Self-similarity of multilayer networks

Research on the self-similarity of multilayer networks is scarce, when compared to the extensive research conducted on the dynamics of these networks. In this paper, we use entropy to determine the edge weights in each sub-network,and apply the degree–degree distance to unify the weight values of connecting edges between different sub-networks, and unify the edges with different meanings in the multilayer network numerically. At this time, the multilayer network is compressed into a single-layer network, also known as the aggregated network. Furthermore, the self-similarity of the multilayer network is represented by analyzing the self-similarity of the aggregate network. The study of self-similarity was conducted on two classical fractal networks and a real-world multilayer network. The results show that multilayer networks exhibit more pronounced self-similarity, and the intensity of self-similarity in multilayer networks can vary with the connection mode of sub-networks.

Honeycomb-spiderweb-inspired self-similar hybrid cellular structures for impact applications

Inspired by nature's self-similar designs,novel honeycomb-spiderweb based self-similar hybrid cellular structures are proposed here for efficient energy absorption in impact applications.The energy absorption is enhanced by optimizing the geometry and topology for a given mass.The proposed hybrid cellular structure is arrived after a thorough analysis of topologically enhanced self-similar structures.The optimized cell designs are rigorously tested considering dynamic loads involving crush and high-velocity bullet impact.Furthermore,the influence of thickness,radial connectivity,and order of patterning at the unit cell level are also investigated.The maximum crushing efficiency attained is found to be more than 95%,which is significantly higher than most existing traditional designs.Later on,the first and second-order hierarchical self-similar unit cell designs developed during crush analysis are used to prepare the cores for sandwich structures.Impact tests are performed on the developed sandwich structures using the standard 9-mm parabellum.The influence of multistaging on impact resistance is also investigated by maintaining a constant total thickness and mass of the sandwich structure.Moreover,in order to avoid layer-wise weak zones and hence,attain a uniform out-of-plane impact strength,off-setting the designs in each stage is proposed.The sandwich structures with first and second-order self-similar hybrid cores are observed to withstand impact velocities as high as 170 m/s and 270 m/s,respectively.

基于色散渐减光纤的自相似子激光器优化设计

为了提高自相似子激光器可容忍的最高增益饱和能量,基于脉冲在色散渐减光纤(DDF)中进行自相似演化时具有较强抗光波分裂特性的原理,采用DDF替代自相似子激光器中的单模光纤(SMF)的方法,进行了理论分析和仿真验证。结果表明,DDF替代SMF后,激光器可容忍的最高增益饱和能量增大33.3%,激光器的输出脉冲能量提高109.2%,脉冲峰值功率提高20.6%,脉宽缩短23.1%,自相似评价因子从0.077降低到0.065;在自相似子激光器中利用DDF替代SMF进行脉冲演化可有效提高激光器的最大增益饱和能量,进而使激光器的输出自相似脉冲的脉冲能量更大、脉冲峰值功率更高、脉宽更窄、脉冲质量更高。此研究对获取高功率自相似脉冲具有一定参考价值。

自相似锁模超短脉冲掺铒光纤激光器

设计并搭建了自相似锁模超短脉冲光纤激光器和掺铒光纤放大器,在种子源部分,利用自制的碳纳米管可饱和吸收体结合色散管理的方式,控制腔内净色散为微正色散产生了自相似抛物线型锁模脉冲,并以此作为种子源进行后续的功率放大和光谱展宽。光纤放大级采用的是双向泵浦的方式,通过高增益低色散的掺铒光纤将种子光充分增益后,得到输出功率39.51 mW、光谱宽度38.11 nm、放大增益20.65 dB的激光输出。最后,采用普通单模光纤对放大后的自相似锁模脉冲进行压缩,获得压缩后脉冲宽度283 fs的超短脉冲激光输出。

全光纤自相似锁模激光器实验及理论研究

在锁模光纤激光器中,本研究基于高集成度器件同时实现了泵浦耦合、光谱滤波和偏振相关隔离损耗,进而在1550 nm波段实现了自相似被动锁模脉冲输出。同时还搭建了全光纤放大器进行非线性增益管理放大,成功将自相似脉冲的10 dB谱宽从25.9 nm拓宽至52.6 nm,然后利用负色散光纤将脉冲宽度压窄至66 fs。最后,基于广义非线性薛定谔方程与激光速率方程的数值模拟,从理论上研究了激光器和光纤放大器的脉冲运转过程。模拟结果表明腔内的窄带滤波器和较长的正色散增益光纤是线性啁啾自相似锁模脉冲产生的必要条件,当自相似脉冲被光纤预压缩后,使用足够长度的正色散增益光纤可同时实现脉冲的自相似放大以及非线性增益管理放大,从而在全光纤结构中输出脉宽小于100 fs的锁模脉冲。

Self-similar very singular solution of a p-Laplacian equation with gradient absorption: existence and uniqueness

This paper investigates the self-similar singular solution of the p-Laplacian evolution equation with the nonlinear gradient absorption terms u t=div(u p-2u)-uq for 1<p<2 and q>in Rn× (0, ∞). It has been proved that when 1<q<p-n/(n+1) there exists a unique self-similar very singular solution.

