Search results for: statistical weather prediction

Authors: Marie Alaghband, Niloofar Yousefi, Ivan Garibay

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Facial expressions are important parts of both gesture and sign language recognition systems. Despite the recent advances in both fields, annotated facial expression datasets in the context of sign language are still scarce resources. In this manuscript, we introduce an annotated sequenced facial expression dataset in the context of sign language, comprising over 3000 facial images extracted from the daily news and weather forecast of the public tv-station PHOENIX. Unlike the majority of currently existing facial expression datasets, FePh provides sequenced semi-blurry facial images with different head poses, orientations, and movements. In addition, in the majority of images, identities are mouthing the words, which makes the data more challenging. To annotate this dataset we consider primary, secondary, and tertiary dyads of seven basic emotions of "sad", "surprise", "fear", "angry", "neutral", "disgust", and "happy". We also considered the "None" class if the image’s facial expression could not be described by any of the aforementioned emotions. Although we provide FePh as a facial expression dataset of signers in sign language, it has a wider application in gesture recognition and Human Computer Interaction (HCI) systems.

Keywords: Annotated Facial Expression Dataset, Sign Language Recognition, Gesture Recognition, Sequenced Facial Expression Dataset.

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Authors: Gitanjali Devi, Kandarpa Kumar Sarma, Pranayee Datta, Anjana Kakoti Mahanta

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Artificial Neural Network (ANN)s can be modeled for High Energy Particle analysis with special emphasis on shower core location. The work describes the use of an ANN based system which has been configured to predict locations of cores of showers in the range 1010.5 to 1020.5 eV. The system receives density values as inputs and generates coordinates of shower events recorded for values captured by 20 core positions and 80 detectors in an area of 100 meters. Twenty ANNs are trained for the purpose and the positions of shower events optimized by using cooperative ANN learning. The results derived with variations of input upto 50% show success rates in the range of 90s.

Keywords: EAS, Shower, Core, ANN, Location.

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Authors: Ernst D. Schmitter

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Monitoring lightning electromagnetic pulses (sferics) and other terrestrial as well as extraterrestrial transient radiation signals is of considerable interest for practical and theoretical purposes in astro- and geophysics as well as meteorology. Managing a continuous flow of data, automisation of the detection and classification process is important. Features based on a combination of wavelet and statistical methods proved efficient for analysis and characterisation of transients and as input into a radial basis function network that is trained to discriminate transients from pulse like to wave like.

Keywords: transient signals, statistics, wavelets, neural networks

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Authors: Kai-Lin Hsu, Jie-Chung Lou, Jia-Yun Han

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In recent years, the underground water sources in southern Taiwan have become salinized because of saltwater intrusions. This study explores the adsorption characteristics of activated carbon on salinizing inorganic salts using isothermal adsorption experiments and provides a model analysis. The temperature range for the isothermal adsorption experiments ranged between 5 to 45 ℃, and the amount adsorbed varied between 28.21 to 33.87 mg/g. All experimental data of adsorption can be fitted to both the Langmuir and the Freundlich models. The thermodynamic parameters for per chlorate onto granular activated carbon were calculated as -0.99 to -1.11 kcal/mol for DG°, -0.6 kcal/mol for DH°, and 1.21 to 1.84 kcal/mol for DS°. This shows that the adsorption process of granular activated carbon is spontaneously exothermic. The observation of adsorption behaviors under low ionic strength, low pH values, and low temperatures is beneficial to the adsorption removal of perchlorate with granular activated carbon.

Keywords: Water Treatment, Per Chlorate, Adsorption, Granular Activated Carbon

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Authors: Attapon Charoenpon, Ekkarach Pankeaw

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This paper present a new way to find the aerodynamic characteristic equation of missile for the numerical trajectories prediction more accurate. The goal is to obtain the polynomial equation based on two missile characteristic parameters, angle of attack (α ) and flight speed (╬¢ ). First, the understudied missile is modeled and used for flow computational model to compute aerodynamic force and moment. Assume that performance range of understudied missile where range -10< α <10 and 0< ╬¢ <200. After completely obtained results of all cases, the data are fit by polynomial interpolation to create equation of each case and then combine all equations to form aerodynamic characteristic equation, which will be used for trajectories simulation.

