Algorithm For Accurate Computation Research Articles

On Uniqueness of Time-Consistent Markov Policies for Quasi-Hyperbolic Consumers Under Uncertainty

We give a set of sufficient conditions for uniqueness of a time-consistent Markov stationary consumption policy for a quasi-hyperbolic household under uncertainty. To the best of our knowledge, this uniqueness result is the first presented in the literature for general settings, i.e. under standard assumptions on preferences, as well as some new condition on a transition probability. This paper advocates a Bellman equation method to overcome some predicaments of the known methods and also extends our recent existence result. Our method also works for returns unbounded from above. We provide few natural followers of optimal policy uniqueness: convergent and accurate computational algorithm, monotone comparative statics results and generalized Euler equation.

An engineering model for yield inception in slip-stick elastic contacts

The failure of the mechanical contact due to plastic yielding is generally predicted employing stress analysis coupled with the von Mises yield criterion, which uses the maximum of the second deviatoric stress invariant as a threshold value. This paper aims to establish the relation between the frictional regime and the normal and tangential loading components which lead to yield inception in the slip-stick spherical contact between similarly elastic materials. The Boussinesq and Cerruti fundamental solutions for the elastic half-space are used in a robust semi-analytical method based on the superposition principle applicable in the frame of linear elasticity, and enhanced with an acceleration technique derived from the convolution theorem. A rapid algorithm for accurate computation of elastic stresses induced in subsurface by a known but arbitrary distribution of surface tractions, normal or shear, is advanced. The obtained data is normalized to allow model extension to any elastic constants or contact curvature, and curve fitting is employed to derive simple empirical formulas pertinent to practical engineering applications.

Numerical Simulation of the Wake Structure and Thrust/Lift Generation of a Pitching Airfoil at Low Reynolds number via an Immersed Boundary Method

In this paper, an accurate computational algorithm in the context of immersed boundary methods is developed and used to analyze an incompressible flow around a pitching symmetric airfoil at Re=225. The boundary condition can be accurately implemented by an iterative procedure applied at each time step and the pressure is also updated simultaneously. Flow phenomena, observed at different oscillation frequencies and amplitudes, are numerically modeled and the physics behind the associated vortex dynamics is explained. It is shown that there are four flow regimes associated with four wake structures. These include three symmetric flow regimes, with adverse, favorable and no vortex effects, and an asymmetric flow regime. The phenomena associated with these flow regimes and the critical or transition Strouhal (St) and normalized amplitude (numbers are discussed. It is shown that at the fixed pitching amplitude, , Transition from adverse (drag generation) to favorable (thrust generation) symmetric flow regime occurs at St=0.23. Moreover, at this particular amplitude, transition from symmetric to asymmetric regime occurs at St=0.48. It is also shown that at St=0.22, the wake is always deflected and the flow is asymmetric for large-enough amplitudes (). The dipole vortices and lift generation are two characteristics of asymmetric vortex street. This numerical study also reveals that the initial phase angle has a dominant effect on the appearance of dipole vortices and vortex sheet deflection direction. Numerical results are in good agreement with the available experimental data.

Evaluation of the Elliptic Integrals

The present paper is devoted for establishing accurate computational algorithms for the incomplete and complete ellipticintegrals (EI) of the first, second and third kind. For these goals, we first derived some properties of EI that could be used tocheck the validity and the accuracy of the algorithms; in addition, particular continued fraction expansion of the ratio of thecomplete elliptic integrals of the second and first kinds is also derived. Secondly, we established the trigonometric seriesexpansions of EI, together with the recurrence formulae of their coefficients so as to facilitate the computations. Also,Gautschi's algorithm of the top-down continued fraction evaluation is described. Numerical applications are performed for:(a) the incomplete elliptic integrals using their trigonometric series expansions, (b) the complete elliptic integrals of thesecond kind from the complete elliptic integrals of the first kind using Gautschi's algorithm. Finally the numerical resultswere checked by two ways:i- by satisfying the conditions given by properties of EI.ii- by comparing their values with those list in slandered tables.In this respect, the numerical results show excellent arguments with these ways, a fact which proves the validity, accuracyand the effeteness of our algorithms

Efficient calculation of local dose distributions for response modeling in proton and heavier ion beams

We present an algorithm for fast and accurate computation of the local dose distribution in MeV beams of protons, carbon ions or other heavy-charged particles. It uses compound Poisson-process modelling of track interaction and succesive convolutions for fast computation. It can handle mixed particle fields over a wide range of fluences. Since the local dose distribution is the essential part of several approaches to model detector efficiency or cellular response it has potential use in ion-beam dosimetry and radiotherapy.

