Search results for: planar shape models

Authors: Bongsoo Jeon, Jayoung Kim, Jihong Lee

Abstract:

Methods for measuring or estimating ground shape by a laser range finder and a vision sensor (Exteroceptive sensors) have critical weaknesses in terms that these methods need a prior database built to distinguish acquired data as unique surface conditions for driving. Also, ground information by Exteroceptive sensors does not reflect the deflection of ground surface caused by the movement of UGVs. Therefore, this paper proposes a method of recognizing exact and precise ground shape using an Inertial Measurement Unit (IMU) as a proprioceptive sensor. In this paper, firstly this method recognizes the attitude of a robot in real-time using IMU and compensates attitude data of a robot with angle errors through analysis of vehicle dynamics. This method is verified by outdoor driving experiments of a real mobile robot.

Keywords: Inertial Measurement Unit, Laser Range Finder, Real-time recognition of the ground shape.

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Authors: Erika Ann Schaub, Christian J Darken

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Sociological models (e.g., social network analysis, small-group dynamic and gang models) have historically been used to predict the behavior of terrorist groups. However, they may not be the most appropriate method for understanding the behavior of terrorist organizations because the models were not initially intended to incorporate violent behavior of its subjects. Rather, models that incorporate life and death competition between subjects, i.e., models utilized by scientists to examine the behavior of wildlife populations, may provide a more accurate analysis. This paper suggests the use of biological models to attain a more robust method for understanding the behavior of terrorist organizations as compared to traditional methods. This study also describes how a biological population model incorporating predator-prey behavior factors can predict terrorist organizational recruitment behavior for the purpose of understanding the factors that govern the growth and decline of terrorist organizations. The Lotka-Volterra, a biological model that is based on a predator-prey relationship, is applied to a highly suggestive case study, that of the Irish Republican Army. This case study illuminates how a biological model can be utilized to understand the actions of a terrorist organization.

Keywords: Biological Models, Lotka-Volterra Predator-Prey Model, Terrorist Organizational Behavior, Terrorist Recruitment.

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Authors: Saih Mohamed, Rouijaa Hicham, Ghammaz Abdelilah

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This paper presents circuit models to analyze the conducted susceptibility of multiconductor shielded cables in frequency domains using Branin’s method, which is referred to as the method of characteristics. These models, which can be used directly in the time and frequency domains, take into account the presence of both the transfer impedance and admittance. The conducted susceptibility is studied by using an injection current on the cable shield as the source. Two examples are studied; a coaxial shielded cable and shielded cables with two parallel wires (i.e., twinax cables). This shield has an asymmetry (one slot on the side). Results obtained by these models are in good agreement with those obtained by other methods.

Keywords: Circuit models, multiconductor shielded cables, Branin’s method, coaxial shielded cable, twinax cables.

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Authors: Mohamed Elhakeem, A. N. Thanos Papanicolaou, Christopher Wilson, Yi-Jia Chang

Abstract:

In this study, a physically-based, modeling framework was developed to predict saturated hydraulic conductivity (K_sat) dynamics in the Clear Creek Watershed (CCW), Iowa. The modeling framework integrated selected pedotransfer functions and watershed models with geospatial tools. A number of pedotransfer functions and agricultural watershed models were examined to select the appropriate models that represent the study site conditions. Models selection was based on statistical measures of the models’ errors compared to the K_sat field measurements conducted in the CCW under different soil, climate and land use conditions. The study has shown that the predictions of the combined pedotransfer function of Rosetta and the Water Erosion Prediction Project (WEPP) provided the best agreement to the measured K_sat values in the CCW compared to the other tested models. Therefore, Rosetta and WEPP were integrated with the Geographic Information System (GIS) tools for visualization of the data in forms of geospatial maps and prediction of K_sat variability in CCW due to the seasonal changes in climate and land use activities. 

Keywords: Saturated hydraulic conductivity, pedotransfer functions, watershed models, geospatial tools.

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Authors: Kanda Wongwailikhit

Abstract:

Copper (I) oxide microparticles with the morphology of cubic and hollow sphere were synthesized with the assistance of surfactant as the shape controller. Both particles were then subjected to study the catalytic activity and observed the results of shape effects of catalysts on rate of catalytic reaction. The decolorizing reaction of crystal violet and sodium hydroxide was chosen and measured the decreasing of reactant with respect to times using spectrophotometer. The result revealed that morphology of crystal had no effect on the catalytic activity for crystal violet reaction but contributed to total surface area predominantly.

