By extending the response function approach developed in nonlinear optics, we analytically derive an expression for the non-Markovianity in the time evolution of a system in contact with a quantum mechanical bath, and find a close connection with the directly observable nonlinear optical response. The result indicates that memory in the bath-induced fluctuations rather than in the dissipation c...

My research work centers around two broad topics: The analysis of nonlinear Partial Differential Equations (PDE) of elliptic and parabolic type (mainly free boundary problems and reaction-diffusion equations) and the study of transport phenomena (particularly the connection between kinetic and hydrodynamic models). My main contributions are described below (preprints are available at http://www...

This paper is intended to give a probabilistic representation for stochastic viscosity solution of semi-linear reflected stochastic partial differential equations with nonlinear Neumann boundary condition. We use its connection with reflected generalized backward doubly stochastic differential equations. AMS Subject Classification: 60H15; 60H20

Abstmct We propose a novel approach for a rigorous analysis of the nonlinear asymmetric dynamics of Linsker's unsupervised Hebbian learning network. The results provide for the Arst time comprehensive explanations of the origin of the various structured connection patterns and of the roles of the different system parameters of the model. Our theoretical predictions are corroborated by numerical...

The goal of this paper is to establish the precise connection between the centro-affine invariants of plane curves and the feedback invariants of nonlinear scalar control systems in the plane. We will also show how the centro-affine structure provides a shortcut to the structure equations for feedback equivalence one obtains by applying Cartan’s equivalence method.

A nonlinear controllable plant, under mild technical conditions, admits a precompensator with the following property: along control trajectories joining pairs of states, the composite system (precompensator plus plant) is, up to first order, isomorphic to a parallel connection of integrators. Appeared in IEEE Trans.Autom.Control, Vol.32, 10, Oct.1987, pp877-888 *Research supported in part by US...

We investigate the separation property for hierarchies of Schrödinger operators for identical particles. We show that such hierarchies of translation invariant second order differential operators are necessarily linear. A weakened form of the separation property, related to a strong form of cluster decomposition, allows for homogeneous hierarchies of nonlinear differential operators. Some conne...

We study synchronization of nonlinear systems that satisfy an incremental passivity property. We consider the case where the control input is subject to a class of disturbances, including constant and sinusoidal disturbances with unknown phases and magnitudes and known frequencies. We design a distributed control law that recovers the synchronization of the nonlinear systems in the presence of ...

Learning is thought to occur by localized, activity-induced changes in the strength of synaptic connections between neurons. Recent work has shown that induction of change at one connection can affect changes at others ("crosstalk"). We studied the role of such crosstalk in nonlinear Hebbian learning using a neural network implementation of independent components analysis. We find that there is...

In this paper, we model time-interleaved analog-to-digital converters (TIADCs) with nonlinear hybrid filter banks (NHFBs), which greatly unifies and simplifies the analysis of TIADCs. The input/output relation of such a nonlinear hybrid filter bank can be used to describe combined offset, gain, aperture delay, input behavior, and nonlinearity mismatches and is therefore an extendable starting p...