Isomorphic classification of mixed sequence spaces and of Besov spaces over [0, 1]d

The aim of this paper is to establish the isomorphic classification of Besov spaces over [0, 1]^d . Using the identification of the Besov space with the ‐infinite direct sum of finite‐dimensional spaces (which holds independently of the dimension and of the smoothness degree of the space ) we show that , , is a family of mutually non‐isomorphic spaces. The only exception is the isomorphism between the spaces and , which follows from Pełczyński's isomorphism between and . We also tell apart the isomorphic classes of spaces from the isomorphic classes of Besov spaces over the Euclidean space .     

On<Emphasis Type="Italic">C</Emphasis><Superscript>*</Superscript>-algebras whose Glimm ideals are primitive

Every Glimm ideal of anAW ^*-algebra is a (minimal) primitive ideal.     

基于Fuzzy理论的数据挖掘算法研究Ⅱ

"数据挖掘"是数据处理的一个新领域.支持向量机是数据挖掘的一种新方法,该技术在很多领域得到了成功的应用.但是,支持向量机目前还存在许多局限,当支持向量机的训练集中含有模糊信息时,支持向量机将无能为力.为解决一般情况下支持向量机中含有模糊信息(模糊参数)问题,研究了模糊机会约束规划、模糊分类中的模糊特征及其表示方法,建立了模糊支持向量分类机理论,给出了模糊线性可分的模糊支持向量分类机算法.     

A Geometric Perspective on Information Plane Analysis

Information plane analysis, describing the mutual information between the input and a hidden layer and between a hidden layer and the target over time, has recently been proposed to analyze the training of neural networks. Since the activations of a hidden layer are typically continuous-valued, this mutual information cannot be computed analytically and must thus be estimated, resulting in apparently inconsistent or even contradicting results in the literature. The goal of this paper is to demonstrate how information plane analysis can still be a valuable tool for analyzing neural network training. To this end, we complement the prevailing binning estimator for mutual information with a geometric interpretation. With this geometric interpretation in mind, we evaluate the impact of regularization and interpret phenomena such as underfitting and overfitting. In addition, we investigate neural network learning in the presence of noisy data and noisy labels.     

Fractional Deng Entropy and Extropy and Some Applications

Deng entropy and extropy are two measures useful in the Dempster–Shafer evidence theory (DST) to study uncertainty, following the idea that extropy is the dual concept of entropy. In this paper, we present their fractional versions named fractional Deng entropy and extropy and compare them to other measures in the framework of DST. Here, we study the maximum for both of them and give several examples. Finally, we analyze a problem of classification in pattern recognition in order to highlight the importance of these new measures.     

A Hyperspectral Image Classification Approach Based on Feature Fusion and Multi-Layered Gradient Boosting Decision Trees

At present, many Deep Neural Network (DNN) methods have been widely used for hyperspectral image classification. Promising classification results have been obtained by utilizing such models. However, due to the complexity and depth of the model, increasing the number of model parameters may lead to an overfitting of the model, especially when training data are insufficient. As the performance of the model mainly depends on sufficient data and a large network with reasonably optimized hyperparameters, using DNNs for classification requires better hardware conditions and sufficient training time. This paper proposes a feature fusion and multi-layered gradient boosting decision tree model (FF-DT) for hyperspectral image classification. First, we fuse extended morphology profiles (EMPs), linear multi-scale spatial characteristics, and nonlinear multi-scale spatial characteristics as final features to extract both special and spectral features. Furthermore, a multi-layered gradient boosting decision tree model is constructed for classification. We conduct experiments based on three datasets, which in this paper are referred to as the Pavia University, Indiana Pines, and Salinas datasets. It is shown that the proposed FF-DT achieves better performance in classification accuracy, training conditions, and time consumption than other current classical hyperspectral image classification methods.     

Improving the Accuracy of Nearest-Neighbor Classification Using Principled Construction and Stochastic Sampling of Training-Set Centroids

A conceptually simple way to classify images is to directly compare test-set data and training-set data. The accuracy of this approach is limited by the method of comparison used, and by the extent to which the training-set data cover configuration space. Here we show that this coverage can be substantially increased using coarse-graining (replacing groups of images by their centroids) and stochastic sampling (using distinct sets of centroids in combination). We use the MNIST and Fashion-MNIST data sets to show that a principled coarse-graining algorithm can convert training images into fewer image centroids without loss of accuracy of classification of test-set images by nearest-neighbor classification. Distinct batches of centroids can be used in combination as a means of stochastically sampling configuration space, and can classify test-set data more accurately than can the unaltered training set. On the MNIST and Fashion-MNIST data sets this approach converts nearest-neighbor classification from a mid-ranking- to an upper-ranking member of the set of classical machine-learning techniques.     

A Thermodynamic Frame for the Kinetics of Polymer Crystallization under Processing Conditions

Summary. A retrospective view is given on work, which has been carried out at the Johannes Kepler University during the last two decades on the structure formation in crystallizable polymers during their processing. Emphasis is laid on some useful principles lend from basic physical chemistry: use of the T,S-diagram and of the temperature dependent courses of (effective) surface tensions along coexistence lines of phases. These considerations should be helpful in creating an overview, where a deficiency of direct experimental crystallization kinetics data exists. For a series of industrially important, mostly fast crystallizing, polymers data are given in the present paper for the quiescent melt (temperature dependences of number densities of nuclei and of growth speeds). Critical minimum cooling speeds for bypassing crystallization are given on the basis of the given data. These critical cooling speeds vary by almost six decades from HDPE to i-PS. These results are also helpful in the formulation of a viable classification of materials in the light of their processing conditions. This classification includes metals and glass forming minerals as limiting cases for extremely fast and extremely slowly crystallizing materials.     

Fluid dynamics analysis of channel flow geometries for materials characterization in microfluidic devices

The fluid dynamics of geometries for liquid state materials characterization in microfluidic devices are investigated. Numerical simulation together with flow classification criteria are used to explore combinations of geometry and boundary conditions for which the flow type can be adjusted between simple shear and extension, while providing adequate flow strength and a stable environment for material observation. Two classes of flow geometries are identified. Both make use of opposing, laterally offset fluid streams that produce a stagnation point in the center of the geometry. In the first class, the flow type is manipulated by changing parameters inherent to the base geometry. This first case serves as a basis for identifying a second class in which the flow type is manipulated by changing the pressure boundary conditions, while keeping the geometry constant.Electronic Supplementary Material is available for this article if you access the article at .

Algebraic classification of the gravitational field

We rewrite the tensorial method of Peres [1] for the Petrov classification in terms of the Newman-Penrose formalism [2]. It results an algorithm computationally simpler that the one proposed by DInverno-Russell Clark [3].This revised version was published online in April 2005. The publishing date was inserted.