基于共形几何代数的3D医学图像配准

随着医学图像处理技术的发展,3D／3D配准益受重视,尤其是在外科手术导航等医学应用中．学者们提出了各种3D／3D配准方法,但大多方法是采用传统代数方法进行配准,配准精度和效率都存在问题．本文利用非经典数学——共形几何代数重建了3D医学图像的位置关系约柬问题,分析了医学图像的共形几何变换,构造了新的3D医学图像配准相似测度,基于此提出了新的3D医学图像配准算法,用于CT和MR图像的3D配准．新算法中,以骨骼轮廓作为配准的基础点集,在骨骼轮廓的基础上采用共形几何代数构造共形几何体,接着采用新的3D医学图像配准相似测度进行三维数据的直接配准．实验表明新算法实现了三维数据的直接对齐,能较好地定位组织器官的三维位置．可以直观地体现配准结果．     

Rough集理论代数与信息论观点的关系研究

Rough集理论是近年来发展起来的一种有效的处理不精确、不确定、代含糊信息的数字理论方法，在机器学习、数据挖掘，智能数据分析，控制算法获取等领域取得了很大的成功，本文对Rough集理论的代数观点和信息论观点进行了研究，分析了二者再相容信息系统中的等价关系，并发现了二者在不同相容信息系统中的不等价关系。这一结论修正了一些学者以前人为Rough集理论的代数观点和信息论观点等价的错误结论。     

Clifford代数与几何定理机器证明

Clifford代数是一种深深根植于几何学之中的代数系统。近年来,它在微分几何、理论物理、经典分析等方面取得了辉煌的成就,是现代理论数学和物理的一个核心工具,并在现代科技的各个领域,如机器人学、计算机视觉等方面有广泛的应用。本文主要介绍Clifford代数在数学机械化的核心内容－几何定理机器证明中的应用。作为一种非常优秀的描述和计算机几何问题的代数语言,Clifford代数对于几何体,几何关系和几何变换有不依赖于坐标的、易于计算的多种表示,因而应用它进行几可自动推理,不仅使困难定理的证明往往变得极为简单,而且能够解决著名的数学公开问题。目前在国际上,几何自动推理已经成为Clifford代数的一个重要应用领域。     

命题演算系统L~*与谓词演算系统κ~*中统一的近似推理理论

引入了度量R0-代数和R0型Hilbert方体的概念. 从语义和语构两个方面建立了同时适用于命题逻辑系统L*与一阶逻辑系统κ*的近似推理理论,并得到了统一的完备性定理.     

模式的语义描述与识别

讨论了代数语义方法用于模式描述和识别的可行性，采用这种方法，模式结构被作为一种代数结构，其语义约束采用等式规范的形式给出，这样可以将识别问题变为一个等式断言采用等式项重写在规范中进行验证，并举例说明这种方法。     

序列递推关系与一类代数几何码的有效译码

对于一类代数几何码，在其错误向量的伴随式序列上引进了一种递推关系，运用广义Ｂｅｒｌｅｋａｍｐ－Ｍａｓｓｅｙ算法，结合大数表决方案，给出了一类代数几何码的一个达到 Ｆｅｎｇ－Ｒａｏ界的有效译码算法，这个算法的复杂度为Ｏ（ｒｏ１ｎ＾２），对于不同的代数曲线，可通过适当选取基函数来降低算法的复杂度。     

具有最优代数免疫的奇数变元Boole函数

首先，给出了三类具有最优代数免疫的奇数变元非对称Boole函数，还给出了奇数变元Boole函数具有最优代数免疫的一些必要条件，有利于判别Boole函数是否具有最优代数免疫．另外，给出择多函数的Walsh谱，由其特征给出了奇数变元Boole函数具有最优代数免疫同时有较高非线性度的几个必要条件，并且给出了一类具有最优代数免疫同时非线性度大于择多函数的非线性度的奇数变元Boole函数．最后给出了奇数变元Boole函数具有最优代数免疫同时是l阶弹性函数的一个等价条件。     

