Simulation for chaos game representation of genomes by recurrent iterated function systems

Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), respectively. In this paper, we consider the CGR of three kinds of sequences from complete genomes: whole genome DNA sequences, linked coding DNA sequences and linked protein sequences. Some fractal patterns are found in these CGRs. A recurrent iterated function systems (RIFS) model is proposed to simulate the CGRs of these sequences from genomes and their induced measures. Numerical results on 50 genomes show that the RIFS model can simulate very well the CGRs and their induced measures. The parameters estimated in the RIFS model reflect information on species classification.

Cantor Type Fixed Sets of Iterated Multifunction Systems Corresponding to Self-Similar Networks

We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph models introduced by Barabási, Ravasz and Vicsek ([1] [2]). We generalize the graph models using stars and cliques: both algorithm construct graph sequences such that the next iteration is always based on n replicas of the current iteration, where n is the size of the initial graph structure, being a star or a clique. We analyze these self-similar graph sequences using IMSs in function of the size of the initial star and clique, respectively. Our research uses the Cantor set for the description of the fixed set of these IMSs, which we interpret as the limit object of the analyzed self-similar networks.

ERGODIC THEOREM FOR INFINITE ITERATED FUNCTION SYSTEMS

A set of contraction maps of a metric space is called an iterated function systems. Iterated function systems with condensation, can be considered infinite iterated function systems. Infinite iterated function systems on compact metric spaces were studied. Using the properties of Banach limit and uniform contractiveness, it was proved that the random iterating algorithms for infinite iterated function systems on compact metric spaces-satisfy ergodicity. So the random iterating algorithms for iterated function systems with condensation satisfy ergodicity, too.

AFFINE TRANSFORMATION IN RANDOM ITERATED FUNCTION SYSTEMS

Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.

SOME NEW ITERATED FUNCTION SYSTEMS CONSISTING OF GENERALIZED CONTRACTIVE MAPPINGS

Iterated function systems （IFS） were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahu and A. Chakraborty introduced K-Iterated Function System using Kannan mapping which would cover a larger range of mappings. In this paper, following Hutchinson, D. R. Sahu and A. Chakraborty, we present some new iterated function systems by using the so-called generalized contractive mappings, which will also cover a large range of mappings. Our purpose is to prove the existence and uniqueness of attractors for such class of iterated function systems by virtue of a Banach-like fixed point theorem concerning generalized contractive mappings.

Fixed Point Theorems of the Iterated Function Systems

In this paper, we present some fixed point theorems of iterated function systems consisting of α-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function systems consisting of Banach contractive mappings in Fractal space constituted by the compact subset of generalized metric space, which is Mso extensively applied in topological dynamic system.

Iterated Function System-Based Crossover Operation for Real-Coded Genetic Algorithm

An iterated function system crossover (IFSX) operation for real-coded genetic algorithms (RCGAs) is presented in this paper. Iterated?function system (IFS) is one type of fractals that maintains a similarity characteristic. By introducing the IFS into the crossover operation, the RCGA performs better searching solution with a faster convergence in a set of benchmark test functions.

基于GRU的仪表着陆系统故障预测方法研究

故障预测技术在保障仪表着陆系统的可靠运行、提高空管效能等方面具有重要应用价值。结合仪表着陆系统运行特征和实际运行维护工作,提出一种基于GRU的仪表着陆系统故障预测方法。以航向信标为研究对象,在分析其监控参数与设备运行状态之间的关系后,将监控参数作为故障特征参数;根据监控参数时间步长、时变性特征显著的特点,采用GRU预测监控参数的未来变化趋势;根据监控参数的隶属函数计算出参数未来时刻可能发生“故障”的概率,实现对航向信标故障的预测。结果表明:基于GRU的仪表着陆系统预测方法的相对预测精度在95%以上。

建筑智能化系统顶层设计方法探讨

通过自上而下地展开,吸收质量功能配置的思想,对建设过程中影响智能化系统的因素进行统筹考量。通过逐层迭代的方式,直观展示不同技术方案对业主满意度的影响,为建筑设计提供可比较的方案效益评价,也为设计明确后续技术路径。

基于转矩跟踪电流误差校正的压缩机转速脉动抑制算法研究

针对空调用永磁压缩机在低频运行中存在转速脉动大、振动噪声高等问题,提出一种基于转矩跟踪电流误差校正的压缩机转速脉动抑制算法。首先对压缩机的周期性转速脉动进行分析,并根据转速脉动特性建立转速环控制系统模型。然后引入迭代学习算法,获得转矩跟踪电流,在此基础上,提出特征滤波函数,用来提取转矩跟踪电流基波分量,有效抑制特定次频率的转速脉动,同时引入转矩跟踪电流误差校正律,对转矩跟踪电流与参考交轴电流的误差进行校正,进一步获得前馈补偿电流,并施加到参考交轴电流中,可以消除传统迭代学习转矩跟踪电流存在的误差累积,跟踪性能好。最后,在空调压缩机实验平台上对算法进行验证,实验结果表明,所提算法可以显著抑制压缩机的转速脉动。

自适应迭代学习控制的发展现状与展望

本文在不同问题框架下阐述了自适应迭代学习控制方法的研究现状,并介绍了该领域未来的一些研究方向.首先,简要概述了自适应迭代学习控制的分析方法与控制器结构;其次,从系统的结构特征和运行特征两个角度,讨论了近年来自适应迭代学习控制领域的研究热点,包括非参数型不确定性、输入不确定性、状态受限、状态不可测、非重复运动等关键问题.针对每一类问题,指出了自适应迭代学习控制器的设计和分析特点;然后,探讨了数据驱动自适应迭代学习控制的设计方法;最后,提出了自适应迭代学习控制领域的一些开放性的、具有挑战性的关键问题,亟待进一步研究和探索.

