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1
Hembree, Ray. "Effects of Noncontent Variables on Mathematics Test Performance." Journal for Research in Mathematics Education 18, no. 3 (May 1987): 197–214. http://dx.doi.org/10.5951/jresematheduc.18.3.0197.
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Results of 120 research studies were combined by meta-analysis to determine effects on mathematics test performance of factors other than knowledge of content. Effect sizes for 18 variables were derived by the method invented by Glass and tested for consistency and significance with inferential statistics provided by Hedges and Olkin. Conditions that enhanced performance included testwiseness training, praise, word-problem pictures, and frequent testing. Conditions that depressed performance included the use of “none of these” as a multiple-choice option and the presence of extraneous information in word problems. Conditions to which performance seemed insensitive included external reward, reproof, and placement of the question in word problems.
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Huang, Junjian, Ming Xu, Hengyi Zheng, and Qian Shang. "Chinese Math Word Problems Generation Network." Journal of Physics: Conference Series 2050, no. 1 (October 1, 2021): 012001. http://dx.doi.org/10.1088/1742-6596/2050/1/012001.
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Abstract Aiming at the feature vector bottleneck problem and the high time cost of the training process in the automatic generation of Chinese math word problems under the end-to-end architecture, we proposed an automatic generation method of Chinese math word problems based on the pre-training model combined with the integration of encoder and decoder. We used a deep neural network to model the mathematical equation sequence and Chinese keyword information, and used the stepped attention matrix to generate word problems. For training and testing on the Ape210K data set, compared with the end-to-end method, the Rouge-1 and Rouge-L evaluation indicators in our method was increased by 14.1% and 12.5%, as well as the training time cost was reduced by nearly 50%.
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Mesa, Vilma, Claire Wladis, and Laura Watkins. "Research Problems in Community College Mathematics Education: Testing the Boundaries of K-12 Research." Journal for Research in Mathematics Education 45, no. 2 (March 2014): 173–92. http://dx.doi.org/10.5951/jresematheduc.45.2.0173.
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The purpose of this commentary is to articulate the need to investigate problems of mathematics instruction at community colleges. We briefly describe some features of this often-ignored institution and the current status of research. We also make an argument for how investigations of instruction in this setting can both advance our understanding of this particular context and give practitioners tools to deal with pressures from policymakers to show short-term results. This work is the result of a collaborative effort between community college practitioners and researchers, responding to the needs of their work in mathematics education.
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Crowley, Mary L. "Aligning Assessment with Classroom Practices: A Promising Testing Format." Mathematics Teacher 90, no. 9 (December 1997): 706–11. http://dx.doi.org/10.5951/mt.90.9.0706.
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The 1990s have emerged as a decade in which the mathematics community is redefining what we teach, how we teach, and, consequently, what and how we assess. What we are teaching has a stronger conceptual orientation than in the past. How we are teaching involves ouT students more actively than ever before. And what and how we are assessing … has caused us some problems. All too often, after creating an environment wherein students have, for example, used calculators and group work to investigate challenging and meaningful mathematical situations, we assess their learning through a standard in-class test. Individuals work independently on questions that, given the short time allowed to complete them, are by necessity less demanding than the previous class work. The assessment is not consistent with the curricular or pedagogical reforms.
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Bakhytkul, Kaskatayeva, and BATYRBAEVA Gulniet Asilkhanovna. "TRAINING OF FUTURE TEACHERS OF MATHEMATICS TO THE FORMATION OF RESEARCH SKILLS OF STUDENTS." International Journal of Engineering Technologies and Management Research 4, no. 12 (February 7, 2020): 13–20. http://dx.doi.org/10.29121/ijetmr.v4.i12.2017.130.
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This article describes the preparation of future teachers of mathematics to the formation of research skills of students. Targeted formation of research skills of students in accordance with the modern model of education of Kazakhstan in the conditions of modernization of secondary education requires: improving the research training of students, ready for effective work in schools. The purpose of the study is to prepare future teachers of mathematics to the formation of research skills of students through solving math problems. The study used research methods as analysis of scientific-methodical and special literature on the research problem; study and analysis of curricula and standards of professional-pedagogical skills, curricula, textbooks and learning materials; pedagogical observation; interview; survey; testing. As a result, students showed willingness to formation of research skills of students through solving math problems. The paper shows methods of solving mathematical problems. The article proposes a solution to the problem of formation of research skills of students on the basis of the decision search task.
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Miller, Jeff. "Hypothesis Testing in the Real World." Educational and Psychological Measurement 77, no. 4 (October 6, 2016): 663–72. http://dx.doi.org/10.1177/0013164416667984.
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Critics of null hypothesis significance testing suggest that (a) its basic logic is invalid and (b) it addresses a question that is of no interest. In contrast to (a), I argue that the underlying logic of hypothesis testing is actually extremely straightforward and compelling. To substantiate that, I present examples showing that hypothesis testing logic is routinely used in everyday life. These same examples also refute (b) by showing circumstances in which the logic of hypothesis testing addresses a question of prime interest. Null hypothesis significance testing may sometimes be misunderstood or misapplied, but these problems should be addressed by improved education.
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Supriyatin, Wahyu, and Kausar Japa Wisesha. "Implementation of Digital Marketing as A Strategy to Improve Marketing and Sales." Majalah Ilmiah Bijak 19, no. 1 (April 10, 2022): 117–26. http://dx.doi.org/10.31334/bijak.v19i1.1691.
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JerseyBolaku distro in Jatiasih, sells conventional and custom jersey. Marketing their products using conventional methods where customers come to see the product and make transactions. The owner wants product promotion, by word of mouth and through social media. The owner do manual bookkeeping by recording every incoming and outgoing product, so there is duplicate and inappropriate data. This makes owners changed the marketing strategy from conventional to digital. The purpose of this research is to distribution using digital marketing. The digital marketing strategy made by owners, used e-commerce website, where it can be accessed by customers anywhere using a smartphone. Customers need access the website if they want to view products and make transactions. Owners find it easy to view sales reports in each period. The method used in making the website is the SDLC method with a prototyping model. The steps taken in the prototyping model is to identifying needs and problems of user, hardware, software, determining the programming language, designing user interfaces for admins and users are using UML diagrams, the prototypes website need to be evaluated before launching and do evaluating and improving if any problems when tested and finally launched the system to be implemented. Website testing is done by using black box testing to test the functionality of the website. Website running successfully using Internet Explorer on PC and smartphone. Website successfully hosted, customers can view and order products more easier and faster. The owner can record sales transactions and record products in more detail.
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Sun, Ping’an. "Wood Quality Defect Detection Based on Deep Learning and Multicriteria Framework." Mathematical Problems in Engineering 2022 (May 26, 2022): 1–9. http://dx.doi.org/10.1155/2022/4878090.
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Traditional nondestructive testing technology for wood defects has a series of problems such as low identification accuracy, high cost, and cumbersome operation, and traditional testing methods cannot accurately show the specific location and size of wood internal defects; it is urgent to explore a new nondestructive testing scheme for wood defects. Aiming at this problem, this paper designs and develops an automatic detection method for wood surface defects based on deep learning algorithm and multicriteria framework. By comparing the performance of different deep learning detection methods on the data set, the advantages and disadvantages of the detection method in this paper are proved. After a series of works, such as the development and optimization of the experimental algorithm, the algorithm proposed meets the requirements in both the detection accuracy and training time.
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Kosova, E. A., and M. Yu Khalilova. "Web Accessibility Analysis of Massive Open Online Courses in Mathematical Disciplines." Vysshee Obrazovanie v Rossii = Higher Education in Russia 28, no. 10 (November 1, 2019): 157–66. http://dx.doi.org/10.31992/0869-3617-2019-28-10-157-166.
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The paper studies the problem of developing the massive open online courses (MOOCs) that conform to the content accessibility principles for persons with disabilities. Using the browsing of MOOCs platform catalogues, a total of 56 Russian-language free MOOCs in mathematical disciplines hosted on 5 platforms has been received. By automatic testing using Web Accessibility Checker, the accessibility of the functional and informational content of the MOOCs was evaluated. 73% of MOOCs were found to conform to the syllabus subjects “Probability Theory and Mathematical Statistics”, “Discrete Mathematics” and “Algebra and Geometry”; 8 basic disciplines of higher mathematics education are not covered by online education; 96,4% of the courses have accessibility limitations, especially for people with visual impairment. Accessibility problems are related to shortcomings of the platforms and MOOC developers’ errors. The results show a weak coverage by MOOCs of the basic mathematical disciplines included in the higher education curriculum in Russia and indicate the low content accessibility of the mathematical MOOCs for students with disabilities. The results of the work imply the need for: expanding the range of MOOCs to cover all basic mathematical disciplines; troubleshooting the accessibility in existing courses (pursuant to WCAG); prescription to platforms and developers to strictly adhere to WCAG in future courses.
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Nurieva, L. M., and S. G. Kiselev. "Problems of analysis of the relationship between the learning context and TIMSS testing results." Education and science journal 25, no. 1 (January 16, 2023): 108–41. http://dx.doi.org/10.17853/1994-5639-2023-1-108-141.
