Optimal Order Research Articles

Quickly Finding the Semantically Optimal Presentation Order for a Set of Text Artifacts

This study considers how to quickly find the order in which to present a set of text artifacts on mobile apps or websites such that those artifacts are maximally semantically separated. Semantic separation is desirable because it ensures that users experience as much novelty as possible from one item to the next, thereby improving user attention and engagement. Since an exhaustive search of all possible sequences of text items becomes increasingly infeasible as the length of the sequence grows, a new algorithm is proposed to quickly find the semantically optimal presentation order for a set of text artifacts. The performance of the proposed algorithm is evaluated using an extensive set of experiments involving three different types of text artifacts, seven different sequence lengths, and more than 600 experimental trials. The results demonstrate that the proposed algorithm can select statistically optimal sequences of text artifacts extremely quickly, regardless of the type of text artifacts being used as input or the length of the sequence. App and website developers who are seeking to hold users’ attention and improve user engagement may therefore find the proposed algorithm very attractive in comparison to an exhaustive search.

Research on the ordering strategy problem in supply chain with profit allocation under two-level price-fluctuation sales.

This paper investigates optimal ordering strategies in supply chains under two-level price fluctuations and initial profit allocation. By utilizing Copula functions to model the complex relationship between fluctuating prices and uncertain demand, the study develops both continuous and discrete decision models for practical applications. A discrete algorithm is proposed to approximate the optimal solution, with its convergence rigorously proven. Numerical experiments demonstrate that profit allocation ratios significantly impact optimal order quantities and overall supply chain profit. Price fluctuations, particularly at the discount level, present critical challenges, necessitating flexible and adaptive ordering strategies. The study also investigates the influence of different Copula relationships on optimal ordering decisions, revealing how varying market conditions-from moderate price sensitivity to high volatility-affect optimal order quantities. By examining ordering strategies in the context of profit allocation contracts, this research offers a new perspective on how supply chain members can collaboratively navigate uncertain markets. The findings provide actionable insights for managers to mitigate risks, improve coordination, and seize new opportunities. Extending traditional models to incorporate price fluctuations and profit allocation, this study makes theoretical and practical contributions to supply chain management, offering robust strategies to strengthen supply chain resilience.

Two‐Grid Finite Element Method for the Time‐Fractional Allen–Cahn Equation With the Logarithmic Potential

ABSTRACTIn this paper, we propose a two‐grid finite element method for solving the time‐fractional Allen–Cahn equation with the logarithmic potential. Firstly, with the L1 method to approximate Caputo fractional derivative, we solve the fully discrete time‐fractional Allen–Cahn equation on a coarse grid with mesh size and time step size . Then, we solve the linearized system with the nonlinear term replaced by the value of the first step on a fine grid with mesh size and the same time step size . We obtain the energy stability of the two‐grid finite element method and the optimal order of convergence of the two‐grid finite element method in the L2 norm when the mesh size satisfies . The theoretical results are confirmed by arithmetic examples, which indicate that the two‐grid finite element method can keep the same convergence rate and save the CPU time.

Application research of convolutional neural network and its optimization in lightning electric field waveform recognition

Quickly identifying and classifying lightning waveforms is the foundation of lightning forecasting and early warning. In this paper, based on the electric field observation of the Beijing lightning location website of the Institute of Atmospheric Physics, Chinese Academy of Sciences, a recognition and classification method of pulse signal waveform based on Convolutional Neural Network(CNN) algorithm is designed and implemented. The CNN network model and its parameters were optimized from three aspects: dataset, model parameters, and network structure, achieving a recognition rate of over 90%. The effects of various optimization terms and their different optimization orders on the training time of the model were studied. The results indicate that the CNN algorithm is suitable for the classification and recognition of lightning electric field (LEF) waveforms. Optimization can significantly improve recognition rate. The optimization method of fitting idealized waveforms can reduce noise in the dataset and significantly improve recognition rate, indicating that noise has a significant impact on waveform recognition. Therefore, it is necessary to perform noise preprocessing before recognition. The optimization has a huge impact on training efficiency, increasing training time by about 51% after optimization, but the influence of optimization order on it can be ignored.

