Frequency-based views to pattern collections

Finding interesting patterns from data is one of the most important problems in data mining and it has been studied actively for more than a decade. However, it is still largely open problem which patterns are interesting and which are not.The problem of detecting the interesting patterns (in a predefined class of patterns) has been attempted to solve by determining quality values for potentially interesting patterns and deciding a pattern to be interesting if its quality value (i.e., the interestingness of the pattern) is higher than a given threshold value. Again, it is very difficult to find a threshold value and a way to determine the quality values such that the collection of patterns with quality values greater than the threshold value would contain almost all truly interesting patterns and only few uninteresting ones.To enable more accurate characterization of interesting patterns, use of constraints to further prune the pattern collection has been proposed. However, most of the constrained pattern discovery research has been focused on structural constraints for the pattern collections and the patterns. We take a complementary approach and focus on constraining the quality values of the patterns.We propose quality value simplifications as a complementary approach to structural constraints on patterns. As a special case of the quality value simplifications, we consider discretizing the quality values. We analyze the worst-case error of certain discretization functions and give efficient discretization algorithms minimizing several loss functions. In addition to that, we show that the discretizations of the quality values can be used to obtain small approximate condensed representations for collections of interesting patterns. We evaluate the proposed condensation approach experimentally using frequent itemsets.     

一个耦合双曲-抛物系统的全局光滑解

考虑一个源自生物学的耦合双曲-抛物模型的初边值问题.当动能函数为非线性函数以及初始值具有小的L~2能量但其H~2能量可能任意大时,得到了初边值问题光滑解的全局存在性和指数稳定性.而且,如果假定非线性动能函数满足一定的条件,在对初值没任何小条件假定下得到光滑解的全局存在性.通过构造一个新的非负凸熵和做精细的能量估计得到了结果的证明.     

Monotonie des Hill-Schätzers in endlichen Stichproben

If the Pareto parameter Alpha of a Pareto-distributed random variable is calculated as Maximum-Likelihood estimator (Hill-estimator) from a random sample, the expected value of the estimator is a decreasing function of the sample size. In the present paper we show this property also to be valid, if a finite collection of positive real numbers is approximated by a Pareto-distribution, the Pareto parameter of which is calculated as Hill-estimator from samples of the collection. Using the Hill-estimator for Alpha, the expected value of the collection can be estimated as the expected value of the corresponding Pareto-distribution. Generally, the expected value of a Pareto-distributed random variable is a decreasing function of Alpha. Paradoxically however, if the mean value of the Pareto-distribution is used as an estimator for the expected value of the above collection, this estimator also proves to be a decreasing function of the sample size. This property is relevant for the quotation of reinsurance contracts.     

An integral semiclassical method for calculating the spectra for centrally symmetric potentials

We develop a new approach to semiclassical quantization conditions that does not involve asymptotic expansions and is based on exact general properties of wave equations and their spectra. For centrally symmetric potentials, the quantization conditions depend only on a collection of integrals involving powers of the classical momentum. The energy levels calculated using these conditions are in good agreement with numerical data. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 3, pp. 463–480, September, 2000.     

General Decay and Blow-Up Results for Nonlinear Fourth-Order Integro-Differential Equation

This study aims at considering an initial-boundary value problem for nonlinear fourth-order viscoelastic equation in a bounded domain. Under suitable conditions of the initial data and of the relaxation function, it is proved that the solution energy is generally decayed. It is also shown that regarding arbitrary positive initial energy, certain solutions blow-up in a finite time.     

The optimal value and optimal solutions of the proximal average of convex functions

The proximal average of a finite collection of convex functions is a parameterized convex function that provides a continuous transformation between the convex functions in the collection. This paper analyzes the dependence of the optimal value and the minimizers of the proximal average on the weighting parameter. Concavity of the optimal value is established and implies further regularity properties of the optimal value. Boundedness, outer semicontinuity, single-valuedness, continuity, and Lipschitz continuity of the minimizer mapping are concluded under various assumptions. Sharp minimizers are given further attention. Several examples are given to illustrate our results.     

