Scholarly Research Excellence

Digital Open Science Index

Commenced in January 2007 Frequency: Monthly Edition: International Abstract Count: 55954

Mathematical and Computational Sciences

904
100049
Predictive Modelling of Aircraft Component Replacement Using Imbalanced Learning and Ensemble Method
Abstract:
Adequate monitoring of vehicle component in other to obtain high uptime is the goal of predictive maintenance, the major challenge faced by businesses in industries is the significant cost associated with a delay in service delivery due to system downtime. Most of those businesses are interested in predicting those problems and proactively prevent them in advance before it occurs, which is the core advantage of Prognostic Health Management (PHM) application. The recent emergence of industry 4.0 or industrial internet of things (IIoT) has led to the need for monitoring systems activities and enhancing system-to-system or component-to- component interactions, this has resulted to a large generation of data known as big data. Analysis of big data represents an increasingly important, however, due to complexity inherently in the dataset such as imbalance classification problems, it becomes extremely difficult to build a model with accurate high precision. Data-driven predictive modeling for condition-based maintenance (CBM) has recently drowned research interest with growing attention to both academics and industries. The large data generated from industrial process inherently comes with a different degree of complexity which posed a challenge for analytics. Thus, imbalance classification problem exists perversely in industrial datasets which can affect the performance of learning algorithms yielding to poor classifier accuracy in model development. Misclassification of faults can result in unplanned breakdown leading economic loss. In this paper, an advanced approach for handling imbalance classification problem is proposed and then a prognostic model for predicting aircraft component replacement is developed to predict component replacement in advanced by exploring aircraft historical data, the approached is based on hybrid ensemble-based method which improves the prediction of the minority class during learning, we also investigate the impact of our approach on multiclass imbalance problem. We validate the feasibility and effectiveness in terms of the performance of our approach using real-world aircraft operation and maintenance datasets, which spans over 7 years. Our approach shows better performance compared to other similar approaches. We also validate our approach strength for handling multiclass imbalanced dataset, our results also show good performance compared to other based classifiers.
903
98818
Study of Electron Cyclotron Resonance Acceleration by Cylindrical TE₀₁₁ Mode
Abstract:
In this work, we present results from analytical and numerical studies of the electron acceleration by a TE₀₁₁ cylindrical microwave mode in a static homogeneous magnetic field under electron cyclotron resonance (ECR) condition. The stability of the orbits is analyzed using the particle orbit theory. In order to get a better understanding of the interaction wave-particle, we decompose the azimuthally electric field component as the superposition of right and left-hand circular polarization standing waves. The trajectory, energy and phase-shift of the electron are found through a numerical solution of the relativistic Newton-Lorentz equation in a finite difference method by the Boris method. It is shown that an electron longitudinally injected with an energy of 7 keV in a radial position r=Rc/2, being Rc the cavity radius, is accelerated up to energy of 90 keV by an electric field strength of 14 kV/cm and frequency of 2.45 GHz. This energy can be used to produce X-ray for medical imaging. These results can be used as a starting point for study the acceleration of electrons in a magnetic field changing slowly in time (GYRAC), which has some important applications as the electron cyclotron resonance ion proton accelerator (ECR-IPAC) for cancer therapy and to control plasma bunches with relativistic electrons.
902
98212
Analysis of Factors Affecting the Number of Infant and Maternal Mortality in East Java with Geographically Weighted Bivariate Generalized Poisson Regression Method
Abstract:
Poisson regression is a non-linear regression model with response variable in the form of count data that follows Poisson distribution. Modeling for a pair of count data that show high correlation can be analyzed by Poisson Bivariate Regression. Data, the number of infant mortality and maternal mortality, are count data that can be analyzed by Poisson Bivariate Regression. The Poisson regression assumption is an equidispersion where the mean and variance values are equal. However, the actual count data has a variance value which can be greater or less than the mean value (overdispersion and underdispersion). Violations of this assumption can be overcome by applying Generalized Poisson Regression. Characteristics of each regency can affect the number of cases occurred. This issue can be overcome by spatial analysis called geographically weighted regression. This study analyzes the number of infant mortality and maternal mortality based on conditions in East Java in 2016 using Geographically Weighted Bivariate Generalized Poisson Regression (GWBGPR) method. Modeling is done with adaptive bisquare Kernel weighting which produces 3 regency groups based on infant mortality rate and 5 regency groups based on maternal mortality rate. Variables that significantly influence the number of infant and maternal mortality are the percentages of pregnant women visit health workers at least 4 times during pregnancy, pregnant women get Fe3 tablets, obstetric complication handled, clean household and healthy behavior, and married women with the first marriage age under 18 years.