Treatment of idiopathic granulomatous mastitis: a retrospective case series.

Idiopathic granulomatous mastitis (IGM) is a rare inflammatory disease of the breast. Various clinical management approaches have been described, but their efficacy and optimal sequential order remain uncertain. We describe the first Canadian cohort of patients with IGM, discuss treatment outcomes and outline a practical management approach. This retrospective study included patients diagnosed with biopsy-confirmed IGM between 2014 and 2023, aged over 18 years. Based on a scoping review of the literature, a diagnostic and management approach was developed, and we present here the disease course and outcomes using this approach. 22 females were included, with a mean age of 40 (24-65) years, mostly presenting with a breast lump (n =22, 100%) and breast pain (n = 15, 68%). Mean rheumatology follow-up was 28.7 months (range 3-79). Mean time from first symptom to diagnosis was 3.5 months (range 1-13). Corynebacterium kroppenstedtii was found in 8 patients. Treatment including lipophilic antibiotics, corticosteroids and disease modifying anti-rheumatic drugs (DMARDs), led to complete remission in 95% of patients, in a mean time of 11.6 months (range 1-36), and relapse in only 1 patient. 11 patients required DMARDs (50%), most commonly methotrexate (n=9). We highlight the variable severity of IGM and the benefits of a severity-based treatment approach. A diligent evaluation and work-up is essential to manage IGM. The proposed severity-based management approach with medical treatment and less aggressive surgical intervention led to complete remission in 95%.

Optimal second order boundary regularity for solutions to p-Laplace equations

Optimal second order boundary regularity for solutions to p-Laplace equations

Weak dependence and optimal quantitative self-normalized central limit theorems

Consider a stationary, weakly dependent sequence of random variables. Given only mild conditions, allowing for polynomial decay of the autocovariance function, we show a Berry–Esseen bound of optimal order n^{-1/2} for studentized (self-normalized) partial sums, both for the Kolmogorov and Wasserstein (and L^{p} ) distances. The results show that in general, (minimax) optimal estimators of the long-run variance lead to suboptimal bounds in the central limit theorem, that is, the rate n^{-1/2} cannot be reached, refuting a popular belief in the literature. This can be salvaged by simple methods. We reveal that in order to maintain the optimal speed of convergence n^{-1/2} , simple over-smoothing within a certain range is necessary and sufficient. The setup contains many prominent dynamical systems and time series models, including random walks on the general linear group, products of positive random matrices, functionals of GARCH models of any order, functionals of dynamical systems arising from stochastic differential equations, iterated random functions and many more.

MAXIMIZING PROFIT POTENTIAL IN SUPPLY CHAIN FROM SUPPLIER-RETAILER INVENTORY REPLENISHMENT IN RURAL AREAS

Successful collaborative relationship enhances profitability in the delivery of products or services to customers in a supply. This study focuses on the impact of successful relationships in supply chain management on customer exploration and profitability. By implementing a strong strategy, more customers can be brought into the supply chain, leading to increased productivity and ultimately, higher profitability. The main objective is to determine the optimal quantity levels in supplier relationships that minimize long-term costs in the supply chain. A mathematical model incorporating shipment consolidation was utilized to derive the profit function. Numerical examples were then employed to illustrate the developed models. The results demonstrate variations in total quantity and relevant costs based on factors such as retailer input, supplier replenishment quantities, optimal order quantities, and total relevant costs within the supply chain, ultimately contributing to enhanced profitability. Our result shows that. there is an increase in the supply chain profitability when the retailer orders greater number of items from the supplier.

