Search results for: prediction equations

Authors: Sokkhey Phauk, Takeo Okazaki

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The challenging task in educational institutions is to maximize the high performance of students and minimize the failure rate of poor-performing students. An effective method to leverage this task is to know student learning patterns with highly influencing factors and get an early prediction of student learning outcomes at the timely stage for setting up policies for improvement. Educational data mining (EDM) is an emerging disciplinary field of data mining, statistics, and machine learning concerned with extracting useful knowledge and information for the sake of improvement and development in the education environment. The study is of this work is to propose techniques in EDM and integrate it into a web-based system for predicting poor-performing students. A comparative study of prediction models is conducted. Subsequently, high performing models are developed to get higher performance. The hybrid random forest (Hybrid RF) produces the most successful classification. For the context of intervention and improving the learning outcomes, a feature selection method MICHI, which is the combination of mutual information (MI) and chi-square (CHI) algorithms based on the ranked feature scores, is introduced to select a dominant feature set that improves the performance of prediction and uses the obtained dominant set as information for intervention. By using the proposed techniques of EDM, an academic performance prediction system (APPS) is subsequently developed for educational stockholders to get an early prediction of student learning outcomes for timely intervention. Experimental outcomes and evaluation surveys report the effectiveness and usefulness of the developed system. The system is used to help educational stakeholders and related individuals for intervening and improving student performance.

Keywords: academic performance prediction system, educational data mining, dominant factors, feature selection method, prediction model, student performance

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Authors: J. P. Chollom, G. M. Kumleng, S. Longwap

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The search for higher order A-stable linear multi-step methods has been the interest of many numerical analysts and has been realized through either higher derivatives of the solution or by inserting additional off step points, supper future points and the likes. These methods are suitable for the solution of stiff differential equations which exhibit characteristics that place a severe restriction on the choice of step size. It becomes necessary that only methods with large regions of absolute stability remain suitable for such equations. In this paper, high order block implicit multi-step methods of the hybrid form up to order twelve have been constructed using the multi-step collocation approach by inserting one or more off step points in the multi-step method. The accuracy and stability properties of the new methods are investigated and are shown to yield A-stable methods, a property desirable of methods suitable for the solution of stiff ODE’s. The new High Order Block Implicit Multistep methods used as block integrators are tested on stiff differential systems and the results reveal that the new methods are efficient and compete favourably with the state of the art Matlab ode23 code.

Keywords: block linear multistep methods, high order, implicit, stiff differential equations

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Authors: Mary Chriselda A

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This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe.

Keywords: Chapman Kolmogorov forward differential equations, fourier transformation, hubble's parameter, ornstein-uhlenbeck process , stochastic differential equations

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Authors: Xiao Zhou, Jianlin Cheng

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A single amino acid mutation can have a significant impact on the stability of protein structure. Thus, the prediction of protein stability change induced by single site mutations is critical and useful for studying protein function and structure. Here, we presented a deep learning network with the dropout technique for predicting protein stability changes upon single amino acid substitution. While using only protein sequence as input, the overall prediction accuracy of the method on a standard benchmark is >85%, which is higher than existing sequence-based methods and is comparable to the methods that use not only protein sequence but also tertiary structure, pH value and temperature. The results demonstrate that deep learning is a promising technique for protein stability prediction. The good performance of this sequence-based method makes it a valuable tool for predicting the impact of mutations on most proteins whose experimental structures are not available. Both the downloadable software package and the user-friendly web server (DNpro) that implement the method for predicting protein stability changes induced by amino acid mutations are freely available for the community to use.

