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Zheng Huang

Publications and source records attributed to Zheng Huang.

At least 73 records · Page 4Linked to original sources
arXiv2016

Bi-directional LSTM Recurrent Neural Network for Chinese Word Segmentation

Recurrent neural network(RNN) has been broadly applied to natural language processing(NLP) problems. This kind of neural network is designed for modeling sequential data and has been testified to be quite efficient in sequential tagging tasks. In this paper, we propose to use bi-directional RNN with long short-term memory(LSTM) units for Chinese word segmentation, which is a crucial preprocess task for modeling Chinese sentences and articles. Classical methods focus on designing and combining hand-craft features from context, whereas bi-directional LSTM network(BLSTM) does not need any prior knowledge or pre-designing, and it is expert in keeping the contextual information in both directions. Experiment result shows that our approach gets state-of-the-art performance in word segmentation on both traditional Chinese datasets and simplified Chinese datasets.

cs.LG↗
arXiv2013

Counting Minimal Surfaces in Quasi-Fuchsian three-Manifolds

It is well known that every quasi-Fuchsian manifold admits at least one closed incompressible minimal surface, and at most finitely many of them. In this paper, for any prescribed integer $N>0$, we construct a quasi-Fuchsian manifold which contains at least $2^N$ such minimal surfaces. As a consequence, there exists some simple close Jordan curve on $S^2_\infty$ such that there are at least $2^N$ disk-type complete minimal surface in $\mathbb{H}^3$ sharing this Jordan curve as the asymptotic boundary.

math.DG↗
arXiv2013

On Almost-Fuchsian Manifolds

Almost-Fuchsian manifold is a class of complete hyperbolic three manifolds. Such a three-manifold is a quasi-Fuchsian manifold which contains a closed incompressible minimal surface with principal curvatures everywhere in the range of (-1, 1). In such a manifold, the minimal surface is unique and embedded, hence one can parametrize these hyperbolic three-manifolds by their minimal surfaces. In this paper we obtain estimates on several geometric and analytical quantities of an almost-Fuchsian manifold M in terms of the data on the minimal surface. In particular, we obtain an upper bound for the hyperbolic volume of the convex core of M, and an upper bound on the Hausdor? dimension of the limit set associated to M. We also constructed a quasi-Fuchsian manifold which admits more than one minimal surface, and it does not admit a foliation of closed surfaces of constant mean curvature.

math.DG↗
arXiv2012

Holomorphic Cubic Differentials and Minimal Lagrangian Surfaces in CH2

Following earlier work of Loftin-McIntosh, we study minimal Lagrangian immersions of the universal cover of a closed surface (of genus at least 2) into CH2, with prescribed data of a conformal structure plus a holomorphic cubic differential. We show existence and non-uniqueness of such minimal Lagrangian immersions. We also establish the surface area with respect to the induced metric as a Weil-Petersson potential function for the space of holomorphic cubic differentials on the Riemann surface.

math.DG↗
arXiv2010

Minimal immersions of closed surfaces in hyperbolic three-manifolds

We study minimal immersions of closed surfaces (of genus $g \ge 2$) in hyperbolic 3-manifolds, with prescribed data $(σ, tα)$, where $σ$ is a conformal structure on a topological surface $S$, and $αdz^2$ is a holomorphic quadratic differential on the surface $(S,σ)$. We show that, for each $t \in (0,τ_0)$ for some $τ_0 > 0$, depending only on $(σ, α)$, there are at least two minimal immersions of closed surface of prescribed second fundamental form $Re(tα)$ in the conformal structure $σ$. Moreover, for $t$ sufficiently large, there exists no such minimal immersion. Asymptotically, as $t \to 0$, the principal curvatures of one minimal immersion tend to zero, while the intrinsic curvatures of the other blow up in magnitude.

math.DG↗
arXiv2010

Mean Curvature Flows in Almost Fuchsian Manifolds

An almost Fuchsian manifold is a quasi-Fuchsian hyperbolic three-manifold that contains a closed incompressible minimal surface with principal curvatures everywhere in the range of (-1,1). In such a hyperbolic three-manifold, the minimal surface is unique and embedded, hence one can parametrize these three-manifolds by their minimal surfaces. We prove that any closed surface which is a graph over any fixed surface of small principal curvatures can be deformed into the minimal surface via the mean curvature flow. We also obtain an upper bound for the hyperbolic volume of the convex core of M, as well as estimates of the Hausdorff dimension of the limit set for $M$.

