arXiv subjects

Bin Guo

Publications and source records attributed to Bin Guo.

211 records · Page 12Linked to original sources

arXiv2015

On Feldman-Ilmanen-Knopf conjecture for the blow-up behavior of the Kahler Ricci flow

We consider the Ricci flow on $\mathbb{CP}^n$ blown-up at one point starting with any $U(n)$-invariant Kähler metric. It is known that the Kähler-Ricci flow must develop Type I singularities. We show that if the total volume does not go to zero at the singular time, then any Type I parabolic blow-up limit of the Ricci flow along the exceptional divisor is the unique $U(n)$-complete shrinking Kähler-Ricci soliton on $\mathbb C^n$ blown-up at one point. This establishes the conjecture of Feldman-Ilmanen-Knopf.

math.DG↗

arXiv2015

Mobile Crowd Sensing and Computing: When Participatory Sensing Meets Participatory Social Media

With the development of mobile sensing and mobile social networking techniques, Mobile Crowd Sensing and Computing (MCSC), which leverages heterogeneous crowdsourced data for large-scale sensing, has become a leading paradigm. Built on top of the participatory sensing vision, MCSC has two characterizing features: (1) it leverages heterogeneous crowdsourced data from two data sources: participatory sensing and participatory social media; and (2) it presents the fusion of human and machine intelligence (HMI) in both the sensing and computing process. This paper characterizes the unique features and challenges of MCSC. We further present early efforts on MCSC to demonstrate the benefits of aggregating heterogeneous crowdsourced data.

cs.HC↗

arXiv2015

Tensor perturbations of Palatini $f(\mathcal{R})$-branes

We investigate the thick brane model in Palatini $f(\mathcal{R})$ gravity. The brane is generated by a real scalar field with a scalar potential. We solve the system analytically and obtain a series of thick brane solutions for the $f(\mathcal{R})=\mathcal{R}+α\mathcal{R}^2$-brane model. It is shown that tensor perturbations of the metric are stable for $df({\mathcal{R}})/d{\mathcal{R}}>0$. For nonconstant curvature solutions, the graviton zero mode can be localized on the brane, which indicates that the four-dimensional gravity can be recovered on the brane. Mass spectrum of graviton KK modes and their corrections to the Newtonian potential are also discussed.

hep-th↗

arXiv2015

Brane worlds in gravity with auxiliary fields

Recently, Pani, Sotiriou, and Vernieri explored a new theory of gravity by adding nondynamical fields, i.e., gravity with auxiliary fields [Phys. Rev. D 88, 121502(R) (2013)]. In this gravity theory, higher-order derivatives of matter fields generically appear in the field equations. In this paper we extend this theory to any dimensions and discuss the thick braneworld model in five dimensions. Domain wall solutions are obtained numerically. The stability of the brane system under the tensor perturbation is analyzed. We find that the system is stable under the tensor perturbation and the gravity zero mode is localized on the brane. Therefore, the four-dimensional Newtonian potential can be realized on the brane.

hep-th↗

arXiv2015

On the Kahler Ricci flow on projective manifolds of general type

We consider the Kähler Ricci flow on a smooth minimal model of general type, we show that if the Ricci curvature is uniformly bounded below along the Kähler-Ricci flow, then the diameter is uniformly bounded. As a corollary we show that under the Ricci curvature lower bound assumption, the Gromov-Hausdorff limit of the flow is homeomorphic to the canonical model. Moreover, we can give a purely analytic proof of a recent result of Tosatti-Zhang (\cite{TZ}) that if the canonical line bundle $K_X$ is big and nef, but not ample, then the flow is of Type IIb.

math.DG↗

arXiv2014

Global quantum discord in infinite quantum spin chains

In this paper, we study global quantum discord (GQD) in infinite-size spin chains. For this purpose, in the framework of matrix product states (MPSs), we propose an effective procedure to calculate GQD (denoted as Gn) for consecutive n-site subchains in infinite chains. For a spin-1/2 three-body interaction model, whose ground state can be exactly expressed as MPSs, We use the procedure to study Gn with n up to $24$. Then for a spin-1/2 XXZ chain, we firstly use infinite time-evolving block decimation (iTEBD) algorithm to obtain the approximate wavefunction in the from of MPSs, and then figure out Gn with n up to $18$. In both models, Gn shows an interesting linear growth as the increase of n, that is, Gn = k*n+b. Moreover, in non-critical regions the slope $k$ of Gn converges very fast, while in critical regions it converges relatively slow, and the behaviors are explained in a clear physical picture with the short-range and long-range correlations. Based on these results, we propose to use Gn/n to describe the global correlations in infinite chains. Gn/n has twofold physical meanings. Firstly, it can be regarded as "global discord per site", very similar to "energy per site" or "magnetization per site" in quantum magnetic systems. Secondly, Gn/n (when n is large enough) describes the quantum correlation between a single site and an (n-1)-site block. Then we successfully apply our theory to an exactly soluble infinite-size spin XY chain which is beyond the matrix product formula, and the Hamiltonian can reduce to the transverse-field Ising model and the XX model. The relation between GQD and quantum phase transitions in these models is discussed.

