snapshot denotes the temporal scale/sliding window of the dynamic network and all the links within the duration of the window are aggregated together irrespective of their order in time. The inherent trade-off in selecting the timescale in analysing dynamic networks is that choosing a short temporal window may lead to chaotic changes in network topology and measures (for example, the actors’ centrality measures and the average path length); however, choosing a long window may compromise the study and the investigation of network dynamics. Therefore, to facilitate the analysis and understand different patterns of actor-oriented evolutionary aspects, it is necessary to define an optimal window length (temporal duration) with which to sample a dynamic network. In addition to determining the optical temporal duration, another key task for understanding the dynamics of evolving networks is being able to predict the likelihood of future links among pairs of actors given the existing states of link structure at present time. This phenomenon is known as the link prediction problem in network science. Instead of considering a static state of a network where the associated topology does not change, dynamic link prediction attempts to predict emerging links by considering different types of historical/temporal information, for example the different types of temporal evolutions experienced by the actors in a dynamic network due to the topological evolution over time, known as actor dynamicities. Although there has been some success in developing various methodologies and metrics for the purpose of dynamic link prediction, mining actor-oriented evolutions to address this problem has received little attention from the research community. In addition to this, the existing methodologies were developed without considering the sampling window size of the dynamic network, even though the sampling duration has a large impact on mining the network dynamics of an evolutionary network. Therefore, although the principal focus of this thesis is link prediction in dynamic networks, the optimal sampling window determination was also considered

Combining network neuroscience and machine learning to discover neurocognitive subgroups in aging individuals at risk of or diagnosed with Alzheimer’s disease

Dementia is a complicated medical condition that negatively impacts an individual’s mental and physical well-being, increasing the risk of early mortality. The risk of developing dementia increases with age, although rates vary according to several factors, such as sex, race, and genetics. While Alzheimer’s disease (AD), the most common form of dementia, is often associated with episodic memory impairment, individuals with AD can present with diverse cognitive profiles. Similarly, heterogeneous subgroups of typically aging individuals may show impairments in both general and specific forms of attention, memory, and/or executive functioning. Individual variation in cognitive impairments experienced by aging individuals, and resistance or resilience to cognitive decline, can be linked to functional brain network organization and communication capacity. This study aimed to disentangle shared and unique aspects of cognitive impairment and functional network topology seen in healthy aging, early-stage or preclinical dementia, and AD. Specifically, Aim 1 sought to establish if weighted metrics that index redundancy in unthresholded functional brain networks, as a proxy of brain and cognitive reserve, support general and/or specific forms of cognition. Aim 2 sought to establish whether a combination of core demographic risk factors (age, sex, and education), cognitive measures, and weighted functional network metrics could accurately distinguish otherwise cognitively normal individuals (CN), from CN who will convert to AD (AD-C), and individuals diagnosed with AD, using supervised machine learning. Aim 3 specifically sought to quantify the presence of data-driven neurocognitive subgroups utilizing a combination of unsupervised and supervised machine learning. In the present study, redundancy-based metrics (global communicability and global clustering coefficient) were not predictive of overall cognitive functioning, nor were they the most informative predictors when attempting to distinguish between CN, AD-C, and AD participants using machine learning. When classifying older individuals with and without AD, neuropsychological measures were more informative than metrics assessing global network topology, including redundancy-based measures. Finally, while this study failed to identify cognitive subgroups previously reported in MCI and AD participants, AD converters correctly classified or misclassified as AD showed diverging neurocognitive profiles and may represent a subset of individuals with primarily executive, as opposed to memory-related impairments, respectively.Doctor of Philosoph

Community landscapes: an integrative approach to determine overlapping network module hierarchy, identify key nodes and predict network dynamics

