Trigonometrical sums connected with the chiral Potts model,Verlinde dimension formula,two-dimensional resistor network,and number theory

We have recently developed methods for obtaining exact two-point resistance of the complete graph minus N$N$ edges. We use these methods to obtain closed formulas of certain trigonometrical sums that arise in connection with one-dimensional lattice, in proving Scott’s conjecture on permanent of Cauchy matrix, and in the perturbative chiral Potts model. The generalized trigonometrical sums of the chiral Potts model are shown to satisfy recursion formulas that are transparent and direct, and differ from those of Gervois and Mehta. By making a change of variables in these recursion formulas, the dimension of the space of conformal blocks of SU(2)$SU\left(2\right)$ and SO(3)$SO\left(3\right)$ WZW models may be computed recursively. Our methods are then extended to compute the corner-to-corner resistance, and the Kirchhoff index of the first non-trivial two-dimensional resistor network, 2×N$2\times N$. Finally, we obtain new closed formulas for variant of trigonometrical sums, some of which appear in connection with number theory.     

Multi-focus image fusion based on robust principal component analysis and pulse-coupled neural network

Multi-focus image fusion combines multiple source images with different focus points into one image, so that the resulting image appears all in-focus. In order to improve the accuracy of focused region detection and fusion quality, a novel multi-focus image fusion scheme based on robust principal component analysis (RPCA) and pulse-coupled neural network (PCNN) is proposed. In this method, registered source images are decomposed into principal component matrices and sparse matrices with RPCA decomposition. The local sparse features computed from the sparse matrix construct a composite feature space to represent the important information from the source images, which become inputs to PCNN to motivate the PCNN neurons. The focused regions of the source images are detected by the firing maps of PCNN and are integrated to construct the final, fused image. Experimental results demonstrate that the superiority of the proposed scheme over existing methods and highlight the expediency and suitability of the proposed method.     

Synchronization of time varying delayed complex networks via impulsive control

In this paper, we investigate the problem of synchronization for the time varying delayed complex dynamical networks via impulsive control method, several sufficient synchronization conditions are given, and we consider the impulsive control matrices are time varying delayed matrices. Furthermore, we found impulsive control does not always play an active role in synchronization although impulsive control strategy is cheaper and simpler than other control strategy. Finally, numerical simulations are also given to demonstrate the effectiveness of the proposed schemes.     

Performance enhanced down-stream signalling for next generation long-reach 10 Gbit/s passive optical networks

In this paper, we have analyzed the signal processing methods both in digital and optical domain to enhance the transmission performance of downstream signalling in long reach passive optical networks (LR-PONs). The impact of non-linear (NL) equalization through signal processing, i.e. Volterra Equalization (VE), Digital Backpropagation (BP) and Optical Phase Conjugation with Non-linearity Module (OPC-NM) is investigated, in 10 Gbit/s (XG) DP-QPSK long-reach wavelength division multiplexed (WDM) PONs without midspan repeaters over 120 km standard single mode fibre (SMF) link for down-stream signals. Due to the compensation of optical Kerr effects, the sensitivity penalty is reduced to 2 dB by BP algorithm, 1.5 dB by VE algorithm and 2.69 dB by OPC-NM. Moreover, with the implementation of NL equalization technique we are able to get the transmission distance of 126.6 km SMF for the 1:1024 split-ratio at 5 GHz channel spacing in the non-linear region. Furthermore, the concept of super passive optical network (S-PON) is also evaluated, which involves a repeater stage consisting of optical amplifiers, to study the feasibility for receiver side signal processing and simplification.     

基于脉冲耦合神经网络的弹簧卡箍缺陷检测

传统的弹簧卡箍缺陷多为产后人工全检,存在漏检与缺陷率上升等现象,这不但会使成本上升、也对人力资源提出了考验。为此实现自动实时在线全检就成为急需解决的课题,设计了基于机器视觉的弹簧卡箍在线自动检测系统,该系统安装在弹簧卡箍流水线两侧,搭建特定光源,通过激光传感器外部触发工业相机对其表面进行图像捕获,送上位机进行缺陷判定与定位,最后通过RS485将判定结果送下位机来控制剔除机制。实验结果显示：该系统采用改进的脉冲神经网络(PCNN)能准确提取目标缺陷区域并对缺陷进行判定,可在0.348 s每个零件的速度下,检测出弹簧卡箍表面大于10像素的缺陷。通过对不同弹簧卡箍进行检测验证实验,证明了PCNN算法对缺陷分割的准确性和有效性。     

