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A reasonable method for estimating alighting stops can provide a data guarantee for schedule design and vehicle scheduling. However, few studies, to our best knowledge, have addressed this problem using the variable distance threshold for different types of passengers. This paper is based on available smart card data, and a two-stage algorithm is designed to obtain missing alighting stations in the entry-only urban public transportation system. This algorithm divides passengers into seven types, determines varying distance thresholds for different passengers, and includes five assumptions. Based on the first three assumptions, the corresponding subalgorithms are designed, respectively, constituting the first-stage algorithm, and the first match for all passengers' alighting stations is carried out. The second-stage algorithm is designed on the basis of the latter two assumptions. A secondary match is conducted on data that were not successfully matched in the first stage to ensure that alighting stops for all passengers are identified. The proposed methods are verified using urban public transport data from the city of Zhuhai as an example. Research results show that the drop-off stops where approximately 74% of passengers can be determined after matching the first-stage algorithm. The distance thresholds for various passengers are different, and the distance thresholds for the same type of passengers over different days are also different. Compared with the traditional fixed distance threshold, the variable distance threshold for various passengers proposed in this paper can improve the match rate of alighting station estimate, about 9%. By appropriately extending the distance thresholds for different passengers, the match rate for passengers who work or live in the suburbs can be further improved, which is in line with the actual travel status of such passengers. The second-stage algorithm can identify alighting sites for a single or unlinked trip. The efficiency of the methodology proposed in this study can meet the needs for practical applications, which may be applied to urban public transport systems. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for organizing and grouping data related to the expenditures by education levels in Bulgaria. The built database is used as a source from which the necessary information is searched depending on the entered indicators and time interval. The considered indicators include the public and private expenditures by education levels for the period2012-2020. The extracted subsets of elements are processed and analyzed. In this connection, four groups of variables are calculated and discussed. The results show that the expenditures in four of the education levels (primaryand pre-primary education as well as upper and lower secondary education) grow over the last five years (2016-2020). The quoted indicator inpost-secondary, non-tertiary education isreduced gradually in 2016-2019. During 2015, as compared to 2014, the expenditures in the considered 7 levels of education decreased in the range from 0.29% to 7.81%. This work calculates the share of expenditure for tertiary educationbachelor, master and doctor in comparison with the total expenditures for education in the indicatedtime period. The obtained value of the variable for this education level is the highest. It is 29.74%. The values of this variable are significantly lower for the following two levels of education - tertiary education-professional bachelor and postsecondary, non-tertiary education. They are 1.54% and 0.29% respectively. [ABSTRACT FROM AUTHOR]

This is the second paper in a series of two. The goal of the series is to give a polynomial-time algorithm for the 4-coloring problem and the 4-precoloring extension problem restricted to the class of graphs with no induced six-vertex path, thus proving a conjecture of Huang. Combined with previously known results, this completes the classification of the complexity of the 4-coloring problem for graphs with a connected forbidden induced subgraph. In this paper we give a polynomial time-algorithm that starts with a 4-precoloring of a graph with no induced six-vertex path and outputs a polynomial-sized collection of so-called excellent precolorings. Excellent precolorings are easier to handle than general ones, and, in addition, in order to determine whether the initial precoloring can be extended to the whole graph, it is enough to answer the same question for each of the excellent precolorings in the collection. The first paper in the series deals with excellent precolorings, thus providing a complete solution to the problem. [ABSTRACT FROM AUTHOR]

This is the first paper in a series whose goal is to give a polynomial-time algorithm for the 4-coloring problem and the 4-precoloring extension problem restricted to the class of graphs with no induced six-vertex path, thus proving a conjecture of Huang. Combined with previously known results, this completes the classification of the complexity of the 4-coloring problem for graphs with a connected forbidden induced subgraph. In this paper we give a polynomial-time algorithm that determines if a special kind of precoloring of a P6-free graph has a precoloring extension, and constructs such an extension if one exists. Combined with the main result of the second paper of the series, this gives a complete solution to the problem. [ABSTRACT FROM AUTHOR]

