Linear Approximation Method Research Articles

Methods for Reducing Ring Artifacts in Tomographic Images Using Wavelet Decomposition and Averaging Techniques

Computed tomography (CT) is one of the fundamental imaging modalities used in medicine, allowing for the acquisition of accurate cross-sectional images of internal body tissues. However, during the acquisition and reconstruction process, various artifacts can arise, and one of them is ring artifacts. These artifacts result from the inherent limitations of CT scanner components and the properties of the scanned material, such as detector defects, non-uniform distribution of radiation from the source, or the presence of metallic elements within the scanning region. The purpose of this study was to identify and reduce ring artifacts in tomographic images using image decomposition and average filtering methods. In this study, tests were conducted on the effectiveness of identifying ring artifacts using wavelet decomposition methods for images. The test was performed on a Shepp–Logan phantom with implemented artifacts of different intensity levels. The analysis was performed using different wavelet families, and linear approximation methods were used to filter the image in the identified areas. Additional filtering was performed using moving average methods and empirical mode decomposition (EMD) techniques. Image comparison methods, i.e., RMSE, SSIM and MS-SSIM, were used to evaluate performance. The results of this study showed a significant improvement in the quality of tomographic phantom images. The authors obtained more than 50% improvement in image quality with reference to the image without any filtration. The different wavelet families had different efficiencies with relation to the identification of the induction regions of ring artifacts. The Haar wavelet and Coiflet 1 showed the best performance in identifying artifact induction regions, with comparative RMSE values for these wavelets of 0.1477 for Haar and 0.1469 for Coiflet 1. The applied additional moving average filtering and EMD permitted us to improve image quality, which is confirmed by the results of the image comparison. The obtained results allow us to assess how the used methods affect the reduction in ring artifacts in phantom images with induced artifacts.

A reconfigurable multi-precision quantization-aware nonlinear activation function hardware module for DNNs

In recent years, the increasing variety of nonlinear activation functions (NAFs) in deep neural networks (DNNs) has led to higher computational demands. However, hardware implementation faces challenges such as lack of flexibility, high hardware cost, and limited accuracy. This paper proposes a highly flexible and low-cost hardware solution for implementing activation functions to overcome these issues. Based on the piecewise linear (PWL) approximation method, our method supports NAFs with different accuracy configurations through a customized implementation strategy to meet the requirements in different scenario applications. In this paper, the symmetry of the activation function is investigated, and incorporate curve translation preprocessing and data quantization to significantly reduce hardware storage costs. The modular hardware architecture proposed in this study supports NAFs of multiple accuracies, which is suitable for designing deep learning neural network accelerators in various scenarios, avoiding the need to design dedicated hardware circuits for the activation function layer and enhances circuit design efficiency. The proposed hardware architecture is validated on the Xilinx XC7Z010 development board. The experimental results show that the average absolute error (AAE) is reduced by about 35.6 % at a clock frequency of 312.5 MHz. Additionally, the accuracy loss of the model is maximized to −0.684 % after replacing the activation layer function of DNNs under the PyTorch framework.

New linear approximation method applied to crude operations scheduling

New linear approximation method applied to crude operations scheduling

Иглоподобные листовые органы хвойных. Часть I. Моделирование периметра поперечного сечения иглы

