International Journal of Mathematical Modelling and Numerical Optimisation (10 papers in press)
Warehousing and Analyzing Textual Data
by Sarah Attaf, Nadjia Benblidia, Omar Boussaid
Abstract: Traditional data warehousing technologies have been widely used for the analysis of simple data. Nonetheless, they are not suitable for textual data. In order to deal with this type of complex data, new systems have been proposed for text OLAP (On-Line Analytical Processing) purposes. However, they only cover partially the complexity of textual data, which might therefore affect decision-making quality. This paper proposes an efficient approach for warehousing and analyzing textual data. To tackle the main challenges facing these data, three major contributions are presented throughout our manuscript: (i) a Semantic Text Cube Model (ST-Cube), (ii) a new ETL approach (Extract Transform and Load), and (iii) an OLAP aggregation operator called Top_KRankedTopics.
For the validation of our approach, we have developed and implemented a platform for the storage and the analysis of text documents. Experimental results show that our ETL approach improves significantly the quality of information, extracted from textual document, compared to two other models while considering three different performance metrics. Moreover, the Top_KRankedTopics operator carry out effectively on-line analyses on textual data while taking different semantic factors into account.
Keywords: data warehousing; textual data analysis; semantic text cube model; ETL approach; semantic factors; On Line Analytical Processing (OLAP) Operators; top_KRankedTopics.
Optimal Design and Analysis of Hybrid Photovoltaic-Fuel Cell Power Generation System for an Advanced Converter Technologies
by Rajanand Patnaik Narasipuram
Abstract: Nowadays entire world is concentrated on Alternative Energy Sources (AES) or Renewable Energy Sources (RES) for developing the power in economical cost and the sources like tidal power, solar energy, geothermal energy, wind energy, biomass, fuel cells etc. Among all those sources solar energy and fuel cells are chosen for developing the Hybrid Power Generation (HPG) system. The Photovoltaic (PV) module is designed with an efficient Maximum Power Point Tracking (MPPT) technique of Neuro-Fuzzy (NF) tracking controller is developed to extract the maximum power and fed to boost DC-DC converter. In the mean while, Air Breathe Fuel Cell (ABFC) is designed and fed to the high step-up DC-DC converter with lesser duty cycle. The main concentration of this paper is to design the efficient Hybrid Power Generation (HPG) system for a competitive Multilevel Inverter (MLI) topology with less device count is the merit of this topology which is called Packed U Cell (PUC). In addition, this paper describes the mathematical analysis, design and operation of PV module, Neuro-Fuzzy (NF) MPPT controller based boost converter, ABFC, high step-up converter and PUC inverter. The P-V, I-V characteristics of PV module and ABFC stack effects on hydrogen pressure changes and temperature is examined. And also, the performance of HPG based PV-FC fed multilevel inverter is sifted for different load conditions. The overall performance is checked in terms of Total Harmonic Distortion (THD) for phase voltages (Vph) and phase currents (Iph) which are accomplished through FFT analysis for each load case. The whole simulations are carried out in MATLAB/Simulink environment.
Keywords: air breathe fuel cell; ABFC; alternative energy sources; AES; DC-DC converters; fuel cell; FC; hybrid power generation; HPG; maximum power point tracking; MPPT; multilevel inverter; MLI; Neuro-Fuzzy; NF; packed u cell inverter topology; PUC; photovoltaic; PV; renewable energy sources; RES; total harmonic distortion; THD;.
Tuning Runge-Kutta parameters on a family of ordinary differential equations
by Charles Audet
Abstract: The Runge-Kutta class of iterative methods is designed to approximate solutions of a system of ordinary differential equations (ODE). The second-order class of Runge-Kutta methods is determined by a system of 3 nonlinear equations and 4 unknowns, and includes the modified-Euler and mid-point methods. The fourth-order class is determined by a system of 8 nonlinear equations and 10 unknowns. This work formulates the question of identifying good values of these 8 parameters for a given family of ODE as a blackbox optimization problem.rnThe objective is to determine the parameter values that minimize the overall error produced by a Runge-Kutta method on a training set of ODE. Numerical experiments are conducted using the Nomad direct-search optimization solver.
