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Ming Xu

Publications and source records attributed to Ming Xu.

At least 181 records · Page 10Linked to original sources
arXiv2017

Geodesic and curvature of piecewise flat Finsler surfaces

A piecewise flat Finsler metric on a triangulated surface $M$ is a metric whose restriction to any triangle is a flat triangle in some Minkowski space with straight edges. One of the main purposes of this work is to study the properties of geodesics on a piecewise flat Finsler surface, especially when it meets a vertex. Using the edge-crossing equation, we define two classes of piecewise flat Finsler surfaces, namely, Landsberg type and Berwald type. We deduce an explicit condition for a geodesic to be extendable at a vertex, and define the curvature which measures the \textit{amount} of such extensions. The dependence of the curvature on an incoming or outgoing tangent direction corresponds to the feature of flag curvature in Finsler geometry. When the piecewise flat Finsler surface is of Landsberg type, the curvature is only relevant to the vertex, and we prove a combinatoric Gauss-Bonnet formula which generalizes both the Gauss-Bonnet formulas for piecewise flat Riemannian manifolds and for smooth Landsberg surfaces.

math.DG↗
arXiv2016

Study of linearity of LYSO crystal for HERD calorimeter

The High Energy cosmic Radiation Detection (HERD) facility is a space mission designed for detecting cosmic ray (CR) electrons, $γ$-rays up to tens of TeV and CR nuclei from proton to iron up to several PeV. The main instrument of HERD is a 3-D imaging calorimeter (CALO) composed of nearly ten thousand cubic LYSO crystals. A large dynamic range of single HERD CALO Cell (HCC) is necessary to achieve HERD's PeV observation objectives, which means that the response of HCC should maintain a good linearity from minimum ionizing particle (MIP) calibration to PeV shower maximum. In order to study the linearity of HCC over such a large energy range, a beam test has been implemented at the E2 and E3 beam lines of BEPC. High intensity pulsed electron beam provided by E2 line are used for producing high energy density within HCC; $π^{+}$/proton provided by E3 line are used for HCC calibration. The results show that no saturation effect occurs and the linearity of HCC is better than 10% from 30 MeV (1 MIP) to 1.1$\times$10$^{3}$ TeV (energy density is 93 TeV/cm$^{3}$), which can meet the requirement mentioned above.

physics.ins-det↗
arXiv2016

$δ$-homogeneity in Finsler geometry and the positive curvature problem

In this paper, we explore the similarity between normal homogeneity and $δ$-homogeneity in Finsler geometry. They are both non-negatively curved Finsler spaces. We show that any connected $δ$-homogeneous Finsler space is $G$-$δ$-homo-geneous, for some suitably chosen connected quasi-compact $G$. So $δ$-homogeneous Finsler metrics can be defined by a bi-invariant singular metric on $G$ and submersion, just as normal homogeneous metrics, using a bi-invariant Finsler metric on $G$ instead. More careful analysis shows, in the space of all Finsler metrics on $G/H$, the subset of all $G$-$δ$-homogeneous ones is in fact the closure for the subset of all $G$-normal ones, in the local $C^0$-topology (Theorem \ref{main-thm-1}). Using this approximation technique, the classification work for positively curved normal homogeneous Finsler spaces can be applied to classify positively curved $δ$-homogeneous Finsler spaces, which provides the same classification list. As a by-product, this argument tells more about $δ$-homogeneous Finsler metrics satisfying the (FP) condition (a weaker version of positively curved condition).

math.DG↗
arXiv2016

Examples of flag-wise positively curved spaces

A Finsler space $(M,F)$ is called flag-wise positively curved, if for any $x\in M$ and any tangent plane $\mathbf{P}\subset T_xM$, we can find a nonzero vector $y\in \mathbf{P}$, such that the flag curvature $K^F(x,y, \mathbf{P})>0$. Though compact positively curved spaces are very rare in both Riemannian and Finsler geometry, flag-wise positively curved metrics should be easy to be found. A generic Finslerian perturbation for a non-negatively curved homogeneous metric may have a big chance to produce flag-wise positively curved metrics. This observation leads our discovery of these metrics on many compact manifolds. First we prove any Lie group $G$ such that its Lie algebra $\mathfrak{g}$ is compact non-Abelian and $\dim\mathfrak{c}(\mathfrak{g})\leq 1$ admits flag-wise positively curved left invariant Finsler metrics. Similar techniques can be applied to our exploration for more general compact coset spaces. We will prove, whenever $G/H$ is a compact simply connected coset space, $G/H$ and $S^1\times G/H$ admit flag-wise positively curved Finsler metrics. This provides abundant examples for this type of metrics, which are not homogeneous in general.