math.DG↗
arXiv2010

Curvatures on the Teichmüller curve

The Teichmüller curve is the fiber space over Teichmüller space of closed Riemann surfaces, where the fiber over a point in Teichmüller space is the underlying surface. We derive formulas for sectional curvatures on the Teichmüller curve. In particular, our method can be applied to investigate the geometry of the Weil-Petersson geodesic as a three-manifold, and the degeneration of the curvatures near the infinity of the augmented Teichmüller space along a Weil-Petersson geodesic, as well as the minimality of hyperbolic surfaces in this three-manifold.

math.DG↗
arXiv2010

Quasi-Fuchsian 3-Manifolds and Metrics on Teichmüller Space

An almost Fuchsian 3-manifold is a quasi-Fuchsian manifold which contains an incompressible closed minimal surface with principal curvatures in the range of $(-1,1)$. Such a 3-manifold $M$ admits a foliation of parallel surfaces, whose locus in Teichmüller space is represented as a path $γ$, we show that $γ$ joins the conformal structures of the two components of the conformal boundary of $M$. Moreover, we obtain an upper bound for the Teichmüller distance between any two points on $γ$, in particular, the Teichmüller distance between the two components of the conformal boundary of $M$, in terms of the principal curvatures of the minimal surface in $M$. We also establish a new potential for the Weil-Petersson metric on Teichmüller space.

math.DG↗
arXiv2010

Surfaces of Prescribed Mean Curvature in Quasi-Fuchsian Manifolds

Let $M$ be a quasi-Fuchsian three-manifold that contains a closed incompressible surface with principal curvatures within the range of the unit interval, for a prescribed function $H$ (with mild conditions) on $M$, we construct a closed incompressible surface with mean curvature $H$ . A direct application is the existence of embedded surfaces of prescribed constant mean curvatures with constants in $(-2,2)$.

math.DG↗
arXiv2006

Asymptotics of the Gaussian Curvatures of the Canonical Metric on the Surface

We study the canonical metric on a compact Riemann surface of genus at least two. While it is known that the canonical metric is of nonpositive curvature, we show that its Gaussian curvatures are not bounded away from zero nor negative infinity when the surface is close to the compactification divisor of Riemann's moduli space.

math.DG↗
arXiv2004

On Asymptotic Weil-Petersson Geometry of Teichmüller Space of Riemann Surfaces

In this paper, we study the asymptotic geometry of Teichmuller space of Riemann surfaces and give bounds on the Weil-Petersson sectional curvature of Teichmuller space, in terms of the length of the shortest geodesic on the surface. This will also imply that the sectional curvature is not pinched from above or below by any negative constant.

math.DG↗
arXiv1997

Partonic Picture of Nuclear Shadowing at Small x

We investigate the nuclear shadowing mechanism in the context of perturbative QCD and the Glauber multiple scattering model. Using recent HERA data on nucleon structure function at small $x$, we put stringent constrains on the nucleon gluon density in the double-logarithm approximation. We suggest that the scaling violation of the nucleon structure function in the region of small $x$ and semihard scale $Q^2$ can be reliably described by perturbative QCD which is a central key to the understanding of the scale dependence of the nuclear shadowing effect. Our results indicate that while the shadowing of the quark density arises from an interplay between the ``soft'' and semihard QCD processes, the gluon shadowing is largely driven by a perturbative shadowing mechanism. We demonstrate that the gluon shadowing is a robust phenomenon at large $Q^2$ and can be unambiguously predicted by perturbative QCD.

hep-ph↗
arXiv1997

Study Medium-induced Parton Energy Loss in Gamma+jet Events of High-Energy Heavy-Ion Collisions

The effect of medium-induced parton energy loss on jet fragmentation is studied in high-energy heavy-ion collisions. It is shown that an effective jet fragmentation function can be extracted from the inclusive $p_T$ spectrum of charged particles in the opposite direction of a tagged direct photon with a fixed transverse energy. We study the modification of the effective jet fragmentation function due to parton energy loss in AA as compared to pp collisions, including $E_T$ smearing from initial state radiations for the photon-tagged jets. The effective fragmentation function at $z=p_T/E_T^γ\sim 1$ in pA collisions is shown to be sensitive to the additional $E_T$ smearing due to initial multiple parton scatterings whose effect must be subtracted out in AA collisions in order to extract the effective parton energy loss. Jet quenching in deeply inelastic lepton-nucleus scatterings as a measure of the parton energy loss in cold nuclear matter is also discussed. We also comment on the experimental feasibilities of the proposed study at the RHIC and LHC energies and some alternative measurements such as using $Z^0$ as a tag at the LHC energy.

hep-ph↗