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Algorithms, Volume 8, Issue 3 (September 2015) – 30 articles , Pages 366-798

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Open AccessArticle
A Family of Newton Type Iterative Methods for Solving Nonlinear Equations
Algorithms 2015, 8(3), 786-798; https://doi.org/10.3390/a8030786 - 22 Sep 2015
Cited by 9 | Viewed by 2205
Abstract
In this paper, a general family of n-point Newton type iterative methods for solving nonlinear equations is constructed by using direct Hermite interpolation. The order of convergence of the new n-point iterative methods without memory is 2n requiring the evaluations of n functions [...] Read more.
In this paper, a general family of n-point Newton type iterative methods for solving nonlinear equations is constructed by using direct Hermite interpolation. The order of convergence of the new n-point iterative methods without memory is 2n requiring the evaluations of n functions and one first-order derivative in per full iteration, which implies that this family is optimal according to Kung and Traub’s conjecture (1974). Its error equations and asymptotic convergence constants are obtained. The n-point iterative methods with memory are obtained by using a self-accelerating parameter, which achieve much faster convergence than the corresponding n-point methods without memory. The increase of convergence order is attained without any additional calculations so that the n-point Newton type iterative methods with memory possess a very high computational efficiency. Numerical examples are demonstrated to confirm theoretical results. Full article
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
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Open AccessArticle
Parallel Variants of Broyden’s Method
Algorithms 2015, 8(3), 774-785; https://doi.org/10.3390/a8030774 - 15 Sep 2015
Cited by 1 | Viewed by 2224
Abstract
In this paper we investigate some parallel variants of Broyden’s method and, for the basic variant, we present its convergence properties. The main result is that the behavior of the considered parallel Broyden’s variants is comparable with the classical parallel Newton method, and [...] Read more.
In this paper we investigate some parallel variants of Broyden’s method and, for the basic variant, we present its convergence properties. The main result is that the behavior of the considered parallel Broyden’s variants is comparable with the classical parallel Newton method, and significantly better than the parallel Cimmino method, both for linear and nonlinear cases. The considered variants are also compared with two more recently proposed parallel Broyden’s method. Some numerical experiments are presented to illustrate the advantages and limits of the proposed algorithms. Full article
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
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Open AccessArticle
Modified Classical Graph Algorithms for the DNA Fragment Assembly Problem
Algorithms 2015, 8(3), 754-773; https://doi.org/10.3390/a8030754 - 10 Sep 2015
Cited by 3 | Viewed by 2195
Abstract
DNA fragment assembly represents an important challenge to the development of efficient and practical algorithms due to the large number of elements to be assembled. In this study, we present some graph theoretical linear time algorithms to solve the problem. To achieve linear [...] Read more.
DNA fragment assembly represents an important challenge to the development of efficient and practical algorithms due to the large number of elements to be assembled. In this study, we present some graph theoretical linear time algorithms to solve the problem. To achieve linear time complexity, a heap with constant time operations was developed, for the special case where the edge weights are integers and do not depend on the problem size. The experiments presented show that modified classical graph theoretical algorithms can solve the DNA fragment assembly problem efficiently. Full article
(This article belongs to the Special Issue Algorithmic Themes in Bioinformatics)
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Open AccessArticle
A CS Recovery Algorithm for Model and Time Delay Identification of MISO-FIR Systems
Algorithms 2015, 8(3), 743-753; https://doi.org/10.3390/a8030743 - 10 Sep 2015
Cited by 23 | Viewed by 2163
Abstract
This paper considers identifying the multiple input single output finite impulse response (MISO-FIR) systems with unknown time delays and orders. Generally, parameters, orders and time delays of an MISO system are separately identified from different algorithms. In this paper, we aim to perform [...] Read more.
