Order Error Research Articles

The reactive Graetz problem for a first order homogeneous decomposition reaction, and the limit of moderately large reaction constants

The long term goal of the present study is to facilitate the inversion of experimental data on cluster evaporation in laminar flow inside tubes. This requires the determination of reactant and product fluxes as functions of three dimensionless governing parameters: the axial position x along the tube, the reaction rate coefficient K, and the ratio γ of product and reactant diffusivities. The reactant flux is first calculated by separation of variables, including the accurate determination of the first 35 eigenvalues for 13 discrete values of K in the range 0<K<500. This approach is far less efficient for the product flux because the eigenfunctions are not standard functions. A numerical solution is also implemented for the reactant and its product, though it can hardly cover the full range of the three relevant parameters. The most common experimental situation involves relatively large values of K, for which a three term asymptotic solution is developed in negative powers of K1/2, with errors of order K−2. These approximate results represent well the numerically calculated reactant fluxes for K > 10 in terms of two functions, H0(s) and H1(s), reported in tables. The product fluxes require two functions, I0(s,γ), I1(s,γ). These we compute for six values of γ, and report as simple analytical fits covering continuously the full physically relevant range 1<γ<1.5. The desired ability to analyze experimental data to yield kinetic information is therefore achieved without the need for additional numerical solutions to partial differential equations.

Full-period fringe order correction method based on dual-threshold cellular automaton

In traditional temporal phase unwrapping (TPU) methods, the fringe order is obtained pixel-to-pixel by multi-frequencies or multi-wavelengths. The direct calculation and error non-accumulation features accelerate the prosperity of TPU. Nevertheless, the noise, defocusing, and non-uniform reflectivity may inevitably lead to some fringe order errors. These errors are powerless against the evolving TPUs such as Gray code and phase coding. In this paper, a full-period fringe order correction method based on dual-threshold cellular automaton is proposed for machine 3D vision. Initially, an advanced dual-threshold cellular automaton algorithm is employed to extract both the strong and weak edges of the wrapped phase individually. Superior to conventional single-threshold edge detection methods, this approach effectively mitigates the edge breakage problem caused by significant height variations. Subsequently, the N-filled map, N-residue mask, and N-start points concepts are introduced to sequentially segment independent connected domains based on the tightly graphical coupling. In addition, by performing edge compensation in the same period, accurate fringe order correction can be achieved even if excessive edge points are identified, as long as the broken edges are effectively connected. The experimental results exhibit exceptional correction performance of the proposed method for intricate isolated objects, objects with non-uniform reflectivity, and dynamic scenes.

Robust joint modelling of sparsely observed paired functional data

AbstractA reduced‐rank mixed‐effects model is developed for robust modelling of sparsely observed paired functional data. In this model, the curves for each functional variable are summarized using a few functional principal components, and the association of the two functional variables is modelled through the association of the principal component scores. A multivariate‐scale mixture of normal distributions is used to model the principal component scores and the measurement errors in order to handle outlying observations and achieve robust inference. The mean functions and principal component functions are modelled using splines, and roughness penalties are applied to avoid overfitting. An EM algorithm is developed for computation of model fitting and prediction. A simulation study shows that the proposed method outperforms an existing method, which is not designed for robust estimation. The effectiveness of the proposed method is illustrated through an application of fitting multiband light curves of Type Ia supernovae.

Second order error bounds for POD-ROM methods based on first order divided differences

This note proves for the heat equation that using BDF2 as time stepping scheme in POD-ROM methods with snapshots based on difference quotients gives both the optimal second order error bound in time and pointwise estimates.

A modified weak Galerkin finite element method for parabolic equations on anisotropic meshes

In this paper, we study a modified weak Galerkin finite element method (MWG-FEM) on anisotropic triangular meshes for a class of parabolic equations. Different from conventional weak Galerkin methods, the MWG-FEM replaces the boundary functions by the average of interior functions, which possesses flexibility in the approximation functions and mesh generation. Moreover, MWG-FEM is compatible with anisotropic meshes and suitable for solving problems with anisotropic property. By using the anisotropic interpolation and projection operators, the optimal order error estimate in L2 norm is derived. Numerical experiments are performed to demonstrate the stability and efficiency of the method.

