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

Nonlinear Feynman-Kac formulae for SPDEs with space-time noise

We study a class of backward doubly stochastic differential equations (BDSDEs) involving martingales with spatial parameters, and show that they provide probabilistic interpretations (Feynman-Kac formulae) for certain semilinear stochastic partial differential equations (SPDEs) with space-time noise. As an application of the Feynman-Kac formulae, random periodic solutions and stationary solutions to certain SPDEs are obtained

Optimal caching placement for wireless femto-caching network

This paper investigates optimal caching placement for wireless femto-caching network. The average bit error rate (BER) is formulated as a function of caching placement under wireless fading. To minimize the average BER, we propose a greedy algorithm finding optimal caching placement with low computational complexity. Exploiting the property of the optimal caching placement which we derive, the proposed algorithm can be performed over considerably reduced search space. Contrary to the optimal caching placement without consideration of wireless fading aspects, we reveal that optimal caching placement can be reached by balancing a tradeoff between two different gains: file diversity gain and channel diversity gain. Moreover, we also identify the conditions that the optimal placement can be found without running the proposed greedy algorithm and derive the corresponding optimal caching placement in closed form.Comment: 32 page

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