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Many complex physical systems exhibit a rich variety of discrete behavioural modes. Often, the system complexity limits the applicability of standard modelling tools. Hence, understanding the underlying physics of different behaviours and distinguishing between them is challenging. Although traditional machine learning techniques could predict and classify behaviour well, typically they do not provide any meaningful insight into the underlying physics of the system. In this paper we present a novel method for extracting physically meaningful clusters of discrete behaviour from limited experimental observations. This method obtains a set of physically plausible functions that both facilitate behavioural clustering and aid in system understanding. We demonstrate the approach on the V-shaped falling paper system, a new falling paper type system that exhibits four distinct behavioural modes depending on a few morphological parameters. Using just 49 experimental observations, the method discovered a set of candidate functions that distinguish behaviours with an error of 2.04%, while also aiding insight into the physical phenomena driving each behaviour. [ABSTRACT FROM AUTHOR]

The Semantic Link Network is a general semantic model for modeling the structure and the evolution of complex systems. Various semantic links play different roles in rendering the semantics of complex system. One of the basic semantic links represents cause-effect relation, which plays an important role in representation and understanding. This paper verifies the role of the Semantic Link Network in representing the core of text by investigating the contribution of cause-effect link to representing the core of scientific papers. Research carries out with the following steps: (1) Two propositions on the contribution of cause-effect link in rendering the core of paper are proposed and verified through a statistical survey, which shows that the sentences on cause-effect links cover about 65% of key words within each paper on average. (2) An algorithm based on syntactic patterns is designed for automatically extracting cause-effect link from scientific papers, which recalls about 70% of manually annotated cause-effect links on average, indicating that the result adapts to the scale of data sets. (3) The effects of cause-effect link on four schemes of incorporating cause-effect link into the existing instances of the Semantic Link Network for enhancing the summarization of scientific papers are investigated. The experiments show that the quality of the summaries is significantly improved, which verifies the role of semantic links. The significance of this research lies in two aspects: (1) it verifies that the Semantic Link Network connects the important concepts to render the core of text; and, (2) it provides an evidence for realizing content services such as summarization, recommendation and question answering based on the Semantic Link Network, and it can inspire relevant research on content computing. [ABSTRACT FROM AUTHOR]

Quantifying the impact of a scholarly paper is of great significance, yet the effect of geographical distance of cited papers has not been explored. In this paper, we examine 30,596 papers published in Physical Review C, and identify the relationship between citations and geographical distances between author affiliations. Subsequently, a relative citation weight is applied to assess the impact of a scholarly paper. A higher-order weighted quantum PageRank algorithm is also developed to address the behavior of multiple step citation flow. Capturing the citation dynamics with higher-order dependencies reveals the actual impact of papers, including necessary self-citations that are sometimes excluded in prior studies. Quantum PageRank is utilized in this paper to help differentiating nodes whose PageRank values are identical. [ABSTRACT FROM AUTHOR]

Research paper recommenders emerged over the last decade to ease finding publications relating to researchers’ area of interest. The challenge was not just to provide researchers with very rich publications at any time, any place and in any form but to also offer the right publication to the right researcher in the right way. Several approaches exist in handling paper recommender systems. However, these approaches assumed the availability of the whole contents of the recommending papers to be freely accessible, which is not always true due to factors such as copyright restrictions. This paper presents a collaborative approach for research paper recommender system. By leveraging the advantages of collaborative filtering approach, we utilize the publicly available contextual metadata to infer the hidden associations that exist between research papers in order to personalize recommendations. The novelty of our proposed approach is that it provides personalized recommendations regardless of the research field and regardless of the user’s expertise. Using a publicly available dataset, our proposed approach has recorded a significant improvement over other baseline methods in measuring both the overall performance and the ability to return relevant and useful publications at the top of the recommendation list. [ABSTRACT FROM AUTHOR]

With the rapid development of information technology, scientific social networks (SSNs) have become the fastest and most convenient way for researchers to communicate with each other. Many published papers are shared via SSNs every day, resulting in the problem of information overload. How to appropriately recommend personalized and highly valuable papers for researchers is becoming more urgent. However, when recommending papers in SSNs, only a small amount of positive instances are available, leaving a vast amount of unlabelled data, in which negative instances and potential unseen positive instances are mixed together, which naturally belongs to One-Class Collaborative Filtering (OCCF) problem. Therefore, considering the extreme data imbalance and data sparsity of this OCCF problem, a hybrid approach of Social and Content aware One-class Recommendation of Papers in SSNs, termed SCORP, is proposed in this study. Unlike previous approaches recommended to address the OCCF problem, social information, which has been proved playing a significant role in performing recommendations in many domains, is applied in both the profiling of content-based filtering and the collaborative filtering to achieve superior recommendations. To verify the effectiveness of the proposed SCORP approach, a real-life dataset from CiteULike was employed. The experimental results demonstrate that the proposed approach is superior to all of the compared approaches, thus providing a more effective method for recommending papers in SSNs. [ABSTRACT FROM AUTHOR]

Summarizes the construction of paper folding. Method for approximating rational subdivisions or arbitrary angles and line segments; Angle-folding algorithm; Approximating angles, regular polygons and star polygons; Dissection of angles into equal parts.

