Search results for: Nonlinear time series analysis

Authors: Yanting Cao, Kazumitsu Nawata

Abstract:

As smartphones are continually upgrading, their software and hardware are getting smarter, so the smartphone-based human activity recognition will be described more refined, complex and detailed. In this context, we analyzed a set of experimental data, obtained by observing and measuring 30 volunteers with six activities of daily living (ADL). Due to the large sample size, especially a 561-feature vector with time and frequency domain variables, cleaning these intractable features and training a proper model become extremely challenging. After a series of feature selection and parameters adjustments, a well-performed SVM classifier has been trained. 

Keywords: smart sensors, human activity recognition, artificial intelligence, SVM

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Authors: Delfim Soares Jr.

Abstract:

In this work, a new family of time marching procedures based on Green’s function matrices is presented. The formulation is based on the development of new recurrence relationships, which employ time integral terms to treat initial condition values. These integral terms are numerically evaluated taking into account Newton-Cotes formulas. The Green’s matrices of the model are also numerically computed, taking into account the generalized-α method and subcycling techniques. As it is discussed and illustrated along the text, the proposed procedure is efficient and accurate, providing a very attractive time marching technique. 

Keywords: Dynamics, Time-Marching, Green’s Function, Generalized-α Method, Subcycling.

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Authors: Amin Lotfi Eghlim, Mehran pourgholi

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Explosion occurs due to sudden release of energy. Common examples of explosion include chemical, atomic, heat, and pressure tank (due to ignition) explosions. Petroleum, gas, and petrochemical industries operations are threatened by natural risks and processes. Fires and explosions are the greatest process risks which cause financial damages. This study aims at designing a single-floor structure for the control room of a petroleum refinery to be resistant against gas explosion loads, and the information related to the structure specifications have been provided regarding the fact that the structure is made on the ground's surface. In this research, the lateral stiffness of single pile is calculated by SPPLN.FOR computer program, and its value for 13624 KN/m single pile has been assessed. The analysis used due to the loading conditions, is dynamic nonlinear analysis with direct integration method.

Keywords: Gas Explosion Load, Petroleum Refinery, Single-Floor Structure

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Authors: Imran Khan, Shujaat Ali Khan Tanoli, Nandana Rajatheva

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This paper presents an analysis on the capacity and performance of MIMO-OFDM systems. The work is focused on the capacity of MIMO-OFDM systems over rician fading channel, in the case of the channel being known at the receiver only, which is more practical case of the channel. Simple expression for capacity is derived for the case of correlated rician fading. The performance of some MIMO-OFDM implementations with rician fading model is presented using an Alamouti coding scheme and Simulation results are obtained for both capacity and performance analysis.

Keywords: MIMO, OFDM, rician distribution, space time blockcodes (STBC).

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Authors: Weifeng Pan

Abstract:

Complex networks have been intensively studied across many fields, especially in Internet technology, biological engineering, and nonlinear science. Software is built up out of many interacting components at various levels of granularity, such as functions, classes, and packages, representing another important class of complex networks. It can also be studied using complex network theory. Over the last decade, many papers on the interdisciplinary research between software engineering and complex networks have been published. It provides a different dimension to our understanding of software and also is very useful for the design and development of software systems. This paper will explore how to use the complex network theory to analyze software structure, and briefly review the main advances in corresponding aspects.

Keywords: Metrics, measurement, complex networks, software.

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Authors: Ghasem Abbasnejad, Soheil Zarkandi, Misagh Imani

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In this article the homotopy continuation method (HCM) to solve the forward kinematic problem of the 3-PRS parallel manipulator is used. Since there are many difficulties in solving the system of nonlinear equations in kinematics of manipulators, the numerical solutions like Newton-Raphson are inevitably used. When dealing with any numerical solution, there are two troublesome problems. One is that good initial guesses are not easy to detect and another is related to whether the used method will converge to useful solutions. Results of this paper reveal that the homotopy continuation method can alleviate the drawbacks of traditional numerical techniques.

Keywords: Forward kinematics, Homotopy continuationmethod, Parallel manipulators, Rotation matrix

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Authors: Donna M. G. Comissiong, Tyrone D. Dass, Harold Ramkissoon, Alana R. Sankar

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The B'enard-Marangoni thermal instability problem for a viscoelastic Jeffreys- fluid layer with internal heat generation is investigated. The fluid layer is bounded above by a realistic free deformable surface and by a plane surface below. Our analysis shows that while the internal heat generation and the relaxation time both destabilize the fluid layer, its stability may be enhanced by an increased retardation time.

