12,384 research outputs found

    On empirical methodology, constraints, and hierarchy in artificial grammar learning

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    This paper considers the AGL literature from a psycholinguistic perspective. It first presents a taxonomy of the experimental familiarization test procedures used, which is followed by a consideration of shortcomings and potential improvements of the empirical methodology. It then turns to reconsidering the issue of grammar learning from the point of view of acquiring constraints, instead of the traditional AGL approach in terms of acquiring sets of rewrite rules. This is, in particular, a natural way of handling long‐distance dependences. The final section addresses an underdeveloped issue in the AGL literature, namely how to detect latent hierarchical structure in AGL response patterns

    Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions

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    We express AKNS hierarchies, admitting reductions to matrix NLS and matrix mKdV hierarchies, in terms of a bidifferential graded algebra. Application of a universal result in this framework quickly generates an infinite family of exact solutions, including e.g. the matrix solitons in the focusing NLS case. Exploiting a general Miura transformation, we recover the generalized Heisenberg magnet hierarchy and establish a corresponding solution formula for it. Simply by exchanging the roles of the two derivations of the bidifferential graded algebra, we recover "negative flows", leading to an extension of the respective hierarchy. In this way we also meet a matrix and vector version of the short pulse equation and also the sine-Gordon equation. For these equations corresponding solution formulas are also derived. In all these cases the solutions are parametrized in terms of matrix data that have to satisfy a certain Sylvester equation

    The King's many bodies: the self-deconstruction of law's hierarchy

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    The article connects two strands of the recent sociolegal debate: (1) the empirical discovery of new forms of spontaneous law in die Course of globalization, and (2) the emergence of deconstructive theories of law that undermine the law's hierarchy. The article puts forward the thesis that law's hierarchy has successfully resisted all old and new attempts at its deconstruction; it breaks, however, under the pressures of globalization that produced a global law without the state, as self-created law of global society that has no institutionalized support whatsoever in international poliucs and public international law. Consequently, the article criticizes deconstructive theories for their lack of autological analysis. These theories do not take into account the historical condicions of deconstruction. Accordingly, deconstructive analysis of law would have to look for new legal distinctions that are plausible under the new condicions of a doubly fragmented global society. The article sketches the contours of an emerging polycontextural law

    Synchronization and Control in Intrinsic and Designed Computation: An Information-Theoretic Analysis of Competing Models of Stochastic Computation

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    We adapt tools from information theory to analyze how an observer comes to synchronize with the hidden states of a finitary, stationary stochastic process. We show that synchronization is determined by both the process's internal organization and by an observer's model of it. We analyze these components using the convergence of state-block and block-state entropies, comparing them to the previously known convergence properties of the Shannon block entropy. Along the way, we introduce a hierarchy of information quantifiers as derivatives and integrals of these entropies, which parallels a similar hierarchy introduced for block entropy. We also draw out the duality between synchronization properties and a process's controllability. The tools lead to a new classification of a process's alternative representations in terms of minimality, synchronizability, and unifilarity.Comment: 25 pages, 13 figures, 1 tabl
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