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Introduction. For more than two decades, the Organisation for Economic Cooperation and Development has been organising a number of comparative studies of the quality of education in different countries. One of them is the study of mathematics and science education TIMSS (Trends in International Mathematics and Science Study), which is conducted jointly with the International Association for the Evaluation of Educational Achievements (IEA). The last, seventh, cycle of the study was conducted in 2019. TIMSS statistics is regularly posted in the public domain on the IEA website so that specialists can independently conduct research in any aspect of their interest. One of the areas of analysis in this case is traditionally the search for the causes of certain test results, which are determined by the peculiarities of the organisation of the educational process and the context of learning in different countries. At the same time, a study of professional literature showed that among the factors of the social and school context, the analysis of which is provided by the research tools, only an extremely limited range of them turned out to be statistically directly related to TIMSS scores. Specialists systematically encounter inexplicable absence or low correlation values of TIMSS test scores and context indicators. The authors think that the main reason for such difficulties is inattention to the peculiarities of the indicators used in the calculation of measures of statistical relationships. Aim. The present research aims to identify a statistical relationship between test results and indicators of the context of schoolchildren’s learning, as well as the influence of the TIMSS information collection and processing system on the productivity of analysing the research results.Methodology and research methodology. The methodological basis of the work is a systematic approach, which is based on the consideration of the results of the international TIMSS study as a whole: i.e. a complex of interrelated elements (organisations, tools, assessment indicators, scoring systems). The work was carried out on the basis of applied research procedures (observation, description, comparison, measurement, etc.), within which general scientific (comparative analysis, systematisation, generalisation) and statistical research methods (statistical and correlation analysis, etc.) were also used. The source of information was the International Database of Electronic Testing TIMSS-2019, hosted in the IEA repository. The TIMSS datasets were analysed using the IEA International Database (IDB) parser plug-in for SPSS (version 4.0).Results. For most indicators of the social and student context of learning, the authors found the absence or low value of statistical relationships with TIMSS scores. The number of books at home and parents’ education turned out to be statistically related to TIMSS scores concerning the indicators of social well-being and home learning conditions envisaged by the organisers. The indicators of learning conditions at school included the frequency of independent work in class; motivational factors included plans to continue education and self-evaluation of students’ math proficiency. Evidently, even these relationships turned out to be weak. It was revealed that the difficulties in detecting a correlation between TIMSS scores and learning conditions are caused by the very nature of the analysed variables: 1. the approximate nature of individual student assessments used in TIMSS; 2. low differentiation of students according to a number of indicators of the learning context; 3. insufficient reliability of information obtained from sociological surveys of schoolchildren.Practical significance. The authors believe that in order to improve the quality of analytical work on relevant topics, it is necessary to pay close attention to the essence behind the variables used in statistical calculations. In turn, the TIMSS organisers need to continue improving the measurement procedures and research tools by introducing additional success criteria that reflect the individual and comparable results of students in the current TIMSS cycle, as well as indicators of the reliability of contextual information obtained by sociological means.
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Biscarini, Chiara, Silvia Di Francesco, Fernando Nardi, and Piergiorgio Manciola. "Detailed Simulation of Complex Hydraulic Problems with Macroscopic and Mesoscopic Mathematical Methods." Mathematical Problems in Engineering 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/928309.
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The numerical simulation of fast-moving fronts originating from dam or levee breaches is a challenging task for small scale engineering projects. In this work, the use of fully three-dimensional Navier-Stokes (NS) equations and lattice Boltzmann method (LBM) is proposed for testing the validity of, respectively, macroscopic and mesoscopic mathematical models. Macroscopic simulations are performed employing an open-source computational fluid dynamics (CFD) code that solves the NS combined with the volume of fluid (VOF) multiphase method to represent free-surface flows. The mesoscopic model is a front-tracking experimental variant of the LBM. In the proposed LBM the air-gas interface is represented as a surface with zero thickness that handles the passage of the density field from the light to the dense phase and vice versa. A single set of LBM equations represents the liquid phase, while the free surface is characterized by an additional variable, the liquid volume fraction. Case studies show advantages and disadvantages of the proposed LBM and NS with specific regard to the computational efficiency and accuracy in dealing with the simulation of flows through complex geometries. In particular, the validation of the model application is developed by simulating the flow propagating through a synthetic urban setting and comparing results with analytical and experimental laboratory measurements.
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Alaroud, Mohammad, Osama Ababneh, Nedal Tahat, and Shrideh Al-Omari. "Analytic technique for solving temporal time-fractional gas dynamics equations with Caputo fractional derivative." AIMS Mathematics 7, no. 10 (2022): 17647–69. http://dx.doi.org/10.3934/math.2022972.
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<abstract><p>Constructing mathematical models of fractional order for real-world problems and developing numeric-analytic solutions are extremely significant subjects in diverse fields of physics, applied mathematics and engineering problems. In this work, a novel analytical treatment technique called the Laplace residual power series (LRPS) technique is performed to produce approximate solutions for a non-linear time-fractional gas dynamics equation (FGDE) in a multiple fractional power series (MFPS) formula. The LRPS technique is a coupling of the RPS approach with the Laplace transform operator. The implementation of the proposed technique to handle time-FGDE models is introduced in detail. The MFPS solution for the target model is produced by solving it in the Laplace space by utilizing the limit concept with fewer computations and more accuracy. The applicability and performance of the technique have been validated via testing three attractive initial value problems for non-linear FGDEs. The impact of the fractional order <italic>β</italic> on the behavior of the MFPS approximate solutions is numerically and graphically described. The <italic>j</italic>th MFPS approximate solutions were found to be in full harmony with the exact solutions. The solutions obtained by the LRPS technique indicate and emphasize that the technique is easy to perform with computational efficiency for different kinds of time-fractional models in physical phenomena.</p></abstract>
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Castro, Mario, and Rob J. de Boer. "Testing structural identifiability by a simple scaling method." PLOS Computational Biology 16, no. 11 (November 3, 2020): e1008248. http://dx.doi.org/10.1371/journal.pcbi.1008248.
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Successful mathematical modeling of biological processes relies on the expertise of the modeler to capture the essential mechanisms in the process at hand and on the ability to extract useful information from empirical data. A model is said to be structurally unidentifiable, if different quantitative sets of parameters provide the same observable outcome. This is typical (but not exclusive) of partially observed problems in which only a few variables can be experimentally measured. Most of the available methods to test the structural identifiability of a model are either too complex mathematically for the general practitioner to be applied, or require involved calculations or numerical computation for complex non-linear models. In this work, we present a new analytical method to test structural identifiability of models based on ordinary differential equations, based on the invariance of the equations under the scaling transformation of its parameters. The method is based on rigorous mathematical results but it is easy and quick to apply, even to test the identifiability of sophisticated highly non-linear models. We illustrate our method by example and compare its performance with other existing methods in the literature.
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Margolina, Natalia Lvovna, and Irina Vladimirovna Nalimova. "Mathematical literacy as an important component of preparing a future teacher." Vestnik of Kostroma State University. Series: Pedagogy. Psychology. Sociokinetics 27, no. 2 (July 30, 2021): 149–53. http://dx.doi.org/10.34216/2073-1426-2021-27-2-149-153.
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The article analyzes the concept of mathematical literacy. The formation of mathematical literacy among members of modern society is a fundamental basis for the formation of functional literacy. Currently, there is no single approach to the interpretation of the concept of "mathematical literacy", the article provides several different approaches to the definition. Based on the analysis of the points of view of different scientists, the authors of the article highlight the main components of the concept of "mathematical literacy". These include: literacy of mathematical speech; possession of mathematical concepts; the ability to correctly formulate definitions and statements; the ability to apply mathematics to research. The paper provides a characteristic of the listed components of mathematical literacy. In addition, in this work, for the first time, an attempt was made to formulate the levels of mathematical literacy – speech, terminological, critical and operational. The article presents the results of testing students in pedagogic areas of training of two universities – Kostroma State University and Yaroslavl State Pedagogic University. The test was aimed at assessing the level of mathematical literacy of future teachers, for whom teaching mathematics will be a part of their professional activities. The test tested not only the knowledge of terms and the ability to give definitions, but also the ability to correctly apply mathematics to solve practical problems with subsequent interpretation, as well as the ability to see errors and inaccuracies in the texts of students' works, Internet sources and teaching aids. The authors identified criteria for assessing the test results and for each criterion; a quantitative indicator was determined equal to the number of correctly completed tasks. The low results of even third-year students show topicality of specific activities that could help improve the mathematical literacy of pedagogues.
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Harari, Isaac, and Danny Avraham. "High-Order Finite Element Methods for Acoustic Problems." Journal of Computational Acoustics 05, no. 01 (March 1997): 33–51. http://dx.doi.org/10.1142/s0218396x97000046.