Keywords: Viscoelastic fluid, Jeffreys' model, Maxwell model, internal heat generation, retardation time, relaxation time.

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Authors: B. Selma

Abstract:

The aim of this study is to test the feasibility of SIPINA method to predict the harmfulness parameters controlling the seismic response. The approach developed takes into consideration both the focal depth and the peak ground acceleration. The parameter to determine is displacement. The data used for the learning of this method and analysis nonlinear seismic are described and applied to a class of models damaged to some typical structures of the existing urban infrastructure of Jassy, Romania. The results obtained indicate an influence of the focal depth and the peak ground acceleration on the displacement.

Keywords: SIPINA method, seism, focal depth, peak ground acceleration, displacement.

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Authors: Sandra Baßler, Peter Dünow, Mathias Marquardt

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A Fourier series based learning control (FSBLC) algorithm for tracking trajectories of mechanical systems with unknown nonlinearities is presented. Two processes are introduced to which the FSBLC with PD controller is applied. One is a simplified service robot capable of climbing stairs due to special wheels and the other is a propeller driven pendulum with nearly the same requirements on control. Additionally to the investigation of learning the feed forward for the desired trajectories some considerations on the implementation of such an algorithm on low cost microcontroller hardware are made. Simulations of the service robot as well as practical experiments on the pendulum show the capability of the used FSBLC algorithm to perform the task of improving control behavior for repetitive task of such mechanical systems.

Keywords: Climbing stairs, FSBLC, ILC, Service robot.

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Authors: K. P. Oyeduntan, K. Oshinubi

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Nigeria is referred as the ‘Giant of Africa’ due to high population, land mass and large economy. However, it still trails far behind many smaller economies in the continent in terms of maritime operations. As we have seen that the maritime industry is the sparkplug for national growth, because it houses the most crucial infrastructure that generates wealth for a nation, it is worrisome that a nation with six seaports lag in maritime activities. In this research, we have studied how the Gross Domestic Product (GDP) of the maritime transport influences the Nigerian economy. To do this, we applied Simple Linear Regression (SLR), Support Vector Machine (SVM), Polynomial Regression Model (PRM), Generalized Additive Model (GAM) and Generalized Linear Mixed Model (GLMM) to model the relationship between the nation’s Total GDP (TGDP) and the Maritime Transport GDP (MGDP) using a time series data of 20 years. The result showed that the MGDP is statistically significant to the Nigerian economy. Amongst the statistical tool applied, the PRM of order 4 describes the relationship better when compared to other methods. The recommendations presented in this study will guide policy makers and help improve the economy of Nigeria.

Keywords: Economy, GDP, maritime transport, port, regression.

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Authors: Tudor Barbu

Abstract:

We provide a supervised speech-independent voice recognition technique in this paper. In the feature extraction stage we propose a mel-cepstral based approach. Our feature vector classification method uses a special nonlinear metric, derived from the Hausdorff distance for sets, and a minimum mean distance classifier.

Keywords: Text-independent speaker recognition, mel cepstral analysis, speech feature vector, Hausdorff-based metric, supervised classification.

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Authors: Salah R. Al Zaidee, Ali S. Mahdi

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Except for simple problems of statically determinate structures, optimum design problems in structural engineering have implicit objective functions where structural analysis and design are essential within each searching loop. With these implicit functions, the structural engineer is usually enforced to write his/her own computer code for analysis, design, and searching for optimum design among many feasible candidates and cannot take advantage of available software for structural analysis, design, and searching for the optimum solution. The meta-model is a regression model used to transform an implicit objective function into objective one and leads in turn to decouple the structural analysis and design processes from the optimum searching process. With the meta-model, well-known software for structural analysis and design can be used in sequence with optimum searching software. In this paper, the meta-model has been used to develop an explicit objective function for plane steel frames subjected to dead, live, and seismic forces. Frame topology is assumed as predefined based on architectural and functional requirements. Columns and beams sections and different connections details are the main design variables in this study. Columns and beams are grouped to reduce the number of design variables and to make the problem similar to that adopted in engineering practice. Data for the implicit objective function have been generated based on analysis and assessment for many design proposals with CSI SAP software. These data have been used later in SPSS software to develop a pure quadratic nonlinear regression model for the explicit objective function. Good correlations with a coefficient, R², in the range from 0.88 to 0.99 have been noted between the original implicit functions and the corresponding explicit functions generated with meta-model.

