Distances and Domination in Graphs

This book presents a compendium of the 10 articles published in the recent Special Issue “Distance and Domination in Graphs”. The works appearing herein deal with several topics on graph theory that relate to the metric and dominating properties of graphs. The topics of the gathered publications deal with some new open lines of investigations that cover not only graphs, but also digraphs. Different variations in dominating sets or resolving sets are appearing, and a review on some networks’ curvatures is also present

Connected Domination Critical Graphs

This thesis investigates the structure of connected domination critical graphs. The characterizations developed provide an important theoretical framework for addressing a number of difficult computational problems in the areas of operations research (for example, facility locations, industrial production systems), security, communication and wireless networks, transportation and logistics networks, land surveying and computational biology. In these application areas, the problems of interest are modelled by networks and graph parameters such as domination numbers reflect the efficiency and performance of the systems

Macrocriminology and Freedom

How can power over others be transformed to 'power with'? It is possible to transform many institutions to build societies with less predation and more freedom. These stretch from families and institutions of gender to the United Nations. Some societies, times and places have crime rates a hundred times higher than others. Some police forces kill at a hundred times the rate of others. Some criminal corporations kill thousands more than others. Micro variables fail to explain these patterns. Prevention principles for that challenge are macrocriminological. Freedom is conceived in a republican way as non-domination. Tempering domination prevents crime; crime prevention reduces domination. Many believe a high crime rate is a price of freedom. Not Braithwaite. His principles of crime control are to build freedom, temper power, lift people from poverty and reduce all forms of domination. Freedom requires a more just normative order. It requires cascading of peace by social movements for non-violence and non-domination. Periods of war, domination and anomie cascade with long lags to elevated crime, violence, inter-generational self-violence and ecocide. Cybercrime today poses risks of anomic nuclear wars. Braithwaite’s proposals refine some of criminology’s central theories and sharpen their relevance to all varieties of freedom. They can be reduced to one sentence. Strengthen freedom to prevent crime, prevent crime to strengthen freedom

IST Austria Thesis

In the first part of this thesis we consider large random matrices with arbitrary expectation and a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent in the bulk and edge regime. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion. In the second part we consider Wigner-type matrices and show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are uni- versal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner- Dyson-Mehta universality conjecture for the last remaining universality type. Our analysis holds not only for exact cusps, but approximate cusps as well, where an ex- tended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp, and extend the fast relaxation to equilibrium of the Dyson Brow- nian motion to the cusp regime. In the third and final part we explore the entrywise linear statistics of Wigner ma- trices and identify the fluctuations for a large class of test functions with little regularity. This enables us to study the rectangular Young diagram obtained from the interlacing eigenvalues of the random matrix and its minor, and we find that, despite having the same limit, the fluctuations differ from those of the algebraic Young tableaux equipped with the Plancharel measure

Macrocriminology and Freedom

How can power over others be transformed to 'power with'? It is possible to transform many institutions to build societies with less predation and more freedom. These stretch from families and institutions of gender to the United Nations. Some societies, times and places have crime rates a hundred times higher than others. Some police forces kill at a hundred times the rate of others. Some criminal corporations kill thousands more than others. Micro variables fail to explain these patterns. Prevention principles for that challenge are macrocriminological. Freedom is conceived in a republican way as non-domination. Tempering domination prevents crime; crime prevention reduces domination. Many believe a high crime rate is a price of freedom. Not Braithwaite. His principles of crime control are to build freedom, temper power, lift people from poverty and reduce all forms of domination. Freedom requires a more just normative order. It requires cascading of peace by social movements for non-violence and non-domination. Periods of war, domination and anomie cascade with long lags to elevated crime, violence, inter-generational self-violence and ecocide. Cybercrime today poses risks of anomic nuclear wars. Braithwaite’s proposals refine some of criminology’s central theories and sharpen their relevance to all varieties of freedom. They can be reduced to one sentence. Strengthen freedom to prevent crime, prevent crime to strengthen freedom