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The goal of this work is to design and analyze quadratic finite elements for problems of time-harmonic acoustics, and to compare the computational efficiency of quadratic elements to that of lower-order elements. Non-reflecting boundary conditions yield an equivalent problem in a bounded region which is suitable for domain-based computation of solutions to exterior problems. Galerkin/least-squares technology is utilized to develop robust methods in which stability properties are enhanced while maintaining higher-order accuracy. The design of Galerkin/least-squares methods depends on the order of interpolation employed, and in this case quadratic elements are designed to yield dispersion-free solutions to model problems. The accuracy of Galerkin/least-squares and traditional Galerkin elements is compared, as well as the accuracy of quadratic versus standard linear interpolation, incorporating the effects of representing the radiation condition in exterior problems. The efficiency of the various methods is measured in terms of the cost of computation, rather than resolution requirements. In this manner, clear guidelines for selecting the order of interpolation are derived. Numerical testing validates the superior performance of the proposed methods. This work is a first step to gaining a thorough analytical understanding of the performance of p refinement as a basis for the development of h-p finite element methods for large-scale computation of solutions to acoustic problems.
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Rukhin, Andrew L. "Distribution of the number of words with a prescribed frequency and tests of randomness." Advances in Applied Probability 34, no. 04 (December 2002): 775–97. http://dx.doi.org/10.1017/s0001867800011915.
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The goal of this paper is to investigate properties of statistical procedures based on numbers of different patterns by using generating functions for the probabilities of a prescribed number of occurrences of given patterns in a random text. The asymptotic formulae are derived for the expected value of the number of words occurring a given number of times and for the covariance matrix. The form of the optimal linear test based on these statistics is established. These problems appear in testing for the randomness of a string of binary bits, DNA sequencing, source coding, synchronization, quality control protocols, etc. Indeed, the probabilities of repeated (overlapping) patterns are important in information theory (the second-order properties of relative frequencies) and molecular biology problems (finding patterns with unexpectedly low or high frequencies).
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Iqbal, Muhammad, Will N. Browne, and Mengjie Zhang. "Extending XCS with Cyclic Graphs for Scalability on Complex Boolean Problems." Evolutionary Computation 25, no. 2 (June 2017): 173–204. http://dx.doi.org/10.1162/evco_a_00167.
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A main research direction in the field of evolutionary machine learning is to develop a scalable classifier system to solve high-dimensional problems. Recently work has begun on autonomously reusing learned building blocks of knowledge to scale from low-dimensional problems to high-dimensional ones. An XCS-based classifier system, known as XCSCFC, has been shown to be scalable, through the addition of expression tree–like code fragments, to a limit beyond standard learning classifier systems. XCSCFC is especially beneficial if the target problem can be divided into a hierarchy of subproblems and each of them is solvable in a bottom-up fashion. However, if the hierarchy of subproblems is too deep, then XCSCFC becomes impractical because of the needed computational time and thus eventually hits a limit in problem size. A limitation in this technique is the lack of a cyclic representation, which is inherent in finite state machines (FSMs). However, the evolution of FSMs is a hard task owing to the combinatorially large number of possible states, connections, and interaction. Usually this requires supervised learning to minimize inappropriate FSMs, which for high-dimensional problems necessitates subsampling or incremental testing. To avoid these constraints, this work introduces a state-machine-based encoding scheme into XCS for the first time, termed XCSSMA. The proposed system has been tested on six complex Boolean problem domains: multiplexer, majority-on, carry, even-parity, count ones, and digital design verification problems. The proposed approach outperforms XCSCFA (an XCS that computes actions) and XCSF (an XCS that computes predictions) in three of the six problem domains, while the performance in others is similar. In addition, XCSSMA evolved, for the first time, compact and human readable general classifiers (i.e., solving any n-bit problems) for the even-parity and carry problem domains, demonstrating its ability to produce scalable solutions using a cyclic representation.
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Fajriah, Noor. "RANCANGAN MASALAH MATEMATIKA UNTUK MENGIDENTIFIKASI BERPIKIR GEOMETRIS SISWA." KALAMATIKA Jurnal Pendidikan Matematika 3, no. 1 (April 2, 2018): 39–50. http://dx.doi.org/10.22236/kalamatika.vol3no1.2018pp39-50.
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Geometric thinking has a very important role in developing students' mathematical thinking. To find out geometric thinking students needed a problem that could identify geometric thinking. The problem must be in accordance with the objectives to be measured, to meet validity and reliability as a valuation tool. The purpose of this research was to obtain the design of geometry problems to be able to identify valid and reliable geometric thinking. The descriptive method was used in this research. There are 6 people as validators and 3 junior high school students for testing. The results obtained prototype problems designed to pay attention to aspects of the material in accordance with the level of junior high school students and bring visualization, construction and reasoning activities. The construction aspect in which the problem does not lead to multiple interpretations. is clear and uses a question word/ command whose completion is a description. Aspects of language where the language is communicative easily understood and in accordance with the rules of the Indonesian language is good and true and meets the criteria of legibility.
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Svetlova, Natalia Ivanovna, Lydia Nikolaevna Vasilieva, and Irina Igorevna Ilyina. "Development of the digital competence of students through the electronic course." SHS Web of Conferences 125 (2021): 05010. http://dx.doi.org/10.1051/shsconf/202112505010.
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The article is concerned with the role of an electronic course in higher mathematics in the development of digital competence of students of technical faculties. The principle of organizing the educational process with the help of an electronic course in higher mathematics, focused on the development of students’ digital competence, is considered. The experience of testing an electronic notebook in higher mathematics, which is part of an electronic course, is presented. The experience of the implementation of an electronic notebook in higher mathematics in teaching students at all its stages is considered: the examples of problems solved in seminars are given; the design of classroom lessons is described taking into account the specifics of the academic subject “Mathematical Analysis”. The structure of the electronic notebook, including test tasks and cases for intermediate certification of students based on the results of the seminar, is given. The effectiveness of the organization of the educational process using an electronic course in higher mathematics to develop the digital competence of students in a technical direction is shown. The work examines the attitude of students to teaching higher mathematics using an electronic course, their self-assessment of involvement in the educational process. Moreover, the educational results of the development of digital competence were demonstrated. A reliable relationship was confirmed between the level of development of digital competence and the positive attitude of students to a new format of teaching mathematics: an interactive electronic course with a component base in the form of an electronic notebook. Based on the results of the experimental work, it can be argued that the students positively assessed the use of the electronic course in teaching, because have constant access to training materials and to information about the individual trajectory of the course. This interactive development is convenient to use when preparing yourself for classes.
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Halford, Graeme S. "Applications of Cognitive Developmental Theory and Data to Educational Psychology." Australian Educational and Developmental Psychologist 8, no. 1 (May 1991): 7–8. http://dx.doi.org/10.1017/s0816512200026304.
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Recent developments in Cognitive Psychology and in the new discipline of Cognitive Science (an integration of Cognitive Psychology, Computer Science, Linguistics, Philosophy of Mind, and Cognitive Neuroscience) have made it appropriate to consider new ways in which Cognitive Development and Educational Psychology can benefit each other. Cognitive Development can contribute to Educational Psychology by specifying cognitive processes entailed in educationally relevant tasks, by analysing processing loads, and by indicating more efficient ways of using available capacity. Cognitive Psychology and Cognitive Science have now produced some penetrating theories of the cognitive processes that underlie a wide variety of intellectual activities. Although there is still much work remaining to be done, these developments can be used to analyse the strategies children and adults use in solving problems in areas such as mathematics and science. This can result in benefits in both learning and remediation. Educational Psychology can benefit Cognitive Development by offering alternativeconcepts, by providing realistic problems for analysis, and by providing a testing ground for its theories. I will illustrate these ideas in the area of mathematics.
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Putra, Fergie Nando Dwi, Ardiansyah Ardiansyah, Dwi Sakethi, and Anie Rose Irawati. "PENGEMBANGAN APLIKASI ANDROID SIMIPA MODUL DOSEN MENGGUNAKAN METODE SCRUM." Jurnal Pepadun 2, no. 3 (December 1, 2021): 412–23. http://dx.doi.org/10.23960/pepadun.v2i3.43.
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The use of mobile-based technology is very useful for all fields, especially education. The rapid development of mobile technology encourages the University to be able to take full advantage of mobile technology. The Faculty of Mathematics and Natural Sciences, University of Lampung currently only has a web-based information system and does not yet have a mobile-based application that can be used to help the learning process, so that problems often occur during the learning process. Problems that often occur are forgetting class schedules, forgetting to attend student seminars, forgetting if there is a guidance schedule, not knowing the progress of guidance student studies, etc., with the development of the SIMIPA application it is hoped that it can help overcome problems that often occur in the learning process. This development focuses on the lecturer module with features such as schedule, agenda, academic calendar, endorsements, and notifications. The method used in the development of SIMIPA is the scrum method. The Scrum method has a product backlog that is divided into eight sprints and must be worked out to meet all application requirements. The Scrum method has three roles at the time of its work, namely the product owner, the Scrum master, and the development team. The scrum method has 4 stages starting from sprint planning, daily scrum, sprint review, and sprint retrospective. The result of this research is the successful development of the SIMIPA application for the Android-based lecturer module. For testing application functionality, the black box testing method is used. The results of the black box testing on the lecturer module SIMIPA application show all functionality in the application is running and as previously expected. Keywords: Black box testing; Lecturers; Mobile technology; Notifications; Scrum
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Pozdnyakov, Sergey N. "The Relationship of Goal-Setting in the Teaching of Mathematics with its Technological Support." Computer tools in education, no. 3 (September 30, 2019): 70–89. http://dx.doi.org/10.32603/2071-2340-2019-3-70-89.
