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Assemble-to-order approaches deal with randomness in demand for end items by producing components under uncertainty, but assembling them only after demand is observed. Such planning problems can be tackled by stochastic programming, but true multistage models are computationally challenging and only a few studies apply them to production planning. Solutions based on two-stage models are often short-sighted and unable to effectively deal with non-stationary demand. A further complication may be the scarcity of available data, especially in the case of correlated and seasonal demand. In this paper, we compare different scenario tree structures. In particular, we enrich a two-stage formulation by introducing a piecewise linear approximation of the value of the terminal inventory, to mitigate the two-stage myopic behaviour. We compare the out-of-sample performance of the resulting models by rolling horizon simulations, within a data-driven setting, characterised by seasonality, bimodality, and correlations in the distribution of end item demand. Computational experiments suggest the potential benefit of adding a terminal value function and illustrate interesting patterns arising from demand correlations and the level of available capacity. The proposed approach can provide support to typical MRP/ERP systems, when a two-level approach is pursued, based on master production and final assembly scheduling. [ABSTRACT FROM AUTHOR]

Fully leveraging the regulatory role of cascade hydropower in river basins and realizing complementary joint power generation between cascade hydropower and photovoltaic (PV) systems is a crucial approach to promoting the consumption of clean energy. Given the uncertainty of PV outputs, this paper introduces a short-term scheduling model for cascade hydropower–PV systems. The model aims to maximize electricity consumption by considering individual units, hydropower plant constraints, unit constraints, and grid constraints. By allocating loads among hydropower plants and periods, it optimizes hydropower's dual roles, supporting grid power supplies and coordinating with PVs, thus boosting the overall system consumption. In terms of model solution, linearization methods and modeling techniques such as piecewise linear approximation, the introduction of 0–1 integer variables, and the discretization of generation headwater are employed to handle the nonlinear constraints in the original model, transforming it into a mixed-integer linear programming problem. Finally, taking a complementary system constructed by 15 units of 4 hydropower stations and 2 photovoltaic groups in a cascade in a river basin in Southwest China as an example, the results show that through the complementary coordination of cascade hydropower and photovoltaic power, under the same grid constraints, the expected value of the power consumption of the complementary system in the model of this paper increased by 863.2 MW·h, among which the power consumption of photovoltaic group 1 increased by 1035.7 MW·h, and the power consumption of photovoltaic group 2 decreased by 172.5 MW·h. [ABSTRACT FROM AUTHOR]

In the context of global climate change, the multi-city interconnected power system offers the potential for low-carbon and efficient energy utilization, addressing the challenge of ensuring safety, stability, and reduced carbon emissions while meeting diverse demands. This study proposes a security region-based method to evaluate the power supply guarantee capability of such systems, employing a collaborative support framework to characterize the low-carbon feasible space of each city system. A multi-dimensional piecewise linear approximation method and model transformation were applied to construct a scheduling and transformation model for the provincial power grid. The proposed approach enhances power supply security, achieving a 7.21% reduction in system operating costs and a 24.7% decrease in carbon emissions. These findings highlight the effectiveness of the security region approach in balancing safety, efficiency, and environmental objectives, providing a scalable solution for interconnected power grids. [ABSTRACT FROM AUTHOR]

Today, huge amounts of time series data are sensed continuously by AIoT devices, transmitted to edge nodes, and to data centers. It costs a lot of energy to transmit these data, store them, and process them. Data compression technologies are commonly used to reduce the data size and thus save energy. When a certain level of data accuracy is sacrificed, lossy compression technologies can achieve better compression ratios. However, different applications may have different requirements for data accuracy. Instead of keeping multiple compressed versions of a time series w.r.t. different error bounds, HIRE hierarchically maintains a tree, where the root records a constant function to approximate the whole time series, and each other node records a constant function to approximate a part of the residual function of its parent for a particular time period. To retrieve data w.r.t. a specific error bound, it traverses the tree from the root down to certain levels according to the requested error bound and aggregates the constant functions on the visited nodes to generate a new bounded error compressed version dynamically. However, the number of nodes to be visited is unknown before the tree traversal completes, and thus the data size of the new version. In this paper, a time series is progressively decomposed into multiple piecewise linear functions. The first function is an approximation of the original time series w.r.t. the largest error bound. The second function is an approximation of the residual function between the original time series and the first function w.r.t. the second largest error bound, and so forth. The sum of the first, second, ..., and m-th functions is an approximation of the original time series w.r.t. the m-th error bound. For each iteration, Swing-RR is used to generate a Bounded Error Piecewise Linear Approximation (BEPLA). Resolution Reduction (RR) plays an important role. Eight real-world datasets are used to evaluate the proposed method. For each dataset, approximations w.r.t. three typical error bounds, 5%, 1%, and 0.5%, are requested. Three BEPLAs are generated accordingly, which can be summed up to form three approximations w.r.t. the three error bounds. For all datasets, the total data size of the three BEPLAs is almost the same with the size used to store just one version w.r.t. the smallest error bound and significantly smaller than the size used to keep three independent versions. The experiment result shows that the proposed method, referred to as PBEPLA-RR, can achieve very good compression ratios and provide multiple approximations w.r.t. different error bounds. [ABSTRACT FROM AUTHOR]

