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Ke Shi

Publications and source records attributed to Ke Shi.

54 records · Page 3Linked to original sources

An End-to-End Document-Level Neural Discourse Parser Exploiting Multi-Granularity Representations

Document-level discourse parsing, in accordance with the Rhetorical Structure Theory (RST), remains notoriously challenging. Challenges include the deep structure of document-level discourse trees, the requirement of subtle semantic judgments, and the lack of large-scale training corpora. To address such challenges, we propose to exploit robust representations derived from multiple levels of granularity across syntax and semantics, and in turn incorporate such representations in an end-to-end encoder-decoder neural architecture for more resourceful discourse processing. In particular, we first use a pre-trained contextual language model that embodies high-order and long-range dependency to enable finer-grain semantic, syntactic, and organizational representations. We further encode such representations with boundary and hierarchical information to obtain more refined modeling for document-level discourse processing. Experimental results show that our parser achieves the state-of-the-art performance, approaching human-level performance on the benchmarked RST dataset.

cs.CL↗

Multilingual Neural RST Discourse Parsing

Text discourse parsing plays an important role in understanding information flow and argumentative structure in natural language. Previous research under the Rhetorical Structure Theory (RST) has mostly focused on inducing and evaluating models from the English treebank. However, the parsing tasks for other languages such as German, Dutch, and Portuguese are still challenging due to the shortage of annotated data. In this work, we investigate two approaches to establish a neural, cross-lingual discourse parser via: (1) utilizing multilingual vector representations; and (2) adopting segment-level translation of the source content. Experiment results show that both methods are effective even with limited training data, and achieve state-of-the-art performance on cross-lingual, document-level discourse parsing on all sub-tasks.

cs.CL↗

Conditional Neural Generation using Sub-Aspect Functions for Extractive News Summarization

Much progress has been made in text summarization, fueled by neural architectures using large-scale training corpora. However, in the news domain, neural models easily overfit by leveraging position-related features due to the prevalence of the inverted pyramid writing style. In addition, there is an unmet need to generate a variety of summaries for different users. In this paper, we propose a neural framework that can flexibly control summary generation by introducing a set of sub-aspect functions (i.e. importance, diversity, position). These sub-aspect functions are regulated by a set of control codes to decide which sub-aspect to focus on during summary generation. We demonstrate that extracted summaries with minimal position bias is comparable with those generated by standard models that take advantage of position preference. We also show that news summaries generated with a focus on diversity can be more preferred by human raters. These results suggest that a more flexible neural summarization framework providing more control options could be desirable in tailoring to different user preferences, which is useful since it is often impractical to articulate such preferences for different applications a priori.

cs.CL↗

A detailed study of massive galaxies in a protocluster at z=3.13

We present a detailed study of Near-IR selected galaxies in a protocluster field at z = 3.13. Protocluster galaxies are selected using the available mutliwavelength data with the photometric redshift (photo-z) at 2.9 < z < 3.3, reaching a mass completeness of ~10^10 M_sun. Diverse types of galaxies have been found in the field including normal star-forming galaxies, quiescent galaxies and dusty star-forming galaxies. The photo-z galaxies form two large overdense structures in the field, largely overlapping with the previously identified galaxy overdensities traced by Lyα emitters (LAEs) and Lyman break galaxies (LBGs) respectively. The northern overdensity consists of a large fraction of old and/or dusty galaxy populations, while the southern one is mainly composed of normal star-forming galaxies which are spatially correlated with the LAEs. This agrees with our previous study arguing the spatial offset of different galaxy overdensities may be due to halo assembly bias. Given the large end-to-end sizes of the two overdensities, one possibility is that they will form into a supercluster by the present day. We also find strong evidence that the star-formation activities of the galaxies in the overdense protocluster regions are enhanced in comparison to their field counterparts, which suggests an accelerated mass assembly in this protocluster.

astro-ph.CO↗

Analysis of a semi-implicit structure-preserving finite element method for the nonstationary incompressible Magnetohydrodynamics equations

We revise the structure-preserving finite element method in [K. Hu, Y. MA and J. Xu. (2017) Stable finite element methods preserving $\nabla \cdot \mathbf{B}=0$ exactly for MHD models. Numer. Math.,135, 371-396]. The revised method is semi-implicit in time-discretization. We prove the linearized scheme preserves the divergence free property for the magnetic field exactly at each time step. Further, we showed the linearized scheme is unconditionally stable and we obtain optimal convergence in the energy norm of the revised method even for solutions with low regularity.

math.NA↗

Improved Finite Difference Results for the Caputo Time-Fractional Diffusion Equation

