132,449 research outputs found
Scaffolding layered control architectures through constraint closure : insights into brain evolution and development
The functional organization of the mammalian brain can be considered to form a layered control architecture, but how this complex system has emerged through evolution and is constructed during development remains a puzzle. Here we consider brain organization through the framework of constraint closure, viewed as a general characteristic of living systems, that they are composed of multiple sub-systems that constrain each other at different timescales. We do so by developing a new formalism for constraint closure, inspired by a previous model showing how within-lifetime dynamics can constrain between-lifetime dynamics, and we demonstrate how this interaction can be generalized to multi-layered systems. Through this model, we consider brain organization in the context of two major examples of constraint closure—physiological regulation and visual orienting. Our analysis draws attention to the capacity of layered brain architectures to scaffold themselves across multiple timescales, including the ability of cortical processes to constrain the evolution of sub-cortical processes, and of the latter to constrain the space in which cortical systems self-organize and refine themselves
Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data
Constraint Programming (CP) has proved an effective paradigm to model and
solve difficult combinatorial satisfaction and optimisation problems from
disparate domains. Many such problems arising from the commercial world are
permeated by data uncertainty. Existing CP approaches that accommodate
uncertainty are less suited to uncertainty arising due to incomplete and
erroneous data, because they do not build reliable models and solutions
guaranteed to address the user's genuine problem as she perceives it. Other
fields such as reliable computation offer combinations of models and associated
methods to handle these types of uncertain data, but lack an expressive
framework characterising the resolution methodology independently of the model.
We present a unifying framework that extends the CP formalism in both model
and solutions, to tackle ill-defined combinatorial problems with incomplete or
erroneous data. The certainty closure framework brings together modelling and
solving methodologies from different fields into the CP paradigm to provide
reliable and efficient approches for uncertain constraint problems. We
demonstrate the applicability of the framework on a case study in network
diagnosis. We define resolution forms that give generic templates, and their
associated operational semantics, to derive practical solution methods for
reliable solutions.Comment: Revised versio
An Improved Tight Closure Algorithm for Integer Octagonal Constraints
Integer octagonal constraints (a.k.a. ``Unit Two Variables Per Inequality''
or ``UTVPI integer constraints'') constitute an interesting class of
constraints for the representation and solution of integer problems in the
fields of constraint programming and formal analysis and verification of
software and hardware systems, since they couple algorithms having polynomial
complexity with a relatively good expressive power. The main algorithms
required for the manipulation of such constraints are the satisfiability check
and the computation of the inferential closure of a set of constraints. The
latter is called `tight' closure to mark the difference with the (incomplete)
closure algorithm that does not exploit the integrality of the variables. In
this paper we present and fully justify an O(n^3) algorithm to compute the
tight closure of a set of UTVPI integer constraints.Comment: 15 pages, 2 figure
Classical general relativity as BF-Plebanski theory with linear constraints
We investigate a formulation of continuum 4d gravity in terms of a
constrained BF theory, in the spirit of the Plebanski formulation, but
involving only linear constraints, of the type used recently in the spin foam
approach to quantum gravity. We identify both the continuum version of the
linear simplicity constraints used in the quantum discrete context and a linear
version of the quadratic volume constraints that are necessary to complete the
reduction from the topological theory to gravity. We illustrate and discuss
also the discrete counterpart of the same continuum linear constraints.
Moreover, we show under which additional conditions the discrete volume
constraints follow from the simplicity constraints, thus playing the role of
secondary constraints.Comment: 16 pages, revtex, changed one cross-reference in sect. IIIC to match
journal versio
Commuting Simplicity and Closure Constraints for 4D Spin Foam Models
Spin Foam Models are supposed to be discretised path integrals for quantum
gravity constructed from the Plebanski-Holst action. The reason for there being
several models currently under consideration is that no consensus has been
reached for how to implement the simplicity constraints. Indeed, none of these
models strictly follows from the original path integral with commuting B
fields, rather, by some non standard manipulations one always ends up with non
commuting B fields and the simplicity constraints become in fact anomalous
which is the source for there being several inequivalent strategies to
circumvent the associated problems. In this article, we construct a new
Euclidian Spin Foam Model which is constructed by standard methods from the
Plebanski-Holst path integral with commuting B fields discretised on a 4D
simplicial complex. The resulting model differs from the current ones in
several aspects, one of them being that the closure constraint needs special
care. Only when dropping the closure constraint by hand and only in the large
spin limit can the vertex amplitudes of this model be related to those of the
FK Model but even then the face and edge amplitude differ. Curiously, an ad hoc
non-commutative deformation of the variables leads from our new model
to the Barrett-Crane Model in the case of Barbero-Immirzi parameter goes to
infinity.Comment: 41 pages, 4 figure
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