A highly accurate peak time formula of epidemic outbreak from the SIR model

Forecasting the epidemic peak time right from the origination of a disease is vital to take over dynamical behaviour of its spread over time. The decision of isolation, social distance and lock down strategic progresses does all rely on an accurate prediction of the peak time so that reduction of the time of peak or of the infected size of population will be made possible. Therefore, recent efforts concentrated on deriving elaborative and analytically accessible expressions representing the peak time of the infected compartment from the classical SIR epidemic mathematical model. In this research paper, two closed-form formulae are introduced to yield a straightforward computation of peak time of an infectious disease with no restrictions on the SIR quantities. In addition to this, the calculations can be implemented on a usual calculator, without requiring the use of advanced mathematical functions, having provided the initial fractions of infected and susceptible populations as well as the recovery to infectious ratio. A comparison including the COVID-19 data is fulfilled with the very recent formulas available in the open literature. With the proposed new scalings, evaluation of the peak time is reduced only to two parameter space and the accuracy of the present formulas in reduced form is ultimately confirmed yielding an error of order of magnitude 10−4 valid for the complete regime of the set of SIR model parameters. Even in the case of an endemic, the past peak time of the illness can also be captured accurately by the given formulae. Two simple approximations in terms of usual geometric series are also provided. These can be safely used with a pocket calculator without sophisticated laboratory equipments.

A Space-Time Finite Element Method for the Fractional Ginzburg–Landau Equation

A fully discrete space-time finite element method for the fractional Ginzburg–Landau equation is developed, in which the discontinuous Galerkin finite element scheme is adopted in the temporal direction and the Galerkin finite element scheme is used in the spatial orientation. By taking advantage of the valuable properties of Radau numerical integration and Lagrange interpolation polynomials at the Radau points of each time subinterval In, the well-posedness of the discrete solution is proven. Moreover, the optimal order error estimate in L∞(L2) is also considered in detail. Some numerical examples are provided to evaluate the validity and effectiveness of the theoretical analysis.

The infinitesimal model with dominance.

The classical infinitesimal model is a simple and robust model for the inheritance of quantitative traits. In this model, a quantitative trait is expressed as the sum of a genetic and an environmental component, and the genetic component of offspring traits within a family follows a normal distribution around the average of the parents' trait values, and has a variance that is independent of the parental traits. In previous work, we showed that when trait values are determined by the sum of a large number of additive Mendelian factors, each of small effect, one can justify the infinitesimal model as a limit of Mendelian inheritance. In this paper, we show that this result extends to include dominance. We define the model in terms of classical quantities of quantitative genetics, before justifying it as a limit of Mendelian inheritance as the number, M, of underlying loci tends to infinity. As in the additive case, the multivariate normal distribution of trait values across the pedigree can be expressed in terms of variance components in an ancestral population and probabilities of identity by descent determined by the pedigree. Now, with just first-order dominance effects, we require two-, three-, and four-way identities. We also show that, even if we condition on parental trait values, the "shared" and "residual" components of trait values within each family will be asymptotically normally distributed as the number of loci tends to infinity, with an error of order 1/M. We illustrate our results with some numerical examples.

Coupling Analysis of Compound Continuum Robots for Surgery: Another Line of Thought.

The compound continuum robot employs both concentric tube components and cable-driven continuum components to achieve its complex motions. Nevertheless, the interaction between these components causes coupling, which inevitably leads to reduced accuracy. Consequently, researchers have been striving to mitigate and compensate for this coupling-induced error in order to enhance the overall performance of the robot. This paper leverages the coupling between the components of the compound continuum robot to accomplish specific surgical procedures. Specifically, the internal concentric tube component is utilized to induce motion in the cable-driven external component, which generates coupled motion under the constraints of the cable. This approach enables the realization of high-precision surgical operations. Specifically, a kinematic model for the proposed robot is established, and an inverse kinematic algorithm is developed. In this inverse kinematic algorithm, the solution of a highly nonlinear system of equations is simplified into the solution of a single nonlinear equation. To demonstrate the effectiveness of the proposed approach, simulations are conducted to evaluate the efficiency of the algorithm. The simulations conducted in this study indicate that the proposed inverse kinematic (IK) algorithm improves computational speed by a significant margin. Specifically, it achieves a speedup of 2.8 × 103 over the Levenberg-Marquardt (LM) method. In addition, experimental results demonstrate that the coupled-motion system achieves high levels of accuracy. Specifically, the repetitive positioning accuracy is measured to be 0.9 mm, and the tracking accuracy is 1.5 mm. This paper is significant for dealing with the coupling of the compound continuum robot.