901
97916
Analysis of Cooperative Learning Behavior Based on the Data of Students' Movement
Abstract:
The purpose of this paper is to analyze the cooperative learning behavior pattern based on the data of students' movement. The study firstly reviewed the cooperative learning theory and its research status, and briefly introduced the k-means clustering algorithm. Then, it used clustering algorithm and mathematical statistics theory to analyze the activity rhythm of individual student and groups in different functional areas, according to the movement data provided by 10 first-year graduate students. It also focused on the analysis of students' behavior in the learning area and explored the law of cooperative learning behavior. The research result showed that the cooperative learning behavior analysis method based on movement data proposed in this paper is feasible. From the results of data analysis, the characteristics of behavior of students and their cooperative learning behavior patterns could be found.
900
97739
Model Predictive Control with Unscented Kalman Filter for Nonlinear Implicit Systems
Abstract:
A class of implicit systems is known as a more generalized class of systems than a class of explicit systems. To establish a control method for such a generalized class of systems, we adopt model predictive control method which is a kind of optimal feedback control with a performance index that has a moving initial time and terminal time. However, model predictive control method is inapplicable to systems whose all state variables are not exactly known. In other words, model predictive control method is inapplicable to systems with limited measurable states. In fact, it is usual that the state variables of systems are measured through outputs, hence, only limited parts of them can be used directly. It is also usual that output signals are disturbed by process and sensor noises. Hence, it is important to establish a state estimation method for nonlinear implicit systems with taking the process noise and sensor noise into consideration. To this purpose, we apply the model predictive control method and unscented Kalman filter for solving the optimization and estimation problems of nonlinear implicit systems, respectively. The objective of this study is to establish a model predictive control with unscented Kalman filter for nonlinear implicit systems.
899
96725
Large-Scale Simulations of Turbulence Using Discontinuous Spectral Element Method
Abstract:
Turbulence can be observed in a variety fluid motions in nature and industrial applications. Recent investment in high-speed aircraft and propulsion systems has revitalized fundamental research on turbulent flows. In these systems, capturing chaotic fluid structures with different length and time scales is accomplished through the Direct Numerical Simulation (DNS) approach since it accurately simulates flows down to smallest dissipative scales, i.e., Kolmogorov’s scales. The discontinuous spectral element method (DSEM) is a high-order technique that uses spectral functions for approximating the solution. The DSEM code has been developed by our research group over the course of more than two decades. Recently, the code has been improved to run large cases in the order of billions of solution points. Running big simulations requires a considerable amount of RAM. Therefore, the DSEM code must be highly parallelized and able to start on multiple computational nodes on an HPC cluster with distributed memory. However, some pre-processing procedures, such as determining global element information, creating a global face list, and assigning global partitioning and element connection information of the domain for communication, must be done sequentially with a single processing core. A separate code has been written to perform the pre-processing procedures on a local machine. It stores the minimum amount of information that is required for the DSEM code to start in parallel, extracted from the mesh file, into text files (pre-files). It packs integer type information with a Stream Binary format in pre-files that are portable between machines. The files are generated to ensure fast read performance on different file-systems, such as Lustre and General Parallel File System (GPFS). A new subroutine has been added to the DSEM code to read the startup files using parallel MPI I/O, for Lustre, in a way that each MPI rank acquires its information from the file in parallel. In case of GPFS, in each computational node, a single MPI rank reads data from the file, which is specifically generated for the computational node, and send them to other ranks on the node using point to point non-blocking MPI communication. This way, communication takes place locally on each node and signals do not cross the switches of the cluster. The read subroutine has been tested on Argonne National Laboratory’s Mira (GPFS), National Center for Supercomputing Application’s Blue Waters (Lustre), San Diego Supercomputer Center’s Comet (Lustre), and UIC’s Extreme (Lustre). The tests showed that one file per node is suited for GPFS and parallel MPI I/O is the best choice for Lustre file system. The DSEM code relies on heavily optimized linear algebra operation such as matrix-matrix and matrix-vector products for calculation of the solution in every time-step. For this, the code can either make use of its matrix math library, BLAS, Intel MKL, or ATLAS. This fact and the discontinuous nature of the method makes the DSEM code run efficiently in parallel. The results of weak scaling tests performed on Blue Waters showed a scalable and efficient performance of the code in parallel computing.
