Diluted neural networks with adapting and correlated synapses

We consider the dynamics of diluted neural networks with clipped and adapting synapses. Unlike previous studies, the learning rate is kept constant as the connectivity tends to infinity: the synapses evolve on a time scale intermediate between the quenched and annealing limits and all orders of synaptic correlations must be taken into account. The dynamics is solved by mean-field theory, the order parameter for synapses being a function. We describe the effects, in the double dynamics, due to synaptic correlations.Comment: 6 pages, 3 figures. Accepted for publication in PR

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.

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

Diagonalization of replicated transfer matrices for disordered Ising spin systems

We present an alternative procedure for solving the eigenvalue problem of replicated transfer matrices describing disordered spin systems with (random) 1D nearest neighbor bonds and/or random fields, possibly in combination with (random) long range bonds. Our method is based on transforming the original eigenvalue problem for a $2^n\times 2^n$ matrix (where $n\to 0$) into an eigenvalue problem for integral operators. We first develop our formalism for the Ising chain with random bonds and fields, where we recover known results. We then apply our methods to models of spins which interact simultaneously via a one-dimensional ring and via more complex long-range connectivity structures, e.g. $1+\infty$ dimensional neural networks and `small world' magnets. Numerical simulations confirm our predictions satisfactorily.Comment: 24 pages, LaTex, IOP macro

Driving the Future: The Relation between Driving and Prospective Memory in Adults with an Autism Spectrum Disorder

Difficulties with autonomy impact several quality-of-life outcomes in people with autism spectrum disorder (ASD). Driving is an important step towards gaining autonomy by allowing the development and maintenance of work- and social-related contacts. Nonetheless, people with ASD depend highly on friends and family for their transportation needs. Due to the complexity of the driving task, specific ASD characteristics might interfere negatively with driving. The driving task consists of several subtasks, running in parallel. This requires the ability to switch in a smooth manner (e.g., shifting, steering, changing lanes, and keeping traffic rules into account). An additional difficulty concerns sudden changes in the traffic environment (e.g., traffic density, weather conditions). Therefore, driving is a complex goal-directed task that places high demands on perceptual, cognitive, and motor processes. The little research that exists suggests that people with ASD experience difficulties more specifically in complex driving situations, requiring multi-tasking and inducing increased cognitive load. Applied to autonomy, in order to maintain work and social contacts, it is not only necessary to handle the vehicle, but also to navigate through rural, urban, and highway traffic environments while concurrently remembering appointments and obeying a schedule. People with ASD however experience difficulties with coordinating and sequencing activities, and with planning ahead. Following this, prospective memory (PM) might interfere negatively with driving. PM is the ability to remember to carry out intended actions in the future while being engaged in other ongoing activities. Two subtypes of PM are event-based PM (EBPM) and time-based PM (TBPM). The former refers to the execution of intentions at certain events (i.e., prospective cues), the latter refers to the execution of intentions at certain times. This driving simulator study aims to investigate PM (i.e., EBPM and TBPM) as an underlying mechanism of driving in adults with ASD. To this end, a pc-based ‘virtual reality (VR) city task’ was translated to a driving simulator environment. The influence of several cognitive abilities (e.g., working memory, planning), from which the importance is indicated in previous literature, is also investigated. Data collection is ongoing and will be finished in December. The analyses are planned in January

Slowly evolving random graphs II: Adaptive geometry in finite-connectivity Hopfield models

We present an analytically solvable random graph model in which the connections between the nodes can evolve in time, adiabatically slowly compared to the dynamics of the nodes. We apply the formalism to finite connectivity attractor neural network (Hopfield) models and we show that due to the minimisation of the frustration effects the retrieval region of the phase diagram can be significantly enlarged. Moreover, the fraction of misaligned spins is reduced by this effect, and is smaller than in the infinite connectivity regime. The main cause of this difference is found to be the non-zero fraction of sites with vanishing local field when the connectivity is finite.Comment: 17 pages, 8 figure

Slowly evolving geometry in recurrent neural networks I: extreme dilution regime

We study extremely diluted spin models of neural networks in which the connectivity evolves in time, although adiabatically slowly compared to the neurons, according to stochastic equations which on average aim to reduce frustration. The (fast) neurons and (slow) connectivity variables equilibrate separately, but at different temperatures. Our model is exactly solvable in equilibrium. We obtain phase diagrams upon making the condensed ansatz (i.e. recall of one pattern). These show that, as the connectivity temperature is lowered, the volume of the retrieval phase diverges and the fraction of mis-aligned spins is reduced. Still one always retains a region in the retrieval phase where recall states other than the one corresponding to the `condensed' pattern are locally stable, so the associative memory character of our model is preserved.Comment: 18 pages, 6 figure

Orbital order in the low-dimensional quantum spin system TiOCl probed by ESR

We present electron spin resonance data of Ti$^{3+}$ (3$d^1$) ions in single crystals of the novel layered quantum spin magnet TiOCl. The analysis of the g tensor yields direct evidence that the d_{xy} orbital from the t_{2g} set is predominantly occupied and owing to the occurrence of orbital order a linear spin chain forms along the crystallographic b axis. This result corroborates recent theoretical LDA+U calculations of the band structure. The temperature dependence of the parameters of the resonance signal suggests a strong coupling between spin and lattice degrees of freedom and gives evidence for a transition to a nonmagnetic ground state at 67 K.Comment: revised version, accepted for publication in Phys. Rev. B, Rapid Com

Exploring the Cost Effectiveness of Shared Decision Making for Choosing between Disease-Modifying Drugs for Relapsing-Remitting Multiple Sclerosis in the Netherlands:A State Transition Model

Background Up to 31% of patients with relapsing-remitting multiple sclerosis (RRMS) discontinue treatment with disease-modifying drug (DMD) within the first year, and of the patients who do continue, about 40% are nonadherent. Shared decision making may decrease nonadherence and discontinuation rates, but evidence in the context of RRMS is limited. Shared decision making may, however, come at additional costs. This study aimed to explore the potential cost-effectiveness of shared decision making for RRMS in comparison with usual care, from a (limited) societal perspective over a lifetime. Methods An exploratory economic evaluation was conducted by adapting a previously developed state transition model that evaluates the cost-effectiveness of a range of DMDs for RRMS in comparison with the best supportive care. Three potential effects of shared decision making were explored: 1) a change in the initial DMD chosen, 2) a decrease in the patient's discontinuation in using the DMD, and 3) an increase in adherence to the DMD. One-way and probabilistic sensitivity analyses of a scenario that combined the 3 effects were conducted. Results Each effect separately and the 3 effects combined resulted in higher quality-adjusted life years (QALYs) and costs due to the increased utilization of DMD. A decrease in discontinuation of DMDs influenced the incremental cost-effectiveness ratio (ICER) most. The combined scenario resulted in an ICER of euro17,875 per QALY gained. The ICER was sensitive to changes in several parameters. Conclusion This study suggests that shared decision making for DMDs could potentially be cost-effective, especially if shared decision making would help to decrease treatment discontinuation. Our results, however, may depend on the assumed effects on treatment choice, persistence, and adherence, which are actually largely unknown