Keywords: Meta-modal, objective function, steel frames, seismic analysis, design.

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Authors: Yanru Wu, Qing Sun

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Sightseeing glass bridges located in steep valley area are being built on a large scale owing to the development of tourism. Consequently, their aerostatic stability is seriously affected by the wind field characteristics created by strong wind and special terrain, such as wind speed and wind attack angle. For instance, a cable-stayed pedestrian bridge without backstays comprised of a 60-m cantilever girder and the glass bridge deck is located in an abrupt valley, acting as a viewing platform. The bridge’s nonlinear aerostatic stability was analyzed by the segmental model test and numerical simulation in this paper. Based on aerostatic coefficients of the main girder measured in wind tunnel tests, nonlinear influences caused by the structure and aerostatic load, inhomogeneous distribution of torsion angle along the bridge axis, and the influence of initial attack angle were analyzed by using the incremental double iteration method. The results show that the aerostatic response varying with speed shows an obvious nonlinearity, and the aerostatic instability mode is of the characteristic of space deformation of bending-twisting coupling mode. The vertical and torsional deformation of the main girder is larger than its lateral deformation, with the wind speed approaching the critical wind speed. The flow of negative attack angle will reduce the bridges’ critical stability wind speed, but the influence of the negative attack angle on the aerostatic stability is more significant than that of the positive attack angle. The critical wind speeds of torsional divergence and lateral buckling are both larger than 200 m/s; namely, the bridge will not occur aerostatic instability under the action of various wind attack angles.

Keywords: Aerostatic nonlinearity, cable-stayed pedestrian bridge, numerical simulation, nonlinear aerostatic stability.

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Authors: Heungsu Lee, Youngseok Kim, Jonghwa Yi, Chul Park

Abstract:

A landing pier is subjected to safety assessment by visual inspection and design data, but it is difficult to check the damage in real-time. In this study, real - time damage detection and safety evaluation methods were studied. As a result of structural analysis of the arbitrary landing pier structure, the inflection point of deformation and moment occurred at 10%, 50%, and 90% of pile length. The critical value of Fiber Bragg Grating (FBG) sensor was set according to the safety factor, and the FBG sensor application method for real - time safety evaluation was derived.

Keywords: FBG sensor, harbor structure, maintenance, safety evaluation system.

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Authors: Akash Rathee, Harish Parthasarathy

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In this paper, a frequency-variation based method has been proposed for transistor parameter estimation in a commonemitter transistor amplifier circuit. We design an algorithm to estimate the transistor parameters, based on noisy measurements of the output voltage when the input voltage is a sine wave of variable frequency and constant amplitude. The common emitter amplifier circuit has been modelled using the transistor Ebers-Moll equations and the perturbation technique has been used for separating the linear and nonlinear parts of the Ebers-Moll equations. This model of the amplifier has been used to determine the amplitude of the output sinusoid as a function of the frequency and the parameter vector. Then, applying the proposed method to the frequency components, the transistor parameters have been estimated. As compared to the conventional time-domain least squares method, the proposed method requires much less data storage and it results in more accurate parameter estimation, as it exploits the information in the time and frequency domain, simultaneously. The proposed method can be utilized for parameter estimation of an analog device in its operating range of frequencies, as it uses data collected from different frequencies output signals for parameter estimation.

Keywords: Perturbation Technique, Parameter estimation, frequency-variation based method.

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Authors: Saeed Mian Qaisar, Laurent Fesquet, Marc Renaudin

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The frequency contents of the non-stationary signals vary with time. For proper characterization of such signals, a smart time-frequency representation is necessary. Classically, the STFT (short-time Fourier transform) is employed for this purpose. Its limitation is the fixed timefrequency resolution. To overcome this drawback an enhanced STFT version is devised. It is based on the signal driven sampling scheme, which is named as the cross-level sampling. It can adapt the sampling frequency and the window function (length plus shape) by following the input signal local variations. This adaptation results into the proposed technique appealing features, which are the adaptive time-frequency resolution and the computational efficiency.

Keywords: Level Crossing Sampling, Activity Selection, Adaptive Resolution Analysis, Computational Complexity.