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Technological support of teaching mathematics depends on what methodological and pedagogical goals are put for learning. Achieving or failing to achieve these goals is connected with the used type of feedback or in other words, the method of assessing the educational activities of students. In this work, two types of assessment are contrasted: a test form of knowledge testing (implemented by a system of mid-term and final exams) and a formative assessment (determined by the teacher’s informal reaction to the student’s productive activities and the way these activities are organized). It is shown that the first type of assessment corresponds to the consideration of the curriculum as a learning goal, the second — as a learning tool. In the first case, the purpose of training is the acquisition of specific knowledge and skills, and in the second, the mastery of the general mechanisms of educational activity inherent in a given subject area (mathematics). For the first goal, it is effective to use template tasks including generated exercises and simulators, for the second — to use various tools that support constructive and research activities. The article shows how “non-invasive monitoring” is used to achieve the second goal, when the teacher and the student are not on opposite sides of the academic barrier (the student answers — the teacher sets a mark), but on the same side and jointly perform actions to create conditions for the most effective mastery of the course material by each student. The basis of non-invasive monitoring is modeling the presentation of the results of this activities to the scientific community, including all intermediate stages of such activities. Instead of testing knowledge and issuing formal marks, feedback is used, various approaches and ways to solve the problem are discussed together, and monitoring is limited to students’ self-esteem, which is not necessarily communicated to the teacher. At the same time, the discussion process itself is open, and the teacher can always evaluate the problems of students, without turning them into an instrument of formal pressure on the student by third parties.
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Vera, Tensi Olga, Putri Yulia, and Nur Rusliah. "Peningkatan Kemampuan Pemecahan Masalah Matematis Melalui Model Problem Based Learning dengan Menggunakan Soal-soal Berbasis Budaya Lokal." Logaritma : Jurnal Ilmu-ilmu Pendidikan dan Sains 9, no. 01 (June 30, 2021): 1–14. http://dx.doi.org/10.24952/logaritma.v9i01.2782.
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The ability to solve problems is part of the purpose of learning mathematics in junior high school, but the reality that occurs in the field is not the case. This can be seen from the lack of trained students and find it difficult to work on the stages of problem solving so that students' mathematical problem-solving abilities are still relatively low. Therefore, Problem Based Learning (PBL) learning model is used by using questions based on local culture. This study aims to look at differences in the improvement of students' mathematical problem-solving abilities between those through the PBL learning model using questions based on local culture and students who use conventional learning in class VII. The method is Quasi Experimental Design with the Random Sampling Cluster technique, VIIB class as the experimental and the VIID class as the control. Data processing is performed by the formula N-gain, then hypothesis testing is done using the t test. From the results of data analysis shows that there are significant differences in the improvement of students' mathematical problem-solving abilities between those who go through the PBL learning model by using questions based on local culture and those using conventional learning.
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Valentina B., Tsyrenova, Lumbunova Natalya B., and Mironova Ekaterina P. "Increasing the Cognitive Activity of Students in Teaching Mathematics." Scholarly Notes of Transbaikal State University 16, no. 3 (September 2021): 48–58. http://dx.doi.org/10.21209/2658-7114-2021-16-3-48-58.
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The article is devoted to the problem of increasing the cognitive activity of students in the current environment of preparing future specialists in accordance with the Federal State Educational Standard of the Secondary Education and the Federal State Educational Standard of Higher Education in teaching mathematical disciplines. The article shows that in the psychological-pedagogical literature cognitive activity is considered both as a personality trait and as a student's activity. The author's definitions of students' cognitive activity¿ and educational-cognitive activity of students¿ are formulated, their correlation is shown. The levels of formation of cognitive activity are highlighted: reproducing, interpreting, searching, and creative. A set of indicators of these levels has been formulated in accordance with the motivational, content-operational, value-volitional and evaluative components for didactic monitoring. The pedagogical conditions for the activation of students' cognitive activities in mathematical subjects have been established, which are the implementation of a differentiated approach and the application of pedagogical technologies, methods and techniques (the use of educational and technological maps, the technology of a portfolio of achievements, the propaedeutics of the professional competencies formation by means of mathematical problems, historical excursions, independent work of students), as well as didactic monitoring of cognitive activity. Experimental testing of pedagogical conditions has demonstrated a positive dynamics of changes in complex indicators of motivational, content-operational, value-volitional and evaluative components. The research results can be used in teaching mathematical subjects in higher educational establishments and specialized secondary-education institutions.students'
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Fernández, Eileen. "Sharing Teaching Ideas: Understanding Functions without Using the Vertical Line Test." Mathematics Teacher 99, no. 2 (September 2005): 96–100. http://dx.doi.org/10.5951/mt.99.2.0096.
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Since I started teaching precalculus eighteen years ago, I have struggled with how to convey a function's definition so that its importance and usefulness comes across to students. This is especially the case with the Vertical Line Test (VLT), a mechanism for testing whether the graph of a relation is a function. (Vertical lines are drawn through the graph. If every vertical line intersects the graph in exactly one point, the relation is a function.) In this era of “learning mathematics with understanding” (NCTM 2000, p. 20), the Vertical (and Horizontal) Line Tests present a challenge. I find that once students are introduced to these devices, they tend to disregard the concepts that the devices are testing and instead mechanically apply the tests. This rote application limits not only the students' understanding of the concepts but also their ability to work within and across representations to solve problems related to identifying functions.
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Saputra, Jusep, Thesa Kandaga, and Anggoro Ari Nurcahyo. "Program Kemitraan Masyarakat (PKM) Guru SMA di Kota dan Kabupaten Bandung dalam Kegiatan Pengolahan Data Berbasis E-Learning." Jurnal Pengabdian Pada Masyarakat 3, no. 2 (December 26, 2018): 201–12. http://dx.doi.org/10.30653/002.201832.64.
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COMMUNITY PARTNERSHIP PROGRAM (CPP/PKM) HIGH SCHOOL TEACHERS IN CITY AND BANDUNG REGENCY IN E-LEARNING DATA PROCESSING ACTIVITIES. The purpose of the Subject Teachers Consultation (STC) is that they are able to support teacher competencies. The STC included in the Community Partnership Program (CPP) is the Bandung and City Mathematics STC. Problems with both partners are: (1) Understanding of some teachers in collecting data according to the formulation of research problems is still lacking, (2) Teachers do not know e-learning applications that use video conferencing. (3) Some teachers in processing research data with SPSS are still lacking, (4) some teachers have not been skilled in making scientific articles. The two partners' solution-resolution procedures will be carried out by the team are training, guidance, and accompaniment. CPP was attended by 14 Mathematics Teachers from the City of Bandung, and 17 Mathematics Teachers The first meeting resulted in the following conclusions: (1) The quality of CPP in formulating problems, testing instruments, using SPSS features, and video conferencing was conducted very good, (2) The abilities of teachers to understand, master, and train in making either test or non-test research instruments are in a pretty good category, (3) t The teacher's ability to input data according to data or the scale of the data is in a good category, (4) The teacher's ability to use video conferencing and guidance in doing the work is in good category, 5) The ability to teach research data with SPSS; analyze, and interpret research data in the good category, (6) The scientific ability is in a good enough category.
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Saputra, Jusep, Thesa Kandaga, and Anggoro Ari Nurcahyo. "Community Partnership Program (CPP/PKM) High School Teachers in Bandung City and District in E-Learning Based Data Collection Activities." International Journal of Community Service Learning 3, no. 1 (May 6, 2019): 33. http://dx.doi.org/10.23887/ijcsl.v3i1.17507.
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The purpose of the Subject Teachers Consultation (STC/MGMP) will be if the teachers are skilled, accustomed and able to develop various activities that are able to support teacher competencies. One of the activities carried out was to participate in the Community Partnership Program (PKM) program development activities with LPTKs such as Pasundan University. The STC included in the Community Partnership Program (CPP/PKM) is the Bandung and City Mathematics STC. Problems with both partners are: (1) Some teachers do not know SPSS and its benefits in research, (2) Understanding of some teachers in collecting data according to the formulation of research problems is still lacking, (3) Some teachers do not know e-learning applications that use video conference. This problem has an impact on the inhibition of research and an increase in the rank of teachers. Approach methods used to overcome problems with training, mentoring, and mentoring. The two partners' solution-resolution procedures will be carried out by the team as follows: (1) Training, mentoring and mentoring in using SPSS features, (2) Training in using e-learning applications (3) Training, mentoring, and mentoring in collect data according to the formulation of research problems. CPP was attended by 14 Mathematics Teachers from the City of Bandung, and 17 Mathematics Teachers from Bandung Regency who were each from the Bandung City and Regency STC. The first meeting resulted in the following conclusions: (1) The quality of CPP in formulating problems, testing instruments, using SPSS features, and video conferencing conducted was very good, (2) The ability of teachers to understand, master, and train in making either test or non-test research instruments are in a pretty good category, (3) the teacher's ability to input data according to data or the scale of the data is in a good category, (4) The teacher's ability to use video conferencing to get guidance and assistance in doing the work is in good category.
