A Survey on Centrality Metrics and Their Implications in Network Resilience

Centrality metrics have been used in various networks, such as communication, social, biological, geographic, or contact networks. In particular, they have been used in order to study and analyze targeted attack behaviors and investigated their effect on network resilience. Although a rich volume of centrality metrics has been developed for decades, a limited set of centrality metrics have been commonly in use. This paper aims to introduce various existing centrality metrics and discuss their applicabilities and performance based on the results obtained from extensive simulation experiments to encourage their use in solving various computing and engineering problems in networks.Comment: Main paper: 36 pages, 2 figures. Appendix 23 pages,45 figure

Beyond Flatland : exploring graphs in many dimensions

Societies, technologies, economies, ecosystems, organisms, . . . Our world is composed of complex networks—systems with many elements that interact in nontrivial ways. Graphs are natural models of these systems, and scientists have made tremendous progress in developing tools for their analysis. However, research has long focused on relatively simple graph representations and problem specifications, often discarding valuable real-world information in the process. In recent years, the limitations of this approach have become increasingly apparent, but we are just starting to comprehend how more intricate data representations and problem formulations might benefit our understanding of relational phenomena. Against this background, our thesis sets out to explore graphs in five dimensions: descriptivity, multiplicity, complexity, expressivity, and responsibility. Leveraging tools from graph theory, information theory, probability theory, geometry, and topology, we develop methods to (1) descriptively compare individual graphs, (2) characterize similarities and differences between groups of multiple graphs, (3) critically assess the complexity of relational data representations and their associated scientific culture, (4) extract expressive features from and for hypergraphs, and (5) responsibly mitigate the risks induced by graph-structured content recommendations. Thus, our thesis is naturally situated at the intersection of graph mining, graph learning, and network analysis.Gesellschaften, Technologien, Volkswirtschaften, Ökosysteme, Organismen, . . . Unsere Welt besteht aus komplexen Netzwerken—Systemen mit vielen Elementen, die auf nichttriviale Weise interagieren. Graphen sind natürliche Modelle dieser Systeme, und die Wissenschaft hat bei der Entwicklung von Methoden zu ihrer Analyse große Fortschritte gemacht. Allerdings hat sich die Forschung lange auf relativ einfache Graphrepräsentationen und Problemspezifikationen beschränkt, oft unter Vernachlässigung wertvoller Informationen aus der realen Welt. In den vergangenen Jahren sind die Grenzen dieser Herangehensweise zunehmend deutlich geworden, aber wir beginnen gerade erst zu erfassen, wie unser Verständnis relationaler Phänomene von intrikateren Datenrepräsentationen und Problemstellungen profitieren kann. Vor diesem Hintergrund erkundet unsere Dissertation Graphen in fünf Dimensionen: Deskriptivität, Multiplizität, Komplexität, Expressivität, und Verantwortung. Mithilfe von Graphentheorie, Informationstheorie, Wahrscheinlichkeitstheorie, Geometrie und Topologie entwickeln wir Methoden, welche (1) einzelne Graphen deskriptiv vergleichen, (2) Gemeinsamkeiten und Unterschiede zwischen Gruppen multipler Graphen charakterisieren, (3) die Komplexität relationaler Datenrepräsentationen und der mit ihnen verbundenen Wissenschaftskultur kritisch beleuchten, (4) expressive Merkmale von und für Hypergraphen extrahieren, und (5) verantwortungsvoll den Risiken begegnen, welche die Graphstruktur von Inhaltsempfehlungen mit sich bringt. Damit liegt unsere Dissertation naturgemäß an der Schnittstelle zwischen Graph Mining, Graph Learning und Netzwerkanalyse

Notes in Pure Mathematics & Mathematical Structures in Physics

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.Comment: Small improvements and addition

Do people communicate about their whereabouts? Investigating the relation between user-generated text messages and Foursquare check-in places

The social functionality of places (e.g. school, restaurant) partly determines human behaviors and reflects a region’s functional configuration. Semantic descriptions of places are thus valuable to a range of studies of humans and geographic spaces. Assuming their potential impacts on human verbalization behaviors, one possibility is to link the functions of places to verbal representations such as users’ postings in location-based social networks (LBSNs). In this study, we examine whether the heterogeneous user-generated text snippets found in LBSNs reliably reflect the semantic concepts attached with check-in places. We investigate Foursquare because its available categorization hierarchy provides rich a-priori semantic knowledge about its check-in places, which enables a reliable verification of the semantic concepts identified from user-generated text snippets. A latent semantic analysis is conducted on a large Foursquare check-in dataset. The results confirm that attached text messages can represent semantic concepts by demonstrating their large correspondence to the official Foursquare venue categorization. To further elaborate the representativeness of text messages, this work also performs an investigation on the textual terms to quantify their abilities of representing semantic concepts (i.e., representativeness), and another investigation on semantic concepts to quantify how well they can be represented by text messages (i.e., representability). The results shed light on featured terms with strong locational characteristics, as well as on distinctive semantic concepts with potentially strong impacts on human verbalizations