Keywords: Copper (I) oxide, Catalytic activity, Crystal violet.

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Authors: F. Sokhanvar, A. B. Khoshnevis

Abstract:

In the present work steady inviscid hypersonic flows are calculated by approximate Method. Maslens' inverse method is the chosen approximate method. For the inverse problem, parabolic shock shape is chosen for the two-dimensional flow, and the body shape and flow field are calculated using Maslen's method. For the axisymmetric inverse problem paraboloidal shock is chosen and the surface distribution of pressure is obtained.

Keywords: Hypersonic flow, Inverse problem method

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Authors: W. M. Wan Muhamad, E. Sujatmika, M.R. Idris, S.A. Syed Ahmad

Abstract:

A finite element analysis (FEA) computer software HyperWorks is utilized in re-designing an automotive component to reduce its mass. Reduction of components mass contributes towards environmental sustainability by saving world-s valuable metal resources and by reducing carbon emission through improved overall vehicle fuel efficiency. A shape optimization analysis was performed on a rear spindle component. Pre-processing and solving procedures were performed using HyperMesh and RADIOSS respectively. Shape variables were defined using HyperMorph. Then optimization solver OptiStruct was utilized with fatigue life set as a design constraint. Since Stress-Number of Cycle (S-N) theory deals with uni-axial stress, the Signed von Misses stress on the component was used for looking up damage on S-N curve, and Gerber criterion for mean stress corrections. The optimization analysis resulted in mass reduction of 24% of the original mass. The study proved that the adopted approach has high potential use for environmental sustainability.

Keywords: Environmental Sustainability, Shape Optimization, Fatigue, Rear Spindle.

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Authors: Keny Ordaz-Hernandez, Xavier Fischer, Fouad Bennis

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This article illustrates a model selection management approach for virtual prototypes in interactive simulations. In those numerical simulations, the virtual prototype and its environment are modelled as a multiagent system, where every entity (prototype,human, etc.) is modelled as an agent. In particular, virtual prototyp ingagents that provide mathematical models of mechanical behaviour inform of computational methods are considered. This work argues that selection of an appropriate model in a changing environment,supported by models? characteristics, can be managed by the deter-mination a priori of specific exploitation and performance measures of virtual prototype models. As different models exist to represent a single phenomenon, it is not always possible to select the best one under all possible circumstances of the environment. Instead the most appropriate shall be selecting according to the use case. The proposed approach consists in identifying relevant metrics or indicators for each group of models (e.g. entity models, global model), formulate their qualification, analyse the performance, and apply the qualification criteria. Then, a model can be selected based on the performance prediction obtained from its qualification. The authors hope that this approach will not only help to inform engineers and researchers about another approach for selecting virtual prototype models, but also assist virtual prototype engineers in the systematic or automatic model selection.

Keywords: Virtual prototype models, domain, qualification criterion, model qualification, model assessment, environmental modelling.

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Authors: Zhou Yu, Jiang Feng

Abstract:

An adaptive Chinese hand-talking system is presented in this paper. By analyzing the 3 data collecting strategies for new users, the adaptation framework including supervised and unsupervised adaptation methods is proposed. For supervised adaptation, affinity propagation (AP) is used to extract exemplar subsets, and enhanced maximum a posteriori / vector field smoothing (eMAP/VFS) is proposed to pool the adaptation data among different models. For unsupervised adaptation, polynomial segment models (PSMs) are used to help hidden Markov models (HMMs) to accurately label the unlabeled data, then the "labeled" data together with signerindependent models are inputted to MAP algorithm to generate signer-adapted models. Experimental results show that the proposed framework can execute both supervised adaptation with small amount of labeled data and unsupervised adaptation with large amount of unlabeled data to tailor the original models, and both achieve improvements on the performance of recognition rate.

Keywords: sign language recognition, signer adaptation, eMAP/VFS, polynomial segment model.

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Authors: Nice Vasconcelos Coimbra, Fábio dos Santos Gonçalves, Marisa Nascimento, Ellen Cristine Giese

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The development of chemical routes for the recovery and separation of rare earth elements (REE) is seen as a priority and strategic action by several countries demanding these elements. Among the possibilities of alternative routes, the biosorption process has been evaluated in our laboratory. In this theme, the present work attempts to assess and fit the solution equilibrium data in Langmuir, Freundlich and DKR isothermal models, based on the biosorption results of the lanthanum and samarium elements by Bacillus subtilis immobilized on calcium alginate gel. It was observed that the preference of adsorption of REE by the immobilized biomass followed the order Sm (III)> La (III). It can be concluded that among the studied isotherms models, the Langmuir model presented better mathematical results than the Freundlich and DKR models.