math.DG↗
arXiv2016

Reversible homogeneous Finsler metrics with positive flag curvature

We classify homogeneous reversible Finsler metrics with positive Flag curvature. We show that if G/H admits a G invariant reversible Finsler metric with positive Flag curvature, then up to a few low dimensional spaces, it also admits a G invariant Riemannian metric with positive sectional curvature. For the exceptions, we do not know if they admit homogeneous Finsler metrics with positive Flag curvature.

math.DG↗
arXiv2016

Rigidity of negatively curved geodesic orbit Finsler spaces

We prove some rigidity results on geodesic orbit Finsler spaces with non-positive curvature. In particular, we show that a geodesic Finsler space with strictly negative flag curvature must be a non-compact Riemannian symmetric space of rank one.

math.DG↗
arXiv2016

Perspective of monochromatic gamma-ray line detection with the High Energy cosmic-Radiation Detection (HERD) facility onboard China's Space Station

HERD is the High Energy cosmic-Radiation Detection instrument proposed to operate onboard China's space station in the 2020s. It is designed to detect energetic cosmic ray nuclei, leptons and photons with a high energy resolution ($\sim1\%$ for electrons and photons and $20\%$ for nuclei) and a large geometry factor ($>3\,{ m^2\,sr}$ for electrons and diffuse photons and $>2\,{ m^2\,sr}$ for nuclei). In this work we discuss the capability of HERD to detect monochromatic $γ$-ray lines, based on simulations of the detector performance. It is shown that HERD will be one of the most sensitive instruments for monochromatic $γ$-ray searches at energies between $\sim10$ to a few hundred GeV. Above hundreds of GeV, Cherenkov telescopes will be more sensitive due to their large effective area. As a specific example, we show that a good portion of the parameter space of a supersymmetric dark matter model can be probed with HERD.

astro-ph.HE↗
arXiv2016

Killing Vector Fields of Constant Length on Riemannian Normal Homogeneous Spaces

Killing vector fields of constant length correspond to isometries of constant displacement. Those in turn have been used to study homogeneity of Riemannian and Finsler quotient manifolds. Almost all of that work has been done for group manifolds or, more generally, for symmetric spaces. This paper extends the scope of research on constant length Killing vector fields to a class of Riemannian normal homogeneous spaces.

math.DG↗
arXiv2016

Global and partitioned reconstructions of undirected complex networks

It is a significant challenge to predict the network topology from a small amount of dynamical observations. Different from the usual framework of the node-based reconstruction, two optimization approaches (i.e., the global and partitioned reconstructions) are proposed to infer the structure of undirected networks from dynamics. These approaches are applied to evolutionary games occurring on both homogeneous and heterogeneous networks via compressed sensing, which can more efficiently achieve higher reconstruction accuracy with relatively small amounts of data. Our approaches provide different perspectives on effectively reconstructing complex networks.

physics.soc-ph↗
arXiv2016

A pathway-based network analysis of hypertension-related genes

Complex network approach has become an effective way to describe interrelationships among large amounts of biological data, which is especially useful in finding core functions and global behavior of biological systems. Hypertension is a complex disease caused by many reasons including genetic, physiological, psychological and even social factors. In this paper, based on the information of biological pathways, we construct a network model of hypertension-related genes of the salt-sensitive rat to explore the interrelationship between genes. Statistical and topological characteristics show that the network has the small-world but not scale-free property, and exhibits a modular structure, revealing compact and complex connections among these genes. By the threshold of integrated centrality larger than 0.71, seven key hub genes are found: Jun, Rps6kb1, Cycs, Creb3l2, Cdk4, Actg1 and RT1-Da. These genes should play an important role in hypertension, suggesting that the treatment of hypertension should focus on the combination of drugs on multiple genes.

q-bio.MN↗
arXiv2015

Discovery of Important Crossroads in Road Network using Massive Taxi Trajectories