This paper considers identifying the multiple input single output finite impulse response (MISO-FIR) systems with unknown time delays and orders. Generally, parameters, orders and time delays of an MISO system are separately identified from different algorithms. In this paper, we aim to perform the model identification and time delay estimation simultaneously from a limited number of observations. For an MISO-FIR system with many inputs and unknown input time delays, the corresponding identification model contains a large number of parameters, requiring a great number of observations for identification and leading to a heavy computational burden. Inspired by the compressed sensing (CS) recovery theory, a threshold orthogonal matching pursuit algorithm (TH-OMP) is presented to simultaneously identify the parameters, the orders and the time delays of the MISO-FIR systems. The proposed algorithm requires only a small number of sampled data compared to the conventional identification methods, such as the least squares method. The effectiveness of the proposed algorithm is verified by simulation results. Full article
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Open AccessArticle
A Comparative Study of Modern Heuristics on the School Timetabling Problem
Algorithms 2015, 8(3), 723-742; https://doi.org/10.3390/a8030723 - 28 Aug 2015
Cited by 3 | Viewed by 2155
Abstract
In this contribution a comparative study of modern heuristics on the school timetabling problem is presented. More precisely, we investigate the application of two population-based algorithms, namely a Particle Swarm Optimization (PSO) and an Artificial Fish Swarm (AFS), on the high school timetabling [...] Read more.
In this contribution a comparative study of modern heuristics on the school timetabling problem is presented. More precisely, we investigate the application of two population-based algorithms, namely a Particle Swarm Optimization (PSO) and an Artificial Fish Swarm (AFS), on the high school timetabling problem. In order to demonstrate their efficiency and performance, experiments with real-world input data have been performed. Both algorithms proposed manage to create feasible and efficient high school timetables, thus fulfilling adequately the timetabling needs of the respective high schools. Computational results demonstrate that both algorithms manage to reach efficient solutions, most of the times better than existing approaches applied to the same school timetabling input instances using the same evaluation criteria. Full article
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Open AccessArticle
Gradient-Based Iterative Identification for Wiener Nonlinear Dynamic Systems with Moving Average Noises
Algorithms 2015, 8(3), 712-722; https://doi.org/10.3390/a8030712 - 26 Aug 2015
Cited by 3 | Viewed by 1968
Abstract
This paper focuses on the parameter identification problem for Wiener nonlinear dynamic systems with moving average noises. In order to improve the convergence rate, the gradient-based iterative algorithm is presented by replacing the unmeasurable variables with their corresponding iterative estimates, and to compute [...] Read more.
This paper focuses on the parameter identification problem for Wiener nonlinear dynamic systems with moving average noises. In order to improve the convergence rate, the gradient-based iterative algorithm is presented by replacing the unmeasurable variables with their corresponding iterative estimates, and to compute iteratively the noise estimates based on the obtained parameter estimates. The simulation results show that the proposed algorithm can effectively estimate the parameters of Wiener systems with moving average noises. Full article
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
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Open AccessArticle
Comparative Study of DE, PSO and GA for Position Domain PID Controller Tuning
Algorithms 2015, 8(3), 697-711; https://doi.org/10.3390/a8030697 - 21 Aug 2015
Cited by 16 | Viewed by 2395
Abstract
Gain tuning is very important in order to obtain good performances for a given controller. Contour tracking performance is mainly determined by the selected control gains of a position domain PID controller. In this paper, three popular evolutionary algorithms are utilized to optimize [...] Read more.
Gain tuning is very important in order to obtain good performances for a given controller. Contour tracking performance is mainly determined by the selected control gains of a position domain PID controller. In this paper, three popular evolutionary algorithms are utilized to optimize the gains of a position domain PID controller for performance improvement of contour tracking of robotic manipulators. Differential Evolution (DE), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) are used to determine the optimal gains of the position domain PID controller, and three distinct fitness functions are also used to quantify the contour tracking performance of each solution set. Simulation results show that DE features the highest performance indexes for both linear and nonlinear contour tracking, while PSO is quite efficient for linear contour tracking. Both algorithms performed consistently better than GA that featured premature convergence in all cases. Full article
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Open AccessArticle
Network Community Detection on Metric Space
Algorithms 2015, 8(3), 680-696; https://doi.org/10.3390/a8030680 - 21 Aug 2015
Cited by 3 | Viewed by 2367
Abstract
Community detection in a complex network is an important problem of much interest in recent years. In general, a community detection algorithm chooses an objective function and captures the communities of the network by optimizing the objective function, and then, one uses various [...] Read more.
