Construction Algorithm Research Articles

An Efficient Algorithm for the 2-Central Path Problem

In this paper we consider the following [Formula: see text]-Central Path Problem (2CPP): Given a set of [Formula: see text] polygonal curves [Formula: see text] in the plane, find two curves [Formula: see text] and [Formula: see text], called [Formula: see text]-central paths, that best represent all curves in [Formula: see text]. Despite its theoretical interest and a wide range of practical applications, 2CPP has not been well studied. In this paper, we first establish criteria that [Formula: see text] and [Formula: see text] ought to meet in order for them to best represent [Formula: see text]. In particular, we require that there exists parametrizations [Formula: see text] and [Formula: see text] ([Formula: see text]) of [Formula: see text] and [Formula: see text] respectively such that the maximum distance from [Formula: see text] to curves in [Formula: see text] is minimized. Then an efficient algorithm is presented to solve 2CPP under certain realistic assumptions. Our algorithm constructs [Formula: see text] and [Formula: see text] in [Formula: see text] time, where [Formula: see text] is the total complexity of [Formula: see text] (i.e., the total number of vertices and edges), [Formula: see text] is the number of curves in [Formula: see text], and [Formula: see text] is the inverse Ackermann function. Our algorithm uses parametric search technique and is considerably faster than arrangement-related algorithms (i.e. [Formula: see text]) when [Formula: see text] as in most real applications.

Research on photovoltaic MPPT under complex conditions based on an advanced great wall construction algorithm method.

To mitigate the challenges posed by the non-linear multi-peak power-voltage output characteristics of photovoltaic (PV) systems operating under partial shading conditions, which often lead to suboptimal performance of conventional Maximum Power Point Tracking (MPPT) algorithms, a novel approach was introduced. We introduce the LGWGCA-P&O method, which synergistically combines an modified Great Wall Construction Algorithm (LGWGCA) with the Perturbation and Observation (P&O) technique. The LGWGCA is refined with a positional update mechanism inspired by the Grey Wolf Optimization (GWO) algorithm, optimizing the distribution of solution agents, while a Levy flight strategy is employed to reduce excessive randomness during agent replacement and recombination, thereby accelerating the tracking process. As the algorithm approaches the maximum power point, it seamlessly transitions to the P&O method, leveraging its rapid convergence to ensure precise and efficient power point identification. Experimental results demonstrate that the LGWGCA-P&O method achieves a PV conversion efficiency exceeding 99.96%, significantly minimizing power losses during MPPT. Furthermore, the method enhances convergence speed by approximately 40% compared to traditional GWO-P&O approaches, and it consistently outperforms Particle Swarm Optimization and Cuckoo Search Optimization algorithms under extreme conditions, demonstrating superior computational efficiency and robustness.

On Process Discovery Experimentation

Process mining aims to derive insights into business processes from event logs recorded from information systems. Process discovery algorithms construct process models that describe the executed process. With the increasing availability of large-scale event logs, process discovery has shifted towards a data-oriented research discipline, aiming to design algorithms that are applicable and useful in practice. This shift has revealed a fundamental problem in process discovery research: Currently, contributions can only be considered in isolation. Researchers conduct experiments to show that they move the field forward, but due to a lack of reliability and validity, the individual contributions are hard to generalise. In this paper, we argue that one reason for these problems is the lack of conventions or standards for experimental design in process discovery. Hence, we propose “process discovery engineering”: a research methodology for process discovery, consisting of a shared terminology and a checklist for conducting experiments. We demonstrate its applicability by means of an example experimental evaluation of process discovery algorithms and discuss the implications of the methodology on the field. This paper is not meant to be prescriptive, but to invite and encourage the community to contribute to this discussion to advance the field as a whole.