quant-ph↗

arXiv2014

Tests for High Dimensional Generalized Linear Models

We consider testing regression coefficients in high dimensional generalized linear models. An investigation of the test of Goeman et al. (2011) is conducted, which reveals that if the inverse of the link function is unbounded, the high dimensionality in the covariates can impose adverse impacts on the power of the test. We propose a test formation which can avoid the adverse impact of the high dimensionality. When the inverse of the link function is bounded such as the logistic or probit regression, the proposed test is as good as Goeman et al. (2011)'s test. The proposed tests provide p-values for testing significance for gene-sets as demonstrated in a case study on an acute lymphoblastic leukemia dataset.

stat.ME↗

arXiv2014

From Participatory Sensing to Mobile Crowd Sensing

The research on the efforts of combining human and machine intelligence has a long history. With the development of mobile sensing and mobile Internet techniques, a new sensing paradigm called Mobile Crowd Sensing (MCS), which leverages the power of citizens for large-scale sensing has become popular in recent years. As an evolution of participatory sensing, MCS has two unique features: (1) it involves both implicit and explicit participation; (2) MCS collects data from two user-participant data sources: mobile social networks and mobile sensing. This paper presents the literary history of MCS and its unique issues. A reference framework for MCS systems is also proposed. We further clarify the potential fusion of human and machine intelligence in MCS. Finally, we discuss the future research trends as well as our efforts to MCS.

cs.HC↗

arXiv2013

Study of Solutions for a quasilinear Elliptic Problem With negative exponents

The authors of this paper deal with the existence and regularities of weak solutions to the homogenous $\hbox{Dirichlet}$ boundary value problem for the equation $-\hbox{div}(|\nabla u|^{p-2}\nabla u)+|u|^{p-2}u=\frac{f(x)}{u^α}$. The authors apply the method of regularization and $\hbox{Leray-Schauder}$ fixed point theorem as well as a necessary compactness argument to prove the existence of solutions and then obtain some maximum norm estimates by constructing three suitable iterative sequences. Furthermore, we find that the critical exponent of $m$ in $\|f\|_{L^{m}(Ω)}$. That is, when $m$ lies in different intervals, the solutions of the problem mentioned belongs to different $\hbox{Sobolev}$ spaces. Besides, we prove that the solution of this problem is not in $W^{1,p}_{0}(Ω)$ when $α>2$, while the solution of this problem is in $W^{1,p}_{0}(Ω)$ when $1<α<2$.

math.AP↗

arXiv2013

Connecting toric manifolds by conical Kahler-Einstein metrics

We give criterions for the existence of toric conical Kahler-Einstein and Kahler-Ricci soliton metrics on any toric manifold in relation to the greatest Ricci and Bakry-Emery-Ricci lower bound. We also show that any two toric manifolds with the same dimension can be joined by a continuous path of toric manifolds with conical Kahler-Einstein metrics in the Gromov-Hausdorff topology.

math.DG↗

arXiv2013

Singular Phenomena of Solutions for Nonlinear Diffusion Equations involving $p(x)$-\hbox{Laplacian} Operator

The authors of this paper study singular phenomena(vanishing and blowing-up in finite time) of solutions to the homogeneous $\hbox{Dirichlet}$ boundary value problem of nonlinear diffusion equations involving $p(x)$-\hbox{Laplacian} operator and a nonlinear source. The authors discuss how the value of the variable exponent $p(x)$ and initial energy(data) affect the properties of solutions. At the same time, we obtain the critical extinction and blow-up exponents of solutions.

math.AP↗

arXiv2010

The Second Variational Formula For the Functional $\int v^{(6)}(g)dV_g$

In this note, we compute the second variational formula for the functional $\int_M v^{(6)}(g)dv_g$, which was introduced by Graham-Juhl and the first variational formula was obtained by Chang-Fang. We also prove that Einstein manifolds (with dimension $\ge 7$) with positive scalar curvature is a strict local maximum within its conformal class, unless the manifold is isometric to round sphere with the standard metric up to a multiple of constant. Note that when $(M,g)$ is locally conformally flat, this functional reduces to the well-studied $\int_M σ_3(g)dv_g$. Hence, our result generalize a previous result of Jeff Viaclovsky without the locally conformally flat restraint.

math.DG↗

arXiv2009

Two Kazdan-Warner type identities for the renormalized volume coefficients and the Gauss-Bonnet curvatures of a Riemannian metric

In this note, we prove two Kazdan-Warner type identities involving $v^{(2k)}$, the renormalized volume coefficients of a Riemannian manifold $(M^n,g)$, and $G_{2r}$, the so-called Gauss-Bonnet curvature, and a conformal Killing vector field on $(M^n,g)$. In the case when the Riemannian manifold is locally conformally flat, $v^{(2k)}=(-2)^{-k}σ_k$, $G_{2r}(g)=\frac{4^r(n-r)!r!}{(n-2r)!}σ_r$, and our results reduce to earlier ones established by Viaclovsky and by the second author.

math.DG↗