1,118 research outputs found

    A Unifying Theory for Graph Transformation

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    The field of graph transformation studies the rule-based transformation of graphs. An important branch is the algebraic graph transformation tradition, in which approaches are defined and studied using the language of category theory. Most algebraic graph transformation approaches (such as DPO, SPO, SqPO, and AGREE) are opinionated about the local contexts that are allowed around matches for rules, and about how replacement in context should work exactly. The approaches also differ considerably in their underlying formal theories and their general expressiveness (e.g., not all frameworks allow duplication). This dissertation proposes an expressive algebraic graph transformation approach, called PBPO+, which is an adaptation of PBPO by Corradini et al. The central contribution is a proof that PBPO+ subsumes (under mild restrictions) DPO, SqPO, AGREE, and PBPO in the important categorical setting of quasitoposes. This result allows for a more unified study of graph transformation metatheory, methods, and tools. A concrete example of this is found in the second major contribution of this dissertation: a graph transformation termination method for PBPO+, based on decreasing interpretations, and defined for general categories. By applying the proposed encodings into PBPO+, this method can also be applied for DPO, SqPO, AGREE, and PBPO

    Classical and quantum algorithms for scaling problems

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    This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Advances and Applications of DSmT for Information Fusion. Collected Works, Volume 5

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    This fifth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents some theoretical advances on DSmT, dealing mainly with modified Proportional Conflict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classifiers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identification of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classification. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classification, and hybrid techniques mixing deep learning with belief functions as well

    Efficient resilience analysis and decision-making for complex engineering systems