密码协议的代数模型及其安全性

引入了一个新的代数系统——称为密码协议代数(cryptographic protocol algebra, CPA), 刻画具有多种密码运算的消息代数性质, 并基于CPA提出了一个新的密码协议代数模型. 模型中, 用子代数、自由生成元和多项式代数等概念刻画主体的知识扩张过程, 并用类似于代数中的正合序列概念描述了密码协议的攻击过程, 从而为密码协议的安全性分析建立了一种数学方法. 基于这个模型, 利用代数的技巧证明了对于具有一定对称性的协议, 任意多主体参与运行的协议安全性分析可归结为几个主体与攻击者参与的协议安全性分析. 研究了密码协议安全的一致性问题, 给出了两个协议合成保持安全性的一个充分条件, 并提供两个安全的密码协议的合成安全的例子, 推广了相关工作.     

基于Hamilton函数方法的非线性微分代数系统反馈控制

基于Hamilton函数方法研究了一类非线性微分代数系统的镇定和H∞控制问题. 首先结合非线性微分代数系统内在的广义能量平衡特性提出了一种新的耗散Hamilton实现结构. 基于该结构, 对不存在外部扰动的非线性微分代数系统设计了镇定控制器, 对存在外部扰动的非线性微分代数系统, 证明了其L2增益分析问题可以归结为广义Hamilton-Jacobi不等式的求解问题, 并给出了H∞控制器的构造方法. 所提出的非线性微分代数系统的镇定和鲁棒控制器设计方法能充分利用非线性微分代数系统的结构特点, 所设计的控制器形式简单, 易于实现.     

动作和进化的模型论基础

在分析改进有关工作的基础上，给出了一种多类逻辑作为刻画动作的形式基础，定义所谓的极小动作理论，并着重从模型论的角度研究它。在此基础上结合数理逻辑的有关方法，分析研究化的概念。     

两交叉直线最短距离的图解法

求解两交叉直线最短距离问题是空间解析几何中的一个重要内容。本文对此问题进行分析，讨论了两交叉直线最短距离的确定，提出两种求解此问题的图解方法，并通过实例，给出具体的图解原理及作图步骤。与画法几何学中常用的换面法和旋转法比较，空间分析和图解原理易于理解，而且图解方法简单直观，作图结果精确。     

Forecast Combination for Euro Area Inflation: A Cure in Times of Crisis?

The period of extraordinary volatility in euro area headline inflation starting in 2007 raised the question whether forecast combination methods can be used to hedge against bad forecast performance of single models during such periods and provide more robust forecasts. We investigate this issue for forecasts from a range of short‐term forecasting models. Our analysis shows that there is considerable variation of the relative performance of the different models over time. To take that into account we suggest employing performance‐based forecast combination methods—in particular, one with more weight on the recent forecast performance. We compare such an approach with equal forecast combination that has been found to outperform more sophisticated forecast combination methods in the past, and investigate whether it can improve forecast accuracy over the single best model. The time‐varying weights assign weights to the economic interpretations of the forecast stemming from different models. We also include a number of benchmark models in our analysis. The combination methods are evaluated for HICP headline inflation and HICP excluding food and energy. We investigate how forecast accuracy of the combination methods differs between pre‐crisis times, the period after the global financial crisis and the full evaluation period, including the global financial crisis with its extraordinary volatility in inflation. Overall, we find that forecast combination helps hedge against bad forecast performance and that performance‐based weighting outperforms simple averaging. Copyright © 2017 John Wiley & Sons, Ltd.     

一种启发式主题爬行算法

为克服传统主题爬行器在爬行速度和主题预测精度上的不足,提高爬行器的查准率和查全率,根据当前常用主题爬行策略的特点,通过页面辐射空间的引入将主题策略中基于链接分析和基于内容分析的方法相结合,并嵌入启发式算法,提出一种基于启发式的主题爬行算法.实验结果表明,该算法较常用爬行算法有较好的爬行效率.     

