1,567 research outputs found
Projective Dirac Operators, Twisted K-Theory and Local Index Formula
We construct a canonical noncommutative spectral triple for every oriented
closed Riemannian manifold, which represents the fundamental class in the
twisted K-homology of the manifold. This so-called "projective spectral triple"
is Morita equivalent to the well-known commutative spin spectral triple
provided that the manifold is spin-c. We give an explicit local formula for the
twisted Chern character for K-theories twisted with torsion classes, and with
this formula we show that the twisted Chern character of the projective
spectral triple is identical to the Poincar\'e dual of the A-hat genus of the
manifold.Comment: Provides complete proofs to the main theorems, and corrected errors
in version 1. Removed the section on Lie Algebroi
On Blow-up criterion for the Nonlinear Schr\"{o}dinger Equation
The blowup is studied for the nonlinear Schr\"{o}dinger equation
with is odd and (the
energy-critical or energy-supercritical case). It is shown that the solution
with negative energy blows up in finite or infinite time. A new
proof is also presented for the previous result in \cite{HoRo2}, in which a
similar result but more general in a case of energy-subcritical was shown.Comment: In this version, we add a reference, and change some expressions in
Englis
Learning with Table Soccer
Our research focuses on learning approaches with robot KiRo. KiRo is
a table soccer robot which can challenge even advanced human
players. Previously, we developed a method using learning by imitation,
by which KiRo can automatically acquire the demonstrated actions. Recently, we
constructed a game-recorder which collects data from the human-played games.
The in-process work is about explaining the recorded data, which is to classify and
to evaluate human\u27s skills. A brief overview of the previous work is addressed,
and the perspective is discussed
Fluctuations in Shear-Jammed States: A Statistical Ensemble Approach
Granular matter exists out of thermal equilibrium, i.e. it is athermal. While
conventional equilibrium statistical mechanics is not useful for characterizing
granular materials, the idea of constructing a statistical ensemble analogous
to its equilibrium counterpart to describe static granular matter was proposed
by Edwards and Oakshott more than two decades ago. Recent years have seen
several implementations of this idea. One of these is the stress ensemble,
which is based on properties of the force moment tensor, and applies to
frictional and frictionless grains. We demonstrate the full utility of this
statistical framework in shear jammed (SJ) experimental states [1,2], a special
class of granular solids created by pure shear, which is a strictly
non-equilbrium protocol for creating solids. We demonstrate that the stress
ensemble provides an excellent quantitative description of fluctuations in
experimental SJ states. We show that the stress fluctuations are controlled by
a single tensorial quantity: the angoricity of the system, which is a direct
analog of the thermodynamic temperature. SJ states exhibit significant
correlations in local stresses and are thus inherently different from
density-driven, isotropically jammed (IJ) states.Comment: 6 pages, 4 figure
A Cost-Sensitive Ensemble Method for Class-Imbalanced Datasets
In imbalanced learning methods, resampling methods modify an imbalanced dataset to form a balanced dataset. Balanced data sets perform better than imbalanced datasets for many base classifiers. This paper proposes a cost-sensitive ensemble method based on cost-sensitive support vector machine (SVM), and query-by-committee (QBC) to solve imbalanced data classification. The proposed method first divides the majority-class dataset into several subdatasets according to the proportion of imbalanced samples and trains subclassifiers using AdaBoost method. Then, the proposed method generates candidate training samples by QBC active learning method and uses cost-sensitive SVM to learn the training samples. By using 5 class-imbalanced datasets, experimental results show that the proposed method has higher area under ROC curve (AUC), F-measure, and G-mean than many existing class-imbalanced learning methods
Image Denoising Based on Artificial Bee Colony and BP Neural Network
Image is often subject to noise pollution during the process of collection, acquisition and transmission, noise is a major factor affecting the image quality, which has greatly impeded people from extracting information from the image. The purpose of image denoising is to restore the original image without noise from the noise image, and at the same time maintain the detailed information of the image as much as possible. This paper, by combining artificial bee colony algorithm and BP neural network, proposes the image denoising method based on artificial bee colony and BP neural network (ABC-BPNN), ABC-BPNN adopts the “double circulation” structure during the training process, after specifying the expected convergence speed and precision, it can adjust the rules according to the structure, automatically adjusts the number of neurons, while the weight of the neurons and relevant parameters are determined through bee colony optimization. The simulation result shows that the algorithm proposed in this paper can maintain the image edges and other important features while removing noise, so as to obtain better denoising effect
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