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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]

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]

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]

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]

[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]

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 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]

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 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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

• A fast contact detection algorithm (FCDA) for ice-ship interaction (ISI) is proposed • The MPI parallelization for 2-D Peridynamic (PD) theory is first introduced • The newly developed ice-ship interaction (ISI) model is effective in predicting ice damage and crack propagation in the icebreaking process • The developed ice-ship interaction (ISI) model is applied to investigate icebreaking effectiveness for two different bow shapes The bow shape is the most critical factor to determine the icebreaking performance of an icebreaker. Mechanism study on the icebreaking process for different bow types is necessary for the initial design of the icebreaker hull form. This paper proposed an ice-ship interaction model based on the meshfree method, Peridynamics, in which the geometric mathematics concept is embedded to detect the contact between material points and ship hull. Furthermore, a fast contact detection algorithm based on Massage Passing Interface (MPI) solver is built to improve the computational efficiency of the developed numerical method. Two typical icebreaker bows, the conventional bow and the unconventional bow, breaking the level ice with constant speed is numerically studied by the above model. The results of the conventional icebreaker bow are compared with the experimental results, which verifies the simulation accuracy of the model developed in the present work. Afterwards, the icebreaking modes and icebreaking loads of two different shapes of icebreaker bows are compared and analysed. The results show that the developed ice-ship interaction model effectively predicts differences of icebreaking processes between different icebreakers, such as ice damage pattern, ice loads, and channel, despite their common point in domain bending failure mode. Moreover, this research significantly improves computational efficiency and provides theoretical guidance for designing the icebreaker bow. [ABSTRACT FROM AUTHOR]