The article discusses the use of blood oxygen level-dependent (BOLD) magnetic resonance (MR) sequences to measure oxygen saturation in great vessels, presenting accuracy, challenges, and potential solutions. A study involving 60 patients with congenital heart disease showed significant correlation between BOLD measurements and saturations obtained during cardiac catheterization. However, flow disturbances remain a significant source of bias in BOLD measurements, requiring individually adapted trigger intervals for improved accuracy. The study highlights the potential of noninvasive assessment of oxygen saturation in great vessels using MR BOLD sequences, despite existing challenges. [Extracted from the article]

We introduce a novel formulation for the evolution of parametric curves by anisotropic curve shortening flow in |${{\mathbb{R}}}^{d}$|⁠ , |$d\geq 2$|⁠. The reformulation hinges on a suitable manipulation of the parameterization's tangential velocity, leading to a strictly parabolic differential equation. Moreover, the derived equation is in divergence form, giving rise to a natural variational numerical method. For a fully discrete finite element approximation based on piecewise linear elements we prove optimal error estimates. Numerical simulations confirm the theoretical results and demonstrate the practicality of the method. [ABSTRACT FROM AUTHOR]

Ahmad et al. (see [1]) presented a piecewise Lagrange interpolation method for solving tumor-immune interaction models with fractal fractional operators using a power law and exponential kernel. We suggest a convergence anal-ysis for this method and we obtain the order of convergence. Of course, there are some mistakes in this numerical method that were corrected. Furthermore, Numerical illustrations are demonstrated to show the effectiveness of the corrected numerical method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The use of electronic systems is widespread in various metrology systems related to the monitoring of acoustic noise in urban or industrial environments. A method for analyzing equipments intended for acousticlocation and acoustic measuring devices and systems (DS) based on structural approximation is proposed. The method involves performing a structural approximation of the devices used based on the developed generalized circuit. In this particular instance, the analysis is conducted utilizing the apparatus of continuous piecewise-linear functions and transfer functions of the signal converter. Their utilization facilitates the investigation of devices (systems) of arbitrary structure, characterized by random nonlinear characteristics and a variety of inertial components such as blocks and units. The study of specific devices is based on the finite expressions of the transfer functions of a generalized signal converter connection. Several levels of disclosure of the converter connection are considered. Using the aforementioned methodology, it is feasible to synthesize acousto-electric devices (systems) at both the analytical and structural levels. As nonlinear differential equations of random order that describe the response of devices and systems can be reduced to linear equations of the first order in the general case, the inverse solution (synthesis) is not a complex task, both at the analytical and programmatic levels. [ABSTRACT FROM AUTHOR]

This article develops a novel decision-oriented framework that strategically deconstructs systems resilience in a way that focuses on systems' design, capabilities, and management. The framework helps evaluate and compare how system design choices impact system resilience. First, we propose a resilience score based on a piecewise linear approximation to a resilience curve. Using multicriteria decision analysis principles, we score system design alternatives in terms of system-specific capabilities. We estimate the relevance of these capabilities to resilience curve parameters associated with resilience phases. Finally, we interpret the derivatives of resilience with respect to the curve parameter values as the leverage of these parameters. Using multiple levels of weighted sums of the scores, we calculate the first order impact of system design choices first on a proxy for the generic resilience parameters and then on resilience, which allows situational characteristics to be incorporated in their natural terminology while mapping their impact on resilience with a traceable logic. We illustrate the approach by using existing materials to develop an example comparing engineered designs for minimizing post-wildfire flood impacts. [ABSTRACT FROM AUTHOR]

The article considers the problem of estimating the error in calculating the gradient of functions of Sobolev classes for piecewise linear approximation on triangulations. Traditionally, problems of this kind are considered for continuously differentiable functions. In this case, the corresponding estimates reflect both the smoothness class of the functions and the quality of the triangulation simplexes. However, in problems of substantiating the existence of a solution to a variational problem in the nonlinear theory of elasticity, conditions arise for permissible deformations in terms of generalized derivatives. Therefore, for the numerical solution of these problems, conditions are required that provide the necessary approximation of the derivatives of continuous functions of the Sobolev classes. In this article, an integral estimate of the indicated error for continuously differentiable functions is obtained in terms of the norms of the corresponding spaces for functions that reflect, on the one hand, the quality of triangulation of the polygonal region, and on the other hand, the class of functions with generalized derivatives. The latter is expressed in terms of the majorant of the modulus of continuity of the gradient. To obtain the final estimate, the possibility of passing to the limit using the norm of the Sobolev space is proven.