898
96373
Numerical Studies for Standard Bi-Conjugate Gradient Stabilized Method and the Parallel Variants for Solving Linear Equations
Authors:
Abstract:
Bi-conjugate gradient (Bi-CG) is a well-known method for solving linear equations Ax = b, for x, where A is a given n-by-n matrix, and b is a given n-vector. Typically, the dimension of the linear equation is high and the matrix is sparse. A number of hybrid Bi-CG methods such as conjugate gradient squared (CGS), Bi-CG stabilized (Bi-CGSTAB), BiCGStab2, and BiCGstab(l) have been developed to improve the convergence of Bi-CG. Bi-CGSTAB has been most often used for efficiently solving the linear equation, but we have seen the convergence behavior with a long stagnation phase. In such cases, it is important to have Bi-CG coefficients that are as accurate as possible, and the stabilization strategy, which stabilizes the computation of the Bi-CG coefficients, has been proposed. It may avoid stagnation and lead to faster computation. Motivated by a large number of processors in present petascale high-performance computing hardware, the scalability of Krylov subspace methods on parallel computers has recently become increasingly prominent. The main bottleneck for efficient parallelization is the inner products which require a global reduction. The resulting global synchronization phases cause communication overhead on parallel computers. The parallel variants of Krylov subspace methods reducing the number of global communication phases and hiding the communication latency have been proposed. However, the numerical stability, specifically, the convergence speed of the parallel variants of Bi-CGSTAB may become worse than that of the standard Bi-CGSTAB. In this paper, therefore, we compare the convergence speed between the standard Bi-CGSTAB and the parallel variants by numerical experiments and show that the convergence speed of the standard Bi-CGSTAB is faster than the parallel variants. Moreover, we propose the stabilization strategy for the parallel variants.
897
96045
Statistical Convergence of the Szasz-Mirakjan-Kantorovich-Type Operators
Abstract:
The main aim of this article is to investigate the statistical convergence of the summation of integral type operators and to obtain the weighted statistical convergence. The rate of statistical convergence by means of modulus of continuity and function belonging to the Lipschitz class are also studied. We discuss the convergence of the defined operators by graphical representation and put a better rate of convergence than the Szasz-Mirakjan-Kantorovich operators. In the last section, we extend said operators into bivariate operators to study about the rate of convergence in sense of modulus of continuity and by means of Lipschitz class by using function of two variables.
896
95482
Theoretical Analysis of the Existing Sheet Thickness in the Calendering of Pseudoplastic Material
Abstract:
The mechanical process of smoothing and compressing a molten material by passing it through a number of pairs of heated rolls in order to produce a sheet of desired thickness is called calendering. The rolls that are in combination are called calenders, a term derived from kylindros the Greek word for the cylinder. It infects the finishing process used on cloth, paper, textiles, leather cloth, or plastic film and so on. It is a mechanism which is used to strengthen surface properties, minimize sheet thickness, and yield special effects such as a glaze or polish. It has a wide variety of applications in industries in the manufacturing of textile fabrics, coated fabrics, and plastic sheeting to provide the desired surface finish and texture. An analysis has been presented for the calendering of Pseudoplastic material. The lubrication approximation theory (LAT) has been used to simplify the equations of motion. For the investigation of the nature of the steady solutions that exist, we make use of the combination of exact solution and numerical methods. The expressions for the velocity profile, rate of volumetric flow and pressure gradient are found in the form of exact solutions. Furthermore, the quantities of interest by engineering point of view, such as pressure distribution, roll-separating force, and power transmitted to the fluid by the rolls are also computed. Some results are shown graphically while others are given in the tabulated form. It is found that the non-Newtonian parameter and Reynolds number serve as the controlling parameters for the calendering process.
