Root N Bandwidth Selection

Motivated by applications of distributed linear estimation, distributed control, and distributed optimization, we consider the question of designing linear iterative algorithms for computing the average of numbers in a network. Specifically, our interest is in designing such an algorithm with the fastest rate of convergence given the topological constraints of the network. As the main result of this paper, we design an algorithm with the fastest possible rate of convergence using a nonreversible Markov chain on the given network graph. We construct such a Markov chain by transforming the standard Markov chain, which is obtained using the Metropolis-Hastings method. We call this novel transformation <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pseudo-lifting</i> . We apply our method to graphs with geometry, or graphs with doubling dimension. Specifically, the convergence time of our algorithm (equivalently, the mixing time of our Markov chain) is proportional to the diameter of the network graph and hence optimal. As a byproduct, our result provides the fastest mixing Markov chain given the network topological constraints, and should naturally find their applications in the context of distributed optimization, estimation and control.

Cardiomyopathy refers to gradual weakening of the muscular walls of the cardiac chambers. Due to the hypertrophic condition of the muscular walls, damage and stretching of the muscle may lead to arrhythmias, which is detectable using the ECG. In the past, any deviations from a healthy rhythm provide cardiologists with accurate information regarding the heart condition. However, cardiologists are prone to making inaccurate interpretation from the visual observation, leading to erroneous diagnosis. Hence, this paper proposes a computerized method for accurate analysis and detection of cardiomyopathy disease using MLP network. Data for normal, cardiomyopathy, and other arrhythmias were obtained from the PTB Diagnostic ECG database. The raw signals were preprocessed for high-frequency noise removal using median and moving average filters. Baseline corrections were conducted using two-stage polynomial fitting method. Nine time-based features were extracted from the three bipolar limb leads. A total of 600 beats were used to train, validate and test five different MLP network structures. Four different learning algorithms were implemented to obtain the best classification accuracy and fastest convergence rate. Results show that the Levenberg-Marquardt algorithm shows the highest average classification accuracy of 98.9% for the different structures with the fastest average convergence rate of 12 epochs.

Consensus conditions and convergence speeds are crucial for distributed consensus algorithms of networked systems. Based on a basic first-order average-consensus protocol with time-varying topologies and additive noises, this paper first investigates its critical consensus condition on network topology by stochastic approximation frameworks. A new joint-connectivity condition called extensible joint-connectivity that contains a parameter $\delta$ (termed the extensible exponent) is proposed. With this and a balanced topology condition, we show that a critical value of $\delta$ for consensus is $1/2$ . Optimization on convergence rate of this protocol is further investigated. It is proved that the fastest convergence rate, which is the theoretic optimal rate among all controls, is of the order $1/t$ for the best topologies, and is of the order $1/t^{1-2\delta }$ for the worst topologies, which are balanced and satisfy the extensible joint-connectivity condition. For practical implementation, certain open-loop control strategies are introduced to achieve consensus with a convergence rate of the same order as the fastest convergence rate. Furthermore, a consensus condition is derived for nonstationary and strongly correlated random topologies. The algorithms and consensus conditions are applied to distributed consensus computation of mobile ad-hoc networks; and their related critical exponents are derived from relative velocities of mobile agents for guaranteeing consensus.

The capacitated arc routing problem (CARP) is a classical NP-Hard combinatorial optimization problem. In this paper, we present a memetic algorithm based on Extension step and Statistical filtering for Large-Scale CARP (ESMAENS) which has improvements in both the global search strategy and the local search strategy. Firstly, ESMAENS adopts the Route Distance Grouping decomposition scheme (RDG) to decompose the large-scale CARP into some independent sub-problems. Then, the initial population would evolve into a new group by using the Evolutionary Algorithm. Furthermore, ESMAENS introduces the extension step search strategy to search the potential solutions around the current solution. As a result, with the increase of the iteration number, it avoids getting to the premature convergence. Meanwhile, the diversity of the population can be increased. Finally, in the local search strategy, the statistical filter is used to filter out some solutions and make the algorithm get the lower bound at a faster convergence rate with a high stability. Compared with RDG-MAENS, experimental results on Beullen’C, D, E, F, egl and EGL-G test set show that ESMAENS has a better convergence rate, and the stability of solutions obtained is improved. Furthermore, ESMAENS achieves a global search for the solutions. Especially for the large-scale EGL-G test set, ESMAENS can converge to a lower bound at a faster convergence rate, and it is suitable for solving large-scale CARP.

This study aims to provide a robust trajectory tracking controller which guarantees the prescribed performance of a robot manipulator, both in transient and steady-state modes, experiencing parametric uncertainties. The main core of the controller is designed based on the adaptive finite-time sliding mode control (SMC) and extreme learning machine (ELM) methods to collectively estimate the parametric model uncertainties and enhance the quality of tracking performance. Accordingly, the global estimation with a fast convergence rate is achieved while the tracking error and the impact of chattering on the control input are mitigated significantly. Following the control design, the stability of the overall control system along with the finite-time convergence rate is proved, and the effectiveness of the proposed method is investigated via extensive simulation studies. The results of simulations confirm that the prescribed transient and steady-state performances are obtained with enough accuracy, fast convergence rate, robustness, and smooth control input which are all required for practical implementation and applications.