We consider a hypersingular integral equation on a convex bounded set on the plane with an integral understood in the sense of Hadamard finite part. In particular, equations of this type arise when solving the Neumann boundary value problem for the Laplace and Helmholtz equations on a flat screen in the case where the solution is sought in the form of a double layer potential. To numerically solve the equation, we use a numerical scheme based on piecewise linear approximation of the unknown function on a triangular conformal grid and the collocation method. The uniform convergence of numerical solutions to an exact solution on a grid when the maximum cell diameter tends to zero has been proven. [ABSTRACT FROM AUTHOR]

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This document is a compilation of articles from the journal "Operations Research" that cover a wide range of topics related to production management, inventory systems, financial networks, audit strategies, online markets, volunteer engagement, and data-driven optimization. The articles provide valuable insights and findings that can enhance efficiency and decision-making in these fields. The research presented in these articles is relevant for practitioners and researchers conducting research in these areas. The articles offer unique perspectives and approaches to solving complex problems in different industries, aiming to provide practical solutions and improve decision-making processes. [Extracted from the article]

Utility Preference Robust Optimization with Moment-Type Information Structure In some decision-making problems, information on the true utility function of the decision maker may be incomplete, which may bring potential modeling risk. In "Utility Preference Robust Optimization with Moment-Type Information Structure," Guo, Xu, and Zhang propose a maximin utility preference robust optimization model where information about the DM's preference is constructed by moment-type conditions. The authors propose a piecewise linear approximation approach to tackle the maximin problem, reformulate the approximate problem as a single mixed integer linear program, and derive error bounds for the approximate ambiguity set, the optimal value, and the optimal solutions. To examine the performance of the model and the computational schemes, they carry out extensive numerical tests and demonstrate the effectiveness of the model and efficiency of the computational methods. Utility preference robust optimization (PRO) models have recently been proposed to deal with decision-making problems where the decision-maker's true utility function is unknown and the optimal decision is based on the worst-case utility function in an ambiguity set of utility functions. In this paper, we consider the case where the ambiguity set is constructed using some moment-type conditions. We propose piecewise linear approximation of the utility functions in the ambiguity set. The approximate maximin problem can be solved directly by derivative-free methods when the utility functions are nonconcave. Alternatively, we can reformulate the approximate problem as a single mixed integer linear program (MILP) and solve the MILP by existing solvers such as Gurobi. To justify the approximation scheme, we derive error bounds for the approximate ambiguity set, the optimal value and optimal solutions of the approximate maximin problem. To address the data perturbation/contamination issues arising from the construction of the ambiguity set, we derive some stability results which quantify the variation of the ambiguity set against perturbations in the elicitation data and its propagation to the optimal value and optimal solutions of the PRO model. Moreover, we extend the PRO models to allow some inconsistencies in the process of eliciting the decision-maker's preferences. Finally, we carry out numerical tests to evaluate the performances of the proposed numerical schemes and show that the computational schemes work fairly efficiently, the PRO model is resilient against small perturbations in data (with respect to both exogenous uncertainty data and preference elicitation data), and there is a potential to improve the efficiency of the preference elicitation by incorporating an optimal selection strategy. Funding: This project is supported by Hong Kong RGC [Grant 14500620] and The Chinese University of Hong Kong start-up grant. The research of S. Guo is supported by the National Key R&D Program of China [Grant 2022YFA1004000] and the Natural Science Foundation of China [Grant 12271077]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2023.2464. [ABSTRACT FROM AUTHOR]

AbstractA simple yet effective way of modeling survival data with cure fraction is by considering Box-Cox transformation cure model (BCTM) that unifies mixture and promotion time cure models. In this article, we numerically study the statistical properties of the BCTM when applied to interval censored data. Time-to-events associated with susceptible subjects are modeled through proportional hazards structure that allows for non-homogeneity across subjects, where the baseline hazard function is estimated by distribution-free piecewise linear function with varied degrees of non-parametricity. Due to missing cured statuses for right censored subjects, maximum likelihood estimates of model parameters are obtained by developing an expectation-maximization (EM) algorithm. Under the EM framework, the conditional expectation of the complete data log-likelihood function is maximized by considering all parameters (including the Box-Cox transformation parameter α) simultaneously, in contrast to conventional profile-likelihood technique of estimating α. The robustness and accuracy of the model and estimation method are established through a detailed simulation study under various parameter settings, and an analysis of real-life data obtained from a smoking cessation study. [ABSTRACT FROM AUTHOR]