Keywords: Runge-Kutta; Parameter tuning; Blackbox optimization; Direct-search.
Modelling and Predicting the Bitcoin Volatility Using GARCH Models
by Viviane Naimy, Marianne Hayek
Abstract: This paper is the first to model and forecast the volatility of the Bitcoin/USD exchange rate. It assesses and compares the predictive ability of the Generalized AutoRegressive Conditional Heteroskedasticity GARCH (1,1), the Exponentially Weighted Moving Average EWMA, and the Exponential Generalized AutoRegressive Conditional Heteroskedasticity EGARCH (1,1) in forecasting the volatility of the Bitcoin/USD exchange rate. Models parameters are first estimated from the in sample Bitcoin/USD exchange rate returns and in sample volatility is calculated. Out of sample volatility is forecasted afterward. Estimated volatilities are then compared to realized volatilities relying on error statistics, after which the models are ranked. The EGARCH (1,1) model outperforms the GARCH (1,1) and EWMA models in both in sample and out of sample contexts with increased accuracy in the out of sample period. Results show an original reflection concern with regard to the nature of the Bitcoin, which behaves differently than traditional currencies. Given the early-stage behavior of the Bitcoin, results might change in the future.
Keywords: Bitcoin; Modelling Volatility; Realized Volatility; Predictive Ability; GARCH(1,1); EWMA; EGARCH; in sample; out of sample; Optimization; Errors Test Statistics; MAE; RMSE; MAPE.
Stellar Population Analysis of Galaxies Based on Improved Flower Pollination Algorithm
by Mohamed Abdo., Yongquan Zhou, Ibrahim M. Hezam
Abstract: When numerical simulations are used for determining the age and contribution of different stellar populations in the integrated color of a galaxy some problems were encountered. In this paper, a modified flower pollination algorithm (MFPA) is proposed for determining the age and relative contribution of different stellar populations of galaxies. The results show that the proposed algorithm can search efficiently through the very large space of the possible ages for different integrated color of galaxies. The proposed algorithm will be applied to integrated color of galaxy NGC 3384. The numerical results and statistical analysis show that the proposed algorithm perform significantly better than previously used genetic algorithm, . The study revealed that the proposed algorithm can successfully be applied to a wide range of stellar population and space optimization problems.
Keywords: flower pollination algorithm; Meta-heuristics; Optimization; Stellar Population; Galaxies.
Uniformly convergent numerical method for singularly perturbed 2D delay parabolic convection-diffusion problems on Bakhvalov-Shishkin mesh
by Srinivasan Natesan, Abhishek Das
Abstract: In this article, we consider a class of singularly perturbed 2D delay parabolic convection-diffusion initial-boundary-value problems. To solve the problem numerically, we consider upwind finite difference scheme on a modified Shishkin mesh (Bakhvalov-Shishkin mesh) to discretize the domain in spatial directions and we apply implicit-Euler scheme for the time derivative on uniform mesh in the temporal direction. We derive some conditions on the mesh-generating functions which are useful for the convergence of the method, uniformly with respect to the perturbation parameter. We prove that the applied scheme on the Bakhvalov-Shishkin mesh is first-order convergent in the discrete supremum norm, which is optimal and does not require any extra computational effort compare to the standard Shishkin mesh. Numerical experiments verify the theoretical results.
Keywords: Singularly perturbed 2D delay parabolic convection-diffusion problems; boundary layers; finite difference scheme; Bakhvalov-Shishkin mesh; uniform convergence.