Optimized Graph Sample and Aggregate‐Attention Network‐Based High Gain Meta Surface Antenna Design for IoT Application

ABSTRACTThis paper presents a High Gain Metasurface (HGM) antenna design optimized for IoT applications. The antenna operates at a 5.8 GHz frequency and utilizes a quarter‐wavelength unit cell structure. The design employs a Graph Sample and Aggregate‐Attention Network (GSAAN) to enhance the transmission characteristics of the metasurface. To optimize the performance of GSAAN, the Giza Pyramids Construction Algorithm (GPCN) is applied to adjust the weight parameters, leading to significant improvements in radiation efficiency, bandwidth, gain, directivity, and return loss. The proposed HGM antenna is simulated in MATLAB 2023b, where it demonstrates substantial performance gains over existing methods. Specifically, the proposed design achieves 28.34% higher gain compared to the MSA‐RHCOA method, 24.47% improvement over HGM‐AD‐MATCS, 26.34% better gain than BR‐HGA‐PGM, and a 32.12% gain increase relative to MSA‐Hyb‐ADSA‐HMSOA. These enhancements make the proposed antenna design a competitive solution for high‐gain applications in wireless communication, satellite communication, and radar systems. The integration of GSAAN with GPCN optimization in the HGM antenna design enables the creation of highly directive radiation patterns, making it well‐suited for IoT applications that require high performance and reliability. The results of this study demonstrate the effectiveness of the proposed approach in achieving superior antenna performance, positioning it as a strong alternative to existing metasurface antenna designs.

ON THE ISSUE OF DESIGNING WEAVES OF TWO-HOLLOW FABRICS WITH LINING BASES

The article analyses works devoted to the development of design methods for warp-pile fabrics with lining, which showed that methods for calculating the parameters and algorithms for constructing such weaves are absent in known literary sources. The authors propose a method for designing weaves of two-piece warp-pile fabrics with lining bases, with the possibility of their production on a loom with single-shed and double-shed weaving methods. An algorithm for construction has been developed, formulas for calculating the parameters of weaves have been proposed, allowing increasing the thickness, strengthen the structure and increase the service life of warp-pile fabrics. An example of constructing a filling pattern of a two-piece warp-pile fabric with lining bases with single-shed and double-shed weaving methods is given. Velvets, plush, artificial fur and carpets with cut pile are produced according to the considered technology.

Route planning and obstacle avoidance using Q-Learning in MATLAB

Abstract. Recently, autonomous navigation has become important for many applications like self-driving cars, delivery drones, and robots. These domains are typically characterized by issues in planning an efficient route and object avoidance. Therefore, the paper describes work that utilizes Q-Learning as a means of reinforcement learning for autonomous navigation in terrain based on grid representations. Q-Learning allows an agent to acquire optimal signals in terms of strategy without the need for awareness of the surrounding environment. MATLAB was employed for the construction of the Q-Learning algorithm, as it was necessary to execute, evaluate, and simulate the algorithm in a controlled setting. In this study, the agent was tested in other environments of varying sizes (1010, 1515, and 2020) populated with randomly generated obstacles. Benchmark values such as average path length, number of collisions and convergence speed were observed as a measure of the agents performance. The analysis of the values obtained confirms that the agent is able to capture the shortest path from the starting point to the goal while avoiding the obstacles. Q-Learning is found to be flexible and effective in solving the presented navigation problems in this research. The future work would include the enhancement of the efficiency of the algorithm along with the applying of the system in dynamic and more complex scenarios, in order to solve practical problems.

A Set of Models for Device Positioning in Sixth Generation Networks. Part 2. Review of Algorithms and Accuracy Assessment

Relevance. This work is the second part of a series devoted to the study of a set of positioning models in sixth-generation terahertz networks and solves the problems of systematizing algorithms and assessing the accuracy of determining the location of a user device depending on the configuration and size of the antenna array at the base station.Purpose. Within the framework of the scientific problem of searching for means of achieving decimeter accuracy of coordinate estimates, outlined in the first part of the cycle, the analysis of accuracy assessment models, a review of algorithms and ways of their optimization, as well as a numerical experiment, performed in this study serve the purpose of justifying the configuration and dimensions of the antenna array used at the base station.The research method is an analytical review of the state of the problem based on current scientific publications, conceptual modeling, categorical approach, expert combination, comparative analysis, formalization, mathematical and simulation modeling.Solution / results. The paper presents models for assessing the accuracy of positioning in 6G terahertz networks, formalizes the relationship between primary measurements and coordinate estimates for multi-position and single-position positioning in the near and far zones. It provides an overview of algorithms for geometric positioning and positioning with training for cases of one-stage and two-stage processing; analyzes the specifics of implementing algorithms for simultaneous tracking and map construction. It provides an analysis of the features of optimizing algorithms in offline and online modes. Simulation modeling is used to assess the accuracy for a scenario of territorial distribution with direct visibility and ideal synchronization.Novelty. Using simulation modeling tools, the achievement of decimeter accuracy of coordinate and orientation estimates of 1° in the terahertz range for a far-field model using a 1 GHz band and a composite antenna array of more than half a thousand elements has been scientifically substantiated.The theoretical significance lies in establishing the dependence of the accuracy of coordinate and orientation estimates of the device on the configuration and dimensions of the antenna array at the base station.The practical significance of the developed simulation model lies in the numerical justification of the limits of device positioning accuracy in sixth-generation networks depending on the antenna array used at the base station for a given scenario.

