Bistability and Stabilization of Human Visual Perception under Ambiguous Stimulation.

We discuss a computational model that describes stabilization of percept choices under intermittent viewing of an ambiguous visual stimulus at long stimulus intervals. Let T_off and T_on be the time that the stimulus is off and on, respectively. The behavior was studied by direct numerical simulation in a grid of (T_off, T_on) values in a 2007 paper of Noest, van Ee, Nijs, and van Wezel. They found that both alternating and repetitive sequences of percepts can appear stably, sometimes even for the same values of T_off and T_on. Longer T_off, however, always leads to a situation where, after transients, only repetitive sequences of percepts exist. We incorporate T_off and T_on explicitly as bifurcation parameters of an extended mathematical model of the perceptual choices. We elucidate the bifurcations of periodic orbits responsible for switching between alternating and repetitive sequences. We show that the stability borders of the alternating and repeating sequences in the (T_off, T_on) -parameter plane consist of curves of limit point and period-doubling bifurcations of periodic orbits. The stability regions overlap, resulting in a wedge with bistability of both sequences. We conclude by comparing our modeling results with the experimental results obtained by Noest, van Ee, Nijs, and van Wezel.

Neural field models with transmission delays and diffusion.

A neural field models the large scale behaviour of large groups of neurons. We extend previous results for these models by including a diffusion term into the neural field, which models direct, electrical connections. We extend known and prove new sun-star calculus results for delay equations to be able to include diffusion and explicitly characterise the essential spectrum. For a certain class of connectivity functions in the neural field model, we are able to compute its spectral properties and the first Lyapunov coefficient of a Hopf bifurcation. By examining a numerical example, we find that the addition of diffusion suppresses non-synchronised steady-states while favouring synchronised oscillatory modes.

A Rate-Reduced Neuron Model for Complex Spiking Behavior.

We present a simple rate-reduced neuron model that captures a wide range of complex, biologically plausible, and physiologically relevant spiking behavior. This includes spike-frequency adaptation, postinhibitory rebound, phasic spiking and accommodation, first-spike latency, and inhibition-induced spiking. Furthermore, the model can mimic different neuronal filter properties. It can be used to extend existing neural field models, adding more biological realism and yielding a richer dynamical structure. The model is based on a slight variation of the Rulkov map.

Structure and stability of chiral beta-tapes: a computational coarse-grained approach.

We present two coarse-grained models of different levels of detail for the description of beta-sheet tapes obtained from equilibrium self-assembly of short rationally designed oligopeptides in solution. Here we only consider the case of the homopolymer oligopeptides with the identical sidegroups attached, in which the tapes have a helicoid surface with two equivalent sides. The influence of the chirality parameter on the geometrical characteristics, namely the diameter, interstrand distance, and pitch, of the tapes has been investigated. The two models are found to produce equivalent results suggesting a considerable degree of universality in conformations of the tapes.

Size and persistence length of molecular bottle-brushes by Monte Carlo simulations.

Single-chain simulations of densely branched comb polymers, or "molecular bottle-brushes" with side-chains attached to every (or every second) backbone monomer, were carried out by off-lattice Monte Carlo technique. A coarse-grained model, described by hard spheres connected by harmonic springs, was employed. Backbone lengths of up to 100 units were considered, and compared with the corresponding linear chains. The backbone molecular size was investigated as a function of its length at fixed arm size, and as a function of the arm size at fixed backbone length. The apparent swelling exponents obtained by a power-law fit were found to be larger than those for the corresponding linear polymers, indicative of stiffening of the comb backbone. The probability distribution function for the backbone end-to-end distance was also investigated for different backbone lengths and arm sizes. Analysis of this function yielded the critical exponents, which revealed an increase in the swelling exponent consistent with values found from the molecular size. The apparent persistence length of the backbone was also determined, and was found to increase with increasing branching density. Finally, the static structure factors of the whole bottle-brushes and of their backbones are discussed, which provides another consistent estimate of the swelling exponents.