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Authors: Farnaz Nazem

Abstract:

The aim of sustainable architecture is to design buildings with the least adverse effects on the environment and provide better conditions for people. What building forms make the best use of land? This question was addressed in the late 1960s at the center of Land Use and Built Form Studies in Cambridge. This led to a number of influential papers which had a great influence on the practice of urban design. This paper concentrates on the results of sustainability caused by climatic conditions in Iranian traditional architecture in hot-arid regions. As people spent a significant amount of their time in houses, it was very important to have such houses to fulfill their needs physically and spiritually as well as satisfying their cultural and religious aspects of their lifestyles. In a vast country such as Iran with different climatic zones, traditional builders have presented series of logical solutions for human comfort. These solutions have been able to response to the environmental problems for a long period of time. As a result, by considering the experience in traditional architecture of hot–arid climate in Iran, it is possible to attain sustainable architecture.

Keywords: Hot-arid climate, Iran, sustainable traditional architecture, urban planning.

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Authors: Emad Amar, Tawfik Khattab, Fatma Zada

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Predicting earthquakes is an important issue in the study of geography. Accurate prediction of earthquakes can help people to take effective measures to minimize the loss of personal and economic damage, such as large casualties, destruction of buildings and broken of traffic, occurred within a few seconds. United States Geological Survey (USGS) science organization provides reliable scientific information about Earthquake Existed throughout history & the Preliminary database from the National Center Earthquake Information (NEIC) show some useful factors to predict an earthquake in a seismic area like Aleutian Arc in the U.S. state of Alaska. The main advantage of this prediction method that it does not require any assumption, it makes prediction according to the future evolution of the object's time series. The article compares between simulation data result from trained BP and RBF neural network versus actual output result from the system calculations. Therefore, this article focuses on analysis of data relating to real earthquakes. Evaluation results show better accuracy and higher speed by using radial basis functions (RBF) neural network.

Keywords: BP neural network, Prediction, RBF neural network.

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Authors: Lianglin Xiong, Shouming Zhong, Mao Ye

Abstract:

This paper considers the robust exponential stability issues for a class of uncertain switched neutral system which delays switched according to the switching rule. The system under consideration includes both stable and unstable subsystems. The uncertainties considered in this paper are norm bounded, and possibly time varying. Based on multiple Lyapunov functional approach and dwell-time technique, the time-dependent switching rule is designed depend on the so-called average dwell time of stable subsystems as well as the ratio of the total activation time of stable subsystems and unstable subsystems. It is shown that by suitably controlling the switching between the stable and unstable modes, the robust stabilization of the switched uncertain neutral systems can be achieved. Two simulation examples are given to demonstrate the effectiveness of the proposed method.

Keywords: Switched neutral system, exponential stability, multiple Lyapunov functional, dwell time technique, time-dependent switching rule.

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Authors: Jorge A. Ruiz-Vanoye, Ocotlán Díaz-Parra, Alejandro Fuentes-Penna, Daniel Vélez-Díaz, Edith Olaco García

Abstract:

In this paper, we present the use of the discriminant analysis to select evolutionary algorithms that better solve instances of the vehicle routing problem with time windows. We use indicators as independent variables to obtain the classification criteria, and the best algorithm from the generic genetic algorithm (GA), random search (RS), steady-state genetic algorithm (SSGA), and sexual genetic algorithm (SXGA) as the dependent variable for the classification. The discriminant classification was trained with classic instances of the vehicle routing problem with time windows obtained from the Solomon benchmark. We obtained a classification of the discriminant analysis of 66.7%.

Keywords: Intelligent transportation systems, data-mining techniques, evolutionary algorithms, discriminant analysis, machine learning.

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Authors: Zhenying Hong, Guangwei Yuan, Xuedong Fu, Shulin Yang

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In this paper, the typical exponential method, diamond difference and modified time discrete scheme is researched for self adaptive time step. The second-order time evolution scheme is applied to time-dependent spherical neutron transport equation by discrete ordinates method. The numerical results show that second-order time evolution scheme associated exponential method has some good properties. The time differential curve about neutron current is more smooth than that of exponential method and diamond difference and modified time discrete scheme.

Keywords: Exponential method, diamond difference, modified time discrete scheme, second-order time evolution scheme.

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Authors: Sun K. Yoo, Hee Cheol Kang

Abstract:

Analysis of amplitude and phase characteristics for delta, theta, and alpha bands at localized time instant from EEG signals is important for the characterizing information processing in the brain. In this paper, complex demodulation method was used to analyze EEG (Electroencephalographic) signal, particularly for auditory evoked potential response signal, with sufficient time resolution and designated frequency bandwidth resolution required. The complex demodulation decomposes raw EEG signal into 3 designated delta, theta, and alpha bands with complex EEG signal representation at sampled time instant, which can enable the extraction of amplitude envelope and phase information. Throughout simulated test data, and real EEG signal acquired during auditory attention task, it can extract the phase offset, phase and frequency changing instant and decomposed amplitude envelope for delta, theta, and alpha bands. The complex demodulation technique can be efficiently used in brain signal analysis in case of phase, and amplitude information required.