Конструктивные алгоритмы автоматизированного решения позиционных задач

This paper presents the theoretical foundations for an approach to automated solutions of positional problems involving intersections of geometric objects in Euclidean space. A conceptual framework is developed based on concepts and definitions related to the equivalence relation known in set theory. This framework includes: an equivalence relation defined on the set of geometric objects in Euclidean space; the dimension and factorization of the object set, represented as a collection of equivalence classes; and the projected factor set of space. A set-theoretic basis for representing the projection operation is provided, enabling the development of constructive algorithms to solve positional problems involving intersections of spatial geometric objects. These algorithms have been implemented within the KOMPAS-3D CAD environment. The theoretical foundations and analysis of the algorithm functionality establish definitions for "geometric modeling" and "3D modeling." The proposed approach to automating positional problem solutions essentially constitutes a 3D model of these solutions through the creation of a virtual model. The paper includes examples of automated 3D solutions to intersection problems, descriptions of the algorithms used in their design, and examples of practical applications of these algorithms.

Research on imaging biomarkers for chronic subdural hematoma recurrence.

This study utilizes radiomics to explore imaging biomarkers for predicting the recurrence of chronic subdural hematoma (CSDH), aiming to improve the prediction of CSDH recurrence risk. Analyzing CT scans from 64 patients with CSDH, we extracted 107 radiomic features and employed recursive feature elimination (RFE) and the XGBoost algorithm for feature selection and model construction. The feature selection process identified six key imaging biomarkers closely associated with CSDH recurrence: flatness, surface area to volume ratio, energy, run entropy, small area emphasis, and maximum axial diameter. The selection of these imaging biomarkers was based on their significance in predicting CSDH recurrence, revealing deep connections between postoperative variables and recurrence. After feature selection, there was a significant improvement in model performance. The XGBoost model demonstrated the best classification performance, with the average accuracy improving from 46.82% (before feature selection) to 80.74% and the AUC value increasing from 0.5864 to 0.7998. These results prove that precise feature selection significantly enhances the model's predictive capability. This study not only reveals imaging biomarkers for CSDH recurrence but also provides valuable insights for future personalized treatment strategies.

TDOA-AOA Localization Algorithm for 5G Intelligent Reflecting Surfaces

5G positioning technology has become deeply integrated into daily life. However, in wireless signal propagation environments, there may exist non-line-of-sight (NLOS) conditions, which lead to signal blockage and subsequently hinder the provision of positioning services. To address this issue, this paper proposes an intelligent reflecting surface (IRS) NLOS time difference of arrival–angle of arrival (TDOA-AOA) localization (INTAL) algorithm. First, the algorithm constructs a system model for 5G IRS localization, effectively overcoming the challenges of positioning in NLOS paths. Then, by applying the multiple signal classification algorithm to estimate the time delay and angle, and using the Chan algorithm to obtain the user’s estimated coordinates, an optimization problem is formulated to minimize the distance between the estimated and actual coordinates. The tent–snake optimization algorithm is employed to solve this optimization problem, thereby reducing localization errors. Finally, simulations demonstrate that the INTAL algorithm outperforms the snake optimization (SO) algorithm and the gray wolf optimization (GWO) algorithm under the same conditions, reducing the localization error by 56% and 60% on average, respectively. Additionally, when the signal-to-noise ratio is 30 dB, the localization error of the INTAL algorithm is only 0.2968 m, while the errors for the SO and GWO algorithms are 0.6733 m and 0.7398 m, respectively. This further proves the significant improvement of the algorithm in terms of localization accuracy.