Keywords: bioinformatics, deep learning, protein stability prediction, biological data mining

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Authors: Jayanta Kumar Ghosh, Swastik Sunil Goriwale, Himangshu Sarkar

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Groundwater is one of the most valuable natural resources that society consumes for its domestic, industrial, and agricultural water supply. Its bulk and indiscriminate consumption affects the groundwater resource. Often, it has been found that the groundwater recharge rate is much lower than its demand. Thus, to maintain water and food security, it is necessary to monitor and management of groundwater storage. However, it is challenging to estimate groundwater storage (GWS) by making use of existing hydrological models. To overcome the difficulties, machine learning (ML) models are being introduced for the evaluation of groundwater level (GWL). Thus, the objective of this research work is to develop an ML-based model for the prediction of GWL. This objective has been realized through the development of an artificial neural network (ANN) model based on hydro-gravimetry. The model has been developed using training samples from field observations spread over 8 months. The developed model has been tested for the prediction of GWL in an observation well. The root means square error (RMSE) for the test samples has been found to be 0.390 meters. Thus, it can be concluded that the hydro-gravimetric-based ANN model can be used for the prediction of GWL. However, to improve the accuracy, more hydro-gravimetric parameter/s may be considered and tested in future.

Keywords: machine learning, hydro-gravimetry, ground water level, predictive model

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Authors: K. Roushanger, A. Soleymanzadeh

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Weirs are structures often used in irrigation techniques, sewer networks and flood protection. However, the hydraulic behavior of this type of weir is complex and difficult to predict accurately. An accurate flow prediction over a weir mainly depends on the proper estimation of discharge coefficient. In this study, the Genetic Expression Programming (GEP) approach was used for predicting trapezoidal and rectangular sharp-crested side weirs discharge coefficient. Three different performance indexes are used as comparing criteria for the evaluation of the model’s performances. The obtained results approved capability of GEP in prediction of trapezoidal and rectangular side weirs discharge coefficient. The results also revealed the influence of downstream Froude number for trapezoidal weir and upstream Froude number for rectangular weir in prediction of the discharge coefficient for both of side weirs.

Keywords: discharge coefficient, genetic expression programming, trapezoidal weir

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Authors: Ramzi B. Albadarneh

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In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given.

Keywords: conformable fractional derivative, finite difference formula, fractional derivative, finite difference formula

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Authors: Baeza S. Roberto

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The knitted fabric suffers a deformation in its dimensions due to stretching and tension factors, transverse and longitudinal respectively, during the process in rectilinear knitting machines so it performs a dry relaxation shrinkage procedure and thermal action of prefixed to obtain stable conditions in the knitting. This paper presents a dry relaxation shrinkage prediction of Bordeaux fiber using a feed forward neural network and linear regression models. Six operational alternatives of shrinkage were predicted. A comparison of the results was performed finding neural network models with higher levels of explanation of the variability and prediction. The presence of different reposes are included. The models were obtained through a neural toolbox of Matlab and Minitab software with real data in a knitting company of Southern Guanajuato. The results allow predicting dry relaxation shrinkage of each alternative operation.

Keywords: neural network, dry relaxation, knitting, linear regression

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Authors: Ch. Surawut, D. Sukawat

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In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. These equations provide downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM.

Keywords: dynamic equation, downscaling, inverse distance, weight interpolation

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Authors: Danilo López, Edwin Rivas, Fernando Pedraza

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Currently, one of the major challenges in wireless networks is the optimal use of radio spectrum, which is managed inefficiently. One of the solutions to existing problem converges in the use of Cognitive Radio (CR), as an essential parameter so that the use of the available licensed spectrum is possible (by secondary users), well above the usage values that are currently detected; thus allowing the opportunistic use of the channel in the absence of primary users (PU). This article presents the results found when estimating or predicting the future use of a spectral transmission band (from the perspective of the PU) for a chaotic type channel arrival behavior. The time series prediction method (which the PU represents) used is ANFIS (Adaptive Neuro Fuzzy Inference System). The results obtained were compared to those delivered by the RNA (Artificial Neural Network) algorithm. The results show better performance in the characterization (modeling and prediction) with the ANFIS methodology.