Keywords: Rare earth elements, biosorption, Bacillus subtilis, adsorption isotherm models.

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Authors: Amar Partap Singh Pharwaha, Shweta Rani

Abstract:

To develop a reliable and cost effective communication platform for the telemedicine applications, novel antenna design has been presented using bacterial foraging optimization (BFO) technique. The proposed antenna geometry is achieved by etching a modified Koch curve fractal shape at the edges and a square shape slot at the center of the radiating element of a patch antenna. It has been found that the new antenna has achieved 43.79% size reduction and better resonating characteristic than the original patch. Representative results for both simulations and numerical validations are reported in order to assess the effectiveness of the developed methodology.

Keywords: BFO, electrical permittivity, fractals, Koch curve.

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Authors: Mikhail Gritskevich, Sebastian Hohenstein

Abstract:

The paper presents the results of a detailed assessment of several modern Reynolds Averaged Navier-Stokes (RANS) turbulence models for prediction of C3X vane film cooling at various injection regimes. Three models are considered, namely the Shear Stress Transport (SST) model, the modification of the SST model accounting for the streamlines curvature (SST-CC), and the Explicit Algebraic Reynolds Stress Model (EARSM). It is shown that all the considered models face with a problem in prediction of the adiabatic effectiveness in the vicinity of the cooling holes; however, accounting for the Reynolds stress anisotropy within the EARSM model noticeably increases the solution accuracy. On the other hand, further downstream all the models provide a reasonable agreement with the experimental data for the adiabatic effectiveness and among the considered models the most accurate results are obtained with the use EARMS.

Keywords: Discrete holes film cooling, Reynolds Averaged Navier-Stokes, Reynolds stress tensor anisotropy, turbulent heat transfer.

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Authors: John P. O’Sullivan, Thomas M. P. Ratouis, Michael J. O’Sullivan

Abstract:

As the use of geothermal energy grows internationally more effort is required to monitor and protect areas with rare and important geothermal surface features. A number of approaches are presented for developing and calibrating numerical geothermal reservoir models that are capable of accurately representing geothermal surface features. The approaches are discussed in the context of cases studies of the Rotorua geothermal system and the Orakei-korako geothermal system, both of which contain important surface features. The results show that models are able to match the available field data accurately and hence can be used as valuable tools for predicting the future response of the systems to changes in use.

Keywords: Geothermal reservoir models, surface features, monitoring, TOUGH2.

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Authors: N. Sopipan, A. Intarasit, K. Chuarkham

Abstract:

 In this paper, we forecast the volatility of Baht/USDs using Markov Regime Switching GARCH (MRS-GARCH) models. These models allow volatility to have different dynamics according to unobserved regime variables. The main purpose of this paper is to find out whether MRS-GARCH models are an improvement on the GARCH type models in terms of modeling and forecasting Baht/USD volatility. The MRS-GARCH is the best performance model for Baht/USD volatility in short term but the GARCH model is best perform for long term.

Keywords: Volatility, Markov Regime Switching, Forecasting.

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Authors: Daniel Amariei, Calin O. Miclosina, Ion Vela, Marius Tufoi, Cornel Mituletu

Abstract:

Even it has been recognized that Shape Memory Alloys (SMA) have a significant potential for deployment actuators, the number of applications of SMA-based actuators to the present day is still quite small, due to the need of deep understanding of the thermo-mechanical behavior of SMA, causing an important need for a mathematical model able to describe all thermo-mechanical properties of SMA by relatively simple final set of constitutive equations. SMAs offer attractive potentials such as: reversible strains of several percent, generation of high recovery stresses and high power / weight ratios. The paper tries to provide an overview of the shape memory functions and a presentation of the designed and developed temperature control system used for a gripper actuated by two pairs of differential SMA active springs. An experimental setup was established, using electrical energy for actuator-s springs heating process. As for holding the temperature of the SMA springs at certain level for a long time was developed a control system in order to avoid the active elements overheating.

