World Academy of Science, Engineering and Technology

Authors: S. K. Appiah, E. N. Aidoo, D. Asamoah Owusu, M. W. Nuonabuor

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Urbanization remains one of the unique predominant factors which is linked to the destruction of urban environment and its associated cases of soil contamination by heavy metals through the natural and anthropogenic activities. These activities are important sources of toxic heavy metals such as arsenic (As), cadmium (Cd), chromium (Cr), copper (Cu), iron (Fe), manganese (Mn), and lead (Pb), nickel (Ni) and zinc (Zn). Often, these heavy metals lead to increased levels in some areas due to the impact of atmospheric deposition caused by their proximity to industrial plants or the indiscriminately burning of substances. Information gathered on potentially hazardous levels of these heavy metals in soils leads to establish serious health and urban agriculture implications. However, characterization of spatial variations of soil contamination by heavy metals in Ghana is limited. Kumasi is a Metropolitan city in Ghana, West Africa and is challenged with the recent spate of deteriorating soil quality due to rapid economic development and other human activities such as “Galamsey”, illegal mining operations within the metropolis. The paper seeks to use both univariate and multivariate geostatistical techniques to assess the spatial distribution of heavy metals in soils and the potential risk associated with ingestion of sources of soil contamination in the Metropolis. Geostatistical tools have the ability to detect changes in correlation structure and how a good knowledge of the study area can help to explain the different scales of variation detected. To achieve this task, point referenced data on heavy metals measured from topsoil samples in a previous study, were collected at various locations. Linear models of regionalisation and coregionalisation were fitted to all experimental semivariograms to describe the spatial dependence between the topsoil heavy metals at different spatial scales, which led to ordinary kriging and cokriging at unsampled locations and production of risk maps of soil contamination by these heavy metals. Results obtained from both the univariate and multivariate semivariogram models showed strong spatial dependence with range of autocorrelations ranging from 100 to 300 meters. The risk maps produced show strong spatial heterogeneity for almost all the soil heavy metals with extremely risk of contamination found close to areas with commercial and industrial activities. Hence, ongoing pollution interventions should be geared towards these highly risk areas for efficient management of soil contamination to avert further pollution in the metropolis.

Keywords: coregionalization, heavy metals, multivariate geostatistical analysis, soil contamination, spatial distribution

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Authors: Mohammed A. Alazawi, Shiguo Jiang, Steven F. Messner

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Research has long focused on two main spatial aspects of crime: spatial patterns and spatial processes. When analyzing these patterns and processes, a key issue has been to determine the proper spatial scale. In addition, it is important to consider the possibility that these patterns and processes might differ appreciably for different temporal scales and might vary across geographic units of analysis. We examine the spatial-temporal dependence of residential burglary. This dependence is tested at varying geographical scales and temporal aggregations. The analyses are based on recorded incidents of crime in Columbus, Ohio during the 1994-2002 period. We implement point pattern analysis on the crime points using Ripley’s K function. The results indicate that spatial point patterns of residential burglary reveal spatial scales of clustering relatively larger than the average size of census tracts of the study area. Also, spatial scale is independent of temporal scale. The results of our analyses concerning the geographic scale of spatial patterns and processes can inform the development of effective policies for crime control.

Keywords: inhomogeneous K function, residential burglary, spatial point pattern, spatial scale, temporal scale

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Authors: Mohsen Ziaee

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In this paper, a mixed integer linear programming (MILP) model is presented to solve the flexible job shop scheduling problem (FJSP). This problem is one of the hardest combinatorial problems. The objective considered is the minimization of the makespan. The computational results of the proposed MILP model were compared with those of the best known mathematical model in the literature in terms of the computational time. The results show that our model has better performance with respect to all the considered performance measures including relative percentage deviation (RPD) value, number of constraints, and total number of variables. By this improved mathematical model, larger FJS problems can be optimally solved in reasonable time, and therefore, the model would be a better tool for the performance evaluation of the approximation algorithms developed for the problem.

Keywords: scheduling, flexible job shop, makespan, mixed integer linear programming

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Authors: Mohsen Ziaee

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Almost all existing researches on the flowshop scheduling problems focus on the permutation schedules and there is insufficient study dedicated to the general flowshop scheduling problems in the literature, since the modeling and solving of the general flowshop scheduling problems are more difficult than the permutation ones, especially for the large-size problem instances. This paper considers the general flowshop scheduling problem with the objective function of the makespan (F//Cmax). We first find the optimal solution of the problem by solving a mixed integer linear programming model. An efficient heuristic method is then presented to solve the problem. An ant colony optimization algorithm is also proposed for the problem. In order to evaluate the performance of the methods, computational experiments are designed and performed. Numerical results show that the heuristic algorithm can result in reasonable solutions with low computational effort and even achieve optimal solutions in some cases.

