1,063 research outputs found
Stochastic learning in a neural network with adapting synapses
We consider a neural network with adapting synapses whose dynamics can be
analitically computed. The model is made of neurons and each of them is
connected to input neurons chosen at random in the network. The synapses
are -states variables which evolve in time according to Stochastic Learning
rules; a parallel stochastic dynamics is assumed for neurons. Since the network
maintains the same dynamics whether it is engaged in computation or in learning
new memories, a very low probability of synaptic transitions is assumed. In the
limit with large and finite, the correlations of neurons and
synapses can be neglected and the dynamics can be analitically calculated by
flow equations for the macroscopic parameters of the system.Comment: 25 pages, LaTeX fil
A recurrent neural network with ever changing synapses
A recurrent neural network with noisy input is studied analytically, on the
basis of a Discrete Time Master Equation. The latter is derived from a
biologically realizable learning rule for the weights of the connections. In a
numerical study it is found that the fixed points of the dynamics of the net
are time dependent, implying that the representation in the brain of a fixed
piece of information (e.g., a word to be recognized) is not fixed in time.Comment: 17 pages, LaTeX, 4 figure
Hierarchical Self-Programming in Recurrent Neural Networks
We study self-programming in recurrent neural networks where both neurons
(the `processors') and synaptic interactions (`the programme') evolve in time
simultaneously, according to specific coupled stochastic equations. The
interactions are divided into a hierarchy of groups with adiabatically
separated and monotonically increasing time-scales, representing sub-routines
of the system programme of decreasing volatility. We solve this model in
equilibrium, assuming ergodicity at every level, and find as our
replica-symmetric solution a formalism with a structure similar but not
identical to Parisi's -step replica symmetry breaking scheme. Apart from
differences in details of the equations (due to the fact that here
interactions, rather than spins, are grouped into clusters with different
time-scales), in the present model the block sizes of the emerging
ultrametric solution are not restricted to the interval , but are
independent control parameters, defined in terms of the noise strengths of the
various levels in the hierarchy, which can take any value in [0,\infty\ket.
This is shown to lead to extremely rich phase diagrams, with an abundance of
first-order transitions especially when the level of stochasticity in the
interaction dynamics is chosen to be low.Comment: 53 pages, 19 figures. Submitted to J. Phys.
A solvable model of the genesis of amino-acid sequences via coupled dynamics of folding and slow genetic variation
We study the coupled dynamics of primary and secondary structure formation
(i.e. slow genetic sequence selection and fast folding) in the context of a
solvable microscopic model that includes both short-range steric forces and and
long-range polarity-driven forces. Our solution is based on the diagonalization
of replicated transfer matrices, and leads in the thermodynamic limit to
explicit predictions regarding phase transitions and phase diagrams at genetic
equilibrium. The predicted phenomenology allows for natural physical
interpretations, and finds satisfactory support in numerical simulations.Comment: 51 pages, 13 figures, submitted to J. Phys.
The XY Spin-Glass with Slow Dynamic Couplings
We investigate an XY spin-glass model in which both spins and couplings
evolve in time: the spins change rapidly according to Glauber-type rules,
whereas the couplings evolve slowly with a dynamics involving spin correlations
and Gaussian disorder. For large times the model can be solved using replica
theory. In contrast to the XY-model with static disordered couplings, solving
the present model requires two levels of replicas, one for the spins and one
for the couplings. Relevant order parameters are defined and a phase diagram is
obtained upon making the replica-symmetric Ansatz. The system exhibits two
different spin-glass phases, with distinct de Almeida-Thouless lines, marking
continuous replica-symmetry breaking: one describing freezing of the spins
only, and one describing freezing of both spins and couplings.Comment: 7 pages, Latex, 3 eps figure
Statistical mechanics of clonal expansion in lymphocyte networks modelled with slow and fast variables
We study the Langevin dynamics of the adaptive immune system, modelled by a
lymphocyte network in which the B cells are interacting with the T cells and
antigen. We assume that B clones and T clones are evolving in different thermal
noise environments and on different timescales. We derive stationary
distributions and use statistical mechanics to study clonal expansion of B
clones in this model when the B and T clone sizes are assumed to be the slow
and fast variables respectively and vice versa. We derive distributions of B
clone sizes and use general properties of ferromagnetic systems to predict
characteristics of these distributions, such as the average B cell
concentration, in some regimes where T cells can be modelled as binary
variables. This analysis is independent of network topologies and its results
are qualitatively consistent with experimental observations. In order to obtain
full distributions we assume that the network topologies are random and locally
equivalent to trees. The latter allows us to employ the Bethe-Peierls approach
and to develop a theoretical framework which can be used to predict the
distributions of B clone sizes. As an example we use this theory to compute
distributions for the models of immune system defined on random regular
networks.Comment: A more recent version (accepted for publication in Journal of Physics
A: Mathematical and Theoretical) with improved figures, references, et
Validity of a pictorial perceived exertion scale for effort estimation and effort production during stepping exercise in adolescent children
This is the author's PDF version of an article published in European Physical Education Review ©2002. The definitive version is available at http://epe.sagepub.com.Recent developments in the study of paediatric effort perception have continued to emphasise the importance of child-specific rating scales. The purpose of this study was to examine the validity of an illustrated 1 – 10 perceived exertion scale; the Pictorial Children’s Effort Rating Table (PCERT). 4 class groups comprising 104 children; 27 boys and 29 girls, aged 12.1±0.3 years and 26 boys, 22 girls, aged 15.3±0.2 years were selected from two schools and participated in the initial development of the PCERT. Subsequently, 48 of these children, 12 boys and 12 girls from each age group were randomly selected to participate in the PCERT validation study. Exercise trials were divided into 2 phases and took place 7 to 10 days apart. During phase 1, children completed 5 x 3-minute incremental stepping exercise bouts interspersed with 2-minute recovery periods. Heart rate (HR) and ratings of exertion were recorded during the final 15 s of each exercise bout. In phase 2 the children were asked to regulate their exercising effort during 4 x 4-minute bouts of stepping so that it matched randomly prescribed PCERT levels (3, 5, 7 and 9). Analysis of data from Phase 1 yielded significant (P<0.01) relationships between perceived and objective (HR) effort measures for girls. In addition, the main effects of exercise intensity on perceived exertion and HR were significant (P<0.01); perceived exertion increased as exercise intensity increased and this was reflected in simultaneous significant rises in HR. During phase 2, HR and estimated power output (POapprox) produced at each of the four prescribed effort levels were significantly different (P<0.01). The children in this study were able to discriminate between 4 different exercise intensities and regulate their exercise intensity according to 4 prescribed levels of perceived exertion. In seeking to contribute towards children’s recommended physical activity levels and helping them understand how to self-regulate their activity, the application of the PCERT within the context of physical education is a desirable direction for future research
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