Keywords: Aerodynamic, Characteristic Equation, Angle ofAttack, Polynomial interpolation, Trajectories

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Authors: Mou-Yuan Liao, Chien-Wei Wu, Chien-Hua Lin

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Process capability index Cpk is the most widely used index in making managerial decisions since it provides bounds on the process yield for normally distributed processes. However, existent methods for assessing process performance which constructed by statistical inference may unfortunately lead to fine results, because uncertainties exist in most real-world applications. Thus, this study adopts fuzzy inference to deal with testing of Cpk . A brief score is obtained for assessing a supplier’s process instead of a severe evaluation.

Keywords: Process capability analysis, quality control.

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Authors: Anukriti Kumar, Tanmay Singh, Dinesh Kumar Vishwakarma

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Traffic control has been one of the most common and irritating problems since the time automobiles have hit the roads. Problems like traffic congestion have led to a significant time burden around the world and one significant solution to these problems can be the proper implementation of the Intelligent Transport System (ITS). It involves the integration of various tools like smart sensors, artificial intelligence, position technologies and mobile data services to manage traffic flow, reduce congestion and enhance driver's ability to avoid accidents during adverse weather. Road and traffic signs’ recognition is an emerging field of research in ITS. Classification problem of traffic signs needs to be solved as it is a major step in our journey towards building semi-autonomous/autonomous driving systems. The purpose of this work focuses on implementing an approach to solve the problem of traffic sign classification by developing a Convolutional Neural Network (CNN) classifier using the GTSRB (German Traffic Sign Recognition Benchmark) dataset. Rather than using hand-crafted features, our model addresses the concern of exploding huge parameters and data method augmentations. Our model achieved an accuracy of around 97.6% which is comparable to various state-of-the-art architectures.

Keywords: Multiclass classification, convolution neural network, OpenCV, Data Augmentation.

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Authors: S. Saehana, F. Iskandar, M. Abdullah, Khairurrijal

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A numerical simulation of optimization all of electrospinning processing parameters to obtain smallest nanofiber diameter have been performed by employing genetic algorithm (GA). Fitness function in genetic algorithm methods, which was different for each parameter, was determined by simulation approach based on the Reneker’s model. Moreover, others genetic algorithm parameter, namely length of population, crossover and mutation were applied to get the optimum electrospinning processing parameters. In addition, minimum fiber diameter, 32 nm, was achieved from a simulation by applied the optimum parameters of electrospinning. This finding may be useful for process control and prediction of electrospun fiber production. In this paper, it is also compared between predicted parameters with some experimental results.

Keywords: Diameter, Electrospinning, GA, Nanofiber.

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Authors: Suk-Hyun Yu, Heeyong Kwon

Abstract:

Recently PM-10 has become a social and global issue. It is one of major air pollutants which affect human health. Therefore, it needs to be forecasted rapidly and precisely. However, PM-10 comes from various emission sources, and its level of concentration is largely dependent on meteorological and geographical factors of local and global region, so the forecasting of PM-10 concentration is very difficult. Neural network model can be used in the case. But, there are few cases of high concentration PM-10. It makes the learning of the neural network model difficult. In this paper, we suggest a simple input balancing method when the data distribution is uneven. It is based on the probability of appearance of the data. Experimental results show that the input balancing makes the neural networks’ learning easy and improves the forecasting rates.

Keywords: AI, air quality prediction, neural networks, pattern recognition, PM-10.

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Authors: Komeil Jahanifar, Zahra Abedi, Yaghob Zeraatkish

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This research was conducted for the first time at the southeastern coasts of the Caspian Sea in order to evaluate the performance of osteichthyes cooperatives through production (catch) function. Using one of the indirect valuation methods in this research, contributory factors in catch were identified and were inserted into the function as independent variables. In order to carry out this research, the performance of 25 Osteichthyes catching cooperatives in the utilization year of 2009 which were involved in fishing in Miankale wildlife refuge region. The contributory factors in catch were divided into groups of economic, ecological and biological factors. In the mentioned function, catch rate of the cooperative were inserted into as the dependant variable and fourteen partial variables in terms of nine general variables as independent variables. Finally, after function estimation, seven variables were rendered significant at 99 percent reliably level. The results of the function estimation indicated that human resource (fisherman quantity) had the greatest positive effect on catch rate with an influence coefficient of 1.7 while weather conditions had the greatest negative effect on the catch rate of cooperatives with an influence coefficient of -2.07. Moreover, factors like member's share, experience and fisherman training and fishing effort played the main roles in the catch rate of cooperative with influence coefficients of 0.81, 0.5 and 0.21, respectively.