A positional statistic for 1324-avoiding permutations

We consider the class $S_n(1324)$ of permutations of size $n$ that avoid the pattern 1324 and examine the subset $S_n^{a\prec n}(1324)$ of elements for which $a\prec n\prec [a-1]$, $a\ge 1$. This notation means that, when written in one line notation, such a permutation must have $a$ to the left of $n$, and the elements of $\{1,\dots,a-1\}$ must all be to the right of $n$. For $n\ge 2$, we establish a connection between the subset of permutations in $S_n^{1\prec n}(1324)$ having the 1 adjacent to the $n$ (called primitives), and the set of 1324-avoiding dominoes with $n-2$ points. For $a\in\{1,2\}$, we introduce constructive algorithms and give formulas for the enumeration of $S_n^{a\prec n}(1324)$ by the position of $a$ relative to the position of $n$. For $a\ge 3$, we formulate some conjectures for the corresponding generating functions.

L2T-DFM: Learning to Teach with Dynamic Fused Metric

The loss function plays a crucial role in the construction of machine learning algorithms. Employing a teacher model to set loss functions dynamically for student models has attracted attention. In existing works, (1) the characterization of the dynamic loss suffers from some inherent limitations, ie, the computational cost of loss networks and the restricted similarity measurement handcrafted loss functions; and (2) the states of the student model are provided to the teacher model directly without integration, causing the teacher model to underperform when trained on insufficient amounts of data. To alleviate the above-mentioned issues, in this paper, we select and weigh a set of similarity metrics by a confidence-based selection algorithm and a temporal teacher model to enhance the dynamic loss functions. Subsequently, to integrate the states of the student model, we employ statistics to quantify the information loss of the student model. Extensive experiments demonstrate that our approach can enhance student learning and improve the performance of various deep models on real-world tasks, including classification, object detection, and semantic segmentation scenarios.

Unified algorithms for distributed regularized linear regression model

In recent years, distributed statistical models have received increasing attention for large-scale data analysis. On the one hand, data sets come from multiple data sources, and are stored in different locations due to limited bandwidth and storage, or privacy protocols, directly centralizing all data together is impossible. On the other hand, the size of data is so large that it is difficult or inefficient to analyze data together. There are two main research aspects to using distributed statistical models to analyze large-scale data. The first one is to study the statistical convergence rate under some mild assumptions. The second one is to establish fast and efficient optimization algorithms considering the property of the loss function. There is a lot of research on the first aspect, but relatively little research on the second one. Motivated by this, we consider the construction of unified algorithms for distributed linear regression with different losses and regularizers. As a result, we designed two type methods, proximal alternating direction method of multipliers (pADMM) and distributed accelerated proximal gradient method with line-search (DAPGL). In order to demonstrate the efficiency of the proposed algorithms, we perform numerical experiments on the distributed Huber-Lasso model and Huber-Group-Lasso model. In view of the numerical results, we can observe that these two algorithms are more competitive than some of state-of-art algorithms. In particular, DAPGL algorithm performs better than pADMM in most cases.

Using generative neural networks when training digital engineers to improve the quality of their training

The problem and the aim of the study. Modernized higher education provides great prospects for artificial intelligence technologies to be introduced when training engineers for knowledge-intensive and high-tech industries. Applying generative neural networks makes it possible to meet the requirements both for programs to train relevant specialists and for the level of developed skills key to Industry 4.0 and for further Industry 5.0. The purpose of the study is to identify the possibilities of using generative neural networks when training digital engineers to improve the quality of their professional training. Research methods. The authors consider the generative neural network as an open resource with which it is possible to design, individualize and fill educational content in accordance with the professional interests of the participants in the interaction. The choice of service is justified by the type of information being processed and the engineer's work function being implemented. 68 bachelors of Vyatka State University are involved (Russian Federation). Training program: 08.03.01 – Construction. Focus: hydraulic engineering, industrial and civil engineering, Digital technologies for the examination of construction sites and real estate management. The assessment of the quality (level) of training is carried out with the help of materials from the fund of complex qualification tasks. For statistical processing of data, Pearson's chi-squared test is used. Results. The directions of work of students of the experimental group studying the discipline "Information Technology", including interactive communication supported by neural networks: generation of images and 3D-models, search for original titles, selection of a list of references, construction of diagrams and algorithms, etc. Statistically significant differences were revealed in the changes that occurred in the pedagogical system (χ2 = 9.095; p < 0.05). Conclusion. The summary are formulated that neural network services contribute to improving the quality of training due to the following didactic capabilities: presentation of information in various forms, automation of calculations, analysis of large amounts of data, decision support, etc. Difficulties are also highlighted: constantly updated features of services, the English-language interface, compliance with copyright and ethics of interaction on the network