Keywords: ANFIS, cognitive radio, prediction primary user, RNA

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Authors: Kennedy Efosa Ehimwenma, Sujatha Krishnamoorthy, Safiya Al‑Sharji

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The probability computation of events is in the interval of [0, 1], which are values that are determined by the number of outcomes of events in a sample space S. The probability Pr(A) that an event A will never occur is 0. The probability Pr(B) that event B will certainly occur is 1. This makes both events A and B a certainty. Furthermore, the sum of probabilities Pr(E₁) + Pr(E₂) + … + Pr(Eₙ) of a finite set of events in a given sample space S equals 1. Conversely, the difference of the sum of two probabilities that will certainly occur is 0. This paper first discusses Bayes, the complement of probability, and the difference of probability for occurrences of learning-events before applying them in the prediction of learning objects in student learning. Given the sum of 1; to make a recommendation for student learning, this paper proposes that the difference of argMaxPr(S) and the probability of student-performance quantifies the weight of learning objects for students. Using a dataset of skill-set, the computational procedure demonstrates i) the probability of skill-set events that have occurred that would lead to higher-level learning; ii) the probability of the events that have not occurred that requires subject-matter relearning; iii) accuracy of the decision tree in the prediction of student performance into class labels and iv) information entropy about skill-set data and its implication on student cognitive performance and recommendation of learning.

Keywords: complement of probability, Bayes’ rule, prediction, pre-assessments, computational education, information theory

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Authors: Alireza Lohrasbi, Alireza Lavaei, Mohammadali M. Shahlaei

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The liquid flow and the free surface shape during the initial stage of dam breaking are investigated. A numerical scheme is developed to predict the wave of an unsteady, incompressible viscous flow with free surface. The method involves a two dimensional finite element (2D), in a vertical plan. The Naiver-Stokes equations for conservation of momentum and mass for Newtonian fluids, continuity equation, and full nonlinear kinematic free-surface equation were used as the governing equations. The mapping developed to solve highly deformed free surface problems common in waves formed during wave propagation, transforms the run up model from the physical domain to a computational domain with Arbitrary Lagrangian Eulerian (ALE) finite element modeling technique.

Keywords: dam break, Naiver-Stokes equations, free-surface flows, Arbitrary Lagrangian-Eulerian

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Authors: Farid Khosravikia, Patricia Clayton

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The main objective of this study is to evaluate the advantages and disadvantages of various machine learning techniques in forecasting ground-motion intensity measures given source characteristics, source-to-site distance, and local site condition. Intensity measures such as peak ground acceleration and velocity (PGA and PGV, respectively) as well as 5% damped elastic pseudospectral accelerations at different periods (PSA), are indicators of the strength of shaking at the ground surface. Estimating these variables for future earthquake events is a key step in seismic hazard assessment and potentially subsequent risk assessment of different types of structures. Typically, linear regression-based models, with pre-defined equations and coefficients, are used in ground motion prediction. However, due to the restrictions of the linear regression methods, such models may not capture more complex nonlinear behaviors that exist in the data. Thus, this study comparatively investigates potential benefits from employing other machine learning techniques as a statistical method in ground motion prediction such as Artificial Neural Network, Random Forest, and Support Vector Machine. The algorithms are adjusted to quantify event-to-event and site-to-site variability of the ground motions by implementing them as random effects in the proposed models to reduce the aleatory uncertainty. All the algorithms are trained using a selected database of 4,528 ground-motions, including 376 seismic events with magnitude 3 to 5.8, recorded over the hypocentral distance range of 4 to 500 km in Oklahoma, Kansas, and Texas since 2005. The main reason of the considered database stems from the recent increase in the seismicity rate of these states attributed to petroleum production and wastewater disposal activities, which necessities further investigation in the ground motion models developed for these states. Accuracy of the models in predicting intensity measures, generalization capability of the models for future data, as well as usability of the models are discussed in the evaluation process. The results indicate the algorithms satisfy some physically sound characteristics such as magnitude scaling distance dependency without requiring pre-defined equations or coefficients. Moreover, it is shown that, when sufficient data is available, all the alternative algorithms tend to provide more accurate estimates compared to the conventional linear regression-based method, and particularly, Random Forest outperforms the other algorithms. However, the conventional method is a better tool when limited data is available.