基于相似日筛选与组合深度学习模型的日前电价预测方法

准确的日前电价预测是市场运行和政策规划的基础,而市场披露信息是电价预测的重要依据。提出了引入Self-attention机制的CNN-GRU组合深度学习电价预测模型。首先,针对山西电力现货市场交易流程及日前电价形成机制,采用最大互信息系数法对市场披露的日前边界条件等信息数据进行特征提取,以确定电价关键影响因素及其权重系数。其次,基于加权灰色关联度的历史相似日筛选方法生成电价预测历史数据集,并挖掘电价及其特征的内部变化规律。然后,基于历史数据集,采用引入Self-attention机制的CNN-GRU模型得到预测电价。最后,通过算例验证了所提预测方法的有效性及准确性。

融合相似预报方法在陇东南短期强降水预报中的应用

基于逐步过滤相似法和自组织映射(SOM)神经网络方法,提出了一种融合相似预报方法。利用ECMWF模式预报产品、ERA5再分析资料和地面气象台站观测数据,使用该方法对2021-2022年陇东南地区开展了时效为72 h的强降水预报试验,并对预报效果进行了检验。结果表明:(1)融合相似预报方法的TS评分处于4.5%~9.1%之间,与ECMWF模式预报结果相比表现出一定的优势。随着预报时效的增长,强降水预报的TS评分呈现减小的趋势,其在08:00(北京时,下同)起报的TS评分相对较高。(2)相比于单独使用逐步过滤相似预报,融合相似预报方法的准确性有所提升,并能在一定程度上降低空报率。其中08:00起报和20:00起报的TS评分提高了1.31%和0.63%,而FAR同时下降了2.39%和1.25%。

A NEGATIVE ANSWER TO A CONJECTURE ON SELF-SIMILAR SETS WITH OPEN SET CONDITION

Zhou and Feng posed a conjecture on self-similar set in 2004. In this paper, a self-similar set is constructed which has a best covering but its natural covering is not a best one. Thus, we indeed give a negative answer to the conjecture.

AN ANSWER TO A CONJECTURE ON SELF-SIMILAR SETS

In this paper, we construct a self-similar set which has a best covering but it is not the natural covering, thus negate the conjecture on self-similar sets posed by Z. Zhou in 2004.

An Intrusion Alarming System Based on Self-Similarity of Network Traffic

Intrusion detection system ean make effective alarm for illegality of networkusers, which is absolutely necessarily and important to build security environment of communicationbase service According to the principle that the number of network traffic can affect the degree ofself-similar traffic, the paper investigates the variety of self-similarity resulted fromunconventional network traffic. A network traffic model based on normal behaviors of user isproposed and the Hursl parameter of this model can be calculated. By comparing the Hurst parameterof normal traffic and the self-similar parameter, we ean judge whether the network is normal or notand alarm in time.

THE REGULARITY OF RANDOM GRAPH DIRECTED SELF-SIMILAR SETS

A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..

MULTIRESOLUTION ANALYSIS, SELF-SIMILAR TILINGS AND HAAR WAVELETS ON THE HEISENBERG GROUP

In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L^2（H^d） by using self-similar tilings for the acceptable dilations on the Heisenberg group.

Spatiotemporal self-similar solutions for the nonautonomous (3+1)-dimensional cubic-quintic Gross-Pitaevskii equation

With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous （3＋1）-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction, nonlinearity, harmonic potential and gain or loss when two constraints are satisfied. These constraints between the system parameters hint that self-similar solutions form and transmit stably without the distortion of shape based on the exact balance between the diffraction, nonlinearity and the gain/loss. Based on these analytical results, we investigate the dynamic behaviours in a periodic distributed amplification system.

ON THE SELF-SIMILAR SOLUTIONS OF THE MAGNETO-HYDRO-DYNAMIC EQUATIONS

In this paper, we show that, for the three dimensional incompressible magnetohydro-dynamic equations, there exists only trivial backward self-similar solution in L^p（R^3） for p ≥ 3, under some smallness assumption on either the kinetic energy of the self-similar solution related to the velocity field, or the magnetic field. Second, we construct a class of global unique forward self-similar solutions to the three-dimensional MHD equations with small initial data in some sense, being homogeneous of degree -1 and belonging to some Besov space, or the Lorentz space or pseudo-measure space, as motivated by the work in [5].

SELF-SIMILAR SOLUTIONS TO THE HYPERBOLIC MEAN CURVATURE FLOW

This article concerns the self-similar solutions to the hyperbolic mean curvature flow （HMCF） for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity.

On the Self-Similarity in Biological Processes

We show that the processes described by Avrami functions are self-similar. A comparative function characterizes a self-similar process by a certain Avrami exponent. We define the self-similar categories of some well-known biological processes. The method to determine the Avrami exponent by choosing the comparative function is demonstrated on the diffusion model of the growth of nuclei. We generalize the results.

SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM

In this article, we consider a two-component nonlinear shallow water system, which includes the famous 2-component Camassa-Holm and Degasperis-Procesi equations as special cases. The local well-posedess for this equations is established. Some sufficient conditions for blow-up of the solutions in finite time are given. Moreover, by separation method, the self-similar solutions for the nonlinear shallow water equations are obtained, and which local or global behavior can be determined by the corresponding Emden equation.

The Exact Measure Functions of the Images for a Class of Self-Similar Processes

Let X= (Ω, ■, ■_t, X_t,, θ_t, p~x) be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the image X([0,t] ) are obtained.

The effect of gravity on self-similarity of Worthington jet after water entry of a two-dimensional wedge

The effect of gravity on the self-similarity of jet shape at late stage of Worthington jet development is investigated by experiment in the study.In addition,the particle image velocimetry(PIV)method is introduced to analyze the development of flow field.There is a linear scaling regarding the axial velocity of the jet and the scaling coefficient increases with the Froude number.