Bayesian inference and learning in Gaussian process state-space models with Particle MCMC

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference and learning (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and, instead, infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity.

An adaptive controller for a class of nonlinear system using direction basis function

For a class of nonlinear dynamical systems, the adaptive controllers are investigated using direction basis function (DBF) in this paper. Based on the criterion of Lyapunov' stability, DBF is designed which guarantees that the output of the controlled system asymptotically tracks the reference signals. Finally, the simulation shows the good tracking effectiveness of the adaptive controller.

基于复合离散混沌动力系统的序列密码算法

利用复合离散混沌系统的特性,提出了两个基于复合离散混沌系统的序列密码算法.算法的加密和解密过程都是同一个复合离散混沌系统的迭代过程,取迭代的初始状态作为密钥,以明文序列作为复合系统的复合序列,它决定了迭代过程中迭代函数的选择(或明文与密钥),然后将迭代轨迹粗粒化后作为密文.由于迭代对初始条件的敏感性和迭代函数选择的随机性,密钥、明文与密文之间形成了复杂而敏感的非线性关系,而且密文和明文的相关度也很小,从而可以有效地防止密文对密钥和明文信息的泄露.复合离散混沌系统均匀的不变分布还使密文具有很好的随机特性.经分析表明,系统具有很高的安全性.

Study of double barrier superlattice by synchrotron radiation and double-crystal x-ray diffraction

An (A1As/GaAs/A1As/A1GaAs)/GaAs(001) double-barrier superlattice grown by molecular beam epitaxy (MBE) is studied by combining synchrotron radiation and double-crystal x-ray diffraction (DCD). The intensity of satellite peaks is modulated by the wave function of each sublayer in one superlattice period. Simulated by the x-ray dynamical diffraction theory, it is discovered that the intensity of the satellite peaks situated near the modulating wave node point of each sublayer is very sensitive to the variation of the layer structural parameters, The accurate layer thickness of each sublayer is obtained with an error less than 1 Angstrom. Furthermore, x-ray kinematical diffraction theory is used to explain the modulation phenomenon. (C) 1996 American Institute of Physics.

奇异摄动控制系统:理论与应用

系统地回顾了近年来奇异摄动控制技术的发展 ,主要包括线性奇异摄动系统的稳定性分析与镇定、最优控制、H∞ 控制 ,非线性奇异摄动系统的镇定、优化控制和基于积分流形的几何方法 ,以及奇异摄动技术在实际工业 ,例如机器人领域、航天技术领域和工程工业、制造业等中的成功应用 .并指出了这一领域进一步研究的方向

From epistemic origins to journal impact factors: what do citations tell us?

Urquhart, C. (2006). From epistemic origins to journal impact factors: what do citations tell us? International Journal of Nursing Studies, 43(1), 1-2.

Achieving continuous professional development in higher education

Traditional higher education technology emphasizes knowledge transmission. In contrast, the Community platform presented in this paper follows a social approach that interleaves knowledge delivery with social and professional skills development, engaging with others, and personal growth. In this paper, we apply learning and complex adaptive systems theory to motivate and justify a continuous professional development model that improves higher education outcomes such as placement. The paper follows action design research (ADR) as the research method to propose and evaluate design principles.

Counterstories: who counts as lesbian?

Coming out midlife is a profound and life‐changing experience—it is an experience of self‐shattering that entails the destabilisation of identity, and of family relationships. Entailing a displacement from social insider to outsider, it is a difficult, but also exhilarating, journey of self, and sexual, discovery. This thesis is an examination of the experiences of nine women who undertook that journey. This dissertation is very much a search for understanding—for understanding how one can be lesbian, and how one can not have known, following a lifetime of heterosexual identification—as well as a search for why those questions arise in the first place. I argue that the experience of coming out midlife exposes the fundamental ambiguity of sexuality; and has a significance that ranges beyond the particularity of the participants’ experiences and speaks to the limitations of the hegemonic sexual paradigm itself. Using the theoretical lens of three diverse conceptual approaches—the dynamic systems theory of sexual fluidity; liminality; and narrative identity—to illuminate their transition, I argue that the event of coming out midlife should be viewed not merely as an atypical experience, but rather we should ask what such events can tell us about women’s sexuality in particular, and the sexual paradigm more generally. I argue that women who come out midlife challenge those dominant discourses of sexuality that would entail that women who come out midlife were either in denial of their “true” sexuality throughout their adult lives; or that they are not really lesbian now. The experiences of the women I interviewed demonstrate the inadequacy of the sexual paradigm as a framework within which to understand and research the complexity of human sexuality; they also challenge hegemonic understandings of sexuality as innate and immutable. In this thesis, I explore that challenge.

Broadband chaos generated by an optoelectronic oscillator.

We study an optoelectronic time-delay oscillator that displays high-speed chaotic behavior with a flat, broad power spectrum. The chaotic state coexists with a linearly stable fixed point, which, when subjected to a finite-amplitude perturbation, loses stability initially via a periodic train of ultrafast pulses. We derive approximate mappings that do an excellent job of capturing the observed instability. The oscillator provides a simple device for fundamental studies of time-delay dynamical systems and can be used as a building block for ultrawide-band sensor networks.

Invariant measure selection by noise. An example

We consider a deterministic system with two conserved quantities and infinity many invariant measures. However the systems possess a unique invariant measure when enough stochastic forcing and balancing dissipation are added. We then show that as the forcing and dissipation are removed a unique limit of the deterministic system is selected. The exact structure of the limiting measure depends on the specifics of the stochastic forcing.

Sensitivity to switching rates in stochastically switched ODEs

We consider a stochastic process driven by a linear ordinary differential equation whose right-hand side switches at exponential times between a collection of different matrices. We construct planar examples that switch between two matrices where the individual matrices and the average of the two matrices are all Hurwitz (all eigenvalues have strictly negative real part), but nonetheless the process goes to infinity at large time for certain values of the switching rate. We further construct examples in higher dimensions where again the two individual matrices and their averages are all Hurwitz, but the process has arbitrarily many transitions between going to zero and going to infinity at large time as the switching rate varies. In order to construct these examples, we first prove in general that if each of the individual matrices is Hurwitz, then the process goes to zero at large time for sufficiently slow switching rate and if the average matrix is Hurwitz, then the process goes to zero at large time for sufficiently fast switching rate. We also give simple conditions that ensure the process goes to zero at large time for all switching rates. © 2014 International Press.

Stochastic switching in infinite dimensions with applications to random parabolic PDE

© 2015 Society for Industrial and Applied Mathematics.We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.

Positive dilations of piecewise monotonic Markov maps

We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems.

Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.