In the studies of unit commitment or optimal power flow, to formulate a mixed-integer linear programming model that can be efficiently solved with commercial solvers, it is necessary to approximate the quadratic cost curves of thermal units as piecewise linear (PWL) functions. The conventional approach involves evenly spaced piecewise linear (ES-PWL) interpolation, which often results in relatively large approximation errors. In order to reduce the error, this paper proposes a more accurate PWL method for approximating the quadratic cost functions of thermal units. The method employs a linear least-squares fit instead of linear interpolation within each subinterval and introduces a one-terminal-constraint approach to ensure the continuity of the piecewise function. Subsequently, a straightforward equation is derived, applicable to the widely used ES-PWL interpolation, with the potential to enhance the accuracy of the approximation. Mathematical verification attests that the proposed method substantially diminishes the squared 2-norm error, less than 37.5% of the error associated with ES-PWL interpolation. Subsequent numerical investigations are carried out on a 10-unit system, the IEEE RTS-79, and a real industrial system. The findings validate that all the approximation errors of the proposed method are within 37.5% of the errors associated with the ES-PWL interpolation, meaning that a unit commitment solution that closely approximates the outcome of the quadratic function is obtained. The computational time is also acceptable. [ABSTRACT FROM AUTHOR]

The main issue in the present article is to investigate how to solve a mixed integer fractional signomial geometric programing problem (MIFSGP). In the first step to achieving this idea, we must convert a fractional signomial programing problem into a non-fractional problem via a simple conversion technique. Then, a convex relaxation with a new modified piecewise linear approximation with integer break points as a pre-solve method is used to reach an integer global optimum solution. A few numerical examples are included to illustrate the advantages of the proposed method [ABSTRACT FROM AUTHOR]

Assessment of the current state of the near-surface part of the geological environment and understanding of its layered structure play an important role in various scientific and applied fields. The presented work is devoted to the application of phasometric modifications of geoelectric control methods to solve the problem of the detailed complex study of the underground layers of the environment in the process of drilling operations with the use of special equipment. These studies are based on the analysis of variations in phase parameters and characteristics of an artificially excited multiphase electric field to assess poorly distinguishable details and changes in the layered structure of the medium. The proposed method has increased accuracy, sensitivity and noise proofness of measurements, which allows for extracting detailed information about the heterogeneity, composition and stratification of underground geological formations not only in the zone where the drill makes contact with the medium, but also in the entire control zone. This paper considers practical mathematical models of phase images for basic scenarios of drill penetration between the layers of the near-surface part of the geological medium with different characteristics, obtained by means of approximation apparatus based on continuous piecewise linear functions, and also suggests the use of modern machine learning methods for intelligent analysis of its structure. Studying the phase shifts in electrical signals during drilling highlights their value for understanding the dynamics of soil response to the process. The observed signal changes during the drilling cycle reveal in detail the heterogeneity in soil structure and its response to changes caused by drilling. The stability of phase shifts at the last stages of the process indicates a quasi-equilibrium state. The results make a significant contribution to geotechnical science by offering an improved approach to monitoring a layered structure without the need for deep drilling. [ABSTRACT FROM AUTHOR]

Introduction The survivable Capacitated Networks Design Problem (SCNDP for short) is one of the most essential issues in telecommunication and transportation networks. A survivable network is a network that is designed to remain operational in the event of a component(s) failure(s) (cable cuts, electronic failures on switching centers, and so forth). In SCNDP, researchers usually consider survivability in two different ways diversification and reservation. Diversification consists of dividing the demand of source-sink node pairs into two or more node-disjoint (or arc-disjoint) paths, and in reservation after the failure of a component(s) of the network, part of the demand for node pairs can still be satisfied by rerouting. To implement reservation, the links on the network ought to have enough capacity to support the new flows after the rerouting has been made. Therefore, in this paper, we first present one model for the problem of survivable capacitated network design based on the reservation strategy. In many real-world applications, the observed values are often uncertain, for example random, fuzzy, etc. Therefore, we consider the demand vector (the right-hand side values) randomly and then by using joint chance-constrained and probability concepts, obtain the corresponding deterministic model. Then, we propose an approximation optimization approach and use piecewise tangent approximation and piecewise linear methods to obtain its lower and upper bounds, respectively. Finally, computational results show the efficiency of the proposed model and approximation methods for relatively large-scale networks. Material and Methods In many real-world applications, the values of parameters are often uncertain. There are several methods available to tackle this uncertainty, including: 1. Fuzzy programming, 2. Stochastic programming based on scenarios, 3. Robust optimization, 4. Probabilistic programming. In this paper, we will use the probabilistic programming (joint chance-constrained) method to obtain the corresponding deterministic model according to the type of the initial model and assume an independent non-deterministic demand vector. The resulting model is the mixed integer non-convex non-linear model which we will use iterative and approximate piecewise tangent and piecewise linear methods to solve it. Results and discussion In this article, we first presented a model for the survivable capacitated network design problem, and then by considering the demand vector as nondeterministic and assuming the independence of random variables, we presented the corresponding deterministic model by using joint-chance constrained and probability concepts. Because the resulting model is the mixed integer non-convex non-linear model, two approximations were used to solve the problem. The numerical results obtained from GAMS software and the CPLEX solver were reported for medium to large-scale networks. Next, we will examine the initial model under the assumption of dependence between random variables. Conclusion The following conclusions were drawn from this research. • This paper develops a cost-capacity efficient model for the SCNDP with different capacity levels and piecewise linear convex objective function based on the reservation strategy. • We suppose the demand vector can be reported as random variables in the case of independence. To deal with uncertainty, we focus on the joint chance-constrained programming method. • This paper develops a mixed integer non-convex non-linear programming model and finds a lower and upper approximation, using the piecewise tangent approximation and piecewise linear approximation, respectively. [ABSTRACT FROM AUTHOR]