Community detection in a complex network is an important problem of much interest in recent years. In general, a community detection algorithm chooses an objective function and captures the communities of the network by optimizing the objective function, and then, one uses various heuristics to solve the optimization problem to extract the interesting communities for the user. In this article, we demonstrate the procedure to transform a graph into points of a metric space and develop the methods of community detection with the help of a metric defined for a pair of points. We have also studied and analyzed the community structure of the network therein. The results obtained with our approach are very competitive with most of the well-known algorithms in the literature, and this is justified over the large collection of datasets. On the other hand, it can be observed that time taken by our algorithm is quite less compared to other methods and justifies the theoretical findings. Full article
(This article belongs to the Special Issue Clustering Algorithms)
Open AccessArticle
Expanding the Applicability of a Third Order Newton-Type Method Free of Bilinear Operators
Algorithms 2015, 8(3), 669-679; https://doi.org/10.3390/a8030669 - 21 Aug 2015
Cited by 5 | Viewed by 2018
Abstract
This paper is devoted to the semilocal convergence, using centered hypotheses, of a third order Newton-type method in a Banach space setting. The method is free of bilinear operators and then interesting for the solution of systems of equations. Without imposing any type [...] Read more.
This paper is devoted to the semilocal convergence, using centered hypotheses, of a third order Newton-type method in a Banach space setting. The method is free of bilinear operators and then interesting for the solution of systems of equations. Without imposing any type of Fréchet differentiability on the operator, a variant using divided differences is also analyzed. A variant of the method using only divided differences is also presented. Full article
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
Open AccessArticle
Fifth-Order Iterative Method for Solving Multiple Roots of the Highest Multiplicity of Nonlinear Equation
Algorithms 2015, 8(3), 656-668; https://doi.org/10.3390/a8030656 - 20 Aug 2015
Cited by 2 | Viewed by 2257
Abstract
A three-step iterative method with fifth-order convergence as a new modification of Newton’s method was presented. This method is for finding multiple roots of nonlinear equation with unknown multiplicity m whose multiplicity m is the highest multiplicity. Its order of convergence is analyzed [...] Read more.
A three-step iterative method with fifth-order convergence as a new modification of Newton’s method was presented. This method is for finding multiple roots of nonlinear equation with unknown multiplicity m whose multiplicity m is the highest multiplicity. Its order of convergence is analyzed and proved. Results for some numerical examples show the efficiency of the new method. Full article
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
Open AccessArticle
Local Convergence of an Optimal Eighth Order Method under Weak Conditions
Algorithms 2015, 8(3), 645-655; https://doi.org/10.3390/a8030645 - 19 Aug 2015
Cited by 3 | Viewed by 2091
Abstract
We study the local convergence of an eighth order Newton-like method to approximate a locally-unique solution of a nonlinear equation. Earlier studies, such as Chen et al. (2015) show convergence under hypotheses on the seventh derivative or even higher, although only the first [...] Read more.
We study the local convergence of an eighth order Newton-like method to approximate a locally-unique solution of a nonlinear equation. Earlier studies, such as Chen et al. (2015) show convergence under hypotheses on the seventh derivative or even higher, although only the first derivative and the divided difference appear in these methods. The convergence in this study is shown under hypotheses only on the first derivative. Hence, the applicability of the method is expanded. Finally, numerical examples are also provided to show that our results apply to solve equations in cases where earlier studies cannot apply. Full article
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
Open AccessArticle
Data Fusion Modeling for an RT3102 and Dewetron System Application in Hybrid Vehicle Stability Testing
Algorithms 2015, 8(3), 632-644; https://doi.org/10.3390/a8030632 - 12 Aug 2015
Cited by 1 | Viewed by 2907
Abstract
More and more hybrid electric vehicles are driven since they offer such advantages as energy savings and better active safety performance. Hybrid vehicles have two or more power driving systems and frequently switch working condition, so controlling stability is very important. In this [...] Read more.
More and more hybrid electric vehicles are driven since they offer such advantages as energy savings and better active safety performance. Hybrid vehicles have two or more power driving systems and frequently switch working condition, so controlling stability is very important. In this work, a two-stage Kalman algorithm method is used to fuse data in hybrid vehicle stability testing. First, the RT3102 navigation system and Dewetron system are introduced. Second, a modeling of data fusion is proposed based on the Kalman filter. Then, this modeling is simulated and tested on a sample vehicle, using Carsim and Simulink software to test the results. The results showed the merits of this modeling. Full article
(This article belongs to the Special Issue Machine Learning Algorithms for Big Data)
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Open AccessArticle
One-Bit Quantization and Distributed Detection with an Unknown Scale Parameter
Algorithms 2015, 8(3), 621-631; https://doi.org/10.3390/a8030621 - 11 Aug 2015
Cited by 4 | Viewed by 2062
Abstract
We examine a distributed detection problem in a wireless sensor network, where sensor nodes collaborate to detect a Gaussian signal with an unknown change of power, i.e., a scale parameter. Due to power/bandwidth constraints, we consider the case where each sensor quantizes its [...] Read more.
