Search results for: Estimation algorithms

Authors: Ahmad M. Shafiee, Mehrdad Montazeri, Mahdi Nikdast

Abstract:

Every day human life experiences new equipments more automatic and with more abilities. So the need for faster processors doesn-t seem to finish. Despite new architectures and higher frequencies, a single processor is not adequate for many applications. Parallel processing and networks are previous solutions for this problem. The new solution to put a network of resources on a chip is called NOC (network on a chip). The more usual topology for NOC is mesh topology. There are several routing algorithms suitable for this topology such as XY, fully adaptive, etc. In this paper we have suggested a new algorithm named Intermittent X, Y (IX/Y). We have developed the new algorithm in simulation environment to compare delay and power consumption with elders' algorithms.

Keywords: Computer architecture, parallel computing, NOC, routing algorithm.

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Authors: Taiyo Matsumura, Kuninori Takahashi, Takashi Ono

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The purpose of this research is to improve the convenience of waiting for trains at level crossings and stations and to prevent accidents resulting from forcible entry into level crossings, by providing level crossing users and passengers with information that tells them when the next train will pass through or arrive. For this paper, we proposed methods for estimating operation by means of an average value method, variable response smoothing method, and exponential smoothing method, on the basis of open data, which has low accuracy, but for which performance schedules are distributed in real time. We then examined the accuracy of the estimations. The results showed that the application of an exponential smoothing method is valid.

Keywords: Exponential smoothing method, open data, operation estimation, train schedule.

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Authors: M. Pourgholi, V.J.Majd

Abstract:

This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.

Keywords: Adaptive observer, linear matrix inequality, nonlinear systems, nonlinear observer, resilient observer, robust estimation.

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Authors: Tim Byrnes

Abstract:

Quantum computation using qubits made of two component Bose-Einstein condensates (BECs) is analyzed. We construct a general framework for quantum algorithms to be executed using the collective states of the BECs. The use of BECs allows for an increase of energy scales via bosonic enhancement, resulting in two qubit gate operations that can be performed at a time reduced by a factor of N, where N is the number of bosons per qubit. We illustrate the scheme by an application to Deutsch-s and Grover-s algorithms, and discuss possible experimental implementations. Decoherence effects are analyzed under both general conditions and for the experimental implementation proposed.

Keywords: Quantum, computing, information, Bose-Einstein condensates, macroscopic.

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Authors: Ahmad Tariq Sheikh, Shahzad Amin Sheikh

Abstract:

A new distance-adjusted approach is proposed in which static square contours are defined around an estimated symbol in a QAM constellation, which create regions that correspond to fixed step sizes and weighting factors. As a result, the equalizer tap adjustment consists of a linearly weighted sum of adaptation criteria that is scaled by a variable step size. This approach is the basis of two new algorithms: the Variable step size Square Contour Algorithm (VSCA) and the Variable step size Square Contour Decision-Directed Algorithm (VSDA). The proposed schemes are compared with existing blind equalization algorithms in the SCA family in terms of convergence speed, constellation eye opening and residual ISI suppression. Simulation results for 64-QAM signaling over empirically derived microwave radio channels confirm the efficacy of the proposed algorithms. An RTL implementation of the blind adaptive equalizer based on the proposed schemes is presented and the system is configured to operate in VSCA error signal mode, for square QAM signals up to 64-QAM.

Keywords: Adaptive filtering, Blind Equalization, Square Contour Algorithm.

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Authors: George Karkavitsas, Maria Rangoussi

Abstract:

We present a genetic algorithm application to the problem of object registration (i.e., object detection, localization and recognition) in a class of medical images containing various types of blood cells. The genetic algorithm approach taken here is seen to be most appropriate for this type of image, due to the characteristics of the objects. Successful cell registration results on real life microscope images of blood cells show the potential of the proposed approach.

Keywords: Genetic algorithms, object registration, pattern recognition, blood cell microscope images.