895
95455
The Non-Existence of Perfect 2-Error Correcting Lee Codes of Word Length 7 over Z
Abstract:
Tiling problems have been capturing the attention of many mathematicians due to their real-life applications. In this study, we deal with tilings of Zⁿ by Lee spheres, where n is a positive integer number, being these tilings related with error correcting codes on the transmission of information over a noisy channel. We focus our attention on the question ‘for what values of n and r does the n-dimensional Lee sphere of radius r tile Zⁿ?’. It seems that the n-dimensional Lee sphere of radius r does not tile Zⁿ for n ≥ 3 and r ≥ 2. Here, we prove that is not possible to tile Z⁷ with Lee spheres of radius 2 presenting a proof based on a combinatorial method and faithful to the geometric idea of the problem. The non-existence of such tilings has been studied by several authors being considered the most difficult cases those in which the radius of the Lee spheres is equal to 2. The relation between these tilings and error correcting codes is established considering the center of a Lee sphere as a codeword and the other elements of the sphere as words which are decoded by the central codeword. When the Lee spheres of radius r centered at elements of a set M ⊂ Zⁿ tile Zⁿ, M is a perfect r-error correcting Lee code of word length n over Z, denoted by PL(n, r). Our strategy to prove the non-existence of PL(7, 2) codes are based on the assumption of the existence of such code M. Without loss of generality, we suppose that O ∈ M, where O = (0, ..., 0). In this sense and taking into account that we are dealing with Lee spheres of radius 2, O covers all words which are distant two or fewer units from it. By the definition of PL(7, 2) code, each word which is distant three units from O must be covered by a unique codeword of M. These words have to be covered by codewords which dist five units from O. We prove the non-existence of PL(7, 2) codes showing that it is not possible to cover all the referred words without superposition of Lee spheres whose centers are distant five units from O, contradicting the definition of PL(7, 2) code. We achieve this contradiction by combining the cardinality of particular subsets of codewords which are distant five units from O. There exists an extensive literature on codes in the Lee metric. Here, we present a new approach to prove the non-existence of PL(7, 2) codes.
894
95439
Restrictedly-Regular Map Representation of n-Dimensional Abstract Polytopes
Abstract:
Regularity has often been present in the form of regular polyhedra or tessellations; classical examples are the nine regular polyhedra consisting of the five Platonic solids (regular convex polyhedra) and the four Kleper-Poinsot polyhedra. These polytopes can be seen as regular maps. Maps are cellular embeddings of graphs (with possibly multiple edges, loops or dangling edges) on compact connected (closed) surfaces with or without boundary. The n-dimensional abstract polytopes, particularly the regular ones, have gained popularity over recent years. The main focus of research has been their symmetries and regularity. Planification of polyhedra helps its spatial construction, yet it destroys its symmetries. To our knowledge there is no "planification" for n-dimensional polytopes. However we show that it is possible to make a "surfacification" of the n-dimensional polytope, that is, it is possible to construct a restrictedly-marked map representation of the abstract polytope on some surface that describes its combinatorial structures as well as all of its symmetries. We also show that there are infinitely many ways to do this; yet there is one that is more natural that describes reflections on the sides ((n−1)-faces) of n-simplices with reflections on the sides of n-polygons. We illustrate this construction with the 4-tetrahedron (a regular 4-polytope with automorphism group of size 120) and the 4-cube (a regular 4-polytope with automorphism group of size 384).
893
95355
Improved Estimation Strategies of Sensitive Characteristics Using Scrambled Response Techniques in Successive Sampling
Abstract:
This research work is an effort to analyse the consequences of scrambled response technique to estimate the current population mean in two-occasion successive sampling when the characteristic of interest is sensitive in nature. The generalized estimation procedures have been proposed using sensitive auxiliary variables under additive and multiplicative scramble models. The properties of resultant estimators have been deeply examined. Simulation, as well as empirical studies, are carried out to evaluate the performances of the proposed estimators with respect to other competent estimators. The results of our studies suggest that the proposed estimation procedures are highly effective under the presence of non-response situation. The result of this study also suggests that additive scrambled response model is a better choice in the perspective of cost of the survey and privacy of the respondents.