电机温度时滞耦合系统自抗扰控制仿真研究

电机温度过高会造成绝缘性能老化,电机安全性能下降。电机控制系统是典型的非线性系统,电机温度也因此具有时滞性和耦合性的特点,难以建立准确的数学模型。传统的方法对电机温度的控制精度较差,从而导致电机温度失控。为此,提出基于BP神经网络自抗扰控制算法的电机时滞耦合关系下温度控制方法。将BP神经网络与PID控制方法相结合建立电机温度网络自抗扰控制器模型,利用梯度下降法修正电机温度控制器模型的权值系数,从而实现了BP神经网络自抗扰控制器参数的实时调整。实验结果表明,利用BP神经网络自抗扰算法进行电机时滞耦合关系下温度调整,能够有效提高控制的精确度,缩短了控制过程中的时间延时。     

基于DNA损伤的蛋白调控网络研究

细胞生长的每个阶段都离不开蛋白质相互作用.研究细胞周期的功能、调控机理及参与调控的蛋白质之间的关系对生物工程等领域有重大的应用价值.本文通过研究电离辐射下生物体细胞的DNA损伤后,细胞内以p53为核心的扩展蛋白调控网络的功能、原理及其自修复机理,在现有蛋白网络基础上引入更多蛋白网络调控因子来建立蛋白调控网络,仿真模拟更为全面的细胞周期进程;并且从复杂网络图论和细胞周期调控两个方面分析扩展PMP调控网络的抗扰能力及自修复机理,结果表明:1)蛋白网络在对抗环境中出现的小扰动时具有较强的稳定性.但在面对蓄意攻击时网络的稳定性较差.2)受损的DNA能否被修复取决于p53蛋白的动力学行为,即低损伤与中损伤情况下,p53可诱导细胞周期进程阻滞来完成细胞的自修复;而当高损伤或过损伤时,p53蛋白浓度表现为周期振荡行为并诱导细胞凋亡.     

一种基于激光直写的水浊度传感结构

提出并制作了一种基于激光照射改变折射率方法的光度比浊度传感单元,综合了导波光学及检测相关知识原理.以UV光敏树脂为基底材料,采用“气体干法”除胶及分步固化的方法获得了该芯片化结构.传感器整个制作过程仅仅需要7~8 min因而使本方法具有很高的效率.由直写成型的单元组建传感系统对标准悬浊液样品进行了实验测试,所得的相关数据在SISO算法神经元网络系统中进行处理,获得了传感器浊度与对应散射系数的关系曲线.通过试剂检验的方法得知实际相对误差在5%左右.     

Plasticity-induced characteristic changes of pattern dynamics and the related phase transitions in small-world neuronal networks

Phase transitions widely exist in nature and occur when some control parameters are changed. In neural systems, their macroscopic states are represented by the activity states of neuron populations, and phase transitions between different activity states are closely related to corresponding functions in the brain. In particular, phase transitions to some rhythmic synchronous firing states play significant roles on diverse brain functions and disfunctions, such as encoding rhythmical external stimuli, epileptic seizure, etc. However, in previous studies, phase transitions in neuronal networks are almost driven by network parameters （e.g., external stimuli）, and there has been no investigation about the transitions between typical activity states of neuronal networks in a self-organized way by applying plastic connection weights. In this paper, we discuss phase transitions in electrically coupled and lattice-based small-world neuronal networks （LBSW networks） under spike-timing-dependent plasticity （STDP）. By applying STDP on all electrical synapses, various known and novel phase transitions could emerge in LBSW networks, particularly, the phenomenon of self-organized phase transitions （SOPTs）： repeated transitions between synchronous and asynchronous firing states. We further explore the mechanics generating SOPTs on the basis of synaptic weight dynamics.     

高光谱成像技术的柑橘植株叶片含氮量预测模型

氮素是果树生长发育的一种大量必需元素,及时准确地监控果树的氮营养状况,对果树的合理施肥、增产、优化果实品质以及减缓过量施氮引起的水资源污染具有重要意义。利用高光谱成像技术结合多变量统计学方法,建立了柑橘植株叶片的含氮量预测模型。研究步骤为：高光谱扫描、提取平均光谱曲线、预处理原始光谱数据、采用连续投影法提取特征波段和建立含氮量预测模型。从SG平滑、SNV、MSC、1-Der等11种预处理方法中筛选出的较优预处理方法是SG平滑、Detrending和SG平滑-Detrending。对应这三种最优预处理方法,先采用连续投影法挑选出各自的特征波长,然后将各特征波段下的光谱反射率作为偏最小二乘、多元线性回归和反向传播人工神经网络模型的输入,各自建立三个预测模型。从以上获得的9个预测模型中,得出两个最优模型SG平滑-Detrending-SPA-BPNN(R_p：0.851 3,RMSEP：0.188 1)和Detrending-SPA-BPNN(R_p：0.8609,RMSEP：0.159 5)。结果表明,利用高光谱数据测定柑橘叶片含氮量具有可行性。这为实时、准确地监控柑橘植株生长过程中叶片含氮量的变化以及合理科学的氮肥施加提供了一定的理论基础。