Keywords: scheduling, general flow shop scheduling problem, makespan, heuristic

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Authors: Salihah Alghamdi, Surajit Ray

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Space-time data can be observed over irregularly shaped manifolds, which might have complex boundaries or interior gaps. Most of the existing methods do not consider the shape of the data, and as a result, it is difficult to model irregularly shaped data accommodating the complex domain. We used a method that can deal with space-time data that are distributed over non-planner shaped regions. The method is based on partial differential equations and finite element analysis. The model can be estimated using a penalized least squares approach with a regularization term that controls the over-fitting. The model is regularized using two roughness penalties, which consider the spatial and temporal regularities separately. The integrated square of the second derivative of the basis function is used as temporal penalty. While the spatial penalty consists of the integrated square of Laplace operator, which is integrated exclusively over the domain of interest that is determined using finite element technique. In this paper, we applied a spatio-temporal regression model with partial differential equations regularization (ST-PDE) approach to analyze a remote sensing data measuring the greenness of vegetation, measure by an index called enhanced vegetation index (EVI). The EVI data consist of measurements that take values between -1 and 1 reflecting the level of greenness of some region over a period of time. We applied (ST-PDE) approach to irregular shaped region of the EVI data. The approach efficiently accommodates the irregular shaped regions taking into account the complex boundaries rather than smoothing across the boundaries. Furthermore, the approach succeeds in capturing the temporal variation in the data.

Keywords: irregularly shaped domain, partial differential equations, finite element analysis, complex boundray

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Authors: Analen Malnegro, Gina Malacas

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Dominating sets and related topics have been studied extensively in the past few decades. A dominating set of a graph G is a subset D of V such that every vertex not in D is adjacent to at least one member of D. The domination number γ(G) is the number of vertices in a smallest dominating set for G. Some problems involving detection devices can be modeled with graphs. Finding the minimum number of devices needed according to the type of devices and the necessity of locating the object gives rise to locating-dominating sets. A subset S of vertices of a graph G is called locating-dominating set, LD-set for short, if it is a dominating set and if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. The location-domination number λ(G) is the minimum cardinality of an LD-set for G. The complement of a graph G is a graph Ḡ on same vertices such that two distinct vertices of Ḡ are adjacent if and only if they are not adjacent in G. An LD-set of a graph G is global if it is an LD-set of both G and its complement Ḡ. The global location-domination number λg(G) is defined as the minimum cardinality of a global LD-set of G. In this paper, global LD-sets on the join of two graphs are characterized. Global location-domination numbers of these graphs are also determined.

Keywords: dominating set, global locating-dominating set, global location-domination number, locating-dominating set, location-domination number

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Authors: Jean-Marie Vilaire, Ricardo Abreu-Blaya, Juan Bory-Reyes

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The classical Beltrami system of elliptic equations generalizes the Cauchy Riemann equation in the complex plane and offers the possibility to consider homogeneous system with no terms of zero order. The theory of Douglis-valued functions, called Hyper-analytic functions, is special case of the above situation. In this note, we prove an analogue of the N. Davydov theorem in the framework of the theory of hyperanalytic functions. The used methodology contemplates characteristic methods of the hypercomplex analysis as well as the singular integral operators and elliptic systems of the partial differential equations theories.

Keywords: Beltrami equation, Douglis algebra-valued function, Hypercomplex Cauchy type integral, Sokhotski-Plemelj formulae

