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 $N$ neurons and each of them is connected to $K$ input neurons chosen at random in the network. The synapses are $n$-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 $N\to\infty$ with $K$ 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 $L$ 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 $L$-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 $m_i$ of the emerging ultrametric solution are not restricted to the interval $[0,1]$, 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