A self-adaptive sampling digital image correlation algorithm for accurate displacement measurement

Digital image correlation (DIC) is nowadays widely applied to many engineering areas as an effective optical displacement measurement technique. To minimize the potential effect of spatial sampling locations on full-field displacement measurement, this paper develops a self-adaptive sampling DIC algorithm for accurate and reliable displacement computation over entire specimen surfaces. Depending on local deformation states, the algorithm can automatically optimize spatial distribution of sampling points over specimen surfaces in a self-adaptive manner in combination with the well-developed DIC algorithm with Gaussian windows. Both a series of well-designed computer-simulated speckle images and actual cell-substrate deformation ones are employed to verify the feasibility and effectiveness of the proposed algorithm, which demonstrates that the set of self-adaptive sampling algorithm is capable of recovering more accurate and precise full-field displacements compared to the conventional DIC algorithm with equidistant sampling.

An efficient algorithm for accurate computation of the Dirichlet-multinomial log-likelihood function.

The Dirichlet-multinomial (DMN) distribution is a fundamental model for multicategory count data with overdispersion. This distribution has many uses in bioinformatics including applications to metagenomics data, transctriptomics and alternative splicing. The DMN distribution reduces to the multinomial distribution when the overdispersion parameter ψ is 0. Unfortunately, numerical computation of the DMN log-likelihood function by conventional methods results in instability in the neighborhood of [Formula: see text]. An alternative formulation circumvents this instability, but it leads to long runtimes that make it impractical for large count data common in bioinformatics. We have developed a new method for computation of the DMN log-likelihood to solve the instability problem without incurring long runtimes. The new approach is composed of a novel formula and an algorithm to extend its applicability. Our numerical experiments show that this new method both improves the accuracy of log-likelihood evaluation and the runtime by several orders of magnitude, especially in high-count data situations that are common in deep sequencing data. Using real metagenomic data, our method achieves manyfold runtime improvement. Our method increases the feasibility of using the DMN distribution to model many high-throughput problems in bioinformatics. We have included in our work an R package giving access to this method and a vingette applying this approach to metagenomic data.

Component selection in additive quantile regression models

Nonparametric additive models are powerful techniques for multivariate data analysis. Although many procedures have been developed for estimating additive components both in mean regression and quantile regression, the problem of selecting relevant components has not been addressed much especially in quantile regression. We present a doubly-penalized estimation procedure for component selection in additive quantile regression models that combines basis function approximation with a ridge-type penalty and a variant of the smoothly clipped absolute deviation penalty. We show that the proposed estimator identifies relevant and irrelevant components consistently and achieves the nonparametric optimal rate of convergence for the relevant components. We also provide an accurate and efficient computation algorithm to implement the estimator and demonstrate its performance through simulation studies. Finally, we illustrate our method via a real data example to identify important body measurements to predict percentage of body fat of an individual.

Accurate Computation of Multiphase Synchronous Machine Inductances Based on Winding Function Theory

An electric machine equipped with n stator phases is characterized by a set of n × n phase inductances as concerns the stator section. In the case of nonuniform air gap, these inductances vary as the rotor moves. For their numerical determination as functions of the rotor position an accurate computation algorithm is proposed in this paper based on winding function theory. For permeance function identification, a numerically efficient method is employed based on the magnetostatic finite-element analysis of only three appropriately simplified machine models. In the presence of a field circuit, computation of mutual inductances among it and stator phases is also covered with the same approach. An extension of the method to permanent-magnet machines is also presented. Results are assessed on a six-phase synchronous generator prototype equipped with either a salient-pole wound-field rotor or with an interior permanent-magnet rotor.

