Non-perturbative positive Lyapunov exponent of Schr\"odinger equations and its applications to skew-shift

We first study the discrete Schr\"odinger equations with analytic potentials given by a class of transformations. It is shown that if the coupling number is large, then its logarithm equals approximately to the Lyapunov exponents. When the transformation becomes the skew-shift, we prove that the Lyapunov exponent is week H\"older continuous, and the spectrum satisfies Anderson Localization and contains large intervals. Moreover, all of these conclusions are non-perturbative

H\"older continuity of the integrated density of states for quasi-periodic Jacobi operators

We show H\"older continuity for the integrated density of states of a quasi-periodic Jacobi operator with analytic coefficients, in the regime of positive Lyapunov exponent and with a strong Diophantine condition on the frequency. In particular, when the coefficients are trigonometric polynomials we express the H\"older exponent in terms of the degrees of the coefficients.Comment: v.2: fixed some typo

Once for All: a Two-flow Convolutional Neural Network for Visual Tracking

One of the main challenges of visual object tracking comes from the arbitrary appearance of objects. Most existing algorithms try to resolve this problem as an object-specific task, i.e., the model is trained to regenerate or classify a specific object. As a result, the model need to be initialized and retrained for different objects. In this paper, we propose a more generic approach utilizing a novel two-flow convolutional neural network (named YCNN). The YCNN takes two inputs (one is object image patch, the other is search image patch), then outputs a response map which predicts how likely the object appears in a specific location. Unlike those object-specific approach, the YCNN is trained to measure the similarity between two image patches. Thus it will not be confined to any specific object. Furthermore the network can be end-to-end trained to extract both shallow and deep convolutional features which are dedicated for visual tracking. And once properly trained, the YCNN can be applied to track all kinds of objects without further training and updating. Benefiting from the once-for-all model, our algorithm is able to run at a very high speed of 45 frames-per-second. The experiments on 51 sequences also show that our algorithm achieves an outstanding performance

Direct optical detection of pure spin current in semiconductors

We suggest a new practical scheme for the direct detection of pure spin current by using the two-color Faraday rotation of optical quantum interference process (QUIP) in a semiconductor system. We demonstrate theoretically that the Faraday rotation of QUIP depends sensitively on the spin orientation and wave vector of the carriers, and can be tuned by the relative phase and the polarization direction of the $\omega$ and $2\omega$ laser beams. By adjusting these parameters, the magnitude and direction of the spin current can be detected.Comment: 4 pages, 3 figure

Payoff Control in the Iterated Prisoner's Dilemma

Repeated game has long been the touchstone model for agents' long-run relationships. Previous results suggest that it is particularly difficult for a repeated game player to exert an autocratic control on the payoffs since they are jointly determined by all participants. This work discovers that the scale of a player's capability to unilaterally influence the payoffs may have been much underestimated. Under the conventional iterated prisoner's dilemma, we develop a general framework for controlling the feasible region where the players' payoff pairs lie. A control strategy player is able to confine the payoff pairs in her objective region, as long as this region has feasible linear boundaries. With this framework, many well-known existing strategies can be categorized and various new strategies with nice properties can be further identified. We show that the control strategies perform well either in a tournament or against a human-like opponent

SentiBERT: A Transferable Transformer-Based Architecture for Compositional Sentiment Semantics

We propose SentiBERT, a variant of BERT that effectively captures compositional sentiment semantics. The model incorporates contextualized representation with binary constituency parse tree to capture semantic composition. Comprehensive experiments demonstrate that SentiBERT achieves competitive performance on phrase-level sentiment classification. We further demonstrate that the sentiment composition learned from the phrase-level annotations on SST can be transferred to other sentiment analysis tasks as well as related tasks, such as emotion classification tasks. Moreover, we conduct ablation studies and design visualization methods to understand SentiBERT. We show that SentiBERT is better than baseline approaches in capturing negation and the contrastive relation and model the compositional sentiment semantics.Comment: ACL-202