Heat Transfer in a Silo Containing Rice: Solution by the Explicit Method of the Finite Differences with Approximations of Order 2 and 4 for a One-Dimensional Transient Model

Rice is one of the most consumed cereals in the world, and the cultivation of this crop has significant relevance in the southern region of Brazil. When subjected to inadequate conditions of temperature and humidity, rice becomes susceptible to attacks from pests and fungi and, therefore, care in the storage process is of paramount importance, since this is largely responsible for the quality of the harvest. Such care allows the food to arrive without harm to the consumer. In this sense, the mathematical modeling, among numerous possibilities, allows for evaluating the internal temperature of a silo and, through this, taking preventive measures so that the grains maintain their quality. The objective of this work is to model the heat transfer process in a silo prototype containing rice in husk through the explicit finite difference method for a one-dimensional and transient model considering two approaches centered on the spatial derivative: error of order 2 and 4. In addition, the thermal diffusivity of the grain with average value was analyzed. The results obtained by the solutions were analyzed through graphs and statistical indexes comparing with the experimental data of the literature, and the computer simulation was performed through the Google Colab platform. The chosen methodology proved effective for the work, and the predicted temperatures for the approximations of order 2 and 4 denote similarities both graphically and in the precision of the statistical indexes.

Tuberculosis Disease Detection through CXR Images based on Deep Neural Network Approach

Tuberculosis (TB) is a disease that, if left untreated for an extended period of time, can ultimately be fatal. Early TB detection can be aided by using a deep learning ensemble. In previous work, ensemble classifiers were only trained on images that shared similar characteristics. It is necessary for an ensemble to produce a diverse set of errors in order for it to be useful; this can be accomplished by making use of a number of different classifiers and/or features. In light of this, a brand-new framework has been constructed in this study for the purpose of segmenting and identifying TB in human Chest X-ray. It was determined that searching traditional web databases for chest X-ray was necessary. At this point, we pass the photos that we have collected over to Swin ResUnet3 so that they may be segmented. After the segmented chest X-ray have been provided to it, the Multi-scale Attention-based Densenet with Extreme Learning Machine (MAD-ELM) model will be applied in the detection stage in order to effectively diagnose tuberculosis from human chest X-ray. This will be done in order to maximize efficiency. Because it increased the variety of errors made by the basic classifiers, the supplied variation of the approach that was proposed was able to detect tuberculosis more effectively. The proposed ensemble method produced results with an accuracy of 94.2 percent, which are comparable to those obtained by past efforts.

Virtual element method for the modified transmission eigenvalue problem in inverse scattering theory

In this paper, we present the virtual element approximation for the modified transmission eigenvalue problem. The eigenvalue problem arises in inverse scattering theory for artificial inhomogeneous media characterized as a metamaterial. By the shifting argument and spectral approximation theory of compact operators, we prove the correct spectral approximation of the virtual element scheme, and derive the optimal order error estimates for the eigenfunctions and the double order for the eigenvalues. Finally, we implement numerical experiments to illustrate behaviors of the standard and serendipity virtual element schemes, and the finite element scheme.