The investigation of fatigue behavior typically involves time‐consuming tests, leading some researchers to explore methodologies based on self‐heating tests to reduce the process. For composite materials, the conventional approach involves piecewise linear approximations of the self‐heating curve and the stress transition between the first and second regimes is arbitrarily associated with a fatigue lifetime equal to 106 cycles. This paper proposes a novel methodology to address these simplifications. First, a non‐linear viscoelastic model is used to describe the self‐heating curve. Based on the mechanisms established in the literature, a link is proposed between the dissipation and the fatigue limit. The load leading to a significant contribution of non‐linear mechanisms is associated with an infinite life time. It allows the identification of an S– N curve and prediction of fatigue behavior through a minimal number of tests. The comparison with fatigue results is satisfactory. Highlights: A link is proposed between dissipation and fatigue.Modeling of the dissipation in laminated composites subjected to cyclic loadings.A criterion is proposed to identify the fatigue limit based on the dissipation.A S– N curve is identified and extrapolated up to high cycles fatigue. [ABSTRACT FROM AUTHOR]

New necessary and sufficient stability tests for neutral‐type linear time delay systems are presented. They are based on functionals with prescribed derivative depending on the delay Lyapunov matrix and recent stability/instability theorems. A piecewise linear approximation of the initial function argument in the functional is employed. As a result, the functional is approximated via a quadratic form whose matrix provides stability criteria. This matrix involves the integrals based on the delay Lyapunov matrix which are handled via an efficient computational procedure. The main feature of these tests is that they are verified in a finite number of operations, which is achieved through rigorous bounding of the approximation error on a specific class of functions. Some examples which validate the obtained results are presented and discussed. [ABSTRACT FROM AUTHOR]

Due to the structural breaks in time series, estimated current trend of product sales differs between the case where data for the entire span are used and the case where only the most recent data are used. The purpose of this study is to establish the piecewise linear approximation (PLA) as a trend analysis method that accounts for the structural breaks. PLA uses the complete data to simultaneously estimate the breakpoints and the continuously connected trends, immediately before and after the break. Thus, PLA not only ensures the ease of interpretation of the results, but also eliminates the probability of using discretion by uniquely determining the current trend, making the estimated result reliable. The case study demonstrates the proposition that, several products' sales trends and the necessity of determining an appropriate time span for data analysis, underwent changes at least once. The method's validity is demonstrated by showing the changes of the sales trends immediately after analyzed store's renovation. Data collection from the time period immediately prior to a structural break can help identify the factors changing the product sales. [ABSTRACT FROM AUTHOR]

We revisit an approximate stochastic dynamic programming method that we proposed earlier for the optimization of multireservoir problems. The method exploited the convexity properties of the value function to sample the reservoir level space based on the local curvature of the value function, which is estimated by the difference between a lower and an upper bounds (error bound). Unlike the previous approach in which the state space is exhaustively partitioned into full dimensional simplices whose vertices formed a discrete grid over which the value function was approximated, here we propose instead a new randomized approach for selecting the grid points from a small number of randomly sampled simplices from which an error bound is estimated. Results of numerical experiments on three literature test problems and simulated midterm reservoir optimization problems illustrate the advantages of the randomized approach which can solve models of higher dimensions than with the exhaustive approach. [ABSTRACT FROM AUTHOR]

This article examines the impact of import constraints on global supply chains and inflation during the post-pandemic economic recovery. The authors argue that production capacity constraints in the supply chain have influenced US inflation. They specifically focus on import constraints, which limit the quantity of imports at a given time, and suggest that these constraints may be caused by shipping or import logistics capacity. The analysis explores the effects of import constraints on prices and trade costs, and indicates that import constraints may not have played a significant role in explaining inflation based on post-pandemic data. Additionally, the article presents a model that considers monopolistic competition, import constraints, and trade intermediation, and explores how import prices are determined under different scenarios. The conclusion suggests that import constraints alone do not necessarily result in higher import price inflation, and proposes that other factors may be responsible for changes in import prices and quantities. [Extracted from the article]

