Forecasting Issues in Energy Markets within a Reg-ARIMA Framework
Electricity markets throughout the world have
undergone substantial changes. Accurate, reliable, clear and
comprehensible modeling and forecasting of different variables
(loads and prices in the first instance) have achieved increasing
importance. In this paper, we describe the actual state of the
art focusing on reg-SARMA methods, which have proven to be
flexible enough to accommodate the electricity price/load behavior
satisfactory. More specifically, we will discuss: 1) The dichotomy
between point and interval forecasts; 2) The difficult choice between
stochastic (e.g. climatic variation) and non-deterministic predictors
(e.g. calendar variables); 3) The confrontation between modelling
a single aggregate time series or creating separated and potentially
different models of sub-series. The noteworthy point that we would
like to make it emerge is that prices and loads require different
approaches that appear irreconcilable even though must be made
reconcilable for the interests and activities of energy companies.
Three-Dimensional Generalized Thermoelasticity with Variable Thermal Conductivity
In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity has been constructed. The resulting non-dimensional governing equations together with the Laplace and double Fourier transforms techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free in the directions of the principle co-ordinates. The inverses of double Fourier transforms, and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of the thermal conductivity has significant effects on the thermal and the mechanical waves.
Location Choice of Firms in an Unequal Length Streets Model: Game Theory Approach as an Extension of the Spoke Model
Locating is one of the key elements in success and survival of industrial centers and has great impact on cost reduction of establishment and launching of various economic activities. In this study, streets with unequal length model have been used that is the classic extension of Spoke model; however with unlimited number of streets with uneven lengths. The results showed that the spoke model is a special case of streets with unequal length model. According to the results of this study, if the strategy of enterprises and firms is to select both price and location, there would be no balance in the game. Furthermore, increased length of streets leads to increased profit of enterprises and with increased number of streets, the enterprises choose locations that are far from center (the maximum differentiation), and the enterprises' output will decrease. Moreover, the enterprise production rate will incline toward zero when the number of streets goes to infinity, and complete competition outcome will be achieved.
Analysis and Modelling of Monthly Records of Arrivals and Departures of Airline Passengers Using Vector Autoregressive Distributed Lag Models: A Case of Akwa Ibom International Airport, Nigeria
This paper considers bivariate analysis of arrivals and departures of airline data at Ibom International Airport, with the aim to investigate if there exists causation between the arrivals and departures. Data for the analysis are monthly statistics of airline passengers recorded from January 2010 to December 2016 at Ibom International Airport. vector autoregressive distributed lag models (VARDLM) have been developed and adopted for the analysis. The VARDLM are developed and proved from the existing vector regression models (VRM) and vector autoregressive lag models (VARLM). The two models are combined to form the VARDLM. X1t and X2t represent arrivals and departures of airline passengers respectively. From the models, it is established that the arrivals of airline passengers at a specific time period depend on the departures at the same time period, and vice versa. There is an indication of long run causation between the present and previous time arrivals, and also with the departures. From the estimated models '14' and '15', it was found that long period of departures contributes negatively to present arrival and vice versa. The significant contribution of the arrivals to departures and departures to arrivals at the same time period is accounted for by a strong correlation between the arrivals and departures within a specific time period. Hence, there is causation between arrivals and departures.
Construction of Finite Woven Frames through Bounded Linear Operators
Two frames in a Hilbert space are called woven or weaving if all possible merge combinations between them generate frames of the Hilbert space with uniform frame bounds. Weaving frames are powerful tools in wireless sensor networks which require distributed data processing. Considering the practical applications, this article deals with finite woven frames. We provide methods of constructing finite woven frames, in particular, bounded linear operators are used to construct woven frames from a given frame. Several examples are discussed. We also introduce the notion of woven frame sequences and characterize them through the concepts of gaps and angles between spaces.
Polynomial Chaos Expansion Combined with Exponential Spline for Singularly Perturbed Boundary Value Problems with Random Parameter
So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order.
