International Science Index

International Journal of Mathematical and Computational Sciences

A Fundamental Functional Equation for Lie Algebras
Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?
Differential Equation of Bernoulli with GeoGebra Software
In this work, solutions of ordinary differential equations of first order nonlinear Bernoulli type are presented through the use of GeoGebra software. The objective of this work is to provide the student reader with a guide that will allow benefits from the use of these computational tools. The commands for the solutions in this package are explained by a series of representative examples obtained from the book Dennis Zill of Differential Equations with ninth edition modeling applications. Emphasis will be applied to Bernoulli equations with constant coefficients by powers of x. Keeping constant the exponent 'n' of the dependent variable, the two constant coefficients will be changed showing the changes in the solutions. Different values of n will be also considered. These lessons will be made in the course of differential equations of the University of Antofagasta of Chile. In this way the students visualize the graphics solutions and they understand the differential equations in a better way.
Parametric Dependence of the Advection-Diffusion Equation in Two Dimensions
In this work, we have solved the two-dimensional advection-diffusion equation numerically for a spatially dependent solute dispersion along non-uniform flow with a pulse type source in order to make a systematic study on the influence of medium heterogeneity, initial flow velocity, and initial dispersion coefficient parameters on the solutions of the equation. The behavior of the solutions is then investigated as we change the three parameters independently. Our results show that even though the parameters represent different physical features of the system, the effect on their variation is very similar. We also observe that the effects caused by the parameters on the concentration depend on the distance from the source. Finally, our numerical results are in good agreement with the exact solutions for all values of the parameters we used in our analysis.
Covariate-Adjusted Response-Adaptive Designs for Semi-Parametric Survival Responses
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.
Application of Mathematical Sciences to Farm Management
Agriculture has been the mainstay of the nation’s economy in Nigeria. It provides food for the ever rapidly increasing population and raw materials for the industries. People especially the rural dwellers are gainfully employed on their crop farms and small-scale livestock farms for income earning. In farming, availability of funds and time management are one of the major factors that influence the system of farming in Nigeria in which mathematical science knowledge was highly required in order for farms to be managed effectively. Farmers often applied mathematics, almost every day for a variety of tasks, ranging from measuring and weighing, to land marking. This paper, therefore, explores some of the ways math is used in farming. For instance, farmers use arithmetic variety of farm activities such as seed planting, harvesting crop, cultivation and mulching. It is also important in helping farmers to know how much their livestock weighs, how much milk their cows produce and crop yield per acres, among others.
Nonlinear Evolution on Graphs
We are concerned with abstract fully nonlinear differential equations having the form y’(t)=Ay(t)+f(t,y(t)) where A is an m—dissipative operator (possibly multi—valued) defined on a subset D(A) of a Banach space X with values in X and f is a given function defined on I×X with values in X. We consider a graph K in I×X. We recall that K is said to be viable with respect to the above abstract differential equation if for each initial data in K there exists at least one trajectory starting from that initial data and remaining in K at least for a short time. The viability problem has been studied by many authors by using various techniques and frames. If K is closed, it is shown that a tangency condition, which is mainly linked to the dynamic, is crucial for viability. In the case when X is infinite dimensional, compactness and convexity assumptions are needed. In this paper, we are concerned with the notion of near viability for a given graph K with respect to y’(t)=Ay(t)+f(t,y(t)). Roughly speaking, the graph K is said to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)), if for each initial data in K there exists at least one trajectory remaining arbitrary close to K at least for short time. It is interesting to note that the near viability is equivalent to an appropriate tangency condition under mild assumptions on the dynamic. Adding natural convexity and compactness assumptions on the dynamic, we may recover the (exact) viability. Here we investigate near viability for a graph K in I×X with respect to y’(t)=Ay(t)+f(t,y(t)) where A and f are as above. We emphasis that the t—dependence on the perturbation f leads us to introduce a new tangency concept. In the base of a tangency conditions expressed in terms of that tangency concept, we formulate criteria for K to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)). As application, an abstract null—controllability theorem is given.
Location-Domination on Join of Two Graphs and their Complements
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.
The Non-Existence of Perfect 2-Error Correcting Lee Codes of Word Length 7 over Z
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.
A Study of Two Disease Models: One with Incubation Period and Another without Incubation Period
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.