Despite the availability of measuring systems for estimating the surface area of leaf organs of higher plants, the need for simple standard methods for determining this indicator area remains relevant for plant physiologists. The methods for estimating the surface area of needle-like leaf organs of conifers, based on the geometry of an individual needle rest on the general principle of calculating the needle surface area as the product of its length by the perimeter of its cross-section. This makes the cross-section perimeter one of the most important parameters needed to characterize the needle surface area. The strong variability of this parameter depending on the species necessitates the development of individual models of the cross-section of individual needles. The aim of this study has been to create a universal model for estimating the needle cross-section perimeter, irrespective of the tree species. For the practical implementation of the aim, a method was proposed for estimating the perimeter of the needle cross-section, based on the well-known fact that any closed line is transformable into an equivalent circle, while the length of the closed line does not change. The perimeter of the equivalent circle can be related to the parameters of the geometric figure before the transformation. This approach allows us to relate the width and thickness of the needle cross-section to its perimeter. The developed universal model of the needle cross-section has been verified on cross-sections of Siberian fir (Abies sibirica L.) and common juniper (Juniperus communis L.) needles. The samples of needles of these woody plants have been collected from a bilberry-sphagnum spruce forest in the boreal zone of the north-east of the European part of Russia (Knyazhpogostkiy district, the Komi Republic). Statistical analysis has shown the significance and adequacy of the model. It can be used to assess the perimeter of coniferous needles, irrespective of their species. In this case, the accuracy of perimeter estimation is comparable to the accuracy of direct perimeter measurement by the piecewise linear approximation method.

A 3-D extension of the Multiscale Control Volume method for the simulation of the single-phase flow in anisotropic and heterogeneous porous media

The level of detail on modern geological models requires higher resolution grids that may render the simulation of multiphase flow in porous media intractable. Moreover, these models may comprise highly heterogeneous media with phenomena taking place in different scales. Scale transferring techniques allow for the solution of such problems in a lower resolution scale at reduced computational cost. Among these techniques, the Multiscale Finite Volume (MsFV) method constructs a set of numerical operators in order to map quantities from the fine-scale mesh to a coarser one and vice-versa while maintaining flux conservation on both scales. However, the MsFV formulation, as originally stated, is only consistent on k-orthogonal grids since it uses a linear Two-point Flux Approximation (TPFA) method and may struggle to generate consistent primal-dual coarse grids pairs on unstructured grids. The Multiscale Restriction Smoothed-Basis method (MsRSB) improves on the MsFV by introducing a new iterative procedure to find the multiscale operators and the concept of support regions which reduces the method's complexity when applied to unstructured fine and coarse grids. The original version was only consistent on k-orthogonal fine grids due to the TPFA discretization, but filtering methods have been developed to also enable consistent multipoint schemes on the fine scale. Meanwhile, the Multiscale Control Volume method (MsCV) replaces the TPFA by the Multipoint Flux Approximation with a Diamond stencil (MPFA-D) scheme on the fine-scale while further enhancing the generation of the geometric entities to allow unstructured grids on the fine and coarse scales for two-dimensional simulations. In this work we propose an extension to three-dimensional geometries of both the MsCV and the algorithm to obtain the multiscale geometric entities based on the concept of a background grid, a coarser grid used as a proxy for the primal coarse grid. We modify the original MPFA-D method to use the very robust Global Least Squares (GLS) interpolation technique to obtain the required auxiliary nodal unknowns. We also introduce an enhanced version of the 3-D MsCV with the incorporation of the enhanced MsRSB (E-MsRSB) to enforce M-matrix properties and improve convergence. Finally, we employ the MsCV operators in a two-stage smoother to show how it can be used as a good iterative procedure to recover the fine-scale solution. We show that the 3-D MsCV method produces good results employing unstructured grids on both scales to handle the simulation of the single-phase flow in anisotropic, and heterogeneous porous media and that the smoothing procedure is able to accurately retrieve the fine-scale solution within a few iterations.

Latent event history models for quasi-reaction systems

Various processes, such as cell differentiation and disease spreading, can be modelled as quasi-reaction systems of particles using stochastic differential equations. The existing Local Linear Approximation (LLA) method infers the parameters driving these systems from measurements of particle abundances over time. While dense observations of the process in time should in theory improve parameter estimation, LLA fails in these situations due to numerical instability. Defining a latent event history model of the underlying quasi-reaction system resolves this problem. A computationally efficient Expectation-Maximization algorithm is proposed for parameter estimation, incorporating an extended Kalman filter for evaluating the latent reactions. A simulation study demonstrates the method's performance and highlights the settings where it is particularly advantageous compared to the existing LLA approaches. An illustration of the method applied to the diffusion of COVID-19 in Italy is presented.