Sieving the Landscape of Gravity Theories. From the Equivalence Principles to the Near-Planck Regime

This thesis focusses on three main aspects of the foundations of any theory of gravity where the gravitational field admits a geometric interpretation: (a) the principles of equivalence; (b) their role as selection rules in the landscape of extended theories of gravity; and (c) the possible modifications of the spacetime structure at a "mesoscopic" scale, due to underlying, microscopic-level, quantum-gravitational effects. The first result of the work is the introduction of a formal definition of the Gravitational Weak Equivalence Principle, which expresses the universality of free fall of test objects with non-negligible self-gravity, in a matter-free environment. This principle extends the Galilean universality of free-fall world-lines for test bodies with negligible self-gravity (Weak Equivalence Principle). Second, we use the Gravitational Weak Equivalence Principle to build a sieve for some classes of extended theories of gravity, to rule out all models yielding non-universal free-fall motion for self-gravitating test bodies. When applied to metric theories of gravity in four spacetime dimensions, the method singles out General Relativity (both with and without the cosmological constant term), whereas in higher-dimensional scenarios the whole class of Lanczos--Lovelock gravity theories also passes the test. Finally, we focus on the traditional, manifold-based model of spacetime, and on how it could be modified, at a "mesoscopic" (experimentally attainable) level, by the presence of an underlying, sub-Planckian quantum regime. The possible modifications are examined in terms of their consequences on the hypotheses at the basis of von Ignatowski's derivation of the Lorentz transformations. It results that either such modifications affect sectors already tightly constrained (e.g. violations of the principle of relativity and/or of spatial isotropy), or they demand a radical breakdown of the operative interpretation of the coordinates as readings of clocks and rods

Three Risky Decades: A Time for Econophysics?

Our Special Issue we publish at a turning point, which we have not dealt with since World War II. The interconnected long-term global shocks such as the coronavirus pandemic, the war in Ukraine, and catastrophic climate change have imposed significant humanitary, socio-economic, political, and environmental restrictions on the globalization process and all aspects of economic and social life including the existence of individual people. The planet is trapped—the current situation seems to be the prelude to an apocalypse whose long-term effects we will have for decades. Therefore, it urgently requires a concept of the planet's survival to be built—only on this basis can the conditions for its development be created. The Special Issue gives evidence of the state of econophysics before the current situation. Therefore, it can provide excellent econophysics or an inter-and cross-disciplinary starting point of a rational approach to a new era

COrE (Cosmic Origins Explorer) A White Paper

COrE (Cosmic Origins Explorer) is a fourth-generation full-sky, microwave-band satellite recently proposed to ESA within Cosmic Vision 2015-2025. COrE will provide maps of the microwave sky in polarization and temperature in 15 frequency bands, ranging from 45 GHz to 795 GHz, with an angular resolution ranging from 23 arcmin (45 GHz) and 1.3 arcmin (795 GHz) and sensitivities roughly 10 to 30 times better than PLANCK (depending on the frequency channel). The COrE mission will lead to breakthrough science in a wide range of areas, ranging from primordial cosmology to galactic and extragalactic science. COrE is designed to detect the primordial gravitational waves generated during the epoch of cosmic inflation at more than $3\sigma$ for $r=(T/S)>=10^{-3}$. It will also measure the CMB gravitational lensing deflection power spectrum to the cosmic variance limit on all linear scales, allowing us to probe absolute neutrino masses better than laboratory experiments and down to plausible values suggested by the neutrino oscillation data. COrE will also search for primordial non-Gaussianity with significant improvements over Planck in its ability to constrain the shape (and amplitude) of non-Gaussianity. In the areas of galactic and extragalactic science, in its highest frequency channels COrE will provide maps of the galactic polarized dust emission allowing us to map the galactic magnetic field in areas of diffuse emission not otherwise accessible to probe the initial conditions for star formation. COrE will also map the galactic synchrotron emission thirty times better than PLANCK. This White Paper reviews the COrE science program, our simulations on foreground subtraction, and the proposed instrumental configuration.Comment: 90 pages Latex 15 figures (revised 28 April 2011, references added, minor errors corrected

Modelling the Eddy Pattern in the harbour of Zeebrugge

Hydrodynamic

Nonlinear Dynamics

This volume covers a diverse collection of topics dealing with some of the fundamental concepts and applications embodied in the study of nonlinear dynamics. Each of the 15 chapters contained in this compendium generally fit into one of five topical areas: physics applications, nonlinear oscillators, electrical and mechanical systems, biological and behavioral applications or random processes. The authors of these chapters have contributed a stimulating cross section of new results, which provide a fertile spectrum of ideas that will inspire both seasoned researches and students