Keywords: Production Function, Coefficient, Variable, Osteichthyes, Caspian Sea

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Authors: Zhankuliyeva S. A.

Abstract:

This article considers the main features of party construction in the course of political modernization of Kazakhstan. Along with consideration of party construction author analyzed how the transformation of the party system was fulfilled in Kazakhstan. Besides the basic stages in the course of party construction were explained by the author. The statistical data is cited.

Keywords: elections, multi-party system, party construction, political pluralism, political party, Republic of Kazakhstan (RK)

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Authors: Seyed Fazel Ziaei Asl, Ali Karami, Gholamreza Ashari, Azam Behrang, Arezoo Assareh, N.Hedayat

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Predict daily global solar radiation (GSR) based on meteorological variables, using Multi-layer perceptron (MLP) neural networks is the main objective of this study. Daily mean air temperature, relative humidity, sunshine hours, evaporation, wind speed, and soil temperature values between 2002 and 2006 for Dezful city in Iran (32° 16' N, 48° 25' E), are used in this study. The measured data between 2002 and 2005 are used to train the neural networks while the data for 214 days from 2006 are used as testing data.

Keywords: Multi-layer Perceptron (MLP) Neural Networks;Global Solar Radiation (GSR), Meteorological Parameters, Prediction.

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Authors: M.A. Kamely, S.M. Kamil, C.W. Chong

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A mathematical model of the surface roughness has been developed by using response surface methodology (RSM) in grinding of AISI D2 cold work tool steels. Analysis of variance (ANOVA) was used to check the validity of the model. Low and high value for work speed and feed rate are decided from design of experiment. The influences of all machining parameters on surface roughness have been analyzed based on the developed mathematical model. The developed prediction equation shows that both the feed rate and work speed are the most important factor that influences the surface roughness. The surface roughness was found to be the lowers with the used of low feed rate and low work speed. Accuracy of the best model was proved with the testing data.

Keywords: Mathematical Modeling, Response surfacemethodology, Surface roughness, Cylindrical Grinding.

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Authors: Tsuyoshi Okita, Tatsuya Niwa

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For a given specific problem an efficient algorithm has been the matter of study. However, an alternative approach orthogonal to this approach comes out, which is called a reduction. In general for a given specific problem this reduction approach studies how to convert an original problem into subproblems. This paper proposes a formal modeling language to support this reduction approach. We show three examples from the wide area of learning problems. The benefit is a fast prototyping of algorithms for a given new problem.

Keywords: Formal language, statistical inference problem, reduction.

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Authors: Hussam Al-Shorman, Yosef Hasan Jbara

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A business case is a proposal for an investment initiative to satisfy business and functional requirements. The business case provides the foundation for tactical decision making and technology risk management. It helps to clarify how the organization will use its resources in the best way by providing justification for investment of resources. This paper describes how simulation was used for business case benefits and return on investment for the procurement of 8 production machines. With investment costs of about 4.7 million dollars and annual operating costs of about 1.3 million, we needed to determine if the machines would provide enough cost savings and cost avoidance. We constructed a model of the existing factory environment consisting of 8 machines and subsequently, we conducted average day simulations with light and heavy volumes to facilitate planning decisions required to be documented and substantiated in the business case.

Keywords: Investment cost, business case, return on investment, simulation.

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Authors: S. M. Munde, N. R. Hazari, A. P. Thorat, S. B. Gaikwad, V. S. Hatolkar

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This study was conducted to examine the possible role of serum Gamma-glutamyltransferase (GGT) and Lactate dehydrogenase (LDH) in the prediction of severity of preeclampsia. The study group comprised of 40 preeclamptic cases (22 with mild and 18 with severe) and 40 healthy normotensive pregnant controls. Serum samples of all the cases were assayed for GGT and LDH. Demographic, hemodynamic and laboratory data as well as serum GGT and LDH levels were compared among the three groups.

The results indicated that severe preeclamptic cases had significantly increased levels of serum GGT and LDH. The symptoms in severe preeclamptic women were significantly increased in patients with GGT > 70 IU/L and LDH >800 IU/L. Elevated levels of serum GGT and LDH can be used as biochemical markers which reflects the severity of preeclampsia and useful for the management of preeclampsia to decrease maternal and fetal morbidity and mortality.