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Authors: Richard Molyneux, Christopher Parrott, Kirill Horoshenkov

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This paper aims to demonstrate how various algorithms can be implemented within swarms of autonomous robots to provide continuous inspection within underground pipeline networks. Current methods of fault detection within pipes are costly, time consuming and inefficient. As such, solutions tend toward a more reactive approach, repairing faults, as opposed to proactively seeking leaks and blockages. The paper presents an efficient inspection method, showing that autonomous swarm robotics is a viable way of monitoring underground infrastructure. Tailored adaptations of various Vehicle Routing Problems (VRP) and path-planning algorithms provide a customised inspection procedure for complicated networks of underground pipes. The performance of multiple algorithms is compared to determine their effectiveness and feasibility. Notable inspirations come from ant colonies and stigmergy, graph theory, the k-Chinese Postman Problem ( -CPP) and traffic theory. Unlike most swarm behaviours which rely on fast communication between agents, underground pipe networks are a highly challenging communication environment with extremely limited communication ranges. This is due to the extreme variability in the pipe conditions and relatively high attenuation of acoustic and radio waves with which robots would usually communicate. This paper illustrates how to optimise the inspection process and how to increase the frequency with which the robots pass each other, without compromising the routes they are able to take to cover the whole network.

Keywords: Autonomous inspection, buried pipes, stigmergy, swarm intelligence, vehicle routing problem.

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Authors: Y. N. Phang, E. F. Loh

Abstract:

The zero truncated model is usually used in modeling count data without zero. It is the opposite of zero inflated model. Zero truncated Poisson and zero truncated negative binomial models are discussed and used by some researchers in analyzing the abundance of rare species and hospital stay. Zero truncated models are used as the base in developing hurdle models. In this study, we developed a new model, the zero truncated strict arcsine model, which can be used as an alternative model in modeling count data without zero and with extra variation. Two simulated and one real life data sets are used and fitted into this developed model. The results show that the model provides a good fit to the data. Maximum likelihood estimation method is used in estimating the parameters.

Keywords: Hurdle models, maximum likelihood estimation method, positive count data.

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Authors: Hesheng Wang, Haoyu Wang, Chungang Zhuang

Abstract:

Estimating the 6D pose of objects is a core step for robot bin-picking tasks. The problem is that various objects are usually randomly stacked with heavy occlusion in real applications. In this work, we propose a method to regress 6D poses by predicting three points for each object in the 3D point cloud through deep learning. To solve the ambiguity of symmetric pose, we propose a labeling method to help the network converge better. Based on the predicted pose, an iterative method is employed for pose optimization. In real-world experiments, our method outperforms the classical approach in both precision and recall.

Keywords: Pose estimation, deep learning, point cloud, bin-picking, 3D computer vision.

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Authors: Said Baadel, Fadi Thabtah, Joan Lu

Abstract:

Clustering involves the partitioning of n objects into k clusters. Many clustering algorithms use hard-partitioning techniques where each object is assigned to one cluster. In this paper we propose an overlapping algorithm MCOKE which allows objects to belong to one or more clusters. The algorithm is different from fuzzy clustering techniques because objects that overlap are assigned a membership value of 1 (one) as opposed to a fuzzy membership degree. The algorithm is also different from other overlapping algorithms that require a similarity threshold be defined a priori which can be difficult to determine by novice users.

Keywords: Data mining, k-means, MCOKE, overlapping.

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Authors: Si-Gwan Kim

Abstract:

Small-size and low-power sensors with sensing, signal processing and wireless communication capabilities is suitable for the wireless sensor networks. Due to the limited resources and battery constraints, complex routing algorithms used for the ad-hoc networks cannot be employed in sensor networks. In this paper, we propose node-disjoint multi-path hexagon-based routing algorithms in wireless sensor networks. We suggest the details of the algorithm and compare it with other works. Simulation results show that the proposed scheme achieves better performance in terms of efficiency and message delivery ratio.

Keywords: Clustering, multi-path, routing protocol, sensor network.

