Search results for: Probabilistic Models

Authors: Rehab Abdulmajed, Amr Hamada, Ahmed Elsaid, Hisashi Hayakawa, Ayman Mahrous

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Solar emissions have a high impact on the Earth’s magnetic field, and the prediction of solar events is of high interest. Various techniques have been used in the prediction of the solar wind using mathematical models, MHD models and neural network (NN) models. This study investigates the coronal hole (CH) derived high-speed streams (HSSs) and their correlation to the CH area and create a neural network model to predict the HSSs. Two different algorithms were used to compare different models to find a model that best simulated the HSSs. A dataset of CH synoptic maps through Carrington rotations 1601 to 2185 along with Omni-data set solar wind speed averaged over the Carrington rotations is used, which covers Solar Cycles (SC) 21, 22, 23, and most of 24.

Keywords: Artificial Neural Network, ANN, Coronal Hole Area Feed-Forward neural network models, solar High-Speed Streams, HSSs.

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Authors: A. Pereira, S. Haffner, L. V. Gasperin

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This paper presents two simplified models to determine nodal voltages in power distribution networks. These models allow estimating the impact of the installation of reactive power compensations equipments like fixed or switched capacitor banks. The procedure used to develop the models is similar to the procedure used to develop linear power flow models of transmission lines, which have been widely used in optimization problems of operation planning and system expansion. The steady state non-linear load flow equations are approximated by linear equations relating the voltage amplitude and currents. The approximations of the linear equations are based on the high relationship between line resistance and line reactance (ratio R/X), which is valid for power distribution networks. The performance and accuracy of the models are evaluated through comparisons with the exact results obtained from the solution of the load flow using two test networks: a hypothetical network with 23 nodes and a real network with 217 nodes.

Keywords: Distribution network models, distribution systems, optimization, power system planning.

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Authors: Parikshit Dutta, Mathieu Saujot, Elise Arnaud, Benoit Lefevre, Emmanuel Prados

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In this work, propagation of uncertainty during calibration process of TRANUS, an integrated land use and transport model (ILUTM), has been investigated. It has also been examined, through a sensitivity analysis, which input parameters affect the variation of the outputs the most. Moreover, a probabilistic verification methodology of calibration process, which equates the observed and calculated production, has been proposed. The model chosen as an application is the model of the city of Grenoble, France. For sensitivity analysis and uncertainty propagation, Monte Carlo method was employed, and a statistical hypothesis test was used for verification. The parameters of the induced demand function in TRANUS, were assumed as uncertain in the present case. It was found that, if during calibration, TRANUS converges, then with a high probability the calibration process is verified. Moreover, a weak correlation was found between the inputs and the outputs of the calibration process. The total effect of the inputs on outputs was investigated, and the output variation was found to be dictated by only a few input parameters.

Keywords: Uncertainty propagation, sensitivity analysis, calibration under uncertainty, hypothesis testing, integrated land use and transport models, TRANUS, Grenoble.

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Authors: R. Kara, M. Can

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In this paper we study a food chain model with three trophic levels and Michaelis-Menten type ratio-dependent functional response. Distinctive feature of this model is the sensitive dependence of the dynamical behavior on the initial populations and parameters of the real world. The stability of the equilibrium points are also investigated.

Keywords: Food chain, Ratio dependent models, Three level models.

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Authors: R. K. Dubey

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Bianchi type cosmological models have been studied on the basis of Lyra’s geometry. Exact solution has been obtained by considering a time dependent displacement field for constant deceleration parameter and varying cosmological term of the universe. The physical behavior of the different models has been examined for different cases.

Keywords: Bianchi type-I cosmological model, variable gravitational coupling (G) and Cosmological Constant term (β).

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Authors: H. Al-Sholigom, Z. Al-Mostafa

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Many associations and experimental models have been developed to estimate solar radiation around the world. The duration of sunshine is the most commonly used parameter for estimating global solar radiation because it can be easily and reliably measured. To estimate the global monthly solar average on horizontal surfaces, we used 52 models with widely available data in Hutat Suder, Saudi Arabia. After testing the models, some were not suitable for use in this area, while others differed in performance. The best models have been identified.

Keywords: Earth, Global solar radiation, Hutat Suder, Saudi Arabia, sunshine, measured data.

