Overlapping cell assemblies from correlators.

This paper introduces compensatory learning and shows how it can lead to the formation of Cell Assemblies (CAs) that share neurons. The work starts with standard Hebbian learning then adds a compensatory modifier that forces the total synaptic weight leaving a neuron toward a constant. This enables overlapping CAs because neurons that are in multiple categories have reduced weight stopping Assemblies merging. This provides a biologically plausible learning rule that eases the ability of CAs to overlap. A more complex CA system based on this work, is being developed as part of a current EPSRC grant (EP/D059720/1)

Fluctuating Filaments I: Statistical Mechanics of Helices

We examine the effects of thermal fluctuations on thin elastic filaments with non-circular cross-section and arbitrary spontaneous curvature and torsion. Analytical expressions for orientational correlation functions and for the persistence length of helices are derived, and it is found that this length varies non-monotonically with the strength of thermal fluctuations. In the weak fluctuation regime, the local helical structure is preserved and the statistical properties are dominated by long wavelength bending and torsion modes. As the amplitude of fluctuations is increased, the helix ``melts'' and all memory of intrinsic helical structure is lost. Spontaneous twist of the cross--section leads to resonant dependence of the persistence length on the twist rate.Comment: 5 figure

Observation of liquid glass in suspensions of ellipsoidal colloids

Despite the omnipresence of colloidal suspensions, little is known about the influence of shape on phase transformations, especially in nonequilibrium. To date, real-space imaging results are limited to systems composed of spherical colloids. In most natural and technical systems, however, particles are non-spherical and their structural dynamics are determined by translational and rotational degrees of freedom. Using confocal microscopy, we reveal that suspensions of ellipsoidal colloids form an unexpected state of matter, a liquid glass in which rotations are frozen while translations remain fluid. Image analysis unveils hitherto unknown nematic precursors as characteristic structural elements of this state. The mutual obstruction of these ramified clusters prevents liquid crystalline order. Our results give unique insight into the interplay between local structures and phase transformations. This helps to guide applications such as self-assembly of colloidal superstructures and also gives first evidence of the importance of shape on the glass transition in general.Comment: 19 pages, 6 figures; additional SI; submitte

Hard sphere crystallization gets rarer with increasing dimension

We recently found that crystallization of monodisperse hard spheres from the bulk fluid faces a much higher free energy barrier in four than in three dimensions at equivalent supersaturation, due to the increased geometrical frustration between the simplex-based fluid order and the crystal [J.A. van Meel, D. Frenkel, and P. Charbonneau, Phys. Rev. E 79, 030201(R) (2009)]. Here, we analyze the microscopic contributions to the fluid-crystal interfacial free energy to understand how the barrier to crystallization changes with dimension. We find the barrier to grow with dimension and we identify the role of polydispersity in preventing crystal formation. The increased fluid stability allows us to study the jamming behavior in four, five, and six dimensions and compare our observations with two recent theories [C. Song, P. Wang, and H. A. Makse, Nature 453, 629 (2008); G. Parisi and F. Zamponi, Rev. Mod. Phys, in press (2009)].Comment: 15 pages, 5 figure

The nature of the memory trace and its neurocomputational implications

The brain processes underlying cognitive tasks must be very robust. Disruptions such as the destruction of large numbers of neurons, or the impact of alcohol and lack of sleep do not have negative effects except when they occur in an extreme form. This robustness implies that the parameters determining the functioning of networks of individual neurons must have large ranges or there must exist stabilizing mechanisms that keep the functioning of a network within narrow bounds. The simulation of a minimal neuronal architecture necessary to study cognitive tasks is described, which consists of a loop of three cell-assemblies. A crucial factor in this architecture is the critical threshold of a cell-assembly. When activated at a level above the critical threshold, the activation in a cell-assembly is subject to autonomous growth, which leads to an oscillation in the loop. When activated below the critical threshold, excitation gradually extinguishes. In order to circumvent the large parameter space of spiking neurons, a rate-dependent model of neuronal firing was chosen. The resulting parameter space of 12 parameters was explored by means of a genetic algorithm. The ranges of the parameters for which the architecture produced the required oscillations and extinctions, turned out to be relatively narrow. These ranges remained narrow when a stabilizing mechanism, controlling the total amount of activation, was introduced. The architecture thus shows chaotic behaviour. Given the overall stability of the operation of the brain, it can be concluded that there must exist other mechanisms that make the network robust. Three candidate mechanisms are discussed: synaptic scaling, synaptic homeostasis, and the synchronization of neural spikes

Variable binding by synaptic strength change

Variable binding is a difficult problem for neural networks. Two new mechanisms for binding by synaptic change are presented, and in both, bindings are erased and can be reused. The first is based on the commonly used learning mechanism of permanent change of synaptic weight, and the second on synaptic change which decays. Both are biologically motivated models. Simulations of binding on a paired association task are shown with the first mechanism succeeding with a 97.5% F-Score, and the second performing perfectly. Further simulations show that binding by decaying synaptic change copes with cross talk, and can be used for compositional semantics. It can be inferred that binding by permanent change accounts for these, but it faces the stability plasticity dilemma. Two other existing binding mechanism, synchrony and active links, are compatible with these new mechanisms. All four mechanisms are compared and integrated in a Cell Assembly theory