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Authors: Martin A. Smith, Xiaogang Chen

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This paper proposes new algorithms for the computeraided design and manufacture (CAD/CAM) of 3D woven multi-layer textile structures. Existing commercial CAD/CAM systems are often restricted to the design and manufacture of 2D weaves. Those CAD/CAM systems that do support the design and manufacture of 3D multi-layer weaves are often limited to manual editing of design paper grids on the computer display and weave retrieval from stored archives. This complex design activity is time-consuming, tedious and error-prone and requires considerable experience and skill of a technical weaver. Recent research reported in the literature has addressed some of the shortcomings of commercial 3D multi-layer weave CAD/CAM systems. However, earlier research results have shown the need for further work on weave specification, weave generation, yarn path editing and layer binding. Analysis of 3D multi-layer weaves in this research has led to the design and development of efficient and robust algorithms for the CAD/CAM of 3D woven multi-layer textile structures. The resulting algorithmically generated weave designs can be used as a basis for lifting plans that can be loaded onto looms equipped with electronic shedding mechanisms for the CAM of 3D woven multi-layer textile structures.

Keywords: CAD/CAM, Multi-layer, Textile, Weave.

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Authors: Ameur Abdelkader, Abed Bouarfa Hafida

Abstract:

Since its inception, predictive analysis has revolutionized the IT industry through its robustness and decision-making facilities. It involves the application of a set of data processing techniques and algorithms in order to create predictive models. Its principle is based on finding relationships between explanatory variables and the predicted variables. Past occurrences are exploited to predict and to derive the unknown outcome. With the advent of big data, many studies have suggested the use of predictive analytics in order to process and analyze big data. Nevertheless, they have been curbed by the limits of classical methods of predictive analysis in case of a large amount of data. In fact, because of their volumes, their nature (semi or unstructured) and their variety, it is impossible to analyze efficiently big data via classical methods of predictive analysis. The authors attribute this weakness to the fact that predictive analysis algorithms do not allow the parallelization and distribution of calculation. In this paper, we propose to extend the predictive analysis algorithm, Classification And Regression Trees (CART), in order to adapt it for big data analysis. The major changes of this algorithm are presented and then a version of the extended algorithm is defined in order to make it applicable for a huge quantity of data.

Keywords: Predictive analysis, big data, predictive analysis algorithms. CART algorithm.

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Authors: Thomas O. Olwal, Michael A. van Wyk, Barend J. van Wyk

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In this paper we present a soft timing phase estimation (STPE) method for wireless mobile receivers operating in low signal to noise ratios (SNRs). Discrete Polyphase Matched (DPM) filters, a Log-maximum a posterior probability (MAP) and/or a Soft-output Viterbi algorithm (SOVA) are combined to derive a new timing recovery (TR) scheme. We apply this scheme to wireless cellular communication system model that comprises of a raised cosine filter (RCF), a bit-interleaved turbo-coded multi-level modulation (BITMM) scheme and the channel is assumed to be memory-less. Furthermore, no clock signals are transmitted to the receiver contrary to the classical data aided (DA) models. This new model ensures that both the bandwidth and power of the communication system is conserved. However, the computational complexity of ideal turbo synchronization is increased by 50%. Several simulation tests on bit error rate (BER) and block error rate (BLER) versus low SNR reveal that the proposed iterative soft timing recovery (ISTR) scheme outperforms the conventional schemes.

Keywords: discrete polyphase matched filters, maximum likelihood estimators, soft timing phase estimation, wireless mobile systems.

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Authors: Halim Djerroud, Arab Ali Cherif

Abstract:

We assume that conscious functions are implemented automatically. In other words that consciousness as well as the non-consciousness aspect of human thought, planning and perception, are produced by biologically adaptive algorithms. We propose that the mechanisms of consciousness can be produced using similar adaptive algorithms to those executed by the mechanism. In this paper, we present a computational model of consciousness, the ”Global Abstraction Workspace” which is an internal environmental modelling perceived as a multi-agent system. This system is able to evolve and generate new data and processes as well as actions in the environment.

Keywords: Artificial consciousness, cognitive architecture, global abstraction workspace, mutli-agents system.

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Authors: S. Balaji, V. Swaminathan, K. Kannan

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The Minimum Vertex Cover (MVC) problem is a classic graph optimization NP - complete problem. In this paper a competent algorithm, called Vertex Support Algorithm (VSA), is designed to find the smallest vertex cover of a graph. The VSA is tested on a large number of random graphs and DIMACS benchmark graphs. Comparative study of this algorithm with the other existing methods has been carried out. Extensive simulation results show that the VSA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

Keywords: vertex cover, vertex support, approximation algorithms, NP - complete problem.