Evolutionary mechanics

Evolution im modernen Sinn ist die dynamische Beschreibung eines Systems, welches aus einer sehr großen Anzahl von Elementen besteht, deren relative Häufiggkeit sich durch das Zusammenspiel von Wechselwirkungen zwischen ihnen ändert. Dieses Verständnis kann in einer Vielfalt von Zusammenhängen angewendet werden, sei es biologisch, ökologisch, ökonomisch oder sozial, und führt zu den Beobachtungen dass diese Systeme ständig Variationen hervorbringen und selektiven Kräften unterliegen. Untersuchungen von evolutionären Systemen kann man in zwei Klassen einteilen. Ihr Verhalten kann mit Hilfe von Differentialgleichungen direkt modelliert werden, dies erfordert es jedoch jede mögliche Wechselwirkung im vorhinein zu spezifizieren. Dadurch ist es schwer, wenn nicht unmöglich, eine der Haupteigenschaften von evolutionären Systemen zu beschreiben, die fortwährende Produktion von Innovationen. Zweitens kann man abstraktere und stilisiertere Modelle untersuchen, die dann zu einem großen Teil auf ad hoc Annahmen über die vorliegenden evolutionären Prozesse beruhen. Dadurch tragen sie nicht dazu bei unser Verständnis davon zu erweitern, wie beobachtete Effekte wie punktuierte Gleichgewichte und evolutionäre Phasenübergänge von grundlegende Prinzipien aus emergieren. In dieser Arbeit schlagen wir ein Modell der statistischen Physik vor, welches darauf abzielt das 'Beste beider Welten' zu vereinigen. Wir verwenden eine Diversitätsbeschreibung die es ermöglicht die allgemeinste Form von evolutionären Wechselwirkungen paradigmatisch zu formulieren. Für diese Wechselwirkungen (und auch für eine wesentlich größere Klasse von dynamischen Systemen) entwickeln wir ein Variationsprinzip durch welches wir Ergebnisse und Methoden der Statistischen Mechanik benützen können. Die asymptotische Diversität solcher Systeme kann in einer Mean Field Näherung analytisch berechnet werden, andere wichtige Observable werden quantitativ ausgewertet. Wir bauen dann schrittweise spezifizierende Annahmen in unser Modell ein und testen seine Vorhersagen an gemessenen Daten aus ökonomischen, biologischen und sozialen Umfeldern.Evolution in its modern sense is the dynamical description of a system composed of a vast number of elements whose abundances change over time due to the accumulated interplay of interactions between them. This reasoning applies in a multitude of contexts, be it biological, ecological, economical or social, and gives rise to the observations that evolutionary systems are subject to continual variations under selective forces. Traditional evolutionary approaches to study these systems can be divided into two classes. Their behavior can be modelled directly in the framework of differential equations, which makes it necessary to prestate each possible interaction. In this framework it is hard or even impossible to account for one of the main ingredients of evolutionary systems, the never-ending production of innovations. Secondly, more abstract and stylized models are studied relying to a large extend on ad hoc assumptions about the evolutionary processes at work. Thus they do not contribute to our understanding of how observed effects like punctuated equlibria and evolutionary phase transitions emerge from first principles. In this work we propose a statistical physics model aimed at bringing together the 'best of both worlds'. We adopt a diversity framework which makes it possible to formalize the most general evolutionary interactions in a paradigmatic way. For these interactions (and also for a much larger class of dynamical systems) we develop a variational principle allowing us to employ the statistical mechanics machinery. The asymptotic diversity of such systems is worked out analytically in the mean field approximation, other key observables are quantitatively assessed. We succinctly incorporate specifying assumptions in our model and test its prediction against real world data in economic, biological and social settings

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Ecology-based planning. Italian and French experimentations

This paper examines some French and Italian experimentations of green infrastructures’ (GI) construction in relation to their techniques and methodologies. The construction of a multifunctional green infrastructure can lead to the generation of a number of relevant bene fi ts able to face the increasing challenges of climate change and resilience (for example, social, ecological and environmental through the recognition of the concept of ecosystem services) and could ease the achievement of a performance-based approach. This approach, differently from the traditional prescriptive one, helps to attain a better and more fl exible land-use integration. In both countries, GI play an important role in contrasting land take and, for their adaptive and cross-scale nature, they help to generate a res ilient approach to urban plans and projects. Due to their fl exible and site-based nature, GI can be adapted, even if through different methodologies and approaches, both to urban and extra-urban contexts. On one hand, France, through its strong national policy on ecological networks, recognizes them as one of the major planning strategies toward a more sustainable development of territories; on the other hand, Italy has no national policy and Regions still have a hard time integrating them in already existing planning tools. In this perspective, Italian experimentations on GI construction appear to be a simple and sporadic add-on of urban and regional plans