Enhancing Online Job Shop Scheduling Efficiency: Simulation-Based Optimization Incorporating Human Productivity Factors and TOPSIS Ranking

Abstract The job shop scheduling problem is a classical optimization challenge aimed at determining the optimal processing order by assigning a set of resources to a corresponding set of operations. This article investigates various approaches to address the online job shop scheduling problem, employing a simulation-based study. Dispatching rules are applied to allocate resources to operations, with discrete event simulation used for problem assessment. The study also incorporates human productivity factors, specifically investigating the shortest processing time (SPT) dispatching rule in a separate scenario. Five distinct scenarios are simulated, including four dispatching rules (first in, first out; last in, first out; longest processing time; and SPT) and an additional scenario integrating the SPT rule and human productivity factors. The simulation results are used to compare makespan across these scenarios, revealing that the scenario involving the SPT dispatching rule and human productivity factors represents the shortest makespan. Through a TOPSIS technique-based ranking, considering makespan and cost as criteria, the study identifies the SPT rule and human productivity factors as the most efficient scenario. The findings imply that employing human productivity factors with effective dispatching rules, such as SPT, can significantly improve job shop scheduling operational efficiency and lead to more optimal results in both makespan and overall operational costs.

Machine learning optimal ordering in global routing problems in semiconductors

In this work, we propose a new method for ordering nets during the process of layer assignment in global routing problems. The global routing problems that we focus on in this work are based on routing problems that occur in the design of substrates in multilayered semiconductor packages. The proposed new method is based on machine learning techniques and we show that the proposed method supersedes conventional net ordering techniques based on heuristic score functions. We perform global routing experiments in multilayered semiconductor package environments in order to illustrate that the routing order based on our new proposed technique outperforms previous methods based on heuristics. Our approach of using machine learning for global routing targets specifically the net ordering step which we show in this work can be significantly improved by deep learning.

Optimal convergence analysis of second‐order time‐discrete stabilized scheme for the thermally coupled incompressible MHD system

AbstractIn this paper, we construct an optimal convergence analysis of second‐order stabilized scheme for the thermally coupled incompressible magnetohydrodynamic (MHD) system. First, we construct first‐ and second‐order time‐discrete schemes in which the time derivative term is treated by the first‐order backward Euler method and the second‐order backward difference formulation, respectively. And the nonlinear terms are treated by semi‐implicit method. Importantly, we use the Gauge–Uzawa method to decouple velocity and pressure. The proposed schemes have the following two distinct features: they do not need to give an initial value of the pressure, and they do not require artificial boundary conditions on the pressure. Second, the unconditional energy stability of the two schemes is proved. Then, through rigorous error analysis, we provide optimal convergence orders for all unknowns. Finally, some numerical experiments demonstrate the accuracy and effectiveness of the proposed schemes.

Truncated amplitude flow with coded diffraction patterns

Abstract The phase retrieval problem, which involves Fourier transforms with random masks, has a wide range of applications in signal and image processing, such as diffraction imaging. In recent years, various first-order methods have been explored, including truncated amplitude flow (TAF). These methods are considered to be simple and effective for solving the phase retrieval problem. However, existing convergence results for TAF mainly focus on random Gaussian measurements, which is very far from practical scenarios. In this paper, we analyze the convergence of a revised TAF (RTAF) for the phase retrieval problem. We focus on coded diffraction patterns composed of Fourier transforms and random masks. Then we justify the linear convergence behavior of such algorithm when near the true solution. By utilizing the local initializer found by a non-truncated spectral method, we establish the exact convergence rates in both the noiseless case and the bounded noise case. Further, we have shown that a general signal x ∈ C^n can be estimated
 on an optimal sampling order (specifically, O(nlogn)). Moreover, our demonstrations indicate that sharp stability can be maintained even when the observations are contaminated by bounded noise. Our experiments have revealed that the RTAF algorithm can reliably estimate the original signal using fewer measurements, aligning with our theoretical analysis. Additionally, numerical experiments have highlighted that the RTAF algorithm outperforms the truncated Wirtinger flow (TWF) and truncated Riemannian gradient descent (TRGrad) algorithms in terms of efficiency and stability, showcasing its superior performance over state-of-the-art algorithms.