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Authors: Cheng Zeng, George Michailidis, Hitoshi Iyatomi, Leo L Duan

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The conditional density characterizes the distribution of a response variable y given other predictor x, and plays a key role in many statistical tasks, including classification and outlier detection. Although there has been abundant work on the problem of Conditional Density Estimation (CDE) for a low-dimensional response in the presence of a high-dimensional predictor, little work has been done for a high-dimensional response such as images. The promising performance of normalizing flow (NF) neural networks in unconditional density estimation acts a motivating starting point. In this work, we extend NF neural networks when external x is present. Specifically, they use the NF to parameterize a one-to-one transform between a high-dimensional y and a latent z that comprises two components [zP , zN]. The zP component is a low-dimensional subvector obtained from the posterior distribution of an elementary predictive model for x, such as logistic/linear regression. The zN component is a high-dimensional independent Gaussian vector, which explains the variations in y not or less related to x. Unlike existing CDE methods, the proposed approach, coined Augmented Posterior CDE (AP-CDE), only requires a simple modification on the common normalizing flow framework, while significantly improving the interpretation of the latent component, since zP represents a supervised dimension reduction. In image analytics applications, AP-CDE shows good separation of x-related variations due to factors such as lighting condition and subject id, from the other random variations. Further, the experiments show that an unconditional NF neural network, based on an unsupervised model of z, such as Gaussian mixture, fails to generate interpretable results.

Keywords: Conditional density estimation, image generation, normalizing flow, supervised dimension reduction.

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Authors: S. Ramana Babu, V. Ramachandra Raju, K. Ramji

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This paper presents the effect of actuation schemes on the performance of parallel manipulators and also how the singularity loci have been changed in the reachable workspace of the manipulator with the choice of actuation scheme to drive the manipulator. The performance of the eight possible actuation schemes of 3RRR planar parallel manipulator is compared with each other. The optimal design problem is formulated to find the manipulator geometry that maximizes the singularity free conditioned workspace for all the eight actuation cases, the optimization problem is solved by using genetic algorithms.

Keywords: Actuation schemes, GCI, genetic algorithms.

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Authors: Chang-le Lu, Yong Chen

Abstract:

The shortest path question is in a graph theory model question, and it is applied in many fields. The most short-path question may divide into two kinds: Single sources most short-path, all apexes to most short-path. This article mainly introduces the problem of all apexes to most short-path, and gives a new parallel algorithm of all apexes to most short-path according to the Dijkstra algorithm. At last this paper realizes the parallel algorithms in the technology of C # multithreading.

Keywords: Dijkstra algorithm, parallel algorithms, multi-thread technology, most short-path, ratio.

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Authors: Ana Clara Santos, Maria Manuela Portela, Bettina Schaefli

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This work assesses the performance of an analytical model framework to generate daily flow duration curves, FDCs, based on climatic characteristics of the catchments and on their streamflow recession coefficients. According to the analytical model framework, precipitation is considered to be a stochastic process, modeled as a marked Poisson process, and recession is considered to be deterministic, with parameters that can be computed based on different models. The analytical model framework was tested for three case studies with different hydrological regimes located in Switzerland: pluvial, snow-dominated and glacier. For that purpose, five time intervals were analyzed (the four meteorological seasons and the civil year) and two developments of the model were tested: one considering a linear recession model and the other adopting a nonlinear recession model. Those developments were combined with recession coefficients obtained from two different approaches: forward and inverse estimation. The performance of the analytical framework when considering forward parameter estimation is poor in comparison with the inverse estimation for both, linear and nonlinear models. For the pluvial catchment, the inverse estimation shows exceptional good results, especially for the nonlinear model, clearing suggesting that the model has the ability to describe FDCs. For the snow-dominated and glacier catchments the seasonal results are better than the annual ones suggesting that the model can describe streamflows in those conditions and that future efforts should focus on improving and combining seasonal curves instead of considering single annual ones.

Keywords: Analytical streamflow distribution, stochastic process, linear and non-linear recession, hydrological modelling, daily discharges.