In this paper, we study a discrete momentum consensus-based optimization (Momentum-CBO) algorithm which corresponds to a second-order generalization of the discrete first-order CBO [S.-Y. Ha, S. Jin and D. Kim, Convergence of a first-order consensus-based global optimization algorithm, Math. Models Methods Appl. Sci. 30 (2020) 2417–2444]. The proposed algorithm can be understood as the modification of ADAM-CBO, replacing the normalization term by unity. For the proposed Momentum-CBO, we provide a sufficient framework which guarantees the convergence of algorithm toward a global minimum of the objective function. Moreover, we present several experimental results showing that Momentum-CBO has an improved success rate of finding the global minimum compared to vanilla-CBO and show the stability of Momentum-CBO under different initialization schemes. We also show that Momentum-CBO can be used as the alternative of ADAM-CBO which does not have a proper convergence analysis. Finally, we give an application of Momentum-CBO for Lyapunov function approximation using symbolic regression techniques. [ABSTRACT FROM AUTHOR]

There are several classical characterisations of the valuative dimension of a commutative ring. Constructive versions of this dimension have been given and proven to be equivalent to the classical notion within classical mathematics, and they can be used for the usual examples of commutative rings. To the contrary of the classical versions, the constructive versions have a clear computational content. This paper investigates the computational relationship between three possible constructive definitions of the valuative dimension of a commutative ring. In doing so, it proves these constructive versions to be equivalent within constructive mathematics. [ABSTRACT FROM AUTHOR]

Many results have been obtained when studying scientific papers citations databases in a network perspective. Articles can be ranked according to their current in-degree and their future popularity or citation counts can even be predicted. The dynamical properties of such networks and the observation of the time evolution of their nodes started more recently. This work adopts an evolutionary perspective and proposes an original algorithm for the construction of genealogical trees of scientific papers on the basis of their citation count evolution in time. The fitness of a paper now amounts to its in-degree growing trend and a “dying” paper will suddenly see this trend declining in time. It will give birth and be taken over by some of its most prevalent citing “offspring”. Practically, this might be used to trace the successive published milestones of a research field. [ABSTRACT FROM AUTHOR]

This note tries to answer issues raised in Bhardwaj and Kumar (J Optim Theory Appl 163(2): 685-696, 2014). The research summarizes that the results obtained in Khan et al. (J Optim Theory Appl 159: 536-546, 2013) are sound and correct and it fulfills all the necessary requirements of its scope and objectives. [ABSTRACT FROM AUTHOR]

In the 1610s and 1620s, a new computational technology took hold in England: printed mathematical tables for compound interest and discounting ("present value") problems. Historians of finance and accounting have long recognized these paper tools as predecessors of essential modern techniques like "discounted cash flow." Yet the history of these tables remains hazy. What did early seventeenth-century users do with them? Who used them? Why did they appear when they did? This article turns to one obscure but influential text—Ambrose Acroyd's Tables of Leasses and Interest (1628)—as a guide to these questions. Two key facts emerge. First, despite the prominence of similar calculations in financial applications today, these early tables were not confined to England's nascent financial sector. Rather, their foremost use related to agricultural property, specifically in assessing certain payments ("fines") landlords charged tenants for farm leases. Second, among the leading "early adopters" were institutions of the Church of England. Amidst the inflation of the early modern "price revolution," bishops, cathedrals, and colleges confronted a complex of economic, political, and social pressures. Mathematical tables like Acroyd's emerged out of long-running conflicts between church landlords and tenants over how to determine just and reasonable fines on church lands. Discounting tables were thus not tools of instrumental rationality evincing a new capitalist mentality, but tools of social accommodation and products of the era's "economy of obligation." This early modern tale offers a vivid example of how and why one community turned to a mathematical algorithm to resolve conflicts about fairness. [ABSTRACT FROM AUTHOR]

[M. Ma, The connectivity of exchanged hypercubes, Discrete Math., Algorithms Appl. 2(2) (2010) 213–220.] proved that the vertex connectivity and the edge connectivity of the exchanged hypercube are each equal to the minimum degree of the graph. This paper presents a proof of that result, which is substantially simpler and more intuitive. [ABSTRACT FROM AUTHOR]

In this paper we consider finding a second-order stationary point (SOSP) of nonconvex equality constrained optimization when a nearly feasible point is known. In particular, we first propose a new Newton-conjugate gradient (Newton-CG) method for finding an approximate SOSP of unconstrained optimization and show that it enjoys a substantially better complexity than the Newton-CG method in [C. W. Royer, M. O'Neill, and S. J. Wright, Math. Program., 180 (2020), pp. 451-488]. We then propose a Newton-CG based augmented Lagrangian (AL) method for finding an approximate SOSP of nonconvex equality constrained optimization, in which the proposed Newton-CG method is used as a subproblem solver. We show that under a generalized linear independence constraint qualification (GLICQ), our AL method enjoys a total inner iteration complexity of O(ε7/peration complexity of O(ε7/2 min\{ n, ε3/4\}) for finding an (ε, ε)-SOSP of nonconvex equality constrained optimization with high probability, which are significantly better than the ones achieved by the proximal AL method in [Y. Xie and S. J. Wright, J. Sci. Comput., 86 (2021), pp. 1-30]. In addition, we show that it has a total inner iteration complexity of O(ε11/2) and an operation complexity of O(ε11/2 min\{ n, ε5/4\}) when the GLICQ does not hold. To the best of our knowledge, all the complexity results obtained in this paper are new for finding an approximate SOSP of nonconvex equality constrained optimization with high probability. Preliminary numerical results also demonstrate the superiority of our proposed methods over the other competing algorithms. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we focus on the proposed algorithms to solve a linear programming problem with the convex combination of the max–min and the max–average composition and the max–star composition, respectively. They have been proposed by Ghodousian and Khorram [A. Ghodousian, E. Khorram, Solving a linear programming problem with the convex combination of the max–min and the max–average fuzzy relation equations, Appl. Math. Comput. 180 (2006) 411–418] and Khorram et al. [E. Khorram, A. Ghodousian, A. Abbasi Molai, Solving linear optimization problems with max–star composition equation constraints, Appl. Math. Comput. 179 (2006) 654–661], respectively. Firstly, we show that the “Tabular method algorithm” in the first paper and the “First procedure” in the second paper may not lead to the optimal solutions of the two models in some cases. Secondly, we generalize the proposed algorithm by Abbasi Molai and Khorram [A. Abbasi Molai, E. Khorram, A modified algorithm for solving the proposed models by Ghodousian and Khorram and Khorram and Ghodousian, Appl. Math. Comput. 190 (2007) 1161–1167] to solve the two models. In fact, it modifies the presented algorithms in the two papers. Finally, some numerical examples are given to illustrate the purposes. [Copyright &y& Elsevier]