A Solution-Structure B-Spline-Based Framework for Hybrid Boundary Problems on Implicit Domains

Solving partial differential equations (PDEs) on complex domains with hybrid boundary conditions presents significant challenges in numerical analysis. In this paper, we introduce a solution-structure-based framework that transforms non-homogeneous hybrid boundary problems into homogeneous ones, allowing exact conformity to the boundary conditions. By leveraging B-splines within the R-function method structure and adopting the stability principles of the WEB method, we construct a well-conditioned basis for numerical analysis. The framework is validated through a number of numerical examples of Poisson equations with hybrid boundary conditions on different implicit domains in two and three dimensions. The results reflect that the approach can achieve the optimal approximation order in solving hybrid problems.

A Global Coverage Path Planning Method for Multi-UAV Maritime Surveillance in Complex Obstacle Environments

The study of unmanned aerial vehicle (UAV) coverage path planning is of great significance for ensuring maritime situational awareness and monitoring. In response to the problem of maritime multi-region coverage surveillance in complex obstacle environments, this paper proposes a global path planning method capable of simultaneously addressing the multiple traveling salesman problem, coverage path planning problem, and obstacle avoidance problem. Firstly, a multiple traveling salesmen problem–coverage path planning (MTSP-CPP) model with the objective of minimizing the maximum task completion time is constructed. Secondly, a method for calculating obstacle-avoidance path costs based on the Voronoi diagram is proposed, laying the foundation for obtaining the optimal access order. Thirdly, an improved discrete grey wolf optimizer (IDGWO) algorithm integrated with variable neighborhood search (VNS) operations is proposed to perform task assignment for multiple UAVs and achieve workload balancing. Finally, based on dynamic programming, the coverage path points of the area are solved precisely to generate the globally coverage path. Through simulation experiments with scenarios of varying scales, the effectiveness and superiority of the proposed method are validated. The experimental results demonstrate that this method can effectively solve MTSP-CPP in complex obstacle environments.

Winter Wheat SPAD Prediction Based on Multiple Preprocessing, Sequential Module Fusion, and Feature Mining Methods

Chlorophyll is a crucial indicator for monitoring crop growth and assessing nutritional status. Hyperspectral remote sensing plays an important role in precision agriculture, offering a non-destructive approach to predicting leaf chlorophyll. However, crop canopy spectra often face background noise and data redundancy challenges. To tackle these issues, this study develops an integrated processing strategy incorporating multiple preprocessing techniques, sequential module fusion, and feature mining methods. Initially, the original spectrum (OS) from 2021, 2022, and the fusion year underwent preprocessing through Fast Fourier Transform (FFT) smoothing, multiple scattering correction (MSC), the first derivative (FD), and the second derivative (SD). Secondly, feature mining was conducted using Competitive Adaptive Reweighted Sampling (CARS), Iterative Retention of Information Variables (IRIV), and Principal Component Analysis (PCA) based on the optimal preprocessing order module fusion data. Finally, Partial Least Squares Regression (PLSR) was used to construct a prediction model for winter wheat SPAD to compare the prediction effects in different years and growth stages. The findings show that the preprocessing sequential module fusion of FFT-MSC (firstly pre-processing using FFT, and secondly secondary processing of FFT spectral data using MSC) effectively reduced issues such as noisy signals and baseline drift. The FFT-MSC-IRIV-PLSR model (based on the combined FFT-MSC preprocessed spectral data, feature screening using IRIV, and then combining with PLSR to construct a prediction model) predicts SPAD with the highest overall accuracy, with an R2 of 0.79–0.89, RMSE of 4.51–5.61, and MAE of 4.01–4.43. The model performed best in 2022, with an R2 of 0.84–0.89 and RMSE of 4.51–6.74. The best prediction during different growth stages occurred in the early filling stage, with an R2 of 0.75 and RMSE of 0.58. On the basis of this research, future work will focus on optimizing the data processing process and incorporating richer environmental data, so as to further enhance the predictive capability and applicability of the model.