This paper addresses the stability of plane Couette flow in the presence of strong density and viscosity stratifications. It demonstrates the existence of a generalised inflection point that satisfies the generalised Fjørtoft criterion of instability when a minimum of kinematic viscosity is present in the base flow. The characteristic scales associated with this minimum are identified as the primary controlling parameters of the associated instability, regardless of the type of stratification. To support this finding, analytical stability models are derived in the long-wave approximation using piecewise linear base flows. Numerical stability calculations are carried out to validate these models and to provide further information on the production of disturbance vorticity. All instabilities are interpreted as arising from the interaction between two vorticity waves. Depending on the type of stratification, these two waves are produced by different physical mechanisms. When both strong density and viscosity stratifications are present, we show that they result from the concurrent action of shear and inertial baroclinic effects. The stability models developed for simple fluid models ultimately shed light on a recently observed unstable mode in supercritical fluids (Ren et al. , J. Fluid Mech. , vol. 871, 2019, pp. 831–864), providing a quantitative prediction of the stability diagram and identifying the dominant mechanisms at play. Furthermore, our study suggests that the minimum of kinematic viscosity reached at the Widom line in these fluids is the leading cause of their instability. The existence of similar instabilities in different fluids and flows (e.g. miscible fluids) is finally discussed. [ABSTRACT FROM AUTHOR]

This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products where both variables are bounded and extend the well-known MIP relaxation normalized multiparametric disaggregation technique(NMDT), applying a sophisticated discretization to both variables. We refer to this approach as doubly discretized normalized multiparametric disaggregation technique (D-NMDT). In a comprehensive theoretical analysis, we underline the theoretical advantages of the enhanced method D-NMDT compared to NMDT. Furthermore, we perform a broad computational study to demonstrate its effectiveness in terms of producing tight dual bounds for MIQCQPs. Finally, we compare D-NMDT to the separable MIP relaxations from Part I and a state-of-the-art MIQCQP solver. [ABSTRACT FROM AUTHOR]

We consider the constrained piecewise Levenberg--Marquardt method globalized by linesearch, and apply it to "min" reformulations of the optimality systems for generalized Nash equilibrium problems. Numerical comparison of the performance of this method with some relevant existing alternatives is provided. [ABSTRACT FROM AUTHOR]

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. Originality / value: 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.

WPREs (wind power ramp events) are one of the most critical factors affecting the security and protection of the electrical system. Accurate ramp event detection may help power systems better manage extreme events and reduce financial damage. In this study, We present an improved piecewise linear approximation for recognizing wind ramps in Kanyakumari district. In practise, wind power ramps can be decreased by properly managing and dispatching flexible reserve and associated services. This necessitates the use of proper ramp detection techniques as well as precise ramp forecasts. The method’s plan to break down wind power signal into increasing with increasing ramps, making ramp identification easier and ensuring that all conceivable ramps of varying lengths are identified. Using observed wind power data, the ramp detection method is used to assess the performance of an energy wind farm. The results reveal that identifying wind power ramps using the segmentation method is equivalent to optical ramp identification.

Stationary operation of a thermoelectric system is often not economical due to the impossibility of soft adjustment of the microclimate. The aspect makes relevant the research of the transient modes of Peltier elements and thermoelectric systems built on their basis. The study of the dynamic properties of thermoelectric devices and systems with high accuracy requires the use of complex high-order models, which makes it difficult to obtain analytical solutions. Using the spectral approach and piecewise linear approximation, analytical formulae of the transient modes of Peltier thermoelectric elements for various deviations of control currents are obtained. The calculated relations of piecewise linear approximating functions, spectral densities and time forms of input and output parameters of the model under study are presented. Time diagrams of the temperature response of a particular Peltier element in linear and nonlinear modes are constructed, calculated for the sinusoidal deviation of the control current from the stationary value. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain convergence in mean in the uniform topology of piecewise linear approximations of stochastic differential equations (SDEs) with C1 drift and C2 diffusion coefficients with uniformly bounded derivatives. Convergence analyses for such Wong-Zakai approximations most often assume that the coefficients of the SDE are uniformly bounded. Almost sure convergence in the unbounded case can be obtained using now standard rough path techniques, although Lq convergence appears yet to be established and is of importance for several applications involving Monte-Carlo approximations. We consider L2 convergence in the unbounded case using a combination of traditional stochastic analysis and rough path techniques. We expect our proof technique extend to more general piecewise smooth approximations. [ABSTRACT FROM AUTHOR]

Cure models are widely popular in modeling time-to-event data that are characterized by cure fraction owing to long-term survivors. Mixture cure models are perhaps the most studied cure models in the literature. In this article, however, we consider a competing risks scenario where the number of competing causes is modeled by flexible Conway-Maxwell (COM) Poisson distribution, and the lifetimes corresponding to the competing causes are assumed to be independently distributed following proportional hazards model. The baseline hazard function is modeled by a piecewise linear function, and hence, estimated non parametrically. Probability of obtaining zero competing causes is used to estimate the cure rate. Collectively, the resultant cure model is exceedingly general and flexible. The estimation of the parameters is carried out using maximum likelihood (ML) method by implementing the expectation-maximization (EM) algorithm, except for the dispersion parameter of the COM-Poisson distribution, which is estimated by the profile likelihood method. The performance of the model is tested under various settings of censoring rate, sample size and mean lifetime. Discrimination of models is performed and carried out with likelihood-based and information-based criteria. Performance of the proposed model is further illustrated using a real-world data on cutaneous melanoma. [ABSTRACT FROM AUTHOR]

