Goodness-of-fit testing in growth curve models: A general approach based on finite differences

Growth curve models are routinely used in various fields such as biology, ecology, demography, population dynamics, finance, econometrics, etc. to study the growth pattern of different populations and the variables linked with them. Many different kinds of growth patterns have been used in the literature to model the different types of realistic growth mechanisms. It is generally a matter of substantial benefit to the data analyst to have a reasonable idea of the nature of the growth pattern under study. As a result, goodness-of-fit tests for standard growth models are often of considerable practical value. In this paper we develop some natural goodness-of-fit tests based on finite differences of the size variables under consideration. The method is general in that it is not limited to specific parametric forms underlying the hypothesized model so long as an appropriate finite difference of some function of the size variables can be made to vanish. In addition it allows the testing process to be carried out under a set up which manages to relax most of the assumptions made by Bhattacharya et al. (2009); these assumptions are generally reasonable but not guaranteed to hold universally. Thus our proposed method has a very wide scope of application. The performance of the theory developed is illustrated numerically through several sets of real data and through simulations.     

The effect of inner products for discrete vector fields on the accuracy of mimetic finite difference methods

The support operators method of discretizing partial differential equations produces discrete analogs of continuum initial boundary value problems that exactly satisfy discrete conservation laws analogous to those satisfied by the continuum system. Thus, the stability of the method is assured, but currently there is no theory that predicts the accuracy of the method on nonuniform grids. In this paper, we numerically investigate how the accuracy, particularly the accuracy of the fluxes, depends on the definition of the inner product for discrete vector fields. We introduce two different discrete inner products, the standard inner product that we have used previously and a new more accurate inner product. The definitions of these inner products are based on interpolation of the fluxes of vector fields. The derivation of the new inner product is closely related to the use of the Piola transform in mixed finite elements. Computing the formulas for the new accurate inner product requires a nontrivial use of computer algebra. From the results of our numerical experiments, we can conclude that using more accurate inner product produces a method with the same order of convergence as the standard inner product, but the constant in error estimate is about three times less. However, the method based on the standard inner product is easier to compute with and less sensitive to grid irregularities, so we recommend its use for rough grids.     

Evaluate the number of clusters in finite mixture models with the penalized histogram difference criterion

Aimed at the determination of the number of mixtures for finite mixture models (FMMs), in this work, a new method called the penalized histogram difference criterion (PHDC) is proposed and evaluated with other criteria such as Akaike information criterion (AIC), the minimum message length (MML), the information complexity (ICOMP) and the evidence of data criterion (EDC). The new method, which calculates the penalized histogram difference between the data generated from estimated FMMs and those for modeling purpose, turns out to be better than others for data with complicate mixtures patterns. It is demonstrated in this work that the PHDC can determine the optimal number of clusters of the FMM. Furthermore, the estimated FMMs asymptotically approximate the true model. The utility of the new method is demonstrated through synthetic data sets analysis and the batch-wise comparison of citric acid fermentation processes.     

The finite volume spectral element method to solve Turing models in the biological pattern formation

It is well known that reaction-diffusion systems describing Turing models can display very rich pattern formation behavior. Turing systems have been proposed for pattern formation in various biological systems, e.g. patterns in fish, butterflies, lady bugs and etc. A Turing model expresses temporal behavior of the concentrations of two reacting and diffusing chemicals which is represented by coupled reaction-diffusion equations. Since the base of these reaction-diffusion equations arises from the conservation laws, we develop a hybrid finite volume spectral element method for the numerical solution of them and apply the proposed method to Turing system generated by the Schnakenberg model. Also, as numerical simulations, we study the variety of spatio-temporal patterns for various values of diffusion rates in the problem.     

A basis-set based Fortran program to solve the Gross-Pitaevskii equation for dilute Bose gases in harmonic and anharmonic traps

Inhomogeneous boson systems, such as the dilute gases of integral spin atoms in low-temperature magnetic traps, are believed to be well described by the Gross-Pitaevskii equation (GPE). GPE is a nonlinear Schrödinger equation which describes the order parameter of such systems at the mean field level. In the present work, we describe a Fortran 90 computer program developed by us, which solves the GPE using a basis set expansion technique. In this technique, the condensate wave function (order parameter) is expanded in terms of the solutions of the simple-harmonic oscillator (SHO) characterizing the atomic trap. Additionally, the same approach is also used to solve the problems in which the trap is weakly anharmonic, and the anharmonic potential can be expressed as a polynomial in the position operators x, y, and z. The resulting eigenvalue problem is solved iteratively using either the self-consistent-field (SCF) approach, or the imaginary time steepest-descent (SD) approach. Iterations can be initiated using either the simple-harmonic-oscillator ground state solution, or the Thomas-Fermi (TF) solution. It is found that for condensates containing up to a few hundred atoms, both approaches lead to rapid convergence. However, in the strong interaction limit of condensates containing thousands of atoms, it is the SD approach coupled with the TF starting orbitals, which leads to quick convergence. Our results for harmonic traps are also compared with those published by other authors using different numerical approaches, and excellent agreement is obtained. GPE is also solved for a few anharmonic potentials, and the influence of anharmonicity on the condensate is discussed. Additionally, the notion of Shannon entropy for the condensate wave function is defined and studied as a function of the number of particles in the trap. It is demonstrated numerically that the entropy increases with the particle number in a monotonic way.