Noise and interference are the two most common and basic problems in wireless communication systems. The noise in wireless communication channels has the characteristics of randomness and impulsivity, so the performance of adaptive filtering algorithms based on geometric algebra (GA) and second-order statistics is greatly reduced in the wireless communication systems. In order to improve the performance of adaptive filtering algorithms in wireless communication systems, this paper proposes two novel GA-based adaptive filtering algorithms, which are deduced from the robust algorithms based on the minimum error entropy (MEE) criterion and the joint criterion (MSEMEE) of the MEE and the mean square error (MSE) with the help of GA theory. The noise interference in wireless communication is modeled by alpha-stable distribution which is in good agreement with the actual data in this paper. Simulation results show that for the mean square deviation (MSD) learning curve, the GA-based MEE (GA-MEE) algorithm has faster convergence rate and better steady-state accuracy compared to the GA-based maximum correntropy criterion algorithm (GA-MCC) under the same generalized signal-to-noise ratio (GSNR). The GA-MEE algorithm reduces the convergence rate, but improves the steady-state accuracy by 10–15 dB compared to the adaptive filtering algorithms based on GA and second-order statistics. For GA-based MSEMEE (GA-MSEMEE) algorithm, when GA-MSEMEE and the adaptive filtering algorithms based on GA and second-order statistics keep the same convergence rate, its steady-state accuracy is improved by 10–15 dB, and when GA-MSEMEE and GA-MEE maintain approximately steady-state accuracy, its convergence rate is improved by nearly 100 iterations. In addition, when the algorithms are applied to noise cancellation, the average recovery error of the two proposed algorithms is 7 points lower than that of other GA-based adaptive filtering algorithms. The results validate the effectiveness and superiority of the GA-MEE and GA-MSEMEE algorithms in the alpha-stable noise environment, providing new methods to deal with multi-channel interference in wireless networks.

In this paper, we build bounded error observers for a common class of partially known bioreactor models. The main idea is to construct hybrid bounded observers "between" high gain observer, which has an adjustable convergence rate but requires perfect knowledge of the model, and asymptotic observer which is very robust towards uncertainty but has a fixed convergence rate. An hybrid bounded error observer which reconstructs the two state variables is constructed considering two steps: first step is similar to a high gain observer meaning that fast convergence rate but error depending on the knowledge of the model are obtained; second step is a switch to an observer similar to the asymptotic one meaning that fixed convergence rate towards an error as small as desired is obtained. Thus, a better convergence rate of estimated variables than the classical asymptotic observer is obtained.

Motivated by classical vortex blob methods for the Euler equations, we develop a numerical blob method for the aggregation equation. This provides a counterpoint to existing literature on particle methods. By regularizing the velocity field with a mollifier or “blob function”, the blob method has a faster rate of convergence and allows a wider range of admissible kernels. In fact, we prove arbitrarily high polynomial rates of convergence to classical solutions, depending on the choice of mollifier. The blob method conserves mass and the corresponding particle system is energy decreasing for a regularized free energy functional and preserves the Wasserstein gradient flow structure. We consider numerical examples that validate our predicted rate of convergence and illustrate qualitative properties of the method.

A well-known clustering algorithm is K-means. This algorithm, besides advantages such as high speed and ease of employment, suffers from the problem of local optima. In order to overcome this problem, a lot of studies have been done in clustering. This paper presents a hybrid Extended Cuckoo Optimization Algorithm (ECOA) and K-means (K), which is called ECOA-K. The COA algorithm has advantages such as fast convergence rate, intelligent operators and simultaneous local and global search which are the motivations behind choosing this algorithm. In the Extended Cuckoo Algorithm, we have enhanced the operators in the classical version of the Cuckoo algorithm. The proposed operator of production of the initial population is based on a Chaos trail whereas in the classical version, it is based on randomized trail. Moreover, allocating the number of eggs to each cuckoo in the revised algorithm is done based on its fitness. Another improvement is in cuckoos’ migration which is performed with different deviation degrees. The proposed method is evaluated on several standard data sets at UCI database and its performance is compared with those of Black Hole (BH), Big Bang Big Crunch (BBBC), Cuckoo Search Algorithm (CSA), traditional Cuckoo Optimization Algorithm (COA) and K-means algorithm. The results obtained are compared in terms of purity degree, coefficient of variance, convergence rate and time complexity. The simulation results show that the proposed algorithm is capable of yielding the optimized solution with higher purity degree, faster convergence rate and stability in comparison to the other compared algorithms.

