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

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

Re-initialization Free Level Set Evolution via Reaction Diffusion

This paper presents a novel reaction-diffusion (RD) method for implicit active contours, which is completely free of the costly re-initialization procedure in level set evolution (LSE). A diffusion term is introduced into LSE, resulting in a RD-LSE equation, to which a piecewise constant solution can be derived. In order to have a stable numerical solution of the RD based LSE, we propose a two-step splitting method (TSSM) to iteratively solve the RD-LSE equation: first iterating the LSE equation, and then solving the diffusion equation. The second step regularizes the level set function obtained in the first step to ensure stability, and thus the complex and costly re-initialization procedure is completely eliminated from LSE. By successfully applying diffusion to LSE, the RD-LSE model is stable by means of the simple finite difference method, which is very easy to implement. The proposed RD method can be generalized to solve the LSE for both variational level set method and PDE-based level set method. The RD-LSE method shows very good performance on boundary anti-leakage, and it can be readily extended to high dimensional level set method. The extensive and promising experimental results on synthetic and real images validate the effectiveness of the proposed RD-LSE approach.Comment: IEEE Trans. on Image Processing, to appea

Fano Resonance Induced Anomalous Collective Hotspots in Metallic Nanoparticle Dimer Chains

Hotspots with strong near fields due to localized surface plasmons (LSPs) in metallic nanostructures have various applications, such as surface enhanced Raman scattering (SERS). The long range Coulomb coupling between LSPs in periodic metallic nanostructures may lead to interesting collective effects. In this paper, we investigate the combination effects of the local field enhancement and collective plasmon resonances in one dimensional metallic nanoparticle dimer chains. It is found that the strong near field in the gap and the far field interactions among the metallic nanoparticles lead to anomalous collective hotspots with dual enhancement of the electromagnetic field. In particular, the interference between the incident field and the induced internal field leads to Fano-type effect with Wood anomaly related destructive interference and the strong resonance with an extremely narrow width. Our systematic study shows that the correlation between the local structure and the global structure has important impact on the collective spots, which leads to an optimal orientation of the dimer (about 60{\deg} with respect to the chain direction) for the largest gap field enhancement with the incident field polarization parallel to the long axis of the dimer.Comment: 14 pages, 7 figure

Mean-field analysis of two-species TASEP with attachment and detachment

In cells, most of cargos are transported by motor proteins along microtubule. Biophysically, unidirectional motion of large number of motor proteins along a single track can be described by totally asymmetric simple exclusion process (TASEP). From which many meaningful properties, such as the appearance of domain wall (defined as the borderline of high density and low density of motor protein along motion track) and boundary layers, can be obtained. However, it is biologically obvious that a single track may be occupied by different motor species. So previous studies based on TASEP of one particle species are not reasonable enough to find more detailed properties of the motion of motors along a single track. To address this problem, TASEP with two particle species is discussed in this study. Theoretical methods to get densities of each particle species are provided. Using these methods, phase transition related properties of particle densities are obtained. Our analysis show that domain wall and boundary layer of single species densities always appear simultaneously with those of the total particle density. The height of domain wall of total particle density is equal to the summation of those of single species. Phase diagrams for typical model parameters are also presented. The methods presented in this study can be generalized to analyze TASEP with more particle species

Mean-field approximation for the chiral soliton in a chiral phase transition

In the mean-field approximation we study the chiral soliton within the linear sigma model in a thermal vacuum. The chiral soliton equations with different boundary conditions are solved at finite temperatures and densities. The solitons are discussed before and after the chiral restoration. We find that the system has soliton solutions even after the chiral restoration and they are very different from those before the chiral restoration, which indicates that the quarks are still bounded after the chiral restoration.Comment: 9 pages, 11 figures. Some sentences and words have been correcte

Reproducing Kernel Banach Spaces with the l1 Norm II: Error Analysis for Regularized Least Square Regression

A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space that satisfies the linear representer theorem brings the advantage of discarding the hypothesis error from the sum automatically. Following this direction, we illustrate how reproducing kernel Banach spaces with the l1 norm can be applied to improve the learning rate estimate of l1-regularization in machine learning

Monomorphism operator and perpendicular operator

For a quiver $Q$, a $k$-algebra $A$, and a full subcategory $\mathcal X$ of $A$-mod, the monomorphism category ${\rm Mon}(Q, \mathcal X)$ is introduced. The main result says that if $T$ is an $A$-module such that there is an exact sequence $0\rightarrow T_m\rightarrow...\rightarrow T_0\rightarrow D(A_A)\rightarrow 0$ with each $T_i\in {\rm add} (T)$, then ${\rm Mon}(Q, \ ^\perp T) = \ ^\perp (kQ\otimes_k T)$; and if$T$is cotilting, then$kQ\otimes_k T$is a unique cotilting$\m$-module, up to multiplicities of indecomposable direct summands, such that${\rm Mon}(Q, \ ^\perp T)= \ ^\perp (kQ \otimes_k T)$. As applications, the category of the Gorenstein-projective$(kQ\otimes_kA)$-modules is characterized as${\rm Mon}(Q, \mathcal{GP}(A))$if$A$is Gorenstein; the contravariantly finiteness of${\rm Mon}(Q, \mathcal X)$can be described; and a sufficient and necessary condition for${\rm Mon}(Q, A)$ being of finite type is given

Deciphering Interactions in Causal Networks without Parametric Assumptions

With the assumption that the effect is a mathematical function of the cause in a causal relationship, FunChisq, a chi-square test defined on a non-parametric representation of interactions, infers network topology considering both interaction directionality and nonlinearity. Here we show that both experimental and in silico biological network data suggest the importance of directionality as evidence for causality. Counter-intuitively, patterns in those interactions effectively revealed by FunChisq enlist an experimental design principle essential to network inference -- perturbations to a biological system shall make it transits between linear and nonlinear working zones, instead of operating only in a linear working zone.Comment: 15 pages, 5 figure

Effects of non-radial magnetic field on measuring magnetic helicity transport across solar photosphere

It is generally believed that the evolution of magnetic helicity has a close relationship with solar activity. Before the launch of SDO, earlier studies have mostly used MDI/SOHO line of sight magnetograms and assumed that magnetic fields are radial when calculating magnetic helicity injection rate from photospheric magnetograms. However, this assumption is not necessarily true. Here we use the vector magnetograms and line of sight magnetograms, both taken by HMI/SDO, to estimate the effects of non-radial magnetic field on measuring magnetic helicity injection rate. We find that: 1) The effect of non-radial magnetic field on estimating tangential velocity is relatively small; 2) On estimating magnetic helicity injection rate, the effect of non-radial magnetic field is strong when active regions are observed near the limb and is relatively small when active regions are close to disk center; 3) The effect of non-radial magnetic field becomes minor if the amount of accumulated magnetic helicity is the only concern.Comment: 30 pages, including 13 figures; accepted for publication in the Ap