Keywords: active element, actuator, model, Nitinol, prehension

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Authors: Olga Kononova, Andrejs Krasnikovs , Videvuds Lapsa, Jurijs Kalinka, Angelina Galushchak

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Post cracking behavior and load –bearing capacity of the steel fiber reinforced high-strength concrete (SFRHSC) are dependent on the number of fibers are crossing the weakest crack (bridged the crack) and their orientation to the crack surface. Filling the mould by SFRHSC, fibers are moving and rotating with the concrete matrix flow till the motion stops in each internal point of the concrete body. Filling the same mould from the different ends SFRHSC samples with the different internal structures (and different strength) can be obtained. Numerical flow simulations (using Newton and Bingham flow models) were realized, as well as single fiber planar motion and rotation numerical and experimental investigation (in viscous flow) was performed. X-ray pictures for prismatic samples were obtained and internal fiber positions and orientations were analyzed. Similarly fiber positions and orientations in cracked cross-section were recognized and were compared with numerically simulated. Structural SFRHSC fracture model was created based on single fiber pull-out laws, which were determined experimentally. Model predictions were validated by 15x15x60cm prisms 4 point bending tests.

Keywords: fibers, orientation, high strength concrete, flow

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Authors: Oh-Yeol Kwon, Sung-Il Chien

Abstract:

A conventional image posterization method occasionally fails to preserve the shape and color of objects due to the uneffective color reduction. This paper proposes a new image posterizartion method by using modified color quantization for preserving the shape and color of objects and color contrast enhancement for improving lightness contrast and saturation. Experiment results show that our proposed method can provide visually more satisfactory posterization result than that of the conventional method.

Keywords: Color contrast enhancement, color quantization, color segmentation, image posterization

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Authors: Abdullahi Jibrin, Aishetu Abdulkadir

Abstract:

The development of allometric models is crucial to accurate forest biomass/carbon stock assessment. The aim of this study was to develop a set of biomass prediction models that will enable the determination of total tree aboveground biomass for savannah woodland area in Niger State, Nigeria. Based on the data collected through biometric measurements of 1816 trees and destructive sampling of 36 trees, five species specific and one site specific models were developed. The sample size was distributed equally between the five most dominant species in the study site (Vitellaria paradoxa, Irvingia gabonensis, Parkia biglobosa, Anogeissus leiocarpus, Pterocarpus erinaceous). Firstly, the equations were developed for five individual species. Secondly these five species were mixed and were used to develop an allometric equation of mixed species. Overall, there was a strong positive relationship between total tree biomass and the stem diameter. The coefficient of determination (R2 values) ranging from 0.93 to 0.99 P < 0.001 were realised for the models; with considerable low standard error of the estimates (SEE) which confirms that the total tree above ground biomass has a significant relationship with the dbh. F-test values for the biomass prediction models were also significant at p < 0.001 which indicates that the biomass prediction models are valid. This study recommends that for improved biomass estimates in the study site, the site specific biomass models should preferably be used instead of using generic models.

Keywords: Allometriy, biomass, carbon stock, model, regression equation, woodland, inventory.

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Authors: Ammar Mahjoubi, Ridha Fethi Mechlouch, Belgacem Mahdhaoui, Ammar Ben Brahim

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This purpose of this paper is to develop and validate a model to accurately predict the cell temperature of a PV module that adapts to various mounting configurations, mounting locations, and climates while only requiring readily available data from the module manufacturer. Results from this model are also compared to results from published cell temperature models. The models were used to predict real-time performance from a PV water pumping systems in the desert of Medenine, south of Tunisia using 60-min intervals of measured performance data during one complete year. Statistical analysis of the predicted results and measured data highlight possible sources of errors and the limitations and/or adequacy of existing models, to describe the temperature and efficiency of PV-cells and consequently, the accuracy of performance of PV water pumping systems prediction models.

Keywords: Temperature of a photovoltaic module, Predicted models, PV water pumping systems efficiency, Simulation, Desert of southern Tunisia.

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Authors: Lenka Ševelová, Aleš Florian

Abstract:

Appropriate and progressive tool for analyzing behavior of low volume roads are probabilistic models used in reliability analyses. The necessary part of the probabilistic model is the deterministic model of structural behavior. The FE model of low volume roads is created in the ANSYS software. It is able to determine the state of stress and deformation in any point of the structure and thus generate data required for the reliability analysis. The paper compares two material constitutive models used for modeling of unbound non-homogenous materials used in low volume roads. The first model is linear elastic model according to Hook theory (H model), the second one is nonlinear elastic-plastic Drucker-Prager model (D-P model).