A new gradient based particle swarm optimization algorithm for accurate computation of global minimum

Stochastic optimization algorithms like genetic algorithms (GAs) and particle swarm optimization (PSO) algorithms perform global optimization but waste computational effort by doing a random search. On the other hand deterministic algorithms like gradient descent converge rapidly but may get stuck in local minima of multimodal functions. Thus, an approach that combines the strengths of stochastic and deterministic optimization schemes but avoids their weaknesses is of interest. This paper presents a new hybrid optimization algorithm that combines the PSO algorithm and gradient-based local search algorithms to achieve faster convergence and better accuracy of final solution without getting trapped in local minima. In the new gradient-based PSO algorithm, referred to as the GPSO algorithm, the PSO algorithm is used for global exploration and a gradient based scheme is used for accurate local exploration. The global minimum is located by a process of finding progressively better local minima. The GPSO algorithm avoids the use of inertial weights and constriction coefficients which can cause the PSO algorithm to converge to a local minimum if improperly chosen. The De Jong test suite of benchmark optimization problems was used to test the new algorithm and facilitate comparison with the classical PSO algorithm. The GPSO algorithm is compared to four different refinements of the PSO algorithm from the literature and shown to converge faster to a significantly more accurate final solution for a variety of benchmark test functions.

Uniform convergence and numerical computation of the Hubbell radiation rectangular source integral

In this paper, we investigate uniform convergence of the improper Hubbell radiation rectangular source (HRS) integral H( a, b). We prove that HRS integral H ( a , b ) is uniform convergent in the domain D ≔ { ( a , b ) ∈ [ 0 , A ] × [ 0 , ∞ ) } for any positive finite number A. Then we give an accurate and efficient computation algorithm for the HRS integral.

Computational Issues in Sensitivity Analysis for 1D Interface Problems

This paper is concerned with the construction of accurate and ecient computational algorithms for the numerical approximation of sensitivities with respect to a parameter dependent interface location. Motivated by sensitivity analysis with respect to piezoelectric actuator placement on an Euler-Bernoulli beam, this work illustrates the key concepts related to sensitivity equation formulation for interface problems where the parameter of interest determines the location of the interface. A fourth order model problem is considered, and a homogenization procedure for sensitivity computation is constructed using standard nite element methods. Numerical results show that proper formulation and approximation of the sensitivity interface conditions is critical to obtaining convergent numerical sensitivity approximations. A second order elliptic interface model problem is also mentioned, and the homogenization procedure is outlined briey for this model.

Accurate HLA type inference using a weighted similarity graph

BackgroundThe human leukocyte antigen system (HLA) contains many highly variable genes. HLA genes play an important role in the human immune system, and HLA gene matching is crucial for the success of human organ transplantations. Numerous studies have demonstrated that variation in HLA genes is associated with many autoimmune, inflammatory and infectious diseases. However, typing HLA genes by serology or PCR is time consuming and expensive, which limits large-scale studies involving HLA genes. Since it is much easier and cheaper to obtain single nucleotide polymorphism (SNP) genotype data, accurate computational algorithms to infer HLA gene types from SNP genotype data are in need. To infer HLA types from SNP genotypes, the first step is to infer SNP haplotypes from genotypes. However, for the same SNP genotype data set, the haplotype configurations inferred by different methods are usually inconsistent, and it is often difficult to decide which one is true.ResultsIn this paper, we design an accurate HLA gene type inference algorithm by utilizing SNP genotype data from pedigrees, known HLA gene types of some individuals and the relationship between inferred SNP haplotypes and HLA gene types. Given a set of haplotypes inferred from the genotypes of a population consisting of many pedigrees, the algorithm first constructs a weighted similarity graph based on a new haplotype similarity measure and derives constraint edges from known HLA gene types. Based on the principle that different HLA gene alleles should have different background haplotypes, the algorithm searches for an optimal labeling of all the haplotypes with unknown HLA gene types such that the total weight among the same HLA gene types is maximized. To deal with ambiguous haplotype solutions, we use a genetic algorithm to select haplotype configurations that tend to maximize the same optimization criterion. Our experiments on a previously typed subset of the HapMap data show that the algorithm is highly accurate, achieving an accuracy of 96% for gene HLA-A, 95% for HLA-B, 97% for HLA-C, 84% for HLA-DRB1, 98% for HLA-DQA1 and 97% for HLA-DQB1 in a leave-one-out test.ConclusionsOur algorithm can infer HLA gene types from neighboring SNP genotype data accurately. Compared with a recent approach on the same input data, our algorithm achieved a higher accuracy. The code of our algorithm is available to the public for free upon request to the corresponding authors.

