Conditioning analysis of block incomplete factorization and its application to elliptic equations

The paper deals with eigenvalue estimates for block incomplete fac- torization methods for symmetric matrices. First, some previous results on upper bounds for the maximum eigenvalue of preconditioned matrices are generalized to each eigenvalue. Second, upper bounds for the maximum eigenvalue of the preconditioned matrix are further estimated, which presents a substantial im- provement of earlier results. Finally, the results are used to estimate bounds for every eigenvalue of the preconditioned matrices, in particular, for the maximum eigenvalue, when a modified block incomplete factorization is used to solve an elliptic equation with variable coefficients in two dimensions. The analysis yields a new upper bound of type γh−1 for the condition number of the preconditioned matrix and shows clearly how the coefficients of the differential equation influ- ence the positive constant γ

Compositional coding capsule network with k-means routing for text classification

Text classification is a challenging problem which aims to identify the category of texts. Recently, Capsule Networks (CapsNets) are proposed for image classification. It has been shown that CapsNets have several advantages over Convolutional Neural Networks (CNNs), while, their validity in the domain of text has less been explored. An effective method named deep compositional code learning has been proposed lately. This method can save many parameters about word embeddings without any significant sacrifices in performance. In this paper, we introduce the Compositional Coding (CC) mechanism between capsules, and we propose a new routing algorithm, which is based on k-means clustering theory. Experiments conducted on eight challenging text classification datasets show the proposed method achieves competitive accuracy compared to the state-of-the-art approach with significantly fewer parameters

School Quality and Housing Prices: Empirical Evidence Based on a Natural Experiment in Shanghai, China

The extent to which the quantity and quality of education is capitalized into housing prices is a key issue in understanding the relationship between allocation of educational resources and the housing market. Using monthly panel data of 52 residential areas in Shanghai and employing a natural experiment of designating Shanghai Experimental Model Senior High Schools (EMSHS), we find that housing prices in Shanghai have capitalized the access to quality schools and other public goods. One quality school per square kilometer raises average housing prices by approximately 19%, and one best EMSHS per square kilometer increases housing prices by 21%. We also match the schools designated for EMSHS with schools of similar quality but not designated for EMSHS, and compare housing prices in the corresponding areas. We find that the designation increased the housing prices, showing that dissemination of information about school quality was significantly affected by the designation.education, housing market, capitalization, public goods, natural experiment

Evaluating Generalization Ability of Convolutional Neural Networks and Capsule Networks for Image Classification via Top-2 Classification

Image classification is a challenging problem which aims to identify the category of object in the image. In recent years, deep Convolutional Neural Networks (CNNs) have been applied to handle this task, and impressive improvement has been achieved. However, some research showed the output of CNNs can be easily altered by adding relatively small perturbations to the input image, such as modifying few pixels. Recently, Capsule Networks (CapsNets) are proposed, which can help eliminating this limitation. Experiments on MNIST dataset revealed that capsules can better characterize the features of object than CNNs. But it's hard to find a suitable quantitative method to compare the generalization ability of CNNs and CapsNets. In this paper, we propose a new image classification task called Top-2 classification to evaluate the generalization ability of CNNs and CapsNets. The models are trained on single label image samples same as the traditional image classification task. But in the test stage, we randomly concatenate two test image samples which contain different labels, and then use the trained models to predict the top-2 labels on the unseen newly-created two label image samples. This task can provide us precise quantitative results to compare the generalization ability of CNNs and CapsNets. Back to the CapsNet, because it uses Full Connectivity (FC) mechanism among all capsules, it requires many parameters. To reduce the number of parameters, we introduce the Parameter-Sharing (PS) mechanism between capsules. Experiments on five widely used benchmark image datasets demonstrate the method significantly reduces the number of parameters, without losing the effectiveness of extracting features. Further, on the Top-2 classification task, the proposed PS CapsNets obtain impressive higher accuracy compared to the traditional CNNs and FC CapsNets by a large margin.Comment: This paper is under consideration at Computer Vision and Image Understandin

Dyonic (A)dS Black Holes in Einstein-Born-Infeld Theory in Diverse Dimensions

We study Einstein-Born-Infeld gravity and construct the dyonic (A)dS planar black holes in general even dimensions, that carry both the electric charge and magnetic fluxes along the planar space. In four dimensions, the solution can be constructed with also spherical and hyperbolic topologies. We study the black hole thermodynamics and obtain the first law. We also classify the singularity structure.Comment: Latex, 21 pages, typos corrected and references adde

Power load forecasting

For the electric power factory, the power load forecasting problem, including load forecasting and consumption predicting, is crucial to work planning. According to the predicting time, it can be divided into long-term forecasting, mid-term forecasting, short-term forecasting and ultra-short-term forecasting. The long-term and mid-term forecasting are mainly used for macro control, and their forecasting time arrange are from one year to ten years and from one month to twelve months respectively. The short-term forecasting which prediction time is from one day to seven days is used in generators macroeconomic control, power exchange plan and some other areas. Predicting the situation in next 24 hours is named as the ultra-short-term forecasting which is used for failure prediction, emergency treatment and frequency control. In general, the forecast accuracy is different for different prediction time. The longer is the time, the lower accurate is the prediction. As the unique power supplier in Huizhou (China), Huizhou Electric Power wants to know the solution to the problems: 1. Prediction of the total electrical consumption and the peak load of the city in 2006 based on the economy development and the feature of the city. 2. Monthly prediction of the consumption and peak load in 2006. 3. Daily prediction of the consumption and peak load from July 10th to 16th in 2006. 4. Prediction of the load every 15 minutes of July 10th. 5. Real-time forecasting which means to amend the existing load prediction for next 15 minute