Keywords: FEA, FEM, geotechnical materials, low volume roads, material constitutive models, pavement.

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Authors: Faisal A. Aburub

Abstract:

Organizations today need to invest in software in order to run their businesses, and to the organizations’ objectives, the software should be in line with the business process. This research presents an approach for linking process models and system models. Particularly, the new approach aims to synthesize sequence diagram based on role activity diagram (RAD) model. The approach includes four steps namely: Create business process model using RAD, identify computerized activities, identify entities in sequence diagram and identify messages in sequence diagram. The new approach has been validated using the process of student registration in University of Petra as a case study. Further research is required to validate the new approach using different domains.

Keywords: Business process modelling, system models, role activity diagrams, sequence diagrams.

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Authors: T. Watanabe

Abstract:

Combustion analysis of suspended sodium droplet is performed by solving numerically the Navier-Stokes equations and the energy conservation equations. The combustion model consists of the pre-ignition and post-ignition models. The reaction rate for the pre-ignition model is based on the chemical kinetics, while that for the post-ignition model is based on the mass transfer rate of oxygen. The calculated droplet temperature is shown to be in good agreement with the existing experimental data. The temperature field in and around the droplet is obtained as well as the droplet shape variation, and the present numerical model is confirmed to be effective for the combustion analysis.

Keywords: Combustion, analysis, sodium, droplet.

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Authors: Jianguo Tang, Kun She, William Zhu

Abstract:

Covering-based rough sets is an extension of rough sets and it is based on a covering instead of a partition of the universe. Therefore it is more powerful in describing some practical problems than rough sets. However, by extending the rough sets, covering-based rough sets can increase the roughness of each model in recognizing objects. How to obtain better approximations from the models of a covering-based rough sets is an important issue. In this paper, two concepts, determinate elements and indeterminate elements in a universe, are proposed and given precise definitions respectively. This research makes a reasonable refinement of the covering-element from a new viewpoint. And the refinement may generate better approximations of covering-based rough sets models. To prove the theory above, it is applied to eight major coveringbased rough sets models which are adapted from other literature. The result is, in all these models, the lower approximation increases effectively. Correspondingly, in all models, the upper approximation decreases with exceptions of two models in some special situations. Therefore, the roughness of recognizing objects is reduced. This research provides a new approach to the study and application of covering-based rough sets.

Keywords: Determinate element, indeterminate element, refinementof covering-element, refinement of covering, covering-basedrough sets.

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Authors: Nnamdi I. Nwulu, Shola G. Oroja

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It has become crucial over the years for nations to improve their credit scoring methods and techniques in light of the increasing volatility of the global economy. Statistical methods or tools have been the favoured means for this; however artificial intelligence or soft computing based techniques are becoming increasingly preferred due to their proficient and precise nature and relative simplicity. This work presents a comparison between Support Vector Machines and Artificial Neural Networks two popular soft computing models when applied to credit scoring. Amidst the different criteria-s that can be used for comparisons; accuracy, computational complexity and processing times are the selected criteria used to evaluate both models. Furthermore the German credit scoring dataset which is a real world dataset is used to train and test both developed models. Experimental results obtained from our study suggest that although both soft computing models could be used with a high degree of accuracy, Artificial Neural Networks deliver better results than Support Vector Machines.

Keywords: Artificial Neural Networks, Credit Scoring, SoftComputing Models, Support Vector Machines.

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Authors: Luciana Montera

Abstract:

DNA shuffling is a powerful method used for in vitro evolute molecules with specific functions and has application in areas such as, for example, pharmaceutical, medical and agricultural research. The success of such experiments is dependent on a variety of parameters and conditions that, sometimes, can not be properly pre-established. Here, two computational models predicting DNA shuffling results is presented and their use and results are evaluated against an empirical experiment. The in silico and in vitro results show agreement indicating the importance of these two models and motivating the study and development of new models.

Keywords: Computer simulation, DNA shuffling, in silico andin vitro comparison.

