Order-indices and order-periods of 3x3 matrices over commutative inclines

An incline is an additively idempotent semiring in which the product of two elements is always less than or equal to either factor. By making use of prime numbers, this paper proves that A^{11} is less than or equal to A^5 for all 3x3 matrices A over an arbitrary commutative incline, thus giving an answer to an open problem "For 3x3 matrices over any incline (even noncommutative) is X^5 greater than or equal to X^{11}?", proposed by Cao, Kim and Roush in a monograph Incline Algebra and Applications, 1984.Comment: 6 page

Incorporating Context and External Knowledge for Pronoun Coreference Resolution

Linking pronominal expressions to the correct references requires, in many cases, better analysis of the contextual information and external knowledge. In this paper, we propose a two-layer model for pronoun coreference resolution that leverages both context and external knowledge, where a knowledge attention mechanism is designed to ensure the model leveraging the appropriate source of external knowledge based on different context. Experimental results demonstrate the validity and effectiveness of our model, where it outperforms state-of-the-art models by a large margin.Comment: Accepted by NAACL-HLT 201

Third-order nonlinearity by the inverse Faraday effect in planar magnetoplasmonic structures

We predict a new type of ultrafast third-order nonlinearity of surface plasmon polaritons (SPP) in planar magneto-plasmonic structures caused by the inverse Faraday effect (IFE). Planar SPPs with a significant longitudinal component of the electric field act via the IFE as an effective transverse magnetic field. Its response to the plasmon propagation leads to strong ultrafast self-action which manifests itself through a third-order nonlinearity. We derive a general formula and analytical expressions for the IFE-related nonlinear susceptibility for two specific planar magneto-plasmonic structures from the Lorentz reciprocity theorem. Our estimations predict a very large nonlinear third-order nonlinear susceptibility exceeding those of typical metals such as gold

Fractional stochastic wave equation driven by a Gaussian noise rough in space

In this article, we consider fractional stochastic wave equations on $\mathbb R$ driven by a multiplicative Gaussian noise which is white/colored in time and has the covariance of a fractional Brownian motion with Hurst parameter $H\in(\frac14, \frac12)$ in space. We prove the existence and uniqueness of the mild Skorohod solution, establish lower and upper bounds for the $p$-th moment of the solution for all $p\ge2$, and obtain the H\"older continuity in time and space variables for the solution

Plasmonic amplification and suppression in nanowaveguide coupled to gain-assisted high-quality plasmon resonances

We theoretically study transmission in nanowaveguide coupled to high-quality plasmon resonances for which the metal loss is overcompensated by gain. The on-resonance transmission can vary widely from lower than --20dB to higher than 20dB for a range of gain coefficient. A reversible transition between the high-quality amplification and the suppression can be induced by a quite small change of gain coefficient for a moderately increased distance between the waveguide and the resonator. It is expected that in practice a small change of gain coefficient can be made by flexibly controlling pumping rate or utilizing nonlinear gain. Additionally, based on the frequency-dependant model for gain-transition susceptibility, it is shown that the wide variation of the on-resonance transmission can also be observed for defferent detuning of the gain-transition line-center. Such a widely controllable on-resonance transmission is promising for applications such as well-controlled lumped amplification of surface plasmon-polariton as well as plasmonic switching.Comment: submitted to Laser Physics Letter

Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT

We study superconformal indices of 4d N=2 class S theories with certain irregular punctures called type $I_{k, N}$. This class of theories include generalized Argyres-Douglas theories of type $(A_{k-1}, A_{N-1})$ and more. We conjecture the superconformal indices in certain simplified limits based on the TQFT structure of the class S theories by writing an expression for the wave function corresponding to the puncture $I_{k, N}$. We write the Schur limit of the wave function when $k$ and $N$ are coprime. When $k=2$, we also conjecture a closed-form expression for the Hall-Littlewood index and the Macdonald index for odd $N$. From the index, we argue that certain short-multiplet which can appear in the OPE of the stress-energy tensor is absent in the $(A_1, A_{2n})$ theory. We also discuss the mixed Schur indices for the N=1 class S theories with irregular punctures.Comment: 28 pages, 2 figures, v3: corrections and simplification of some formula

Hall universal group has ample generic automorphisms

We show that the automorphism group of Philip Hall's universal locally finite group has ample generics,that is, it admits comeager diagonal conjugacy classes in all dimensions.Consequently, it has the small index property, is not the union of a countable chain of non-open subgroups, and has the automatic continuity property. Also, we discuss some algebraic and topological properties of the automorphism group of Hall universal group. For example, we show that every generic automorphism of Hall universal group is conjugate to all of its powers, and hence has roots of all orders

Nonlocality and the Correlation of Measurement Bases

Nonlocal nature apparently shown in entanglement is one of the most striking features of quantum theory. We examine the locality assumption in Bell-type proofs for entangled qubits, i.e. the outcome of a qubit at one end is independent of the basis choice at the other end. It has recently been claimed that in order to properly incorporate the phenomenon of self-observation, the Heisenberg picture with time going backwards provides a consistent description. We show that, if this claim holds true, the assumption in nonlocality proofs that basis choices at two ends are independent of each other may no longer be true, and may pose a threat to the validity of Bell-type proofs.Comment: 6 page

Characterizations of processes with stationary and independent increments under GG-expectation

Our purpose is to investigate properties for processes with stationary and independent increments under $G$-expectation. As applications, we prove the martingale characterization to $G$-Brownian motion and present a decomposition for generalized $G$-Brownian motion.Comment: 2

Feynman Algorithm Implementation for Comparison with Euler in a Uniform Elastic Two-Layer 2D and 3D Object Dynamic Deformation Framework in OpenGL with GUI

We implement for comparative purposes the Feynman algorithm within a C++-based framework for two-layer uniform facet elastic object for real-time softbody simulation based on physics modeling methods. To facilitate the comparison, we implement initial timing measurements on the same hardware against that of Euler integrator in the softbody framework by varying different algorithm parameters. Due to a relatively large number of such variations we implement a GLUI-based user-interface to allow for much more finer control over the simulation process at real-time, which was lacking completely in the previous versions of the framework. We show our currents results based on the enhanced framework. The two-layered elastic object consists of inner and outer elastic mass-spring surfaces and compressible internal pressure. The density of the inner layer can be set differently from the density of the outer layer; the motion of the inner layer can be opposite to the motion of the outer layer. These special features, which cannot be achieved by a single layered object, result in improved imitation of a soft body, such as tissue's liquid non-uniform deformation. The inertial behavior of the elastic object is well illustrated in environments with gravity and collisions with walls, ceiling, and floor. The collision detection is defined by elastic collision penalty method and the motion of the object is guided by the Ordinary Differential Equation computation. Users can interact with the modeled objects, deform them, and observe the response to their action in real-time and we provide an extensible framework and its implementation for comparative studies of different physical-based modeling and integration algorithm implementations.Comment: 28 pages, 15 figures; from June 2008; portions of this work have been subsequently published in conference