In our previous research applied to the job shop scheduling problem (JSSP) for machine tool production, the multi-objective optimisation model based on the particle swarm optimization (PSO) research had an imbalance performance between the convergence rate and the convergence precision. In this article, a new hybrid algorithm using PSO and generic algorithm (GA) is proposed to solve this particular problem. In this new algorithm, named hybrid PSO-GA algorithm (HPGA), the PSO algorithm is redefined and modified by introducing genetic operators, i.e. the crossover operator and the mutation operator, to update the particles in the population. The HPGA is then applied in heavy machinery company with minimising machines’ makespan and minimising jobs’ tardiness as the two optimal objectives. The comparisons with actual application report have illustrated that the proposed HPGA can obtain higher quality of schedule solution for machine tool production. Furthermore, with solution quality and convergence rate as the two estimation measurements metrics, some comparisons are performed in order to illustrate that the HPGA has superiority over the PSO, GA and simulated annealing algorithm (SA). Results have indicated that, with the combination of the merits of PSO and GA, the proposed HPGA approach can achieve not only better solution quality but also faster convergence rate than the PSO, GA and SA, within a reasonable computation time for high dimensions JSSP.

In this paper the new iterative learning control algorithm is proposed and its properties are derived. An important characteristic of the algorithm is that they use the polynomial representations of the inverse plant G to construct the new control law. The approach is based on the parameter optimization through a quadratic performance index which its solution will convert in norm to zero. It is capable to produce an improvement to the convergence rate. As the number of polynomial term increases, faster convergence rate is accomplished and the ideal plant inverse algorithm is approached. A comparison between the proposed algorithm and the inverse type parameter optimal ILC is also presented based significantly on the convergence rate.

Traditional equalization algorithms for multiple input multiple output (MIMO) systems suffer from high complexity and low convergence rate. So an improved adaptive reduced-rank joint detection algorithm of multistage Wiener filter (MSWF) based on rectangle blocking matrices is proposed. The MSWF is implemented by the correlation subtraction algorithm (CSA) structure and is called unitary multistage Wiener filter (UMSWF). The new scheme adopts rectangle submatrix as blocking matrix, which is chosen from the square blocking matrix for UMSWF. The proposed algorithm can reduce the size of the observation data vectors step by step in the forward recursion decomposition of UMSWF. Thus, the computational complexity is reduced and the convergence rate is increased. Theoretical analysis and simulation results show that this improved adaptive reduced-rank joint detection algorithm of UMSWF based on rectangle blocking matrix has better performance such as lower complexity and faster convergence rate. In particular, simulations are conducted in the vertical-Bell Labs layered space-time (V-BLAST) system which adopts BPSK modulation, where 4 and 8 antennas are equipped at the transmitter and receiver, respectively. Compared with traditional equalization algorithm based on UMSWF, our new method can achieve the same BER performance at high SNR with only 0.5 times that of computational complexity.

The rapid convergence rate, high fidelity learning outcome and low computational cost are key targets in solving the learning problem of the complex physical system. Guided by physical laws of wave propagation, in full waveform inversion (FWI), we learn the subsurface images through optimizing the media velocity model in a large scale non-linear problem. In this paper, we combine randomized subsampling techniques with a second-order optimization algorithm to propose the Sub-Sampled Newton (SSN) method for learning velocity model of FWI. By incorporating the curvature information, SSN preserves comparable convergence rate to Newtons method and significantly reduces the iteration cost by approximating the Hessian matrix through a non-uniform subsampling scheme. The numerical experiments demonstrate that the proposed SSN method has a faster convergence rate, and achieves a more accurate velocity model in terms of mean squared error than commonly used methods.

This article investigates the problem of distributed hypothesis testing over networks. By introducing double and triple cumulations of historical observations, two novel distributed learning algorithms are developed to solve the considered problem. Within this framework, we study the convergence rates of the proposed algorithms. More specifically: 1) It is proven that the algorithm with double cumulation of historical observations has a faster convergence rate than those of the existing algorithms. 2) Furthermore, it is proven that the algorithm with triple cumulation of historical observations can be further accelerated. Especially, based on the theoretical results, this article shows that a tradeoff among convergence rate, transient performance, and memory burden exists in the proposed algorithms. Finally, simulation examples verify the theoretical results.

Underwater acoustic communications especially over shallow water channels suffer from multipath spread that causes inter-symbol interference (ISI). One of the best ways for overcoming ISI is to use adaptive equalizers. In addition to convergence rate and steady-state error, computational complexity influences adaptive equalizers performance. In this paper, we apply least mean fourth-power of two quantizer (LMFPTQ) also we suggest proposed affine projection algorithm (Proposed APA) and proposed normalized least mean fourth (Proposed NLMF) as new algorithms with lower steady-state error and faster convergence rate in comparison with LMF-PTQ, for equalizing underwater acoustic communications. We apply experimental data from Persian Gulf for examining and showing that the proposed method provides a good trade-off between convergence rate and computational complexity over shallow water channels.