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Authors: Muhammad Rehan Usman, Muhammad Arslan Usman, Soo Young Shin

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The new era of digital communication has brought up many challenges that network operators need to overcome. The high demand of mobile data rates require improved networks, which is a challenge for the operators in terms of maintaining the quality of experience (QoE) for their consumers. In live video transmission, there is a sheer need for live surveillance of the videos in order to maintain the quality of the network. For this purpose objective algorithms are employed to monitor the quality of the videos that are transmitted over a network. In order to test these objective algorithms, subjective quality assessment of the streamed videos is required, as the human eye is the best source of perceptual assessment. In this paper we have conducted subjective evaluation of videos with varying spatial and temporal impairments. These videos were impaired with frame freezing distortions so that the impact of frame freezing on the quality of experience could be studied. We present subjective Mean Opinion Score (MOS) for these videos that can be used for fine tuning the objective algorithms for video quality assessment.

Keywords: Frame freezing, mean opinion score, objective assessment, subjective evaluation.

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Authors: V. Sudha, D. Sriram Kumar

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Orthogonal Frequency Division Multiplexing (OFDM) has been used in many advanced wireless communication systems due to its high spectral efficiency and robustness to frequency selective fading channels. However, the major concern with OFDM system is the high peak-to-average power ratio (PAPR) of the transmitted signal. Some of the popular techniques used for PAPR reduction in OFDM system are conventional partial transmit sequences (CPTS) and clipping. In this paper, a parallel combination/hybrid scheme of PAPR reduction using clipping and CPTS algorithms is proposed. The proposed method intelligently applies both the algorithms in order to reduce both PAPR as well as computational complexity. The proposed scheme slightly degrades bit error rate (BER) performance due to clipping operation and it can be reduced by selecting an appropriate value of the clipping ratio (CR). The simulation results show that the proposed algorithm achieves significant PAPR reduction with much reduced computational complexity.

Keywords: CCDF, OFDM, PAPR, PTS.

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Authors: Michela Lecca

Abstract:

System MEMORI automatically detects and recognizes rotated and/or rescaled versions of the objects of a database within digital color images with cluttered background. This task is accomplished by means of a region grouping algorithm guided by heuristic rules, whose parameters concern some geometrical properties and the recognition score of the database objects. This paper focuses on the strategies implemented in MEMORI for the estimation of the heuristic rule parameters. This estimation, being automatic, makes the system a self configuring and highly user-friendly tool.

Keywords: Automatic Object Recognition, Clustering, Contentbased Image Retrieval System, Image Segmentation, Region Adjacency Graph, Region Grouping.

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Authors: Safeer Hussain Khan

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In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms.

Keywords: Contractive-like operator, iterative algorithm, fixed point, strong convergence.

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Authors: Hanan Ahmed-Hosni Mahmoud, Nadia Al-Ghreimil

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In-place sorting algorithms play an important role in many fields such as very large database systems, data warehouses, data mining, etc. Such algorithms maximize the size of data that can be processed in main memory without input/output operations. In this paper, a novel in-place sorting algorithm is presented. The algorithm comprises two phases; rearranging the input unsorted array in place, resulting segments that are ordered relative to each other but whose elements are yet to be sorted. The first phase requires linear time, while, in the second phase, elements of each segment are sorted inplace in the order of z log (z), where z is the size of the segment, and O(1) auxiliary storage. The algorithm performs, in the worst case, for an array of size n, an O(n log z) element comparisons and O(n log z) element moves. Further, no auxiliary arithmetic operations with indices are required. Besides these theoretical achievements of this algorithm, it is of practical interest, because of its simplicity. Experimental results also show that it outperforms other in-place sorting algorithms. Finally, the analysis of time and space complexity, and required number of moves are presented, along with the auxiliary storage requirements of the proposed algorithm.

Keywords: Auxiliary storage sorting, in-place sorting, sorting.

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Authors: Reza Ghaemi, Amin Milani Fard, Hamid Tabatabaee, Mahdi Sadeghizadeh

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Due to new distributed database applications such as huge deductive database systems, the search complexity is constantly increasing and we need better algorithms to speedup traditional relational database queries. An optimal dynamic programming method for such high dimensional queries has the big disadvantage of its exponential order and thus we are interested in semi-optimal but faster approaches. In this work we present a multi-agent based mechanism to meet this demand and also compare the result with some commonly used query optimization algorithms.