A multirepeat in a string is a substring (factor) that appears a predefined number of times. A multirepeat is maximal if it cannot be extended either to the right or to the left and produce a multirepeat. In this paper, we present algorithms for two different versions of the problem of finding maximal multirepeats in a set of strings. In the case of arbitrary gaps, we propose an algorithm with O(σN2n + α) time complexity. When the gap is bounded in a small range c, we propose an algorithm with O((c2 + σ2)mN2n log(Nn) + α) time complexity. Here, N is the number of strings, n the mean length of each string, m the multiplicity of the multirepeat and α the number of reported occurrences. Our results extend previous work by considering sets of strings as well as by generalizing pairs to multirepeats. [ABSTRACT FROM AUTHOR]

Purpose. As a scientific field, bioinformatics has drawn remarkable attention from various fields, such as information technology, mathematics, and modern biological sciences, in recent years. The topic models originating from the field of natural language processing have become the focus of attention with the rapid accumulation of biological datasets. Thus, this research is aimed at modeling the topic content of the bioinformatics literature presented by Iranian researchers in the Scopus Citation Database. Methodology. This research was a descriptive-exploratory study, and the studied population included 3899 papers indexed in the Scopus database, which had been indexed in this database until March 9, 2022. The topic modeling was then performed on the abstracts and titles of the papers. A combination of LDA and TF-IDF was utilized for topic modeling. Findings. The data analysis with topic modeling resulted in identifying seven main topics "Molecular Modeling," "Gene Expression," "Biomarker," "Coronavirus," "Immunoinformatics," "Cancer Bioinformatics," and "Systems Biology." Moreover, "Systems Biology" and "Coronavirus" had the largest and smallest clusters, respectively. Conclusion. The present investigation demonstrated an acceptable performance for the LDA algorithm in classifying the topics included in this field. The extracted topic clusters indicated excellent consistency and topic connection with each other. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of gossiping with interference constraint in radio ring networks. Gossiping (or total exchange information) is a protocol where each node in the network has a message and is expected to distribute its own message to every other node in the network. The gossiping problem consists in finding the minimum running time (makespan) of a gossiping protocol and algorithms that attain this makespan. We focus on the case where the transmission network is a ring network. We consider synchronous protocols where it takes one unit of time (step) to transmit a unit-length message. During one step, a node receives at most one message only through one of its two neighbors. We also suppose that, during one step, a node cannot be both a sender and a receiver (half duplex model). Moreover communication is subject to interference constraints. We use a primary node interference model where, if a node receives a message from one of its neighbors, its other neighbor cannot send at the same time. With these assumptions we completely solve the problem for ring networks. We first show lower bounds and then give gossiping algorithms which meet these lower bounds and so are optimal. The number of rounds depends on the congruences of n modulo 12. [ABSTRACT FROM AUTHOR]

We generalize the familiar notion of periodicity in sequences to a new kind of pseudoperiodicity, and we prove some basic results about it. We revisit the results of a 2012 paper of Shevelev and reprove his results in a simpler and more unified manner, and provide a complete answer to one of his previously unresolved questions. We consider finding words with specific pseudoperiod and having the smallest possible critical exponent. Finally, we consider the problem of determining whether a finite word is pseudoperiodic of a given size, and show that it is NP-complete. [ABSTRACT FROM AUTHOR]

Mixed graphs have both directed and undirected edges. We consider mixed graphs that are regular in both directed and undirected degree and with given girth. Araujo-Pardo, Hern'andez-Cruz, andMontellano-Ballesteros recently established a lower bound for regular mixed graphs with directed degree one that generalizes the Moore bound. In this paper we show that, in at least one non-trivial case, their bound can be achieved. For a few other specific values of direct degree, undirected degree and girth we are able to identify graphs (mixed cages) of minimum possible order. We also obtain some fairly tight bounds for a few other cases. [ABSTRACT FROM AUTHOR]

The (bitwise) complement x of a binary word x is obtained by changing each 0 in x to 1 and vice versa. An antisquare is a nonempty word of the form x x. In this paper, we study infinite binary words that do not contain arbitrarily large antisquares. For example, we show that the repetition threshold for the language of infinite binary words containing exactly two distinct antisquares is (5 +√5)/2. We also study repetition thresholds for related classes, where "two" in the previous sentence is replaced by a larger number. We say a binary word is good if the only antisquares it contains are 01 and 10. We characterize the minimal antisquares, that is, those words that are antisquares but all proper factors are good. We determine the growth rate of the number of good words of length n and determine the repetition threshold between polynomial and exponential growth for the number of good words. [ABSTRACT FROM AUTHOR]

