181 research outputs found

    Informal proof, formal proof, formalism

    Get PDF
    Increases in the use of automated theorem-provers have renewed focus on the relationship between the informal proofs normally found in mathematical research and fully formalised derivations. Whereas some claim that any correct proof will be underwritten by a fully formal proof, sceptics demur. In this paper I look at the relevance of these issues for formalism, construed as an anti-platonistic metaphysical doctrine. I argue that there are strong reasons to doubt that all proofs are fully formalisable, if formal proofs are required to be finitary, but that, on a proper view of the way in which formal proofs idealise actual practice, this restriction is unjustified and formalism is not threatened

    Automatic Service Composition. Models, Techniques and Tools.

    Get PDF
    Maurizio Lenzerini, Giuseppe De Giacomo, Massimo Mecell

    Use of trusts as a vehicle for estate (tax) planning in South Africa

    Get PDF
    Estate planning has been described as the process whereby a person acquires property, ensuring that he derives maximum benefits from his ownership and the enjoyment thereof during his lifetime, and that as much as possible and in the most economical manner with the minimum erosion thereof shall devolve upon his heirs when he dies. ( 1) The objective of estate planning is thus, in essence, the disposal of property during the estate owner's ('the planner') lifetime or upon his death

    Exciton band topology in spontaneous quantum anomalous Hall insulators: applications to twisted bilayer graphene

    Full text link
    We uncover topological features of neutral particle-hole pair excitations of correlated quantum anomalous Hall (QAH) insulators whose approximately flat conduction and valence bands have equal and opposite non-zero Chern number. Using an exactly solvable model we show that the underlying band topology affects both the center-of-mass and relative motion of particle-hole bound states. This leads to the formation of topological exciton bands whose features are robust to nonuniformity of both the dispersion and the Berry curvature. We apply these ideas to recently-reported broken-symmetry spontaneous QAH insulators in substrate aligned magic-angle twisted bilayer graphene.Comment: 5+10 pages, 2+2 figures; improved treatment of interaction effects, leading to |C|=1 exciton

    A mathematical theory of semantic development in deep neural networks

    Full text link
    An extensive body of empirical research has revealed remarkable regularities in the acquisition, organization, deployment, and neural representation of human semantic knowledge, thereby raising a fundamental conceptual question: what are the theoretical principles governing the ability of neural networks to acquire, organize, and deploy abstract knowledge by integrating across many individual experiences? We address this question by mathematically analyzing the nonlinear dynamics of learning in deep linear networks. We find exact solutions to this learning dynamics that yield a conceptual explanation for the prevalence of many disparate phenomena in semantic cognition, including the hierarchical differentiation of concepts through rapid developmental transitions, the ubiquity of semantic illusions between such transitions, the emergence of item typicality and category coherence as factors controlling the speed of semantic processing, changing patterns of inductive projection over development, and the conservation of semantic similarity in neural representations across species. Thus, surprisingly, our simple neural model qualitatively recapitulates many diverse regularities underlying semantic development, while providing analytic insight into how the statistical structure of an environment can interact with nonlinear deep learning dynamics to give rise to these regularities
    • …
    corecore