Keywords: Information retrieval systems, list fusion methods, document score, multi-agent systems.

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Authors: N. Mamode Khan, V. Jowaheer

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In this paper, we apply and compare two generalized estimating equation approaches to the analysis of car breakdowns data in Mauritius. Number of breakdowns experienced by a machinery is a highly under-dispersed count random variable and its value can be attributed to the factors related to the mechanical input and output of that machinery. Analyzing such under-dispersed count observation as a function of the explanatory factors has been a challenging problem. In this paper, we aim at estimating the effects of various factors on the number of breakdowns experienced by a passenger car based on a study performed in Mauritius over a year. We remark that the number of passenger car breakdowns is highly under-dispersed. These data are therefore modelled and analyzed using Com-Poisson regression model. We use the two types of quasi-likelihood estimation approaches to estimate the parameters of the model: marginal and joint generalized quasi-likelihood estimating equation approaches. Under-dispersion parameter is estimated to be around 2.14 justifying the appropriateness of Com-Poisson distribution in modelling underdispersed count responses recorded in this study.

Keywords: Breakdowns, under-dispersion, com-poisson, generalized linear model, marginal quasi-likelihood estimation, joint quasi-likelihood estimation.

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Authors: Yitao Lei, Xingxiang Zhai, Burra Venkata Durga Kumar

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As the quantity and complexity of computing in large-scale software systems increase, distributed system computing becomes increasingly important. The distributed system realizes high-performance computing by collaboration between different computing resources. If there are no efficient resource scheduling resources, the abuse of distributed computing may cause resource waste and high costs. However, resource scheduling is usually an NP-hard problem, so we cannot find a general solution. However, some optimization algorithms exist like genetic algorithm, ant colony optimization, etc. The large scale of distributed systems makes this traditional optimization algorithm challenging to work with. Heuristic and machine learning algorithms are usually applied in this situation to ease the computing load. As a result, we do a review of traditional resource scheduling optimization algorithms and try to introduce a deep reinforcement learning method that utilizes the perceptual ability of neural networks and the decision-making ability of reinforcement learning. Using the machine learning method, we try to find important factors that influence the performance of distributed system computing and help the distributed system do an efficient computing resource scheduling. This paper surveys the application of deep reinforcement learning on distributed system computing resource scheduling. The research proposes a deep reinforcement learning method that uses a recurrent neural network to optimize the resource scheduling. The paper concludes the challenges and improvement directions for Deep Reinforcement Learning-based resource scheduling algorithms.

Keywords: Resource scheduling, deep reinforcement learning, distributed system, artificial intelligence.

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Authors: Meiling Yang, Shuguo Xie, Yilong Zhu

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Nowadays, due to diverse electric products and complex electromagnetic environment, the localization and troubleshooting of the electromagnetic radiation source is urgent and necessary especially on the condition of far field. However, based on the existing DOA positioning method, the system or devices are complex, bulky and expensive. To address this issue, this paper proposes a single antenna radiation source localization method. A single antenna moves to form a virtual antenna array combined with DOA and MUSIC algorithm to position accurately, meanwhile reducing the cost and simplify the equipment. As shown in the results of simulations and experiments, the virtual antenna array DOA estimation modeling is correct and its positioning is credible.

Keywords: Virtual antenna array, DOA, localization, far field.

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Authors: Said Ali Al-Hadhrami

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Ranked set sampling (RSS) was first suggested to increase the efficiency of the population mean. It has been shown that this method is highly beneficial to the estimation based on simple random sampling (SRS). There has been considerable development and many modifications were done on this method. When a concomitant variable is available, ratio estimation based on ranked set sampling was proposed. This ratio estimator is more efficient than that based on SRS. In this paper some ratio type estimators of the population mean based on RSS are suggested. These estimators are found to be more efficient than the estimators of similar form using simple random sample.

Keywords: Bias, Efficiency, Ranked Set Sampling, Ratio Type Estimator

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