脉冲噪声滤波的无监督鲁棒递归最小二乘方法

在未知期望信号的条件下,提出一种能够抑制脉冲噪声的鲁棒递归最小二乘自适应滤波方法.与传统最小二乘法的代价函数不同,通过引入饱和非线性约束,降低可能出现的脉冲噪声对滤波器权值更新的影响.此外,提出一种多步预测器来重构滤波器的输入信号,通过比较判断滤波器输入信号可能受到脉冲噪声干扰时,采用预测值来替代原始观测信号.实验结果表明,提出的无监督鲁棒递归最小二乘自适应滤波方法在未受到脉冲噪声干扰时与传统的递归最小二乘法具有相近的收敛性能;在脉冲噪声条件下,传统递归最小二乘法和其他的无监督自适应滤波方法性能都变得很差,但本文提出的方法几乎未受到脉冲噪声的影响.     

Stochastic stability of quasi-integrable Hamiltonian systems with time delay by using Lyapunov function method

The asymptotic Lyapunov stability of one quasi-integrable Hamiltonian system with time-delayed feedback control is studied by using Lyapunov functions and stochastic averaging method. First, a quasi-integrable Hamiltonian system with time-delayed feedback control subjected to Gaussian white noise excitation is approximated by a quasi-integrable Hamiltonian system without time delay. Then, stochastic averaging method for quasi-integrable Hamiltonian system is used to reduce the dimension of the original syst...     

Building Scenarios of Multiple Time Series that Take into Account the Effects of an Expected Intervention

We consider a forecasting problem that arises when an intervention is expected to occur on an economic system during the forecast horizon. The time series model employed is seen as a statistical device that serves to capture the empirical regularities of the observed data on the variables of the system without relying on a particular theoretical structure. Either the deterministic or the stochastic structure of a vector autoregressive error correction model of the system is assumed to be affected by the intervention. The information about the intervention effect is just provided by some linear restrictions imposed on the future values of the variables involved. Formulas for restricted forecasts with intervention effects and their mean squared errors are derived as a particular case of Catlin's static updating theorem. An empirical illustration uses Mexican macroeconomic data on five variables and the restricted forecasts consider targets for years 2011–2014. Copyright © 2013 John Wiley & Sons, Ltd.     

Banach空间中时变广义分布参数系统的可解性

广义分布参数系统是比分布参数系统更常见的一类系统,二者有着本质的区别,如广义分布参数系统受到干扰时会引起脉冲行为等．广义分布参数系统的可解性问题是广义分布参数系统研究的重要问题之一．本文主要研究Banach空间中时变广义分布参数系统的可解性问题．首先,讨论Banach空间中由有界线性算子所引导的广义发展算子及其性质,定义了广义发展算子的生成元．证明了广义发展算子的存在性;然后,应用广义发展算子研究时变广义分布参数系统的可解性问题,证明了强解的存在性和唯一性,并应用广义发展算子给出了时变广义分布参数系统强解的构造性表达式．所得结果对于研究时变广义分布参数系统的稳定性问题、能控性问题及最优控制问题等都有重要的理论及应用价值．     

The landing zone – Ground for model transfer in chemistry

This essay proposes a new notion - the landing zone - in order to identify conceptual features that allow modelers to transfer mathematical tools across disciplinary borders. This discussion refers to the transferable models as ‘templates’. Templates are functions, equations, or computational methods that are capable of being generalized from a particular subject matter. There are formal and conceptual prerequisites for the transfer of a template to a new domain. A landing zone is an ontology that contributes to the satisfaction of these conditions for successful transfer. This paper presents a case study on a model in chemistry - the Quantum Theory of Atoms in Molecules (QTAIM) - that makes use of transferred templates from physics - the virial theorem and the wave function. The landing zone in this case is a new ontological notion, that of the topological atom, which prepares ground for the use of the virial theorem and the wave function in chemistry. The virial theorem requires that there exists in-principle stability to the system that it represents, and the wave function requires transformation in its representation that is justified. The ontology of QTAIM - the landing zone for these templates - grounds the scientific use of these templates in the context of chemistry.     

On the origins and foundations of Laplacian determinism

In this paper I examine the foundations of Laplace’s famous statement of determinism in 1814, and argue that rather than derived from his mechanics, this statement is based on general philosophical principles, namely the principle of sufficient reason and the law of continuity. It is usually supposed that Laplace’s statement is based on the fact that each system in classical mechanics has an equation of motion which has a unique solution. But Laplace never proved this result, and in fact he could not have proven it, since it depends on a theorem about uniqueness of solutions to differential equations that was only developed later on. I show that the idea that is at the basis of Laplace’s determinism was in fact widespread in enlightenment France, and is ultimately based on a re-interpretation of Leibnizian metaphysics, specifically the principle of sufficient reason and the law of continuity. Since the law of continuity also lies at the basis of the application of differential calculus in physics, one can say that Laplace’s determinism and the idea that systems in physics can be described by differential equations with unique solutions have a common foundation.     

