6,527 research outputs found
An associative network with spatially organized connectivity
We investigate the properties of an autoassociative network of
threshold-linear units whose synaptic connectivity is spatially structured and
asymmetric. Since the methods of equilibrium statistical mechanics cannot be
applied to such a network due to the lack of a Hamiltonian, we approach the
problem through a signal-to-noise analysis, that we adapt to spatially
organized networks. The conditions are analyzed for the appearance of stable,
spatially non-uniform profiles of activity with large overlaps with one of the
stored patterns. It is also shown, with simulations and analytic results, that
the storage capacity does not decrease much when the connectivity of the
network becomes short range. In addition, the method used here enables us to
calculate exactly the storage capacity of a randomly connected network with
arbitrary degree of dilution.Comment: 27 pages, 6 figures; Accepted for publication in JSTA
Associative memory on a small-world neural network
We study a model of associative memory based on a neural network with
small-world structure. The efficacy of the network to retrieve one of the
stored patterns exhibits a phase transition at a finite value of the disorder.
The more ordered networks are unable to recover the patterns, and are always
attracted to mixture states. Besides, for a range of the number of stored
patterns, the efficacy has a maximum at an intermediate value of the disorder.
We also give a statistical characterization of the attractors for all values of
the disorder of the network.Comment: 5 pages, 4 figures (eps
An exploration into aesthetic association of product form
Creating a relevant and pleasing design aesthetic is a fundamental aim designers
endeavour to achieve. Perception of aesthetics takes place both during the design
process when the designer creates a form, and later, through the users’
interpretation of the form. Within the perception process, association plays a
significant role. This paper addresses the stage research results of our exploration
into the associative meanings of a product. By analysing the evaluation of a series of
top award winning designs, it was found that some associative meanings
(represented by descriptive words) are correlated, such as ‘pure-architecturalgeometrical’,
‘delicate-curvaceous-organic’ etc. By conducting a series of
workshops, both in the UK and China, we have been able to explore the extent to
which young designers are able to manipulate form, style and create an overall
perception of a positive aesthetic. One of the main outputs during the workshops
was to design a MP3 player with speaker units, styled in line with three topics of
aesthetic association: topic 1 – pure, architectural, geometrical and technical; topic 2 – curvaceous, organic, and fun; topic 3 – graceful, cheerful, and powerful. Three non-correlated associative descriptors were deliberately used in topic 3. Results suggest that young designers tend to differ in their ability and success of manipulating form to match different aesthetic targets. When the descriptive words in one aesthetic topic are correlated, student designers seem to find it easier to manipulate the form matching the topic. Comparative analysis between the results from the workshops in the UK (Southampton Solent University) and in China
(Tsinghua University) is also presented in the paper
The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein
The folding pathway and rate coefficients of the folding of a knotted protein
are calculated for a potential energy function with minimal energetic
frustration. A kinetic transition network is constructed using the discrete
path sampling approach, and the resulting potential energy surface is
visualized by constructing disconnectivity graphs. Owing to topological
constraints, the low-lying portion of the landscape consists of three distinct
regions, corresponding to the native knotted state and to configurations where
either the N- or C-terminus is not yet folded into the knot. The fastest
folding pathways from denatured states exhibit early formation of the
N-terminus portion of the knot and a rate-determining step where the C-terminus
is incorporated. The low-lying minima with the N-terminus knotted and the
C-terminus free therefore constitute an off-pathway intermediate for this
model. The insertion of both the N- and C-termini into the knot occur late in
the folding process, creating large energy barriers that are the rate limiting
steps in the folding process. When compared to other protein folding proteins
of a similar length, this system folds over six orders of magnitude more
slowly.Comment: 19 page
Tensorial dynamics on the space of quantum states
A geometric description of the space of states of a finite-dimensional
quantum system and of the Markovian evolution associated with the
Kossakowski-Lindblad operator is presented. This geometric setting is based on
two composition laws on the space of observables defined by a pair of
contravariant tensor fields. The first one is a Poisson tensor field that
encodes the commutator product and allows us to develop a Hamiltonian
mechanics. The other tensor field is symmetric, encodes the Jordan product and
provides the variances and covariances of measures associated with the
observables. This tensorial formulation of quantum systems is able to describe,
in a natural way, the Markovian dynamical evolution as a vector field on the
space of states. Therefore, it is possible to consider dynamical effects on
non-linear physical quantities, such as entropies, purity and concurrence. In
particular, in this work the tensorial formulation is used to consider the
dynamical evolution of the symmetric and skew-symmetric tensors and to read off
the corresponding limits as giving rise to a contraction of the initial Jordan
and Lie products.Comment: 31 pages, 2 figures. Minor correction
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