Linear analysis of degree correlations in complex networks

Many real-world networks such as the protein–protein interaction networks and metabolic networks often display nontrivial correlations between degrees of vertices connected by edges. Here, we analyse the statistical methods used usually to describe the degree correlation in the networks, and analytically give linear relation in the degree correlation. It provides a simple and interesting perspective on the analysis of the degree correlation in networks, which is usefully complementary to the existing methods for degree correlation in networks. Especially, the slope in the linear relation corresponds exactly to the degree correlation coefficient in networks, meaning that it can not only characterize the level of degree correlation in networks, but also reflects the speed that the average nearest neighbours’ degree varies with the vertex degree. Finally, we applied our results to several real-world networks, validating the conclusions of the linear analysis of degree correlation. We hope that the work in this paper can be helpful for further understanding the degree correlation in complex networks.     

面向低强度无线网络信号接收谱参数估计研究

针对以北斗卫星导航信号为代表的亚纳秒级的低强度无线网络信号在定位中难以获取精确时间估计及角度估计,且易受环境噪声影响,使其定位精度不高等难题,本文提出了基于亚纳秒级的低强度无线网络信号接收谱参数估计方法。首先通过抽样方式,将发射信号抽样为多维独立子信号并独立建模,通过构造噪声空间与子信号空间在对应列向量正交化的基础上精确获取TOA估计;随后利用复数域映射,在获取TOA估计基础上采取比对方式精确地获取DOA估计。最后对本文参数估计方法进行了精度分析。测试数据显示：与 PM算法、ESPRIT算法相比,本文技术在TOA及DOA估计上更为精确;同时在信号强度低且背景噪声干扰严重的情况下,本文方法仍可有效的维持参数估计精度。     

快脉冲直线变压器驱动源模块的原理及实验

 介绍了直线型变压器驱动源（LTD）产生快脉冲的基本原理及技术优势,阐述了快脉冲LTD模块设计的要点,设计了输出脉冲上升时间小于100 ns的快脉冲LTD模块,并进行了初步的实验研究。实验得到该LTD模块充电±16 kV时,短路放电的电流峰值为23.7 kA,电流振荡1/4周期为69.6 ns;充电±50 kV驱动0.85 Ω负载时,电流峰值为41.4 kA,上升时间为36.8 ns（10%~90%）和60.8 ns（0~100%）。     

薄膜法布里-珀罗滤光片中的超棱镜效应

基于薄膜法布里珀罗滤光片在其峰值波长处具有较大群延迟的特性,设计并从实验上验证了光束倾斜入射时这种结构中存在的超棱镜效应。根据光学薄膜理论中的特征矩阵法,数值模拟计算了器件的群延迟和空间色散曲线,镀制并对器件进行了测试。测试结果表明器件在透射峰值波长处因超棱镜效应引起的空间色散最大位移值达到65μm,与理论计算结果非常吻合;相对于传统的光栅和棱镜器件而言器件具有更高的空间角度色散,实际测试在784.5 nm至786.5 nm波长范围内器件的角色散达到30°/nm。     

Generation of Bianchi type V cosmological models with varying Λ-term

Bianchi type V perfect fluid cosmological models are investigated with cosmological term varying with time. Using a generation technique (Camci et al., 2001), it is shown that Einsteins field equations are solvable for any arbitrary cosmic scale function. Solutions for particular forms of cosmic scale functions are also obtained. The cosmological constant is found to be a decreasing function of time, which is supported by results from recent type Ia supernovae observations. Some physical aspects of the models are also discussed.     

Periodic Solutions for Completely Resonant Nonlinear Wave Equations with Dirichlet Boundary Conditions

We consider the nonlinear string equation with Dirichlet boundary conditions u_tt–u_xx=(u), with (u)=u³+O(u⁵) odd and analytic, 0, and we construct small amplitude periodic solutions with frequency for a large Lebesgue measure set of close to 1. This extends previous results where only a zero-measure set of frequencies could be treated (the ones for which no small divisors appear). The proof is based on combining the Lyapunov-Schmidt decomposition, which leads to two separate sets of equations dealing with the resonant and non-resonant Fourier components, respectively the Q and the P equations, with resummation techniques of divergent powers series, allowing us to control the small divisors problem. The main difficulty with respect to the nonlinear wave equations u_tt–u_xx+Mu=(u), M0, is that not only the P equation but also the Q equation is infinite-dimensional.     

Characterization of electrical charge separation at the interface of two aqueous solutions in the presence of concentration gradients and cation/anion mobility ratio asymmetry

Physical consequences of ionic diffusion processes play a major role on the outcome of electrophysiology experiments due to both their contribution to the ionic transmembrane transport and phenomena taking place at the measuring instruments interface. As most of the time heterogenities in biological media with respect to ionic diffusion constants are disregarded, we intended to look upon the general case of ionic diffusion at the interface of two liquids on which gradients of these diffusion constants no longer can be neglected. We developed a theoretical model for the diffusion potential which emerges at an aqueous interface under gradients of concentration and diffusion constants. The experimental validation of our model was achieved through potential difference measurements of the diffusion potential between two solutions containing sodium chloride (NaCl) and glycerine solutions of various concentrations. Within the studied domain of the electrical charge mobility ratio, we noticed that experimental results are in agreement with the theoretically inferred diffusion potential values. This demonstrates that the resulting relationship for the diffusion potential inferred from our model could be applied for other cases, as well. When the ionic solutions contains an indefinite quantity of glycerine or an unknown substance able to modify diffusion constants of sodium and chloride, it was shown that through measurements of the diffusion potential one can infer the unknown concentration of glycerine and the modified ionic mobility ratio. This, in turn, builds up the foundation for a novel yet simple and efficient analitycal sensing device for quantitative determination in the field.