有色噪声下随机时滞传染病模型的稳定性

本文运用O-U过程刻画环境变化性,在Edoardo Beretta基础上构造了有色噪声影响下的随机时滞的传染病模型。运用一般Lyapunonv方法研究了有色噪声对该系统的影响并得到系统正平衡点保持稳定的充分条件。最后通过对比发现随机扰动对系统稳定性影响仅仅与其随机过程的方差有关。     

Simultaneous transfer functions versus vector arma models

This work compares two classes of multiple time series models which have been developed in past decades and are usually believed to be equivalent: the vector ARMA model and the system of simultaneous transfer functions (STF). The first part analyzes the mathematical structure of the two schemes; their properties of stability, structural identification and realization. In the second, algorithms of order identification and parameter estimation are derived, following the approach of stochastic approximation. The proposed solutions are easily implementable on standard statistical software and in an extended empirical example their performance is checked. The superiority of the STF model will be well established.     

基于真值的SBL_～公理化扩张系统的计量化

本文首先在带有对合否定的△模糊逻辑系统SBL～中,运用△演绎定理和真值分布,论证了SBL～系统中有效推理的真值关系定理.其次以SBL～系统的公理化扩张Godel～为例,提出了△相似度、△距离,运用真值关系定理论证了△度量空间逻辑算子→,～的连续性,给出了公式与理论间距离的计算方法,从而实现了△模糊逻辑系统的计量化.最后在Godel～系统中提出了3种近似推理模式,并讨论了3种模式之间的关系.     

Modeling eBay price using stochastic differential equations

Online auctions have become increasingly popular in recent years. There is a growing body of research on this topic, whereas modeling online auction price curves constitutes one of the most interesting problems. Most research treats price curves as deterministic functions, which ignores the random effects of external and internal factors. To account for the randomness, a more realistic model using stochastic differential equations is proposed in this paper. The online auction price is modeled by a stochastic differential equation in which the deterministic part is equivalent to the second‐order differential equation model proposed in Wang et al. (Journal of the American Statistical Association, 2008, 103, 1100–1118). The model also includes a component representing the measurement errors. Explicit expressions for the likelihood function are also obtained, from which statistical inference can be conducted. Forecast accuracy of the proposed model is compared with the ODE (ordinary differential equation) approach. Simulation results show that the proposed model performs better.     

Discretization of stochastic differential equations and econometric forecasting: An application to time-varying autoregressions

Continuous time versions of time varying Vector Autoregressions are stochastic differential equations. Optimal discretization of Stochastic Differential Equations cannot be obtained by replacing all differentials by the corresponding first differences. In this paper we obtain the optimal discretization for time varying VARS. The results are applied to predicting the consumer price index.     

Reconceptualising equilibrium in Boltzmannian statistical mechanics and characterising its existence

In Boltzmannian statistical mechanics macro-states supervene on micro-states. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable micro-states. The largest of these regions is singled out as the equilibrium region of the system. What justifies this association? We review currently available answers to this question and find them wanting both for conceptual and for technical reasons. We propose a new conception of equilibrium and prove a mathematical theorem which establishes in full generality – i.e. without making any assumptions about the system׳s dynamics or the nature of the interactions between its components – that the equilibrium macro-region is the largest macro-region. We then turn to the question of the approach to equilibrium, of which there exists no satisfactory general answer so far. In our account, this question is replaced by the question when an equilibrium state exists. We prove another – again fully general – theorem providing necessary and sufficient conditions for the existence of an equilibrium state. This theorem changes the way in which the question of the approach to equilibrium should be discussed: rather than launching a search for a crucial factor (such as ergodicity or typicality), the focus should be on finding triplets of macro-variables, dynamical conditions, and effective state spaces that satisfy the conditions of the theorem.     

Stability of trajectories from Poincaré to Birkhoff: approaching a qualitative definition

The article investigates the different conceptions of stability found in qualitative studies on the solutions of differential equations. We start from the definitions proposed by Poincaré and criticized by Birkhoff for not being fully qualitative, and show that the clarification of the criterion for stating that a property is qualitative comes precisely with Birkhoff. In addition, we note that the stability conceptions of Lyapunov and Levi-Civita are also important in this transition from the appearance of the first qualitative tools in the study of differential equations to the definition of stability in use in dynamical systems theory. The history of stability can help to explain the meaning of the word “qualitative” in this context.     