We are interested in creating statistical methods to provide informative summaries of random fields through the geometry of their excursion sets. To this end, we introduce an estimator for the length of the perimeter of excursion sets of random fields on ℝ2$$ {\mathbb{R}}^2 $$ observed over regular square tilings. The proposed estimator acts on the empirically accessible binary digital images of the excursion regions and computes the length of a piecewise linear approximation of the excursion boundary. The estimator is shown to be consistent as the pixel size decreases, without the need of any normalization constant, and with neither assumption of Gaussianity nor isotropy imposed on the underlying random field. In this general framework, even when the domain grows to cover ℝ2$$ {\mathbb{R}}^2 $$, the estimation error is shown to be of smaller order than the side length of the domain. For affine, strongly mixing random fields, this translates to a multivariate Central Limit Theorem for our estimator when multiple levels are considered simultaneously. Finally, we conduct several numerical studies to investigate statistical properties of the proposed estimator in the finite‐sample data setting. [ABSTRACT FROM AUTHOR]

This paper studies a fusion of concepts from stochastic programming and non-parametric statistical learning in which data is available in the form of covariates interpreted as predictors and responses. Such models are designed to impart greater agility, allowing decisions under uncertainty to adapt to the knowledge of predictors (leading indicators). This paper studies two classes of methods for such joint prediction-optimization models. One of the methods may be classified as a first-order method, whereas the other studies piecewise linear approximations. Both of these methods are based on coupling non-parametric estimation for predictive purposes, and optimization for decision-making within one unified framework. In addition, our study incorporates several non-parametric estimation schemes, including k nearest neighbors (kNN) and other standard kernel estimators. Our computational results demonstrate that the new algorithms proposed in this paper outperform traditional approaches which were not designed for streaming data applications requiring simultaneous estimation and optimization as important design features for such algorithms. For instance, coupling kNN with Stochastic Decomposition (SD) turns out to be over 40 times faster than an online version of Benders Decomposition while finding decisions of similar quality. Such computational results motivate a paradigm shift in optimization algorithms that are intended for modern streaming applications. [ABSTRACT FROM AUTHOR]

Approximating Bézier curve by polygon is a traditional technique in computer-aided geometric design, and there are several methods for constructing such polygons. In this paper, we propose to approximate Bézier curve by the least square polygon (LSP). LSP was derived by least square fitting which minimizes the integral of approximating errors. We provide a closed formula for the vertices of LSP. Because of its optimization method, LSP has lower approximation errors than existing approximating polygons. This observation is verified by many numerical examples we tested and several typical examples are included in this paper. [ABSTRACT FROM AUTHOR]

Left truncated right censored (LTRC) data arise quite commonly from survival studies. In this article, a model based on piecewise linear approximation is proposed for the analysis of LTRC data with covariates. Specifically, the model involves a piecewise linear approximation for the cumulative baseline hazard function of the proportional hazards model. The principal advantage of the proposed model is that it does not depend on restrictive parametric assumptions while being flexible and data‐driven. Likelihood inference for the model is developed. Through detailed simulation studies, the robustness property of the model is studied by fitting it to LTRC data generated from different processes covering a wide range of lifetime distributions. A sensitivity analysis is also carried out by fitting the model to LTRC data generated from a process with a piecewise constant baseline hazard. It is observed that the performance of the model is quite satisfactory in all those cases. Analyses of two real LTRC datasets by using the model are provided as illustrative examples. Applications of the model in some practical prediction issues are discussed. In summary, the proposed model provides a comprehensive and flexible approach to model a general structure for LTRC lifetime data. [ABSTRACT FROM AUTHOR]

A novel algorithm is proposed for quantitative comparisons between compact surfaces embedded in the three-dimensional Euclidian space. The key idea is to identify those objects with the associated surface measures and compute a weak distance between them using the Fourier transform on the ambient space. In particular, the inhomogeneous Sobolev norm of negative order for a difference between two surface measures is evaluated via the Plancherel theorem, which amounts to approximating a weighted integral norm of smooth data on the frequency space. This approach allows several advantages, including high accuracy due to fast-converging numerical quadrature rules, acceleration by the nonuniform fast Fourier transform, and parallelization on many-core processors. In numerical experiments, the 2-sphere, which is an example whose Fourier transform is explicitly known, is compared with its icosahedral discretization, and it is observed that the piecewise linear approximations converge to the smooth object at the quadratic rate up to small truncation. [ABSTRACT FROM AUTHOR]

Dynamic programming (DP) is frequently used to obtain the optimal solution to the hybrid electric vehicle (HEV) energy management. The trade-off between the accuracy and the computational effort is the biggest problem for the DP method. The closed-form solution to the DP is proposed to solve this problem. Firstly, the affine linear model of the engine fuel rate is obtained based on engine test data. The piecewise linear approximation of the motor power demand is obtained considering the different energy flows in the charging and discharging stages of the battery. Then, the second-order Taylor expansion for the cost matrix at each time and state grid point is introduced to get the closed-form solution of the optimal torque split. The results show that this method can greatly reduce the computing burden by 93% while ensuring near-optimal fuel economy compared with the conventional DP method. [ABSTRACT FROM AUTHOR]