We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution kernel.\iffalse The order of fractional derivative, $α$, is tied to finite difference methods and is of great interest.\fi We examine this new equation and utilize a numerical scheme that is derived in parallel to the L1-method for the time variable and a usual fourth order approximation in the spatial variable. The main method derived in this paper has a rate of convergence of $O(k^{2}+h^4)$ for $u(x,t) \in C^6(Ω)\times C^2[0,T]$, which improves previous estimates by a factor of $k^α$. We also present a novel alternative method for a first order approximation in time, which allows us to relax our regularity assumption to $u(x,t) \in C^6(Ω)\times C^1[0,T]$, while exhibiting order of convergence slightly less than $O(k^{1+α})$ in time. This allows for a much wider class of functions to be analyzed which was previously not possible under the L1-method. We present numerical examples demonstrating these results and discuss future improvements and implications by using these techniques.

math.NA↗

How Do Galaxies trace a large scale structure?: A case study around a massive protocluster at $z=3.13$

In the hierarchical theory of galaxy formation, a galaxy overdensity is a hallmark of a massive cosmic structure. However, it is less well understood how different types of galaxies trace the underlying large-scale structure. Motivated by the discovery of a z=3.13 protocluster, we examine how the same structure is populated by Ly$α$-emitting galaxies (LAEs). To this end, we have undertaken a deep narrow-band imaging survey sampling Ly$α$ emission at this redshift. Of the 93 LAE candidates within a 36'x36'~(70x70~Mpc^2) field, 21 galaxies form a significant surface overdensity (delta_g=3.3+/-0.9), which is spatially segregated from the Lyman break galaxy (LBG) overdensity. One possible interpretation is that they trace two separate structures of comparable masses (~ 10^{15}M_sun) where the latter is hosted by a halo assembled at an earlier time. We speculate that the dearth of LAEs in the LBG overdensity region may signal the role of halo assembly bias in galaxy formation, which would suggest that different search techniques may be biased accordingly to the formation age or dynamical state of the host halo. The median Ly$α$- and UV luminosity is 30--70\% higher for the protocluster LAEs relative to the field. This difference cannot be explained by the galaxy overdensity alone, and may require a top-heavy mass function, higher star formation efficiency for protocluster halos, or suppression of galaxy formation in low-mass halos. A luminous Ly$α$ blob and an ultramassive galaxy found in this region paint a picture consistent with the expected early growth of galaxies in clusters.

astro-ph.GA↗

Convergence of a $B$-$E$ based finite element method for MHD models on Lipschitz domains

We discuss a class of magnetic-electric fields based finite element schemes for stationary magnetohydrodynamics (MHD) systems with two types of boundary conditions. We establish a key $L^{3}$ estimate for divergence-free finite element functions for a new type of boundary conditions. With this estimate and a similar one in [Hu&Xu,2018], we rigorously prove the convergence of Picard iterations and the finite element schemes with weak regularity assumptions. These results demonstrate the convergence of the finite element methods for singular solutions.

math.NA↗

A Mixed DG method and an HDG method for incompressible magnetohydrodynamics

In this paper we propose and analyze a mixed DG method and an HDG method for the stationary Magnetohydrodynamics (MHD) equations with two types of boundary (or constraint) conditions. The mixed DG method is based a recent work proposed by Houston et. al. for the linearized MHD. With two novel discrete Sobolev embedding type estimates for the discontinuous polynomials, we provide a priori error estimates for the method on the nonlinear MHD equations. In the smooth case, we have optimal convergence rate for the velocity, magnetic field and pressure in the energy norm, the Lagrange multiplier only has suboptimal convergence order. With the minimal regularity assumption on the exact solution, the approximation is optimal for all unknowns. To the best of our knowledge, this is the first a priori error estimates of DG methods for nonlinear MHD equations. In addition, we also propose and analyze the first divergence-free HDG method for the problem with several unique features comparing with the mixed DG method.

math.NA↗

A census of galaxy constituents in a Coma Progenitor observed at z>3

We present a detailed census of galaxies in and around PC217.96+32.3, a spectroscopically confirmed Coma analog at z=3.78. Diverse galaxy types identified in the field include Lya emitters (LAEs), massive star-forming galaxies, and ultra-massive galaxies (log (Mstar/Msun)>= 11) which may have already halted their star formation. The sky distribution of the star-forming galaxies suggests the presence of a significant overdensity (delta_g=8+/-2), which is spatially offset from the previously confirmed members by 3-4 Mpc to the west. Candidate quiescent and post-starburst galaxies are also found in large excess (a factor of ~ 8-15 higher surface density than the field) although their redshifts are less certain. We estimate that the total enclosed mass traced by star-forming galaxy candidates is roughly comparable to that of PC217.96+32.3 traced by the LAEs. We speculate that the true extent of PC217.96+32.3 may be larger than previously known, a half of which is missed by our LAE selection. Alternatively, the newly discovered overdensity may belong to another Coma progenitor not associated with PC217.96+32.3. Expectations from theory suggest that both scenarios are equally unlikely (<1%), particularly in the cosmic volume probed in our survey. If confirmed as a single structure, its total mass will be well in excess of Coma, making this a singularly large cosmic structure rarely seen even in large cosmological simulations. Finally, we find that the protocluster galaxies follow the same SFR-M_star scaling relation as the field galaxies, suggesting that the environmental effect at z~4 is a subtle one at best for normal star-forming galaxies.