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。     

基于随机时间自动机和统计模型检验技术的无线传感网络协议建模与分析

近年来,传感器技术得到了长足而有效的提升,无线传感网络（WSN）以其开放、动态的特征获得了极大的关注,并成为了互联网计算的一个重要组成．WSN系统行为复杂,经常面临信息丢失、节点动态变化等不确定因素,且网络中的节点一旦部署将很难更改、维护．因此,为了保证相关应用的正常工作,在系统设计阶段对WSN中的底层协议进行质量保障就成为了一项非常重要的研究问题．系统设计人员不仅需要保证协议功能上的正确性,还应该评估协议在目标工作环境下的性能,以保证其可以胜任相应的工作需求．针对以上问题,本文提出了一种基于随机时间自动机和统计模型检验技术的WSN协议建模、分析和评估途径．在建模阶段,首先将采用时间自动机对协议在理想环境下的基本业务流程进行建模．考虑到WSN系统实际工作中会遇到的各种不确定性因素,将用带权分枝来对模型进行扩展,生成协议的随机时间自动机．在验证阶段,首先采用经典模型检验技术,在理想时间自动机上检验相关功能性质,保证协议工作逻辑的正确性．为评估协议在不同条件下的具体性能,则在随机时间自动机上用统计模型检验技术对其进行数值分析,以进行参数配置、性能预测、协议比较等工作．为展示该途径的可用性及其技术细节,本文对两种著名的WSN时间同步协议,TPSN和FTSP分别进行了完整的建模与评估．     

Continued fractions and the origins of the Perron–Frobenius theorem

The theory of nonnegative matrices is an example of a theory motivated in its origins and development by purely mathematical concerns that later proved to have a remarkably broad spectrum of applications to such diverse fields as probability theory, numerical analysis, economics, dynamical programming, and demography. At the heart of the theory is what is usually known as the Perron–Frobenius Theorem. It was inspired by a theorem of Oskar Perron on positive matrices, usually called Perron’s Theorem. This paper is primarily concerned with the origins of Perron’s Theorem in his masterful work on ordinary and generalized continued fractions (1907) and its role in inspiring the remarkable work of Frobenius on nonnegative matrices (1912) that produced, inter alia, the Perron–Frobenius Theorem. The paper is not at all intended exclusively for readers with expertise in the theory of nonnegative matrices. Anyone with a basic grounding in linear algebra should be able to read this article and come away with a good understanding of the Perron–Frobenius Theorem as well as its historical origins. The final section of the paper considers the first major application of the Perron–Frobenius Theorem, namely, to the theory of Markov chains. When he introduced the eponymous chains in 1908, Markov adumbrated several key notions and results of the Perron–Frobenius theory albeit within the much simpler context of stochastic matrices; but it was by means of Frobenius’ 1912 paper that the linear algebraic foundations of Markov’s theory for nonpositive stochastic matrices were first established by R. Von Mises and V.I. Romanovsky.     

Two No-Go Theorems for Modal Interpretations of Quantum Mechanics

Modal interpretations take quantum mechanics as a theory which assigns at all times definite values to magnitudes of quantum systems. In the case of single systems, modal interpretations manage to do so without falling prey to the Kochen and Specker no-go theorem, because they assign values only to a limited set of magnitudes. In this paper I present two further no-go theorems which prove that two modal interpretations become nevertheless problematic when applied to more than one system. The first theorem proves that the modal interpretation proposed by Kochen and by Dieks cannot correlate the values simultaneously assigned to three systems. The second and new theorem proves that the atomic modal interpretation proposed by Bacciagaluppi and Dickson and by Dieks cannot correlate the values simultaneously and sequentially assigned to two systems if one assumes that these correlations are uniquely related to the dynamics of the state of the systems.     

Interpreting the Wigner–Eckart Theorem

The Wigner–Eckart theorem is central to the application of symmetry principles throughout atomic, molecular, and nuclear physics. Nevertheless, the theorem has a puzzling feature: it is dispensable for solving problems within these domains, since elementary methods suffice. To account for the significance of the theorem, I first contrast it with an elementary approach to calculating matrix elements. Next, I consider three broad strategies for interpreting the theorem: conventionalism, fundamentalism, and conceptualism. I argue that the conventionalist framework is unnecessarily pragmatic, while the fundamentalist framework requires more ontological commitments than necessary. Conceptualism avoids both defects, accounting for the theorem’s significance in terms of how it epistemically restructures the calculation of matrix elements. Specifically, the Wigner–Eckart theorem modularizes and unifies matrix element problems, thereby changing what we need to know to solve them.