In this article we present the supervised iterative projections and rotations (s-ipr) algorithm, a method for learning discriminative incoherent subspaces from data. We derive s-ipr as a supervised extension of our previously proposed iterative projections and rotations (ipr) algorithm for incoherent dictionary learning, and we employ it to learn incoherent sub-spaces that model signals belongi...

We consider the temporal evolution of an incoherent optical wave that propagates in a noninstantaneous response nonlinear medium, such as single mode optical fibers. In contrast with the expected Raman-like spectral redshift due to a delayed nonlinear response, we show that a highly noninstantaneous response leads to a genuine modulational instability of the incoherent optical wave. We derive a...

We formulate the theory of incoherent dark spatial solitons in noninstantaneous self-defocusing nonlinear media. We find that the basic modal constituents of these incoherent dark soliton entities are radiation modes as well as bound states. Our results explain for the first time why incoherent dark solitons are in fact gray and why a transverse p-phase flip can facilitate their observation. [S...

In this paper we present results obtained using wavelet methods for the analysis and simulation of two-dimensional turbulence, and a preliminary study of a three-dimensional turbulent channel ow. The two-dimensional results show the eeciency of wavelets for the numerical simulation of turbulence, and suggest new methods for modelling the ow, based on a decomposition into coherent and incoherent...

Arrays of interacting identical neurons can develop coherent firing patterns, such as moving stripes that have been suggested as possible explanations of hallucinatory phenomena. Other known formations include rotating spirals and expanding concentric rings. We obtain all of them using a novel two-variable description of integrate-and-fire neurons that allows for a continuum formulation of neur...

The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e., when the population is not synchronous. This demonstration is facilitated by the construction of a nonequilibrium statistical field theoretic formulation of a generic mo...

This paper presents an analysis of stability and resolution analysis of broadband (passive or active) array imaging in the Rician fading media. The main theoretical result is the stability condition KBN M where K is the Rician factor, B is the effective number of incoherent frequencies, N is the effective number of array elements and M is the number of sufficiently separated targets. The resolu...

Entangled-photon pairs ~biphotons! generated by spontaneous optical parametric down-conversion exhibit a number of properties that are analogous to those of ordinary photons generated by incoherent sources. The spatial pump-field distribution and the two-particle wave function in the biphoton case play the respective roles of the source intensity distribution and the second-order coherence func...

We propose the application of volume holography to fourdimensional (4-D) spatiospectral imaging. The proposed systems use materials and techniques developed for holographic data storage and interconnections to capture three-dimensional (3-D) spatial and one-dimensional (1-D) spectral information about a remote light source or scatterer. We analyze case studies of simple architectures using sphe...

We discuss a theory of the ultrafast non-linear optical response of excitons in the Quantum Hall system. Our theory focusses on the role of the low energy collective electronic excitations of the cold, strongly correlated, two–dimensional electron gas (2DEG) present in the ground state. It takes into account ground state electron correlations and Pauli exchange and interaction effects between t...