Automatic construction and verification algorithm for smart contracts based on formal verification

As an emerging technology, blockchain demonstrates strong potential for applications in digital finance. As a core component of blockchain, the security and reliability of smart contracts is crucial. To ensure the high reliability of smart contracts, this study employs formal construction and verification techniques based on game theory. Initially, the profit function is defined using distortion techniques, and a game model for supply chain participation is designed. However, the equilibrium solution of the two-party game does not represent the optimal solution for the supply chain system. Therefore, the study introduces third-party participation to optimize the equilibrium solution. Finally, a probability model detection method is used to verify the constructed smart contract model. The results show that the supply chain model, analyzed through formal methods, has attributes consistent with theoretical analysis. Consequently, the research on automatic construction and verification algorithms for smart contracts based on formal verification proves to be effective and feasible in practical applications.

COMONOTONICITY AND PARETO OPTIMALITY, WITH APPLICATION TO COLLABORATIVE INSURANCE

Two by-now folkloric results in the theory of risk sharing are that (i) any feasible allocation is convex-order-dominated by a comonotonic allocation; and (ii) an allocation is Pareto optimal for the convex order if and only if it is comonotonic. Here, comonotonicity corresponds to the so-called no-sabotage condition, which aligns the interests of all parties involved. Several proofs of these two results have been provided in the literature, all based on a version of the comonotonic improvement algorithm of Landsberger and Meilijson (1994) and a limit argument based on the Martingale Convergence Theorem. However, no proof of (i) is explicit enough to allow for an easy algorithmic implementation in practice; and no proof of (ii) provides a closed-form characterization of Pareto optima. In addition, while all of the existing proofs of (i) are provided only for the case of a two-agent economy with the observation that they can be easily extended beyond two agents, such an extension is far from being trivial in the context of the algorithm of Landsberger and Meilijson (1994) and it has never been explicitly implemented. In this paper, we provide novel proofs of these foundational results. Our proof of (i) is based on the theory of majorization and an extension of a result of Lorentz and Shimogaki (1968), which allows us to provide an explicit algorithmic construction that can be easily implemented beyond the case of two agents. In addition, our proof of (ii) leads to a crisp closed-form characterization of Pareto-optimal allocations in terms of α-quantiles (mixed quantiles). An application to peer-to-peer insurance, or collaborative insurance, illustrates the relevance of these results.Acknowledgements: The authors thank the Editor and two anonymous Referees for numerous suggestions which helped to improve the text compared to its previous versions. We are grateful to K.C. Cheung for comments on an earlier version of this paper, and to Christopher Blier-Wong for his excellent research assistance in the numerical example. We thank the Associate Editor and two anonymous reviewers for comments and suggestions. Michel Denuit and Jan Dhaene gratefully acknowledge funding from the FWO and F.R.S.-FNRS under the Excellence of Science (EOS) programme, project ASTeRISK (40007517). Jan Dhaene acknowledges the financial support of BOF KU Leuven (project C14/21/089). Mario Ghossoub acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada NSERC Grant No. 2018-03961 and 2024-03744).