Program summary

Title of program:bose.xCatalogue identifier:ADWZ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWZ_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandDistribution format:tar.gzComputers:PC's/Linux, Sun Ultra 10/Solaris, HP Alpha/Tru64, IBM/AIXProgramming language used:mostly Fortran 90Number of bytes in distributed program, including test data, etc.:27 313Number of lines in distributed program, including test data, etc.:28 015Card punching code:ASCIINature of physical problem:It is widely believed that the static properties of dilute Bose condensates, as obtained in atomic traps, can be described to a fairly good accuracy by the time-independent Gross-Pitaevskii equation. This program presents an efficient approach of solving this equation.Method of solution:The solutions of the Gross-Pitaevskii equation corresponding to the condensates in atomic traps are expanded as linear combinations of simple-harmonic oscillator eigenfunctions. Thus, the Gross-Pitaevskii equation which is a second-order nonlinear differential equation, is transformed into a matrix eigenvalue problem. Thereby, its solutions are obtained in a self-consistent manner, using methods of computational linear algebra.Unusual features of the program:None     

A new approach to solve the k-server problem based on network flows and flow cost reduction

This paper is concerned with two algorithms for solving the k-server problem: the optimal off-line algorithm (OPT) and the on-line work function algorithm (WFA). Both algorithms are usually implemented by network flow techniques including the flow augmentation method. In the paper a new implementation approach is proposed, which is again based on network flows, but uses simpler networks and the cost reduction method. The paper describes in detail the corresponding new implementations of OPT and WFA, respectively. All necessary correctness proofs are given. Also, experiments are presented, which confirm that the new approach assures faster execution of both algorithms.     

A finite element modeling-based approach to predict vibrations transmitted through different body segments of the operator within the workspace of a small tractor

Agricultural tractor drivers are subjected to high levels of whole-body vibrations and hand arm vibrations during most part of the farm activities due to unevenness of field surface, uneasy posture, improper workplace design, moving parts of the tractor, and other unavoidable circumstances. The comfort level of the operator inside a dynamic tractor is dependent on the level of vibration generated inside the different human body segments. In the present study, a finite element modeling was proposed to predict vertical vibrations (Z-axis) and frequencies at the different body segments of the seated small tractor operator. The forces required for different controls of the tractor were measured to be used as input parameters in the finite element modeling. The maximum mean forces of the brake (172.8 N) and clutch (153.2 N) were used as the input parameters for the simulation study. The simulated results were validated with the field measured values of vertical accelerations at selected body segments of the operator. The simulation could successfully predict vertical vibrations at selected points of interest (i.e., foot, leg, thigh, lower arm, upper arm, back, and head) except the chest of the body, as the buttock of the operator model was fixed (degree of freedom is equal to zero) in the simulation. The obtained results were compared with the international standards ISO 2631-1 (1985/1997) and ISO 5349-1 (2001) to assess the vibration characteristics at the different body segments of the operator. The foot, leg, lower arm, and upper arm of the operator were subjected to vertical vibration frequencies from 10 to 200 Hz. Most of the resonance of vertical accelerations occurred in one-third octave bands of 20–80 Hz frequencies. The thigh, chest, back, and head of the operator were exposed to vibration frequencies below 40 Hz during field operation. At these parts of the body, the vertical acceleration resonated at lower frequencies, between 2 and 8 Hz.     

A compensation approach to the tool used in autoclave based on FEA

Optimization of the curing process can not control the deformation of composite part prepared in autoclave accurately.And traditional "trial-and-error" tool surface compensation approach is low efficiency,high cost and can not control part deformation quantificationally.In order to address these issues,tool compensation approach based on FEA is presented.Model of multi-field coupling relationship in autoclave is realized.And finite element analysis model of composite part’s curing process is developed to analyze part deformation.According to displacement of the part surface nodes after deformation,tool surface which compensated by the displacement of composite part which analyzed by FEA is used to control part deformation.A cylindrical composite part is analyzed to verify the approach,and the result proves the correctness and validity of the approach.     

A rule‐based approach to detect and prevent inconsistency in the domain‐engineering process

A medium‐sized domain‐engineering process can contain thousands of features that all have constraint dependency rules between them. Therefore, the validation of the content of domain‐engineering process is vital to produce high‐quality software products. However, it is not feasible to do this manually. This paper aims to improve the quality of the software products generated by the domain‐engineering process by ensuring the validity of the results of that process. We propose rules for two operations: inconsistency detection and inconsistency prevention. We introduce first‐order logic (FOL) rules to detect three types of inconsistency and prevent the direct inconsistency in the domain‐engineering process. Developing FOL rules to detect and prevent inconsistency in the domain‐engineering process directly without the need to the configuration process is our main contribution. We performed some experiments to test the scalability and applicability of our approach on domain‐engineered software product lines containing 1000 assets to 20000 assets. The results show that our approach is scalable and could be utilized to improve the domain‐engineering process.     

A backward approach to certain class of transport equations in any dimension based on the Shannon sampling theorem

A backward method is proposed to compute the solutions to some class of transport equations at any temporal instant regardless of the dimension. The widely adopted Shannon sampling in information theory and signal processing is employed for the reconstruction of solutions through truncated cardinal series, citing its properties of accuracy in approximation and convenience in construction. With the method of characteristics, approximation coefficients at sampling nodes are obtained via backward tracking along the characteristics. This approach, due to Gobbi et al. [Numerical solution of certain classes of transport equations in any dimension by Shannon sampling, J. Comput. Phys. 229 (2010), pp. 3502–5322], can be considered as either a spectral or a wavelet method. The proposed method is further extended to a backward–forward scheme to solve Cauchy problems by employing a forward evolution along the characteristics. Numerical experiments are presented to verify the effectiveness, efficiency and high accuracy of the proposed method.