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Authors: Ayon Mukherjee

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Covariate-adjusted response-adaptive (CARA) designs use the available responses to skew the treatment allocation in a clinical trial in towards treatment found at an interim stage to be best for a given patient's covariate profile. Extensive research has been done on various aspects of CARA designs with the patient responses assumed to follow a parametric model. However, ranges of application for such designs are limited in real-life clinical trials where the responses infrequently fit a certain parametric form. On the other hand, robust estimates for the covariate-adjusted treatment effects are obtained from the parametric assumption. To balance these two requirements, designs are developed which are free from distributional assumptions about the survival responses, relying only on the assumption of proportional hazards for the two treatment arms. The proposed designs are developed by deriving two types of optimum allocation designs, and also by using a distribution function to link the past allocation, covariate and response histories to the present allocation. The optimal designs are based on biased coin procedures, with a bias towards the better treatment arm. These are the doubly-adaptive biased coin design (DBCD) and the efficient randomized adaptive design (ERADE). The treatment allocation proportions for these designs converge to the expected target values, which are functions of the Cox regression coefficients that are estimated sequentially. These expected target values are derived based on constrained optimization problems and are updated as information accrues with sequential arrival of patients. The design based on the link function is derived using the distribution function of a probit model whose parameters are adjusted based on the covariate profile of the incoming patient. To apply such designs, the treatment allocation probabilities are sequentially modified based on the treatment allocation history, response history, previous patients’ covariates and also the covariates of the incoming patient. Given these information, an expression is obtained for the conditional probability of a patient allocation to a treatment arm. Based on simulation studies, it is found that the ERADE is preferable to the DBCD when the main aim is to minimize the variance of the observed allocation proportion and to maximize the power of the Wald test for a treatment difference. However, the former procedure being discrete tends to be slower in converging towards the expected target allocation proportion. The link function based design achieves the highest skewness of patient allocation to the best treatment arm and thus ethically is the best design. Other comparative merits of the proposed designs have been highlighted and their preferred areas of application are discussed. It is concluded that the proposed CARA designs can be considered as suitable alternatives to the traditional balanced randomization designs in survival trials in terms of the power of the Wald test, provided that response data are available during the recruitment phase of the trial to enable adaptations to the designs. Moreover, the proposed designs enable more patients to get treated with the better treatment during the trial thus making the designs more ethically attractive to the patients. An existing clinical trial has been redesigned using these methods.

Keywords: censored response, Cox regression, efficiency, ethics, optimal allocation, power, variability

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Authors: Waheed Zahra, Mohamed El-Beltagy, Ashraf El Mhlawy, Reda Elkhadrawy

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In this paper, we consider singular perturbation reaction-diffusion boundary value problems, which contain a small uncertain perturbation parameter. To solve these problems, we propose a numerical method which is based on an exponential spline and Shishkin mesh discretization. While interval analysis principle is used to deal with the uncertain parameter, sensitivity analysis has been conducted using different methods. Numerical results are provided to show the applicability and efficiency of our method, which is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, shishkin mesh, two small parameters, exponential spline, interval analysis, sensitivity analysis

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Authors: Jorge Olivares, Fernando Maass, Pablo Martin

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Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function.

Keywords: Caputo, modified Bessel functions, hypergeometric, linear fractional differential equations, transform Laplace

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

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Authors: Yeliz Karaca, Rana Karabudak

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Multifractal Denoising techniques are used in the identification of significant attributes by removing the noise of the dataset. Magnetic resonance (MR) image technique is the most sensitive method so as to identify chronic disorders of the nervous system such as Multiple Sclerosis. MRI and Expanded Disability Status Scale (EDSS) data belonging to 120 individuals who have one of the subgroups of MS (Relapsing Remitting MS (RRMS), Secondary Progressive MS (SPMS), Primary Progressive MS (PPMS)) as well as 19 healthy individuals in the control group have been used in this study. The study is comprised of the following stages: (i) L2 Norm Multifractal Denoising technique, one of the multifractal technique, has been used with the application on the MS data (MRI and EDSS). In this way, the new dataset has been obtained. (ii) The new MS dataset obtained from the MS dataset and L2 Multifractal Denoising technique has been applied to the K-Means and Fuzzy C Means clustering algorithms which are among the unsupervised methods. Thus, the clustering performances have been compared. (iii) In the identification of significant attributes in the MS dataset through the Multifractal denoising (L2 Norm) technique using K-Means and FCM algorithms on the MS subgroups and control group of healthy individuals, excellent performance outcome has been yielded. According to the clustering results based on the MS subgroups obtained in the study, successful clustering results have been obtained in the K-Means and FCM algorithms by applying the L2 norm of multifractal denoising technique for the MS dataset. Clustering performance has been more successful with the MS Dataset (L2_Norm MS Data Set) K-Means and FCM in which significant attributes are obtained by applying L2 Norm Denoising technique.