Advancements in new technologies, a reduction in CO2 emissions, and the rising demand for energy are causing a growth in the share of renewable energy sources. In distribution networks, an increasing number of distributed generators (DGs) makes the utility grid's protection complex and demanding. Vector surge and rate-of-change-of-frequency are the established anti-islanding protection methods, recognizing that the standard paradigm for protection, involving distributed generation, cannot be set only once but has to be continuously updated following the requirements and changes in the system. One of the requirements is active participation in the preservation of system frequency and voltage, which can be interrupted if the DG trips and disconnects from the utility grid. Anti-islanding protection and spurious tripping can be avoided by implementing new algorithms and techniques. This paper presents a novel protection scheme based on a voltage frequency differential. The proposed algorithm employs remote and local frequency measurements in such a manner that, for the occurrence of a frequency difference, it is assumed that the DG is in an islanding state. In this article, we demonstrate the feasibility of the algorithm through numerical analysis of grid events and laboratory testing emulating real grid-measured values. The test results show that the algorithm is resilient to false tripping for non-islanding events and more reliable than conventional methods in islanding detection. The algorithm can be set to low-frequency differential values, drastically reducing the non-detection zone in any DG type, regardless of its size and voltage level at the point of common coupling. Unlike standard anti-islanding methods, the algorithm supports the ability of the DG to fault-ride through demand. [ABSTRACT FROM AUTHOR]

The purpose of this article is to present grassroots concepts and ideas about "the algorithm" in the religious context. The power and causality of algorithms are based on lines of computer code, making a society influenced by "black boxes" or "enigmatic technologies" (as they are incomprehensible to most people). On the other hand, the power of algorithms lies in the meanings that we attribute to them. The extent of the power, agency, and control that algorithms have over us depends on how much power, agency, and control we are willing to give to algorithms and artificial intelligence, which involves building the idea of their omnipotence. The key question is about the meanings and the ideas about algorithms that are circulating in society. This paper is focused on the analysis of "vernacular/folk" theories on algorithms, reconstructed based on posts made by the users of Polish Catholic forums. The qualitative analysis of online discourse makes it possible to point out several themes, i.e., according to the linguistic concept, "algorithm" is the source domain used in explanations of religious issues (God as the creator of the algorithm, the soul as the algorithm); algorithms and the effects of their work are combined with the individualization and personalization of religion; algorithms are perceived as ideological machines. [ABSTRACT FROM AUTHOR]

Nowadays, web applications play central roles in information systems using the Internet. Then, client-side web programming using HTML, CSS, and JavaScript should be mastered first by novice students. Previously, we have presented the element fill-in-blank problem (EFP) for its self-study. An EFP instance requests to fill in the blank elements in the given source code by referring to the screenshots of the corresponding web page. The correctness of any answer is marked through string matching. However, these blanks were manually selected by considering the importance of elements and the uniqueness of their correct answers. In this paper, we propose a blank element selection algorithm to automatically generate a new EFP instance from a given source code for client-side web programming. We define the seven rules on blank element selections from the code, and implement the procedure in Python using the open source BeautifulSoup and regular expressions' ' For evaluations, we applied the algorithm to the 47 source codes used for manual generations and obtained the better EFP instances with more blanks. Besides, we verified the effectiveness by generating 10 new instances with the algorithm and assigning them to 40 students. In addition, we extended its application to three source codes for games and verified the effectiveness by assigning them to 20 students, to further validate the applicability of the algorithm in EFP instance generations. We also evaluated the relationships between the number of blanks, the number of lines in source codes, the submission times and answer rates of students to further assess the adaptability of the algorithm. These results allow us to measure the algorithm's versatility in generating a wide range of EFP instances and contributes to comprehensive understanding of instance difficulties and learning outcomes. [ABSTRACT FROM AUTHOR]

The paper considers algorithms for solving inverse scattering problems based on the discretization of the Gelfand–Levitan–Marchenko integral equations, associated with the system of nonlinear Schrödinger equations of the Manakov model. The numerical algorithm of the first order approximation for solving the scattering problem is reduced to the inversion of a series of nested block Toeplitz matrices using the Levinson-type bordering method. Increasing the approximation accuracy violates the Toeplitz structure of block matrices. Two algorithms are described that solve this problem for second order accuracy. One algorithm uses a block version of the Levinson bordering algorithm, which recovers the Toeplitz structure of the matrix by moving some terms of the systems of equations to the right-hand side. Another algorithm is based on the Toeplitz decomposition of an almost block-Toeplitz matrix and the Tyrtyshnikov bordering algorithm. The speed and accuracy of calculations using the presented algorithms are compared on an exact solution (the Manakov vector soliton). [ABSTRACT FROM AUTHOR]

