Constructing Four-Photon States for Quantum Communication and Information Processing

We provide a method for constructing a set of four-photon states suitable for quantum communication applications. Among these states is a set of concatenated quantum code states that span a decoherence-free subspace that is robust under collective-local as well as global dephasing noise. This method requires only the use of spontaneous parametric down-conversion, quantum state post-selection, and linear optics. In particular, we show how this method can be used to produce all sixteen elements of the second-order Bell gem , which includes these codes states and is an orthonormal basis for the Hilbert space of four qubits composed entirely of states that are fully entangled under the four-tangle measure.     

Intensity analysis methods for transient signals

Conventionally, the Fourier transform is applied for sound intensity analysis of stationary signals, but this method can be applied for analyzing non-stationary transient signals. Instead of the Fourier transform analysis, instantaneous spectrum analysis methods such as the Wigner-Ville distribution and the wavelet transform are proposed. By using the mathematical example as a transient signal, advantages and disadvantages of these methods including the short-time Fourier transform are compared. From calculation results, it is considered that the STFT method is the most suitable for the accurate measurement of sound intensity levels, but the WT method is also recommended from its higher resolution of transient signals.     

Application of multifractal wavelet analysis to spontaneous fermentation processes

An algorithm is presented here to get more detailed information, of mixed-culture type, based exclusively on the biomass concentration data for fermentation processes. The analysis is performed with only the on-line measurements of the redox potential being available. It is a two-step procedure which includes an Artificial Neural Network (ANN) that relates the redox potential to the biomass concentrations in the first step. Next, a multifractal wavelet analysis is performed using the biomass estimates of the process. In this context, our results show that the redox potential is a valuable indicator of microorganism metabolic activity during the spontaneous fermentation. In this paper, the detailed design of the multifractal wavelet analysis is presented, as well as its direct experimental application at the laboratory level.     

阿达玛变换在激光告警技术中的应用

系统信噪比一直是制约激光探测武器性能的关键性因素之一。为提高系统探测信噪比,利用阿达玛变换方法,在计算模板大小（17.48×17.48mm）和码元数N=255的基础上,详细介绍了Sn循环矩阵的生成,最后选择液晶空间光调制器充当编码模板。通过在液晶面板上不同位置施加不同的电压,利用旋光效应对通过的激光衍射条纹进行控制,按其通过与否（1/0）进行编码。在这一方法指导下进行了系统的仿真实验研究并获得成功。实验结果表明：将阿达玛变换应用于激光光谱测量,在不增加测量次数的情况下,可以有效地提高系统的信噪比。     

光学移相干涉仪抗振系统的鲁棒μ控制器设计

将结构奇异值μ综合鲁棒控制技术应用于主动抗振控制系统中,并用于解决光学移相干涉仪抗振系统的不确定性问题.采用小波分析方法将随机振动信号进行时频分析后得到低频全局信息,随后运用μ综合D-K迭代法设计鲁棒μ控制器对低频振动进行抑制.该方法克服了由模型自身和外部干扰所引起的不确定性,使得控制系统能够有效地抑制抗振模型的不确定性和外部振动的干扰,同时也具有很高的控制准确度和灵敏度.仿真结果表明,该方法使光学移相干涉仪在外部振动的干扰下具有较好的鲁棒稳定性和控制准确度,同时也能较好地抑制低频振动.     

Intertwining wavelets or multiresolution analysis on graphs through random forests

We propose a new method for performing multiscale analysis of functions defined on the vertices of a finite connected weighted graph. Our approach relies on a random spanning forest to downsample the set of vertices, and on approximate solutions of Markov intertwining relation to provide a subgraph structure and a filter bank leading to a wavelet basis of the set of functions. Our construction involves two parameters q and $q^{\prime }$. The first one controls the mean number of kept vertices in the downsampling, while the second one is a tuning parameter between space localization and frequency localization. We provide an explicit reconstruction formula, bounds on the reconstruction operator norm and on the error in the intertwining relation, and a Jackson-like inequality. These bounds lead to recommend a way to choose the parameters q and $q^{\prime }$. We illustrate the method by numerical experiments.     

Duality and interpolation of anisotropic Triebel–Lizorkin spaces

We study properties of anisotropic Triebel–Lizorkin spaces associated with general expansive dilations and doubling measures on using wavelet transforms. This paper is a continuation of (Bownik in J Geom Anal 2007, to appear, Trans Am Math Soc 358:1469–1510, 2006), where we generalized the isotropic methods of dyadic -transforms of Frazier and Jawerth (J Funct Anal 93:34–170, 1990) to non-isotropic settings. By working at the level of sequence spaces, we identify the duals of anisotropic Triebel–Lizorkin spaces. We also obtain several real and complex interpolation results for these spaces. The author was partially supported by the NSF grants DMS-0441817 and DMS-0653881. The author wishes to thank Michael Frazier and Dachun Yang for valuable comments and discussions on this work.     

Roller bearing acoustic signature extraction by wavelet packet transform,applications in fault detection and size estimation

Continuous online monitoring of rotating machines is necessary to assess real-time health conditions so as to enable early detection of operation problems and thus reduce the possibility of downtime. Rolling element bearings are crucial parts of many machines and there has been an increasing demand to find effective and reliable health monitoring technique and advanced signal processing to detect and diagnose the size and location of incipient defects. Condition monitoring of rolling element bearings, comprises four main stages which are, statistical analysis, fault diagnostics, defect size calculation, and prognostics. In this paper the effect of defect size, operating speed, and loading conditions on statistical parameters of acoustic emission (AE) signals, using design of experiment method (DOE), have been investigated to select the most sensitive parameters for diagnosing incipient faults and defect growth on rolling element bearings. A modified and effective signal processing algorithm is designed to diagnose localized defects on rolling element bearings components under different operating speeds, loadings, and defect sizes. The algorithm is based on optimizing the ratio of Kurtosis and Shannon entropy to obtain the optimal band pass filter utilizing wavelet packet transform (WPT) and envelope detection. Results show the superiority of the developed algorithm and its effectiveness in extracting bearing characteristic frequencies from the raw acoustic emission signals masked by background noise under different operating conditions. To experimentally measure the defect size on rolling element bearings using acoustic emission technique, the proposed method along with spectrum of squared Hilbert transform are performed under different rotating speeds, loading conditions, and defect sizes to measure the time difference between the double AE impulses. Measurement results show the power of the proposed method for experimentally measuring size of different fault shapes using acoustic emission signals.     

The movement towards a more experimental approach to problem solving in mathematics using coding

Motivated by a problem proposed in a coding competition for secondary students, I will show on this paper how coding substantially changed the problem-solving process towards a more experimental approach.     

定点脉冲线性预测编码方法研究*

在多脉冲线性预测编码的基础上,本文提出了位置无关脉冲搜索算法。该算法不需要搜索脉冲位置,而是根据给定的脉冲位置一次性解出脉冲幅度矢量。这就保证了得到的脉冲组合在最小二乘意义下是最优的,为改进合成语音质量提供了理论基础。进而在激励脉冲与位置无关的理论基础上,提出了定点脉冲线性预测编码方法。对所提出的算法在MATLAB下进行了仿真,仿真结果发现位置无关脉冲搜索算法得到的合成语音质量优于序贯法,编码时间也要比序贯法短。定点脉冲线性预测编码方法可以在2.7 kbps的编码速率下获得与G.729相近的合成语音。