Keywords: clinical decision support, clustering algorithms, multiple sclerosis, multifractal techniques

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Authors: Carol Anne Hargreaves

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A key issue in stock investment is how to select representative features for stock selection. The objective of this paper is to firstly determine whether an automated stock investment system, using machine learning techniques, may be used to identify a portfolio of growth stocks that are highly likely to provide returns better than the stock market index. The second objective is to identify the technical features that best characterize whether a stock’s price is likely to go up and to identify the most important factors and their contribution to predicting the likelihood of the stock price going up. Unsupervised machine learning techniques, such as cluster analysis, were applied to the stock data to identify a cluster of stocks that was likely to go up in price – portfolio 1. Next, the principal component analysis technique was used to select stocks that were rated high on component one and component two – portfolio 2. Thirdly, a supervised machine learning technique, the logistic regression method, was used to select stocks with a high probability of their price going up – portfolio 3. The predictive models were validated with metrics such as, sensitivity (recall), specificity and overall accuracy for all models. All accuracy measures were above 70%. All portfolios outperformed the market by more than eight times. The top three stocks were selected for each of the three stock portfolios and traded in the market for one month. After one month the return for each stock portfolio was computed and compared with the stock market index returns. The returns for all three stock portfolios was 23.87% for the principal component analysis stock portfolio, 11.65% for the logistic regression portfolio and 8.88% for the K-means cluster portfolio while the stock market performance was 0.38%. This study confirms that an automated stock investment system using machine learning techniques can identify top performing stock portfolios that outperform the stock market.

Keywords: machine learning, stock market trading, logistic regression, cluster analysis, factor analysis, decision trees, neural networks, automated stock investment system

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Authors: Ben Clapperton, Daniel Stahl, Kimberley Goldsmith, Trudie Chalder

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Chronic fatigue syndrome (CFS) is a condition characterised by chronic disabling fatigue and other symptoms that currently can't be explained by any underlying medical condition. Although clinical trials support the effectiveness of cognitive behaviour therapy (CBT), the success rate for individual patients is modest. Patients vary in their response and little is known which factors predict or moderate treatment outcomes. The aim of the project is to develop a prediction model from baseline characteristics of patients, such as demographics, clinical and psychological variables, which may predict likely treatment outcome and provide guidance for clinical decision making and help clinicians to recommend the best treatment. The project is aimed at identifying subgroups of patients with similar baseline characteristics that are predictive of treatment effects using modern cluster analyses and data mining machine learning algorithms. The characteristics of these groups will then be used to inform the types of individuals who benefit from a specific treatment. In addition, results will provide a better understanding of for whom the treatment works. The suitability of different clustering methods to identify subgroups and their response to different treatments of CFS patients is compared.

Keywords: chronic fatigue syndrome, latent class analysis, prediction modelling, self-organizing maps

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Authors: Yeliz Karaca, Carlo Cattani

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This study focuses on the local Holder exponent as a measure of the function regularity for time series related to finance data. In this study, the attributes of the finance dataset belonging to 13 countries (India, China, Japan, Sweden, France, Germany, Italy, Australia, Mexico, United Kingdom, Argentina, Brazil, USA) located in 5 different continents (Asia, Europe, Australia, North America and South America) have been examined.These countries are the ones mostly affected by the attributes with regard to financial development, covering a period from 2012 to 2017. Our study is concerned with the most important attributes that have impact on the development of finance for the countries identified. Our method is comprised of the following stages: (a) among the multi fractal methods and Brownian motion Holder regularity functions (polynomial, exponential), significant and self-similar attributes have been identified (b) The significant and self-similar attributes have been applied to the Artificial Neuronal Network (ANN) algorithms (Feed Forward Back Propagation (FFBP) and Cascade Forward Back Propagation (CFBP)) (c) the outcomes of classification accuracy have been compared concerning the attributes that have impact on the attributes which affect the countries’ financial development. This study has enabled to reveal, through the application of ANN algorithms, how the most significant attributes are identified within the relevant dataset via the Holder functions (polynomial and exponential function).

Keywords: artificial neural networks, finance data, Holder regularity, multifractals

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Authors: A. Giniatoulline

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We consider the internal oscillations of the ocean which are caused by the gravity force and the Coriolis force, for different models with changeable density, heat transfer, and salinity. Traditionally, the mathematical description of the resonance effect is related to the growing amplitude as a result of input vibrations. We offer a different approach: the study of the relation between the spectrum of the internal oscillations and the properties of the limiting amplitude of the solution for the harmonic input vibrations of the external forces. Using the results of the spectral theory of self-adjoint operators in Hilbert functional spaces, we prove that there exists an explicit relation between the localization of the frequency of the external input vibrations with respect to the essential spectrum of proper inner oscillations and the non-uniqueness of the limiting amplitude. The results may find their application in various problems concerning mathematical modeling of turbulent flows in the ocean.