In schools, children are taught algorithm for extracting the square and cube roots of a number. However, they are not informed that Aryabhata (b. 476 CE) was the first Indian mathematician to present a systematic algorithm for the extraction of the square and cube root of a number. This algorithm has been succinctly presented by Aryabhata in two successive verses in the Ganitapada of his Aryabhatiyam composed in 499 CE. A careful study of the algorithm given by Aryabhata shows that it can be easily extended to find higher order roots. It also clearly reveals that the decimal place value system should have been in vogue in India for quite a long time before him, because this algorithm is heavily based on a thorough understanding of the decimal place value system. In our paper, we will discuss some of these aspects as well as outline how his algorithm can be extended to find the higher order roots. [ABSTRACT FROM AUTHOR]

To enable organizations to achieve carbon neutrality through agile capabilities, this paper establishes an integrative framework of carbon-zero agility consisting of three dimensions: search scope agility, search locus agility, and search pace agility. However, applying common agile methodologies like Scrum, Kanban, and Lean to cultivate these capabilities inevitably introduces feedback ambiguity, which can paralyze decision-making and increase errors due to inherent human cognitive limitations. To address this, tailored carbon-zero feedback algorithms are proposed to complement human judgment in agile workflows. Specifically, prescriptive analytics, federated learning, and probabilistic programming are injected into Scrum, Kanban, and Lean respectively to restore clarity amidst ambiguity. The framework is grounded in cases from the textile industry to demonstrate applicability in practical settings. By targeting the roots of distortions with human-algorithm collaborations, it provides an actionable roadmap to implement carbon-zero agility. • Establishes carbon-zero agility framework: search scope, locus, and pace agility. • Identifies behavioral challenges, and feedback ambiguity in agile for carbon-zero. • Proposes tailored carbon-zero feedback algorithms to enhance agility. • Connects agile processes with broader organizational sustainability capabilities. [ABSTRACT FROM AUTHOR]

The Minimum Vertex Cover P roblem is the optimization problem of finding a vertex cover V c of minimal cardinality in a given graph. It is a classic NP-hard problem, and various algorithms have been suggested for it. In this paper, we start with a basic algorithm for solving the problem. Using a probabilistic idea, we use it to develop an improved algorithm. The algorithm is greedy; at each step it adds to the cover a vertex such that the expected cover size, if we continue randomly after this step, is minimal. We study the new algorithm theoretically and empirically, and run simulations to compare its performance to that of some algorithms of a similar nature. [ABSTRACT FROM AUTHOR]

• A novel algorithm is developed to model the aggregates geometrically. • 3D meso-scale concrete model is developed, considering aggregate parameters. • Inclusion of aggregates in mortar, increases the strength of obtained concrete. • In impact loading, mortar and Interfacial transition zone fail simultaneously. • Extent of damage depends on the loading rate. In this paper, a novel algorithm is developed to generate the geometrical model of coarse aggregate based on its physical properties. The size, elongation index, and flakiness index are considered while developing the algorithm. The developed geometrical model of aggregate is further used for generating the finite element (FE) meso-model of concrete. Three distinct phases are considered in the FE model, i.e., aggregate, mortar, and interfacial transition zone. Further, numerical simulation has been performed under different loading conditions (i.e., quasi-static and high-strain loading rate). Additional considerations are discussed to develop a suitable FE model for a 3D split Hopkinson pressure bar specimen. The finite element (FE) simulation results are compared with available literature to verify the developed meso-model. It is verified that the mortar and ITZ fail during the quasi-static loading, whereas the structural effect (lateral inertia confinement) plays a significant role in the high-strain loading rate. [ABSTRACT FROM AUTHOR]

With the increasing demand for information, the number of nodes in the network is increasing rapidly, followed by the problem of information loss and communication delay caused by insufficient communication. Therefore, how to effectively transmit data and minimize communication delay has been a key issue in networks. In this paper, we first propose a fault-tolerant path algorithm of the k -ary n -cube network Q n k to obtain a fault-free path between any two distinct fault-free nodes with a faulty node set F ⊂ V (Q n k) and | F | ≤ 2 n − 1. Then, we design two algorithms to construct disjoint paths between any two distinct nodes of Q n k without any faults according to whether the two nodes are adjacent or not. Extensive evaluations show that the proposed algorithms has great advantages in average running time. • We propose a fault-tolerant path algorithm of Q n k to obtain a fault-free path between any two distinct fault-free nodes. • We design two algorithms, called DPQ1 and DPQ2, to construct disjoint paths between any two distinct nodes of Q n k. • We compare our algorithms with the algorithm Dijkstra to discuss the average running time and average path length generated by the algorithms. [ABSTRACT FROM AUTHOR]