Simple Summary: Cancer is basically a tough condition on a patient's body where cell grows uncontrollably. Normal cells are affected, which destroys the health of the patient. The main problem in cancer is spreading from one part to another. Therefore, the mathematical modeling of cancerous tumors integrates to check overall stability. A novel approach is introduced such as Bernstein polynomial with combination of genetic algorithm, sliding mode controller, and synergetic control. The proposed solution has easily eliminated cancerous cells within five days using synergetic control. In addition, five cases are incorporated to evaluate error function. In addition, a brief comparative study is added to contrast the simulation results with theoretical modeling. Cancerous tumor cells divide uncontrollably, which results in either tumor or harm to the immune system of the body. Due to the destructive effects of chemotherapy, optimal medications are needed. Therefore, possible treatment methods should be controlled to maintain the constant/continuous dose for affecting the spreading of cancerous tumor cells. Rapid growth of cells is classified into primary and secondary types. In giving a proper response, the immune system plays an important role. This is considered a natural process while fighting against tumors. In recent days, achieving a better method to treat tumors is the prime focus of researchers. Mathematical modeling of tumors uses combined immune, vaccine, and chemotherapies to check performance stability. In this research paper, mathematical modeling is utilized with reference to cancerous tumor growth, the immune system, and normal cells, which are directly affected by the process of chemotherapy. This paper presents novel techniques, which include Bernstein polynomial (BSP) with genetic algorithm (GA), sliding mode controller (SMC), and synergetic control (SC), for giving a possible solution to the cancerous tumor cells (CCs) model. Through GA, random population is generated to evaluate fitness. SMC is used for the continuous exponential dose of chemotherapy to reduce CCs in about forty-five days. In addition, error function consists of five cases that include normal cells (NCs), immune cells (ICs), CCs, and chemotherapy. Furthermore, the drug control process is explained in all the cases. In simulation results, utilizing SC has completely eliminated CCs in nearly five days. The proposed approach reduces CCs as early as possible. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of computing the rank of a block-structured symbolic matrix (a generic partitioned matrix) A = (A α β x α β) , where A α β is a 2 × 2 matrix over a field F and x α β is an indeterminate for α = 1 , 2 , ⋯ , μ and β = 1 , 2 , ⋯ , ν . This problem can be viewed as an algebraic generalization of the bipartite matching problem and was considered by Iwata and Murota (SIAM J Matrix Anal Appl 16(3):719–734, 1995). Recent interests in this problem lie in the connection with non-commutative Edmonds' problem by Ivanyos et al. (Comput Complex 27:561–593, 2018) and Garg et al. (Found. Comput. Math. 20:223–290, 2020), where a result by Iwata and Murota implicitly states that the rank and non-commutative rank (nc-rank) are the same for this class of symbolic matrices. The main result of this paper is a simple and combinatorial O ((μ ν) 2 min { μ , ν }) -time algorithm for computing the symbolic rank of a (2 × 2) -type generic partitioned matrix of size 2 μ × 2 ν . Our algorithm is inspired by the Wong sequence algorithm by Ivanyos et al. for the nc-rank of a general symbolic matrix, and requires no blow-up operation, no field extension, and no additional care for bounding the bit-size. Moreover it naturally provides a maximum rank completion of A for an arbitrary field F . [ABSTRACT FROM AUTHOR]

Background: Readability metrics provide us with an objective and efficient way to assess the quality of educational texts. We can use the readability measures for finding assessment items that are difficult to read for a given grade level. Hard‐to‐read math word problems can put some students at a disadvantage if they are behind in their literacy learning. Despite their math abilities, these students can perform poorly on difficult‐to‐read word problems because of their poor reading skills. Less readable math tests can create equity issues for students who are relatively new to the language of assessment. Less readable test items can also affect the assessment's construct validity by partially measuring reading comprehension. Objectives: This study shows how large language models help us improve the readability of math assessment items. Methods: We analysed 250 test items from grades 3 to 5 of EngageNY, an open‐source curriculum. We used the GPT‐3 AI system to simplify the text of these math word problems. We used text prompts and the few‐shot learning method for the simplification task. Results and Conclusions: On average, GPT‐3 AI produced output passages that showed improvements in readability metrics, but the outputs had a large amount of noise and were often unrelated to the input. We used thresholds over text similarity metrics and changes in readability measures to filter out the noise. We found meaningful simplifications that can be given to item authors as suggestions for improvement. Takeaways: GPT‐3 AI is capable of simplifying hard‐to‐read math word problems. The model generates noisy simplifications using text prompts or few‐shot learning methods. The noise can be filtered using text similarity and readability measures. The meaningful simplifications AI produces are sound but not ready to be used as a direct replacement for the original items. To improve test quality, simplifications can be suggested to item authors at the time of digital question authoring. Lay Description: What is Known About the Subject: Difficult to read math assessment items cause measurement and equity issuesReadability of math word problems negatively correlated with outcomes What Our Paper Adds: GPT‐3 AI system is capable to simplify math word problemsPrompt‐based and few‐shot learning‐based approaches are able to create meaningful simplifications, but with a very low accuracy rateText similarity and readability measures can be used to filter out noisy outputs and discover interesting simplifications What are the Implications for Practitioners: GPT‐3 AI is capable of generating relevant math world problem simplificationsSimplified text can be used as suggestions to question authors during the digital item authoring process [ABSTRACT FROM AUTHOR]

Introduction: This paper seeks to identify which of three published formulas used for estimating the blood volume of normal human subjects correlates most closely with blood volumes measured in a published study where erythrocyte volume was determined by a method using 51Cr and a nonradioactive dye was used to determine the plasma volume. Methods: Blood volumes predicted by three published algorithms were compared with blood volume estimates from a study by Retzlaff et al. using the two-tailed Wilcoxon signed rank test and a robust version of the Bland–Altman test. Results: When applied to a sample of normal subjects selected from Mayo Clinic personnel and patients, the Nadler formula correlated more closely with blood volume measured using a radio nucleotide technique than did the Allen formula or one based on a saline haemodilution technique. Conclusions: The Nadler formula correlated more closely with blood volume measurements derived from Retzlaff's study than the other formulas for estimating blood volume in a population with height and weight distribution more consistent with that seen in North America. It should be used in preference to the Allen formula for estimating blood volume in adult patients currently undergoing cardiac surgical procedures. Saline haemodilution techniques used to measure blood volume require validation against more recently developed nuclear medicine techniques using statistical methods other than regression analysis. Until validated, they should be used with caution for estimating blood volume in adult patients currently undergoing cardiac surgical procedures. If a formula using height, weight and sex is used to estimate blood volume in the context of cardiac surgery, then it must be derived using a much more comprehensive sample of the population to which it is applied than has occurred to date. In particular, it should include broader distributions of height, weight and the presence or absence and type of significant valvular disease. [ABSTRACT FROM AUTHOR]

