245 research outputs found

    Higher Structures in M-Theory

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    The key open problem of string theory remains its non-perturbative completion to M-theory. A decisive hint to its inner workings comes from numerous appearances of higher structures in the limits of M-theory that are already understood, such as higher degree flux fields and their dualities, or the higher algebraic structures governing closed string field theory. These are all controlled by the higher homotopy theory of derived categories, generalised cohomology theories, and L∞L_\infty-algebras. This is the introductory chapter to the proceedings of the LMS/EPSRC Durham Symposium on Higher Structures in M-Theory. We first review higher structures as well as their motivation in string theory and beyond. Then we list the contributions in this volume, putting them into context.Comment: 22 pages, Introductory Article to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018, references update

    Causal structures and causal boundaries

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    We give an up-to-date perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications, and the definition and construction of causal boundaries and of causal symmetries, mostly for Lorentzian manifolds but also in more abstract settings.Comment: Final version. To appear in Classical and Quantum Gravit

    Courbure discrÚte : théorie et applications

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    International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor

    The Necessary Structure of the All-pervading Aether: Discrete or Continuous? Simple or Symmetric?

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    In this book I investigate the necessary structure of the aether – the stuff that fills the whole universe. Some of my conclusions are. 1. There is an enormous variety of structures that the aether might, for all we know, have. 2. Probably the aether is point-free. 3. In that case, it should be distinguished from Space-time, which is either a fiction or a construct. 4. Even if the aether has points, we should reject the orthodoxy that all regions are grounded in points by summation. 5. If the aether is point-free but not continuous, its most likely structure has extended atoms that are not simples. 6. Space-time is symmetric if and only if the aether is continuous. 7. If the aether is continuous, we should reject the standard interpretation of General Relativity, in which geometry determines gravity. 8. Contemporary physics undermines an objection to discrete aether based on scale invariance, but does not offer much positive support

    The Markov-Dubins Problem with Free Terminal Direction in a Nonpositively Curved Cube Complex

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    State complexes are nonpositively curved cube complexes that model the state spaces of reconfigurable systems. The problem of determining a strategy for reconfiguring the system from a given initial state to a given goal state is equivalent to that of finding a path between two points in the state complex. The additional requirement that allowable paths must have a prescribed initial direction and minimal turning radius determines a Markov-Dubins problem with free terminal direction (MDPFTD). Given a nonpositively curved, locally finite cube complex X, we consider the set of unit-speed paths which satisfy a certain smoothness condition in addition to the boundary conditions and curvature constraint that define a MDPFTD. We show that this set either contains a path of minimal length, or is empty. We then focus on the case that X is a surface with a nonpositively curved cubical structure. We show that any solution to a MDPFTD in X must consist of finitely many geodesic segments and arcs of constant curvature, and we give an algorithm for determining those solutions to the MDPFTD in X which are CL paths, that is, made up of an arc of constant curvature followed by a geodesic segment. Finally, under the assumption that the 1-skeleton of X is d-regular, we give sufficient conditions for a topological ray in X of constant curvature to be a rose curve or a proper ray

    How to Make n-D Plain Maps defined on Discrete Surfaces Alexandrov-Well-Composed in a Self-dual Way

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    International audienceIn 2013, Najman and GĂ©raud proved that by working on a well-composed discrete representation of a gray-level image, we can compute what is called its tree of shapes, a hierarchical representation of the shapes in this image. This way, we can proceed to morphological filtering and to image segmentation. However , the authors did not provide such a representation for the non-cubical case. We propose in this paper a way to compute a well-composed representation of any gray-level image defined on a discrete surface, which is a more general framework than the usual cubical grid. Furthermore, the proposed representation is self-dual in the sense that it treats bright and dark components in the image the same way. This paper can be seen as an extension to gray-level images of the works of Daragon et al. on discrete surfaces

    Complexity, Emergent Systems and Complex Biological Systems:\ud Complex Systems Theory and Biodynamics. [Edited book by I.C. Baianu, with listed contributors (2011)]

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    An overview is presented of System dynamics, the study of the behaviour of complex systems, Dynamical system in mathematics Dynamic programming in computer science and control theory, Complex systems biology, Neurodynamics and Psychodynamics.\u
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