Keywords: EEG, Complex Demodulation, Amplitude, Phase.

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Authors: Geeta Partap, Nitika Chugh

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The present paper deals with the flexural vibrations of homogeneous, isotropic, generalized micropolar microstretch thermoelastic thin Euler-Bernoulli beam resonators, due to Exponential time varying load. Both the axial ends of the beam are assumed to be at simply supported conditions. The governing equations have been solved analytically by using Laplace transforms technique twice with respect to time and space variables respectively. The inversion of Laplace transform in time domain has been performed by using the calculus of residues to obtain deflection.The analytical results have been numerically analyzed with the help of MATLAB software for magnesium like material. The graphical representations and interpretations have been discussed for Deflection of beam under Simply Supported boundary condition and for distinct considered values of time and space as well. The obtained results are easy to implement for engineering analysis and designs of resonators (sensors), modulators, actuators.

Keywords: Microstretch, deflection, exponential load, Laplace transforms, Residue theorem, simply supported.

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Authors: A.L. Seetharam, B.L. Udaya Simha

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The Bangalore City is facing the acute problem of pollution in the atmosphere due to the heavy increase in the traffic and developmental activities in recent years. The present study is an attempt in the direction to assess trend of the ambient air quality status of three stations, viz., AMCO Batteries Factory, Mysore Road, GRAPHITE INDIA FACTORY, KHB Industrial Area, Whitefield and Ananda Rao Circle, Gandhinagar with respect to some of the major criteria pollutants such as Total Suspended particular matter (SPM), Oxides of nitrogen (NOx), and Oxides of sulphur (SO2). The sites are representative of various kinds of growths viz., commercial, residential and industrial, prevailing in Bangalore, which are contributing to air pollution. The concentration of Sulphur Dioxide (SO2) at all locations showed a falling trend due to use of refined petrol and diesel in the recent years. The concentration of Oxides of nitrogen (NOx) showed an increasing trend but was within the permissible limits. The concentration of the Suspended particular matter (SPM) showed the mixed trend. The correlation between model and observed values is found to vary from 0.4 to 0.7 for SO2, 0.45 to 0.65 for NOx and 0.4 to 0.6 for SPM. About 80% of data is observed to fall within the error band of ±50%. Forecast test for the best fit models showed the same trend as actual values in most of the cases. However, the deviation observed in few cases could be attributed to change in quality of petro products, increase in the volume of traffic, introduction of LPG as fuel in many types of automobiles, poor condition of roads, prevailing meteorological conditions, etc.

Keywords: Bangalore, urban air pollution, time series analysis.

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Authors: Ritu Ahlawat

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Among all geo-hydrological relationships, rainfallrunoff relationship is of utmost importance in any hydrological investigation and water resource planning. Spatial variation, lag time involved in obtaining areal estimates for the basin as a whole can affect the parameterization in design stage as well as in planning stage. In conventional hydrological processing of data, spatial aspect is either ignored or interpolated at sub-basin level. Temporal variation when analysed for different stages can provide clues for its spatial effectiveness. The interplay of space-time variation at pixel level can provide better understanding of basin parameters. Sustenance of design structures for different return periods and their spatial auto-correlations should be studied at different geographical scales for better management and planning of water resources. In order to understand the relative effect of spatio-temporal variation in hydrological data network, a detailed geo-hydrological analysis of Betwa river catchment falling in Lower Yamuna Basin is presented in this paper. Moreover, the exact estimates about the availability of water in the Betwa river catchment, especially in the wake of recent Betwa-Ken linkage project, need thorough scientific investigation for better planning. Therefore, an attempt in this direction is made here to analyse the existing hydrological and meteorological data with the help of SPSS, GIS and MS-EXCEL software. A comparison of spatial and temporal correlations at subcatchment level in case of upper Betwa reaches has been made to demonstrate the representativeness of rain gauges. First, flows at different locations are used to derive correlation and regression coefficients. Then, long-term normal water yield estimates based on pixel-wise regression coefficients of rainfall-runoff relationship have been mapped. The areal values obtained from these maps can definitely improve upon estimates based on point-based extrapolations or areal interpolations.