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    Modern societies around the world are increasingly dependent on the smooth functionality of progressively more complex systems, such as infrastructure systems, digital systems like the internet, and sophisticated machinery. They form the cornerstones of our technologically advanced world and their efficiency is directly related to our well-being and the progress of society. However, these important systems are constantly exposed to a wide range of threats of natural, technological, and anthropogenic origin. The emergence of global crises such as the COVID-19 pandemic and the ongoing threat of climate change have starkly illustrated the vulnerability of these widely ramified and interdependent systems, as well as the impossibility of predicting threats entirely. The pandemic, with its widespread and unexpected impacts, demonstrated how an external shock can bring even the most advanced systems to a standstill, while the ongoing climate change continues to produce unprecedented risks to system stability and performance. These global crises underscore the need for systems that can not only withstand disruptions, but also, recover from them efficiently and rapidly. The concept of resilience and related developments encompass these requirements: analyzing, balancing, and optimizing the reliability, robustness, redundancy, adaptability, and recoverability of systems -- from both technical and economic perspectives. This cumulative dissertation, therefore, focuses on developing comprehensive and efficient tools for resilience-based analysis and decision-making of complex engineering systems. The newly developed resilience decision-making procedure is at the core of these developments. It is based on an adapted systemic risk measure, a time-dependent probabilistic resilience metric, as well as a grid search algorithm, and represents a significant innovation as it enables decision-makers to identify an optimal balance between different types of resilience-enhancing measures, taking into account monetary aspects. Increasingly, system components have significant inherent complexity, requiring them to be modeled as systems themselves. Thus, this leads to systems-of-systems with a high degree of complexity. To address this challenge, a novel methodology is derived by extending the previously introduced resilience framework to multidimensional use cases and synergistically merging it with an established concept from reliability theory, the survival signature. The new approach combines the advantages of both original components: a direct comparison of different resilience-enhancing measures from a multidimensional search space leading to an optimal trade-off in terms of system resilience, and a significant reduction in computational effort due to the separation property of the survival signature. It enables that once a subsystem structure has been computed -- a typically computational expensive process -- any characterization of the probabilistic failure behavior of components can be validated without having to recompute the structure. In reality, measurements, expert knowledge, and other sources of information are loaded with multiple uncertainties. For this purpose, an efficient method based on the combination of survival signature, fuzzy probability theory, and non-intrusive stochastic simulation (NISS) is proposed. This results in an efficient approach to quantify the reliability of complex systems, taking into account the entire uncertainty spectrum. The new approach, which synergizes the advantageous properties of its original components, achieves a significant decrease in computational effort due to the separation property of the survival signature. In addition, it attains a dramatic reduction in sample size due to the adapted NISS method: only a single stochastic simulation is required to account for uncertainties. The novel methodology not only represents an innovation in the field of reliability analysis, but can also be integrated into the resilience framework. For a resilience analysis of existing systems, the consideration of continuous component functionality is essential. This is addressed in a further novel development. By introducing the continuous survival function and the concept of the Diagonal Approximated Signature as a corresponding surrogate model, the existing resilience framework can be usefully extended without compromising its fundamental advantages. In the context of the regeneration of complex capital goods, a comprehensive analytical framework is presented to demonstrate the transferability and applicability of all developed methods to complex systems of any type. The framework integrates the previously developed resilience, reliability, and uncertainty analysis methods. It provides decision-makers with the basis for identifying resilient regeneration paths in two ways: first, in terms of regeneration paths with inherent resilience, and second, regeneration paths that lead to maximum system resilience, taking into account technical and monetary factors affecting the complex capital good under analysis. In summary, this dissertation offers innovative contributions to efficient resilience analysis and decision-making for complex engineering systems. It presents universally applicable methods and frameworks that are flexible enough to consider system types and performance measures of any kind. This is demonstrated in numerous case studies ranging from arbitrary flow networks, functional models of axial compressors to substructured infrastructure systems with several thousand individual components.Moderne Gesellschaften sind weltweit zunehmend von der reibungslosen Funktionalität immer komplexer werdender Systeme, wie beispielsweise Infrastruktursysteme, digitale Systeme wie das Internet oder hochentwickelten Maschinen, abhängig. Sie bilden die Eckpfeiler unserer technologisch