Numerical Investigation and Optimization of the Effect of Number of Blade and Blade Type on the Suction Pressure and Outlet Mass Flow Rate of a Centrifugal Fan
Number of blade and blade type of centrifugal fans are the most decisive factor on the field of application, noise level, suction pressure and outlet mass flow rate. Nowadays, in order to determine these effects on centrifugal fans, numerical studies are carried out in addition to experimental studies. In this study, it is aimed to numerically investigate the changes of suction pressure and outlet mass flow rate values of a centrifugal fan according to the number of blade and blade type. Centrifugal fans of the same size with forward, backward and straight blade type were analyzed by using a simulation program and compared with each other. This analysis was carried out under steady state condition by selecting k-Ɛ turbulence model and air is assumed incompressible. Then, 16, 32 and 48 blade centrifugal fans were again analyzed by using same simulation program, and the optimum number of blades was determined for the suction pressure and the outlet mass flow rate. According to the results of the analysis, it was obtained that the suction pressure in the 32 blade fan was twice the value obtained in the 16 blade fan. In addition, the outlet mass flow rate increased by 45% with the increase in the number of blade from 16 to 32. There is no significant change observed on the suction pressure and outlet mass flow rate when the number of blades increased from 32 to 48. In the light of the analysis results, the optimum blade number was determined as 32.
Bayesian Meta-Analysis to Account for Heterogeneity in Studies Relating Life Events to Disease
Associations between life events and various forms of cancers have been identified. The purpose of a recent random-effects meta-analysis was to identify studies that examined the association between adverse events associated with changes to financial status including decreased income and breast cancer risk. The same association was studied in four separate studies which displayed traits that were not consistent between studies such as the study design, location and time frame. It was of interest to pool information from various studies to help identify characteristics that differentiated study results. Two random-effects Bayesian meta-analysis models are proposed to combine the reported estimates of the described studies. The proposed models allow major sources of variation to be taken into account, including study level characteristics, between study variance, and within study variance and illustrate the ease with which uncertainty can be incorporated using a hierarchical Bayesian modelling approach.
Predictive Modelling of Aircraft Component Replacement Using Imbalanced Learning and Ensemble Method
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.
Improvement a Lower Bound of Energy for Some Family of Graphs, Related to Determinant of Adjacency Matrix
Let G be a simple graph with the vertex set V (G) and with the adjacency matrix A (G). The energy E (G) of G is defined to be the sum of the absolute values of all eigenvalues of A (G). Also let n and m be number of edges and vertices of the graph respectively. A regular graph is a graph where each vertex has the same number of neighbours. Given a graph G, its line graph L(G) is a graph such that each vertex of L(G) represents an edge of G; and two vertices of L(G) are adjacent if and only if their corresponding edges share a common endpoint in G. In this paper we show that for every regular graphs and also for every line graphs such that (G) 3 we have, E(G) 2nm + n 1. Also at the other part of the paper we prove that 2 (G) E(G) for an arbitrary graph G.
Assessing the Role of Human Mobility on Malaria Transmission in South Sudan
Over the past few decades, the unprecedented increase in mobility has raised considerable concern about the relationship between mobility and vector-borne diseases and malaria in particular. Thus, one can claim that human mobility is one of the contributing factors to the resurgence of malaria. To assess human mobility on malaria burden among hosts, we formulate a movement-based model on a network of patches. We then extend human multi-group SEIAR deterministic epidemic models into a system of stochastic differential equations (SDEs). Our quantitative stochastic model which is expressed in terms of average rates of movement between compartments is fitted to time-series data (weekly malaria data of 2011 for each patch) using the maximum likelihood approach. Using the metapopulation (multi-group) model, we compute and analyze the basic reproduction number. The result shows that human movement is sufficient to preserve malaria disease firmness in the patches with the low transmission. With these results, we concluded that the sensitivity of malaria to the human mobility is turning to be greatly important over the implications of future malaria control in South Sudan.
Study of Electron Cyclotron Resonance Acceleration by Cylindrical TE₀₁₁ Mode
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.
