1,334 research outputs found

    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

    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

    Collective agency:From philosophical and logical perspectives

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    People inhabit a vast and intricate social network nowadays. In addition to our own decisions and actions, we confront those of various groups every day. Collective decisions and actions are more complex and bewildering compared to those made by individuals. As members of a collective, we contribute to its decisions, but our contributions may not always align with the outcome. We may also find ourselves excluded from certain groups and passively subjected to their influences without being aware of the source. We are used to being in overlapping groups and may switch identities, supporting or opposing the claims of particular groups. But rarely do we pause to think: What do we talk about when we talk about groups and their decisions?At the heart of this dissertation is the question of collective agency, i.e., in what sense can we treat a group as a rational agent capable of its action. There are two perspectives we take: a philosophical and logical one. The philosophical perspective mainly discusses the ontological and epistemological issues related to collective agency, sorts out the relevant philosophical history, and argues that the combination of a relational view of collective agency and a dispositional view of collective intentionality provides a rational and realistic account. The logical perspective is associated with formal theories of groups, it disregards the psychological content involved in the philosophical perspective, establishes a logical system that is sufficiently formal and objective, and axiomatizes the nature of a collective

    Automatic Generation of Personalized Recommendations in eCoaching

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    Denne avhandlingen omhandler eCoaching for personlig livsstilsstøtte i sanntid ved bruk av informasjons- og kommunikasjonsteknologi. Utfordringen er å designe, utvikle og teknisk evaluere en prototyp av en intelligent eCoach som automatisk genererer personlige og evidensbaserte anbefalinger til en bedre livsstil. Den utviklede løsningen er fokusert på forbedring av fysisk aktivitet. Prototypen bruker bærbare medisinske aktivitetssensorer. De innsamlede data blir semantisk representert og kunstig intelligente algoritmer genererer automatisk meningsfulle, personlige og kontekstbaserte anbefalinger for mindre stillesittende tid. Oppgaven bruker den veletablerte designvitenskapelige forskningsmetodikken for å utvikle teoretiske grunnlag og praktiske implementeringer. Samlet sett fokuserer denne forskningen på teknologisk verifisering snarere enn klinisk evaluering.publishedVersio

    Data-driven Reachability of Non-linear Systems via Optimization of Chen-Fliess Series

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    A reachable set is the set of all possible states produced by applying a set of inputs, initial states, and parameters. The fundamental problem of reachability is checking if a set of states is reached provided a set of inputs, initial states, and parameters, typically, in a finite time. In the engineering field, reachability analysis is used to test the guarantees of the operation’s safety of a system. In the present work, the reachability analysis of nonlinear control affine systems is studied by means of the Chen-Fliess series. Different perspectives for addressing the reachability problem, such as interval arithmetic, mixed-monotonicity, and optimization, are used in this dissertation. The first two provide, in general, an overestimation of the reachable set that is not guaranteed to be the smallest. To improve these methods and obtainthe minimum bounding box of the reachable set, the derivative-based optimization of Chen-Fliess series is developed. To achieve this, the closed form of the Gâteaux and Fréchet derivatives of Chen-Fliess series and several other tools from analysis are obtained. To provide a representation of these tools practically and systematically, an abstract algebraic derivative acting on words of a monoid is defined. Three nonconvex optimization algorithms are implemented for Chen-Fliess series. The problem of computing an inner approximation of the reachable set via Chen-Fliess series is also solved by means of convex analysis tools. Furthermore, a method for the computation of the backward reachable set of an output set is also provided. In this case, different from forward reachability analysis, the feasibility problem represents a challenge and requires using the Positivestellensatz. Examples and simulations are provided for every method presented. The application of control barrier functions via Chen-Fliess series is outlined. Finally, the future work and conclusions are stated in the last chapter

    On the Verification of Parametric Systems

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    We present an approach to the verification of systems for whose description some elements - constants or functions - are underspecified and can be regarded as parameters, and, in particular, describe a method for automatically generating constraints on such parameters under which certain safety conditions are guaranteed to hold. We present an implementation and illustrate its use on several examples.Comment: 26 pages. arXiv admin note: text overlap with arXiv:1910.0520

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Security of systems: modeling and analysis methodology

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    Die Security-Bewertung eines Systems erfordert eine Systembeschreibung. Die Beschreibung bestimmt die Qualität der Analyse und die Qualität der entsprechenden Security-Lösung. In der Arbeit wird eine Methodik zur Bewertung der Security von Systemen entwickelt. Es wird mit einem einfachen Modell begonnen und dieses iterativ verfeinert. Das resultierende Modell repräsentiert eine möglichst vollständige Sicht auf das zu evaluierende System, wobei die einzelnen Schritte überschaubar bleiben. In der Praxis variiert der Grad der verfügbaren Informationen. Der Ansatz kann mit fehlenden Informationen über Teile des Systems umgehen. Das Modell beinhaltet schließlich Teilsysteme auf verschiedenen Abstraktionsebenen. Nach jedem atomaren Schritt der Modellierung kann eine Analyse durchgeführt werden, um die Security des modellierten Systems zu bewerten. Die Analyse ermittelt die Pfade, die ein Angreifer durch das System nehmen könnte. Da sich bei einem komplexen System eine große Anzahl an Pfaden ergibt, können diese für eine detailliertere Betrachtung priorisiert werden. Die Methodik kann in allen Phasen des Systemlebenszyklus eingesetzt werden. Sie ist erweiterbar gehalten, um zusätzliche Informationen und Konzepte einbeziehen zu können.The evaluation of security of a system requires a system description. The description determines the quality of the analysis and the quality of the corresponding security solution. The thesis introduces a methodology for evaluating the security of systems. By starting with a simple model and iteratively refining it, the resulting model represents an as complete as needed view on the system under evaluation by keeping the single steps manageable. In real world scenarios, it is a common case that the degree of information available varies. The approach can deal with missing information on parts of the system. Finally, it leads to a model of different levels of abstraction for each subsystem. After each atomic step of modeling, an analysis can be executed to evaluate the security of the modeled system. The analysis determines the paths an attacker could take through the system. As there will be a large number of paths for a complex system, they can be sorted for prioritized in depth inspection. The methodology is intended to be used at all steps of system life cycle. Additionally, it is extendable to allow inclusion of further information and concepts

    On Making Fiction: Frankenstein and the Life of Stories

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    Fiction is generally understood to be a fascinating, yet somehow deficient affair, merely derivative of reality. What if we could, instead, come up with an affirmative approach that takes stories seriously in their capacity to bring forth a substance of their own? Iconic texts such as Mary Shelley's Frankenstein and its numerous adaptations stubbornly resist our attempts to classify them as mere representations of reality. The author shows how these texts insist that we take them seriously as agents and interlocutors in our world- and culture-making activities. Drawing on this analysis, she develops a theory of narrative fiction as a generative practice
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