Let G = (V;E) be a given graph of order n. A function f: V ! f0; 1; 2g is an independent Roman dominating function (IRDF) on G if for every vertex v 2 V with f(v) = 0 there is a vertex u adjacent to v with f(u) = 2 and fv 2 V: f(v) > 0g is an independent set. The weight of an IRDF f on G is the value f(V) = P v2V f(v). The minimum weight of an IRDF among all IRDFs on G is called the independent Roman domination number of G. In this paper, we give algorithms for computing the independent Roman domination number of G in O(jV j) time when G = (V;E) is a tree, unicyclic graph or proper interval graph. [ABSTRACT FROM AUTHOR]

Let k 1 be an integer, and let G be a finite and simple graph with vertex set V (G). A signed total Italian k-dominating function on a graph G is a function f: V (G) ! f1; 1; 2g such that P u2N(v) f(u) ≥ k for every v 2 V (G), where N(v) is the neighborhood of v, and each vertex u with f(u) = 1 is adjacent to a vertex v with f(v) = 2 or to two vertices w and z with f(w) = f(z) = 1. A set ff1; f2;: ::; fdg of distinct signed total Italian k-dominating functions on G with the property that Pd i=1 fi(v) ≤ k for each v 2 V (G), is called a signed total Italian k-dominating family (of functions) on G. The maximum number of functions in a signed total Italian k-dominating family on G is the signed total Italian k-domatic number of G, denoted by dk stI (G). In this paper we initiate the study of signed total Italian k-domatic numbers in graphs, and we present sharp bounds for dk stI (G). In addition, we determine the signed total Italian k-domatic number of some graphs. [ABSTRACT FROM AUTHOR]

Theory of quasi-orthogonal polynomials is significantly related to constructing vector Padé approximations. The present paper introduces an efficient procedure to compute adjacent families of quasi-orthogonal polynomials as defined in Sadaka (Appl. Numer. Math. 21:57–70, 1996) and Sadaka (Appl. Numer. Math. 24:483–499, 1997). The derived algorithm uses short recursive relations whose coefficients are written in terms of lower triangular block determinants. The strategy of computing such determinants is given and analyzed. [ABSTRACT FROM AUTHOR]

In order to improve the effect of classroom teaching and realize the improvement of mathematics teaching quality, this article combines data-driven decision-making technology to design a mathematics teaching plan system and applies data-driven decision-making technology to the design of mathematics teaching plan by improving the big data algorithm. In addition, this paper designs a mathematics teaching plan design system based on data-driven decision-making technology. The system learning module displays the knowledge points in a chapter-sequential navigation mode and stores data or information in the nodes, which are connected to form a network structure through chains. Finally, this paper verifies the designed system with experiments. From the results of the experimental research data, it can be seen that the mathematical teaching plan design system based on the data-driven decision-making technology constructed in this article has good practical effects. On this basis, the system constructed in this article can be verified through further practice. [ABSTRACT FROM AUTHOR]

With the increasing importance of mathematics in basic education, how to evaluate and analyze the intelligent effect of mathematics teaching classroom through scientific methods has become one of the indicators to evaluate the intelligent classroom. This paper studies the design and application of mathematics teaching intelligent classroom based on the PCA-NN (principal component analysis-neural network) algorithm. Firstly, this paper briefly describes the current research status of mathematics teaching intelligent classroom design and PCA-NN algorithm. Secondly, combined with the key factors of mathematics teaching, it formulates specific standards and puts forward an adaptive strategy of intelligent and personalized intelligent mathematics teaching classroom. Finally, the algorithm is verified by experiments. The results show that, for students with different mathematics basic levels, the mathematics teaching intelligent classroom based on the PCA-NN algorithm can effectively improve the quality of mathematics classroom teaching. Through the research on the factors such as teaching quality, effect, and interaction mode involved in the process of mathematics teaching classroom design, the intelligent classroom design factors affecting teaching quality are determined. This paper analyzes and studies the system from different angles. The research results provide some help for the current quality evaluation of classroom teaching and use the PCA-NN algorithm to make quantitative analysis and multivariate verification of mathematics classroom teaching effect. [ABSTRACT FROM AUTHOR]

This article investigates subject-related research metrics from the most popular scientometrics platforms with the capability of citation count. Quantitative analyses have been carried out to determine the most- to the least-cited subject areas to indicate the most active and dynamic fields in research. Subject areas are classified based on statistical analyses and the number of citations received in the period of search. Numerous articles were analyzed from top-ranked journals in all research fields covered by SCImago journal classification. A comprehensive data set was generated in 27 research subject areas, including 313 subject categories and 81 high-ranked journals. Results showed that the highest number of citations were related to the sciences and science-related subject areas. The subject areas of computer science and mathematics had the lowest research metrics and the smallest number of highly cited publications. Web of Science performed better than Scopus for subject-related evaluations. Analysis of frequency data showed that Google Scholar cited fewer papers for low-cited publications than did Scopus or Web of Science. For highly cited publications, however, Google Scholar was found to have better performance. Web of Science showed the best consistency in citation coverage in most of the investigated subject areas. [ABSTRACT FROM AUTHOR]

Abstract: In 1.9 of the paper [A. Hahn, A Hermitian Morita theorem for algebras with anti-structure, J. Algebra 93 (1985) 215–235], should be replaced by . This leads to minor changes in the rest of the paper where the ring should be replaced by its opposite and vice versa. [Copyright &y& Elsevier]