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Authors: Andrej Golowin, Viktor Denk, Axel Riepe

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Solid fan blades and discs in aero engines are subjected to high combined low and high cycle fatigue loads especially around the contact areas between blade and disc. Therefore, special coatings (e.g. dry film lubricant) and surface treatments (e.g. shot peening or laser shock peening) are applied to increase the strength with respect to combined cyclic fatigue and fretting fatigue, but also to improve damage tolerance capability. The traditional deterministic damage tolerance assessment based on fracture mechanics analysis, which treats service damage as an initial crack, often gives overly conservative results especially in the presence of vibratory stresses. A probabilistic damage tolerance methodology using crack initiation data has been developed for fan discs exposed to relatively high vibratory stresses in cross- and tail-wind conditions at certain resonance speeds for limited time periods. This Monte-Carlo based method uses a damage databank from similar designs, measured vibration levels at typical aircraft operations and wind conditions and experimental crack initiation data derived from testing of artificially damaged specimens with representative surface treatment under combined fatigue conditions. The proposed methodology leads to a more realistic prediction of the minimum damage tolerance life for the most critical locations applicable to modern fan disc designs.

Keywords: Damage tolerance, Monte-Carlo method, fan blade and disc, laser shock peening.

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Authors: Bala Dhandayuthapani Veerasamy

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Parallel programming models exist as an abstraction of hardware and memory architectures. There are several parallel programming models in commonly use; they are shared memory model, thread model, message passing model, data parallel model, hybrid model, Flynn-s models, embarrassingly parallel computations model, pipelined computations model. These models are not specific to a particular type of machine or memory architecture. This paper expresses the model program for concurrent approach to data parallel model through java programming.

Keywords: Concurrent, Data Parallel, JDK, Parallel, Thread

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Authors: Tadeusz Nowicki, Radosław Pytlak, Robert Waszkowski, Jerzy Bertrandt, Anna Kłos

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This paper presents methods for formal modeling of activities in the area of sanitary inspectors outbreak of food-borne diseases. The models allow you to measure the characteristics of the activities of sanitary inspection and as a result allow improving the performance of sanitary services and thus food security.

Keywords: Food-borne disease, epidemic, sanitary inspection, mathematical models.

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Authors: Wardah, T., Kamil, A.A., Sahol Hamid, A.B., Maisarah, W.W.I

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Quantitative precipitation forecast (QPF) from atmospheric model as input to hydrological model in an integrated hydro-meteorological flood forecasting system has been operational in many countries worldwide. High-resolution numerical weather prediction (NWP) models with grid cell sizes between 2 and 14 km have great potential in contributing towards reasonably accurate QPF. In this study the potential of two NWP models to forecast precipitation for a flood-prone area in a tropical region is examined. The precipitation forecasts produced from the Fifth Generation Penn State/NCAR Mesoscale (MM5) and Weather Research and Forecasting (WRF) models are statistically verified with the observed rain in Kelantan River Basin, Malaysia. The statistical verification indicates that the models have performed quite satisfactorily for low and moderate rainfall but not very satisfactory for heavy rainfall.

Keywords: MM5, Numerical weather prediction (NWP), quantitative precipitation forecast (QPF), WRF

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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

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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: 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

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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: Mikhail Gritskevich, Sebastian Hohenstein

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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

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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

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 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: Abdullahi Jibrin, Aishetu Abdulkadir

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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: Faisal A. Aburub

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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: Jianguo Tang, Kun She, William Zhu

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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

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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

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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

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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: 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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Authors: Ashwini V. Chavan, Sukhanand S. Bhosale

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Challenges of weak soil subgrade are often resolved either by stabilization or reinforcing it. However, it is also practiced to reinforce the granular fill to improve the load-settlement behavior of it over weak soil strata. The inclusion of reinforcement in the engineered granular fill provided a new impetus for the development of enhanced Soil-Structure Interaction (SSI) models, also known as mechanical foundation models or lumped parameter models. Several researchers have been working in this direction to understand the mechanism of granular fill-reinforcement interaction and the response of weak soil under the application of load. These models have been developed by extending available SSI models such as the Winkler Model, Pasternak Model, Hetenyi Model, Kerr Model etc., and are helpful to visualize the load-settlement behavior of a physical system through 1-D and 2-D analysis considering beam and plate resting on the foundation, respectively. Based on the literature survey, these models are categorized as ‘Reinforced Pasternak Model,’ ‘Double Beam Model,’ ‘Reinforced Timoshenko Beam Model,’ and ‘Reinforced Kerr Model’. The present work reviews the past 30+ years of research in the field of SSI models for reinforced foundation systems, presenting the conceptual development of these models systematically and discussing their limitations. A flow-chart showing procedure for compution of deformation and mobilized tension is also incorporated in the paper. Special efforts are taken to tabulate the parameters and their significance in the load-settlement analysis, which may be helpful in future studies for the comparison and enhancement of results and findings of physical models. 

Keywords: geosynthetics, mathematical modeling, reinforced foundation, soil-structure interaction, ground improvement, soft soil

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Authors: Om Parkash, C.P.Gandhi

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Probabilistic measures of uncertainty have been obtained as functions of time and birth and death rates in a queuing process. The variation of different entropy measures has been studied in steady and non-steady processes of queuing theory.

Keywords: Uncertainty, steady state, non-steady state, trafficintensity, monotonocity

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