Information technology value model and its optimal application in IT-based firms
by Lukman Abdurrahman, Suhardi Suhardi, Armein Z.R. Langi, Togar M. Simatupang
Abstract: This paper proposes the developed business performance based on the IT value model, which offers superior performance with profit maximization due to increased revenue and reduced costs. The model stands on the resource-based view theory, the partial adjustment valuation theory, and the systems engineering approach. Therefore, the model consists of firm performance, firm core competence, firm capability, and information technology resource subsystems. Each subsystem has inputs, i.e. the regular capital (K), the regular labour expense (L), and IT capital (I) where the output is y (the gross revenue). In addition, the synthesis result states that the model with the structure of the composition of each subsystem with the addition operation is more acceptable. The data used came from Telkom, Indosat, and XL, which are telco firms in Indonesia. Similarly, the IT value model optimization testing displays that the model is able to provide superior performance with increased revenue, but at a lower cost. Thus, the proposed model can address the mentioned main problems. However, it needs further studies to enhance this model.
Keywords: capital;systems engineering;information technology;model;partial adjustment;performance;revenue;cost;value.
Weerakoon-Fernando Method with accelerated third order convergence for systems of nonlinear equations
by H. P. S. Nishani, Sunethra Weerakoon, T. G. I. Fernando, Menaka Liyanage
Abstract: Weerakoon-Fernando Method (WFM) is a widely accepted third order iterative method introduced in the late 90s to solve nonlinear equations. Even though it has become so popular among numerical analysts resulting in hundreds of similar work for single variable case, after nearly two decades, nobody took the challenge of extending the method to multivariable systems. In this paper, we extend the WFM to functions of several variables and provide a rigorous proof for the third order convergence. This theory was supported by computational results using several systems of nonlinear equations. Computational algorithms were implemented using MATLAB. We further analyze the method mathematically and demonstrate the reason for the strong performance of WFM computationally, despite it requiring more function evaluations.
Keywords: Functions of several variables; Iterative Methods; Third Order Convergence; Weerakoon-Fernando Method; Newton’s Method.
An inventory System with Two Heterogeneous Servers and Orbital Search for Feedback Customers
by Suganya C, Amirthakodi M, Sivakumar B
Abstract: This model deals a continuous review (s, S) inventory system two heterogeneous servers, say, server - 1, server - 2. Server - 1 serve for primary customers and server - 2 is served for both primary and feedback customers. The primary customers arrival according to a Markovian arrival process (MAP) and service time for both servers has exponential distribution. The lead time is assumed to be exponential distribution. The primary customers, who finds either two servers are busy or no item is in the stock, waits in the finite waiting hall. If the waiting hall is full, then arriving, customer considered to be lost. After the completion of service the primary customer will decide either to join the orbit, which is an infinite size, for additional service or leaves the system according to a Bernoulli trail. These orbiting (feedback) customers compete for their service according to constant retrial policy, and the service times for these feedback customers are assumed to be exponential distribution. After completing the service for feedback customers server - 2 becomes idle or busy for primary customer. If the server - 2 completes the service for a primary customer, then he searches the customers in the orbit or idle according to a Bernoulli trail. The results are illustrated numerically.
Keywords: Markovian arrival process; Feedback customers; Heterogeneous serves; Service facility; Orbital search.
The impact of hygiene care and maternal immunity on stability behavior of rotavirus infection model for children under the age of five in Thailand
by RATCHADA VIRIYAPONG, Gunyarat Koompawan
Abstract: Rotavirus infection is one of the significant causes of death in infants and children under five years of age in Thailand and worldwide. In this paper, a deterministic model for rotavirus transmission of children under five years old in Thailand incorporating with hygiene care control and maternal immunity is developed. The basic reproduction number (Rv) is derived and becomes a threshold indicating the stability of both disease-free and endemic equilibrium points. Through the analysis, the results show that the disease-free equilibrium point is locally asymptotically stable when Rv < 1 and the endemic equilibrium point is locally stable when Rv > 1 and satisfies the Routh-Hurwitz criteria. Further, numerical simulation demonstrates that both hygiene care and maternal immunity to the infection due to breastfeeding should be encouraged as strategy to control rotavirus infection.
Keywords: diarrhea; rotavirus; mathematical modeling; basic reproduction
number; hygiene care; breastfeeding.