52,285 research outputs found

    Bott-Kitaev Periodic Table and the Diagonal Map

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    Building on the 10-way symmetry classification of disordered fermions, the authors have recently given a homotopy-theoretic proof of Kitaev's "Periodic Table" for topological insulators and superconductors. The present paper offers an introduction to the physical setting and the mathematical model used. Basic to the proof is the so-called Diagonal Map, a natural transformation akin to the Bott map of algebraic topology, which increases by one unit both the momentum-space dimension and the symmetry index of translation-invariant ground states of gapped free-fermion systems. This mapping is illustrated here with a few examples of interest.Comment: Based on a talk delivered by the senior author at the Nobel Symposium on "New Forms of Matter: Topological Insulators and Superconductors" (Stockholm, June 13-15, 2014

    Science-in-brief: Clinical highlights from BEVA Congress 2016

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    A portable battery for objective, non-obstrusive measures of human performances

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    The need for a standardized battery of human performance tests to measure the effects of various treatments is pointed out. Progress in such a program is reported. Three batteries are available which differ in length and the number of tests in the battery. All tests are implemented on a portable, lap held, briefcase size microprocessor. Performances measured include: information processing, memory, visual perception, reasoning, and motor skills, programs to determine norms, reliabilities, stabilities, factor structure of tests, comparisons with marker tests, apparatus suitability. Rationale for the battery is provided

    Noncommutative Choquet theory

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    We introduce a new and extensive theory of noncommutative convexity along with a corresponding theory of noncommutative functions. We establish noncommutative analogues of the fundamental results from classical convexity theory, and apply these ideas to develop a noncommutative Choquet theory that generalizes much of classical Choquet theory. The central objects of interest in noncommutative convexity are noncommutative convex sets. The category of compact noncommutative sets is dual to the category of operator systems, and there is a robust notion of extreme point for a noncommutative convex set that is dual to Arveson's notion of boundary representation for an operator system. We identify the C*-algebra of continuous noncommutative functions on a compact noncommutative convex set as the maximal C*-algebra of the operator system of continuous noncommutative affine functions on the set. In the noncommutative setting, unital completely positive maps on this C*-algebra play the role of representing measures in the classical setting. The continuous convex noncommutative functions determine an order on the set of unital completely positive maps that is analogous to the classical Choquet order on probability measures. We characterize this order in terms of the extensions and dilations of the maps, providing a powerful new perspective on the structure of completely positive maps on operator systems. Finally, we establish a noncommutative generalization of the Choquet-Bishop-de Leeuw theorem asserting that every point in a compact noncommutative convex set has a representing map that is supported on the extreme boundary. In the separable case, we obtain a corresponding integral representation theorem.Comment: 81 pages; minor change

    Bott periodicity for Z2Z_2 symmetric ground states of gapped free-fermion systems

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    Building on the symmetry classification of disordered fermions, we give a proof of the proposal by Kitaev, and others, for a "Bott clock" topological classification of free-fermion ground states of gapped systems with symmetries. Our approach differs from previous ones in that (i) we work in the standard framework of Hermitian quantum mechanics over the complex numbers, (ii) we directly formulate a mathematical model for ground states rather than spectrally flattened Hamiltonians, and (iii) we use homotopy-theoretic tools rather than K-theory. Key to our proof is a natural transformation that squares to the standard Bott map and relates the ground state of a d-dimensional system in symmetry class s to the ground state of a (d+1)-dimensional system in symmetry class s+1. This relation gives a new vantage point on topological insulators and superconductors.Comment: 55 pages; one figure added; corrections in Section 8; proofs in Section 6 expande

    Comparative effects of prolonged rotation at 10 rpm on postural equilibrium in vestibular normal and vestibular defective human subjects

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    Comparative effects of prolonged rotation on postural equilibrium in vestibular normal and defective human subject

    Indigenous Intellectual Property Rights: Ethical Insights for Marketers

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    Present copyright laws do not protect Indigenous intellectual property (IIP) sufficiently. Indigenous cultural artefacts, myths, designs and songs (among other aspects) are often free to be exploited by marketers for business\u27 gain. Use of IIP by marketers is legal as intellectual property protection is based on the lifetime of the person who has put the IP in tangible form. However, Indigenous groups often view ownership in a very different light, seeing aspects of their culture as being owned by the group in perpetuity. Misuse of their cultural heritage by marketers in products often denies the Indigenous group a monetary benefit from their use and is frequently disrespectful. This article discusses ethical insights that might shed moral weight on this issue

    Motion Sickness Symptomatology of Labyrinthine Defective and Normal Subjects During Zero Gravity Maneuvers

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    Motion sickness symptomology of labyrinthine defective and normal human subjects during zero gravity maneuver
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