We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of such penalties as our motivating examples: 1) overlapping group lasso penalty, based on the 1 / 2 mixed-norm penalty, and 2) graph-guided fusion penalty. For both types of penalties, due to their non-separability, developing an efficient optimization method has remained a challenging problem. In this paper, we propose a general optimization approach, called smoothing proximal gradient method, which can solve the structured sparse regression problems with a smooth convex loss and a wide spectrum of structured-sparsityinducing penalties. Our approach is based on a general smoothing technique of Nesterov. It achieves a convergence rate faster than the standard first-order method, subgradient method, and is much more scalable than the most widely used interior-point method. Numerical results are reported to demonstrate the efficiency and scalability of the proposed method.
The charge states of single molecular magnetic chains were manipulated with a scanning tunneling microscope and identified by spin-flip inelastic tunneling spectroscopy. We show that the charged and neutral states have different spin structures and therefore exhibit different features associated with the spin-flip processes in tunneling spectra. The experiment demonstrates a general approach for detecting the charge states at the nanometer scale in a more straightforward manner than using indirect information.
We report a transport study of ultrathin Bi 2 Se 3 topological insulators with thickness from one quintuple layer to six quintuple layers grown by molecular beam epitaxy. At low temperatures, the film resistance increases logarithmically with decreasing temperature, revealing an insulating ground state. The sharp increase of resistance with magnetic field, however, indicates the existence of weak antilocalization, which should reduce the resistance as temperature decreases. We show that these apparently contradictory behaviors can be understood by considering the electron interaction effect, which plays a crucial role in determining the electronic ground state of topological insulators in the two dimensional limit.
2D SnTe films with a thickness of as little as 2 atomic layers (ALs) have recently been shown to be ferroelectric with in‐plane polarization. Remarkably, they exhibit transition temperatures (Tc
) much higher than that of bulk SnTe. Here, combining molecular beam epitaxy, variable temperature scanning tunneling microscopy, and ab initio calculations, the underlying mechanism of the Tc
enhancement is unveiled, which relies on the formation of γ‐SnTe, a van der Waals orthorhombic phase with antipolar inter‐layer coupling in few‐AL thick SnTe films. In this phase, 4n − 2 AL (n = 1, 2, 3…) thick films are found to possess finite in‐plane polarization (space group Pmn21), while 4n AL thick films have zero total polarization (space group Pnma). Above 8 AL, the γ‐SnTe phase becomes metastable, and can convert irreversibly to the bulk rock salt phase as the temperature is increased. This finding unambiguously bridges experiments on ultrathin SnTe films with predictions of robust ferroelectricity in GeS‐type monochalcogenide monolayers. The observed high transition temperature, together with the strong spin‐orbit coupling and van der Waals structure, underlines the potential of atomically thin γ‐SnTe films for the development of novel spontaneous polarization‐based devices.
Many real world learning problems can be recast as multi-task learning problems which utilize correlations among different tasks to obtain better generalization performance than learning each task individually. The feature selection problem in multi-task setting has many applications in fields of computer vision, text classification and bio-informatics. Generally, it can be realized by solving a L-1-infinity regularized optimization problem. And the solution automatically yields the joint sparsity among different tasks. However, due to the nonsmooth nature of the L-1-infinity norm, there lacks an efficient training algorithm for solving such problem with general convex loss functions. In this paper, we propose an accelerated gradient method based on an "optimal" first order black-box method named after Nesterov and provide the convergence rate for smooth convex loss functions. For nonsmooth convex loss functions, such as hinge loss, our method still has fast convergence rate empirically. Moreover, by exploiting the structure of the L-1-infinity ball, we solve the black-box oracle in Nesterov's method by a simple sorting scheme. Our method is suitable for large-scale multi-task learning problem since it only utilizes the first order information and is very easy to implement. Experimental results show that our method significantly outperforms the most state-of-the-art methods in both convergence speed and learning accuracy.
The latest discovery of possible high-temperature superconductivity in the single-layer FeSe film grown on a SrTiO 3 substrate has generated much attention. Initial work found that, while the single-layer FeSe/SrTiO 3 film exhibits a clear signature of superconductivity, the double-layer film shows an insulating behaviour. Such a marked layer-dependent difference is surprising and the underlying origin remains unclear. Here we report a comparative angleresolved photoemission study between the single-layer and double-layer FeSe/SrTiO 3 films annealed in vacuum. We find that, different from the single-layer FeSe/SrTiO 3 film, the double-layer FeSe/SrTiO 3 film is hard to get doped and remains in the semiconducting/ insulating state under an extensive annealing condition. Such a behaviour originates from the much reduced doping efficiency in the bottom FeSe layer of the double-layer FeSe/SrTiO 3 film from the FeSe-SrTiO 3 interface. These observations provide key insights in understanding the doping mechanism and the origin of superconductivity in the FeSe/SrTiO 3 films.
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