We examine a distributed detection problem in a wireless sensor network, where sensor nodes collaborate to detect a Gaussian signal with an unknown change of power, i.e., a scale parameter. Due to power/bandwidth constraints, we consider the case where each sensor quantizes its observation into a binary digit. The binary data are then transmitted through error-prone wireless links to a fusion center, where a generalized likelihood ratio test (GLRT) detector is employed to perform a global decision. We study the design of a binary quantizer based on an asymptotic analysis of the GLRT. Interestingly, the quantization threshold of the quantizer is independent of the unknown scale parameter. Numerical results are included to illustrate the performance of the proposed quantizer and GLRT in binary symmetric channels (BSCs). Full article
(This article belongs to the Special Issue Algorithms for Sensor Networks)
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Open AccessReview
An Overview of a Class of Clock Synchronization Algorithms for Wireless Sensor Networks: A Statistical Signal Processing Perspective
Algorithms 2015, 8(3), 590-620; https://doi.org/10.3390/a8030590 - 06 Aug 2015
Cited by 6 | Viewed by 2943
Abstract
Recently, wireless sensor networks (WSNs) have drawn great interest due to their outstanding monitoring and management potential in medical, environmental and industrial applications. Most of the applications that employ WSNs demand all of the sensor nodes to run on a common time scale, [...] Read more.
Recently, wireless sensor networks (WSNs) have drawn great interest due to their outstanding monitoring and management potential in medical, environmental and industrial applications. Most of the applications that employ WSNs demand all of the sensor nodes to run on a common time scale, a requirement that highlights the importance of clock synchronization. The clock synchronization problem in WSNs is inherently related to parameter estimation. The accuracy of clock synchronization algorithms depends essentially on the statistical properties of the parameter estimation algorithms. Recently, studies dedicated to the estimation of synchronization parameters, such as clock offset and skew, have begun to emerge in the literature. The aim of this article is to provide an overview of the state-of-the-art clock synchronization algorithms for WSNs from a statistical signal processing point of view. This article focuses on describing the key features of the class of clock synchronization algorithms that exploit the traditional two-way message (signal) exchange mechanism. Upon introducing the two-way message exchange mechanism, the main clock offset estimation algorithms for pairwise synchronization of sensor nodes are first reviewed, and their performance is compared. The class of fully-distributed clock offset estimation algorithms for network-wide synchronization is then surveyed. The paper concludes with a list of open research problems pertaining to clock synchronization of WSNs. Full article
(This article belongs to the Special Issue Algorithms for Sensor Networks)
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Open AccessArticle
Robust Rank Reduction Algorithm with Iterative Parameter Optimization and Vector Perturbation
Algorithms 2015, 8(3), 573-589; https://doi.org/10.3390/a8030573 - 05 Aug 2015
Cited by 2 | Viewed by 2235
Abstract
In dynamic propagation environments, beamforming algorithms may suffer from strong interference, steering vector mismatches, a low convergence speed and a high computational complexity. Reduced-rank signal processing techniques provide a way to address the problems mentioned above. This paper presents a low-complexity robust data-dependent [...] Read more.
In dynamic propagation environments, beamforming algorithms may suffer from strong interference, steering vector mismatches, a low convergence speed and a high computational complexity. Reduced-rank signal processing techniques provide a way to address the problems mentioned above. This paper presents a low-complexity robust data-dependent dimensionality reduction based on an iterative optimization with steering vector perturbation (IOVP) algorithm for reduced-rank beamforming and steering vector estimation. The proposed robust optimization procedure jointly adjusts the parameters of a rank reduction matrix and an adaptive beamformer. The optimized rank reduction matrix projects the received signal vector onto a subspace with lower dimension. The beamformer/steering vector optimization is then performed in a reduced dimension subspace. We devise efficient stochastic gradient and recursive least-squares algorithms for implementing the proposed robust IOVP design. The proposed robust IOVP beamforming algorithms result in a faster convergence speed and an improved performance. Simulation results show that the proposed IOVP algorithms outperform some existing full-rank and reduced-rank algorithms with a comparable complexity. Full article
(This article belongs to the Special Issue Algorithms for Sensor Networks)
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Open AccessArticle
Modeling Documents with Event Model
Algorithms 2015, 8(3), 562-572; https://doi.org/10.3390/a8030562 - 04 Aug 2015
Cited by 2 | Viewed by 2207
Abstract
Currently deep learning has made great breakthroughs in visual and speech processing, mainly because it draws lessons from the hierarchical mode that brain deals with images and speech. In the field of NLP, a topic model is one of the important ways for [...] Read more.
