241 research outputs found

    Covering and Separation for Permutations and Graphs

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    This is a thesis of two parts, focusing on covering and separation topics of extremal combinatorics and graph theory, two major themes in this area. They entail the existence and properties of collections of combinatorial objects which together either represent all objects (covering) or can be used to distinguish all objects from each other (separation). We will consider a range of problems which come under these areas. The first part will focus on shattering k-sets with permutations. A family of permutations is said to shatter a given k-set if the permutations cover all possible orderings of the k elements. In particular, we investigate the size of permutation families which cover t orders for every possible k-set as well as study the problem of determining the largest number of k-sets that can be shattered by a family with given size. We provide a construction for a small permutation family which shatters every k-set. We also consider constructions of large families which do not shatter any triple. The second part will be concerned with the problem of separating path systems. A separating path system for a graph is a family of paths where, for any two edges, there is a path containing one edge but not the other. The aim is to find the size of the smallest such family. We will study the size of the smallest separating path system for a range of graphs, including complete graphs, complete bipartite graphs, and lattice-type graphs. A key technique we introduce is the use of generator paths - constructed to utilise the symmetric nature of Kn. We continue this symmetric approach for bipartite graphs and study the limitations of the method. We consider lattice-type graphs as an example of the most efficient possible separating systems for any graph

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Study of Climate Variability Patterns at Different Scales – A Complex Network Approach

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    Das Klimasystem der Erde besteht aus zahlreichen interagierenden Teilsystemen, die sich über verschiedene Zeitskalen hinweg verändern, was zu einer äußerst komplizierten räumlich-zeitlichen Klimavariabilität führt. Das Verständnis von Prozessen, die auf verschiedenen räumlichen und zeitlichen Skalen ablaufen, ist ein entscheidender Aspekt bei der numerischen Wettervorhersage. Die Variabilität des Klimas, ein sich selbst konstituierendes System, scheint in Mustern auf großen Skalen organisiert zu sein. Die Verwendung von Klimanetzwerken hat sich als erfolgreicher Ansatz für die Erkennung der räumlichen Ausbreitung dieser großräumigen Muster in der Variabilität des Klimasystems erwiesen. In dieser Arbeit wird mit Hilfe von Klimanetzwerken gezeigt, dass die Klimavariabilität nicht nur auf größeren Skalen (Asiatischer Sommermonsun, El Niño/Southern Oscillation), sondern auch auf kleineren Skalen, z.B. auf Wetterzeitskalen, in Mustern organisiert ist. Dies findet Anwendung bei der Erkennung einzelner tropischer Wirbelstürme, bei der Charakterisierung binärer Wirbelsturm-Interaktionen, die zu einer vollständigen Verschmelzung führen, und bei der Untersuchung der intrasaisonalen und interannuellen Variabilität des Asiatischen Sommermonsuns. Schließlich wird die Anwendbarkeit von Klimanetzwerken zur Analyse von Vorhersagefehlern demonstriert, was für die Verbesserung von Vorhersagen von immenser Bedeutung ist. Da korrelierte Fehler durch vorhersagbare Beziehungen zwischen Fehlern verschiedener Regionen aufgrund von zugrunde liegenden systematischen oder zufälligen Prozessen auftreten können, wird gezeigt, dass Fehler-Netzwerke helfen können, die räumlich kohärenten Strukturen von Vorhersagefehlern zu untersuchen. Die Analyse der Fehler-Netzwerk-Topologie von Klimavariablen liefert ein erstes Verständnis der vorherrschenden Fehlerquelle und veranschaulicht das Potenzial von Klimanetzwerken als vielversprechendes Diagnoseinstrument zur Untersuchung von Fehlerkorrelationen.The Earth’s climate system consists of numerous interacting subsystems varying over a multitude of time scales giving rise to highly complicated spatio-temporal climate variability. Understanding processes occurring at different scales, both spatial and temporal, has been a very crucial problem in numerical weather prediction. The variability of climate, a self-constituting system, appears to be organized in patterns on large scales. The climate networks approach has been very successful in detecting the spatial propagation of these large scale patterns of variability in the climate system. In this thesis, it is demonstrated using climate network approach that climate variability is organized in patterns not only at larger scales (Asian Summer Monsoon, El Niño-Southern Oscillation) but also at shorter scales, e.g., weather time scales. This finds application in detecting individual tropical cyclones, characterizing binary cyclone interaction leading to a complete merger, and studying the intraseasonal and interannual variability of the Asian Summer Monsoon. Finally, the applicability of the climate network framework to understand forecast error properties is demonstrated, which is crucial for improvement of forecasts. As correlated errors can arise due to the presence of a predictable relationship between errors of different regions because of some underlying systematic or random process, it is shown that error networks can help to analyze the spatially coherent structures of forecast errors. The analysis of the error network topology of a climate variable provides a preliminary understanding of the dominant source of error, which shows the potential of climate networks as a very promising diagnostic tool to study error correlations

    Can Competition Outperform Collaboration? The Role of Misbehaving Agents

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    We investigate a novel approach to resilient distributed optimization with quadratic costs in a multi-agent system prone to unexpected events that make some agents misbehave. In contrast to commonly adopted filtering strategies, we draw inspiration from phenomena modeled through the Friedkin-Johnsen dynamics and argue that adding competition to the mix can improve resilience in the presence of misbehaving agents. Our intuition is corroborated by analytical and numerical results showing that (i) there exists a nontrivial trade-off between full collaboration and full competition and (ii) our competition-based approach can outperform state-of-the-art algorithms based on Weighted Mean Subsequence Reduced. We also study impact of communication topology and connectivity on resilience, pointing out insights to robust network design.Comment: Submitted to IEEE TAC - first revisio

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    50 Years of quantum chromodynamics – Introduction and Review

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    Social Shaping for Multi-Agent Systems

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    Multi-agent systems have gained attention due to advances in automation, technology, and AI. In these systems, intelligent agents collaborate through networks to achieve goals. Despite successes, multi-agent systems pose social challenges. Problems include agents finding resource prices unacceptable due to efficient allocation, interactions being cooperative/competitive, leading to varying outcomes, and sensitive data being at risk due to sharing. Problems are: 1. Price Acceptance; 2. Agent Cooperation and Competition; 3. Privacy Risks. For Price Acceptance, we address decentralized resource allocation systems as markets. We solve price acceptance in static systems with quadratic utility functions by defining allowed quadratic ranges. For dynamic systems, we present dynamic competitive equilibrium computation and propose a horizon strategy for smoothing dynamic pricing. Concerning Agent Cooperation and Competition, we study the well-known Regional Integrated Climate-Economy model (RICE). It's a dynamic game. We analyze cooperative and competitive solutions, showing impact on negotiations and consensus for regional climate action. Regarding Privacy Risks, we infer network structures from linear-quadratic game best-response dynamics to reveal agent vulnerabilities. We prove network identifiability tied to controllability conditions. A stable, sparse system identification algorithm learns network structures despite noise. Lastly, we contribute privacy-aware algorithms. We address network games where agents aggregate under differential privacy. Extending to network games, we propose a Laplace linear-quadratic functional perturbation algorithm. A tutorial example demonstrates meeting privacy needs through tuning. In summary, this thesis solves social challenges in multi-agent systems: Price Acceptance, Agent Cooperation and Competition, and Privacy Risks

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum

    LIPIcs, Volume 258, SoCG 2023, Complete Volume

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    LIPIcs, Volume 258, SoCG 2023, Complete Volum

    Classical simulations of Gaussian boson sampling

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