Adaptive path tracking control for autonomous vehicles with sideslip effects and unknown input delays

This paper presents an adaptive path-tracking control of autonomous ground vehicles with sideslip effects and time-varying input delays. To handle the problem of unknown time-varying input delays, the vehicle kinematic model is transformed into a novel chain model, and a delay-based auxiliary integral term is introduced for the estimation of the unknown terms caused by time-varying delays. To avoid modeling errors caused by existing linear approximation methods, a new adaptive path-tracking control strategy is proposed, such that the optimal tracking performance is achieved by appropriately adjusting certain design parameters. In addition, the inherent complexity explosion issue is avoided with the aid of a boundary estimation strategy. All signals of the closed-loop systems are guaranteed to be bounded. Simulation results illustrate the effectiveness of the method proposed.

A Linear Fit for Atomic Force Microscopy Nanoindentation Experiments on Soft Samples

Atomic Force Microscopy (AFM) nanoindentation is a powerful technique for determining the mechanical properties of soft samples at the nanoscale. The Hertz model is typically used for data processing when employing spherical indenters for small indentation depths (h) compared to the radius of the tip (R). When dealing with larger indentation depths, Sneddon’s equations can be used instead. In such cases, the fitting procedure becomes more intricate. Nevertheless, as the h/R ratio increases, the force–indentation curves tend to become linear. In this paper the potential of using the linear segment of the curve (for h > R) to determine Young’s modulus is explored. Force–indentation data from mouse and human lung tissues were utilized, and Young’s modulus was calculated using both conventional and linear approximation methods. The linear approximation proved to be accurate in all cases. Gaussian functions were applied to the results obtained from both classic Sneddon’s equations and the simplified approach, resulting in identical distribution means. Moreover, the simplified approach was notably unaffected by contact point determination. The linear segment of the force–indentation curve in deep spherical indentations can accurately determine the Young’s modulus of soft materials at the nanoscale.

Dynamical analysis and optimal control of an age‐structured epidemic model with asymptomatic infection and multiple transmission pathways

The diversity of transmission modes and the heterogeneity of populations in the transmission of infectious diseases are issues that have to be faced in the current disease protection. In this paper, an infectious disease model incorporating age structure and horizontal and environmental spread, along with asymptomatic infection, is proposed to describe diversification of disease transmission routes and population heterogeneity. The expression of the basic reproduction number is derived by a linear approximation method, and it is concluded that if , the disease‐free steady state is globally asymptotically stable; if , the model has a unique endemic steady state which is locally asymptotically stable under certain conditions. Further, the uniform persistence of disease is proved using the persistence theory of the infinite‐dimensional dynamical system when . In additional, the issue of optimal control problem according to this model is investigated, and the representation of optimal control with respect to state variables and adjoint variables is obtained which also imply the existence and uniqueness of optimal control. Finally, numerical simulations are carried out to interpret the theoretical results and to discuss the impact of age and control measures in disease transmission.

Rich phenomenology of the solutions in a fractional Duffing equation

In this paper, we characterize the chaos in the Duffing equation with negative linear stiffness and a fractional damping term given by a Caputo fractional derivative of order α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} ranging from 0 to 2. We use two different numerical methods to compute the solutions, one of them new. We discriminate between regular and chaotic solutions by means of the attractor in the phase space and the values of the Lyapunov Characteristic Exponents. For this, we have extended a linear approximation method to this equation. The system is very rich with distinct behaviours. In the limits α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} to 0 or α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} to 2, the system tends to basically the same undamped system with a behaviour clearly different from the classical Duffing equation.