Keywords: computational fluid dynamics, essential spectrum, limiting amplitude, rotating fluid, spectral theory, stratified fluid, the uniqueness of solutions of PDE equations

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Authors: Taehan Bae

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In this paper, a class of length-biased Weibull mixtures is presented to model loss severity data. The proposed model generalizes the Erlang mixtures with the common scale parameter, and it shares many important modelling features, such as flexibility to fit various data distribution shapes and weak-denseness in the class of positive continuous distributions, with the Erlang mixtures. We show that the asymptotic tail estimate of the length-biased Weibull mixture is Weibull-type, which makes the model effective to fit loss severity data with heavy-tailed observations. A method of statistical estimation is discussed with applications on real catastrophic loss data sets.

Keywords: Erlang mixture, length-biased distribution, transformed gamma distribution, asymptotic tail estimate, EM algorithm, expectation-maximization algorithm

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Authors: Nadarajah I. Ramesh

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Much of the research on stochastic point process models for rainfall has focused on Poisson cluster models constructed from either the Neyman-Scott or Bartlett-Lewis processes. The doubly stochastic Poisson process provides a rich class of point process models, especially for fine-scale rainfall modelling. This paper provides an account of recent development on this topic and presents the results based on some of the fine-scale rainfall models constructed from this class of stochastic point processes. Amongst the literature on stochastic models for rainfall, greater emphasis has been placed on modelling rainfall data recorded at hourly or daily aggregation levels. Stochastic models for sub-hourly rainfall are equally important, as there is a need to reproduce rainfall time series at fine temporal resolutions in some hydrological applications. For example, the study of climate change impacts on hydrology and water management initiatives requires the availability of data at fine temporal resolutions. One approach to generating such rainfall data relies on the combination of an hourly stochastic rainfall simulator, together with a disaggregator making use of downscaling techniques. Recent work on this topic adopted a different approach by developing specialist stochastic point process models for fine-scale rainfall aimed at generating synthetic precipitation time series directly from the proposed stochastic model. One strand of this approach focused on developing a class of doubly stochastic Poisson process (DSPP) models for fine-scale rainfall to analyse data collected in the form of rainfall bucket tip time series. In this context, the arrival pattern of rain gauge bucket tip times N(t) is viewed as a DSPP whose rate of occurrence varies according to an unobserved finite state irreducible Markov process X(t). Since the likelihood function of this process can be obtained, by conditioning on the underlying Markov process X(t), the models were fitted with maximum likelihood methods. The proposed models were applied directly to the raw data collected by tipping-bucket rain gauges, thus avoiding the need to convert tip-times to rainfall depths prior to fitting the models. One advantage of this approach was that the use of maximum likelihood methods enables a more straightforward estimation of parameter uncertainty and comparison of sub-models of interest. Another strand of this approach employed the DSPP model for the arrivals of rain cells and attached a pulse or a cluster of pulses to each rain cell. Different mechanisms for the pattern of the pulse process were used to construct variants of this model. We present the results of these models when they were fitted to hourly and sub-hourly rainfall data. The results of our analysis suggest that the proposed class of stochastic models is capable of reproducing the fine-scale structure of the rainfall process, and hence provides a useful tool in hydrological modelling.

Keywords: fine-scale rainfall, maximum likelihood, point process, stochastic model

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Authors: Galal Elkobrosy, Amr M. Abdelrazek, Bassuny M. Elsouhily, Mohamed E. Khidr

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Crank shaft length, connecting rod length, crank angle, engine rpm, cylinder bore, mass of piston and compression ratio are the inputs that can control the performance of the slider crank mechanism and then its efficiency. Several combinations of these seven inputs are used and compared. The throughput engine torque predicted by the simulation is analyzed through two different regression models, with and without interaction terms, developed according to multi-linear regression using LU decomposition to solve system of algebraic equations. These models are validated. A regression model in seven inputs including their interaction terms lowered the polynomial degree from 3^rd degree to 1^st degree and suggested valid predictions and stable explanations.