Visual and refractive outcomes after photorefractive keratectomy (PRK) and femto-SMILE (small-incision lenticule extraction) for Myopia

Background The objective of refractive surgery is to lessen the patient’s reliance on contact lenses or glasses for everyday activities. Photorefractive Keratectomy (PRK) is a popular surgical procedure that reshapes the cornea in individuals with refractive errors in order to enhance their vision. PRK differs from previous laser-based eye operations in that there are no corneal incisions created during the procedure. Objective To compare the visual and refractive outcomes following PRK and femto-small-incision Lenticule extraction (SMILE) for myopic patients. Patients and methods This retrospective comparative research was conducted in Ophthalmology Department, Faculty of Medicine–Tanta University on 80 eyes (of 40 cases) who underwent Corneal Refractive Surgery. They were equally allocated into two groups; PRK group and 2- femto-SMILE group. They were compared before surgery and 6 months after surgery for clinical and topographical outcomes. Results There was a significant difference between both groups as regard of Postoperative UCVA, Degree of Myopia before and after surgery, and Analysis of thinnest location. There were no significant difference between both groups as regard of demographic data or degree of Astigmatism. Conclusion After 6 months of surgery, the visual outcome of PRK was better than femto-SMILE, however, femto- SMILE was more effective in astigmatic correction compared with PRK.

Adaptive timing in a dynamic field architecture for natural human–robot interactions

A close temporal coordination of actions and goals is crucial for natural and fluent human–robot interactions in collaborative tasks. How to endow an autonomous robot with a basic temporal cognition capacity is an open question. In this paper, we present a neurodynamics approach based on the theoretical framework of dynamic neural fields (DNF) which assumes that timing processes are closely integrated with other cognitive computations. The continuous evolution of neural population activity towards an attractor state provides an implicit sensation of the passage of time. Highly flexible sensorimotor timing can be achieved through manipulations of inputs or initial conditions that affect the speed with which the neural trajectory evolves. We test a DNF-based control architecture in an assembly paradigm in which an assistant hands over a series of pieces which the operator uses among others in the assembly process. By watching two experts, the robot first learns the serial order and relative timing of object transfers to subsequently substitute the assistant in the collaborative task. A dynamic adaptation rule exploiting a perceived temporal mismatch between the expected and the realized transfer timing allows the robot to quickly adapt its proactive motor timing to the pace of the operator even when an additional assembly step delays a handover. Moreover, the self-stabilizing properties of the population dynamics support the fast internal simulation of acquired task knowledge allowing the robot to anticipate serial order errors.

Direct numerical solutions of the SIR and SEIR models via the Dirichlet series approach.

Compartment models are implemented to understand the dynamic of a system. To analyze the models, a numerical tool is required. This manuscript presents an alternative numerical tool for the SIR and SEIR models. The same idea could be applied to other compartment models. The result starts with transforming the SIR model to an equivalent differential equation. The Dirichlet series satisfying the differential equation leads to an alternative numerical method to obtain the model's solutions. The derived Dirichlet solution not only matches the numerical solution obtained by the fourth-order Runge-Kutta method (RK-4), but it also carries the long-run behavior of the system. The SIR solutions obtained by the RK-4 method, an approximated analytical solution, and the Dirichlet series approximants are graphically compared. The Dirichlet series approximants order 15 and the RK-4 method are almost perfectly matched with the mean square error less than 2 × 10-5. A specific Dirichlet series is considered in the case of the SEIR model. The process to obtain a numerical solution is done in the similar way. The graphical comparisons of the solutions achieved by the Dirichlet series approximants order 20 and the RK-4 method show that both methods produce almost the same solution. The mean square errors of the Dirichlet series approximants order 20 in this case are less than 1.2 × 10-4.

Local discontinuous Galerkin method on graded meshes for a third‐order singularly perturbed problem

AbstractWe consider the local discontinuous Galerkin (LDG) method for a third order singularly perturbed problem with different kinds of boundary layer. On graded Duran‐Shishkin and Duran type meshes, we prove optimal order error estimate in the energy‐norm which is valid uniformly up to a logarithmic factor. Numerical experiments are given to confirm our theoretical findings.

PERANCANGAN SISTEM INFORMASI MANAJEMEN STOK PADA TB. CENTRAL BANGUN JAYA

Central Bangun Jaya is engaged in the sale of building materials. In processing every day inventory control records, its still manually, in order that mistakes frequently arise in pricing items when making income because of the huge variety of styles of merchandise being sold. Similarly, the store frequently does now not reduce stock at some point of a income transaction, ensuing in a difference between the real inventory and the manual recording stock. Because of the problem, this have a look at goals to provide a technique to the difficulties experienced through TB. Central Bangun Jaya. This machine uses programming language PHP, framework laravel, visual Studio Code, and also MySQL. where on this study the use of the waterfall method with the gadget testing approach the use of the Blackbox method and system modeling used, particularly use case diagrams, activity diagrams, and sophistication diagrams. it can be concluded from this studies, the machine created can facilitate the shop in processing inventory management statistics, in order that gadget customers can minimize errors in order to arise and may be predicted to resolve problems that exist in TB. Central Bangun Jaya.