Uniform convergence and computation of the generalized exponential integrals

In this paper, uniform convergence of the generalized exponential (GE) integrals is investigated. We also study the continuity, differentiability, summability and asymptotic behaviour of GE integrals. Then we give an accurate and efficient computation algorithm for these integrals.

IAlign: a method for the structural comparison of protein–protein interfaces

Protein-protein interactions play an essential role in many cellular processes. The rapid accumulation of protein-protein complex structures provides an unprecedented opportunity for comparative studies of protein-protein interactions. To facilitate such studies, it is necessary to develop an accurate and efficient computational algorithm for the comparison of protein-protein interaction modes. While there are many structural comparison approaches developed for individual proteins, very few methods are available for protein-protein complexes. We present a novel interface alignment method, iAlign, for the structural alignment of protein-protein interfaces. New scoring schemes for measuring interface similarity are introduced, and an iterative dynamic programming algorithm is implemented. We find that the similarity scores follow extreme value distributions. Using statistical models, we empirically estimate their statistical significance, which is in good agreement with manual classifications by human experts. Large-scale tests of iAlign were conducted on both artificial docking models and experimental structures. In a benchmark test on 1517 dimers, iAlign successfully detects biologically related, structurally similar protein-protein interfaces at a coverage percentage of 90% and an error per query of 0.05. When compared against previously published methods, iAlign is substantially more accurate and efficient. The iAlign software package is freely available at http://cssb.biology.gatech.edu/iAlign.

Fast and accurate computation of two-dimensional non-separable quadratic-phase integrals

We report a fast and accurate algorithm for numerical computation of two-dimensional non-separable linear canonical transforms (2D-NS-LCTs). Also known as quadratic-phase integrals, this class of integral transforms represents a broad class of optical systems including Fresnel propagation in free space, propagation in graded-index media, passage through thin lenses, and arbitrary concatenations of any number of these, including anamorphic/astigmatic/non-orthogonal cases. The general two-dimensional non-separable case poses several challenges which do not exist in the one-dimensional case and the separable two-dimensional case. The algorithm takes approximately N log N time, where N is the two-dimensional space-bandwidth product of the signal. Our method properly tracks and controls the space-bandwidth products in two dimensions, in order to achieve information theoretically sufficient, but not wastefully redundant, sampling required for the reconstruction of the underlying continuous functions at any stage of the algorithm. Additionally, we provide an alternative definition of general 2D-NS-LCTs that shows its kernel explicitly in terms of its ten parameters, and relate these parameters bidirectionally to conventional ABCD matrix parameters.

Application of Chebyshev polynomials to predict phase behavior of fluids containing asphaltene and associating components using SAFT equation of state