Malignant melanoma is one of the most threatening cancers to human health. Only 14% of patients with malignant melanoma have a remaining life span of 5 years. At present, there have been some studies looking for potential prognostic indicators of esophageal cancer from the level of genes and infiltrating immune cells, but there are still some problems that need to be resolved urgently. This paper proposes IGHG3 as the immune infiltration of malignant melanoma, which takes into account the computational mathematics. It aims to deduce the characteristics of immune cell infiltration in malignant melanoma and study the relationship between different immune cell infiltration characteristics and prognosis. The method in this article is to establish a computational mathematical model for the immunotherapy of melanoma, then study the method of identification of the affinity of the IGHG3 reagent, and finally obtain the gene expression of immune infiltration. The functions of these methods are, respectively, to predict the dynamic behavior of T cells with two different specificities through mathematical models and to test the matching degree of different concentrations of IGHG3 reagent with the human body. Then use the ssGSEA algorithm to obtain immune infiltration related data and calculate the difference between the weighted empirical cumulative distribution function of all genes in the effect of IGHG3 on melanoma that was carried out. The experimental results showed the computational mathematical method genome and all the remaining genes. In this study, a computational mathematical method to detect the IGHG3 gene expression had a significant inhibitory effect on A375 cells in the experimental group, and the knockdown efficiency reached 85.6%. [ABSTRACT FROM AUTHOR]

Multiple external representations (MERs) play an important role in the learning field of mathematics. Whereas the cognitive theory of multimedia learning and the integrative text and picture comprehension model assume that the heterogeneous combination of symbolic and analogous representations fosters learning; the design, functions, and tasks framework holds that learning benefits depend on the specific functions of MERs. The current paper describes a conceptual replication study of one of the few studies comparing single representations, heterogeneous, and homogeneous MERs in the context of mathematics learning. In a balanced incomplete block design, the participants were provided single representations (a graphic, text, or formula) or a heterogeneous (e.g., text + graphic) or homogeneous (text + formula) combination of these to solve linear system of equations problems. In accordance with previous research, performance was superior in conditions providing MERs compared to single‐representation conditions. Moreover, heterogeneous MERs led to time savings over homogeneous MERs which triggered an increase in cognitive load. Contrary to previous research, text was the least fixated representation whereas the graphical representation proved to be most beneficial. With regard to practical implications, experts should be fostered through more challenging homogeneous MERs whereas novices should be supported through the accessible graphic contained in heterogeneous MERs. Lay Description: What is already known about this topic: Providing multiple instead of single representations can foster mathematics learning.However, some combinations of representations hamper the performance of novice learners.The classical multimedia view explains the positive effect of combining text with picture.Recent research suggests the combination of multiple symbolic representations (text and formula). What this paper adds: The study replicated the effect of multiple symbolic representations for equation solving.In contrast to former research, each representation (text, formula, and graphic) was functionally equivalent.Tasks with differently coded representations were solved faster and with less mental effort.Gaze behavior indicated that students mostly used the graphical representation. Implications for practice and/or policy: Beginners should be supported with a graphic when solving equations.Experts should be challenged with a combination of symbolic representations to benefit the most. [ABSTRACT FROM AUTHOR]

This paper provides results in the area of the analytical derivation of the efficient set of a mean-variance portfolio selection problem that has more than three criteria. By "analytical" we mean derived by formula as opposed to being computed by algorithm. By "more than three criteria", we mean that beyond the mean and variance of regular portfolio selection, the problems addressed have two or more additional linear objectives. The additional objectives might include sustainability, dividend yield, liquidity, and R&D as extra objectives like these are being seen with greater frequency. While not all multiple criteria portfolio selection problems lend themselves to an analytical derivation, a certain class does and the problems in this class are covered by the mathematics of this paper. [ABSTRACT FROM AUTHOR]

A recursive algorithm for the determinant evaluation of general opposite-bordered tridiagonal matrices has been proposed by Jia et al. (J Comput Appl Math 290:423–432, 2015). Since the algorithm is a symbolic algorithm, it never suffers from breakdown. However, it may be time-consuming when many symbolic names emerge during the symbolic computation. In this paper, without using symbolic computation, first we present a novel breakdown-free numerical algorithm for computing the determinant of an n-by-n opposite-bordered tridiagonal matrix, which does not require any extra memory storage for the implementation. Then, we present a cost-efficient algorithm for the determinants of opposite-bordered tridiagonal matrices based on the use of the combination of an elementary column operation and Sylvester's determinant identity. Furthermore, we provide some numerical results with simulations in Matlab implementation in order to demonstrate the accuracy and efficiency of the proposed algorithms, and their competitiveness with other existing algorithms. The corresponding results in this paper can be readily obtained for computing the determinants of singly-bordered tridiagonal matrices. [ABSTRACT FROM AUTHOR]

With the rapid development of artificial intelligence (AI) concept technology, it promotes the innovation of educational concept. Mostly for the education information analysis in the class of mathematics in the university, it should be based on a big data-driven system to promote the quality of teaching in the classroom. In the method of teaching math in university, teachers should take full advantage of the benefits of a big data-driven system powered by AI, grow a good teaching model for students, promote education through big data, progressively teach students according to their aptitude, develop in a tailored direction, increase teaching quality and effectiveness, and finally create more great talents for our country. For the sake of improving the resource sharing and the management level of the curriculum which teaches advanced knowledge about mathematics teaching, based on a particle swarm optimization algorithm, an advanced math teaching system is proposed in this paper. The fusion model that can be used in the teaching process of math in university is constructed, the adaptive scheduling of the curriculum which teaches advanced knowledge about mathematics auxiliary teaching resources is realized by an optimization algorithm used for fusion particle swarm, the autocorrelation feature of the curriculum which teaches advanced knowledge about mathematics auxiliary teaching resources is extracted, and the adaptive optimization of the curriculum which teaches advanced knowledge about mathematics auxiliary teaching resource fusion is realized by fuzzy correlation feature matching and statistical analysis. In the process of particle swarm optimization, the combination of statistical features is studied and managed, the resource scheduling and information fusion are realized, and the management capability of the curriculum which teaches advanced knowledge about mathematics auxiliary teaching is promoted, and the experimental results demonstrate that the designed system has a high integration of teaching information resources and strong information scheduling ability and improved the management level of the curriculum which teaches advanced knowledge about mathematics complementary teaching. [ABSTRACT FROM AUTHOR]

