Construction of Wannier Functions in Disordered Systems

We propose a general method of constructing Wannier functions in disordered systems directly out of energy eigenstates. This method consists of two successive operations: (i) a phase transformation setting the proper localization center; (ii) the mixing of adjacent states in energy to sufficiently minimize the spread of the Wannier functions. The latter operation can be well approximated by a band matrix, further facilitating the calculation. Detailed implementation of our method is illustrated with one dimensional systems; the generalization to higher dimensions is straightforward.Comment: 7 pages, 4 figure

Local theta correspondence and nilpotent invariants

We consider two types of nilpotent invariants associated to smooth representations, namely generalized Whittaker models, and associated characters (in the case of a real reductive group). We survey some recent results on the behavior of these nilpotent invariants under local theta correspondence, and highlight the special role of a certain double fiberation of moment maps.Comment: Submitted to the conference proceedings in honor of Joseph Bernstei

Exponentially Consistent Kernel Two-Sample Tests

Given two sets of independent samples from unknown distributions $P$ and $Q$, a two-sample test decides whether to reject the null hypothesis that $P=Q$. Recent attention has focused on kernel two-sample tests as the test statistics are easy to compute, converge fast, and have low bias with their finite sample estimates. However, there still lacks an exact characterization on the asymptotic performance of such tests, and in particular, the rate at which the type-II error probability decays to zero in the large sample limit. In this work, we establish that a class of kernel two-sample tests are exponentially consistent with Polish, locally compact Hausdorff sample space, e.g., $\mathbb R^d$. The obtained exponential decay rate is further shown to be optimal among all two-sample tests satisfying the level constraint, and is independent of particular kernels provided that they are bounded continuous and characteristic. Our results gain new insights into related issues such as fair alternative for testing and kernel selection strategy. Finally, as an application, we show that a kernel based test achieves the optimal detection for off-line change detection in the nonparametric setting.Comment: 17 pages. Added application to off-line change detectio

Family income affects children's altruistic behavior in the dictator game.

This study aimed to examine how family income and social distance influence young rural Chinese children's altruistic behavior in the dictator game (DG). A total of 469 four-year-old children from eight rural areas in China, including many children left behind by parents who had migrated to urban areas for work, played the DG. Stickers comprised the resource, while recipients in the game were assumed to be either their friends or strangers, with the social distance (i.e., strangers compared to friends) as a between-subjects variable. Children donated significantly more stickers to their friends than to strangers. Moreover, children from lower income families donated more stickers than children from higher income families. However, no gender and parental migrant status differences in children's prosocial behaviors were evident in this sample. Findings of this study suggest that children's altruistic behaviours to peers are influenced by family characteristics since preschool age. The probable influence of local socialization practices on development and the possible adaptive significance were discussed

Revisiting Street-to-Aerial View Image Geo-localization and Orientation Estimation

Street-to-aerial image geo-localization, which matches a query street-view image to the GPS-tagged aerial images in a reference set, has attracted increasing attention recently. In this paper, we revisit this problem and point out the ignored issue about image alignment information. We show that the performance of a simple Siamese network is highly dependent on the alignment setting and the comparison of previous works can be unfair if they have different assumptions. Instead of focusing on the feature extraction under the alignment assumption, we show that improvements in metric learning techniques significantly boost the performance regardless of the alignment. Without leveraging the alignment information, our pipeline outperforms previous works on both panorama and cropped datasets. Furthermore, we conduct visualization to help understand the learned model and the effect of alignment information using Grad-CAM. With our discovery on the approximate rotation-invariant activation maps, we propose a novel method to estimate the orientation/alignment between a pair of cross-view images with unknown alignment information. It achieves state-of-the-art results on the CVUSA dataset.Comment: WACV 202

Dropout Training for SVMs with Data Augmentation

Dropout and other feature noising schemes have shown promising results in controlling over-fitting by artificially corrupting the training data. Though extensive theoretical and empirical studies have been performed for generalized linear models, little work has been done for support vector machines (SVMs), one of the most successful approaches for supervised learning. This paper presents dropout training for both linear SVMs and the nonlinear extension with latent representation learning. For linear SVMs, to deal with the intractable expectation of the non-smooth hinge loss under corrupting distributions, we develop an iteratively re-weighted least square (IRLS) algorithm by exploring data augmentation techniques. Our algorithm iteratively minimizes the expectation of a re-weighted least square problem, where the re-weights are analytically updated. For nonlinear latent SVMs, we consider learning one layer of latent representations in SVMs and extend the data augmentation technique in conjunction with first-order Taylor-expansion to deal with the intractable expected non-smooth hinge loss and the nonlinearity of latent representations. Finally, we apply the similar data augmentation ideas to develop a new IRLS algorithm for the expected logistic loss under corrupting distributions, and we further develop a non-linear extension of logistic regression by incorporating one layer of latent representations. Our algorithms offer insights on the connection and difference between the hinge loss and logistic loss in dropout training. Empirical results on several real datasets demonstrate the effectiveness of dropout training on significantly boosting the classification accuracy of both linear and nonlinear SVMs. In addition, the nonlinear SVMs further improve the prediction performance on several image datasets.Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:1404.417

Very free curves on Fano Complete Intersections

In this paper, we show that general Fano complete intersections over an algebraically closed field of arbitrary characteristics are separably rationally connected. Our proof also implies that general log Fano complete intersections with smooth tame boundary divisors admit very free $A^1$-curves.Comment: 17 pages; final versio

Representations of the Drazin inverse involving idempotents in a ring

We present some formulae for the Drazin inverse of difference and product of idempotents in a ring. A number of results of bounded linear operators in Banach spaces are extended to the ring case.Comment: 11 page

Cyclic DNA codes over F2+uF2+vF2+uvF2

In this work, we study the structure of cyclic DNA codes of arbitrary lengths over the ring R=F2+uF2+vF2+uvF2 and establish relations to codes over R1=F2+uF2 by defining a Gray map between R and R1^2 where R1 is the ring with 4 elements. Cyclic codes of arbitrary lengths over R satisfied the reverse constraint and the reverse-complement constraint are studied in this paper. The GC content constraint is considered in the last

A Game-Theoretic Framework for Resilient and Distributed Generation Control of Renewable Energies in Microgrids

The integration of microgrids that depend on the renewable distributed energy resources with the current power systems is a critical issue in the smart grid. In this paper, we propose a non-cooperative game-theoretic framework to study the strategic behavior of distributed microgrids that generate renewable energies and characterize the power generation solutions by using the Nash equilibrium concept. Our framework not only incorporates economic factors but also takes into account the stability and efficiency of the microgrids, including the power flow constraints and voltage angle regulations. We develop two decentralized update schemes for microgrids and show their convergence to a unique Nash equilibrium. Also, we propose a novel fully distributed PMU-enabled algorithm which only needs the information of voltage angle at the bus. To show the resiliency of the distributed algorithm, we introduce two failure models of the smart grid. Case studies based on the IEEE 14-bus system are used to corroborate the effectiveness and resiliency of the proposed algorithms.Comment: 11 pages; This paper has been accepted to publish in IEEE Transactions on Smart Grid. This is the final versio