匹多莫德治疗小儿呼吸系统反复感染的临床效果

目的探讨匹多莫德治疗小儿呼吸系统反复感染的临床效果。方法选取2022年1月至12月安丘市人民医院治疗的96例呼吸系统反复感染患儿作为研究对象,按照随机数字表法分为对照组和观察组,每组各48例。对照组采用美洛西林钠联合布地奈德治疗,观察组在对照组基础上采用匹多莫德治疗。比较两组炎症因子水平、免疫球蛋白水平、临床症状消失时间、肺功能、临床疗效、不良反应发生情况和再次感染情况。结果治疗后,观察组γ干扰素、白细胞介素-2水平高于对照组,肿瘤坏死因子-α、白细胞介素-4水平低于对照组(P<0.05);观察组各项临床症状消失时间均短于对照组(P<0.05);观察组免疫球蛋白A、免疫球蛋白G、免疫球蛋白M水平均高于对照组(P<0.05);观察组第1秒用力呼气容积、用力肺活量、最高呼气流速变异率、一秒率水平均高于对照组(P<0.05);观察组临床总有效率高于对照组(P<0.05);观察组不良反应总发生率低于对照组(P<0.05);观察组再次感染次数少于对照组,再感染持续时间短于对照组(P<0.05)。结论匹多莫德治疗小儿呼吸系统反复感染的临床效果较好,值得推广。

Observer-based Adaptive Iterative Learning Control for Nonlinear Systems with Time-varying Delays

An observer-based adaptive iterative learning control （AILC） scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality （LMI） method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative （PID） feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function （CEF）, we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.

Chaos game representation of functional protein sequences,and simulation and multifractal analysis of induced measures

Investigating the biological function of proteins is a key aspect of protein studies. Bioinformatic methods become important for studying the biological function of proteins. In this paper, we first give the chaos game representation （CGR） of randomly-linked functional protein sequences, then propose the use of the recurrent iterated function systems （RIFS） in fractal theory to simulate the measure based on their chaos game representations. This method helps to extract some features of functional protein sequences, and furthermore the biological functions of these proteins. Then multifractal analysis of the measures based on the CGRs of randomly-linked functional protein sequences are performed. We find that the CGRs have clear fractal patterns. The numerical results show that the RIFS can simulate the measure based on the CGR very well. The relative standard error and the estimated probability matrix in the RIFS do not depend on the order to link the functional protein sequences. The estimated probability matrices in the RIFS with different biological functions are evidently different. Hence the estimated probability matrices in the RIFS can be used to characterise the difference among linked functional protein sequences with different biological functions. From the values of the Dq curves, one sees that these functional protein sequences are not completely random. The Dq of all linked functional proteins studied are multifractal-like and sufficiently smooth for the Cq （analogous to specific heat） curves to be meaningful. Furthermore, the Dq curves of the measure μ based on their CCRs for different orders to link the functional protein sequences are almost identical if q 〉 0. Finally, the Ca curves of all linked functional proteins resemble a classical phase transition at a critical point.

ON THE EXISTENCE AND UNIQUENESS THEOREMS OF SOLUTIONS FOR THE SYSTEMS OF MIXED MONOTONE OPERATOR EQUATIONS WITH APPLICATIONS

The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].

ON THE BOX DIMENSION FOR A CLASS OF NONAFFINE FRACTAL INTERPOLATION FUNCTIONS

We present lower and upper bounds for the box dimension of the graphs of certain nonaffine fractal interpolation functions by generalizing the results that hold for the affine case.

An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems

This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

CONSTRUCTION OF SOME KIESSWETTER-LIKE FUNCTIONS-THE CONTINUOUS BUT NON-DIFFERENT-IABLE FUNCTION DEFINED BY QUINARY DECIMAL

In this paper, we construct some continuous but non-differentiable functions defined by quinary dec-imal, that are Kiesswetter-like functions. We discuss their properties, then investigate the Hausdorff dimensions of graphs of these functions and give a detailed proof.

Graph-Directed Coalescence Hidden Variable Fractal Interpolation Functions

Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article, graph directed iterated function system for a finite number of generalized data sets is considered and it is shown that the projection of the attractors on is the graph of the CHFIFs interpolating the corresponding data sets.

Discussion of stability in a class of models on recurrent wavelet neural networks

Based on wavelet neural networks （WNNs） and recurrent neural networks （RNNs）, a class of models on recurrent wavelet neural networks （RWNNs） is proposed. The new networks possess the advantages of WNNs and RNNs. In this paper, asymptotic stability of RWNNs is researched.according to the Lyapunov theorem, and some theorems and formulae are given. The simulation results show the excellent performance of the networks in nonlinear dynamic system recognition.