Keywords: Severe Preeclampsia, GGT, LDH.

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Authors: K. K. Aggarwal, Yogesh Singh, Arvinder Kaur, Ruchika Malhotra

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Importance of software quality is increasing leading to development of new sophisticated techniques, which can be used in constructing models for predicting quality attributes. One such technique is Artificial Neural Network (ANN). This paper examined the application of ANN for software quality prediction using Object- Oriented (OO) metrics. Quality estimation includes estimating maintainability of software. The dependent variable in our study was maintenance effort. The independent variables were principal components of eight OO metrics. The results showed that the Mean Absolute Relative Error (MARE) was 0.265 of ANN model. Thus we found that ANN method was useful in constructing software quality model.

Keywords: Software quality, Measurement, Metrics, Artificial neural network, Coupling, Cohesion, Inheritance, Principal component analysis.

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Authors: Martin Kendra, Jaroslav Mašek, Juraj Čamaj, Matej Babin

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The railway transport is considered as a one of the most environmentally friendly mode of transport. With future prediction of increasing of freight transport there are lines facing problems with demanded capacity. Increase of the track capacity could be achieved by infrastructure constructive adjustments. The contribution shows how the travel time can be minimized and the track capacity increased by changing some of the basic infrastructure and operation parameters, for example, the minimal curve radius of the track, the number of tracks, or the usable track length at stations. Calculation of the necessary parameter changes is based on the fundamental physical laws applied to the train movement, and calculation of the occupation time is dependent on the changes of controlling the traffic between the stations.

Keywords: Curve radius, maximum curve speed, track mass capacity, reconstruction.

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Authors: Khin May Win, Nan Sai Moon Kham

Abstract:

Identification of cancer genes that might anticipate the clinical behaviors from different types of cancer disease is challenging due to the huge number of genes and small number of patients samples. The new method is being proposed based on supervised learning of classification like support vector machines (SVMs).A new solution is described by the introduction of the Maximized Margin (MM) in the subset criterion, which permits to get near the least generalization error rate. In class prediction problem, gene selection is essential to improve the accuracy and to identify genes for cancer disease. The performance of the new method was evaluated with real-world data experiment. It can give the better accuracy for classification.

Keywords: Microarray data, feature selection, recursive featureelimination, support vector machines.

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Authors: S. Golmohammadi, M. Noorian Bidgoli

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Because the status and mechanical parameters of discontinuities in the rock mass are included in the calculations, various methods of rock engineering classification are often used as a starting point for the design of different types of structures. The Q-system is one of the most frequently used methods for stability analysis and determination of support systems of underground structures in rock, including tunnel. In this method, six main parameters of the rock mass, namely, the Rock Quality Designation (RQD), joint set number (Jn), joint roughness number (Jr), joint alteration number (Ja), joint water parameter (Jw) and Stress Reduction Factor (SRF) are required. In this regard, in order to achieve a reasonable and optimal design, identifying the effective parameters for the stability of the mentioned structures is one of the most important goals and the most necessary actions in rock engineering. Therefore, it is necessary to study the relationships between the parameters of a system and how they interact with each other and, ultimately, the whole system. In this research, it has been attempted to determine the most effective parameters (key parameters) from the six parameters of rock mass in the Q-system using the Rock Engineering System (RES) method to improve the relationships between the parameters in the calculation of the Q value. The RES system is, in fact, a method by which one can determine the degree of cause and effect of a system's parameters by making an interaction matrix. In this research, the geomechanical data collected from the water conveyor tunnel of Azad Dam were used to make the interaction matrix of the Q-system. For this purpose, instead of using the conventional methods that are always accompanied by defects such as uncertainty, the Q-system interaction matrix is coded using a technique that is actually a statistical analysis of the data and determining the correlation coefficient between them. So, the effect of each parameter on the system is evaluated with greater certainty. The results of this study show that the formed interaction matrix provides a reasonable estimate of the effective parameters in the Q-system. Among the six parameters of the Q-system, the SRF and Jr parameters have the maximum and minimum impact on the system, respectively, and also the RQD and Jw parameters have the maximum and minimum impact on the system, respectively. Therefore, by developing this method, we can obtain a more accurate relation to the rock mass classification by weighting the required parameters in the Q-system.