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Allender, Eric, V. Arvind, Rahul Santhanam, and Fengming Wang. "Uniform derandomization from pathetic lower bounds." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1971 (July 28, 2012): 3512–35. http://dx.doi.org/10.1098/rsta.2011.0318.
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The notion of probabilistic computation dates back at least to Turing, who also wrestled with the practical problems of how to implement probabilistic algorithms on machines with, at best, very limited access to randomness. A more recent line of research, known as derandomization, studies the extent to which randomness is superfluous. A recurring theme in the literature on derandomization is that probabilistic algorithms can be simulated quickly by deterministic algorithms, if one can obtain impressive (i.e. superpolynomial, or even nearly exponential) circuit size lower bounds for certain problems. In contrast to what is needed for derandomization, existing lower bounds seem rather pathetic. Here, we present two instances where ‘pathetic’ lower bounds of the form n 1+ ϵ would suffice to derandomize interesting classes of probabilistic algorithms. We show the following: — If the word problem over S 5 requires constant-depth threshold circuits of size n 1+ ϵ for some ϵ >0, then any language accepted by uniform polynomial size probabilistic threshold circuits can be solved in subexponential time (and, more strongly, can be accepted by a uniform family of deterministic constant-depth threshold circuits of subexponential size). — If there are no constant-depth arithmetic circuits of size n 1+ ϵ for the problem of multiplying a sequence of n 3×3 matrices, then, for every constant d , black-box identity testing for depth- d arithmetic circuits with bounded individual degree can be performed in subexponential time (and even by a uniform family of deterministic constant-depth AC 0 circuits of subexponential size).
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Wang, G. Gary, and S. Shan. "Review of Metamodeling Techniques in Support of Engineering Design Optimization." Journal of Mechanical Design 129, no. 4 (May 4, 2006): 370–80. http://dx.doi.org/10.1115/1.2429697.
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Computation-intensive design problems are becoming increasingly common in manufacturing industries. The computation burden is often caused by expensive analysis and simulation processes in order to reach a comparable level of accuracy as physical testing data. To address such a challenge, approximation or metamodeling techniques are often used. Metamodeling techniques have been developed from many different disciplines including statistics, mathematics, computer science, and various engineering disciplines. These metamodels are initially developed as “surrogates” of the expensive simulation process in order to improve the overall computation efficiency. They are then found to be a valuable tool to support a wide scope of activities in modern engineering design, especially design optimization. This work reviews the state-of-the-art metamodel-based techniques from a practitioner’s perspective according to the role of metamodeling in supporting design optimization, including model approximation, design space exploration, problem formulation, and solving various types of optimization problems. Challenges and future development of metamodeling in support of engineering design is also analyzed and discussed.
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Muti’ah, Rahma. "GAMBARAN PELAKSANAAN KONSELING KELOMPOK DENGAN TEKNIK REBT (RATIONAL EMOTIVE BEHAVIOUR THERAPY) DALAM UPAYA MENGATASI KECEMASAN MATEMATIKA SISWA SMP." RISTEKDIK : Jurnal Bimbingan dan Konseling 4, no. 1 (March 21, 2019): 37. http://dx.doi.org/10.31604/ristekdik.v4i1.37-44.
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Abstract: Mathematical learning anxiety (anxiety mathematic) has a very important role in mathematics learning activities. This is because the anxiety felt by students influences the students' concentration ability to take part in learning activities. Besides that mathematics anxiety also influences students' ability in understanding concepts and reasoning abilities which both of these aspects greatly influence the results of a student's mathematics learning. Mathematical anxiety can be derived from the irrational belief and emotional belief and students' mastery of the basic concepts of mathematics in calculating students. To overcome the above problems, the most appropriate solution to be used is the implementation of group counseling with the REBT technique, so that expectations with students' mathematical anxiety will be low so that student learning outcomes will increase.The method used in this study is descriptive qualitative. The population in this study were 115 students with high anxiety and low initial numeracy abilities. Consisting of 5 study groups, namely groups A, B, C, D and E, and the sample used was group A based on random results. Data collection tools used are observation and interviews, by testing the validity of the data using triangulation of sources (students, teachers and parents) and place.From the results of the implementation it was concluded that there was a decrease in mathematics anxiety of students after participating in group counseling activities with the REBT technique. The description of the implementation of group counseling with group REBT techniques consists of 5 stages of activity, namely 1) first meeting consisting of 4 steps, namely a) initial disputing, b) identification of self-condition, c) stop irrational belief and emotional belief, d) formulate thoughts and rational feeling about mathematics, 2) second meeting, namely a) persuasive stage, b) relaxation exercise, c) home work, 3) third meeting consists of 2 steps namely a) confrontation stage, and self talk writing, 4) fourth meeting namely a) working on the task and b) facing the real situation, 5) the fifth meeting namely a) homework discussion and b) conducting an evaluation. Keywords: REBT Counseling (Rational Emotive Behavior Theray), group, Mathematical Anxiety Abstrak Kecemasan belajar matematika (anxiety mathematic) memiliki peran yang sangat penting pada kegiatan pembelajaran matematika. Ini karena kecemasan yang dirasakan siswa mempengaruhi kemampuan konsentrasi siswa untuk mengikuti kegiatan pembelajaran. Selain itu kecemasan matematika juga mempengaruhi kemampuan siswa dalam pemahaman konsep dan kemampuan penalaran yang mana kedua aspek ini sangat mempengaruhi hasil belajar matematika seorang siswa. Kecemasan matematika bisa berasal dari irational belief dan emotional belief serta penguasaan siswa terhadap konsep-konsep dasar matematika siswa dalam berhitung. Untuk mengatasi permasalahan diatas maka solusi yang paling tepat digunakan adalah pelaksanaan konseling kelompok dengan teknik REBT, sehingga harapannya dengan kecemasan matematika siswa menjadi rendah maka hasil belajar siswa akan meningkat.Metode yang digunakan dalam penelitian ini adalah kualitatif deskriptif. Populasi dalam penelitian ini adalah 115 siswa dengan kecemasan tinggi dan kemampuan awal berhitung rendah. Terdiri dari 5 kelompok belajar yaitu kelompok A, B, C, D dan E, dan sampel yang digunakan adalah kelompok A berdasarkan hasil random. Alat pengumpul data yang digunakan adalah observasi dan wawancara, dengan pengujian keabsahan data dengan menggunakan triangulasi sumber (siswa, guru dan orangtua) dan tempat.Dari hasil pelaksanaan diperoleh kesimpulan terjadi penurunan kecemasan matematika siswa setelah mengikuti kegiatan konseling kelompok dengan teknik REBT. Adapun gambaran pelaksanaan konseling kelompok dengan teknik REBT kelompok terdiri dari 5 tahap kegiatan yaitu 1) pertemuan pertama yang terdiri dari 4 langkah yaitu a) disputing awal, b) identifikasi keadaan diri, c) menghentikan irrational belief dan emotional belief, d) merumuskan pemikiran dan perasaan yang rasional tentang matematika, 2) Pertemuan kedua, yaitu a) tahap persuasif, b) latihan relaksasi, c) home work, 3) pertemuan ketiga terdiri dari 2 langkah yaitu a) tahap konfrontasi, dan menulis self talk, 4) pertemuan keempat yaitu a) mengerjakan tugas dan b) menghadapi situasi nyata, 5) pertemuan kelima yaitu a) pembahasan homework dan b) melakukan evaluasi. Kata kunci: Konseling REBT (Rational Emotive Behaviour Theray), kelompok, Kecemasan Matematika
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Bonomi, Andrea, Thomas De Min, Enrico Zardini, Enrico Blanzieri, Valter Cavecchia, and Davide Pastorello. "Quantum annealing learning search implementations." Quantum Information and Computation 22, no. 3&4 (February 2022): 181–208. http://dx.doi.org/10.26421/qic22.3-4-1.
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This paper presents the details and testing of two implementations (in C++ and Python) of the hybrid quantum-classical algorithm Quantum Annealing Learning Search (QALS) on a D-Wave quantum annealer. QALS was proposed in 2019 as a novel technique to solve general QUBO problems that cannot be directly represented into the hardware architecture of a D-Wave machine. Repeated calls to the quantum machine within a classical iterative structure and a related convergence proof originate a learning mechanism to find an encoding of a given problem into the quantum architecture. The present work considers the Number Partitioning Problem (NPP) and the Travelling Salesman Problem (TSP) for the testing of QALS. The results turn out to be quite unexpected, with QALS not being able to perform as well as the other considered methods, especially in NPP, where classical methods outperform quantum annealing in general. Nevertheless, looking at the TSP tests, QALS has fulfilled its primary goal, i.e., processing QUBO problems not directly mappable to the QPU topology.
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NOVYTSKA, Lyudmyla. "THE ROLE OF MATHEMATICAL EDUCATION IN PROFESSIONAL TRAINING OF SPECIALISTS FOR THE TOURISM SECTOR." "EСONOMY. FINANСES. MANAGEMENT: Topical issues of science and practical activity", no. 3 (43) (March 2019): 78–85. http://dx.doi.org/10.37128/2411-4413-2019-3-7.