Currently deep learning has made great breakthroughs in visual and speech processing, mainly because it draws lessons from the hierarchical mode that brain deals with images and speech. In the field of NLP, a topic model is one of the important ways for modeling documents. Topic models are built on a generative model that clearly does not match the way humans write. In this paper, we propose Event Model, which is unsupervised and based on the language processing mechanism of neurolinguistics, to model documents. In Event Model, documents are descriptions of concrete or abstract events seen, heard, or sensed by people and words are objects in the events. Event Model has two stages: word learning and dimensionality reduction. Word learning is to learn semantics of words based on deep learning. Dimensionality reduction is the process that representing a document as a low dimensional vector by a linear mode that is completely different from topic models. Event Model achieves state-of-the-art results on document retrieval tasks. Full article
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Open AccessArticle
Some Improvements to a Third Order Variant of Newton’s Method from Simpson’s Rule
Algorithms 2015, 8(3), 552-561; https://doi.org/10.3390/a8030552 - 29 Jul 2015
Cited by 1 | Viewed by 2312
Abstract
In this paper, we present three improvements to a three-point third order variant of Newton’s method derived from the Simpson rule. The first one is a fifth order method using the same number of functional evaluations as the third order method, the second [...] Read more.
In this paper, we present three improvements to a three-point third order variant of Newton’s method derived from the Simpson rule. The first one is a fifth order method using the same number of functional evaluations as the third order method, the second one is a four-point 10th order method and the last one is a five-point 20th order method. In terms of computational point of view, our methods require four evaluations (one function and three first derivatives) to get fifth order, five evaluations (two functions and three derivatives) to get 10th order and six evaluations (three functions and three derivatives) to get 20th order. Hence, these methods have efficiency indexes of 1.495, 1.585 and 1.648, respectively which are better than the efficiency index of 1.316 of the third order method. We test the methods through some numerical experiments which show that the 20th order method is very efficient. Full article
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
Open AccessArticle
Target Detection Algorithm Based on Two Layers Human Visual System
Algorithms 2015, 8(3), 541-551; https://doi.org/10.3390/a8030541 - 29 Jul 2015
Cited by 8 | Viewed by 2300
Abstract
Robust small target detection of low signal-to-noise ratio (SNR) is very important in infrared search and track applications for self-defense or attacks. Due to the complex background, current algorithms have some unsolved issues with false alarm rate. In order to reduce the false [...] Read more.
Robust small target detection of low signal-to-noise ratio (SNR) is very important in infrared search and track applications for self-defense or attacks. Due to the complex background, current algorithms have some unsolved issues with false alarm rate. In order to reduce the false alarm rate, an infrared small target detection algorithm based on saliency detection and support vector machine was proposed. Firstly, we detect salient regions that may contain targets with phase spectrum Fourier transform (PFT) approach. Then, target recognition was performed in the salient regions. Experimental results show the proposed algorithm has ideal robustness and efficiency for real infrared small target detection applications. Full article
(This article belongs to the Special Issue Machine Learning Algorithms for Big Data)
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Open AccessArticle
A Parallel Search Strategy Based on Sparse Representation for Infrared Target Tracking
Algorithms 2015, 8(3), 529-540; https://doi.org/10.3390/a8030529 - 27 Jul 2015
Cited by 1 | Viewed by 2238
Abstract
A parallel search strategy based on sparse representation (PS-L1 tracker) is proposed in the particle filter framework. To obtain the weights of state particles, target templates are represented linearly with the dictionary of target candidates. Sparse constraints on the coefficient guarantee that only [...] Read more.
