d-Wave Checkerboard Order in Cuprates

We show that the d-wave ordering in particle-hole channels, dubbed d-wave checkerboard order, possesses important physics that can sufficiently explain the scanning tunneling microscopy (STM) results in cuprates. A weak d-wave checkerboard order can effectively suppress the coherence peak in the single-particle spectrum while leaving the spectrum along the nodal direction almost unaffected. Simultaneously, it generates a Fermi arc with little dispersion around the nodal points at finite temperature that is consistent with the results of angle-resolved photoemission spectroscopy (ARPES) experiments in the pseudogap phase. We also show that there is a general complementary connection between the d-wave checkerboard order and the pair-density-wave order. Suppressing superconductivity locally or globally through phase fluctuations should induce both orders in underdoped cuprates and explain the nodal-antinodal dichotomy observed in ARPES and STM experiments

Image Question Answering using Convolutional Neural Network with Dynamic Parameter Prediction

We tackle image question answering (ImageQA) problem by learning a convolutional neural network (CNN) with a dynamic parameter layer whose weights are determined adaptively based on questions. For the adaptive parameter prediction, we employ a separate parameter prediction network, which consists of gated recurrent unit (GRU) taking a question as its input and a fully-connected layer generating a set of candidate weights as its output. However, it is challenging to construct a parameter prediction network for a large number of parameters in the fully-connected dynamic parameter layer of the CNN. We reduce the complexity of this problem by incorporating a hashing technique, where the candidate weights given by the parameter prediction network are selected using a predefined hash function to determine individual weights in the dynamic parameter layer. The proposed network---joint network with the CNN for ImageQA and the parameter prediction network---is trained end-to-end through back-propagation, where its weights are initialized using a pre-trained CNN and GRU. The proposed algorithm illustrates the state-of-the-art performance on all available public ImageQA benchmarks

Complementary Pair Density Wave and d-wave Checkerboard Order in High Temperature Superconductors

The competing orders in the particle-particle (P-P) channel and the particle-hole (P-H) channel have been proposed separately to explain the pseudogap physics in cuprates. By solving the Bogoliubov-deGennes equation self-consistently, we show that there is a general complementary connection between the d-wave checkerboard order (DWCB) in the particle-hole (P-H) channel and the pair density wave order (PDW) in the particle-particle (P-P) channel. A small pair density localization generates DWCB and PDW orders simultaneously. The result suggests that suppressing superconductivity locally or globally through phase fluctuation should induce both orders in underdoped cuprates. The presence of both DWCB and PDW orders with $4a \times 4a$ periodicity can explain the checkerboard modulation observed in FT-STS from STM and the puzzling dichotomy between the nodal and antinodal regions as well as the characteristic features such as non-dispersive Fermi arc in the pseudogap state

Topology-Guided Path Integral Approach for Stochastic Optimal Control in Cluttered Environment

This paper addresses planning and control of robot motion under uncertainty that is formulated as a continuous-time, continuous-space stochastic optimal control problem, by developing a topology-guided path integral control method. The path integral control framework, which forms the backbone of the proposed method, re-writes the Hamilton-Jacobi-Bellman equation as a statistical inference problem; the resulting inference problem is solved by a sampling procedure that computes the distribution of controlled trajectories around the trajectory by the passive dynamics. For motion control of robots in a highly cluttered environment, however, this sampling can easily be trapped in a local minimum unless the sample size is very large, since the global optimality of local minima depends on the degree of uncertainty. Thus, a homology-embedded sampling-based planner that identifies many (potentially) local-minimum trajectories in different homology classes is developed to aid the sampling process. In combination with a receding-horizon fashion of the optimal control the proposed method produces a dynamically feasible and collision-free motion plans without being trapped in a local minimum. Numerical examples on a synthetic toy problem and on quadrotor control in a complex obstacle field demonstrate the validity of the proposed method.Comment: arXiv admin note: text overlap with arXiv:1510.0534

Modeling the response of groundwater levels in wells to changes in barometric pressure

In many cases, water levels in wells are observed to fluctuate significantly in response to changes in barometric pressure. In this study, a physically based conceptual model for the influence of barometric pressure on groundwater wells was developed and tested;It is proposed that water level fluctuations in response to barometric pressure are due, in large part, to the different manner in which the pressure is propagated through the water column in the well and the porous media outside the well. Changes in pressure transmit through the water column in the well to the screened region with essentially negligible loss in pressure. On the contrary, pressure changes transferred through the porous media to the screened elevation outside the well undergo an irreversible transformation of fluid potential (head loss). Consequently, the loss in pressure head through the porous medium causes a lateral hydraulic head gradient to be developed around the well-screen region, as well as a vertical one through the porous medium. In response to the head gradient developed due to changes in barometric pressure, groundwater flows are induced through the well screen, with subsequent changes in well-casing storage. In the proposed model the well itself is an essential element. The well-water flux across the screen and the consequent change in wellcasing storage were appropriatety linked with groundwater flow in the surrounding porous medium and estimated through an iteration technique. This approach incorporates the traditional governing theories on groundwater flow: conservation of mass and Darcy\u27s Law; Groundwater was modeled as two-dimensional (radial and vertical) unsteady flow, and solved by using finite element approximations. The basic concept of the model was successfully applied to the modeling of slug tests and furthermore it was demonstrated that a series of slug/bad tests and effects of barometric pressure on wells are theoretically related to each other in physical and numerical senses through the principle of super position;The results suggest that the physically based model in this study is very effective in estimating the water level fluctuations in a well due to changes in barometric pressure. The magnitude and behavior of the well response varies with the hydraulic properties (hydraulic conductivity and specific storage) and well geometry (casing radius, screened length, and depth of well)