Keywords: Q-system, Rock Engineering System, statistical analysis, rock mass, tunnel.

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Authors: A. Johannet, B. Vayssade, D. Bertin

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Neural networks are well known for their ability to model non linear functions, but as statistical methods usually does, they use a no parametric approach thus, a priori knowledge is not obvious to be taken into account no more than the a posteriori knowledge. In order to deal with these problematics, an original way to encode the knowledge inside the architecture is proposed. This method is applied to the problem of the evapotranspiration inside karstic aquifer which is a problem of huge utility in order to deal with water resource.

Keywords: Neural-Networks, Hydrology, Evapotranpiration, Hidden Function Modeling.

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Authors: Hajir Karimi, Fakheri Yousefi, Mahmood Reza Rahimi

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An accurate and proficient artificial neural network (ANN) based genetic algorithm (GA) is developed for predicting of nanofluids viscosity. A genetic algorithm (GA) is used to optimize the neural network parameters for minimizing the error between the predictive viscosity and the experimental one. The experimental viscosity in two nanofluids Al2O3-H2O and CuO-H2O from 278.15 to 343.15 K and volume fraction up to 15% were used from literature. The result of this study reveals that GA-NN model is outperform to the conventional neural nets in predicting the viscosity of nanofluids with mean absolute relative error of 1.22% and 1.77% for Al2O3-H2O and CuO-H2O, respectively. Furthermore, the results of this work have also been compared with others models. The findings of this work demonstrate that the GA-NN model is an effective method for prediction viscosity of nanofluids and have better accuracy and simplicity compared with the others models.

Keywords: genetic algorithm, nanofluids, neural network, viscosity

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Authors: Iacopo Testi, Diego Pajarito, Nicoletta Roberto, Carmen Greco

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Today, a consistent segment of the world’s population lives in urban areas, and this proportion will vastly increase in the next decades. Therefore, understanding the key trends in urbanization, likely to unfold over the coming years, is crucial to the implementation of sustainable urban strategies. In parallel, the daily amount of digital data produced will be expanding at an exponential rate during the following years. The analysis of various types of data sets and its derived applications have incredible potential across different crucial sectors such as healthcare, housing, transportation, energy, and education. Nevertheless, in city development, architects and urban planners appear to rely mostly on traditional and analogical techniques of data collection. This paper investigates the prospective of the data science field, appearing to be a formidable resource to assist city managers in identifying strategies to enhance the social, economic, and environmental sustainability of our urban areas. The collection of different new layers of information would definitely enhance planners' capabilities to comprehend more in-depth urban phenomena such as gentrification, land use definition, mobility, or critical infrastructural issues. Specifically, the research results correlate economic, commercial, demographic, and housing data with the purpose of defining the youth economic discomfort index. The statistical composite index provides insights regarding the economic disadvantage of citizens aged between 18 years and 29 years, and results clearly display that central urban zones and more disadvantaged than peripheral ones. The experimental set up selected the city of Rome as the testing ground of the whole investigation. The methodology aims at applying statistical and spatial analysis to construct a composite index supporting informed data-driven decisions for urban planning.

Keywords: Data science, spatial analysis, composite index, Rome, urban planning, youth economic discomfort index.

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Authors: Maassoumeh Bemani Naeini

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Studies on interlanguage have long been engaged in describing the phenomenon of variation in SLA. Pursuing the same goal and particularly addressing the role of linguistic features, this study describes the use of Persian morphology in the interlanguage of two adult English-speaking learners of Persian L2. Taking the general approach of a combination of contrastive analysis, error analysis and interlanguage analysis, this study focuses on the identification and prediction of some possible instances of transfer from English L1 to Persian L2 across six elicitation tasks aiming to investigate whether any of contextual features may variably influence the learners’ order of morpheme accuracy in the areas of copula, possessives, articles, demonstratives, plural form, personal pronouns, and genitive cases.  Results describe the existence of task variation in the interlanguage system of Persian L2 learners.

Keywords: English L1, Interlanguage Analysis, Persian L2, SLA variation.

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Authors: Andrea Gelmini

Abstract:

This paper considers the advent of 5G and the use of it in a Based Control System (BCS), posing as a basic concept the question of what the real differences and practical improvements are compared to 4G. To this purpose, a testbed hardware simulator has been designed and built where identical machines with the same sensors and management systems will communicate with different radio access network connections. This allows an objective statistical comparison of performance on the real functioning and improvement of the infrastructure with the Industrial Internet of Things (IIoT) connected to it.

