Dynamical Systems on Networks: A Tutorial

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than original version, some reorganization and also more pointers to interesting direction

Applications of Artificial Intelligence in Battling Against Covid-19: A Literature Review

© 2020 Elsevier Ltd. All rights reserved.Colloquially known as coronavirus, the Severe Acute Respiratory Syndrome CoronaVirus 2 (SARS-CoV-2), that causes CoronaVirus Disease 2019 (COVID-19), has become a matter of grave concern for every country around the world. The rapid growth of the pandemic has wreaked havoc and prompted the need for immediate reactions to curb the effects. To manage the problems, many research in a variety of area of science have started studying the issue. Artificial Intelligence is among the area of science that has found great applications in tackling the problem in many aspects. Here, we perform an overview on the applications of AI in a variety of fields including diagnosis of the disease via different types of tests and symptoms, monitoring patients, identifying severity of a patient, processing covid-19 related imaging tests, epidemiology, pharmaceutical studies, etc. The aim of this paper is to perform a comprehensive survey on the applications of AI in battling against the difficulties the outbreak has caused. Thus we cover every way that AI approaches have been employed and to cover all the research until the writing of this paper. We try organize the works in a way that overall picture is comprehensible. Such a picture, although full of details, is very helpful in understand where AI sits in current pandemonium. We also tried to conclude the paper with ideas on how the problems can be tackled in a better way and provide some suggestions for future works.Peer reviewe

INDIGO: a generalized model and framework for performance prediction of data dissemination

According to recent studies, an enormous rise in location-based mobile services is expected in future. People are interested in getting and acting on the localized information retrieved from their vicinity like local events, shopping offers, local food, etc. These studies also suggested that local businesses intend to maximize the reach of their localized offers/advertisements by pushing them to the maxi- mum number of interested people. The scope of such localized services can be augmented by leveraging the capabilities of smartphones through the dissemination of such information to other interested people. To enable local businesses (or publishers) of localized services to take in- formed decision and assess the performance of their dissemination-based localized services in advance, we need to predict the performance of data dissemination in complex real-world scenarios. Some of the questions relevant to publishers could be the maximum time required to disseminate information, best relays to maximize information dissemination etc. This thesis addresses these questions and provides a solution called INDIGO that enables the prediction of data dissemination performance based on the availability of physical and social proximity information among people by collectively considering different real-world aspects of data dissemination process. INDIGO empowers publishers to assess the performance of their localized dissemination based services in advance both in physical as well as the online social world. It provides a solution called INDIGO–Physical for the cases where physical proximity plays the fundamental role and enables the tighter prediction of data dissemination time and prediction of best relays under real-world mobility, communication and data dissemination strategy aspects. Further, this thesis also contributes in providing the performance prediction of data dissemination in large-scale online social networks where the social proximity is prominent using INDIGO–OSN part of the INDIGO framework under different real-world dissemination aspects like heterogeneous activity of users, type of information that needs to be disseminated, friendship ties and the content of the published online activities. INDIGO is the first work that provides a set of solutions and enables publishers to predict the performance of their localized dissemination based services based on the availability of physical and social proximity information among people and different real-world aspects of data dissemination process in both physical and online social networks. INDIGO outperforms the existing works for physical proximity by providing 5 times tighter upper bound of data dissemination time under real-world data dissemination aspects. Further, for social proximity, INDIGO is able to predict the data dissemination with 90% accuracy and differently, from other works, it also provides the trade-off between high prediction accuracy and privacy by introducing the feature planes from an online social networks

Networking - A Statistical Physics Perspective

Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption require new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with non-linear large scale systems. This paper aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.Comment: (Review article) 71 pages, 14 figure

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Diffusion and Supercritical Spreading Processes on Complex Networks