Keywords: design of experiments, regression analysis, SI engine, statistical modeling

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Authors: Muhammad Abdullah, Asma Rashid Butt, Nauman Raza

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Biomagnetic fluids like blood play key role in different applications of medical science and bioengineering. In this paper, the magnetohydrodynamic flow of a viscous fluid with magnetic particles through a cylindrical tube is investigated. The fluid is electrically charged in the presence of a uniform external magnetic field. The movement in the fluid is produced due to the cylindrical tube. Initially, the fluid and tube are at rest and at time t=0⁺, the tube starts to move along its axis. To obtain the mathematical model of flow with fractional derivatives fractional calculus approach is used. The solution of the flow model is obtained by using Laplace transformation. The Simon's numerical algorithm is employed to obtain inverse Laplace transform. The hybrid technique, we are employing has less computational effort as compared to other methods. The numerical calculations have been performed with Mathcad software. As the special cases of our problem, the solution of flow model with ordinary derivatives and flow without magnetic particles has been procured. Finally, the impact of non-integer fractional parameter alpha, Hartmann number Ha, and Reynolds number Re on flow and magnetic particles velocity is analyzed and depicted by graphs.

Keywords: viscous fluid, magnetic particles, fractional calculus, laplace transformation

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Authors: Shumaila Ehtisham

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In Statistical Distribution Theory, considering an additional parameter to classical distributions is a usual practice. In this study, a new distribution referred to as α-Power Pareto distribution is introduced by including an extra parameter. Several properties of the proposed distribution including explicit expressions for the moment generating function, mode, quantiles, entropies and order statistics are obtained. Unknown parameters have been estimated by using maximum likelihood estimation technique. Two real datasets have been considered to examine the usefulness of the proposed distribution. It has been observed that α-Power Pareto distribution outperforms while compared to different variants of Pareto distribution on the basis of model selection criteria.

Keywords: α-power transformation, maximum likelihood estimation, moment generating function, Pareto distribution

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Authors: S. B. Provost, Hossein Zareamoghaddam

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A univariate density approximation technique whereby the derivative of the logarithm of a density function is assumed to be expressible as a rational function is introduced. This approach which extends Pearson’s curve system is solely based on the moments of a distribution up to a determinable order. Upon solving a system of linear equations, the coefficients of the polynomial ratio can readily be identified. An explicit solution to the integral representation of the resulting density approximant is then obtained. It will be explained that when utilised in conjunction with sample moments, this methodology lends itself to the modelling of ‘big data’. Applications to sets of univariate and bivariate observations will be presented.

Keywords: density estimation, log-density, moments, Pearson's curve system

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Authors: Malika Yaici, Kamel Hariche

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In control engineering, systems described by matrix fractions are studied through properties of block roots, also called solvents. These solvents are usually dealt with in a block Vandermonde matrix form. Inverses and determinants of Vandermonde matrices and block Vandermonde matrices are used in solving problems of numerical analysis in many domains but require costly computations. Even though Vandermonde matrices are well known and method to compute inverse and determinants are many and, generally, based on interpolation techniques, methods to compute the inverse and determinant of a block Vandermonde matrix have not been well studied. In this paper, some properties of these matrices and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given. These methods are deducted from the partitioned matrix inversion and determinant computing methods. Due to their great size, parallelization may be a solution to reduce the computations cost, so a parallelization of these algorithms is proposed and validated by a comparison using algorithmic complexity.

Keywords: block vandermonde matrix, solvents, matrix polynomial, matrix inverse, matrix determinant, parallelization

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Authors: Abhilash Sahu, Amit Priyadarshi

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In this paper, we will discuss the existence of weak solutions of the Kirchhoff type boundary value problem on the Sierpinski gasket. Where S denotes the Sierpinski gasket in R² and S₀ is the intrinsic boundary of the Sierpinski gasket. M: R → R is a positive function and h: S × R → R is a suitable function which is a part of our main equation. ∆p denotes the p-Laplacian, where p > 1. First of all, we will define a weak solution for our problem and then we will show the existence of at least two solutions for the above problem under suitable conditions. There is no well-known concept of a generalized derivative of a function on a fractal domain. Recently, the notion of differential operators such as the Laplacian and the p-Laplacian on fractal domains has been defined. We recall the result first then we will address the above problem. In view of literature, Laplacian and p-Laplacian equations are studied extensively on regular domains (open connected domains) in contrast to fractal domains. In fractal domains, people have studied Laplacian equations more than p-Laplacian probably because in that case, the corresponding function space is reflexive and many minimax theorems which work for regular domains is applicable there which is not the case for the p-Laplacian. This motivates us to study equations involving p-Laplacian on the Sierpinski gasket. Problems on fractal domains lead to nonlinear models such as reaction-diffusion equations on fractals, problems on elastic fractal media and fluid flow through fractal regions etc. We have studied the above p-Laplacian equations on the Sierpinski gasket using fibering map technique on the Nehari manifold. Many authors have studied the Laplacian and p-Laplacian equations on regular domains using this Nehari manifold technique. In general Euler functional associated with such a problem is Frechet or Gateaux differentiable. So, a critical point becomes a solution to the problem. Also, the function space they consider is reflexive and hence we can extract a weakly convergent subsequence from a bounded sequence. But in our case neither the Euler functional is differentiable nor the function space is known to be reflexive. Overcoming these issues we are still able to prove the existence of at least two solutions of the given equation.