Keywords: artificial neural network, ground-motion models, machine learning, random forest, support vector machine

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Authors: Jiashu Shen

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Objectives: Spirometry is a basic reference for health evaluation which is widely used in clinical. Previous reference of spirometry is not applicable because of drastic changes of social and natural circumstance in China. A new reference values for the spirometry of the Chinese population is extremely needed. Method: Spirometric reference value was established using the statistical modeling method Generalized Additive Models for Location, Scale and Shape for forced expiratory volume in 1 s (FEV1), forced vital capacity (FVC), FEV1/FVC, and maximal mid-expiratory flow (MMEF). Results: Data from 236,606 healthy non-smokers aged 4–90 years was collected from the MJ Health Check database. Spirometry equations for FEV1, FVC, MMEF, and FEV1/FVC were established, including the predicted values and lower limits of normal (LLNs) by sex. The predictive equations that were developed for the spirometric results elaborated the relationship between spirometry and age, and they eliminated the effects of height as a variable. Most previous predictive equations for Chinese spirometry were significantly overestimated (to be exact, with mean differences of 22.21% in FEV1 and 31.39% in FVC for males, along with differences of 26.93% in FEV1 and 35.76% in FVC for females) or underestimated (with mean differences of -5.81% in MMEF and -14.56% in FEV1/FVC for males, along with a difference of -14.54% in FEV1/FVC for females) the results of lung function measurements as found in this study. Through cross-validation, our equations were established as having good fit, and the means of the measured value and the estimated value were compared, with good results. Conclusions: Our study updates the spirometric reference equations for Chinese people of all ages and provides comprehensive values for both physical examination and clinical diagnosis.

Keywords: Chinese, GAMLSS model, reference values, spirometry

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Authors: Xiaodong Li, Peng Gao, Chao-Jung Huang, Shiying Hao, Xuefeng B. Ling, Yongxia Han, Yaqi Zhang, Le Zheng, Chengyin Ye, Modi Liu, Minjie Xia, Changlin Fu, Bo Jin, Karl G. Sylvester, Eric Widen

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Predicting the risk of Pancreatic Adenocarcinoma (PA) in advance can benefit the quality of care and potentially reduce population mortality and morbidity. The aim of this study was to develop and prospectively validate a risk prediction model to identify patients at risk of new incident PA as early as 3 months before the onset of PA in a statewide, general population in Maine. The PA prediction model was developed using Deep Neural Networks, a deep learning algorithm, with a 2-year electronic-health-record (EHR) cohort. Prospective results showed that our model identified 54.35% of all inpatient episodes of PA, and 91.20% of all PA that required subsequent chemoradiotherapy, with a lead-time of up to 3 months and a true alert of 67.62%. The risk assessment tool has attained an improved discriminative ability. It can be immediately deployed to the health system to provide automatic early warnings to adults at risk of PA. It has potential to identify personalized risk factors to facilitate customized PA interventions.

Keywords: cancer prediction, deep learning, electronic health records, pancreatic adenocarcinoma

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Authors: Marine Segui, Ruxandra Mihaela Botez

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OpenVSP is an aerodynamic solver developed by National Aeronautics and Space Administration (NASA) that allows building a reliable model of an aircraft. This software performs an aerodynamic simulation according to the angle of attack of the aircraft makes between the incoming airstream, and its speed. A reliable aerodynamic model of the Cessna Citation X was designed but it required a lot of computation time. As a consequence, a prediction method was established that allowed predicting lift and drag coefficients for all Mach numbers and for all angles of attack, exclusively for stall conditions, from a computation of three angles of attack and only one Mach number. Aerodynamic coefficients given by the prediction method for a Cessna Citation X model were finally compared with aerodynamics coefficients obtained using a complete OpenVSP study.