Building 1-Well-Covered Graphs by Corona, Join, and Rooted Product of Graphs
A graph is well-covered if all its maximal independent sets are of the same size. A well-covered graph is 1-well-covered if deletion of every vertex of the graph leaves it well-covered. It is known that a graph without isolated vertices is 1-well-covered if and only if every two disjoint independent sets are included in two disjoint maximum independent sets. Well-covered graphs are related to combinatorial commutative algebra (e.g., every Cohen-Macaulay graph is well-covered, while each Gorenstein graph without isolated vertices is 1-well-covered). Our intent is to construct several infinite families of 1-well-covered graphs using the following known graph operations: corona, join, and rooted product of graphs. Adopting some known techniques used to advantage for well-covered graphs, one can prove that: if the graph G has no isolated vertices, then the corona of G and H is 1-well-covered if and only if H is a complete graph of order two at least; the join of the graphs G and H is 1-well-covered if and only if G and H have the same independence number and both are 1-well-covered; if H satisfies the property that every three pairwise disjoint independent sets are included in three pairwise disjoint maximum independent sets, then the rooted product of G and H is 1-well-covered, for every graph G. These findings show not only how to generate some more families of 1-well-covered graphs, but also that, to this aim, sometimes, one may use graphs that are not necessarily 1-well-covered.
Spectral Clustering from the Discrepancy View and Generalized Quasirandomness
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.
Application of Latent Class Analysis and Self-Organizing Maps for the Prediction of Treatment Outcomes for Chronic Fatigue Syndrome
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.
Regularization of Gene Regulatory Networks Perturbed by White Noise
Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models.
Proficient Estimation Procedure for a Rare Sensitive Attribute Using Poisson Distribution
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.
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
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.
Mixtures of Length-Biased Weibull Distributions for Loss Severity Modelling
In this paper, a class of length-biased Weibull mixtures is newly introduced 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.
On Block Vandermonde Matrix Constructed from Matrix Polynomial Solvents
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.
Calculation of the Thermal Stresses in an Elastoplastic Plate Heated by Local Heat Source
The work is devoted to the task of thermal stresses Explored the temperature stresses, caused by the heating point of the round plate. The plate is made of elastoplastic material, so the Prandtl-Reis model is used. A piecewise-linear condition of the Ishlinsky-Ivlev flow is taken as the loading surface, in which the yield stress depends on the temperature. Piecewise-linear conditions (Treska or Ishlinsky-Ivlev), in contrast to the Mises condition, make it possible to obtain solutions of the equilibrium equation in an analytical form. In the problem under consideration, using the conditions of Tresca, it is impossible to obtain a solution. This is due to the fact that the equation of equilibrium ceases to be satisfied when the two Tresca conditions are fulfilled at once. Using the conditions of plastic flow Ishlinsky-Ivlev allows you to solve the problem. At the same time, there are also no solutions on the edge of the Ishlinsky-Ivlev hexagon in the plane-stressed state. Therefore, the authors of the article propose to jump from the edge to the edge of the mine edge, which gives an opportunity to obtain an analytical solution. At the same time, there is also no solution on the edge of the Ishlinsky-Ivlev hexagon in a plane stressed state, therefore, in this paper; the authors of the article propose to jump from the side to the side of the mine edge, which gives an opportunity to receive an analytical solution. The paper compares solutions of the problem of plate thermal deformation. One of the solutions was obtained under the condition that the elastic moduli (Young's modulus, Poisson's ratio) depend on temperature. The yield point is assumed to be parabolically temperature dependent. The main results of the comparisons are that the region of irreversible deformation is larger in the calculations obtained for solving the problem with constant elastic moduli. There is no repeated plastic flow in the solution of the problem with elastic moduli depending on temperature. The absolute value of the irreversible deformations is higher for the solution of the problem in which the elastic moduli are constant; there are also insignificant differences in the distribution of the residual stresses.
Numerical Study of Laminar Natural Flow Transitions in Rectangular Cavity
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.