astro-ph.GA↗

Discovery of a Very Large (~20 kpc) Galaxy at z=3.72

We report the discovery and spectroscopic confirmation of a very large star-forming Lyman Break galaxy, G6025, at z_spec=3.721+/-0.003. In the rest-frame ~2100A, G6025 subtends ~24 kpc in physical extent when measured from the 1.5-sigma isophote, in agreement with the parametric size measurements which yield the half-light radius of 4.9+/-0.5 kpc and the semi-major axis of 12.5+/-0.1 kpc. G6025 is also very UV-luminous (~5L*(z~4}) and young (~140+/-60 Myr). Despite its unusual size and luminosity, the stellar population parameters and dust reddening (M_star~M*(z~4)$, and E(B-V)=0.18+/-0.05) estimated from the integrated light, are similar to those of smaller galaxies at comparable redshifts. The ground-based morphology and spectroscopy show two dominant components, both located off-center, embedded in more diffuse emission. We speculate that G6025 may be a scaled-up version of chain galaxies seen in deep HST imaging, or alternatively, a nearly equal-mass merger involving two super-L* galaxies in its early stage. G6025 lies close to but not within a known massive protocluster at z=3.78. We find four companions within 6 Mpc from G6025, two of which lie within 1.6 Mpc. While the limited sensitivity of the existing spectroscopy does not allow us to robustly characterize the local environment of G6025, it likely resides in a locally overdense environment. The luminosity, size, and youth of G6025 make it uniquely suited to study the early formation of massive galaxies in the universe.

astro-ph.GA↗

Exploratory investigation of the HIPPO gas-jet target fluid dynamic properties

In order to optimize the performance of gas-jet targets for future nuclear reaction measurements, a detailed understanding of the dependence of the gas-jet properties on experiment design parameters is required. Common methods of gas-jet characterization rely on measuring the effective thickness using nuclear elastic scattering and energy loss techniques; however, these tests are time intensive and limit the range of design modifications which can be explored to improve the properties of the jet as a nuclear reaction target. Thus, a more rapid jet-characterization method is desired. We performed the first steps towards characterizing the gas-jet density distribution of the HIPPO gas-jet target at the University of Notre Dame's Nuclear Science Laboratory by reproducing results from $^{20}\rm{Ne}(α,α)^{20}\rm{Ne}$ elastic scattering measurements with computational fluid dynamics (CFD) simulations performed with the state-of-the-art CFD software ANSYS Fluent. We find a strong sensitivity to experimental design parameters of the gas-jet target, such as the jet nozzle geometry and ambient pressure of the target chamber. We argue that improved predictive power will require moving to three-dimensional simulations and additional benchmarking with experimental data.

physics.ins-det↗

A superconvergent HDG method for the Maxwell equations

We present and analyze a new hybridizable discontinuous Galerkin (HDG) method for the steady state Maxwell equations. In order to make the problem well-posed, a condition of divergence is imposed on the electric field. Then a Lagrange multiplier $p$ is introduced, and the problem becomes the solution of a mixed curl-curl formulation of the Maxwell's problem. We use polynomials of degree $k+1$, $k$, $k$ to approximate $\bfu,\nabla \times \bfu$ and $p$ respectively. In contrast, we only use a non-trivial subspace of polynomials of degree $k+1$ to approximate the numerical tangential trace of the electric field and polynomials of degree $k+1$ to approximate the numerical trace of the Lagrange multiplier on the faces. On the simplicial meshes, a special choice of the stabilization parameters is applied, and the HDG system is shown to be well-posed. Moreover, we show that the convergence rates for $\boldsymbol{u}$ and $\nabla \times \boldsymbol{u}$ are independent of the Lagrange multiplier $p$. If we assume the dual operator of the Maxwell equation on the domain has adequate regularity, we show that the convergence rate for $\boldsymbol{u}$ is $O(h^{k+2})$. From the point of view of degrees of freedom of the globally coupled unknown: numerical trace, this HDG method achieves superconvergence for the electric field without postprocessing. Finally, we show that on general polyhedral elements, by a particular choice of the stabilization parameters again, the HDG system is also well-posed and the superconvergence of the HDG method is derived.

