297 research outputs found
Events in computation
SIGLEAvailable from British Library Document Supply Centre- DSC:D36018/81 / BLDSC - British Library Document Supply CentreGBUnited Kingdo
Compact Hypergroups from Discrete Subfactors
Conformal inclusions of chiral conformal field theories, or more generally
inclusions of quantum field theories, are described in the von Neumann
algebraic setting by nets of subfactors, possibly with infinite Jones index if
one takes non-rational theories into account. With this situation in mind, we
study in a purely subfactor theoretical context a certain class of braided
discrete subfactors with an additional commutativity constraint, that we call
locality, and which corresponds to the commutation relations between field
operators at space-like distance in quantum field theory. Examples of
subfactors of this type come from taking a minimal action of a compact group on
a factor and considering the fixed point subalgebra. We show that to every
irreducible local discrete subfactor of type
there is an associated canonical compact hypergroup (an invariant
for the subfactor) which acts on by unital completely positive
(ucp) maps and which gives as fixed points. To show this, we
establish a duality pairing between the set of all -bimodular ucp
maps on and a certain commutative unital -algebra, whose
spectrum we identify with the compact hypergroup. If the subfactor has depth 2,
the compact hypergroup turns out to be a compact group. This rules out the
occurrence of compact \emph{quantum} groups acting as global gauge symmetries
in local conformal field theory.Comment: 58 page
Spin Torque Dynamics with Noise in Magnetic Nano-System
We investigate the role of equilibrium and nonequilibrium noise in the
magnetization dynamics on mono-domain ferromagnets. Starting from a microscopic
model we present a detailed derivation of the spin shot noise correlator. We
investigate the ramifications of the nonequilibrium noise on the spin torque
dynamics, both in the steady state precessional regime and the spin switching
regime. In the latter case we apply a generalized Fokker-Planck approach to
spin switching, which models the switching by an Arrhenius law with an
effective elevated temperature. We calculate the renormalization of the
effective temperature due to spin shot noise and show that the nonequilibrium
noise leads to the creation of cold and hot spot with respect to the noise
intensity.Comment: 10 pages, 7 figure
On the Realisability of Chemical Pathways
The exploration of pathways and alternative pathways that have a specific
function is of interest in numerous chemical contexts. A framework for
specifying and searching for pathways has previously been developed, but a
focus on which of the many pathway solutions are realisable, or can be made
realisable, is missing. Realisable here means that there actually exists some
sequencing of the reactions of the pathway that will execute the pathway. We
present a method for analysing the realisability of pathways based on the
reachability question in Petri nets. For realisable pathways, our method also
provides a certificate encoding an order of the reactions which realises the
pathway. We present two extended notions of realisability of pathways, one of
which is related to the concept of network catalysts. We exemplify our findings
on the pentose phosphate pathway. Lastly, we discuss the relevance of our
concepts for elucidating the choices often implicitly made when depicting
pathways.Comment: Accepted in LNBI proceeding
Metastability, Criticality and Phase Transitions in brain and its Models
This essay extends the previously deposited paper "Oscillations, Metastability and Phase Transitions" to incorporate the theory of Self-organizing Criticality. The twin concepts of Scaling and Universality of the theory of nonequilibrium phase transitions is applied to the role of reentrant activity in neural circuits of cerebral cortex and subcortical neural structures
Topological Foundations of Cognitive Science
A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers:
** Topological Foundations of Cognitive Science, Barry Smith
** The Bounds of Axiomatisation, Graham White
** Rethinking Boundaries, Wojciech Zelaniec
** Sheaf Mereology and Space Cognition, Jean Petitot
** A Mereotopological Definition of 'Point', Carola Eschenbach
** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel
** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda
** Defining a 'Doughnut' Made Difficult, N .M. Gotts
** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts
** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi
** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki
Phase coexistence of gradient Gibbs states
We consider the (scalar) gradient fields --with denoting
the nearest-neighbor edges in --that are distributed according to the
Gibbs measure proportional to \texte^{-\beta H(\eta)}\nu(\textd\eta). Here
is the Hamiltonian, is a symmetric potential,
is the inverse temperature, and is the Lebesgue measure on the linear
space defined by imposing the loop condition
for each plaquette
in . For convex , Funaki and Spohn have shown that
ergodic infinite-volume Gibbs measures are characterized by their tilt. We
describe a mechanism by which the gradient Gibbs measures with non-convex
undergo a structural, order-disorder phase transition at some intermediate
value of inverse temperature . At the transition point, there are at
least two distinct gradient measures with zero tilt, i.e., .Comment: 3 figs, PTRF style files include
Geometry and dynamics in Gromov hyperbolic metric spaces: With an emphasis on non-proper settings
Our monograph presents the foundations of the theory of groups and semigroups
acting isometrically on Gromov hyperbolic metric spaces. Our work unifies and
extends a long list of results by many authors. We make it a point to avoid any
assumption of properness/compactness, keeping in mind the motivating example of
, the infinite-dimensional rank-one symmetric space of
noncompact type over the reals. The monograph provides a number of examples of
groups acting on which exhibit a wide range of phenomena not
to be found in the finite-dimensional theory. Such examples often demonstrate
the optimality of our theorems. We introduce a modification of the Poincar\'e
exponent, an invariant of a group which gives more information than the usual
Poincar\'e exponent, which we then use to vastly generalize the Bishop--Jones
theorem relating the Hausdorff dimension of the radial limit set to the
Poincar\'e exponent of the underlying semigroup. We give some examples based on
our results which illustrate the connection between Hausdorff dimension and
various notions of discreteness which show up in non-proper settings. We
construct Patterson--Sullivan measures for groups of divergence type without
any compactness assumption. This is carried out by first constructing such
measures on the Samuel--Smirnov compactification of the bordification of the
underlying hyperbolic space, and then showing that the measures are supported
on the bordification. We study quasiconformal measures of geometrically finite
groups in terms of (a) doubling and (b) exact dimensionality. Our analysis
characterizes exact dimensionality in terms of Diophantine approximation on the
boundary. We demonstrate that some Patterson--Sullivan measures are neither
doubling nor exact dimensional, and some are exact dimensional but not
doubling, but all doubling measures are exact dimensional.Comment: A previous version of this document included Section 12.5 (Tukia's
isomorphism theorem). The results of that subsection have been split off into
a new document which is available at arXiv:1508.0696
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