892
95238
Spectral Clustering from the Discrepancy View and Generalized Quasirandomness
Abstract:
The aim of this paper is to compare spectral, discrepancy, and degree properties of expanding graph sequences. As we can prove equivalences and implications between them and the definition of the generalized (multiclass) quasirandomness of Lovasz–Sos (2008), they can be regarded as generalized quasirandom properties akin to the equivalent quasirandom properties of the seminal Chung-Graham-Wilson paper (1989) in the one-class scenario. Since these properties are valid for deterministic graph sequences, irrespective of stochastic models, the partial implications also justify for low-dimensional embedding of large-scale graphs and for discrepancy minimizing spectral clustering.
891
95219
Proficient Estimation Procedure for a Rare Sensitive Attribute Using Poisson Distribution
Abstract:
The present manuscript addresses the estimation procedure of population parameter using Poisson probability distribution when characteristic under study possesses a rare sensitive attribute. The generalized form of unrelated randomized response model is suggested in order to acquire the truthful responses from respondents. The resultant estimators have been proposed for two situations when the information on an unrelated rare non-sensitive characteristic is known as well as unknown. The properties of the proposed estimators are derived, and the measure of confidentiality of respondent is also suggested for respondents. Empirical studies are carried out in the support of discussed theory.
890
94746
Method to Find a ε-Optimal Control of Stochastic Differential Equation Driven by a Brownian Motion
Abstract:
We present a general solution for finding the ε-optimal controls for non-Markovian stochastic systems as stochastic differential equations driven by Brownian motion, which is a problem recognized as a difficult solution. The contribution appears in the development of mathematical tools to deal with modeling and control of non-Markovian systems, whose applicability in different areas is well known. The methodology used consists to discretize the problem through a random discretization. In this way, we transform an infinite dimensional problem in a finite dimensional, thereafter we use measurable selection arguments, to find a control on an explicit form for the discretized problem. Then, we prove the control found for the discretized problem is a ε-optimal control for the original problem. Our theory provides a concrete description of a rather general class, among the principals, we can highlight financial problems such as portfolio control, hedging, super-hedging, pairs-trading and others. Therefore, our main contribution is the development of a tool to explicitly the ε-optimal control for non-Markovian stochastic systems. The pathwise analysis was made through a random discretization jointly with measurable selection arguments, has provided us with a structure to transform an infinite dimensional problem into a finite dimensional. The theory is applied to stochastic control problems based on path-dependent stochastic differential equations, where both drift and diffusion components are controlled. We are able to explicitly show optimal control with our method.
889
94257
Relation between Roots and Tangent Lines of Function in Fractional Dimensions: A Method for Optimization Problems
Authors:
Abstract:
In this paper, a basic schematic of fractional dimensional optimization problem is introduced. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with known appropriate fractional dimensions can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions.
888
93937
Dynamic Analysis of Differential Systems with Infinite Memory and Damping
Abstract:
In this work, we are concerned with the dynamic behaviors of solutions to some coupled systems with infinite memory, which consist of two partial differential equations where only one partial differential equation has damping. Such coupled systems are good mathematical models to describe the deformation and stress characteristics of some viscoelastic materials affected by temperature change, external forces, and other factors. By using the theory of operator semigroups, we give wellposedness results for the Cauchy problem for these coupled systems. Then, with the help of some auxiliary functions and lemmas, which are specially designed for overcoming difficulties in the proof, we show that the solutions of the coupled systems decay to zero in a strong way under a few basic conditions. The results in this dynamic analysis of coupled systems are generalizations of many existing results.