A parallel search strategy based on sparse representation (PS-L1 tracker) is proposed in the particle filter framework. To obtain the weights of state particles, target templates are represented linearly with the dictionary of target candidates. Sparse constraints on the coefficient guarantee that only true target candidates can be selected, and the nonnegative entries denote the associate weights of efficient target states. Then the optimal target state can be estimated by the linear combination of above weighted states. In this way, efficient target states are selected simultaneously from all the particles, which we call a parallel search strategy. Experimental results demonstrate excellent performance of the proposed method on challenging infrared images. Full article
(This article belongs to the Special Issue Machine Learning Algorithms for Big Data)
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Open AccessArticle
On the Accessibility of Newton’s Method under a Hölder Condition on the First Derivative
Algorithms 2015, 8(3), 514-528; https://doi.org/10.3390/a8030514 - 23 Jul 2015
Cited by 2 | Viewed by 2129
Abstract
We see how we can improve the accessibility of Newton’s method for approximating a solution of a nonlinear equation in Banach spaces when a center Hölder condition on the first derivative is used to prove its semi-local convergence. Full article
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
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Open AccessArticle
Multi-Feedback Interference Cancellation Algorithms for OFDM Systems over Doubly-Selective Channels
Algorithms 2015, 8(3), 484-513; https://doi.org/10.3390/a8030484 - 14 Jul 2015
Cited by 3 | Viewed by 2498
Abstract
Orthogonal frequency-division multiplexing (OFDM) systems over rapidly time varying channels may suffer from significant inter-carrier interference (ICI), which destroys the orthogonality between subcarriers and degrades the detection performance. Without sufficient ICI suppression, OFDM systems usually experience an error floor. According to the approximate [...] Read more.
Orthogonal frequency-division multiplexing (OFDM) systems over rapidly time varying channels may suffer from significant inter-carrier interference (ICI), which destroys the orthogonality between subcarriers and degrades the detection performance. Without sufficient ICI suppression, OFDM systems usually experience an error floor. According to the approximate matched filter bound (AMFB), the error floor in a coded OFDM system is not irreducible. In this work, we introduce novel multiple feedback matched filter (MBMF)-based ICI cancellation receivers. Based on the output of a novel MBMF scheme, the approach employs a multiple ICI cancellation strategy with or without signal-to-interference-plus-noise-ratio (SINR) ordering. The developed schemes can significantly improve the performance and remove the error floor with a negligible complexity increase. Given the multiple cancellation approach, we compare the SINR performance of the MBMF outputs with that employing single feedback and show that the SINR performance with multiple cancellation candidates is improved over that with a single one at practical SNR values. Additionally, for time-varying channels, we exploit partial fast Fourier transform (PFFT) by splitting one OFDM symbol into multiple segments; the channel state is separately estimated by least-squares (LS) methods without inserting more pilots. Simulation results demonstrate the superiority of the proposed methods over serial and block equalizers and the robustness to the Doppler effects compared to conventional single-segment method. Full article
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Open AccessReview
Conditional Random Fields for Pattern Recognition Applied to Structured Data
Algorithms 2015, 8(3), 466-483; https://doi.org/10.3390/a8030466 - 14 Jul 2015
Cited by 1 | Viewed by 2171
Abstract
Pattern recognition uses measurements from an input domain, X, to predict their labels from an output domain, Y. Image analysis is one setting where one might want to infer whether a pixel patch contains an object that is “manmade” (such as [...] Read more.
Pattern recognition uses measurements from an input domain, X, to predict their labels from an output domain, Y. Image analysis is one setting where one might want to infer whether a pixel patch contains an object that is “manmade” (such as a building) or “natural” (such as a tree). Suppose the label for a pixel patch is “manmade”; if the label for a nearby pixel patch is then more likely to be “manmade” there is structure in the output domain that can be exploited to improve pattern recognition performance. Modeling P(X) is difficult because features between parts of the model are often correlated. Therefore, conditional random fields (CRFs) model structured data using the conditional distribution P(Y|X = x), without specifying a model for P(X), and are well suited for applications with dependent features. This paper has two parts. First, we overview CRFs and their application to pattern recognition in structured problems. Our primary examples are image analysis applications in which there is dependence among samples (pixel patches) in the output domain. Second, we identify research topics and present numerical examples. Full article
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Open AccessArticle
Solving the (n2 − 1)-Puzzle with 8/3 n3 Expected Moves
Algorithms 2015, 8(3), 459-465; https://doi.org/10.3390/a8030459 - 10 Jul 2015
Cited by 4 | Viewed by 2554
Abstract
It is shown that the greedy algorithm for the \((n^2-1)\)-puzzle makes \(\tfrac{8}{3}n^3 +O(n^2)\) expected moves. This analysis is verified experimentally on 10,000 random instances each of the \((n^2-1)\)-puzzle for \(4 \leq n \leq 200\). Full article
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Open AccessArticle
A Benchmarking Algorithm to Determine Minimum Aggregation Delay for Data Gathering Trees and an Analysis of the Diameter-Aggregation Delay Tradeoff
Algorithms 2015, 8(3), 435-458; https://doi.org/10.3390/a8030435 - 10 Jul 2015
Cited by 5 | Viewed by 3177
Abstract
Aggregation delay is the minimum number of time slots required to aggregate data along the edges of a data gathering tree (DG tree) spanning all the nodes in a wireless sensor network (WSN). We propose a benchmarking algorithm to determine the minimum possible [...] Read more.
