On the Origin of the Checkerboard Pattern in Scanning Tunneling Microscopy Maps of Underdoped Cuprate Superconductors

The checkerboard pattern in the differential conductance maps on underdoped cuprates appears when the STM is placed above the O-sites in the outermost CuO$_{\text{2}}$-plane. In this position the interference between tunneling paths through the apical ions above the neighboring Cu-sites leads to an asymmetric weighting of final states in the two antinodal regions of ${\boldsymbol{k}}$-space. The form of the asymmetry in the differential conductance spectra in the checkerboard pattern favors asymmetry in the localization length rather than a nematic displacement as the underlying origin.Comment: 8 pages, 5 figures, final versio

Andreev and Single Particle Tunneling Spectroscopies in Underdoped Cuprates

We study tunneling spectroscopy between a normal metal and underdoped cuprate superconductor modeled by a phenomenological theory in which the pseudogap is a precursor to the undoped Mott insulator. In the transparent tunneling limit, the spectra show a small energy gap associated with Andreev reflection. In the Giaever limit, the spectra show a large energy gap associated with single particle tunneling. Our theory semi-quantitatively describes the two gap behavior observed in tunneling experiments.Comment: 5 pages, 4 figures, submitted to Phys. Rev. Lett. minor changes of reference

A Spiking Neural Network Based Cortex-Like Mechanism and Application to Facial Expression Recognition

In this paper, we present a quantitative, highly structured cortex-simulated model, which can be simply described as feedforward, hierarchical simulation of ventral stream of visual cortex using biologically plausible, computationally convenient spiking neural network system. The motivation comes directly from recent pioneering works on detailed functional decomposition analysis of the feedforward pathway of the ventral stream of visual cortex and developments on artificial spiking neural networks (SNNs). By combining the logical structure of the cortical hierarchy and computing power of the spiking neuron model, a practical framework has been presented. As a proof of principle, we demonstrate our system on several facial expression recognition tasks. The proposed cortical-like feedforward hierarchy framework has the merit of capability of dealing with complicated pattern recognition problems, suggesting that, by combining the cognitive models with modern neurocomputational approaches, the neurosystematic approach to the study of cortex-like mechanism has the potential to extend our knowledge of brain mechanisms underlying the cognitive analysis and to advance theoretical models of how we recognize face or, more specifically, perceive other people’s facial expression in a rich, dynamic, and complex environment, providing a new starting point for improved models of visual cortex-like mechanism

Variance Reduced Random Relaxed Projection Method for Constrained Finite-sum Minimization Problems

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to efficiently solve this problem. Compared with existing RPMs, our proposed algorithm features two useful algorithmic ideas. First, at each iteration, instead of projecting onto the subset defined by one of the constraints, our algorithm only requires projecting onto a half-space approximation of the subset, which significantly reduces the computational cost as it admits a closed-form formula. Second, to exploit the structure that the objective is a sum, variance reduction is incorporated into our algorithm to further improve the performance. As theoretical contributions, under an error bound condition and other standard assumptions, we prove that the proposed RPM converges to an optimal solution and that both optimality and feasibility gaps vanish at a sublinear rate. We also provide sufficient conditions for the error bound condition to hold. Experiments on a beamforming problem and a robust classification problem are also presented to demonstrate the superiority of our RPM over existing ones

Influence of the trap shape on the superfluid-Mott transition in ultracold atomic gases

The coexistence of superfluid and Mott insulator, due to the quadratic confinement potential in current optical lattice experiments, makes the accurate detection of the superfluid-Mott transition difficult. Studying alternative trapping potentials which are experimentally realizable and have a flatter center, we find that the transition can be better resolved, but at the cost of a more difficult tuning of the particle filling. When mapping out the phase diagram using local probes and the local density approximation we find that the smoother gradient of the parabolic trap is advantageous.Comment: 5 pages, 6 figure