In this paper, the theory of viscoelastic material relaxation modulus testing, testing method, and material relaxation modulus parameter solution method is studied. Based on the IoT sensor test devices and the Hertzian mathematics theory, the relationship between the compression amount, pressure, and relaxation modulus of a rigid spherical indenter pressed into a flat viscoelastic material is studied. In combination with the Boltzmann superposition principle, the relaxation modulus test method and theory for viscoelastic materials are proposed. A good fitting curve was obtained to solve the relaxation modulus parameters of various materials under the three-element Maxwell model. The experimental setup and the results of the parameter fitting were analyzed to verify the feasibility and accuracy of the results. [ABSTRACT FROM AUTHOR]

Given a real number α ∈ (0 , 1) , we define the Webster sequence of density α to be W α = (⌈ (n − 1 / 2) / α ⌉) n ∈ N , where ⌈ x ⌉ is the ceiling function. It is known that if α and β are irrational with α + β = 1 , then W α and W β partition N. On the other hand, an analogous result for three-part partitions does not hold: There does not exist a partition of N into sequences W α , W β , W γ with α , β , γ irrational. In this paper, we consider the question of how close one can come to a three-part partition of N into Webster sequences with prescribed densities α , β , γ. We show that if α , β , γ are irrational with α + β + γ = 1 , there exists a partition of N into sequences of densities α , β , γ , in which one of the sequences is a Webster sequence and the other two are "almost" Webster sequences that are obtained from Webster sequences by perturbing some elements by at most 1. We also provide two efficient algorithms to construct such partitions. The first algorithm outputs the n th element of each sequence in O (1) time and the second algorithm gives the assignment of the m th positive integer to a sequence in O (1) time. We show that the results are best-possible in several respects. Moreover, we describe applications of these results to apportionment and optimal scheduling problems. [ABSTRACT FROM AUTHOR]

This research aims to improve the rationality and intelligence of AUTOMATICALLY HIGHER MATHEMATICALLY EXAM SYSTEM (AHMES) through some AI algorithms. AHMES is an intelligent and high-quality higher math examination solution for the Department of Computer Engineering at Pai Chai University. This research redesigned the difficulty system of AHMES and used some AI algorithms for initialization and continuous adjustment. This paper describes the multiple linear regression algorithm involved in this research and the AHMES learning (AL) algorithm improved by the Q-learning algorithm. The simulation test results of the upgraded AHMES show the effectiveness of these algorithms. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this short note is to show on a numerical example that one of the two optimization algorithms proposed in [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886] may not lead to the optimal solution in some cases. Besides it will be pointed out that the other algorithm (correct, but unfortunately ineffective for larger problems) proposed in [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886] can be extended to a wider class of non-convex optimization problems. [Copyright &y& Elsevier]

Fundamental scientific advances can take decades to translate into improvements in human health. Shortening this interval would increase the rate at which scientific discoveries lead to successful treatment of human disease. One way to accomplish this would be to identify which advances in knowledge are most likely to translate into clinical research. Toward that end, we built a machine learning system that detects whether a paper is likely to be cited by a future clinical trial or guideline. Despite the noisiness of citation dynamics, as little as 2 years of postpublication data yield accurate predictions about a paper's eventual citation by a clinical article (accuracy = 84%, F1 score = 0.56; compared to 19% accuracy by chance). We found that distinct knowledge flow trajectories are linked to papers that either succeed or fail to influence clinical research. Translational progress in biomedicine can therefore be assessed and predicted in real time based on information conveyed by the scientific community's early reaction to a paper. [ABSTRACT FROM AUTHOR]

Phylogenetic networks generalize phylogenetic trees by allowing the modelization of events of reticulate evolution. Among the different kinds of phylogenetic networks that have been proposed in the literature, the subclass of binary tree-child networks is one of the most studied ones. However, very little is known about the combinatorial structure of these networks. In this paper we address the problem of generating all possible binary tree-child (BTC) networks with a given number of leaves in an efficient way via reduction/augmentation operations that extend and generalize analogous operations for phylogenetic trees, and are biologically relevant. Since our solution is recursive, this also provides us with a recurrence relation giving an upper bound on the number of such networks. We also show how the operations introduced in this paper can be employed to extend the evolutive history of a set of sequences, represented by a BTC network, to include a new sequence. An implementation in python of the algorithms described in this paper, along with some computational experiments, can be downloaded from . [ABSTRACT FROM AUTHOR]

Past research on the process of extinguishing a fire typically used a traditional linear water jet falling point model and the results ignored external factors, such as environmental conditions and the status of the fire engine, even though the water jet falling point location prediction was often associated with these parameters and showed a nonlinear relationship. This paper constructed a BP (Back Propagation) neural network model. The fire gun nozzle characteristics were included as model inputs, and the water discharge point coordinates were the model outputs; thus, the model could precisely predict the water discharge point with small error and high precision to determine an accurate firing position and allow for the timely adjustment of the spray gun. To improve the slow convergence and local optimality problems of the BP neural network (BPNN), this paper further used a genetic algorithm to optimize the BPNN (GA-BPNN). The BPNN can be used to optimize the weights in the network to train them for global optimization. A genetic algorithm was introduced into the neural network approach, and the water jet landing prediction model was further improved. The simulation results showed that the prediction accuracy of the GA-BP model was better than that of the BPNN alone. The established model can accurately predict the location of the water jet, making the prediction results more useful for firefighters. [ABSTRACT FROM AUTHOR]

