Classification of quasifinite representations with nonzero central charges for type A1A_1 EALA with coordinates in quantum torus

In this paper, we first construct a Lie algebra $L$ from rank 3 quantum torus, and show that it is isomorphic to the core of EALAs of type $A_1$ with coordinates in rank 2 quantum torus. Then we construct two classes of irreducible ${\bf Z}$-graded highest weight representations, and give the necessary and sufficient conditions for these representations to be quasifinite. Next, we prove that they exhaust all the generalized highest weight irreducible ${\bf Z}$-graded quasifinite representations. As a consequence, we determine all the irreducible ${\bf Z}$-graded quasifinite representations with nonzero central charges. Finally, we construct two classes of highest weight ${\bf Z}^2$-graded quasifinite representations by using these ${\bf Z}$-graded modules.Comment: 28 page

Pairing symmetry and spontaneous vortex-antivortex lattice in superconducting twisted-bilayer graphene: Bogoliubov-de Gennes approach

We study the superconducting pairing symmetry in twisted bilayer graphene by solving the Bogoliubov-de Gennes equation for all electrons in moir\'{e} supercells. With increasing the pairing potential, the system evolves from the mixed nontopological $d+id$ and $p+ip$ phase to the $s+p+d$ phase via the first-order phase transition. In the time-reversal symmetry breaking $d+id$ and $p+ip$ phase, vortex and antivortex lattices accompanying spontaneous supercurrent are induced by the twist. The superconducting order parameter is nonuniform in the moir\'{e} unit cell. Nevertheless, the superconducting gap in the local density of states is identical in the unit cell. The twist-induced vortices and nontopological nature of the mixed $d+id$ and $p+ip$ phase are not captured by the existing effective models. Our results suggest the importance of long-range pairing interaction for effective models.Comment: 9 pages, 9 figure

Nontrivial topology and localization in the double exchange model with possible applications to perovskite manganites

The double exchange model describing the coupling between conduction electrons and localized magnetic moments is relevant for a large family of physical systems including manganites. Here we reveal that the one dimensional double exchange model with an incommensurate magnetic elliptical spiral is a topological insulator with a Chern number $2\mathbb{Z}$ in the two dimensional space with one physical dimension and one ancillary dimension spanned by the Goldstone mode of the spiral. Moreover, the electronic states can be localized for a strong local exchange coupling. The topological protected edge states are responsible for the pumping of electron charge, and give rise to multiferroic response. Our work uncovers hitherto undiscovered nontrivial topology and Anderson localization in the double exchange model with possible applications to perovskite manganites.Comment: 8 pages and 10 figure

Weak KAM theory for general Hamilton-Jacobi equations I: the solution semigroup under proper conditions

We consider the following evolutionary Hamilton-Jacobi equation with initial condition: \begin{equation*} \begin{cases} \partial_tu(x,t)+H(x,u(x,t),\partial_xu(x,t))=0,\\ u(x,0)=\phi(x). \end{cases} \end{equation*} Under some assumptions on $H(x,u,p)$ with respect to $p$ and $u$, we provide a variational principle on the evolutionary Hamilton-Jacobi equation. By introducing an implicitly defined solution semigroup, we extend Fathi's weak KAM theory to certain more general cases, in which $H$ explicitly depends on the unknown function $u$. As an application, we show the viscosity solution of the evolutionary Hamilton-Jacobi equation with initial condition tends asymptotically to the weak KAM solution of the following stationary Hamilton-Jacobi equation: \begin{equation*} H(x,u(x),\partial_xu(x))=0. \end{equation*}.Comment: This is a revised version of arXiv:1312.160

Supervisor Obfuscation Against Actuator Enablement Attack

In this paper, we propose and address the problem of supervisor obfuscation against actuator enablement attack, in a common setting where the actuator attacker can eavesdrop the control commands issued by the supervisor. We propose a method to obfuscate an (insecure) supervisor to make it resilient against actuator enablement attack in such a way that the behavior of the original closed-loop system is preserved. An additional feature of the obfuscated supervisor, if it exists, is that it has exactly the minimum number of states among the set of all the resilient and behavior-preserving supervisors. Our approach involves a simple combination of two basic ideas: 1) a formulation of the problem of computing behavior-preserving supervisors as the problem of computing separating finite state automata under controllability and observability constraints, which can be efficiently tackled by using modern SAT solvers, and 2) the use of a recently proposed technique for the verification of attackability in our setting, with a normality assumption imposed on both the actuator attackers and supervisors.Comment: This paper has been accepted by European Control Conference, 2018. The first two authors contribute equally to this wor

On Bernstein Type Inequalities for Stochastic Integrals of Multivariate Point Processes

We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform exponential inequality using a generic chaining argument. As applications, we obtain a upper bound for a sequence of discrete time martingales indexed by a class of functionals, and so derive the rate of convergence for nonparametric maximum likelihood estimators, which is an improvement of earlier work of van de Geer.Comment: 18 page