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At the current stage of social and economic development of Ukraine, the processes of globalization, integration and informatization of society raise qualitatively new challenges in the field of higher education. Ukraine has recently been focusing on European countries, which consider the tourism sector as a priority area for their economic development. This area of investment is very attractive, creates new jobs and is characterized by a high level of efficiency. Therefore, the socio-economic success of the country as a whole depends on the professional training of future tourists. The basis for the development of specialist-tourist skills is mathematical disciplines, including the discipline "Higher and Applied Mathematics". There is an intensive process of mathematization of knowledge, involving mathematical apparatus in the study of natural sciences, humanities, economics and social sciences, which in turn forms a certain level of mathematical culture of students of universities. The purpose of teaching the course "Higher and Applied Mathematics" is to provide students with basic knowledge of mathematics, which enable them to further master the professional disciplines based on mathematical concepts. In this case, considerable attention should be paid to the formation of practical skills, the ability to apply mathematical methods when solving the tasks of professional activity. One of the tools for improving the quality of mathematical education for students-tourists is to update the content of courses that are read in the context of the future profession and modern socio-economic order. When considering a particular material, the idea of its connection with the future profession should be put on the foreground. In this regard, the course "Higher and Applied Mathematics" for students-tourists VNAU contains several critical sections covering all the main areas of application of mathematical methods in the tourism sector. Teaching is carried out in accordance with the typical curriculum for higher education institutions in the discipline "Higher and Applied Mathematics" for the specialty "Tourism", developed by the teachers of the Department of Mathematics, Physics and Computer Technologies, VNU taking into account the principle of professional orientation. Given the fact that for students the most important is the practical aspect of mathematics, the purpose of the course is to familiarize with the basic concepts and methods of studying modern mathematics necessary for further study of professional disciplines, as well as the formation of skills for the correct mathematical formulation of applied problems and the construction of simple mathematical models. The solution of many applications is due to cumbersome mathematical calculations, the need to visually present the results of calculations, check them, so it is advisable to use computer mathematical systems, in particular, Maccats, in practical classes in mathematics. Teachers of the Department of Mathematics of Physics and Computer Technologies are the ones who prefer it. To work with Mathcad, there are basic elementary skills in working with Windows applications, so you need to implement this environment from the first lessons when studying topics such as Linear Algebra, Differential and Integral Computing, Elements of Probability Theory and Mathematical Statistics. The use of information and communication technologies (ICT) in the educational process greatly enhances the opportunities of both the teacher and the student's cognitive abilities. ICTs allow to visualize and dynamize the process of studying the discipline "Higher and Applied Mathematics", to personalize and direct the educational process for the comprehensive development of personality, to substantially increase the volume, sources of receipt and the nature of the information necessary for a person, the means of its processing. They can have a significant impact on the methodology of holding higher and applied mathematics classes, requiring the teacher to use electronic textbooks, lecture notes, practical work, the testing system for assessing student knowledge, and global sources of information. They also facilitate the organization of effective independent work in non-attendance time for students. It should be noted that to date there are quite a few tutorials, collections of tasks that contain applied tasks that can be considered at lectures and practical classes on higher and applied mathematics. Work on the creation of such methodological materials is conducted, in particular, at the Department of Mathematics, Physics and Computer Technologies. Thus, changing requirements for a specialist in the field of tourism, which is conditioned by modernity, requires a permanent rearrangement of the structural elements of its preparation. Fundamental disciplines to a large extent are applied, and therefore a qualitative assimilation of basic and basic concepts of mathematical disciplines will contribute to the competitiveness and qualitative training of the future specialist.
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Кalinin, S. I., and L. V. Pankratova. "Оn the implementation of a transdisciplinary approach in preparing future mathematics teachers." Education and science journal 24, no. 9 (November 15, 2022): 11–42. http://dx.doi.org/10.17853/1994-5639-2022-9-11-42.
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Introduction. The disparate study of certain areas and branches of knowledge, characteristic of the disciplinary approach, has largely lost its position, recognising the inevitability of interdisciplinary cooperation. At present, interdisciplinarity is already being comprehended at a new level, creating the prerequisites for the introduction of a transdisciplinary approach to solving complex problems, including in the educational sphere.Aim. The current research aims to present the transdisciplinary teaching means, which are relevant in the process of training future teachers of mathematics, and which are identified on the basis of an analysis of the content of education.Methodology and research methods. General scientific and empirical methods were used to develop the ideological basis of the study. The aforementioned methods allowed the authors to draw up a complete picture of the problem under study, to identify its patterns and trends, to understand the essence. The search and selection of mathematics subject content with transdisciplinary properties was based on a systematic and interdisciplinary approach. At the stage of testing the research hypothesis, the competency-based approach was decisive, and tactical tasks were solved by referring to the activity approach. In addition, the main provisions of the concepts of humanisation and humanitarisation of education, as well as the principles of fundamentalisation of mathematical education, were taken into account.Results and theoretical significance. The expediency of using inequalities and convex functions in the training of future mathematics teachers in the context of a transdisciplinary approach is substantiated. A phased description of the work carried out allows us to trace the methods of reflecting the modern scientific content of the relevant topics, conditions, means and expected results of pedagogical interaction. The theory and methods of teaching mathematics at the university are enriched with a qualitatively new vision of the educational potential of the concepts of inequality and a convex function.Practical significance. The introduction of inequalities and convex functions in the process of future mathematics teachers training at Vyatka State University made it possible to demonstrate the possibilities of a transdisciplinary approach in the development of students’ worldview and the formation of professionally significant students’ competencies. The presented means of implementing the transdisciplinary approach can also be comprehended in teaching students of other areas of training.
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Malele, James, Phumlani Dlamini, and Simphiwe Simelane. "Highly Accurate Compact Finite Difference Schemes for Two-Point Boundary Value Problems with Robin Boundary Conditions." Symmetry 14, no. 8 (August 18, 2022): 1720. http://dx.doi.org/10.3390/sym14081720.
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In this study, a high-order compact finite difference method is used to solve boundary value problems with Robin boundary conditions. The norm is to use a first-order finite difference scheme to approximate Neumann and Robin boundary conditions, but that compromises the accuracy of the entire scheme. As a result, new higher-order finite difference schemes for approximating Robin boundary conditions are developed in this work. Six examples for testing the applicability and performance of the method are considered. Convergence analysis is provided, and it is consistent with the numerical results. The results are compared with the exact solutions and published results from other methods. The method produces highly accurate results, which are displayed in tables and graphs.
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Lim, Soojong, and Jaemin Shin. "Application of a Deep Neural Network to Phase Retrieval in Inverse Medium Scattering Problems." Computation 9, no. 5 (April 28, 2021): 56. http://dx.doi.org/10.3390/computation9050056.
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We address the inverse medium scattering problem with phaseless data motivated by nondestructive testing for optical fibers. As the phase information of the data is unknown, this problem may be regarded as a standard phase retrieval problem that consists of identifying the phase from the amplitude of data and the structure of the related operator. This problem has been studied intensively due to its wide applications in physics and engineering. However, the uniqueness of the inverse problem with phaseless data is still open and the problem itself is severely ill-posed. In this work, we construct a model to approximate the solution operator in finite-dimensional spaces by a deep neural network assuming that the refractive index is radially symmetric. We are then able to recover the refractive index from the phaseless data. Numerical experiments are presented to illustrate the effectiveness of the proposed model.
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Rojec, Žiga, Tadej Tuma, Jernej Olenšek, Árpád Bűrmen, and Janez Puhan. "Meta-Optimization of Dimension Adaptive Parameter Schema for Nelder–Mead Algorithm in High-Dimensional Problems." Mathematics 10, no. 13 (June 30, 2022): 2288. http://dx.doi.org/10.3390/math10132288.
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Although proposed more than half a century ago, the Nelder–Mead simplex search algorithm is still widely used. Four numeric constants define the operations and behavior of the algorithm. The algorithm with the original constant values performs fine on most low-dimensional, but poorly on high-dimensional, problems. Therefore, to improve its behavior in high dimensions, several adaptive schemas setting the constants according to the problem dimension were proposed in the past. In this work, we present a novel adaptive schema obtained by a meta-optimization procedure. We describe a schema candidate with eight parameters subject to meta-optimization and define an objective function evaluating the candidate’s performance. The schema is optimized on up to 100-dimensional problems using the Parallel Simulated Annealing with Differential Evolution global method. The obtained global minimum represents the proposed schema. We compare the performance of the optimized schema with the existing adaptive schemas. The data profiles on the Gao–Han modified quadratic, Moré–Garbow–Hilstrom, and CUTEr (Constrained and Unconstrained Testing Environment, revisited) benchmark problem sets show that the obtained schema outperforms the existing adaptive schemas in terms of accuracy and convergence speed.
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Тмєнова, Наталія Пилипівна, and Богдан Богданович Сусь. "TECHNOLOGIES IMPROVING FOR KNOWLEDGE AND SKILLS ASSESSING OF STUDENTS OF PHYSICAL AND MATHEMATICAL SPECIALTIES IN E-LEARNING." Information Technologies and Learning Tools 78, no. 4 (September 11, 2020): 163–76. http://dx.doi.org/10.33407/itlt.v78i4.2818.
