18,406 research outputs found
Grand Fujii-Fujii-Nakamoto operator inequality dealing with operator order and operator chaotic order
In this paper, we shall prove that a grand Fujii-Fujii-Nakamoto operator
inequality implies operator order and operator chaotic order under different
conditions
Further development of positive semidefinite solutions of the operator equation
In \cite{Positive semidefinite solutions}, T. Furuta discusses the existence
of positive semidefinite solutions of the operator equation
. In this paper, we shall apply Grand Furuta
inequality to study the operator equation. A generalized special type of is
obtained due to \cite{Positive semidefinite solutions}
H\"older continuity of the integrated density of states for Extended Harper's Model with Liouville frequency
In this paper, we study the non-self-dual extended Harper's model with a
Liouville frequency. Based on the work of \cite{SY}, we show that the
integrated density of states (IDS for short) of the model is
-Hlder continuous. As an application, we also
obtain the Carleson homogeneity of the spectrum.Comment: 1 figur
A sufficient condition on operator order for strictly positive operators
Let , , , be strictly positive operators on a
Hilbert space. This note is to show a sufficient condition of , which extends the related result
before
A "boundedness implies convergence" principle and its applications to collapsing estimates in K\"ahler geometry
We establish a general "boundedness implies convergence" principle for a
family of evolving Riemannian metrics. We then apply this principle to
collapsing Calabi-Yau metrics and normalized K\"ahler-Ricci flows on torus
fibered minimal models to obtain convergence results.Comment: All comments are welcome
Thresholded Multiscale Gaussian Processes with Application to Bayesian Feature Selection for Massive Neuroimaging Data
Motivated by the needs of selecting important features for massive
neuroimaging data, we propose a spatially varying coefficient model (SVCMs)
with sparsity and piecewise smoothness imposed on the coefficient functions. A
new class of nonparametric priors is developed based on thresholded
multiresolution Gaussian processes (TMGP). We show that the TMGP has a large
support on a space of sparse and piecewise smooth functions, leading to
posterior consistency in coefficient function estimation and feature selection.
Also, we develop a method for prior specifications of thresholding parameters
in TMGPs and discuss their theoretical properties. Efficient posterior
computation algorithms are developed by adopting a kernel convolution approach,
where a modified square exponential kernel is chosen taking the advantage that
the analytical form of the eigen decomposition is available. Based on
simulation studies, we demonstrate that our methods can achieve better
performance in estimating the spatially varying coefficient. Also, the proposed
model has been applied to an analysis of resting state functional magnetic
resonance imaging (Rs-fMRI) data from the Autism Brain Imaging Data Exchange
(ABIDE) study, it provides biologically meaningful results.Comment: 37 pages, 7 figure
Convergence of Laplacian Spectra from Point Clouds
The spectral structure of the Laplacian-Beltrami operator (LBO) on manifolds
has been widely used in many applications, include spectral clustering,
dimensionality reduction, mesh smoothing, compression and editing, shape
segmentation, matching and parameterization, and so on. Typically, the
underlying Riemannian manifold is unknown and often given by a set of sample
points. The spectral structure of the LBO is estimated from some discrete
Laplace operator constructed from this set of sample points. In our previous
papers, we proposed the point integral method to discretize the LBO from point
clouds, which is also capable to solve the eigenproblem. Then one fundmental
issue is the convergence of the eigensystem of the discrete Laplacian to that
of the LBO. In this paper, for compact manifolds isometrically embedded in
Euclidean spaces possibly with boundary, we show that the eigenvalues and the
eigenvectors obtained by the point integral method converges to the eigenvalues
and the eigenfunctions of the LBO with the Neumann boundary, and in addition,
we give an estimate of the convergence rate. This result provides a solid
mathematical foundation for the point integral method in the computation of
Laplacian spectra from point clouds
Convergence of the Point Integral method for the Poisson equation with Dirichlet boundary on point cloud
The Poisson equation on manifolds plays an fundamental role in many
applications. Recently, we proposed a novel numerical method called the Point
Integral method (PIM) to solve the Poisson equations on manifolds from point
clouds. In this paper, we prove the convergence of the point integral method
for solving the Poisson equation with the Dirichlet boundary condition
Generalized Gaussian Process Regression Model for Non-Gaussian Functional Data
In this paper we propose a generalized Gaussian process concurrent regression
model for functional data where the functional response variable has a
binomial, Poisson or other non-Gaussian distribution from an exponential family
while the covariates are mixed functional and scalar variables. The proposed
model offers a nonparametric generalized concurrent regression method for
functional data with multi-dimensional covariates, and provides a natural
framework on modeling common mean structure and covariance structure
simultaneously for repeatedly observed functional data. The mean structure
provides an overall information about the observations, while the covariance
structure can be used to catch up the characteristic of each individual batch.
The prior specification of covariance kernel enables us to accommodate a wide
class of nonlinear models. The definition of the model, the inference and the
implementation as well as its asymptotic properties are discussed. Several
numerical examples with different non-Gaussian response variables are
presented. Some technical details and more numerical examples as well as an
extension of the model are provided as supplementary materials
Low temperature properties of one-dimensional SU(4) Hubbard-like model at low concentration
On the basis of Bethe ansatz solution of one dimensional SU(4) Hubbard-like
model, we study its thermodynamics properties by means of Yang-Yang
thermodynamics Bethe ansatz. The Land\'e factor is taken into account so as
to describe electrons with orbital degeneracy. The free energy at low
temperature is given and the specific heat both in strong coupling and weak
coupling limits are obtained.Comment: 11 page
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