Background: Network communities help the functional organization and evolution of complex networks. However, the development of a method, which is both fast and accurate, provides modular overlaps and partitions of a heterogeneous network, has proven to be rather difficult. Methodology/Principal Findings: Here we introduce the novel concept of ModuLand, an integrative method family determining overlapping network modules as hills of an influence function-based, centrality-type community landscape, and including several widely used modularization methods as special cases. As various adaptations of the method family, we developed several algorithms, which provide an efficient analysis of weighted and directed networks, and (1) determine pervasively overlapping modules with high resolution; (2) uncover a detailed hierarchical network structure allowing an efficient, zoom-in analysis of large networks; (3) allow the determination of key network nodes and (4) help to predict network dynamics. Conclusions/Significance: The concept opens a wide range of possibilities to develop new approaches and applications including network routing, classification, comparison and prediction.Comment: 25 pages with 6 figures and a Glossary + Supporting Information containing pseudo-codes of all algorithms used, 14 Figures, 5 Tables (with 18 module definitions, 129 different modularization methods, 13 module comparision methods) and 396 references. All algorithms can be downloaded from this web-site: http://www.linkgroup.hu/modules.ph

Data-Based And Theory-Based Network Models Of Perturbations To Neural Dynamics

Much of neuroscience is centered on uncovering simple principles that constrain the behavior of the brain. When considering the formation of neural architectures, similar structures can be recreated following the principles of minimizing wiring and maximizing topological complexity. However, a similar understanding of neural dynamics on top of these structural connections has not yet been achieved. One promising strategy for identifying underlying principles of neural dynamics is quantifying and modeling the response of neural systems to perturbation. Here, we use a spectrum of data- and theory-based network models to characterize the response of neural systems to different types of perturbations. We report how functional networks change in the context of pathological epileptic activity and brain-computer interface control. We also specifically test one possible principle: that activity is constrained to spread along connections in both the context of brain-computer interfaces and direct electrical stimulation. In the first study, we demonstrate across a wide variety of functional connectivity metrics and frequency bands that epileptic activity increases amplitude-based functional interactions, an observation that can now be incorporated into future theory-based models. In a second study, we determine that modeling activity that is constrained to spread along connections suggests why certain connections are important for brain-computer interface learning; specifically, these connections support sustained activity in attention regions. In our third study, we demonstrate that modeling activity changes from direct electrical stimulation using white matter connectivity explains more variance than models with rewired connections. This model generates testable predictions about which individuals, regions, and time points would lead to successful applications of direct electrical stimulation. Overall, this work demonstrates the potential uses of a range of data- and theory-based models for uncovering simple guiding principles that determine the behavior of a system. It also uses one specific principle - that activity is constrained to spread along connections - to understand the role of specific connections that may support learning, and provide a method to optimize individually tailored stimulation therapies for a specific outcome

Optimisation and information-theoretic principles in multiplex networks.

PhD ThesesThe multiplex network paradigm has proven very helpful in the study of many real-world complex systems, by allowing to retain full information about all the different possible kinds of relationships among the elements of a system. As a result, new non-trivial structural patterns have been found in diverse multi-dimensional networked systems, from transportation networks to the human brain. However, the analysis of multiplex structural and dynamical properties often requires more sophisticated algorithms and takes longer time to run compared to traditional single network methods. As a consequence, relying on a multiplex formulation should be the outcome of a trade-off between the level of information and the resources required to store it. In the first part of the thesis, we address the problem of quantifying and comparing the amount of information contained in multiplex networks. We propose an algorithmic informationtheoretic approach to evaluate the complexity of multiplex networks, by assessing to which extent a given multiplex representation of a system is more informative than a single-layer graph. Then, we demonstrate that the same measure is able to detect redundancy in a multiplex network and to obtain meaningful lower-dimensional representations of a system. We finally show that such method allows us to retain most of the structural complexity of the original system as well as the salient characteristics determining the behaviour of dynamical processes happening on it. In the second part of the thesis, we shift the focus to the modelling and analysis of some structural features of real-world multiplex systems throughout optimisation principles. We demonstrate that Pareto optimal principles provide remarkable tools not only to model real-world multiplex transportation systems but also to characterise the robustness of multiplex systems against targeted attacks in the context of optimal percolation