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Although the problems of obtaining educational information in e-learning have been successfully resolved, the testing of obtained knowledge still requires a solution. Principles of knowledge assessment by means of tests in mathematics subjects administered in e-learning environment have been developed. An algorithm of component analysis and formula expression indexing for automatic analysis is suggested. This approach allows diversifying the types of questions for consequent verification of knowledge in computer systems. Modification of the formula editor provides the creation of templates for formula entering and the use of indexing algorithm of the expression elements. This makes it possible to avoid ambiguity of responses entered by students. Tasks with computer verification of an analytical symbolic expression can be applied to automate the verification of skills and knowledge in natural sciences, in particular, physics, mathematics, by appropriate modification of the template.
Development of information technologies led to the development of new models of teaching and learning, especially in the field of mathematical sciences. It is shown that during experimental laboratory work in engineering subjects especially effective are those activities that combine the use of knowledge and skills acquired during the study of other related disciplines. It is shown that research based on interdisciplinary interaction has great potential.
In addition, the application and advantages of expert systems in open education to improve the teaching-learning process are discussed. It is proposed to use expert systems in the designing of laboratory works and tests. It is also shown how expert systems should be used to optimize the process of creating adaptive type laboratory works and to formulate individual test tasks. The application of the expert system is illustrated on the example of Discrete Mathematics.
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Watson, Michael, Benjamin White, Joseph Lanigan, Tom Slatter, and Roger Lewis. "The composition and friction-reducing properties of leaf layers." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2239 (July 2020): 20200057. http://dx.doi.org/10.1098/rspa.2020.0057.
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Every autumn rail networks across the world suffer delays, accidents and schedule changes due to low friction problems caused by leaves landing on the rails. These leaves form a layer that can reduce the friction between the wheel and the rail to a similar level as that between ice and an ice-skate ( μ = 0.01 – 0.05 ). Previous works have generated several hypotheses for the chemical reactions and low friction mechanism associated with these layers. In this work, the reaction between an aqueous extract of sycamore leaves and metallic iron is investigated. This reaction has been shown to produce a black precipitate, which matches field observations of leaf layers, while friction tests with these extracts produce characteristic ultra low friction. The reaction is investigated through FTIR, XPS, CHNS and ICP-MS analysis as well as wet chemical testing. The impact of the reaction on friction is investigated through three rounds of tribological testing. The results indicate that the black precipitate produced is iron tannate, formed by complexation of tannins with dissolved iron ions. Friction testing showed that eliminating tannins from the leaf extract resulted in a significant increase in the friction coefficient compared with the control.
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Sosa, Juan, and Lina Buitrago. "Illustrating advantages and challenges of Bayesian statistical modelling: An empirical perspective." Model Assisted Statistics and Applications 17, no. 3 (August 26, 2022): 175–87. http://dx.doi.org/10.3233/mas-221342.
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We provide four case studies that use Bayesian machinery to making inductive reasoning. Our main motivation relies in offering several instances where the Bayesian approach to data analysis is exploited at its best to perform complex tasks, such as description, testing, estimation, and prediction. This work is not meant to be either a reference text or a survey in Bayesian statistical inference. Our goal is simply to provide several examples that use Bayesian methodology to solve data-driven problems. The topics we cover here include analysis of times series and analysis of spatial data.
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KHAN, ADNAN, KAMAL SHAH, MUHAMMAD ARFAN, THABET ABDELJAWAD, and FAHD JARAD. "A NEW NUMERICAL TREATMENT FOR FRACTIONAL DIFFERENTIAL EQUATIONS BASED ON NON-DISCRETIZATION OF DATA USING LAGUERRE POLYNOMIALS." Fractals 28, no. 08 (July 6, 2020): 2040046. http://dx.doi.org/10.1142/s0218348x20400460.
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In this research work, we discuss an approximation techniques for boundary value problems (BVPs) of differential equations having fractional order (FODE). We avoid the method from discretization of data by applying polynomials of Laguerre and developed some matrices of operational types for the obtained numerical solution. By applying the operational matrices, the given problem is converted to some algebraic equation which on evaluation gives the required numerical results. These equations are of Sylvester types and can be solved by using matlab. We present some testing examples to ensure the correctness of the considered techniques.
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Muzamil, Sohail, Tassadaq Hussain, Amna Haider, Umber Waraich, Umair Ashiq, and Eduard Ayguadé. "An Intelligent Iris Based Chronic Kidney Identification System." Symmetry 12, no. 12 (December 12, 2020): 2066. http://dx.doi.org/10.3390/sym12122066.
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In recent years, the demand for alternative medical diagnostics of the human kidney or renal is growing, and some of the reasons behind this relate to its non-invasive, early, real-time, and pain-free mechanism. The chronic kidney problem is one of the major kidney problems, which require an early-stage diagnosis. Therefore, in this work, we have proposed and developed an Intelligent Iris-based Chronic Kidney Identification System (ICKIS). The ICKIS takes an image of human iris as input and on the basis of iridology a deep neural network model on a GPU-based supercomputing machine is applied. The deep neural network models are trained while using 2000 subjects that have healthy and chronic kidney problems. While testing the proposed ICKIS on 2000 separate subjects (1000 healthy and 1000 chronic kidney problems), the system achieves iris-based chronic kidney assessment with an accuracy of 96.8%. In the future, we will work to improve our AI algorithm and try data-set cleaning, so that accuracy can be increased by more efficiently learning the features.
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Frost, Miroslav, and Jan Valdman. "Vectorized MATLAB Implementation of the Incremental Minimization Principle for Rate-Independent Dissipative Solids Using FEM: A Constitutive Model of Shape Memory Alloys." Mathematics 10, no. 23 (November 23, 2022): 4412. http://dx.doi.org/10.3390/math10234412.
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The incremental energy minimization principle provides a compact variational formulation for evolutionary boundary problems based on constitutive models of rate-independent dissipative solids. In this work, we develop and implement a versatile computational tool for the resolution of these problems via the finite element method (FEM). The implementation is coded in the MATLAB programming language and benefits from vector operations, allowing all local energy contributions to be evaluated over all degrees of freedom at once. The monolithic solution scheme combined with gradient-based optimization methods is applied to the inherently nonlinear, non-smooth convex minimization problem. An advanced constitutive model for shape memory alloys, which features a strongly coupled rate-independent dissipation function and several constraints on internal variables, is implemented as a benchmark example. Numerical simulations demonstrate the capabilities of the computational tool, which is suited for the rapid development and testing of advanced constitutive laws of rate-independent dissipative solids.
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Et. al., S. V. Kedar,. "Identifying Learning Disability Through Digital Handwriting Analysis." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 1S (April 11, 2021): 46–56. http://dx.doi.org/10.17762/turcomat.v12i1s.1557.
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Handwriting Analysis is described as a scientific study for the analysis of handwriting. It is a way of interpreting and ability to learn from peculiarities in handwriting. Offline handwriting analysis is a traditional approach that cannot be used efficiently for analysis. Online handwriting analysis, on the other hand, can utilize various aspects like pressure on the pen, timestamp and other factors which help in improving the effectiveness of analysis. Learning disabilities are neurological processing problems which can hamper the learning of the children. Dysgraphia is a learning disability that mainly affects a child’s handwriting and motor skills. It is found in 10 to 30% of school-aged children. Dysgraphia can be diagnosed by therapists based on children’s handwriting samples and manual evaluation techniques. This method is lengthy and inaccurate. In this work, automatic identification methods for and classification of dysgraphia in children in the age group 7 to 12 is described. The method performs analyzing of the child’s writing dynamics via blueprints of the pressure the pen puts on paper with the pen’s movements and orientation with the use of a standardized digital writing pad and machine learning algorithms. It basically has two phases, the training phase, and testing phase. In the training phase, handwriting samples of known results are given to the system. Then the model is built using some classifier, Random forest or Support Vector Machine. Once the model is trained, then in testing phase this model is used for classification of unknown samples to predict whether the subject has dysgraphia or not. This is then used to check the accuracy of the designed system.
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Chelabi, M., T. Hacib, Z. Belli, M. R. Mekideche, and Y. Le Bihan. "The combination of adaptive database SDM and multi-output SVM for eddy current testing." COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 34, no. 6 (November 2, 2015): 1731–39. http://dx.doi.org/10.1108/compel-12-2014-0348.
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Purpose – Eddy current testing (ECT) is a nondestructive testing method for the detection of flaws that uses electromagnetic induction to find defects in conductive materials. In this method, eddy currents are generated in a conductive material by a changing magnetic field. A defect is detected when there is a disruption in the flow of the eddy current. The purpose of this paper is to develop a new noniterative inversion methodology for detecting degradation (defect characterization) such as cracking, corrosion and erosion from the measurement of the impedance variations. Design/methodology/approach – The methodology is based on multi-output support vector machines (SVM) combined with the adaptive database schema design method (SDM). The forward problem was solved numerically using finite element method (FEM), with its accuracy experimentally verified. The multi-output SVM is a statistical learning method that has good generalization capability and learning performance. FEM is used to create the adaptive database required to train the multi-output SVM and the genetic algorithm is used to tune the parameters of multi-output SVM model. Findings – The results show the applicability of multi-output SVM to solve eddy current inverse problems instead of using traditional iterative inversion methods which can be very time-consuming. With the experimental results the authors demonstrate the accuracy which can be provided by the multi-output SVM technique. Practical implications – The work allows extending the capability of the experimentation ECT defect characterization system developed at LGEP. Originality/value – A new inversion method is developed and applied to ECT defect characterization. This new concept introduces multi-output SVM in the context of ECT. The real data together with estimated one obtained by multi-output SVM model are compared in order to evaluate the effectiveness of the developed technique.