Invasive Species Population Status Modeling Using Stage Based Matrix -Mount Elgon Ecosystem
The matrix models have been applied to evaluate the impacts and management of tree species. Modeling of invasive species using stage-based matrix methods has not been exploited to understand the population structure of the invasive species. The study simulated using stage-structured Lefkovitch models to assess the population structure and impacts of invasive population growth within Mount Elgon Ecosystem. The survey data was used to calculate the transition probabilities and the growth rate (Kiptogot λ₁=1.074 and Kimothon λ₂=1.115 and Saboti λ₃=1.118) in different forest blocks. These results indicate that Cestrum aurantiacum is increasing in population and could have effects on the population of other native species within ecosystems in the future.
Statistical Convergence of the Szasz-Mirakjan-Kantorovich-Type Operators
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.
Theoretical Analysis of the Existing Sheet Thickness in the Calendering of Pseudoplastic Material
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.
Differentiation of the Functional in an Optimization Problem for Coefficients of Elliptic Equations with Unbounded Nonlinearity
We consider an optimal control problem in the higher coefficient of nonlinear equations with a divergent elliptic operator and unbounded nonlinearity, and the Dirichlet boundary condition. The conditions imposed on the coefficients of the state equation are assumed to hold only in a small neighborhood of the exact solution to the original problem. This assumption suggests that the state equation involves nonlinearities of unlimited growth and considerably expands the class of admissible functions as solutions of the state equation. We obtain formulas for the first partial derivatives of the objective functional with respect to the control functions. To calculate the gradients the numerical solutions of the state and adjoint problems are used. We also prove that the gradient of the cost function is Lipchitz continuous.
Numerical Solution of Magneto-Hydrodynamic Flow of a Viscous Fluid in the Presence of Nanoparticles with Fractional Derivatives through a Cylindrical Tube
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.
The Classification Accuracy of Finance Data through Holder Functions
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).
The Clustering of Multiple Sclerosis Subgroups through L2 Norm Multifractal Denoising Technique
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.
Improved Estimation Strategies of Sensitive Characteristics Using Scrambled Response Techniques in Successive Sampling
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.
Statistical and Land Planning Study of Tourist Arrivals in Greece during the Years 2005-2016
During the last ten years, in spite the economical crisis, the number of tourists arrived in Greece, particularly in the tourist season from April to October, is increased. In this paper, we are studying the number of tourists arrived yearly looking their preference of month and the places which they are selecting, as well the amount of money they are spending. The collected data are processed with statistical methods giving numerical and graphical results. From the computation of statistical parameters and the forecasting with exponential smoothing, we are arriving in useful conclusions which can be used by Greek Government tourist authorities and Greek tourist organizations for the coming years of planning. The results of this paper and the computed forecast can be used for decision taking from private tourist enterprises which are investing in Greece. From the statistical methods, we are using the method of Simple Exponential Smoothing of time series of data. The search of the best forecast for 2017 and 2018 gives the value of the smoothing coefficient. For all statistical computations and graphics, we have used Microsoft Excel.
A Copula-Based Approach for the Assessment of Severity of Illness and Probability of Mortality: An Exploratory Study Applied to Intensive Care Patients
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.
Comparison Study of Capital Protection Risk Management Strategies: Constant Proportion Portfolio Insurance versus Volatility Target Based Investment Strategy with a Guarantee
In the current capital market environment, investors constantly face the challenge of finding a successful and stable investment mechanism. Highly volatile equity markets and extremely low bond returns bring about the demand for sophisticated yet reliable risk management strategies. Investors are looking for risk management solutions to efficiently protect their investments. This study compares a classic Constant Proportion Portfolio Insurance (CPPI) strategy to a Volatility Target portfolio insurance (VTPI). VTPI is an extension of the well-known Option Based Portfolio Insurance (OBPI) to the case where an embedded option is linked not to a pure risky asset such as e.g., S&P 500, but to a Volatility Target (VolTarget) portfolio. VolTarget strategy is a recently emerged rule-based dynamic asset allocation mechanism where the portfolio’s volatility is kept under control. As a result, a typical VTPI strategy allows higher participation rates in the market due to reduced embedded option prices. In addition, controlled volatility levels eliminate the volatility spread in option pricing, one of the frequently cited reasons for OBPI strategy fall behind CPPI. The strategies are compared within the framework of the stochastic dominance theory based on numerical simulations, rather than on the restrictive assumption of the Black-Scholes type dynamics of the underlying asset. An extended comparative quantitative analysis of performances of the above investment strategies in various market scenarios and within a range of input parameter values is presented.