Organic Terahertz Generators with Wide Entire‐Molecular Phonon‐Free Range and Their Application in Broadband Terahertz Spectroscopy

New organic nonlinear optical crystals with a broad range free from strong molecular phonon vibrations have been developed for dimple‐free THz wave generation. The newly designed 7‐fluoro‐2‐(4‐hydroxy‐3‐methylstyryl)‐1‐methylquinolin‐1‐ium (OM7FQ) crystals exhibiting an optimal order parameter feature a unique orthogonal cation–anion dipole coupling, in contrast to the parallel cation–anion dipole coupling found in benchmark organic crystals. The introduction of a fluoro substituent on the cationic electron acceptor, compared to nonfluorinated analogs, results in the additional formation of stronger cation–anion and cation–cation interactions, leading to increased crystal density and reduced void volume. OM7FQ single crystals exhibit a broad phonon‐free range from 0.9 to 2.3 THz, defined by an absorption coefficient ≤15 mm−1. This leads to efficient, dimple‐free THz wave generation with a dimple‐free flat spectral band spanning 0.5–2.7 THz when pumped at the technically significant wavelength of 800 nm. Additionally, OM7FQ crystals produce THz electric fields 3.6 times higher than analogous nonfluorinated benchmark crystals with parallel cation–anion dipole coupling. The application of OM7FQ crystals in broadband THz spectroscopy has been successfully demonstrated for sensing biologically important lactose in commercial infant formulas.

ФОРМОУТВОРЕННЯ НАМОТУВАННЯМ КОМПОЗИТНОГО ПЕРЕДНЬОГО ГОРИЗОНТАЛЬНОГО ОПЕРЕННЯ ЛЕГКОГО ЛІТАКА

A process has been developed for modeling the trajectory of laying reinforcing material (RM) during the formation of composite aerodynamic surfaces (AS). The work provides a brief description of the types of structures of aircraft of complex shape according to the criterion of the possibility of manufacturing by the winding method, in which certain types of surface shapes are highlighted according to the condition of determining the laying trajectory and developing a winding control program (WCP) for CNC machines. It is shown that the process of developing technology for manufacturing structures such as aerodynamic load-bearing surfaces has significant differences from the process of developing technology for axisymmetric products. The general technique for determining the trajectory of laying reinforcing material is shown and new approaches to specifying the reinforcement pattern are described. The general methodology for calculating the WCP for winding the AS is described. Calculation of the movements of the working parts of a winding machine (WM) includes several subtasks: choosing the order of passage of individual turns of the RM, calculating the movements of the working parts of the WM when laying each turn, and determining the program for transition from turn to turn. It is shown that the most important stage in the development of general-type AS winding technology is the choice of a winding scheme that determines the structural-force diagram (SFD) of the structure. For this purpose, the concept of the limiting point of winding has been introduced. The winding pattern of any type of product can be described by an array of coordinates of boundary points and reinforcement angles. An algorithm for calculating the trajectory of RM placement on the surface of the mandrel is presented. The features of choosing the order of passage of turns are described. The order in which the turns pass affects the number of weaves in the structure of the composite material obtained during the winding process and the strength of the product. The optimal order of passing turns according to the strength criterion is determined experimentally through repeated development tests. The features of choosing programs for transition from turn to turn are described. The algorithm of actions of the WM during the transition from one turn to another - the transition program consists of two programs: the program for entering the turn and the program for exiting the turn. The algorithm of transition programs depends on the chosen order of turns and in each specific case depends on the design features of the product. To test the developed methodology, a test calculation of the front horizontal tail of a light aircraft was carried out. As a result of the work done, it was possible to solve the problem of modeling the RM laying trajectory for bodies of complex shape with a fixed type of section, manufactured by the winding method from a polymer composite material (PCM). This technology can be used to produce aircraft structures such as “wing”, “fuselage” of an airplane, helicopter, and the like. Thus, the possibility of winding a general type AS has been proven using the example of the horizontal front tail of a light aircraft. The range of production of wound products has expanded - bodies with an arbitrary convex section and a straight generatrix. A technology has been developed for manufacturing from PCM by winding non-axisymmetric aerodynamic power structural elements such as aircraft wings, helicopter blades, air and water propellers. A surface reinforcement scheme has been found that makes it possible to obtain a variable wall thickness with its decrease from the root to the end rib. The trajectories of laying reinforcing material on a surface with an arbitrary convex section and the movement of working parts for a three-axis winding machine are determined. The developed calculation method can be used to create various aerodynamic structural elements with positive surface curvature from PCM by winding. The use of advanced high-performance technology for automated winding of reinforcing fiber material provides a significant reduction in labor costs in the manufacture of these units, reducing their prices compared to the prices of existing metal and composite aircraft of comparable size and equipment

