Center or Limit Cycle: Renormalization Group as a Probe

Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic solutions in a plethora of nonlinear dynamical systems appearing across disciplines. The technique will be shown to have a non-trivial ability of classifying the solutions into limit cycles and periodic orbits surrounding a center. Moreover, the methodology has a definite advantage over linear stability analysis in analyzing centers

How spiking neurons give rise to a temporal-feature map

A temporal-feature map is a topographic neuronal representation of temporal attributes of phenomena or objects that occur in the outside world. We explain the evolution of such maps by means of a spike-based Hebbian learning rule in conjunction with a presynaptically unspecific contribution in that, if a synapse changes, then all other synapses connected to the same axon change by a small fraction as well. The learning equation is solved for the case of an array of Poisson neurons. We discuss the evolution of a temporal-feature map and the synchronization of the single cells’ synaptic structures, in dependence upon the strength of presynaptic unspecific learning. We also give an upper bound for the magnitude of the presynaptic interaction by estimating its impact on the noise level of synaptic growth. Finally, we compare the results with those obtained from a learning equation for nonlinear neurons and show that synaptic structure formation may profit from the nonlinearity

Dynamics of Simple Balancing Models with State Dependent Switching Control

Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by either a connected movable cart or an applied torque for which the control is turned off when the pendulum is located within certain regions of phase space. Without applying a small angle approximation for deviations about the vertical position, we see structurally stable periodic orbits which may be attracting or repelling. Due to the nonsmooth nature of the control, these periodic orbits are born in various discontinuity-induced bifurcations. Also we show that a coincidence of switching events can produce complicated periodic and aperiodic solutions.Comment: 36 pages, 12 figure

Does congenital deafness affect the structural and functional architecture of primary visual cortex?

Deafness results in greater reliance on the remaining senses. It is unknown whether the cortical architecture of the intact senses is optimized to compensate for lost input. Here we performed widefield population receptive field (pRF) mapping of primary visual cortex (V1) with functional magnetic resonance imaging (fMRI) in hearing and congenitally deaf participants, all of whom had learnt sign language after the age of 10 years. We found larger pRFs encoding the peripheral visual field of deaf compared to hearing participants. This was likely driven by larger facilitatory center zones of the pRF profile concentrated in the near and far periphery in the deaf group. pRF density was comparable between groups, indicating pRFs overlapped more in the deaf group. This could suggest that a coarse coding strategy underlies enhanced peripheral visual skills in deaf people. Cortical thickness was also decreased in V1 in the deaf group. These findings suggest deafness causes structural and functional plasticity at the earliest stages of visual cortex