Keywords: Euler functional, p-Laplacian, p-energy, Sierpinski gasket, weak solution

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Authors: Giulia I. Pintea

Abstract:

The Roma people are a nomadic ethnic group native to India, and they are one of the most prevalent minorities in Europe. In the past, Roma were enslaved and they were imprisoned in concentration camps during the Holocaust; today, Roma are subject to hate crimes and are denied access to healthcare, education, and proper housing. The aim of this project is to analyze how the public perception of the Roma people may be influenced by antiziganist and pro-Roma institutions in Europe. In order to carry out this project, we used social network analysis to build two large social networks: The antiziganist network, which is composed of institutions that oppress and racialize Roma, and the pro-Roma network, which is composed of institutions that advocate for and protect Roma rights. Measures of centrality, density, and modularity were obtained to determine which of the two social networks is exerting the greatest influence on the public’s perception of Roma in European societies. Furthermore, data on hate crimes on Roma were gathered from the Organization for Security and Cooperation in Europe (OSCE). We analyzed the trends in hate crimes on Roma for several European countries for 2009-2015 in order to see whether or not there have been changes in the public’s perception of Roma, thus helping us evaluate which of the two social networks has been more influential. Overall, the results suggest that there is a greater and faster exchange of information in the pro-Roma network. However, when taking the hate crimes into account, the impact of the pro-Roma institutions is ambiguous, due to differing patterns among European countries, suggesting that the impact of the pro-Roma network is inconsistent. Despite antiziganist institutions having a slower flow of information, the hate crime patterns also suggest that the antiziganist network has a higher impact on certain countries, which may be due to institutions outside the political sphere boosting the spread of antiziganist ideas and information to the European public.

Keywords: applied mathematics, oppression, Roma people, social network analysis

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Authors: Yoshifumi Hino

Abstract:

An infinitely repeated prisoner’s dilemma is a typical model that represents teamwork situation. If both players choose costly actions and contribute to the team, then both players are better off. However, each player has an incentive to choose a selfish action. We analyze the game under costly observation. Each player can observe the action of the opponent only when he pays an observation cost in that period. In reality, teamwork situations are often costly observation. Members of some teams sometimes work in distinct rooms, areas, or countries. In those cases, they have to spend their time and money to see other team members if they want to observe it. The costly observation assumption makes the cooperation difficult substantially because the equilibrium must satisfy the incentives not only on the action but also on the observational decision. Especially, it is the most difficult to cooperate each other when the stage-game is prisoner's dilemma because players have to communicate through only two actions. We examine whether or not players can cooperate each other in prisoner’s dilemma under costly observation. Specifically, we check whether symmetric Pareto efficient payoff vectors in repeated prisoner’s dilemma can be approximated by sequential equilibria or not (efficiency result). We show the efficiency result without any randomization device under certain circumstances. It means that players can cooperate with each other without any randomization device even if the observation is costly. Next, we assume that public randomization device is available, and then we show that any feasible and individual rational payoffs in prisoner’s dilemma can be approximated by sequential equilibria under a specific situation (folk theorem). It implies that players can achieve asymmetric teamwork like leadership situation when public randomization device is available.

Keywords: cost observation, efficiency, folk theorem, prisoner's dilemma, private monitoring, repeated games.

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Authors: Md. Abud Darda

Abstract:

Different options for natural gas production in wide geographic areas may be described through diffusion of innovation models. This type of modeling approach provides an indirect estimate of an ultimately recoverable resource, URR, capture the quantitative effects of observed strategic interventions, and allow ex-ante assessments of future scenarios over time. In order to ensure a sustainable energy policy, it is important to forecast the availability of this natural resource. Considering a finite life cycle, in this paper we try to investigate the natural gas production of Myanmar and Algeria, two important natural gas provider in the world energy market. A number of homogeneous and heterogeneous diffusion models, with convenient extensions, have been used. Models validation has also been performed in terms of prediction capability.