Keywords: 4G, 5G, BCS, eSIM, IIoT, SCADA, Testbed.

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Authors: Shuhe Shao

Abstract:

This article provides partial evaluation index and its standard of sports aerobics, including the following 12 indexes: health vitality, coordination, flexibility, accuracy, pace, endurance, elasticity, self-confidence, form, control, uniformity and musicality. The three-layer BP artificial neural network model including input layer, hidden layer and output layer is established. The result shows that the model can well reflect the non-linear relationship between the performance of 12 indexes and the overall performance. The predicted value of each sample is very close to the true value, with a relative error fluctuating around of 5%, and the network training is successful. It shows that BP network has high prediction accuracy and good generalization capacity if being applied in sports aerobics performance evaluation after effective training.

Keywords: BP neural network, sports aerobics, performance, evaluation.

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Authors: Z. Sadeghi, M. R. Omidkhah, M. E. Masoomi

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The purpose of this paper is to examine gas transport behavior of mixed matrix membranes (MMMs) combined with porous particles. Main existing models are categorized in two main groups; two-phase (ideal contact) and three-phase (non-ideal contact). A new coefficient, J, was obtained to express equations for estimating effect of the particle porosity in two-phase and three-phase models. Modified models evaluates with existing models and experimental data using Matlab software. Comparison of gas permeability of proposed modified models with existing models in different MMMs shows a better prediction of gas permeability in MMMs.

Keywords: Mixed Matrix Membrane, Permeation Models, Porous particles, Porosity.

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Authors: Wen-Hong Liu, Hao-Tang Jhan, Kun-Lung Lin, Meng-Tsung Lee

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Weather disaster events were frequent and caused loss of lives and property in Taiwan recently. Excessive concentration of population and lacking of integrated planning led to Taiwanese coastal zone face the impacts of climate change directly. Comparing to many countries which have already set up legislation, competent authorities and national adaptation strategies, the ability of coastal management adapting to climate change is still insufficient in Taiwan. Therefore, it is necessary to establish a complete institutional arrangement for coastal management due to climate change in order to protect environment and sustain socio-economic development. This paper firstly reviews the impact of climate change on Taiwanese coastal zone. Secondly, development of Taiwanese institutional arrangement of coastal management is introduced. Followed is the analysis of four dimensions of legal basis, competent authority, scientific and financial support and international cooperations of institutional arrangement. The results show that Taiwanese government shall: 1) integrate climate change issue into Coastal Act, Wetland Act and territorial planning Act and pass them; 2) establish the high level competent authority for coastal management; 3) set up the climate change disaster coordinate platform; 4) link scientific information and decision markers; 5) establish the climate change adjustment fund; 6) participate in international climate change organizations and meetings actively; 7) cooperate with near countries to exchange experiences.

Keywords: Climate Change, Coastal Zone Management, Institution Arrangement, Adaptation.

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Authors: Majdi M. Alomari, Nafesah I. Alshdaifat, Mohammad S. Widyan

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Different countries have introduced different schemes and policies to counter global warming. The rationale behind the proposed policies and the potential barriers to successful implementation of the policies adopted by the countries were analyzed and estimated based on different models. It is argued that these models enhance the transparency and provide a better understanding to the policy makers. However, these models are underpinned with several structural and baseline assumptions. These assumptions, modeling features and future prediction of emission reductions and other implication such as cost and benefits of a transition to a low-carbon economy and its economy wide impacts were discussed. On the other hand, there are potential barriers in the form political, financial, and cultural and many others that pose a threat to the mitigation options.

Keywords: Economic wide impact, energy models, environmental policy instruments, mitigating CO2 emission.

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Authors: Mahesh K. Chudasama, Harit K. Raval

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3-roller conical bending process is widely used in the industries for manufacturing of conical sections and shells. It involves static as well dynamic bending stages. Analytical models for prediction of bending force during static as well as dynamic bending stage are available in the literature. In this paper bending forces required for static bending stage and dynamic bending stages have been compared using the analytical models. It is concluded that force required for dynamic bending is very less as compared to the bending force required during the static bending stage.

Keywords: Analytical modeling, cone frustum, dynamic bending, static bending.

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