Analysis of Factors Affecting the Number of Infant and Maternal Mortality in East Java with Geographically Weighted Bivariate Generalized Poisson Regression Method
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.
Analysis of Cooperative Learning Behavior Based on the Data of Students' Movement
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.
Adomian’s Decomposition Method to Generalized Magneto-Thermoelasticity
Due to many applications and problems in the fields of plasma physics, geophysics, and other many topics, the interaction between the strain field and the magnetic field has to be considered. Adomian introduced the decomposition method for solving linear and nonlinear functional equations. This method leads to accurate, computable, approximately convergent solutions of linear and nonlinear partial and ordinary differential equations even the equations with variable coefficients. This paper is dealing with a mathematical model of generalized thermoelasticity of a half-space conducting medium. A magnetic field with constant intensity acts normal to the bounding plane has been assumed. Adomian’s decomposition method has been used to solve the model when the bounding plane is taken to be traction free and thermally loaded by harmonic heating. The numerical results for the temperature increment, the stress, the strain, the displacement, the induced magnetic, and the electric fields have been represented in figures. The magnetic field, the relaxation time, and the angular thermal load have significant effects on all the studied fields.
Model Predictive Control with Unscented Kalman Filter for Nonlinear Implicit Systems
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
Convergence of Generalized Jacobi, Gauss-Seidel and Successive Overrelaxation Methods for Various Classes of Matrices
Generalized Jacobi (GJ) and Generalized Gauss-Seidel (GGS) methods are most effective than conventional Jacobi and Gauss-Seidel methods for solving linear system of equations. It is known that GJ and GGS methods converge for strictly diagonally dominant (SDD) and for M-matrices. In this paper, we study the convergence of GJ and GGS converge for symmetric positive definite (SPD) matrices, L-matrices and H-matrices. We introduce a generalization of successive overrelaxation (SOR) method for solving linear systems and discuss its convergence for the classes of SDD matrices, SPD matrices, M-matrices, L-matrices and for H-matrices. Advantages of generalized SOR method are established through numerical experiments over GJ, GGS, and SOR methods.
An Efficient Collocation Method for Solving the Variable-Order Time-Fractional Partial Differential Equations Arising from the Physical Phenomenon
In this work, we present an efficient approach for
solving variable-order time-fractional partial differential equations,
which are based on Legendre and Laguerre polynomials. First, we
introduced the pseudo-operational matrices of integer and variable
fractional order of integration by use of some properties of
Riemann-Liouville fractional integral. Then, applied together with
collocation method and Legendre-Laguerre functions for solving
variable-order time-fractional partial differential equations. Also, an
estimation of the error is presented. At last, we investigate numerical
examples which arise in physics to demonstrate the accuracy of the
present method. In comparison results obtained by the present method
with the exact solution and the other methods reveals that the method
is very effective.
Large-Scale Simulations of Turbulence Using Discontinuous Spectral Element Method
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.
Numerical Studies for Standard Bi-Conjugate Gradient Stabilized Method and the Parallel Variants for Solving Linear Equations
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.
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.
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.
Restrictedly-Regular Map Representation of n-Dimensional Abstract Polytopes
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).
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.
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.
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.
Conditions on Expressing a Matrix as a Sum of α-Involutions
Let F be C or R, where C and R are the set of complex numbers and real numbers, respectively, and n be a natural number. An n-by-n matrix A over the field F is called an α-involutory matrix or an α-involution if there exists an α in the field such that the square of the matrix is equal to αI, where I is the n-by-n identity matrix. If α is a complex number or a nonnegative real number, then an n-by-n matrix A over the field F can be written as a sum of n-by-n α-involutory matrices over the field F if and only if the trace of that matrix is an integral multiple of the square root of α. Meanwhile, if α is a negative real number, then a 2n-by-2n matrix A over R can be written as a sum of 2n-by-2n α-involutory matrices over R if and only the trace of the matrix is zero. Some other properties of α-involutory matrices are also determined
Method to Find a ε-Optimal Control of Stochastic Differential Equation Driven by a Brownian Motion
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.
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.