Keywords: Catchment's runoff estimates, influence area regional regression coefficients, runoff yield series,

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Authors: Sumiko Anno, Keiji Imaoka, Takeo Tadono, Tamotsu Igarashi, Subramaniam Sivaganesh, Selvam Kannathasan, Vaithehi Kumaran, Sinnathamby Noble Surendran

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Dengue outbreaks are affected by biological, ecological, socio-economic and demographic factors that vary over time and space. These factors have been examined separately and still require systematic clarification. The present study aimed to investigate the spatial-temporal clustering relationships between these factors and dengue outbreaks in the northern region of Sri Lanka. Remote sensing (RS) data gathered from a plurality of satellites were used to develop an index comprising rainfall, humidity and temperature data. RS data gathered by ALOS/AVNIR-2 were used to detect urbanization, and a digital land cover map was used to extract land cover information. Other data on relevant factors and dengue outbreaks were collected through institutions and extant databases. The analyzed RS data and databases were integrated into geographic information systems, enabling temporal analysis, spatial statistical analysis and space-time clustering analysis. Our present results showed that increases in the number of the combination of ecological factor and socio-economic and demographic factors with above the average or the presence contribute to significantly high rates of space-time dengue clusters.

Keywords: ALOS/AVNIR-2, Dengue, Space-time clustering analysis, Sri Lanka.

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Authors: Ching Louis Liu, Edmund Kazmierczak, Tim Miller

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Safety analysis for multi-agent systems is complicated by the, potentially nonlinear, interactions between agents. This paper proposes a method for analyzing the safety of multi-agent systems by explicitly focusing on interactions and the accident data of systems that are similar in structure and function to the system being analyzed. The method creates a Bayesian network using the accident data from similar systems. A feature of our method is that the events in accident data are labeled with HAZOP guide words. Our method uses an Ontology to abstract away from the details of a multi-agent implementation. Using the ontology, our methods then constructs an “Interaction Map,” a graphical representation of the patterns of interactions between agents and other artifacts. Interaction maps combined with statistical data from accidents and the HAZOP classifications of events can be converted into a Bayesian Network. Bayesian networks allow designers to explore “what it” scenarios and make design trade-offs that maintain safety. We show how to use the Bayesian networks, and the interaction maps to improve multi-agent system designs.

Keywords: Multi-agent system, safety analysis, safety model.

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Authors: V. Precupas, A. Ivan, M. Ivan

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The dome with ribs and rings, which covers the ROMEXPO pavilion from Bucharest, was designed after the collapse of the single layer reticulated dome. In this paper, it was made the checking of the structure, under the dynamic loads with three recorded accelerograms calibrated according to Romanian seismic design code P100-1/2006. Under the action the dynamic loadings, it was made a time-history analysis to determine the zones where the plastic hinges appear, at what accelerations and their position on the structure. The studied dome is formed by 32 spatial semi arches and three rings: one circular ring located at the top of the dome and another two rings, design as trusses, the first near the supports and the second as an intermediate rings above the skylights. Above the skylights up to the top, the dome is tight together with purlins and bracings.

Keywords: dome, dynamic analysis, plastic hinges, time-history

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Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut

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In the first part of this paper [6], a method to determine Frenet apparatus of the space-like curves in Minkowski space-time is presented. In this work, the mentioned method is developed for the time-like curves in Minkowski space-time. Additionally, an example of presented method is illustrated.

Keywords: Frenet Apparatus, Time-like Curves, MinkowskiSpace-time.

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Authors: Ahmed M. Mansour, Ali M. El-Sawy, Ahmed T Sayed

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Logarithms reduce products to sums and powers to products; they play an important role in signal processing, communication and information theory. They are primarily used for hardware calculations, handling multiplications, divisions, powers, and roots effectively. There are three commonly used bases for logarithms; the logarithm with base-10 is called the common logarithm, the natural logarithm with base-e and the binary logarithm with base-2. This paper demonstrates different methods of calculation for log2 showing the complexity of each and finds out the most accurate and efficient besides giving insights to their hardware design. We present a new method called Floor Shift for fast calculation of log2, and then we combine this algorithm with Taylor series to improve the accuracy of the output, we illustrate that by using two examples. We finally compare the algorithms and conclude with our remarks.

Keywords: Logarithms, log2, floor, iterative, CORDIC, Taylor series.

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