Filling-in the Forms: Surface and Boundary Interactions in Visual Cortex

Defense Advanced Research Projects Agency and the Office of Naval Research (NOOOI4-95-l-0409); Office of Naval Research (NOOO14-95-1-0657)

Probing optically silent superfluid stripes in cuprates

Unconventional superconductivity in the cuprates emerges from, or coexists with, other types of electronic order. However, these orders are sometimes invisible because of their symmetry. For example, the possible existence of superfluid charge stripes in the normal state of single layer cuprates cannot be validated with infrared optics, because interlayer tunneling fluctuations vanish on average. Similarly, it is not easy to establish if charge orders are responsible for dynamical decoupling of the superconducting layers over broad ranges of doping and temperatures. Here, we show that TeraHertz pulses can excite nonlinear tunneling currents between linearly de-coupled charge-ordered planes. A giant TeraHertz third harmonic signal is observed in La1.885Ba0.115CuO4 far above Tc=13 K and up to the charge ordering temperature TCO = 55 K. We model these results by considering large order-parameter-phase oscillations in a pair density wave condensate, and show how nonlinear mixing of optically silent tunneling modes can drive large dipole-carrying super-current oscillations. Our results provide compelling experimental support for the presence of hidden superfluid order in the normal state of cuprates. These experiments also underscore the power of nonlinear TeraHertz optics as a sensitive probe of frustrated excitations in quantum solids.Comment: 9 pages main text, 5 figures, 12 page supplementar

Invisibility and Inverse Problems

This survey of recent developments in cloaking and transformation optics is an expanded version of the lecture by Gunther Uhlmann at the 2008 Annual Meeting of the American Mathematical Society.Comment: 68 pages, 12 figures. To appear in the Bulletin of the AM

Director Field Model of the Primary Visual Cortex for Contour Detection

We aim to build the simplest possible model capable of detecting long, noisy contours in a cluttered visual scene. For this, we model the neural dynamics in the primate primary visual cortex in terms of a continuous director field that describes the average rate and the average orientational preference of active neurons at a particular point in the cortex. We then use a linear-nonlinear dynamical model with long range connectivity patterns to enforce long-range statistical context present in the analyzed images. The resulting model has substantially fewer degrees of freedom than traditional models, and yet it can distinguish large contiguous objects from the background clutter by suppressing the clutter and by filling-in occluded elements of object contours. This results in high-precision, high-recall detection of large objects in cluttered scenes. Parenthetically, our model has a direct correspondence with the Landau - de Gennes theory of nematic liquid crystal in two dimensions.Comment: 9 pages, 7 figure

Topological Phenomena in Classical Optical Networks

We propose a scheme to realize a topological insulator with optical-passive elements, and analyze the effects of Kerr-nonlinearities in its topological behavior. In the linear regime, our design gives rise to an optical spectrum with topological features and where the bandwidths and bandgaps are dramatically broadened. The resulting edge modes cover a very wide frequency range. We relate this behavior to the fact that the effective Hamiltonian describing the system's amplitudes is long-range. We also develop a method to analyze the scheme in the presence of a Kerr medium. We assess robustness and stability of the topological features, and predict the presence of chiral squeezed fluctuations at the edges in some parameter regimes.Comment: 18 pages, 9 figure

Electrical impedance spectroscopy-based nondestructive testing for imaging defects in concrete structures

An electrical impedance spectroscopy-based nondestructive testing (NDT) method is proposed to image both cracks and reinforcing bars in concrete structures. The method utilizes the frequency-dependent behavior of thin insulating cracks: low-frequency electrical currents are blocked by insulating cracks, whereas high-frequency currents can pass through the conducting bars without being blocked by thin cracks. Rigorous mathematical analysis relates the geometric structures of the cracks and bars to the frequency-dependent Neumann-to-Dirichlet data. Various numerical simulations support the feasibility of the proposed method