In this work, a thermodynamic model based on statistical association fluid theory (SAFT) is developed to predict the phase behavior of mixtures containing asphaltene contents. The SAFT equation of state is a good candidate for closing that gap between statistical mechanic models and the classical models dominated by cubic equation of state. A robust, fast and accurate computational algorithm based on Chebyshev polynomial approximation is developed to calculate the density and hence fugacity using SAFT equation of state in order to perform phase equilibrium calculations. Application of Chebyshev polynomials to approximate pressure–density function leads to an interpolation error of degree 10 −13. Application of the proposed algorithm to calculate density of binary systems composed of ethanol and toluene shows an average relative deviation of 0.143% in the temperature range 283.15–353.15 K and for pressures up to 45 MPa. The proposed model is developed to predict the precipitation behavior of petroleum fluids containing asphaltene. The effect of pressure, temperature and solvent concentration on the amount of asphaltene precipitation is investigated. A good agreement with an AAD of 2.593% is observed between experimental and predicted amount of asphaltene precipitate. The model is also tested to investigate the effect of temperature and solvent concentration on asphaltene onset pressures (upper and lower). Again, an excellent agreement is observed between experimental and predicted values of the asphaltene onset pressure at different temperatures and solvent concentrations with an average 0.705% relative error. The accuracy of the proposed model is compared with WinProp software using Peng–Robinson equation of state with average 53.132% and 8.657% relative errors for the amount of asphaltene precipitate and onset pressure, respectively.

WE‐E‐BRD‐07: Algorithm for Accurate Computation of Doses From Large‐Angle Scattering of Scanned Proton Pencil Beams

Purpose: The purpose of this work was to find a technique to improve the accuracy of proton pencil beam dose computation for large scattering angles. Methods: The computed dose from an elementary pencil beam in the scattering medium, like water in our study, comes from a convolution integral of the proton fluence in air and the scattering distribution function in the medium. The incident proton beam profile in air, just outside the target medium, was modeled with a sum of up to three Gaussians fitted with measured data. The proton scattering in the medium, assumed to proceed through Coulomb interactions, was described using the classic Moliere distribution. The convolution integration was performed by a combination of analytical and numerical methods leading to a numerically manageable expression. Results: We compared measured and computed dose profiles at the 2 cm and at the Bragg peak depths for proton pencil beams with low and high energies. In all cases, profile calculations using just one Gaussian term for the beam fluence in air and the first Moliere term for the scattering distribution were in large disagreement with measurements at lateral distances beyond 10% profile falloff. At 2 cm depth in the water, the second and the third terms in Moliere distribution did not contribute significantly. On the other hand, the use of three Gaussians for the proton fluence in air produces nearly perfect agreement for lower energy protons and brings the agreement to within one order of magnitude for the higher proton energies. At Bragg peak depths, higher order Moliere terms are again insignificant for lower energy protons, but become important contributors for higher energy protons. Conclusions: The proposed procedure was shown to achieve a dramatic improvement in the accuracy of computed doses from proton pencil beams at large proton scattering angles.

Constructive learning neural network applied to identification and control of a fuel-ethanol fermentation process

In the present work, a constructive learning algorithm was employed to design a near-optimal one-hidden layer neural network structure that best approximates the dynamic behavior of a bioprocess. The method determines not only a proper number of hidden neurons but also the particular shape of the activation function for each node. Here, the projection pursuit technique was applied in association with the optimization of the solvability condition, giving rise to a more efficient and accurate computational learning algorithm. As each activation function of a hidden neuron is defined according to the peculiarities of each approximation problem, better rates of convergence are achieved, guiding to parsimonious neural network architectures. The proposed constructive learning algorithm was successfully applied to identify a MIMO bioprocess, providing a multivariable model that was able to describe the complex process dynamics, even in long-range horizon predictions. The resulting identification model was considered as part of a model-based predictive control strategy, producing high-quality performance in closed-loop experiments.

Computing Particle Surface Areas and Contact Areas from Three‐Dimensional Tomography Data of Particulate Materials

AbstractMicrotomography is an emerging technique for particle and particulate‐materials characterization. To use this technology effectively, robust and accurate computational algorithms are needed to compute relevant particle properties, including particle surface area and particle‐particle contact area. However, the most accurate algorithms that have been developed for computing the exposed (void/solid) surface area in a microtomography image cannot be used directly for computing surface areas or particle‐particle contact areas for individual particles in a dense packing. This paper presents an algorithm for extracting particle contact areas from a digitized, segmented image of a packed granular material, which in turn can be used to find individual particle surface areas (even if the complete surfaces are not exposed because of contacts in the packing). Results show that small errors in the binary surface‐area computations are magnified in the course of determining particle contact areas; the total error in the computation depends mainly on the size of the contact area in voxel units.