fortgeschrittenen Welt, und ihre Effizienz steht in direktem Zusammenhang mit unserem Wohlbefinden sowie dem Fortschritt der Gesellschaft. Diese wichtigen Systeme sind jedoch einer ständigen und breiten Palette von Bedrohungen natürlichen, technischen und anthropogenen Ursprungs ausgesetzt. Das Auftreten globaler Krisen wie die COVID-19-Pandemie und die anhaltende Bedrohung durch den Klimawandel haben die Anfälligkeit der weit verzweigten und voneinander abhängigen Systeme sowie die Unmöglichkeit einer Gefahrenvorhersage in voller Gänze eindrücklich verdeutlicht. Die Pandemie mit ihren weitreichenden und unerwarteten Auswirkungen hat gezeigt, wie ein externer Schock selbst die fortschrittlichsten Systeme zum Stillstand bringen kann, während der anhaltende Klimawandel immer wieder beispiellose Risiken für die Systemstabilität und -leistung hervorbringt. Diese globalen Krisen unterstreichen den Bedarf an Systemen, die nicht nur Störungen standhalten, sondern sich auch schnell und effizient von ihnen erholen können. Das Konzept der Resilienz und die damit verbundenen Entwicklungen umfassen diese Anforderungen: Analyse, Abwägung und Optimierung der Zuverlässigkeit, Robustheit, Redundanz, Anpassungsfähigkeit und Wiederherstellbarkeit von Systemen -- sowohl aus technischer als auch aus wirtschaftlicher Sicht. In dieser kumulativen Dissertation steht daher die Entwicklung umfassender und effizienter Instrumente für die Resilienz-basierte Analyse und Entscheidungsfindung von komplexen Systemen im Mittelpunkt. Das neu entwickelte Resilienz-Entscheidungsfindungsverfahren steht im Kern dieser Entwicklungen. Es basiert auf einem adaptierten systemischen Risikomaß, einer zeitabhängigen, probabilistischen Resilienzmetrik sowie einem Gittersuchalgorithmus und stellt eine bedeutende Innovation dar, da es Entscheidungsträgern ermöglicht, ein optimales Gleichgewicht zwischen verschiedenen Arten von Resilienz-steigernden Maßnahmen unter Berücksichtigung monetärer Aspekte zu identifizieren. Zunehmend weisen Systemkomponenten eine erhebliche Eigenkomplexität auf, was dazu führt, dass sie selbst als Systeme modelliert werden müssen. Hieraus ergeben sich Systeme aus Systemen mit hoher Komplexität. Um diese Herausforderung zu adressieren, wird eine neue Methodik abgeleitet, indem das zuvor eingeführte Resilienzrahmenwerk auf multidimensionale Anwendungsfälle erweitert und synergetisch mit einem etablierten Konzept aus der Zuverlässigkeitstheorie, der Überlebenssignatur, zusammengeführt wird. Der neue Ansatz kombiniert die Vorteile beider ursprünglichen Komponenten: Einerseits ermöglicht er einen direkten Vergleich verschiedener Resilienz-steigernder Maßnahmen aus einem mehrdimensionalen Suchraum, der zu einem optimalen Kompromiss in Bezug auf die Systemresilienz führt. Andererseits ermöglicht er durch die Separationseigenschaft der Überlebenssignatur eine signifikante Reduktion des Rechenaufwands. Sobald eine Subsystemstruktur berechnet wurde -- ein typischerweise rechenintensiver Prozess -- kann jede Charakterisierung des probabilistischen Ausfallverhaltens von Komponenten validiert werden, ohne dass die Struktur erneut berechnet werden muss. In der Realität sind Messungen, Expertenwissen sowie weitere Informationsquellen mit vielfältigen Unsicherheiten belastet. Hierfür wird eine effiziente Methode vorgeschlagen, die auf der Kombination von Überlebenssignatur, unscharfer Wahrscheinlichkeitstheorie und nicht-intrusiver stochastischer Simulation (NISS) basiert. Dadurch entsteht ein effizienter Ansatz zur Quantifizierung der Zuverlässigkeit komplexer Systeme unter Berücksichtigung des gesamten Unsicherheitsspektrums. Der neue Ansatz, der die vorteilhaften Eigenschaften seiner ursprünglichen Komponenten synergetisch zusammenführt, erreicht eine bedeutende Verringerung des Rechenaufwands aufgrund der Separationseigenschaft der Überlebenssignatur. Er erzielt zudem eine drastische Reduzierung der Stichprobengröße aufgrund der adaptierten NISS-Methode: Es wird nur eine einzige stochastische Simulation benötigt, um Unsicherheiten zu berücksichtigen. Die neue Methodik stellt nicht nur eine Neuerung auf dem Gebiet der Zuverlässigkeitsanalyse dar, sondern kann auch in das Resilienzrahmenwerk integriert werden. Für eine Resilienzanalyse von real existierenden Systemen ist die Berücksichtigung kontinuierlicher Komponentenfunktionalität unerlässlich. Diese wird in einer weiteren Neuentwicklung adressiert. Durch die Einführung der kontinuierlichen Überlebensfunktion und dem Konzept der Diagonal Approximated Signature als entsprechendes Ersatzmodell kann das bestehende Resilienzrahmenwerk sinnvoll erweitert werden, ohne seine grundlegenden Vorteile zu beeinträchtigen. Im Kontext der Regeneration komplexer Investitionsgüter wird ein umfassendes Analyserahmenwerk vorgestellt, um die Übertragbarkeit und Anwendbarkeit aller entwickelten Methoden auf komplexe Systeme jeglicher Art zu demonstrieren. Das Rahmenwerk integriert die zuvor entwickelten Methoden der Resilienz-, Zuverlässigkeits- und Unsicherheitsanalyse. Es bietet Entscheidungsträgern die Basis für die Identifikation resilienter Regenerationspfade in zweierlei Hinsicht: Zum einen im Sinne von Regenerationspfaden mit inhärenter Resilienz und zum anderen Regenerationspfade, die zu einer maximalen Systemresilienz unter Berücksichtigung technischer und monetärer Einflussgrößen des zu analysierenden komplexen Investitionsgutes führen. Zusammenfassend bietet diese Dissertation innovative Beiträge zur effizienten Resilienzanalyse und Entscheidungsfindung für komplexe Ingenieursysteme. Sie präsentiert universell anwendbare Methoden und Rahmenwerke, die flexibel genug sind, um beliebige Systemtypen und Leistungsmaße zu berücksichtigen. Dies wird in zahlreichen Fallstudien von willkürlichen Flussnetzwerken, funktionalen Modellen von Axialkompressoren bis hin zu substrukturierten Infrastruktursystemen mit mehreren tausend Einzelkomponenten demonstriert