Keywords: aerodynamic, coefficient, cruise, improving, longitudinal, openVSP, solver, time

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Authors: E. A. Mlybari, M. S. Elbisy, A. H. Alshahri, O. M. Albarakati

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Sea level rise threatens to increase the impact of future storms and hurricanes on coastal communities. Accurate sea level change prediction and supplement is an important task in determining constructions and human activities in coastal and oceanic areas. In this study, support vector machines (SVM) is proposed to predict daily tidal levels along the Jeddah Coast, Saudi Arabia. The optimal parameter values of kernel function are determined using a genetic algorithm. The SVM results are compared with the field data and with back propagation (BP). Among the models, the SVM is superior to BPNN and has better generalization performance.

Keywords: tides, prediction, support vector machines, genetic algorithm, back-propagation neural network, risk, hazards

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Authors: Hasan G. Elmazoghi, Aisha I. Alzayani, Lubna S. Bentaher

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Rainfall is a highly non-linear phenomena, which requires application of powerful supervised data mining techniques for its accurate prediction. In this study the Artificial Neural Network (ANN) technique is used to predict the mean monthly historical rainfall data collected from BENINA station in Benghazi for 31 years, the period of “1977-2006” and the results are compared against the observed values. The specific objective to achieve this goal was to determine the best combination of weather variables to be used as inputs for the ANN model. Several statistical parameters were calculated and an uncertainty analysis for the results is also presented. The best ANN model is then applied to the data of one year (2007) as a case study in order to evaluate the performance of the model. Simulation results reveal that application of ANN technique is promising and can provide reliable estimates of rainfall.

Keywords: neural networks, rainfall, prediction, climatic variables

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Authors: Ali Reza Sattarzadeh, Ronny J. Kutadinata, Pubudu N. Pathirana, Van Thanh Huynh

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Traffic congestion has become a severe worldwide problem, affecting everyday life, fuel consumption, time, and air pollution. The primary causes of these issues are inadequate transportation infrastructure, poor traffic signal management, and rising population. Traffic flow forecasting is one of the essential and effective methods in urban congestion and traffic management, which has attracted the attention of researchers. With the development of technology, undeniable progress has been achieved in existing methods. However, there is a possibility of improvement in the extraction of temporal and spatial features to determine the importance of traffic flow sequences and extraction features. In the proposed model, we implement the convolutional neural network (CNN) and long short-term memory (LSTM) deep learning models for mining nonlinear correlations and their effectiveness in increasing the accuracy of traffic flow prediction in the real dataset. According to the experiments, the results indicate that implementing Conv-LSTM networks increases the productivity and accuracy of deep learning models for traffic flow prediction.

Keywords: deep learning algorithms, intelligent transportation systems, spatiotemporal features, traffic flow prediction

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Authors: Hamza Nejib, Okba Taouali

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This paper presents two of the most knowing kernel adaptive filtering (KAF) approaches, the kernel least mean squares and the kernel recursive least squares, in order to predict a new output of nonlinear signal processing. Both of these methods implement a nonlinear transfer function using kernel methods in a particular space named reproducing kernel Hilbert space (RKHS) where the model is a linear combination of kernel functions applied to transform the observed data from the input space to a high dimensional feature space of vectors, this idea known as the kernel trick. Then KAF is the developing filters in RKHS. We use two nonlinear signal processing problems, Mackey Glass chaotic time series prediction and nonlinear channel equalization to figure the performance of the approaches presented and finally to result which of them is the adapted one.