887
93935
A Study of Evolutional Control Systems
Abstract:
Controllability is one of the fundamental issues in control systems. In this paper, we study the controllability of second order evolutional control systems in Hilbert spaces with memory and boundary controls, which model dynamic behaviors of some viscoelastic materials. Transferring the control problem into a moment problem and showing the Riesz property of a family of functions related to Cauchy problems for some integrodifferential equations, we obtain a general boundary controllability theorem for these second order evolutional control systems. This controllability theorem is applicable to various concrete 1D viscoelastic systems and recovers some previous related results. It is worth noting that Riesz sequences can be used for numerical computations of the control functions and the identification of new Riesz sequence is of independent interest for the basis-function theory. Moreover, using the Riesz sequences, we obtain the existence and uniqueness of (weak) solutions to these second order evolutional control systems in Hilbert spaces. Finally, we derive the exact boundary controllability of a viscoelastic beam equation, as an application of our abstract theorem.
886
93814
A Flexible Bayesian State-Space Modelling for Population Dynamics of Wildlife and Livestock Populations
Abstract:
We aim to model dynamics of wildlife or pastoral livestock population for understanding of their population change and hence for wildlife conservation and promoting human welfare. The study is motivated by an age-sex structured population counts in different regions of Serengeti-Mara during the period 1989-2003. Developing reliable and realistic models for population dynamics of large herbivore population can be a very complex and challenging exercise. However, the Bayesian statistical domain offers some flexible computational methods that enable the development and efficient implementation of complex population dynamics models. In this work, we have used a novel Bayesian state-space model to analyse the dynamics of topi and hartebeest populations in the Serengeti-Mara Ecosystem of East Africa. The state-space model involves survival probabilities of the animals which further depend on various factors like monthly rainfall, size of habitat, etc. that cause recent declines in numbers of the herbivore populations and potentially threaten their future population viability in the ecosystem. Our study shows that seasonal rainfall is the most important factors shaping the population size of animals and indicates the age-class which most severely affected by any change in weather conditions.
885
93093
Approximation of Geodesics on Meshes with Implementation in Rhinoceros Software
Abstract:
In civil engineering, there is a problem how to industrially produce tensile membrane structures that are non-developable surfaces. Nondevelopable surfaces can only be developed with a certain error and we want to minimize this error. To that goal, the non-developable surfaces are cut into plates along to the geodesic curves. We propose a numerical algorithm for finding approximations of open geodesics on meshes and surfaces based on geodesic curvature flow. For practical reasons, it is important to automatize the choice of the time step. We propose a method for automatic setting of the time step based on the diagonal dominance criterion for the matrix of the linear system obtained by discretization of our partial differential equation model. Practical experiments show reliability of this method. Because approximation of the model is made by numerical method based on classic derivatives, it is necessary to solve obstacles which occur for meshes with sharp corners. We solve this problem for big family of meshes with sharp corners via special rotations which can be seen as partial unfolding of the mesh. In practical applications, it is required that the approximation of geodesic has its vertices only on the edges of the mesh. This problem is solved by a specially designed pointing tracking algorithm. We also partially solve the problem of finding geodesics on meshes with holes. We implemented the whole algorithm in Rhinoceros (commercial 3D computer graphics and computer-aided design software ). It is done by using C# language as C# assembly library for Grasshopper, which is plugin in Rhinoceros.
884
93068
Modeling Spatio-Temporal Variation in Rainfall Using a Hierarchical Bayesian Regression Model
Abstract:
Rainfall is a critical component of climate governing vegetation growth and production, forage availability and quality for herbivores. However, reliable rainfall measurements are not always available, making it necessary to predict rainfall values for particular locations through time. Predicting rainfall in space and time can be a complex and challenging task, especially where the rain gauge network is sparse and measurements are not recorded consistently for all rain gauges, leading to many missing values. Here, we develop a flexible Bayesian model for predicting rainfall in space and time and apply it to Narok County, situated in southwestern Kenya, using data collected at 23 rain gauges from 1965 to 2015. Narok County encompasses the Maasai Mara ecosystem, the northern-most section of the Mara-Serengeti ecosystem, famous for its diverse and abundant large mammal populations and spectacular migration of enormous herds of wildebeest, zebra and Thomson's gazelle. The model incorporates geographical and meteorological predictor variables, including elevation, distance to Lake Victoria and minimum temperature. We assess the efficiency of the model by comparing it empirically with the established Gaussian process, Kriging, simple linear and Bayesian linear models. We use the model to predict total monthly rainfall and its standard error for all 5 * 5 km grid cells in Narok County. Using the Monte Carlo integration method, we estimate seasonal and annual rainfall and their standard errors for 29 sub-regions in Narok. Finally, we use the predicted rainfall to predict large herbivore biomass in the Maasai Mara ecosystem on a 5 * 5 km grid for both the wet and dry seasons. We show that herbivore biomass increases with rainfall in both seasons. The model can handle data from a sparse network of observations with many missing values and performs at least as well as or better than four established and widely used models, on the Narok data set. The model produces rainfall predictions consistent with expectation and in good agreement with the blended station and satellite rainfall values. The predictions are precise enough for most practical purposes. The model is very general and applicable to other variables besides rainfall.