    Clique‐width: Harnessing the power of atoms

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    Many NP-complete graph problems are polynomial-time solvable on graph classes of bounded clique-width. Several of these problems are polynomial-time solvable on a hereditary graph class if they are so on the atoms (graphs with no clique cut-set) of . Hence, we initiate a systematic study into boundedness of clique-width of atoms of hereditary graph classes. A graph is -free if is not an induced subgraph of , and it is -free if it is both -free and -free. A class of -free graphs has bounded clique-width if and only if its atoms have this property. This is no longer true for -free graphs, as evidenced by one known example. We prove the existence of another such pair and classify the boundedness of clique-width on -free atoms for all but 18 cases

    Fast Coloring Despite Congested Relays

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    We provide a O(log6logn)O(\log^6 \log n)-round randomized algorithm for distance-2 coloring in CONGEST with Δ2+1\Delta^2+1 colors. For Δpolylogn\Delta\gg\operatorname{poly}\log n, this improves exponentially on the O(logΔ+polyloglogn)O(\log\Delta+\operatorname{poly}\log\log n) algorithm of [Halld\'orsson, Kuhn, Maus, Nolin, DISC'20]. Our study is motivated by the ubiquity and hardness of local reductions in CONGEST. For instance, algorithms for the Local Lov\'asz Lemma [Moser, Tardos, JACM'10; Fischer, Ghaffari, DISC'17; Davies, SODA'23] usually assume communication on the conflict graph, which can be simulated in LOCAL with only constant overhead, while this may be prohibitively expensive in CONGEST. We hope our techniques help tackle in CONGEST other coloring problems defined by local relations.Comment: 37 pages. To appear in proceedings of DISC 202

    The Potts model and the independence polynomial:Uniqueness of the Gibbs measure and distributions of complex zeros

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    Part 1 of this dissertation studies the antiferromagnetic Potts model, which originates in statistical physics. In particular the transition from multiple Gibbs measures to a unique Gibbs measure for the antiferromagnetic Potts model on the infinite regular tree is studied. This is called a uniqueness phase transition. A folklore conjecture about the parameter at which the uniqueness phase transition occurs is partly confirmed. The proof uses a geometric condition, which comes from analysing an associated dynamical system.Part 2 of this dissertation concerns zeros of the independence polynomial. The independence polynomial originates in statistical physics as the partition function of the hard-core model. The location of the complex zeros of the independence polynomial is related to phase transitions in terms of the analycity of the free energy and plays an important role in the design of efficient algorithms to approximately compute evaluations of the independence polynomial. Chapter 5 directly relates the location of the complex zeros of the independence polynomial to computational hardness of approximating evaluations of the independence polynomial. This is done by moreover relating the set of zeros of the independence polynomial to chaotic behaviour of a naturally associated family of rational functions; the occupation ratios. Chapter 6 studies boundedness of zeros of the independence polynomial of tori for sequences of tori converging to the integer lattice. It is shown that zeros are bounded for sequences of balanced tori, but unbounded for sequences of highly unbalanced tori

    OBSERVATIONAL CAUSAL INFERENCE FOR NETWORK DATA SETTINGS

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    Observational causal inference (OCI) has shown significant promise in recent years, both as a tool for improving existing machine learning techniques and as an avenue to aid decision makers in applied areas, such as health and climate science. OCI relies on a key notion, identification, which links the counterfactual of interest to the observed data via a set of assumptions. Historically, OCI has relied on unrealistic assumptions, such as the ’no latent confounders’ assumption. To address this, Huang and Valtorta (2006) and Shpitser and Pearl (2006) provided sound and complete algorithms for identification of causal effects in causal directed acyclic graphs with latent variables. Nevertheless, these algorithms can only handle relatively simple causal queries. In this dissertation, I will detail my contributions which generalize identification theory in key directions. I will describe theory which enables identification of causal effects when i) data do not satisfy the ’independent and identically distributed’ assumption, as in vaccine or social network data, and ii) the intervention of interest is a function of other model variables, as in off-line, off-policy learning, iii) when these two complicated settings intersect. Additionally, I will highlight some novel ways to conceive of interventions in networks. I will conclude with a discussion of future directions

    Exactly soluble models in many-body physics

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    Almost all phenomena in the universe are described, at the fundamental level, by quantum manybody models. In general, however, a complete understanding of large systems with many degrees of freedom is impossible. While in general many-body quantum systems are intractable, there are special cases for which there are techniques that allow for an exact solution. Exactly soluble models are interesting because they are soluble; beyond this, they can be used to gain intuition for further reaching many-body systems, including when they can be leveraged to help with numerical approximations for general models. The work presented in this thesis considers exactly soluble models of quantum many-body systems. The first part of this thesis extends the family of many-body spin models for which we can find a freefermion solution. A solution method that was developed for a specific free-fermion model is generalized in such a way that allows application to a broader class of many-body spin system than was previously known to be free. Models which admit a solution via this method are characterized by a graph theory invariants: in brief it is shown that a quantum spin system has an exact description via non-interacting fermions if its frustration graph is claw-free and contains a simplicial clique. The second part of this thesis gives an explicit example of how the usefulness of exactly soluble models can extend beyond the solution itself. This chapter pertains to the calculation of the topological entanglement entropy in topologically ordered loop-gas states. Topological entanglement entropy gives an understanding of how correlations may extend throughout a system. In this chapter the topological entanglement entropy of two- and three-dimensional loop-gas states is calculated in the bulk and at the boundary. We obtain a closed form expression for the topological entanglement in terms of the anyonic theory that the models support
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