A more accurate piecewise linear approximation method for quadratic cost curves of thermal generators and its application in unit commitment

A more accurate piecewise linear approximation method for quadratic cost curves of thermal generators and its application in unit commitment

A 0–1 linear relaxation and stochastic approximation method for real-time pricing in a smart grid with non-convex constraints

In this article, real-time pricing (RTP) for a smart grid with complicated non-convex and/or non-smooth constraints is explored. First, piecewise linear functions are adopted to approximate any kinds of utility function and RTP is formulated into bilevel non-convex programming. Then, a 0–1 relaxation method is used to linearize sparse constraints and piecewise linear utility functions, to obtain mixed integer linear programming. Finally, a distributed simultaneous perturbation stochastic approximation (DSPSA) method is designed to solve the bilevel non-convex programming. The RTP strategy is generalizable because sparse constraints and non-differentiable and/or non-concave utility functions are widespread in practice, and the piecewise linear functions approximation method is applicable to all kinds of utility function, not just to non-smooth and/or non-concave utility functions. In addition, the 0–1 linear relaxation and stochastic approximation method make the bilevel non-convex programming easily solvable by DSPSA, which converges rapidly while maintaining the high accuracy of solutions.

A two-step approach for deploying heterogeneous vessels and designing reliable schedule in liner shipping services

Schedule reliability is a crucial metric for measuring liner container shipping service. Due to the inherent uncertainties at sea and ports, schedule delays and unreliable on-time performance have long plagued shipping companies. In practice, the heterogeneity of container vessels also creates challenges for deployment and schedule optimization. To address the problem, we develop a two-step approach with two programming sub-models. In the first step, we tackle the challenges of ship deployment and scheduling by considering heterogeneous vessels and capturing the interarrival time between adjacent ports of call. In the second step, we use the conditional value-at-risk (CVaR) to address the uncertainty risk avoidance in schedule design. To solve the stochastic programming models, we employ a solution framework based on the outer linear approximation method and the risk measure method, where CVaR is specified as the risk measure. We illustrate the application of our model on a case study concerning a real route operated by COSCO Shipping Lines. The results show that the total cost of liner shipping service with heterogeneous fleet on the route can be reduce by 4.77% compared with homogeneous fleet. And the cost of risk with the reliable schedule can be decreased by 8.04% compared with the ideal schedule. The research conclusions can provide some useful decision-making references for shipping companies to deploy heterogeneous vessels and design reliable schedules.

A regularization–correction approach for adapting subdivision schemes to the presence of discontinuities

Linear approximation methods suffer from Gibbs oscillations when approximating functions with jumps. Essentially non oscillatory subcell-resolution (ENO-SR) is a local technique avoiding oscillations and with a full order of accuracy, but a loss of regularity of the approximant appears. The goal of this paper is to introduce a new approach having both properties of full accuracy and regularity. In order to obtain it, we propose a three-stage algorithm: first, the data is smoothed by subtracting an appropriate non-smooth data sequence; then a chosen high order linear approximation operator is applied to the smoothed data and finally, an approximation with the proper jump or corner (jump in the first order derivative) discontinuity structure is reinstated by correcting the smooth approximation with the non-smooth element used in the first stage. This new procedure can be applied as subdivision scheme to design curves and surfaces both in point-value and in cell-average contexts. Using the proposed algorithm, we are able to construct approximations with high precision, with high piecewise regularity, and without smearing nor oscillations in the presence of discontinuities. These are desired properties in real applications as computer aided design or car design, among others.

Dynamical analysis and decision support system of production management

Nonlinear system dynamics and feedback control theory are presented for management optimization of supply chain systems. Linearization and simplification methods are widely used in analyzing the system dynamics of supply chains because actual production models are highly complex and nonlinear systems. With advanced system dynamics, it is possible to deal directly with nonlinear dynamical problems without linear approximate methods so that the decision-makers can obtain more accurate results for systematic management strategies. This paper proposes a nonlinear system theory to explore dynamical behavior and control synthesis of production-distribution systems using Forrester’s model. A novel super-twisting sliding mode control (SWT-SMC) algorithm has been presented based on adaptation law, ensuring management optimization against disruptions. The closed-loop system stability has been guaranteed by using the Lyapunov theory. Extensive numerical simulations have been conducted to validate the efficacy and reliability of the adaptive super-twisting sliding mode control (ASWT-SMC) algorithm. Four types of decision criteria have been employed to compare system performance between control strategies. With a superb decision scheme powered by a control algorithm, novel supply chain software can learn an ever-fluctuating production flow and anticipate the need for changes in a real market.