Die große Menge an Datensätzen, die in den letzten Jahren verfügbar wurden, hat es ermöglicht, sowohl menschlich-getriebene als auch biologische komplexe Systeme in einem beispiellosen Ausmaß empirisch zu untersuchen. Parallel dazu ist die Vorhersage und Kontrolle epidemischer Ausbrüche für Fragen der öffentlichen Gesundheit sehr wichtig geworden. In dieser Arbeit untersuchen wir einige wichtige Aspekte von Diffusionsphänomenen und Ausbreitungsprozeßen auf Netzwerken. Wir untersuchen drei verschiedene Probleme im Zusammenhang mit Ausbreitungsprozeßen im überkritischen Regime. Zunächst untersuchen wir die Reaktionsdiffusion auf Ensembles zufälliger Netzwerke, die durch die beobachteten Levy-Flugeigenschaften der menschlichen Mobilität charakterisiert sind. Das zweite Problem ist die Schätzung der Ankunftszeiten globaler Pandemien. Zu diesem Zweck leiten wir geeignete verborgene Geometrien netzgetriebener Streuprozeße, unter Nutzung der Random-Walk-Theorie, her und identifizieren diese. Durch die Definition von effective distances wird das Problem komplexer raumzeitlicher Muster auf einfache, homogene Wellenausbreitungsmuster reduziert. Drittens führen wir durch die Einbettung von Knoten in den verborgenen Raum, der durch effective distances im Netzwerk definiert ist, eine neuartige Netzwerkzentralität ein, die ViralRank genannt wird und quantifiziert, wie nahe ein Knoten, im Durchschnitt, den anderen Knoten im Netzwerk ist. Diese drei Studien bilden einen einheitlichen Rahmen zur Charakterisierung von Diffusions- und Ausbreitungsprozeßen, die sich auf komplexen Netzwerken allgemein abzeichnen, und bieten neue Ansätze für herausfordernde theoretische Probleme, die für die Bewertung künftiger Modelle verwendet werden können.The large amount of datasets that became available in recent years has made it possible to empirically study humanly-driven, as well as biological complex systems to an unprecedented extent. In parallel, the prediction and control of epidemic outbreaks have become very important for public health issues. In this thesis, we investigate some important aspects of diffusion phenomena and spreading processes unfolding on networks. We study three different problems related to spreading processes in the supercritical regime. First, we study reaction-diffusion on ensembles of random networks characterized by the observed Levy-flight properties of human mobility. The second problem is the estimation of the arrival times of global pandemics. To this end, we derive and identify suitable hidden geometries of network-driven spreading processes, leveraging on random-walk theory. Through the definition of network effective distances, the problem of complex spatiotemporal patterns is reduced to simple, homogeneous wave propagation patterns. Third, by embedding nodes in the hidden space defined by network effective distances, we introduce a novel network centrality, called ViralRank, which quantifies how close a node is, on average, to the other nodes. These three studies constitute a unified framework to characterize diffusion and spreading processes unfolding on complex networks in very general settings, and provide new approaches to challenging theoretical problems that can be used to benchmark future models

Algorithms and Software for the Analysis of Large Complex Networks

The work presented intersects three main areas, namely graph algorithmics, network science and applied software engineering. Each computational method discussed relates to one of the main tasks of data analysis: to extract structural features from network data, such as methods for community detection; or to transform network data, such as methods to sparsify a network and reduce its size while keeping essential properties; or to realistically model networks through generative models

Topology Reconstruction of Dynamical Networks via Constrained Lyapunov Equations

The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using measurements obtained from the network. In this technical note we define the notion of solvability of the network reconstruction problem. Subsequently, we provide necessary and sufficient conditions under which the network reconstruction problem is solvable. Finally, using constrained Lyapunov equations, we establish novel network reconstruction algorithms, applicable to general dynamical networks. We also provide specialized algorithms for specific network dynamics, such as the well-known consensus and adjacency dynamics.Comment: 8 page

An Initial Framework Assessing the Safety of Complex Systems

Trabajo presentado en la Conference on Complex Systems, celebrada online del 7 al 11 de diciembre de 2020.Atmospheric blocking events, that is large-scale nearly stationary atmospheric pressure patterns, are often associated with extreme weather in the mid-latitudes, such as heat waves and cold spells which have significant consequences on ecosystems, human health and economy. The high impact of blocking events has motivated numerous studies. However, there is not yet a comprehensive theory explaining their onset, maintenance and decay and their numerical prediction remains a challenge. In recent years, a number of studies have successfully employed complex network descriptions of fluid transport to characterize dynamical patterns in geophysical flows. The aim of the current work is to investigate the potential of so called Lagrangian flow networks for the detection and perhaps forecasting of atmospheric blocking events. The network is constructed by associating nodes to regions of the atmosphere and establishing links based on the flux of material between these nodes during a given time interval. One can then use effective tools and metrics developed in the context of graph theory to explore the atmospheric flow properties. In particular, Ser-Giacomi et al. [1] showed how optimal paths in a Lagrangian flow network highlight distinctive circulation patterns associated with atmospheric blocking events. We extend these results by studying the behavior of selected network measures (such as degree, entropy and harmonic closeness centrality)at the onset of and during blocking situations, demonstrating their ability to trace the spatio-temporal characteristics of these events.This research was conducted as part of the CAFE (Climate Advanced Forecasting of sub-seasonal Extremes) Innovative Training Network which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 813844