Keywords: online prediction, KAF, signal processing, RKHS, Kernel methods, KRLS, KLMS

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Authors: Prashant G. Metri

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A numerical model is developed to study nano liquid film flow over an unsteady stretching sheet in the presence of hydromagnetic have been investigated. Similarity transformations are used to convert unsteady boundary layer equations to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved numerically using Runge-Kutta-Fehlberg and Newton-Raphson schemes. A relationship between film thickness β and the unsteadiness parameter S is found, the effect of unsteadiness parameter S, and the hydromagnetic parameter S, on the velocity and temperature distributions are presented. The present analysis shows that the combined effect of magnetic field and viscous dissipation has a significant influence in controlling the dynamics of the considered problem. Comparison with known results for certain particular cases is in excellent agreement.

Keywords: boundary layer flow, nanoliquid, thin film, unsteady stretching sheet

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Authors: Helmi Temimi

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In this paper, we study the super-convergence properties of the discontinuous Galerkin (DG) method applied to one-dimensional mth-order ordinary differential equations without introducing auxiliary variables. We found that nth−derivative of the DG solution exhibits an optimal O (hp+1−n) convergence rates in the L2-norm when p-degree piecewise polynomials with p≥1 are used. We further found that the odd-derivatives and the even derivatives are super convergent, respectively, at the upwind and downwind endpoints.

Keywords: discontinuous, galerkin, superconvergence, higherorder, error, estimates

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Authors: Masahiro Ohmura, Koh Kakusho, Takeshi Okadome

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This paper presents a regression model with autocorrelated errors in which the inputs are social moods obtained by analyzing the adjectives in Twitter posts using a document topic model. The regression model predicts Dow Jones Industrial Average (DJIA) more precisely than autoregressive moving-average models.

Keywords: stock market prediction, social moods, regression model, DJIA

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Authors: J. H. Kim, J. H. Kwon, J. S. Park, K. J. Lim

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This paper has investigated a technique that predicts the performance of a bar-type unimorph piezoelectric vibration actuator depending on the frequency. This paper has been proposed an equivalent circuit that can be easily analyzed for the bar-type unimorph piezoelectric vibration actuator. In the dynamic analysis, rigidity and resonance frequency, which are important mechanical elements, were derived using the basic beam theory. In the equivalent circuit analysis, the displacement and bandwidth of the piezoelectric vibration actuator depending on the frequency were predicted. Also, for the reliability of the derived equations, the predicted performance depending on the shape change was compared with the result of a finite element analysis program.

Keywords: actuator, piezoelectric, performance, unimorph

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

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

Keywords: mixed matrix membrane, permeation models, porous particles, porosity

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Authors: Flavia Smarrazzo

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Initial-boundary value problems for nonlinear parabolic equations having a Radon measure as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. On the other hand, if the diffusivity degenerates too fast at infinity, it is well known that function-valued solutions may not exist, singularities may persist, and it looks very natural to consider solutions which, roughly speaking, for positive times describe an orbit in the space of the finite Radon measures. In this general framework, our purpose is to introduce a concept of measure-valued solution which is consistent with respect to regularizing and smoothing approximations, in order to develop an existence theory which does not depend neither on the level of degeneracy of diffusivity at infinity nor on the choice of the initial measures. In more detail, we prove existence of suitably defined measure-valued solutions to the homogeneous Dirichlet initial-boundary value problem for a class of nonlinear parabolic equations without strong coerciveness. Moreover, we also discuss some qualitative properties of the constructed solutions concerning the evolution of their singular part, including conditions (depending both on the initial data and on the strength of degeneracy) under which the constructed solutions are in fact unction-valued or not.

Keywords: degenerate parabolic equations, measure-valued solutions, Radon measures, young measures

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Authors: Ayan Chakraborty, BV. Rathish Kumar