Keywords: diffusion models, energy forecast, natural gas, nonlinear production

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Authors: O. Boussoufi, K. Lamrini Uahabi, M. Atounti

Abstract:

The main purpose of this paper is to calculate the fractal dimension of some Julia Sets and Mandelbrot Set in the Misiurewicz Points. Using Matlab to generate the Julia Sets images that match the Misiurewicz points and using a Fractal software, we were able to find different measures that characterize those fractals in textures and other features. We are actually focusing on fractal dimension and the error calculated by the software. When executing the given equation of regression or the log-log slope of image a Box Counting method is applied to the entire image, and chosen settings are available in a FracLAc Program. Finally, a comparison is done for each image corresponding to the area (boundary) where Misiurewicz Point is located.

Keywords: box counting, FracLac, fractal dimension, Julia Sets, Mandelbrot Set, Misiurewicz Points

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Authors: Ainura Tursunalieva, Irene Hudson

Abstract:

Continuous improvement of both the quality and safety of health care is an important goal in Australia and internationally. The intensive care unit (ICU) receives patients with a wide variety of and severity of illnesses. Accurately identifying patients at risk of developing complications or dying is crucial to increasing healthcare efficiency. Thus, it is essential for clinicians and researchers to have a robust framework capable of evaluating the risk profile of a patient. ICU scoring systems provide such a framework. The Acute Physiology and Chronic Health Evaluation III and the Simplified Acute Physiology Score II are ICU scoring systems frequently used for assessing the severity of acute illness. These scoring systems collect multiple risk factors for each patient including physiological measurements then render the assessment outcomes of individual risk factors into a single numerical value. A higher score is related to a more severe patient condition. Furthermore, the Mortality Probability Model II uses logistic regression based on independent risk factors to predict a patient’s probability of mortality. An important overlooked limitation of SAPS II and MPM II is that they do not, to date, include interaction terms between a patient’s vital signs. This is a prominent oversight as it is likely there is an interplay among vital signs. The co-existence of certain conditions may pose a greater health risk than when these conditions exist independently. One barrier to including such interaction terms in predictive models is the dimensionality issue as it becomes difficult to use variable selection. We propose an innovative scoring system which takes into account a dependence structure among patient’s vital signs, such as systolic and diastolic blood pressures, heart rate, pulse interval, and peripheral oxygen saturation. Copulas will capture the dependence among normally distributed and skewed variables as some of the vital sign distributions are skewed. The estimated dependence parameter will then be incorporated into the traditional scoring systems to adjust the points allocated for the individual vital sign measurements. The same dependence parameter will also be used to create an alternative copula-based model for predicting a patient’s probability of mortality. The new copula-based approach will accommodate not only a patient’s trajectories of vital signs but also the joint dependence probabilities among the vital signs. We hypothesise that this approach will produce more stable assessments and lead to more time efficient and accurate predictions. We will use two data sets: (1) 250 ICU patients admitted once to the Chui Regional Hospital (Kyrgyzstan) and (2) 37 ICU patients’ agitation-sedation profiles collected by the Hunter Medical Research Institute (Australia). Both the traditional scoring approach and our copula-based approach will be evaluated using the Brier score to indicate overall model performance, the concordance (or c) statistic to indicate the discriminative ability (or area under the receiver operating characteristic (ROC) curve), and goodness-of-fit statistics for calibration. We will also report discrimination and calibration values and establish visualization of the copulas and high dimensional regions of risk interrelating two or three vital signs in so-called higher dimensional ROCs.

Keywords: copula, intensive unit scoring system, ROC curves, vital sign dependence

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Authors: Sabrina Nouri, Abderahmane Ghezal, Said Abboudi, Pierre Spiteri

Abstract:

This paper deals with the numerical study of heat and mass transfer of laminar flow transition at low Prandtl numbers. The model includes the two-directional momentum, the energy and mass transfer equations. These equations are discretized by the finite volume method and solved by a self-made simpler like Fortran code. The effect of governing parameters, namely the Lewis and Prandtl numbers, on the transition of the flow and solute distribution is studied for positive and negative thermal and solutal buoyancy forces ratio. Nusselt and Sherwood numbers are derived for of Prandtl [10⁻²-10¹] and Lewis numbers [1-10⁴]. The results show unicell and multi-cell flow. Solute and flow boundary layers appear for low Prandtl number.

Keywords: natural convection, low Prandtl number, heat and mass transfer, finite volume method

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