Supersymmetric Integrable Hamiltonian Systems, Conformal Lie Superalgebras K(1, N = 1, 2, 3), and Their Factorized Semi-Supersymmetric Generalizations

We successively reanalyzed modern Lie-algebraic approaches lying in the background of effective constructions of integrable super-Hamiltonian systems on functional N=1,2,3- supermanifolds, possessing rich supersymmetries and endowed with suitably related compatible Poisson structures. As an application, we describe countable hierarchies of new nonlinear Lax-type integrable N=2,3-semi-supersymmetric dynamical systems and constructed their central extended superconformal Lie superalgebra K(1|3) and its finite-dimensional coadjoint orbits, generated by the related Casimir functionals. Moreover, we generalized these results subject to the suitably factorized super-pseudo-differential Lax-type representations and present the related super-Poisson brackets and compatible suitably factorized Hamiltonian superflows. As an interesting point, we succeeded in the algorithmic construction of integrable super-Hamiltonian factorized systems generated by Casimir invariants of the centrally extended super-pseudo-differential operator Lie superalgebras on the N=1,2,3-supercircle.

Map construction algorithm based on dense point cloud

AbstractIn order to address the issue of the difficulty in constructing maps from sensor‐acquired point clouds, a map construction algorithm is proposed for the effective conversion from sparse point clouds to dense point clouds. First, it constructs a dense point cloud map in real‐time using colour and depth information of keyframes. Then, it generates an accurate point cloud map by voxel filtering and coordinate conversion. Finally, the point cloud map is converted into an octree map using OctoMap. This article uses the TUM dataset for simulation analysis to verify the effectiveness of the algorithm. The results demonstrate that the algorithm can construct dense point cloud maps with high positioning accuracy in sparse point cloud scenarios. The algorithm improves the positioning accuracy by more than 15% under the fr1_xyz, fr1_room, fr1_desk2, fr1_desk1, fr2_desk and fr3_str_tex_near sequences, compared to ORB‐SLAM2, ORB‐SLAM3 and GX ORB‐SLAM2 algorithm

Invariant Checking for SMT-Based Systems with Quantifiers

This article addresses the problem of checking invariant properties for a large class of symbolic transition systems defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort (finite but unbounded) to an interpreted sort, such as the integers under the theory of linear arithmetic. This formalism is very expressive and can be used for modeling parameterized systems, array-manipulating programs, and more. We propose two algorithms for finding universal inductive invariants for such systems. The first algorithm combines an IC3-style loop with a form of implicit predicate abstraction to construct an invariant in an incremental manner. The second algorithm constructs an under-approximation of the original problem and searches for a formula which is an inductive invariant for this case; then, the invariant is generalized to the original case and checked with a portfolio of techniques. We have implemented the two algorithms and conducted an extensive experimental evaluation, considering various benchmarks and different tools from the literature. As far as we know, our method is the first capable of handling in a large class of systems in a uniform way. The experiment shows that both algorithms are competitive with the state of the art.

DFC-Igloo: A dynamic functional connectome learning framework for identifying neurodevelopmental biomarkers in very preterm infants

Background and ObjectiveVery preterm infants are susceptible to neurodevelopmental impairments, necessitating early detection of prognostic biomarkers for timely intervention. The study aims to explore possible functional biomarkers for very preterm infants at born that relate to their future cognitive and motor development using resting-state fMRI. Prior studies are limited by the sample size and suffer from efficient functional connectome (FC) construction algorithms that can handle the noisy data contained in neonatal time series, leading to equivocal findings. Therefore, we first propose an enhanced functional connectome construction algorithm as a prerequisite step. We then apply the new FC construction algorithm to our large prospective very preterm cohort to explore multi-level neurodevelopmental biomarkers. MethodsThere exists an intrinsic relationship between the structural connectome (SC) and FC, with a notable coupling between the two. This observation implies a putative property of graph signal smoothness on the SC as well. Yet, this property has not been fully exploited for constructing intrinsic dFC. In this study, we proposed an advanced dynamic FC (dFC) learning model, dFC-Igloo, which leveraged SC information to iteratively refine dFC estimations by applying graph signal smoothness to both FC and SC. The model was evaluated on artificial small-world graphs and simulated graph signals. ResultsThe proposed model achieved the best and most robust recovery of the ground truth graph across different noise levels and simulated SC pairs from the simulation. The model was further applied to a cohort of very preterm infants from five Neonatal Intensive Care Units, where an enhanced dFC was obtained for each infant. Based on the improved dFC, we identified neurodevelopmental biomarkers for neonates across connectome-wide, regional, and subnetwork scales. ConclusionThe identified markers correlate with cognitive and motor developmental outcomes, offering insights into early brain development and potential neurodevelopmental challenges.