Stabilization of elasticity–viscoporosity system by linear boundary feedback

The initial boundary value problem for linear elastodynamic system for viscoporous materials is considered. Exponential decay of solutions via the linear boundary feedback is established. Existence of solutions is obtained through the method of c₀‐semigroups. Exponential stabilization is derived via a proper collection of ideas of observability inequality, energy identity and c₀‐semigroup of contractions. Copyright © 2008 John Wiley & Sons, Ltd.     

The age pattern of transitory mortality jumps and its impact on the pricing of catastrophic mortality bonds

To value catastrophic mortality bonds, a number of stochastic mortality models with transitory jump effects have been proposed. Rather than modeling the age pattern of jump effects explicitly, most of the existing models assume that the distributions of jump effects and general mortality improvements across ages are identical. Nevertheless, this assumption does not seem to be in line with what we observe from historical data. In this paper, we address this problem by introducing a Lee–Carter variant that captures the age pattern of mortality jumps by a distinct collection of parameters. The model variant is then further generalized to permit the age pattern of jump effects to vary randomly. We illustrate the two proposed models with mortality data from the United States and English and Welsh populations, and use them to value hypothetical mortality bonds with similar specifications to the Atlas IX Capital Class B note that was launched in 2013. It is found that the features we consider have a significant impact on the estimated prices.     

钢铁工业总产值与能源消耗量协整分析及误差修正

选取1978-2006年样本区间内我国钢铁工业总产值和能源消耗的相关数据,通过协整检验、误差修正模型和Granger因果关系检验,对钢铁工业总产值和能源消耗量在时序维度的长期均衡和短期动态性进行实证研究.结果表明,钢铁工业能源消耗结构中燃料煤消耗量与钢铁工业总产值具有长期动态均衡关系,并且燃料煤消耗量还是钢铁工业总产值的单向Granger原因,而电力、重油和焦炭消耗量与钢铁工业总产值之间没有长期均衡关系,印证了我国钢铁工业以燃料煤消耗为主的能源消耗结构的不均衡性.     

惯容器非线性减振与能量采集一体化模型动力学分析

为了解决航天工程中减振和能源供应的问题，构建了一种应用于航天工程的整星减振和能量采集一体化装置，设计并考察了一种基于非线性能量汇(nonlinear energy sink, NES)的新型非线性减振装置，通过以惯容器(inerter)替代传统的惯性元件以减少负载质量，并在该装置中整合了基于超磁致伸缩材料(giant magnetostrictive material, GMM)的能量采集器.在整星减振的实际背景下对其进行了建模、仿真和分析，同时通过数值计算，考察分析了能量采集器采集振动能量的效果，研究结果表明，在合理选择的参数下，该NES-inerter-GMM(NES-I-GMM)装置能够很好地起到减振作用，同时收集一定的振动能量.     

Histogram selection for possibly censored data

We propose in this article a unified approach to functional estimation problems based on possibly censored data. The general framework that we define allows, for instance, to handle density and hazard rate estimation based on randomly right-censored data, or regression. Given a collection of histograms, our estimation procedure consists in selecting the best histogram among that collection from the data, by minimizing a penalized least-squares type criterion. For a general collection of histograms, we obtain nonasymptotic oracle-type inequalities. Then, we consider the collection of histograms built on partitions into dyadic intervals, a choice inspired by an approximation result due to DeVore and Yu. In that case, our estimator is also adaptive in the minimax sense over a wide range of smoothness classes that contain functions of inhomogeneous smoothness. Besides, its computational complexity is only linear in the size of the sample.     

Perturbation theory for the ground singlet state of the Heisenberg spin 1/2 antiferromagnetic chain

The Heisenberg spin 1/2 antiferromagnetic chain is considered. We use the perturbation theory where a collection of noninteracting clusters (chains with a small number of spins) is regarded as an unperturbed system and the interaction between clusters is regarded as a perturbation. The advantage of the perturbation theory is that it results in the proper thermodynamic limit. Expressions for corrections to the energy of the ground state of the chain are obtained up to the fourth order inclusive. The numerical results calculated for the infinite chain with the help of clusters containing 2, 4, 6, or 8 spins show good agreement with the exact value known from the Bethe ansatz. Bibliography: 9 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 224, 1995, pp. 14–35. Translated by I. V. Abarenkov.     