Substantiating the directions of health tourism development in Czechia

<abstract> <p>The purpose of the article is to substantiate the directions of health tourism development in Czechia. The purpose of the study is the subjects of health tourism: well-known rehabilitation centers in Czechia, medical institutions, health resorts. The methodological basis was formed by the following methods: abstract-logical; statistical; expert evaluation; cluster analysis; piecewise linear approximation. Among the most popular regions of Czechia for health tourism, the main places are Prague, Moravian-Silesia, Olomouc, Plzeň, South Moravian and South Bohemian. The increase in the number of patients among residents of the country and foreigners who use health tourism services is studied. The five leaders among the countries that used the services are identified. The main problems and advantages of health tourism in Czechia are identified. The Czech tourism development strategy for 2021–2030 is analyzed and directions for its implementation are proposed. <bold>Originality / value</bold>: the originality of the study lies in forecasting the directions of health tourism development in Czechia using the method of piecewise linear approximation in the following areas: adults with health insurance; adults at their own expense, children and teenagers, which will increase the volume of income for health tourism institutions in Czechia. According to the forecasting results, the demand for health services will increase by 3% annually. The results of this study can be useful for substantiating the directions of further health tourism development in the country, which will ensure the competitiveness and investment attractiveness of the country.</p> </abstract>

Piecewise reconstruction of membership function approximation errors for Takagi–Sugeno fuzzy control

We propose a conservative relaxed control method to stabilize Takagi–Sugeno (TS) fuzzy systems. First, a conventional piecewise linear function approximation method is adopted to consider the membership functions’ information in the closed-loop system’s stability analysis. Subsequently, a model reconstruction method is proposed to reformulate linear approximation error terms in the TS fuzzy form, which can effectively introduce more information into stability conditions and achieve better robust control effects. Then, based on a fuzzy Lyapunov function approach, control design conditions are derived in terms of linear matrix inequalities, with less conservatism for related results in the literature. Finally, via a benchmark experiment, it is verified that the proposed method can show better robustness with fewer decision variables in robust convex conditions.

Analysis of a two pile frame for a horizontal force

The article analyzes a pile frame composed of two bored piles with a diameter of 40 cm. The frame is subjected to a horizontal force. Calculations in three different method are conducted – subgrade reaction approach, 2D plaxis and 3D plaxis, after which a comparison was made between the results of the individual methods. The aim is to see under what conditions a subgrade reaction method is suitable for use without moving away from sure side. Results were also obtained for the distribution of the value of the spring constant by depth, as well as values for the ratio between the resistance of the second and first pile. A proposal has been made for obtaining a p-curve that can be applied to any of the linear approximation methods.

An Efficient Hardware Implementation for Complex Square Root Calculation Using a PWL Method

In this paper, we propose a methodology for computing the square root of a complex number based on a piecewise linear (PWL) approximation method. The proposed method relies on a software-based segmentor that automatically divides the three real square root functions used in complex square root computation into the fewest segments with a predefined fractional bit width and maximum absolute error (MAE). The coefficients, including the start point, end point, slope and y-intercept of each segment, are stored for use in the implementation of the hardware design. The proposed fully pipelined circuit is coded in the Verilog hardware description language (HDL). The results of synthesis in TSMC (Taiwan Semiconductor Manufacturing Company) 65-nm CMOS technology show that our design achieves savings of 64.21% in area, 16.67% in delay and 65.08% in power compared to the existing methods. Moreover, implementation results on an FPGA (Field-Programmable Gate Array) platform (XC7Z020-CLG400) show that the proposed design reduces the number of LUTs by 29.38%, delay by 28.57% and power consumption by 53.47%.

Method of Local Linear Approximation in the Theory of Nonlinear Impulsive Systems

Method of Local Linear Approximation in the Theory of Nonlinear Impulsive Systems