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Authors: Sarah Beaver, Renee Bryce

Abstract:

Audiograms detect hearing impairment, but missing values pose problems. This work explores imputations in an attempt to improve accuracy. This work implements Linear Regression, Lasso, Linear Support Vector Regression, Bayesian Ridge, K Nearest Neighbors (KNN), and Random Forest machine learning techniques to impute audiogram frequencies ranging from 125 Hz to 8000 Hz. The data contain patients who had or were candidates for cochlear implants. Accuracy is compared across two different Nested Cross-Validation k values. Over 4000 audiograms were used from 800 unique patients. Additionally, training on data combines and compares left and right ear audiograms versus single ear side audiograms. The accuracy achieved using Root Mean Square Error (RMSE) values for the best models for Random Forest ranges from 4.74 to 6.37. The R2 values for the best models for Random Forest ranges from .91 to .96. The accuracy achieved using RMSE values for the best models for KNN ranges from 5.00 to 7.72. The R2 values for the best models for KNN ranges from .89 to .95. The best imputation models received R2 between .89 to .96 and RMSE values less than 8dB. We also show that the accuracy of classification predictive models performed better with our imputation models versus constant imputations by a two percent increase.

Keywords: Machine Learning, audiograms, data imputations, single imputations.

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Authors: Spiros Mazarakis, George Matzavinos, Peter P. Groumpos

Abstract:

Economic models are complex dynamic systems with a lot of uncertainties and fuzzy data. Conventional modeling approaches using well known methods and techniques cannot provide realistic and satisfactory answers to today-s challenging economic problems. Qualitative modeling using fuzzy logic and intelligent system theories can be used to model macroeconomic models. Fuzzy Cognitive maps (FCM) is a new method been used to model the dynamic behavior of complex systems. For the first time FCMs and the Mamdani Model of Intelligent control is used to model macroeconomic models. This new model is referred as the Mamdani Rule-Based Fuzzy Cognitive Map (MBFCM) and provides the academic and research community with a new promising integrated advanced computational model. A new economic model is developed for a qualitative approach to Macroeconomic modeling. Fuzzy Controllers for such models are designed. Simulation results for an economic scenario are provided and extensively discussed

Keywords: Macroeconomic Models, Mamdani Rule Based- FCMs(MBFCMs), Qualitative and Dynamics System, Simulation.

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Authors: R. Kiš, M. Malcho, M. Janovcová

Abstract:

This work aims to present a numerical analysis of the natural gas which flows through a high-pressure pipeline and an orifice plate, through the use of CFD methods. The paper contains CFD calculations for the flow of natural gas in a pipe with different geometry used for the orifice plates. One of them has a standard geometry and a shape without any deformation and the other is deformed by the action of the pressure differential. It shows the behavior of natural gas in a pipeline using the velocity profiles and pressure fields of the gas in both models with their differences. The entire research is based on the elimination of any inaccuracy which should appear in the flow of the natural gas measured in the high-pressure pipelines of the gas industry and which is currently not given in the relevant standard.

Keywords: Orifice plate, high-pressure pipeline, natural gas, CFD analysis.

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Authors: Chockpisit Thepsithar, Aree Thongpukdee

Abstract:

Two species of Physalis, P.angulataL. and P. peruviana L. were used as models for comparative study to understand the values of micro-morphological, -anatomical and architectural characteristics of leaf for taxonomic purposes and possibly breeding and commercial applications. Both speciespossess amphistomaticleaves with 1-layer epidermis, 3-4-layer spongy mesophyll andbicollateral bundle midrib. Palisade parenchyma cells of P. angulatawere almost twice longer (65-75 μm) than the other one. Type of stomata was similar as anomocyticbut stomatal index(SI) at adaxial surface and abaxial surface of P. angulata were less than of P. peruvianaas 3.57, 4.00 and6.25, 6.66 respectively. Some leaf architectural characteristics such as leaf shape, order of venationalsoprovided information of taxonomic significance

Keywords: Physalis, Solanaceae, micromorphology, anatomy, leaf architecture.

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Authors: Pradip Kundu, Samarjit Kar, Manoranjan Maiti

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In this paper, some practical solid transportation models are formulated considering per trip capacity of each type of conveyances with crisp and rough unit transportation costs. This is applicable for the system in which full vehicles, e.g. trucks, rail coaches are to be booked for transportation of products so that transportation cost is determined on the full of the conveyances. The models with unit transportation costs as rough variables are transformed into deterministic forms using rough chance constrained programming with the help of trust measure. Numerical examples are provided to illustrate the proposed models in crisp environment as well as with unit transportation costs as rough variables.

Keywords: Solid transportation problem, Rough set, Rough variable, Trust measure.

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