Aggregation delay is the minimum number of time slots required to aggregate data along the edges of a data gathering tree (DG tree) spanning all the nodes in a wireless sensor network (WSN). We propose a benchmarking algorithm to determine the minimum possible aggregation delay for DG trees in a WSN. We assume the availability of a sufficient number of unique CDMA (Code Division Multiple Access) codes for the intermediate nodes to simultaneously aggregate data from their child nodes if the latter are ready with the data. An intermediate node has to still schedule non-overlapping time slots to sequentially aggregate data from its own child nodes (one time slot per child node). We show that the minimum aggregation delay for a DG tree depends on the underlying design choices (bottleneck node-weight based or bottleneck link-weight based) behind its construction. We observe the bottleneck node-weight based DG trees incur a smaller diameter and a larger number of child nodes per intermediate node; whereas, the bottleneck link-weight based DG trees incur a larger diameter and a much lower number of child nodes per intermediate node. As a result, we observe a complex diameter-aggregation delay tradeoff for data gathering trees in WSNs. Full article
(This article belongs to the Special Issue Algorithms for Sensor Networks)
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Open AccessArticle
Multi-Objective Design Optimization of an Over-Constrained Flexure-Based Amplifier
Algorithms 2015, 8(3), 424-434; https://doi.org/10.3390/a8030424 - 08 Jul 2015
Cited by 2 | Viewed by 2326
Abstract
The optimizing design for enhancement of the micro performance of manipulator based on analytical models is investigated in this paper. By utilizing the established uncanonical linear homogeneous equations, the quasi-static analytical model of the micro-manipulator is built, and the theoretical calculation results are [...] Read more.
The optimizing design for enhancement of the micro performance of manipulator based on analytical models is investigated in this paper. By utilizing the established uncanonical linear homogeneous equations, the quasi-static analytical model of the micro-manipulator is built, and the theoretical calculation results are tested by FEA simulations. To provide a theoretical basis for a micro-manipulator being used in high-precision engineering applications, this paper investigates the modal property based on the analytical model. Based on the finite element method, with multipoint constraint equations, the model is built and the results have a good match with the simulation. The following parametric influences studied show that the influences of other objectives on one objective are complicated. Consequently, the multi-objective optimization by the derived analytical models is carried out to find out the optimal solutions of the manipulator. Besides the inner relationships among these design objectives during the optimization process are discussed. Full article
(This article belongs to the Special Issue Machine Learning Algorithms for Big Data)
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Open AccessArticle
A Quartically Convergent Jarratt-Type Method for Nonlinear System of Equations
Algorithms 2015, 8(3), 415-423; https://doi.org/10.3390/a8030415 - 06 Jul 2015
Cited by 5 | Viewed by 2116
Abstract
In this work, we propose a new fourth-order Jarratt-type method for solving systems of nonlinear equations. The local convergence order of the method is proven analytically. Finally, we validate our results via some numerical experiments including an application to the Chandrashekar integral equations. [...] Read more.
In this work, we propose a new fourth-order Jarratt-type method for solving systems of nonlinear equations. The local convergence order of the method is proven analytically. Finally, we validate our results via some numerical experiments including an application to the Chandrashekar integral equations. Full article
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
Open AccessArticle
Implementation of a Parallel Algorithm Based on a Spark Cloud Computing Platform
Algorithms 2015, 8(3), 407-414; https://doi.org/10.3390/a8030407 - 03 Jul 2015
Cited by 9 | Viewed by 3851
Abstract
Parallel algorithms, such as the ant colony algorithm, take a long time when solving large-scale problems. In this paper, the MAX-MIN Ant System algorithm (MMAS) is parallelized to solve Traveling Salesman Problem (TSP) based on a Spark cloud computing platform. We combine MMAS [...] Read more.