A major problem in road network analysis is discovery of important crossroads, which can provide useful information for transport planning. However, none of existing approaches addresses the problem of identifying network-wide important crossroads in real road network. In this paper, we propose a novel data-driven based approach named CRRank to rank important crossroads. Our key innovation is that we model the trip network reflecting real travel demands with a tripartite graph, instead of solely analysis on the topology of road network. To compute the importance scores of crossroads accurately, we propose a HITS-like ranking algorithm, in which a procedure of score propagation on our tripartite graph is performed. We conduct experiments on CRRank using a real-world dataset of taxi trajectories. Experiments verify the utility of CRRank.

cs.AI↗
arXiv2015

Analytical controllability of deterministic scale-free networks and Cayley trees

According to the exact controllability theory, the controllability is investigated analytically for two typical types of self-similar bipartite networks, i.e., the classic deterministic scale-free networks and Cayley trees. Due to their self-similarity, the analytical results of the exact controllability are obtained, and the minimum sets of driver nodes (drivers) are also identified by elementary transformations on adjacency matrices. For these two types of undirected networks, no matter their links are unweighted or (nonzero) weighted, the controllability of networks and the configuration of drivers remain the same, showing a robustness to the link weights. These results have implications for the control of real networked systems with self-similarity.

physics.soc-ph↗
arXiv2015

Towards the classification of odd dimensional homogeneous reversible Finsler spaces with positive flag curvature

In this paper, we use the flag curvature formula for homogeneous Finsler spaces in our previous work to classify odd dimensional smooth coset spaces admitting positively curved reversible homogeneous Finsler metrics. We will show that the most features of L. Bérard-Bergery's classification results for odd dimensional positively curved Riemannian homogeneous spaces can be generalized to reversible Finsler spaces.

math.DG↗
arXiv2015

Even dimensional homogeneous Finsler spaces with positive flag curvature

In this paper, we use the technique of Finslerian submersion to deduce a flag curvature formula for homogeneous Finsler spaces. Based on this formula, we give a complete classification of even-dimensional smooth coset spaces $G/H$ admitting $G$-invariant Finsler metrics with positive flag curvature. It turns out that the classification list coincides with that of the even dimensional homogeneous Riemannian manifolds with positive sectional curvature obtained by N.R. Wallach. We also find out all the coset spaces admitting invariant non-Riemannian Finsler metrics with positive flag curvature.

math.DG↗
arXiv2015

Toward a Classification of Killing Vector Fields of Constant Length on Pseudo--Riemannian Normal Homogeneous Spaces

In this paper we develop the basic tools for a classification of Killing vector fields of constant length on pseudo--riemannian homogeneous spaces. This extends a recent paper of M. Xu and J. A. Wolf, which classified the pairs $(M,ξ)$ where $M = G/H$ is a Riemannian normal homogeneous space, $G$ is a compact simple Lie group, and $ξ\in \mathfrak{g}$ defines a nonzero Killing vector field of constant length on $M$. The method there was direct computation. Here we make use of the moment map $M \to \mathfrak{g}^*$ and the flag manifold structure of Ad(G)$ξ$ to give a shorter, more geometric proof which does not require compactness and which is valid in the pseudo--riemannian setting. In that context we break the classification problem into three parts. The first is easily settled. The second concerns the cases where $ξ$ is elliptic and $G$ is simple (but not necessarily compact); that case is our main result here. The third, which remains open, is a more combinatorial problem involving elements of the first two.

math.DG↗
arXiv2015

Sp(2)/U(1) and a Positive Curvature Problem

A compact Riemannian homogeneous space $G/H$, with a bi--invariant orthogonal decomposition $\mathfrak{g}=\mathfrak{h}+\mathfrak{m}$ is called positively curved for commuting pairs, if the sectional curvature vanishes for any tangent plane in $T_{eH}(G/H)$ spanned by a linearly independent commuting pair in $\mathfrak{m}$. In this paper,we will prove that on the coset space $\mathrm{Sp}(2)/\mathrm{U}(1)$, in which $\mathrm{U}(1)$ corresponds to a short root, admits positively curved metrics for commuting pairs. B. Wilking recently proved that this $\mathrm{Sp}(2)/\mathrm{U}(1)$ can not be positively curved in the general sense. This is the first example to distinguish the set of compact coset spaces admitting positively curved metrics, and that for metrics positively curved only for commuting pairs.

math.DG↗