煤炭低位发热量快速计算新公式

本文介绍的一组计算煤炭低位发热量公式，是在收集了我国各个不同地区、不同煤种的煤样３０００多个的基础上，对其进行分类，采用回归分析的方法得到。与国内外现行公式比较，具有使用简单，计算快捷，更为精确的特点。     

Automated prover for attribute dependencies in data with grades

We present a new axiomatization of logic for dependencies in data with grades, which includes ordinal data and data over domains with similarity relations, and an efficient reasoning method that is based on the axiomatization. The logic has its ordinary-style completeness characterizing the ordinary, bivalent entailment as well as the graded-style completeness characterizing the general, possibly intermediate degrees of entailment. A core of the method is a new inference rule, called the rule of simplification, from which we derive convenient equivalences that allow us to simplify sets of dependencies while retaining semantic closure. The method makes it possible to compute a closure of a given collection of attributes with respect to a collection of dependencies, decide whether a given dependency is entailed by a given collection of dependencies, and more generally, compute the degree to which the dependency is entailed by a collection of dependencies. We also present an experimental evaluation of the presented method.     

Design of a wind farm collection network when several cable types are available

In this article we consider a real-world problem submitted to us by the Hatch company. This problem consists of designing a collection network for a wind farm, assuming that the locations of the turbines and the potential cables are known, several cable types are available, and the cost of the energy that dissipates through the cables is known. We propose a mixed integer quadratic programme to model the network design problem and then linearize the quadratic programme because the latter is too difficult to solve using a standard mathematical programming software. We describe several classes of inequalities that strengthen the resulting mixed integer linear programme. Finally we use real-world data supplied by Hatch to carry out computational experiments with several versions of our model.     

Official recycling and scavengers: Symbiotic or conflicting?

Nowadays, especially in developed countries, the traditional collection of end-of-use products by scavengers has been displaced by formal waste recovery systems. However, scavenging still exists, especially in places with collection capacity shortages and/or low living standards. Besides its obvious social implications, the financial and environmental aspects of scavenging are certainly not trivial. Informal recycling of waste electrical and electronic equipment (WEEE) by scavengers not only constrains profits of the formal system. In their effort to recover the value of end-of-use products, scavengers also pollute the environment if toxic substances leak when WEEE is not properly disposed of. We investigate the impact of scavenging on the operations of the formal recovery system of WEEE, under three regulatory measures, using system dynamics methodology. By using data from a real world closed-loop supply chain that operates in Greece extended numerical experimentation revealed that a legislation incorporating scavengers into the formal waste recovery system (instead of either ignoring or prohibiting their participation) is beneficial for economical, environmental and social sustainability.     

非线性Sobolev-Galpern方程解的blow up

本文研究非线性Ｓｏｂｏｌｅｖ－Ｃａｌｐｅｒｎ方程的初边值问题整体解的不存性即解的爆破问题,用能量估计方法并借助于Ｊｅｎｓｅｎ不等式证明了非线性Ｓｏｂｏｌｉｖ－Ｇａｌｐｅｒｎ方程各种初边值问题在某些假设下不存在整体解。     

Exponential energy decay of solutions for a system of viscoelastic wave equations of Kirchhoff type with strong damping

The initial boundary value problem for a system of viscoelastic wave equations of Kirchhoff type with strong damping is considered. We prove that, under suitable assumptions on relaxation functions and certain initial data, the decay rate of the solutions energy is exponential.     

On Initial-Boundary Value Problem of the Stochastic Heat Equation in Lipschitz Cylinders

We consider the initial boundary value problem of the non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random noises. The space boundary is Lipschitz, and we impose nonzero condition on the parabolic boundary. We prove a regularity result by finding appropriate spaces for solutions and pre-assigned data in the problem. We use a collection of tools from potential theory, harmonic analysis, and probability. Some lemmas are as important as the main theorem.     

基于犹豫模糊相似的网络正能量推荐算法研究

论文依据网络正能量模糊性和多规则的特点,借助语言犹豫模糊集和普通犹豫模糊集建立正能量事件的评价集,针对事件属性对正能量的影响效应确定各属性的模糊熵和权重,建立犹豫模糊推荐模型。借助TOPSIS的思想,从大数据中得到正能量事件的标准值,通过事件与标准值模糊相似度的计算确定推荐阈值以得到满意的正能量事件推荐结果。