Several lifetime distributions have played an important role to fit survival data. However, for some of these models, the computation of maximum likelihood estimators is quite difficult due to presence of flat regions in the search space, among other factors. Several well-known derivative-based optimization tools are unsuitable for obtaining such estimates. To circumvent this problem, we introduce the AdequacyModel computational library version 2.0.0 for the R statistical environment with two major contributions: a general optimization technique based on the Particle Swarm Optimization (PSO) method (with a minor modification of the original algorithm) and a set of statistical measures for assessment of the adequacy of the fitted model. This library is very useful for researchers in probability and statistics and has been cited in various papers in these areas. It serves as the basis for the Newdistns library (version 2.1) published in an impact journal in the area of computational statistics, see . It is also the basis of the Wrapped library (version 2.0), see . A third package making use of the AdequacyModel library can be found in . In addition, the proposed library has proved to be very useful for maximizing log-likelihood functions with complex search regions. The library provides a greater control of the optimization process by introducing a stop criterion based on a minimum number of iterations and the variance of a given proportion of optimal values. We emphasize that the new library can be used not only in statistics but in physics and mathematics as proved in several examples throughout the paper. [ABSTRACT FROM AUTHOR]

It is well known that Krasnoselskii-Mann iteration of nonexpansive mappings find application in many areas of mathematics and know to be weakly convergent in the infinite dimensional setting. In this paper, we introduce and study an explicit iterative scheme by a modified Krasnoselskii-Mann algorithm for approximating fixed points of multivalued quasi-nonexpansive mappings in Banach spaces. Strong convergence of the sequence generated by this algorithm is established. There is no compactness assumption. The results obtained in this paper are significant improvement on important recent results. [ABSTRACT FROM AUTHOR]

This paper proposes an innovative statistical method to measure the impact of the class/school on student achievements in multiple subjects. We propose a semiparametric model for a bivariate response variable with random coefficients, that are assumed to follow a discrete distribution with an unknown number of support points, together with an Expectation-Maximization algorithm—called BSPEM algorithm—to estimate its parameters. In the case study, we apply the BSPEM algorithm to data about Italian middle schools, considering students nested within classes, and we identify subpopulations of classes, standing on their effects on student achievements in reading and mathematics. The proposed model is extremely informative in exploring the correlation between multiple class effects, which are typical of the educational production function. The estimated class effects on reading and mathematics student achievements are then explained in terms of various class and school level characteristics selected by means of a LASSO regression. [ABSTRACT FROM AUTHOR]

Research presented in this paper was initiated by the publication [A. D. Agaltsov and R. G. Novikov, Examples of solving the inverse scattering problem and the equations of the Veselov–Novikov hierarchy from the scattering data of point potentials, Russian Math. Surveys74 (2019), 3, 373–386] and is based on its results. Two sets of the complex monopole scattering coefficients are distinguished among the possible values of these coefficients for nonabsorbing inhomogeneities. These sets differ in phases of the scattering coefficients. In order to analyze the features and possibilities of reconstructing the inhomogeneities of both sets, on the one hand, the inverse problem is solved for each given value of the monopole scattering coefficient using the Novikov functional algorithm. On the other hand, the scatterer is selected in the form of a homogeneous cylinder with the monopole scattering coefficient that coincides with the given one. The results obtained for the monopole inhomogeneity and for the corresponding cylindrical scatterer are compared in the coordinate and spatial-spectral spaces. The physical reasons for the similarities and differences in these results are discussed when the amplitude of the scattering coefficient changes, as well as when passing from one set to another. [ABSTRACT FROM AUTHOR]

Grey wolf optimization (GWO) algorithm is a new emerging algorithm that is based on the social hierarchy of grey wolves as well as their hunting and cooperation strategies. Introduced in 2014, this algorithm has been used by a large number of researchers and designers, such that the number of citations to the original paper exceeded many other algorithms. In a recent study by Niu et al., one of the main drawbacks of this algorithm for optimizing real‐world problems was introduced. In summary, they showed that GWO's performance degrades as the optimal solution of the problem diverges from 0. In this paper, by introducing a straightforward modification to the original GWO algorithm, that is, neglecting its social hierarchy, the authors were able to largely eliminate this defect and open a new perspective for future use of this algorithm. The efficiency of the proposed method was validated by applying it to benchmark and real‐world engineering problems. [ABSTRACT FROM AUTHOR]

This paper is concerned with the topological structure, reachability, and stabilization for Boolean control networks (BCNs) with state constraints via event-triggered control (ETC) scheme. In the first part, the topological structure of BCNs with state constraints is studied. Under the framework of state constrain, the definitions of fixed point and cycle are first defined. A novel phenomenon is that there may exist two kinds constrained fixed points, which are, respectively, named as the livelock and deadlock ones. It is different with the traditional fixed point. Accordingly, a formula is presented to calculate the number of constrained fixed points and constrained cycles. In the second part, the constrained reachability and stabilization problem of the event-triggered controlled BCNs are investigated. Two necessary and sufficient criteria are, respectively, obtained. Furthermore, an algorithm is developed to design all feasible controllers. Finally, a reduced model of the lac operon in the Escherichia coli is shown to illustrate the efficiency of the obtained results. [ABSTRACT FROM AUTHOR]

Multiple imputation is a recommended method for handling incomplete data problems. One of the barriers to its successful use is the breakdown of the multiple imputation procedure, often due to numerical problems with the algorithms used within the imputation process. These problems frequently occur when imputation models contain large numbers of variables, especially with the popular approach of multivariate imputation by chained equations. This paper describes common causes of failure of the imputation procedure including perfect prediction and collinearity, focusing on issues when using Stata software. We outline a number of strategies for addressing these issues, including imputation of composite variables instead of individual components, introducing prior information and changing the form of the imputation model. These strategies are illustrated using a case study based on data from the Longitudinal Study of Australian Children. [ABSTRACT FROM AUTHOR]