STUDENTS’ ERROR ANALYSIS IN WRITING ESSAY OF ENGLISH LANGUAGE TEACHING

One of the successful learning English writings is by knowing students' errors in writing an English essay. Since English writing essay becomes a compulsory subject that must be taken by students at college, therefore the English essay has a big contribution. Although writing an English essay does not pay attention much to the proportional explaining and giving instruction in learning, but it still has meaningful contributions for writing skill. It is not for writing essay but also for other writing skills such as writing paragraph, writing scientific paper, and etc. Type of this research was qualitative content analysis through documents of English essays written by students of third semester of Universitas Dharmas Indonesia. Respondents of this research were 14 students. The analysis of all documents reveals that there are 220 total numbers of students’ errors that classified into 12 types of errors made by the students. Spelling is classified as the biggest error committed by 46 times or 20.90%. Then, verb-agreement is a kind of errors that committed by 38 times or 17.27%. Next is error of sentence fragment that committed by 24 times or 10.90%. Relating to research finding, It is recommended that English writing lecturers should much pay attention to divide, discuss, and explain all these errors in order to minimize and make writing essays easy written and conducted by English students.

Computer Network Redundancy Reduction Using Video Compression

Due to the strong correlation between symmetric frames, video signals have a high degree of temporal redundancy. Motion estimation techniques are computationally expensive and time-consuming processes used in symmetric video compression to reduce temporal redundancy. The block-matching technique is, on the other hand, the most popular and efficient of the different motion estimation and compensation techniques. Motion compensation based on the block-matching technique generally uses the minimization of either the mean square error (MSE) or mean absolute difference (MAD) in order to find the appropriate motion vector. This paper proposes to remove the highly temporally redundant information contained in each block of the video signal using the removing temporal redundancy (RTR) technique in order to improve the data rate and efficiency of the video signal. A comparison between the PSNR values of this technique and those of the JPEG video compression standard is made. As a result of its moderate memory and computation requirements, the algorithm was found to be suitable for mobile networks and embedded devices. Based on a detailed set of testing scenarios and the obtained results, it is evident that the RTR compression technique allowed a compression ratio of 22.71 and 95% loss in bit rate reduction while maintaining sufficient intact signal quality with minimized information loss.

The transposed word effect is consistent with serial word recognition and varies with reading speed

The scientific study of reading has long been animated by questions of parallel vs. serial processing. Do readers recognize words serially, adding each one sequentially to a representation of the sentence structure? One fascinating phenomenon to emerge from this research is the transposed word effect: when asked to judge whether sentences are grammatical, readers often fail to notice grammatical errors caused by transposing two words. This effect could be evidence that readers recognize multiple words in parallel. Here we provide converging evidence that the transposed word effect is also consistent with serial processing because it occurs robustly when the words in each sentence are presented serially. We further investigated how the effect relates to individual differences in reading speed, to gaze fixation patterns, and to differences in difficulty across sentences. In a pretest, we first measured the natural English reading rate of 37 participants, which varied widely. In a subsequent grammatical decision task, we presented grammatical and ungrammatical sentences in two modes: one with all words presented simultaneously, and the other with single words presented sequentially at each participant’s natural rate. Unlike prior studies that used a fixed sequential presentation rate, we found that the magnitude of the transposed word effect was at least as strong in the sequential presentation mode as in the simultaneous mode, for both error rates and response times. Moreover, faster readers were more likely to miss transpositions of words presented sequentially. We argue that these data favor a “noisy channel” model of comprehension in which skilled readers rely on prior knowledge to rapidly infer the meaning of sentences, allowing for apparent errors in spatial or temporal order, even when the individual words are recognized one at a time.