The Way towards Regional Modernities - Joint Works of Dušan Grabrijan and Juraj Neidhardt

The richness and multiplicity of themes addressed in the different contributions made it very difficult to create the optimal order for this issue: every grouping of contributions would undervalue at least one of the aspects of the individual papers. Finally this Journal is structured in three main blocks where the first focusses on the joint origins and joint works of Dušan Grabrjan and Juraj Neidhardt. It includes contributions by Bogo Zupančič, Lejla Džumhur with Aida Idrizbegović-Zgonić and Dijana Alić. The second block of papers has the main focus on Plečnik and Dušan Grabrjan’s work and contains contributions by Miloš Kosec, Mirjana Lozanovska with Viktorija Bogdanova and Aleksa Korolija. The third block of papers focusses on Juraj Neidhardt and is authored by Darja Radović-Mahečić, Aleksandar Bede with Dragana Konstantinović and Slobodan Jović and by Nevena Novaković. As guest-editors, we contributed with a paper on the origins of modernity and the synthesis of the arts with the region in the second and third block.

Performance Improvement by FRFT-OFDM for Visible Light Communication and Positioning Systems

In indoor visible light communication (VLC) and visible light positioning (VLP) systems, the performance of conventional orthogonal frequency-division multiplexing (OFDM) schemes is often compromised due to the nonlinear characteristics and limited modulation bandwidth of light-emitting diodes, the multipath effect in enclosed indoor environments, and the relative positions of transmitters and receivers. This paper proposes an OFDM scheme based on the fractional Fourier transform (FRFT) to address these issues, demonstrating promising results when applied to indoor VLC and VLP systems. The FRFT, a generalization of the conventional Fourier transform (FT) in the fractional domain, captures information in both the time and frequency domains, offering greater flexibility than the FT. In this paper, we first introduce the computation method of the reality-preserving FRFT for an intensity modulation/direct detection VLC system and integrate it with OFDM to optimize system performance. By adopting FRFT-OFDM under the optimal fractional order, we enhance both the bit error ratio (BER) performance and positioning accuracy. Simulation results reveal that the FRFT-OFDM scheme with an optimized fractional order significantly improves the BER and positioning accuracy compared to the FT-OFDM scheme across most receiver positions within the indoor observation plane. For communication, the FRFT-OFDM scheme achieves over 6 dB Eb/N0 gain compared to the FT-OFDM scheme at a BER of 3×10−4 when the receiver is positioned at most locations in the room. For positioning, the FRFT-OFDM scheme enhances positioning accuracy by more than 1 cm relative to the FT-OFDM scheme at most locations in the room. Notably, both systems maintain the same computational complexity and spectral efficiency.

PROVING OPTIMAL MODEL SELECTION AND ZERO COEFFICIENT CASES IN TIME SERIES FORECASTING WITH THE GENERALIZED LEAST DEVIATION ALGORITHM

This article provides a comprehensive analysis and proof of the Generalized Least Deviation Method (GLDM) in the context of time series forecasting, with a particular focus on optimal model order selection and the conditions that lead to zero coefficients. Central to this study is the GLDM Estimator, which determines the coefficients {aj} n(m) j=1 by minimizing the objective function F(a), defined as the sum of the arctangents of the absolute deviations from observed time series data {yt} T t=1 ⊂ R. The research not only proves GLDM’s ability to capture complex data interactions but also demonstrates its adaptability to varying model orders, showing that the selection of the optimal model order is influenced by the underlying characteristics of the data rather than just the data size. For example, temperature data with pronounced seasonal patterns and autocorrelations demands a fifth-order model, whereas wind speed and COVID-19 death cases in Russia are effectively modeled by a second-order structure. The study further examines the implications of higher-order models, advocating for a customized approach to model selection that enhances both predictive accuracy and interpretability in time series forecasting.