883
92998
Mathematical Modelling of Human Cardiovascular-Respiratory System Response to Exercise in Rwanda
Abstract:
In this paper, we present a nonlinear dynamic model for the interactive mechanism of the cardiovascular and respiratory system. The model is designed and analyzed for human during physical exercises. In order to verify the adequacy of the designed model, data collected in Rwanda are used for validation. We have simulated the impact of heart rate and alveolar ventilation as controls of cardiovascular and respiratory system respectively to steady state response of the main cardiovascular hemodynamic quantities i.e., systemic arterial and venous blood pressures, arterial oxygen partial pressure and arterial carbon dioxide partial pressure, to the stabilised values of controls. We used data collected in Rwanda for both male and female during physical activities. We obtained a good agreement with physiological data in the literature. The model may represent an important tool to improve the understanding of exercise physiology.
882
92942
A Study of Two Disease Models: One with Incubation Period and Another without Incubation Period
Abstract:
The incubation period is defined as the time from infection with a microorganism to development of symptoms. In this research, two disease models: one with incubation period and another without incubation period were studied. The study involves the use of an S-I-S mathematical model with a single incubation period. The test for the existence and stability of the disease-free and the endemic equilibrium states for both models were carried out. The fourth order Runge-Kutta method was used to solve both models numerically. Finally, a computer program in MATLAB was developed to run the numerical experiments. From the results, we are able to show that the endemic equilibrium state of the model with incubation period is locally asymptotically stable whereas the endemic equilibrium state of the model without incubation period is unstable under certain conditions on the given model parameters. It was also established that the disease free equilibrium states of the model with and without incubation period are locally asymptotically stable. Furthermore, results from numerical experiments using empirical data obtained from Nigeria Centre for Disease Control (NCDC) showed that the overall population of the infected people for the model with incubation period is higher than that without an incubation period. We also established from the results obtained that as the transmission rate from susceptible to infected population increases, the peak values of the infected population for the model with incubation period decrease and are always less than those for the model without an incubation period.
881
92744
A Discrete Logit Survival Model with a Smooth Baseline Hazard for Age at First Alcohol Intake among Students at Tertiary Institutions in Thohoyandou, South Africa
Abstract:
We employ a discrete logit survival model to investigate the risk factors for early alcohol intake among students at two tertiary institutions in Thohoyandou, South Africa. Data were collected from a sample of 744 students using a self-administered questionnaire. Significant covariates were arrived at through a regularization algorithm implemented using the glmmLasso package. The tuning parameter was determined using a five-fold cross-validation algorithm. The baseline hazard was modelled as a smooth function of time through the use of spline functions. The results show that the hazard of initial alcohol intake peaks at the age of about 16 years and that at any given time, being of a male gender, prior use of other drugs, having drinking peers, having experienced negative life events and physical abuse are associated with a higher risk of alcohol intake debut.
880
92451
Geostatistical Analysis of Contamination of Soils in an Urban Area in Ghana
Abstract:
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.
879
92371
Spatial Scale of Clustering of Residential Burglary and Its Dependence on Temporal Scale
Abstract:
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.
878
92281
A Mixed Integer Linear Programming Model for Flexible Job Shop Scheduling Problem
Authors:
Abstract:
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.
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92277
A Heuristic Approach for the General Flowshop Scheduling Problem to Minimize the Makespan
Authors:
Abstract:
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.
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92276
Application of Regularized Spatio-Temporal Models to the Analysis of Remote Sensing Data
Abstract:
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.
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92257
Location-Domination on Join of Two Graphs and Their Complements
Abstract:
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.