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Off-late many models in viscoelasticity, signal processing or anomalous diffusion equations are formulated in fractional calculus. Tempered fractional calculus is the generalization of fractional calculus and in the last few years several important partial differential equations occurring in the different field of science have been reconsidered in this term like diffusion wave equations, Schr$\ddot{o}$dinger equation and so on. In the present paper, a time-dependent tempered fractional diffusion equation of order $\gamma \in (0,1)$ with forcing function is considered. Existence, uniqueness, stability, and regularity of the solution has been proved. Crank-Nicolson discretization is used in the time direction. B spline finite element approximation is implemented. Generally, B-splines basis are useful for representing the geometry of a finite element model, interfacing a finite element analysis program. By utilizing this technique a priori space-time estimate in finite element analysis has been derived and we proved that the convergent order is $\mathcal{O}(h²+T²)$ where $h$ is the space step size and $T$ is the time. A couple of numerical examples have been presented to confirm the accuracy of theoretical results. Finally, we conclude that the studied method is useful for solving tempered fractional diffusion equations.

Keywords: B-spline finite element, error estimates, Gronwall's lemma, stability, tempered fractional

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Authors: Isaac Mugume, Charles Basalirwa, Daniel Waiswa, Mary Nsabagwa, Triphonia Jacob Ngailo, Joachim Reuder, Sch¨attler Ulrich, Musa Semujju

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The Numerical weather prediction (NWP) models are considered powerful tools for guiding quantitative rainfall prediction. A couple of NWP models exist and are used at many operational weather prediction centers. This study considers two models namely the Consortium for Small–scale Modeling (COSMO) model and the Weather Research and Forecasting (WRF) model. It compares the models’ ability to predict rainfall over Uganda for the period 21st April 2013 to 10th May 2013 using the root mean square (RMSE) and the mean error (ME). In comparing the performance of the models, this study assesses their ability to predict light rainfall events and extreme rainfall events. All the experiments used the default parameterization configurations and with same horizontal resolution (7 Km). The results show that COSMO model had a tendency of largely predicting no rain which explained its under–prediction. The COSMO model (RMSE: 14.16; ME: -5.91) presented a significantly (p = 0.014) higher magnitude of error compared to the WRF model (RMSE: 11.86; ME: -1.09). However the COSMO model (RMSE: 3.85; ME: 1.39) performed significantly (p = 0.003) better than the WRF model (RMSE: 8.14; ME: 5.30) in simulating light rainfall events. All the models under–predicted extreme rainfall events with the COSMO model (RMSE: 43.63; ME: -39.58) presenting significantly higher error magnitudes than the WRF model (RMSE: 35.14; ME: -26.95). This study recommends additional diagnosis of the models’ treatment of deep convection over the tropics.

Keywords: comparative performance, the COSMO model, the WRF model, light rainfall events, extreme rainfall events

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Authors: S. Bennoud, M. Zergoug

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The numerical simulation of electromagnetic interactions is still a challenging problem, especially in problems that result in fully three dimensional mathematical models. The goal of this work is to use mathematical modeling to characterize the reliability and capacity of eddy current technique to detect and characterize defects embedded in aeronautical in-service pieces. The finite element method is used for describing the eddy current technique in a mathematical model by the prediction of the eddy current interaction with defects. However, this model is an approximation of the full Maxwell equations. In this study, the analysis of the problem is based on a three dimensional finite element model that computes directly the electromagnetic field distortions due to defects.

Keywords: eddy current, finite element method, non destructive testing, numerical simulations

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Authors: Gilbert Makanda

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The problem of the teaching of mathematics is studied using differential equations. A mathematical model for knowledge acquisition in mathematics is developed. In this study we adopt the mathematical model that is normally used for disease modelling in the teaching of mathematics. It is assumed that teaching is 'infecting' students with knowledge thereby spreading this knowledge to the students. It is also assumed that students who gain this knowledge spread it to other students making disease model appropriate to adopt for this problem. The results of this study show that increasing recruitment rates, learning contact with teachers and learning materials improves the number of knowledgeable students. High dropout rates and forgetting taught concepts also negatively affect the number of knowledgeable students. The developed model is then solved using Matlab ODE45 and \verb"lsqnonlin" to estimate parameters for the actual data.

Keywords: differential equations, knowledge acquisition, least squares, dynamical systems

Procedia PDF Downloads 405