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. Originality / value: 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. [ABSTRACT FROM AUTHOR]

In this paper, the problem of membership function‐dependent model predictive control (MFD‐MPC) of interval type‐2 Takagi–Sugeno (IT2 T‐S) fuzzy system is investigated. An online MFD‐MPC optimization problem is formulated to minimize an infinite horizon objective function subject to hard constraints on control input and system state. By using the variable dimension expansion method and dividing the operation domain of independent variables into several subdomains, a subregion‐based state feedback model predictive controller that offers more design flexibility is designed to stabilize the open‐loop fuzzy system. Based on descriptor system theory, the variable mismatching phenomenon between MFs and the coupling between plant, controller, and Lyapunov matrix are eliminated. Then, using the piecewise linear approximation technology, MFD sufficient conditions of low conservatism on guaranteeing recursive feasibility and the stability of IT2 closed‐loop fuzzy system are deduced by tightening terminal constraint set. Finally, a numerical example is provided to further explain the advance of the proposed method. [ABSTRACT FROM AUTHOR]

The functioning of a thermoelectric system in a stationary mode is often inefficient because it does not allow flexible control of the temperature regime. The design of thermoelectric devices and systems in transient modes requires identifying their dynamic models, first of all, the control object – the Peltier thermoelectric module. As a rule, well-known identification techniques involve calculating the parameters of a fractional-rational transfer function (or, equivalently, an autoregressive model) of the object of control. At the same time, the increase in the accuracy of identification requirements is associated with significant computational costs. The proposed identification technique requires the determination of the time dependencies of the control current and temperature deviation, the calculation of their spectra based on piecewise linear approximation, and the calculation of the transfer coefficient as the ratio of the spectra of the output and input signals. The calculated relations of piecewise linear approximating functions, spectral densities, and time forms of input and output parameters of the model under study are presented. The amplitude and phase frequency response of the Peltier module are calculated. The low RMS error in the identification of the amplitude-frequency characteristic and phase-frequency characteristic showed the effectiveness of the proposed identification technique. [ABSTRACT FROM AUTHOR]

Multi-energy systems (MESs) combining different energy carriers like electricity and heat allow for more efficient and sustainable energy solutions. However, optimizing the design and operation of MESs is challenging due to non-linearities in the mathematical models used, especially the performance curves of technologies like combined heat and power units. Unlike similar work from the literature, this paper proposes an improved piecewise linearization method to efficiently handle the non-linearities, models an MES as a multi-objective mixed-integer linear program (MILP), and solves the optimization problem over a year with hourly resolution to enable detailed operation and faithful system design. The method uses fewer linear pieces to approximate non-linear functions compared to a standard technique, resulting in lower complexity while preserving accuracy. The MES design and operation problem maximizes cost reduction and the rate of renewable energy sources. A case study on an MES with electricity and heat over one year with hourly resolution demonstrates the effectiveness of the new method. It allows for solving a long-term MES optimization problem in reasonable computation times. [ABSTRACT FROM AUTHOR]

WPREs (wind power ramp events) are one of the most critical factors affecting the security and protection of the electrical system. Accurate ramp event detection may help power systems better manage extreme events and reduce financial damage. In this study, We present an improved piecewise linear approximation for recognizing wind ramps in Kanyakumari district. In practise, wind power ramps can be decreased by properly managing and dispatching flexible reserve and associated services. This necessitates the use of proper ramp detection techniques as well as precise ramp forecasts. The method's plan to break down wind power signal into increasing with increasing ramps, making ramp identification easier and ensuring that all conceivable ramps of varying lengths are identified. Using observed wind power data, the ramp detection method is used to assess the performance of an energy wind farm. The results reveal that identifying wind power ramps using the segmentation method is equivalent to optical ramp identification. [ABSTRACT FROM AUTHOR]

We investigate the optimal piecewise linear interpolation of the bivariate product xy over rectangular domains. More precisely, our aim is to minimize the number of simplices in the triangulation underlying the interpolation, while respecting a prescribed approximation error. First, we show how to construct optimal triangulations consisting of up to five simplices. Using these as building blocks, we construct a triangulation scheme called crossing swords that requires at most - times the number of simplices in any optimal triangulation. In other words, we derive an approximation algorithm for the optimal triangulation problem. We also show that crossing swords yields optimal triangulations in the case that each simplex has at least one axis-parallel edge. Furthermore, we present approximation guarantees for other well-known triangulation schemes, namely for the red refinement and longest-edge bisection strategies as well as for a generalized version of K1-triangulations. Thereby, we are able to show that our novel approach dominates previous triangulation schemes from the literature, which is underlined by illustrative numerical examples. [ABSTRACT FROM AUTHOR]