Optimal convergence properties of kernel density estimators without differentiability conditions

Let X ₁, X ₂, ..., X _n be independent observations from an (unknown) absolutely continuous univariate distribution with density f and let % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmOzayaajaGaaiikaiaadIhacaGGPaGaeyypa0Jaaiikaiaad6ga% caWGObGaaiykamaaCaaaleqabaGaeyOeI0IaaGymaaaakmaaqadaba% Gaam4saiaacUfadaWcgaqaaiaacIcacaWG4bGaeyOeI0Iaamiwamaa% BaaaleaacaWGPbaabeaakiaacMcaaeaacaWGObGaaiyxaaaaaSqaai% aadMgacqGH9aqpcaaIXaaabaGaamOBaaqdcqGHris5aaaa!5356!\[\hat f(x) = (nh)^{ - 1} \sum\nolimits_{i = 1}^n {K[{{(x - X_i )} \mathord{\left/ {\vphantom {{(x - X_i )} {h]}}} \right. \kern-\nulldelimiterspace} {h]}}} \] be a kernel estimator of f(x) at the point x, \s-<x<, with h=h _n (h _n O and nh _n , as n) the bandwidth and K a kernel function of order r. Optimal rates of convergence to zero for the bias and mean square error of such estimators have been studied and established by several authors under varying conditions on K and f. These conditions, however, have invariably included the assumption of existence of the r-th order derivative for f at the point x. It is shown in this paper that these rates of convergence remain valid without any differentiability assumptions on f at x. Instead some simple regularity conditions are imposed on the density f at the point of interest. Our methods are based on certain results in the theory of semi-groups of linear operators and the notions and relations of calculus of finite differences.This research was supported in part by grants from the Natural Sciences and Engineering Research Council of Canada and the University of Alberta Central Research Fund.     

Oligothienylenevinylenes incorporating 3,4-ethylenedioxythiophene (EDOT) units

A new series of π-conjugated oligomers based on various combinations of thiophene and EDOT units and double bonds has been synthesized by Wittig-Horner reactions from phosphonate anions carrying EDOT or bis-EDOT units. Optical and electrochemical results evidence the crucial role of the EDOT moiety for modulating the electronic properties of the oligomers. The insertion of bis-EDOT unit in the middle of the molecule leads to a self-rigidification of the conjugated system due to non covalent S?O intramolecular interactions. The strong electron donor effect of the EDOT units explains the determining role of the relative position of the EDOT units on the localization and stabilization of the positive charges in the radical cation or dication states.     

Significance of Non-isothermal Kinetic Data. A statistical study

Arrhenius parameters values, in non-isothermal kinetic vaporisation processes for a series of compounds with related structures, have been calculated. This was made using a method of calculation that allows to find the most probable vaporisation mechanisms. According to this method DTG curves were compared with some theoretical ones reported in literature, whose shape results to be only a function of the mechanisms. In this way the choice of the mathematical functions which can be inserted in the kinetic equations, was influenced by the shape of the DTG plots and other thermal analysis signals thus allowing to choose the most probable mechanisms. The kinetic parameters derived from these mechanisms were compared, using statistical analysis, with those obtained from another method of calculation based on ‘a priori’ vaporisation mechanism chosen for the investigated liquid–gas transition. The standard deviations of the slope and of the intercept, together with the standard deviation and the square correlation coefficient (r ²) of the linear regression equations related to the mechanisms of the two methods were calculated. Student t-test, Fisher F-test, confidence intervals (c.i.) and residuals valueswere also given. Statistical analysis shows that the mechanisms obtained with the former method (diffusive and geometrical models) and the related Arrhenius parameters result to be more significant (in terms of probability) than the corresponding quantities of the latter for which a first-order model was chosen. This revised version was published online in August 2006 with corrections to the Cover Date.     

环形腔高掺Er3 窄线宽光纤激光器实验研究

报道了采用光纤光栅（FBG）短直腔选频结构的环形腔窄线宽光纤激光器。采用约3m长高掺Er^3光纤，LD抽运阈值功率约为11mW，在25mW976nm有效抽运功率时输出信号功率为2．65mW，斜效率约为15％；输出激光3dB线宽小于0．01nm，20dB线宽小于0．04nm，边模抑制比（SMSR）为48dB；观察到输出信号光波长漂移范围为0．06nm。     

