Dirac spin gapless semiconductors: Ideal platforms for massless and dissipationless spintronics and new (quantum) anomalous spin Hall effects

It is proposed that the new generation of spintronics should be ideally massless and dissipationless for the realization of ultra-fast and ultra-low-power spintronic devices. We demonstrate that the spin-gapless materials with linear energy dispersion are unique materials that can realize these massless and dissipationless states. Furthermore, we propose four new types of spin Hall effects which consist of spin accumulation of equal numbers of electrons and holes having the same or opposite spin polarization at the sample edge in Hall effect measurements, but with vanishing Hall voltage. These new Hall effects can be classified as (quantum) anomalous spin Hall effects. The physics for massless and dissipationless spintronics and the new spin Hall effects are presented for spin-gapless semiconductors with either linear or parabolic dispersion. New possible candidates for Dirac-type or parabolic type spin-gapless semiconductors are demonstrated in ferromagnetic monolayers of simple oxides with either honeycomb or square lattices.Comment: 5 pages, 7 figue

Finite type invariants of integral homology 3-spheres: A survey

This is a survey on the current status of the study of finite type invariants of integral homology 3-spheres based on lectures given in the workshop on knot theory at Banach International Center of Mathematics, Warsaw, July 1995. As a new result, we show that the space of finite type invariants of integral homology 3-spheres is a graded polynomial algebra generated by invariants additive under the connected sum. We also discuss some open questions on this subject.Comment: 27 pages, amslatex. A new section was added surveying recent developments of the subject. To appear in the proceedings of Warsaw knot theory workshop, July-August 199

Modified mean curvature flow of star-shaped hypersurfaces in hyperbolic space

We define a new version of modified mean curvature flow (MMCF) in hyperbolic space $\mathbb{H}^{n+1}$, which interestingly turns out to be the natural negative $L^2$-gradient flow of the energy functional defined by De Silva and Spruck in \cite{DS09}. We show the existence, uniqueness and convergence of the MMCF of complete embedded star-shaped hypersurfaces with fixed prescribed asymptotic boundary at infinity. As an application, we recover the existence and uniqueness of smooth complete hypersurfaces of constant mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity, which was first shown by Guan and Spruck.Comment: 26 pages, 3 figure

An Accelerated Proximal Coordinate Gradient Method and its Application to Regularized Empirical Risk Minimization

We consider the problem of minimizing the sum of two convex functions: one is smooth and given by a gradient oracle, and the other is separable over blocks of coordinates and has a simple known structure over each block. We develop an accelerated randomized proximal coordinate gradient (APCG) method for minimizing such convex composite functions. For strongly convex functions, our method achieves faster linear convergence rates than existing randomized proximal coordinate gradient methods. Without strong convexity, our method enjoys accelerated sublinear convergence rates. We show how to apply the APCG method to solve the regularized empirical risk minimization (ERM) problem, and devise efficient implementations that avoid full-dimensional vector operations. For ill-conditioned ERM problems, our method obtains improved convergence rates than the state-of-the-art stochastic dual coordinate ascent (SDCA) method

Leveraging Visual Question Answering for Image-Caption Ranking

Visual Question Answering (VQA) is the task of taking as input an image and a free-form natural language question about the image, and producing an accurate answer. In this work we view VQA as a "feature extraction" module to extract image and caption representations. We employ these representations for the task of image-caption ranking. Each feature dimension captures (imagines) whether a fact (question-answer pair) could plausibly be true for the image and caption. This allows the model to interpret images and captions from a wide variety of perspectives. We propose score-level and representation-level fusion models to incorporate VQA knowledge in an existing state-of-the-art VQA-agnostic image-caption ranking model. We find that incorporating and reasoning about consistency between images and captions significantly improves performance. Concretely, our model improves state-of-the-art on caption retrieval by 7.1% and on image retrieval by 4.4% on the MSCOCO dataset

A Proximal-Gradient Homotopy Method for the Sparse Least-Squares Problem

We consider solving the $\ell_1$-regularized least-squares ($\ell_1$-LS) problem in the context of sparse recovery, for applications such as compressed sensing. The standard proximal gradient method, also known as iterative soft-thresholding when applied to this problem, has low computational cost per iteration but a rather slow convergence rate. Nevertheless, when the solution is sparse, it often exhibits fast linear convergence in the final stage. We exploit the local linear convergence using a homotopy continuation strategy, i.e., we solve the $\ell_1$-LS problem for a sequence of decreasing values of the regularization parameter, and use an approximate solution at the end of each stage to warm start the next stage. Although similar strategies have been studied in the literature, there have been no theoretical analysis of their global iteration complexity. This paper shows that under suitable assumptions for sparse recovery, the proposed homotopy strategy ensures that all iterates along the homotopy solution path are sparse. Therefore the objective function is effectively strongly convex along the solution path, and geometric convergence at each stage can be established. As a result, the overall iteration complexity of our method is $O(\log(1/\epsilon))$ for finding an $\epsilon$-optimal solution, which can be interpreted as global geometric rate of convergence. We also present empirical results to support our theoretical analysis

Model-Driven Data Collection for Biological Systems

For biological experiments aiming at calibrating models with unknown parameters, a good experimental design is crucial, especially for those subject to various constraints, such as financial limitations, time consumption and physical practicability. In this paper, we discuss a sequential experimental design based on information theory for parameter estimation and apply it to two biological systems. Two specific issues are addressed in the proposed applications, namely the determination of the optimal sampling time and the optimal choice of observable. The optimal design, either sampling time or observable, is achieved by an information-theoretic sensitivity analysis. It is shown that this is equivalent with maximizing the mutual information and contrasted with non-adaptive designs, this information theoretic strategy provides the fastest reduction of uncertainty.Comment: 2014 American Control Conference, Portland, OR, June 201