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 $iu_{t}+\Delta u+ |u|^{p-1}u=0$ with $p$ is odd and $p\ge 1+\frac 4{N-2}$ (the energy-critical or energy-supercritical case). It is shown that the solution with negative energy $E(u_0)<0$ 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