GPS接收机中的码分多址信号处理研究

介绍了基于码分多址信号处理的GPS(全球定位系统)接收机的算法和电路设计。GPS接收机电路的信号处理任务主要是对数字化后的基带扩频信号进行载波跟踪、解调、解扩、码跟踪,从而得到符号数据。着重讨论了GPS接收机中信号处理部分的COSTAS、码跟踪、帧同步生成电路三大模块的功能任务、原理、算法及其相应的电路设计。通过这些研究工作,可以进一步设计出当前应用日益普遍的GPS接收机电路,该电路具有功能全面、通用性好、可靠性高等特点。     

用遗传算法构造光正交码

提出了一种利用遗传算法构造任意码长、码重、自相关限、互相关限光正交码(GA-OOC)的方法,设计了新的码字矩阵;分析了基于GA-OOC的光CDMA系统的误码率性能。仿真结果表明:该算法具有构造算法简单、易于编程实现的特点;与基于PC,EPC,QC和BIBD-OOC的光码分多址系统相比,GA-OOC的光码分多址系统具有更好的误码率性能。GA-OOC有望用于构造二维光地址码。     

基于光码柱面的二维地址码相关性分析和码字容量研究

在谱域和时域同时编码的二维OCDMA系统是增加系统容量的主要方案.在一维光码盘和光码环的基础上,设计出直观描述二维λ-t地址码的几何装置-二维光码柱面,直观便捷地描述二维码字结构,给出基于光码柱面的二维码码字相关性分析方法.并根据光码柱面,建立了在光码集本身导出二维码码字容量的分析理论.所得结果与直接引用电通信中的Johnson界得出的结果一致.因此,二维光码柱面给二维的相关性分析和码字容量研究提供了便捷有效的工具.     

Blind Speech Watermarking Method with Frame Self-Synchronization Based on Spread-Spectrum Using Linear Prediction Residue

State-of-the-art speech watermarking techniques enable speech signals to be authenticated and protected against any malicious attack to ensure secure speech communication. In general, reliable speech watermarking methods must satisfy four requirements: inaudibility, robustness, blind-detectability, and confidentiality. We previously proposed a method of non-blind speech watermarking based on direct spread spectrum (DSS) using a linear prediction (LP) scheme to solve the first two issues (inaudibility and robustness) due to distortion by spread spectrum. This method not only effectively embeds watermarks with small distortion but also has the same robustness as the DSS method. There are, however, two remaining issues with blind-detectability and confidentiality. In this work, we attempt to resolve these issues by developing an approach called the LP-DSS scheme, which takes two forms of data embedding for blind detection and frame synchronization. We incorporate blind detection with frame synchronization into the scheme to satisfy blind-detectability and incorporate two forms of data embedding process, front-side and back-side embedding for blind detection and frame synchronization, to satisfy confidentiality. We evaluated these improved processes by carrying out four objective tests (PESQ, LSD, Bit-error-rate, and accuracy of frame synchronization) to determine whether inaudibility and blind-detectability could be satisfied. We also evaluated all combinations with the two forms of data embedding for blind detection with frame synchronization by carrying out BER tests to determine whether confidentiality could be satisfied. Finally, we comparatively evaluated the proposed method by carrying out ten robustness tests against various processing and attacks. Our findings showed that an inaudible, robust, blindly detectable, and confidential speech watermarking method based on the proposed LP-DSS scheme could be achieved.     

Low-Complexity Alternatives to the Optimal Linear Coding Scheme for Transmitting ARMA Sources

In the era of the Internet of Things, there are many applications where numerous devices are deployed to acquire information and send it to analyse the data and make informed decisions. In these applications, the power consumption and price of the devices are often an issue. In this work, analog coding schemes are considered, so that an ADC is not needed, allowing the size and power consumption of the devices to be reduced. In addition, linear and DFT-based transmission schemes are proposed, so that the complexity of the operations involved is lowered, thus reducing the requirements in terms of processing capacity and the price of the hardware. The proposed schemes are proved to be asymptotically optimal among the linear ones for WSS, MA, AR and ARMA sources.     

对数比放大电路在精密光功率计中的应用

光功率测量是光纤通信系统最基本的测量参数之一.在实际测量中,光功率计要求有很大的动态测量范围.采用传统线性放大电路设计的光功率计,存在着换档误差,动态测量范围也受到限制.由于结果显示要进行对数运算,软件处理也相对比较复杂.为改善上述不足,使用对数比放大电路代替传统的线性放大电路.这样可以避免换档误差和繁琐的对数运算,提高精度.经过实际设计验证,改进设计可获得80 dB动态范围,0.1 dLBm的测量精度,而且电路简洁、易于校准.此设计方法已在实际产品得以应用.