math.NA↗

An HDG method for linear elasticity with strong symmetric stresses

This paper presents a new hybridizable discontinuous Galerkin (HDG) method for linear elasticity on general polyhedral meshes, based on a strong symmetric stress formulation. The key feature of this new HDG method is the use of a special form of the numerical trace of the stresses, which makes the error analysis different from the projection-based error analyzes used for most other HDG methods. For arbitrary polyhedral elements, we approximate the stress by using polynomials of degree k>=1 and the displacement by using polynomials of degree k+1. In contrast, to approximate the numerical trace of the displacement on the faces, we use polynomials of degree k only. This allows for a very efficient implementation of the method, since the numerical trace of the displacement is the only globally-coupled unknown, but does not degrade the convergence properties of the method. Indeed, we prove optimal orders of convergence for both the stresses and displacements on the elements. In the almost incompressible case, we show the error of the stress is also optimal in the standard L2-norm. These optimal results are possible thanks to a special superconvergence property of the numerical traces of the displacement, and thanks to the use of a crucial elementwise Korn's inequality. Several numerical results are presented to support our theoretical findings in the end.

math.NA↗

A superconvergent HDG method for the Incompressible Navier-Stokes Equations on general polyhedral meshes

We present a superconvergent hybridizable discontinuous Galerkin (HDG) method for the steady-state incompressible Navier-Stokes equations on general polyhedral meshes. For arbitrary conforming polyhedral mesh, we use polynomials of degree k+1, k, k to approximate the velocity, velocity gradient and pressure, respectively. In contrast, we only use polynomials of degree k to approximate the numerical trace of the velocity on the interfaces. Since the numerical trace of the velocity field is the only globally coupled unknown, this scheme allows a very efficient implementation of the method. For the stationary case, and under the usual smallness condition for the source term, we prove that the method is well defined and that the global L2-norm of the error in each of the above-mentioned variables and the discrete H1-norm of the error in the velocity converge with the order of k+1 for k>=0. We also show that for k>=1, the global L2-norm of the error in velocity converges with the order of k+2. From the point of view of degrees of freedom of the globally coupled unknown: numerical trace, this method achieves optimal convergence for all the above-mentioned variables in L2-norm for k>=0, superconvergence for the velocity in the discrete H1-norm without postprocessing for k>=0, and superconvergence for the velocity in L2-norm without postprocessing for k>=1.

math.NA↗

A Generalized Multiscale Finite Element Method for the Brinkman Equation

In this paper we consider the numerical upscaling of the Brinkman equation in the presence of high-contrast permeability fields. We develop and analyze a robust and efficient Generalized Multiscale Finite Element Method (GMsFEM) for the Brinkman model. In the fine grid, we use mixed finite element method with the velocity and pressure being continuous piecewise quadratic and piecewise constant finite element spaces, respectively. Using the GMsFEM framework we construct suitable coarse-scale spaces for the velocity and pressure that yield a robust mixed GMsFEM. We develop a novel approach to construct a coarse approximation for the velocity snapshot space and a robust small offline space for the velocity space. The stability of the mixed GMsFEM and a priori error estimates are derived. A variety of two-dimensional numerical examples are presented to illustrate the effectiveness of the algorithm.

math.NA↗

A multiscale HDG method for second order elliptic equations. Part I. Polynomial and homogenization-based multiscale spaces

We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition and the hybrid discontinuous Galerkin methods. The method utilizes three different scales: (1) the scale of the partition of the domain of the problem, (2) the sale of partition of the boundaries of the subdomains (related to the corresponding space of Lagrange multipliers), and (3) the fine grid scale that is assumed to resolve the scale of the heterogeneous variation of the coefficients. Our proposed method gives a flexible framework that (1) couples independently generated multiscale basis functions in each coarse patch (2) provides a stable global coupling independent of local discretization, physical scales and contrast (3) allows avoiding any constraints on coarse spaces. In this paper, we develop and study a multiscale HDG method that uses polynomial and homogenization-based multiscale spaces. These coarse spaces are designed for problems with scale separation. In our consequent paper, we plan to extend our flexible HDG framework to more challenging multiscale problems with non-separable scales and high contrast and consider enriched coarse spaces that use appropriate local spectral problems.

math.NA↗

A comprehensive comparison of cosmological models from latest observational data

We investigate in detail some popular cosmological models in light of the latest observational data, including the Union2.1 supernovae compilation, the baryon acoustic oscillation measurements from the WiggleZ Dark Energy Survey, the cosmic microwave background information from the WMAP 7-year observations along with the observational Hubble parameter data. Based on the model selection statistics such as the Akaike and the Bayesian information criterias, we compare different models to assess the worth of them. We do not assume a flat universe in the fitting. Our results show that the concordance $Λ$CDM model remains the best one to explain the data, while the DGP model is clearly disfavored by the data. Among these models, those whose parameters can reduce themselves to the $Λ$CDM model provide good fits to the data. These results indicate that for the current data, there is no obvious evidence supporting any more complex models over the simplest $Λ$CDM model.

astro-ph.CO↗