20,548 research outputs found

    Handling convexity-like constraints in variational problems

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    We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give estimates of the distance between the approximation space and the admissible set. This framework applies to the approximation of convex functions by piecewise linear functions on a mesh of the domain and by other finite-dimensional spaces such as tensor-product splines. We show how these discretizations are well suited for the numerical solution of problems of calculus of variations under convexity constraints. Our implementation relies on proximal algorithms, and can be easily parallelized, thus making it applicable to large scale problems in dimension two and three. We illustrate the versatility and the efficiency of our approach on the numerical solution of three problems in calculus of variation : 3D denoising, the principal agent problem, and optimization within the class of convex bodies.Comment: 23 page

    Resource theories of knowledge

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    How far can we take the resource theoretic approach to explore physics? Resource theories like LOCC, reference frames and quantum thermodynamics have proven a powerful tool to study how agents who are subject to certain constraints can act on physical systems. This approach has advanced our understanding of fundamental physical principles, such as the second law of thermodynamics, and provided operational measures to quantify resources such as entanglement or information content. In this work, we significantly extend the approach and range of applicability of resource theories. Firstly we generalize the notion of resource theories to include any description or knowledge that agents may have of a physical state, beyond the density operator formalism. We show how to relate theories that differ in the language used to describe resources, like micro and macroscopic thermodynamics. Finally, we take a top-down approach to locality, in which a subsystem structure is derived from a global theory rather than assumed. The extended framework introduced here enables us to formalize new tasks in the language of resource theories, ranging from tomography, cryptography, thermodynamics and foundational questions, both within and beyond quantum theory.Comment: 28 pages featuring figures, examples, map and neatly boxed theorems, plus appendi

    Opinion dynamics and decision of vote in bipolar political systems

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    A model of the opinion dynamics underlying the political decision is proposed. The analysis is restricted to a bipolar scheme with a possible third political area. The interaction among voters is local but the final decision strongly depends on global effects such as, for example, the rating of the governments. As in the realistic case, the individual decision making process is determined by the most relevant personal interests and problems. The phenomenological analysis of the national vote in Italy and Germany has been carried out and a prediction of the next Italian vote as a function of the government rating is presented.Comment: 8 pages, 1 figure. To be published in International Journal of Modern Physics

    Proof Theory, Transformations, and Logic Programming for Debugging Security Protocols

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    We define a sequent calculus to formally specify, simulate, debug and verify security protocols. In our sequents we distinguish between the current knowledge of principals and the current global state of the session. Hereby, we can describe the operational semantics of principals and of an intruder in a simple and modular way. Furthermore, using proof theoretic tools like the analysis of permutability of rules, we are able to find efficient proof strategies that we prove complete for special classes of security protocols including Needham-Schroeder. Based on the results of this preliminary analysis, we have implemented a Prolog meta-interpreter which allows for rapid prototyping and for checking safety properties of security protocols, and we have applied it for finding error traces and proving correctness of practical examples

    Roaming Real-Time Applications - Mobility Services in IPv6 Networks

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    Emerging mobility standards within the next generation Internet Protocol, IPv6, promise to continuously operate devices roaming between IP networks. Associated with the paradigm of ubiquitous computing and communication, network technology is on the spot to deliver voice and videoconferencing as a standard internet solution. However, current roaming procedures are too slow, to remain seamless for real-time applications. Multicast mobility still waits for a convincing design. This paper investigates the temporal behaviour of mobile IPv6 with dedicated focus on topological impacts. Extending the hierarchical mobile IPv6 approach we suggest protocol improvements for a continuous handover, which may serve bidirectional multicast communication, as well. Along this line a multicast mobility concept is introduced as a service for clients and sources, as they are of dedicated importance in multipoint conferencing applications. The mechanisms introduced do not rely on assumptions of any specific multicast routing protocol in use.Comment: 15 pages, 5 figure

    Discounted Stochastic Games with Voluntary Transfers

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    This paper studies discounted stochastic games perfect or imperfect public monitoring and the opportunity to conduct voluntary monetary transfers. We show that for all discount factors every public perfect equilibrium payoff can be implemented with a simple class of equilibria that have a stationary structure on the equilibrium path and optimal penal codes with a stick and carrot structure. We develop algorithms that exactly compute or approximate the set of equilibrium payoffs and find simple equilibria that implement these payoffs.Stochastic games, Monetary transfers, Computation, Imperfect public monitoring, Public perfect equilibria

    Measurement in Economics and Social Science

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    The paper discusses measurement, primarily in economics, from both analytical and historical perspectives. The historical section traces the commitment to ordinalism on the part of economic theorists from the doctrinal disputes between classical economics and marginalism, through the struggle of orthodox economics against socialism down to the cold-war alliance between mathematical social science and anti-communist ideology. In economics the commitment to ordinalism led to the separation of theory from the quantitative measures that are computed in practice: price and quantity indexes, consumer surplus and real national product. The commitment to ordinality entered political science, via Arrow’s ‘impossibility theorem’, effectively merging it with economics, and ensuring its sterility. How can a field that has as its central result the impossibility of democracy contribute to the design of democratic institutions? The analytical part of the paper deals with the quantitative measures mentioned above. I begin with the conceptual clarification that what these measures try to achieve is a restoration of the money metric that is lost when prices are variable. I conclude that there is only one measure that can be embedded in a satisfactory economic theory, free from unreasonable restrictions. It is the Törnqvist index as an approximation to its theoretical counterpart the Divisia index. The statistical agencies have at various times produced different measures for real national product and its components, as well as related concepts. I argue that all of these are flawed and that a single deflator should be used for the aggregate and the components. Ideally this should be a chained Törnqvist price index defined on aggregate consumption. The social sciences are split. The economic approach is abstract, focused on the assumption of rational and informed behavior, and tends to the political right. The sociological approach is empirical, stresses the non-rational aspects of human behavior and tends to the political left. I argue that the split is due to the fact that the empirical and theoretical traditions were never joined in the social sciences as they were in the natural sciences. I also argue that measurement can potentially help in healing this split
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