Nematic antiferromagnetic states in bulk FeSe

We revisit bulk FeSe through the systematic first-principles electronic structure calculations. We find that there are a series of staggered $n$-mer antiferromagnetic (AFM) states with corresponding energies below that of the collinear AFM state which is the ground state for the parent compounds of most iron-based superconductors. Here the staggered $n$-mer ($n$ any integer $>1$) means that a set of $n$ adjacent spins parallel on a line along $b$-axis with spins in antiparallel between $n$-mers and along $a$-axis. Among them, the lowest energy states are quasi-degenerate staggered dimer and staggered trimer AFM states as well as their any staggered combinations. Thus, to have the largest entropy to minimize the free energy at low temperature, the most favorable state is such a quasi-one-dimensional antiferromagnet in which along $b$-axis a variety of $n$-mers, mostly dimers and trimers, are randomly antiparallel aligned while along $a$-axis spins are antiparallel aligned, i.e. actually a nematic paramagnet. This finding accounts well for the absence of long-range magnetic order in bulk FeSe and meanwhile indicates the dominant stripe spin fluctuation and the nematicity as spin-driven.Comment: 6 pages and 3 figures with Supplementary Material

Electronic structures of quasi-one-dimensional cuprate superconductors Ba2_2CuO3+δ_{3+\delta}

An intact CuO$_2$ plane is widely believed to be a prerequisite for the high-$T_c$ superconductivity in cuprate superconductors. However, an exception may exist in the superconducting Ba$_2$CuO$_{3+\delta}$ materials where CuO chains play a more important role. From first-principles density functional theory calculations, we have studied the electronic and magnetic structures of Ba$_2$CuO$_{3+\delta}$. The stoichiometric Ba$_2$CuO$_3$ and Ba$_2$CuO$_4$ contain quasi-one-dimensional CuO chains and intact two-dimensional CuO$_2$ planes, respectively. In comparison with the nonmagnetic metal Ba$_2$CuO$_4$, Ba$_2$CuO$_3$ is found to be an antiferromagnetic (AFM) Mott insulator. It possesses a nearest-neighbor intra-chain antiferromagnetic (AFM) coupling and a weak inter-chain interaction, and its lowest unoccupied band and highest occupied band are contributed by Cu 3$d_{b^2-c^2}$-orbital (or $d_{x^2-y^2}$-orbital if we denote the $bc$-plane as the $xy$-plane) and O 2$p$-orbitals, respectively. Total energy calculations indicate that the oxygen vacancies in Ba$_2$CuO$_{3+\delta}$ prefer to reside in the planar sites rather than the apical oxygens in the CuO chains, in agreement with the experimental observation. Furthermore, we find that the magnetic frustrations or spin fluctuations can be effectively induced by moderate charge doping. This suggests that the superconducting pairing in oxygen-enriched Ba$_2$CuO$_{3+\delta}$ or oxygen-deficient Ba$_2$CuO$_{4-\delta}$ is likely to be mainly driven by the AFM fluctuations within CuO chains.Comment: 7 pages, 7 figures, 3 table

Minkowski formulae and Alexandrov theorems in spacetime

The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit "hidden symmetry" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codimension-two submanifold with constant normalized null expansion (null mean curvature) must lie in a shear-free (umbilical) null hypersurface. These results are generalized for higher order curvature invariants. In particular, the notion of mixed higher order mean curvature is introduced to highlight the special null geometry of the submanifold. Finally, Alexandrov type theorems are established for spacelike submanifolds with constant mixed higher order mean curvature, which are generalizations of hypersurfaces of constant Weingarten curvature in the Euclidean space.Comment: 38 pages. To appear in J. Differential Geometr

H\"older continuity of Lyapunov exponent for quasi-periodic Jacobi operators

We consider the quasi-periodic Jacobi operator $H_{x,\omega}$ in $l^2(\mathbb{Z})$ $(H_{x,\omega}\phi)(n) = -b(x+(n+1)\omega)\phi(n+1) - b(x+n\omega)\phi(n-1) + a(x+n\omega)\phi(n) = E\phi(n),\ n\in\mathbb{Z},$ where $a(x),\ b(x)$ are analytic function on $\mathbb{T}$, $b$ is not identically zero, and $\omega$ obeys some strong Diophantine condition. We consider the corresponding unimodular cocycle. We prove that if the Lyapunov exponent $L(E)$ of the cocycle is positive for some $E=E_0$, then there exists $\rho_0=\rho_0(a,b,\omega,E_0)$, $\beta=\beta(a,b,\omega)$ such that $|L(E)-L(E')|<|E-E'|^\beta$ for any $E,E'\in (E_0-\rho_0,E_0+\rho_0)$. If $L(E)>0$ for all $E$ in some compact interval $I$ then $L(E)$ is H\"{o}lder continuous on $I$ with a H\"{o}lder exponent $\beta=\beta(a,b,\omega,I)$. In our derivation we follow the refined version of the Goldstein-Schlag method \cite{GS} developed by Bourgain and Jitomirskaya \cite{BJ}