Multi‐step forecasting in the presence of breaks

This paper analyzes the relative performance of multi‐step AR forecasting methods in the presence of breaks and data revisions. Our Monte Carlo simulations indicate that the type and timing of the break affect the relative accuracy of the methods. The iterated autoregressive method typically produces more accurate point and density forecasts than the alternative multi‐step AR methods in unstable environments, especially if the parameters are subject to small breaks. This result holds regardless of whether data revisions add news or reduce noise. Empirical analysis of real‐time US output and inflation series shows that the alternative multi‐step methods only episodically improve upon the iterated method.     

Time-series analysis supported by power transformations

This paper presents some procedures aimed at helping an applied time-series analyst in the use of power transformations. Two methods are proposed for selecting a variance-stabilizing transformation and another for bias-reduction of the forecast in the original scale. Since these methods are essentially model-independent, they can be employed with practically any type of time-series model. Some comparisons are made with other methods currently available and it is shown that those proposed here are either easier to apply or are more general, with a performance similar to or better than other competing procedures.     

Non-Gaussian seasonal adjustment: X-12-ARIMA versus robust structural models

This study compares X-12-ARIMA and MING, two new seasonal adjustment methods designed to handle outliers and structural changes in a time series. X-12-ARIMA is a successor to the X-11-ARIMA seasonal adjustment method, and is being developed at the US Bureau of the Census. MING is a ‘Mixture based Non-Gaussian’ method for seasonal adjustment using time series structural models and is implemented as a function in the S-Plus language. The procedures are compared using 29 macroeconomic time series from the US Bureau of the Census. These series have both outliers and structural changes, providing a good testbed for comparing non-Gaussian methods. For the 29 series, the X-12-ARIMA decomposition consistently leads to smoother seasonal factors which are as or more ‘flexible’ than the MING seasonal component. On the other hand, MING is more stable, particularly in the way it handles outliers and level shifts. This study relies heavily on graphical tools for comparing seasonal adjustment methods.     

A comparison of adaptive structural forecasting methods for electricity sales

This paper presents the results of a study to determine whether new forecasting technologies might be of use to electric utilities for sales forecasting up to 3 years into the future. The methods considered included ordinary least squares on dynamic structural models, autocorrelated error models, adaptive variance and adaptive parameter models. Overall, the more adaptive models performed best, but most of the methods proved vastly superior to simple least squares models which do not take dynamics into account.     

Severe weather event attribution: Why values won't go away

We start by reviewing the complicated situation in methods of scientific attribution of climate change to extreme weather events. We emphasize the social values involved in using both so-called ″storyline″ and ordinary probabilistic or ″risk-based″ methods, noting that one important virtue claimed by the storyline approach is that it features a reduction in false negative results, which has much social and ethical merit, according to its advocates. This merit is critiqued by the probabilistic, risk-based, opponents, who claim the high ground; the usual probabilistic approach is claimed to be more objective and more ″scientific″, under the grounds that it reduces false positive error. We examine this mostly-implicit debate about error, which apparently mirrors the old Jeffrey-Rudner debate. We also argue that there is an overlooked component to the role of values in science: that of second-order inductive risk, and that it makes the relative role of values in the two methods different from what it first appears to be. In fact, neither method helps us to escape social values, and be more scientifically ″objective″ in the sense of being removed or detached from human values and interests. The probabilistic approach does not succeed in doing so, contrary to the claims of its proponents. This is important to understand, because neither method is, fundamentally, a successful strategy for climate scientists to avoid making value judgments.     

力学中非线性方程常用解法的比较及其改进

详细分析了力学中非线性问题常用解法Euler—Cauchy及Newton-Raphson法。论证了这两种方法均是将原非线性方程在求解过程中线性化，用一系列线性方程去逼近原非线性问题导致了误差存在。本文详细分析了上述两种算法的优缺点。将两种算法的优点进行组合，推荐一种基于梯形公式的改良算法。在不增加计算工作量的前提下该法不仅收敛快、收敛半径大，而且计算精度高。最后基于Lagrange微分中值定理论述了加权平均刚度法。