The Asteroseismology of ZZ Ceti star GD1212

The ZZ Ceti star GD 1212 was detected to have 19 independent modes from the two-wheel-controlled Kepler Spacecraft in 2014. By asymptotic analysis, we identify most of pulsation modes. We find out two set of complete triplets, and four sets of doublet which are interpreted as rotation modes with $l=1$. For the other five modes, the four modes $f_{13}$, $f_{15}$, $f_{16}$ and $f_{4}$ are identified as ones with $l=2$; and the mode $f_{7}$ is identified to be the one with $l=1$. Meanwhile we derive a mean rotation period of $6.65\pm0.21$ h for GD 1212 according to the rotation splitting. Using the method of matching the observed periods to theoretical ones, we obtain the best-fitting model with the four parameters as $M_{\rm{*}}/M_{\rm{\odot}} = 0.775$, $T_{\rm{eff}} = 11400$ K, $\log (M_{\rm{H}}/M_{\rm{*}}) = -5.0$, $\log (M_{\rm{He}}/M_{\rm{*}})=-2.5$ for GD 1212. We find that due to the gradient of C/O abundance in the interior of white dwarf, some modes can not propagate to the stellar interior, which leads to the period spacing of the adjacent modes to become large. This feature is just proven by the observational data from GD 1212. All of these imply that GD 1212 may be evolved from an intermediate mass star.Comment: 17 pages, 4 figure

Cascaded Pyramid Mining Network for Weakly Supervised Temporal Action Localization

Weakly supervised temporal action localization, which aims at temporally locating action instances in untrimmed videos using only video-level class labels during training, is an important yet challenging problem in video analysis. Many current methods adopt the "localization by classification" framework: first do video classification, then locate temporal area contributing to the results most. However, this framework fails to locate the entire action instances and gives little consideration to the local context. In this paper, we present a novel architecture called Cascaded Pyramid Mining Network (CPMN) to address these issues using two effective modules. First, to discover the entire temporal interval of specific action, we design a two-stage cascaded module with proposed Online Adversarial Erasing (OAE) mechanism, where new and complementary regions are mined through feeding the erased feature maps of discovered regions back to the system. Second, to exploit hierarchical contextual information in videos and reduce missing detections, we design a pyramid module which produces a scale-invariant attention map through combining the feature maps from different levels. Final, we aggregate the results of two modules to perform action localization via locating high score areas in temporal Class Activation Sequence (CAS). Extensive experiments conducted on THUMOS14 and ActivityNet-1.3 datasets demonstrate the effectiveness of our method.Comment: Accepted at ACCV 201

Graph-based Code Design for Quadratic-Gaussian Wyner-Ziv Problem with Arbitrary Side Information

Wyner-Ziv coding (WZC) is a compression technique using decoder side information, which is unknown at the encoder, to help the reconstruction. In this paper, we propose and implement a new WZC structure, called residual WZC, for the quadratic-Gaussian Wyner-Ziv problem where side information can be arbitrarily distributed. In our two-stage residual WZC, the source is quantized twice and the input of the second stage is the quantization error (residue) of the first stage. The codebook of the first stage quantizer must be simultaneously good for source and channel coding, since it also acts as a channel code at the decoder. Stemming from the non-ideal quantization at the encoder, a problem of channel decoding beyond capacity is identified and solved when we design the practical decoder. Moreover,by using the modified reinforced belief-propagation quantization algorithm, the low-density parity check code (LDPC), whose edge degree is optimized for channel coding, also performs well as a source code. We then implement the residual WZC by an LDPC and a low density generator matrix code (LDGM). The simulation results show that our practical construction approaches the Wyner-Ziv bound. Compared with previous works, our construction can offer more design lexibility in terms of distribution of side information and practical code rate selection.Comment: To appear, IEEE International Symposium on Information Theory (ISIT) Jul, 2012, corrected reference [13

Gini-regularized Optimal Transport with an Application to Spatio-Temporal Forecasting

Rapidly growing product lines and services require a finer-granularity forecast that considers geographic locales. However the open question remains, how to assess the quality of a spatio-temporal forecast? In this manuscript we introduce a metric to evaluate spatio-temporal forecasts. This metric is based on an Opti- mal Transport (OT) problem. The metric we propose is a constrained OT objec- tive function using the Gini impurity function as a regularizer. We demonstrate through computer experiments both the qualitative and the quantitative charac- teristics of the Gini regularized OT problem. Moreover, we show that the Gini regularized OT problem converges to the classical OT problem, when the Gini regularized problem is considered as a function of {\lambda}, the regularization parame-ter. The convergence to the classical OT solution is faster than the state-of-the-art Entropic-regularized OT[Cuturi, 2013] and results in a numerically more stable algorithm.Comment: 10 page