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Computational Properties (computational + property)
Selected AbstractsComputational significance of transient dynamics in cortical networksEUROPEAN JOURNAL OF NEUROSCIENCE, Issue 1 2008Daniel Durstewitz Abstract Neural responses are most often characterized in terms of the sets of environmental or internal conditions or stimuli with which their firing rate are correlated increases or decreases. Their transient (nonstationary) temporal profiles of activity have received comparatively less attention. Similarly, the computational framework of attractor neural networks puts most emphasis on the representational or computational properties of the stable states of a neural system. Here we review a couple of neurophysiological observations and computational ideas that shift the focus to the transient dynamics of neural systems. We argue that there are many situations in which the transient neural behaviour, while hopping between different attractor states or moving along ,attractor ruins', carries most of the computational and/or behavioural significance, rather than the attractor states eventually reached. Such transients may be related to the computation of temporally precise predictions or the probabilistic transitions among choice options, accounting for Weber's law in decision-making tasks. Finally, we conclude with a more general perspective on the role of transient dynamics in the brain, promoting the view that brain activity is characterized by a high-dimensional chaotic ground state from which transient spatiotemporal patterns (metastable states) briefly emerge. Neural computation has to exploit the itinerant dynamics between these states. [source] Grid cells: The position code, neural network models of activity, and the problem of learningHIPPOCAMPUS, Issue 12 2008Peter E. Welinder Abstract We review progress on the modeling and theoretical fronts in the quest to unravel the computational properties of the grid cell code and to explain the mechanisms underlying grid cell dynamics. The goals of the review are to outline a coherent framework for understanding the dynamics of grid cells and their representation of space; to critically present and draw contrasts between recurrent network models of grid cells based on continuous attractor dynamics and independent-neuron models based on temporal interference; and to suggest open questions for experiment and theory. © 2008 Wiley-Liss, Inc. [source] Solving time-dependent PDEs using the material point method, a case study from gas dynamicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2010L. T. Tran Abstract The material point method (MPM) developed by Sulsky and colleagues is currently being used to solve many challenging problems involving large deformations and/or fragementations with some success. In order to understand the properties of this method, an analysis of the considerable computational properties of MPM is undertaken in the context of model problems from gas dynamics. The MPM method in the form used here is shown both theoretically and computationally to have first-order accuracy for a standard gas dynamics test problem. Copyright © 2009 John Wiley & Sons, Ltd. [source] A Tractable and Expressive Class of Marginal Contribution Nets and Its ApplicationsMLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 4 2009Edith Elkind Abstract Coalitional games raise a number of important questions from the point of view of computer science, key among them being how to represent such games compactly, and how to efficiently compute solution concepts assuming such representations. Marginal contribution nets (MC-nets), introduced by Ieong and Shoham, are one of the simplest and most influential representation schemes for coalitional games. MC-nets are a rulebased formalism, in which rules take the form pattern , value, where "pattern " is a Boolean condition over agents, and "value " is a numeric value. Ieong and Shoham showed that, for a class of what we will call "basic" MC-nets, where patterns are constrained to be a conjunction of literals, marginal contribution nets permit the easy computation of solution concepts such as the Shapley value. However, there are very natural classes of coalitional games that require an exponential number of such basic MC-net rules. We present read-once MC- nets, a new class of MC-nets that is provably more compact than basic MC-nets, while retaining the attractive computational properties of basic MC-nets. We show how the techniques we develop for read-once MC-nets can be applied to other domains, in particular, computing solution concepts in network flow games on series-parallel networks (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Effective Borel measurability and reducibility of functionsMLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 1 2005Vasco Brattka Abstract The investigation of computational properties of discontinuous functions is an important concern in computable analysis. One method to deal with this subject is to consider effective variants of Borel measurable functions. We introduce such a notion of Borel computability for single-valued as well as for multi-valued functions by a direct effectivization of the classical definition. On Baire space the finite levels of the resulting hierarchy of functions can be characterized using a notion of reducibility for functions and corresponding complete functions. We use this classification and an effective version of a Selection Theorem of Bhattacharya-Srivastava in order to prove a generalization of the Representation Theorem of Kreitz-Weihrauch for Borel measurable functions on computable metric spaces: such functions are Borel measurable on a certain finite level, if and only if they admit a realizer on Baire space of the same quality. This Representation Theorem enables us to introduce a realizer reducibility for functions on metric spaces and we can extend the completeness result to this reducibility. Besides being very useful by itself, this reducibility leads to a new and effective proof of the Banach-Hausdorff-Lebesgue Theorem which connects Borel measurable functions with the Baire functions. Hence, for certain metric spaces the class of Borel computable functions on a certain level is exactly the class of functions which can be expressed as a limit of a pointwise convergent and computable sequence of functions of the next lower level. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Unified multipliers-free theory of dual-primal domain decomposition methodsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2009Ismael Herrera Abstract The concept of dual-primal methods can be formulated in a manner that incorporates, as a subclass, the non preconditioned case. Using such a generalized concept, in this article without recourse to "Lagrange multipliers," we introduce an all-inclusive unified theory of nonoverlapping domain decomposition methods (DDMs). One-level methods, such as Schur-complement and one-level FETI, as well as two-level methods, such as Neumann-Neumann and preconditioned FETI, are incorporated in a unified manner. Different choices of the dual subspaces yield the different dual-primal preconditioners reported in the literature. In this unified theory, the procedures are carried out directly on the matrices, independently of the differential equations that originated them. This feature reduces considerably the code-development effort required for their implementation and permit, for example, transforming 2D codes into 3D codes easily. Another source of this simplification is the introduction of two projection-matrices, generalizations of the average and jump of a function, which possess superior computational properties. In particular, on the basis of numerical results reported there, we claim that our jump matrix is the optimal choice of the B operator of the FETI methods. A new formula for the Steklov-Poincaré operator, at the discrete level, is also introduced. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] Inferring planar disorder in close-packed structures via,-machine spectral reconstruction theory: structure and intrinsic computation in zinc sulfideACTA CRYSTALLOGRAPHICA SECTION B, Issue 2 2007D. P. Varn We apply ,-machine spectral reconstruction theory to analyze structure and disorder in four previously published zinc sulfide diffraction spectra and contrast the results with the most common alternative theory, the fault model. In each case we find that the reconstructed ,-machine provides a more comprehensive and detailed understanding of the stacking structure, often detecting stacking structures not previously found. Using the ,-machines reconstructed for each spectrum, we calculate a number of physical parameters , such as configurational energies, configurational entropies and hexagonality , and several quantities , including statistical complexity and excess entropy , that describe the intrinsic computational properties of the stacking structures. [source] Emergent biological principles and the computational properties of the universe: Explaining it or explaining it awayCOMPLEXITY, Issue 2 2004P. C. W. Davies First page of article [source] | |||||||||||||