Parallel algorithms, such as the ant colony algorithm, take a long time when solving large-scale problems. In this paper, the MAX-MIN Ant System algorithm (MMAS) is parallelized to solve Traveling Salesman Problem (TSP) based on a Spark cloud computing platform. We combine MMAS with Spark MapReduce to execute the path building and the pheromone operation in a distributed computer cluster. To improve the precision of the solution, local optimization strategy 2-opt is adapted in MMAS. The experimental results show that Spark has a very great accelerating effect on the ant colony algorithm when the city scale of TSP or the number of ants is relatively large. Full article
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Open AccessReview
Algorithms for Computerized Fetal Heart Rate Diagnosis with Direct Reporting
Algorithms 2015, 8(3), 395-406; https://doi.org/10.3390/a8030395 - 29 Jun 2015
Cited by 5 | Viewed by 2450
Abstract
Aims: Since pattern classification of fetal heart rate (FHR) was subjective and enlarged interobserver difference, objective FHR analysis was achieved with computerized FHR diagnosis. Methods: The computer algorithm was composed of an experts’ knowledge system, including FHR analysis and FHR score calculation, and [...] Read more.
Aims: Since pattern classification of fetal heart rate (FHR) was subjective and enlarged interobserver difference, objective FHR analysis was achieved with computerized FHR diagnosis. Methods: The computer algorithm was composed of an experts’ knowledge system, including FHR analysis and FHR score calculation, and also of an objective artificial neural network system with software. In addition, a FHR frequency spectrum was studied to detect ominous sinusoidal FHR and the loss of baseline variability related to fetal brain damage. The algorithms were installed in a central-computerized automatic FHR monitoring system, which gave the diagnosis rapidly and directly to the attending doctor. Results: Clinically perinatal mortality decreased significantly and no cerebral palsy developed after introduction of the centralized system. Conclusion: The automatic multichannel FHR monitoring system improved the monitoring, increased the objectivity of FHR diagnosis and promoted clinical results. Full article
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Open AccessArticle
Improving CLOPE’s Profit Value and Stability with an Optimized Agglomerative Approach
Algorithms 2015, 8(3), 380-394; https://doi.org/10.3390/a8030380 - 26 Jun 2015
Cited by 4 | Viewed by 2339
Abstract
CLOPE (Clustering with sLOPE) is a simple and fast histogram-based clustering algorithm for categorical data. However, given the same data set with the same input parameter, the clustering results by this algorithm would possibly be different if the transactions are input in a [...] Read more.
CLOPE (Clustering with sLOPE) is a simple and fast histogram-based clustering algorithm for categorical data. However, given the same data set with the same input parameter, the clustering results by this algorithm would possibly be different if the transactions are input in a different sequence. In this paper, a hierarchical clustering framework is proposed as an extension of CLOPE to generate stable and satisfactory clustering results based on an optimized agglomerative merge process. The new clustering profit is defined as the merge criteria and the cluster graph structure is proposed to optimize the merge iteration process. The experiments conducted on two datasets both demonstrate that the agglomerative approach achieves stable clustering results with a better profit value, but costs much more time due to the worse complexity. Full article
(This article belongs to the Special Issue Clustering Algorithms)
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Open AccessArticle
Identification of Dual-Rate Sampled Hammerstein Systems with a Piecewise-Linear Nonlinearity Using the Key Variable Separation Technique
Algorithms 2015, 8(3), 366-379; https://doi.org/10.3390/a8030366 - 24 Jun 2015
Cited by 4 | Viewed by 2179
Abstract
The identification difficulties for a dual-rate Hammerstein system lie in two aspects. First, the identification model of the system contains the products of the parameters of the nonlinear block and the linear block, and a standard least squares method cannot be directly applied [...] Read more.
The identification difficulties for a dual-rate Hammerstein system lie in two aspects. First, the identification model of the system contains the products of the parameters of the nonlinear block and the linear block, and a standard least squares method cannot be directly applied to the model; second, the traditional single-rate discrete-time Hammerstein model cannot be used as the identification model for the dual-rate sampled system. In order to solve these problems, by combining the polynomial transformation technique with the key variable separation technique, this paper converts the Hammerstein system into a dual-rate linear regression model about all parameters (linear-in-parameter model) and proposes a recursive least squares algorithm to estimate the parameters of the dual-rate system. The simulation results verify the effectiveness of the proposed algorithm. Full article
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