Mammalian cochlea as a physics guided evolution-optimized hearing sensor

Nonlinear physics plays an essential role in hearing, from sound signal generation to sound sensing to the processing of complex sound environments. We demonstrate that the evolution of the biological hearing sensors demonstrates a dramatic reduction in the solution space available for hearing sensors due to nonlinear physics principles. More specifically, our analysis hints at that the differences between amniotic lineages hearing, could be recast into a scaleable and a non-scaleable arrangement of nonlinear sound detectors. The scalable solution employed in mammals, as the most advanced design, provides a natural context that demands the ultimate characterization of complex sounds through pitch

Modeling of linear fading memory systems

Motivated by questions of approximate modeling and identification, we consider various classes of linear time-varying bounded-input-bounded output (BIBO) stable fading memory systems and the characterizations are proved. These include fading memory systems in general, almost periodic systems, and asymptotically periodic systems. We also show that the norm and strong convergence coincide for BIBO stable causal fading memory system

An exactly solvable nonlinear model: Constructive effects of correlations between Gaussian noises

A system with two correlated Gaussian white noises is analysed. This system can describe both stochastic localization and long tails in the stationary distribution. Correlations between the noises can lead to a nonmonotonic behaviour of the variance as function of the intensity of one of the noises and to a stochastic resonance. A method for improving the transmission of external periodic signal by tuning parameters of the system discussed in this paper is proposed

One-Dimensional Population Density Approaches to Recurrently Coupled Networks of Neurons with Noise

Mean-field systems have been previously derived for networks of coupled, two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting exponential (AdEx) and quartic integrate and fire (QIF), among others. Unfortunately, the mean-field systems have a degree of frequency error and the networks analyzed often do not include noise when there is adaptation. Here, we derive a one-dimensional partial differential equation (PDE) approximation for the marginal voltage density under a first order moment closure for coupled networks of integrate-and-fire neurons with white noise inputs. The PDE has substantially less frequency error than the mean-field system, and provides a great deal more information, at the cost of analytical tractability. The convergence properties of the mean-field system in the low noise limit are elucidated. A novel method for the analysis of the stability of the asynchronous tonic firing solution is also presented and implemented. Unlike previous attempts at stability analysis with these network types, information about the marginal densities of the adaptation variables is used. This method can in principle be applied to other systems with nonlinear partial differential equations.Comment: 26 Pages, 6 Figure