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Koksharova, M. V., S. V. Morozova, and O. G. Belchikova. "The use of modular-rating technology of teaching mathematics to students of Altai State Agricultural University." Professional education in the modern world 12, no. 2 (July 13, 2022): 289–98. http://dx.doi.org/10.20913/2618-7515-2022-2-12.
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Introduction. New requirements are put forward for the organization of educational process, and improving the quality of training of graduates. Purpose setting. Therefore, teachers are faced with the need to apply modular-rating training technology which instantly reacts to changes in the situation in the labor market and can adjust the specialist model. It is democratic in its principles, content, and organization of the educational process. Modular-rating technology provides individualization of educational programs and the ways of their assimilation depending on the abilities and interests of students. Methodology of the study. The authors carried out modular structuring of the “Mathematics” course; methodological support (tests, individual tasks, etc.) of the modular-rating program was developed. A special role in the technology of modular-rating education is assigned to control over the knowledge of students, the authors used current, midterm and fi control. The quality of knowledge and skills of students in mastering the module was determined by various control methods: oral and written survey, control work, individual task, calculate and graphic work, etc. In addition, a testing method was used. To assess the effectiveness of student educational activities, a rating is used which is determined by points set in a selected unifi scale with a clear gradation of the level of theoretical knowledge, practical skills and abilities. The rating is formed during the entire period of the student training. Results. In modern conditions, higher education is faced with the tasks of forming a specialist with stable incentives for further professional self-improvement, activation and development of student cognitive abilities, differentiation of training content and individualization of pedagogical infl in accordance with the level of student training. Conclusion. The authors conclude that one of the effective ways to solve these problems is to train students according to the modular-rating system.
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Patil, Shruti, Vijayakumar Varadarajan, Devika Walimbe, Siddharth Gulechha, Sushant Shenoy, Aditya Raina, and Ketan Kotecha. "Improving the Robustness of AI-Based Malware Detection Using Adversarial Machine Learning." Algorithms 14, no. 10 (October 15, 2021): 297. http://dx.doi.org/10.3390/a14100297.
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Cyber security is used to protect and safeguard computers and various networks from ill-intended digital threats and attacks. It is getting more difficult in the information age due to the explosion of data and technology. There is a drastic rise in the new types of attacks where the conventional signature-based systems cannot keep up with these attacks. Machine learning seems to be a solution to solve many problems, including problems in cyber security. It is proven to be a very useful tool in the evolution of malware detection systems. However, the security of AI-based malware detection models is fragile. With advancements in machine learning, attackers have found a way to work around such detection systems using an adversarial attack technique. Such attacks are targeted at the data level, at classifier models, and during the testing phase. These attacks tend to cause the classifier to misclassify the given input, which can be very harmful in real-time AI-based malware detection. This paper proposes a framework for generating the adversarial malware images and retraining the classification models to improve malware detection robustness. Different classification models were implemented for malware detection, and attacks were established using adversarial images to analyze the model’s behavior. The robustness of the models was improved by means of adversarial training, and better attack resistance is observed.
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del Alamo, Miguel, Housen Li, Axel Munk, and Frank Werner. "Variational Multiscale Nonparametric Regression: Algorithms and Implementation." Algorithms 13, no. 11 (November 13, 2020): 296. http://dx.doi.org/10.3390/a13110296.
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Many modern statistically efficient methods come with tremendous computational challenges, often leading to large-scale optimisation problems. In this work, we examine such computational issues for recently developed estimation methods in nonparametric regression with a specific view on image denoising. We consider in particular certain variational multiscale estimators which are statistically optimal in minimax sense, yet computationally intensive. Such an estimator is computed as the minimiser of a smoothness functional (e.g., TV norm) over the class of all estimators such that none of its coefficients with respect to a given multiscale dictionary is statistically significant. The so obtained multiscale Nemirowski-Dantzig estimator (MIND) can incorporate any convex smoothness functional and combine it with a proper dictionary including wavelets, curvelets and shearlets. The computation of MIND in general requires to solve a high-dimensional constrained convex optimisation problem with a specific structure of the constraints induced by the statistical multiscale testing criterion. To solve this explicitly, we discuss three different algorithmic approaches: the Chambolle-Pock, ADMM and semismooth Newton algorithms. Algorithmic details and an explicit implementation is presented and the solutions are then compared numerically in a simulation study and on various test images. We thereby recommend the Chambolle-Pock algorithm in most cases for its fast convergence. We stress that our analysis can also be transferred to signal recovery and other denoising problems to recover more general objects whenever it is possible to borrow statistical strength from data patches of similar object structure.
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del Águila Ferrandis, J., M. S. Triantafyllou, C. Chryssostomidis, and G. E. Karniadakis. "Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2245 (January 2021): 20190897. http://dx.doi.org/10.1098/rspa.2019.0897.
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Predicting motions of vessels in extreme sea states represents one of the most challenging problems in naval hydrodynamics. It involves computing complex nonlinear wave-body interactions, hence taxing heavily computational resources. Here, we put forward a new simulation paradigm by training recurrent type neural networks (RNNs) that take as input the stochastic wave elevation at a certain sea state and output the main vessel motions, e.g. pitch, heave and roll. We first compare the performance of standard RNNs versus GRU and LSTM neural networks (NNs) and show that LSTM NNs lead to the best performance. We then examine the testing error of two representative vessels, a catamaran in sea state 1 and a battleship in sea state 8. We demonstrate that good accuracy is achieved for both cases in predicting the vessel motions for unseen wave elevations. We train the NNs with expensive CFD simulationsoffline, but upon training, the prediction of the vessel dynamicsonlinecan be obtained at a fraction of a second. This work is motivated by the universal approximation theorem for functionals (Chen & Chen, 1993.IEEE Trans. Neural Netw.4, 910–918 (doi:10.1109/72.286886)), and it is the first implementation of such theory to realistic engineering problems.
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Chytrý, Vlastimil, Janka Medová, Jaroslav Říčan, and Jiří Škoda. "Relation between Pupils’ Mathematical Self-Efficacy and Mathematical Problem Solving in the Context of the Teachers’ Preferred Pedagogies." Sustainability 12, no. 23 (December 7, 2020): 10215. http://dx.doi.org/10.3390/su122310215.
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In research focused on self-efficacy it is usually teacher-related phenomena that are studied, while the main aspects related to pupils are rather neglected, although self-efficacy itself is perceived as a belief in one’s own abilities. Evidently, this strongly influences the behavior of individuals in terms of the goal and success in mathematical problem-solving. Considering that alternative teaching methods are based on the principle of belief in one’s own ability (mainly in the case of group work), higher self-efficacy can be expected in the pupils of teachers who use predominantly the well-working pupil-centered pedagogies. A total of 1133 pupils in grade 5 from 36 schools in the Czech Republic were involved in the testing of their ability to solve mathematical problems and their mathematical self-efficacy as well. Participants were divided according to the above criteria as follows: (i) 73 from Montessori primary schools, (ii) 332 pupils educated in mathematics according to the Hejný method, (iii) 510 pupils from an ordinary primary school, and (iv) 218 pupils completing the Dalton teaching plan. In the field of mathematical problem-solving the pupils from the Montessori primary schools clearly outperformed pupils from the Dalton Plan schools (p = 0.027) as well as pupils attending ordinary primary schools (p = 0.009), whereas the difference between the Montessori schools and Hejný classes was not significant (p = 0.764). There is no statistically significant difference in the level of self-efficacy of pupils with respect to the preferred strategies for managing learning activities (p = 0.781). On the other hand, correlation between mathematical problem-solving and self-efficacy was confirmed in all the examined types of schools. However, the correlation coefficient was lower in the case of the pupils from the classes applying the Hejný method in comparison with the pupils attending the Montessori schools (p = 0.073), Dalton Plan schools (p = 0.043), and ordinary primary schools (p = 0.002). Even though the results in mathematical problem-solving are not consistent across the studies, the presented results confirm better performance of pupils in some constructivist settings, particularly in the case of individual constructivism in the Montessori primary schools. The factors influencing lower correlation of self-efficacy and performance in mathematical problem-solving ought to be subject to further investigation.
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Gismeros Moreno, Raúl, Eduardo Corral Abad, Jesús Meneses Alonso, María Jesús Gómez García, and Cristina Castejón Sisamón. "Modelling multiple-simultaneous impact problems with a nonlinear smooth approach: pool/billiard application." Nonlinear Dynamics 107, no. 3 (December 14, 2021): 1859–86. http://dx.doi.org/10.1007/s11071-021-07117-4.
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AbstractSmooth approaches are able to model reasonably well contact/impact events between two bodies, showing some peculiarities when dealing with certain geometries and arising certain issues with the detection of the initial instant of contact. The characterization of multiple-simultaneous interaction systems, considering (or not) energy dissipation phenomena (mainly friction), is always an interesting research topic, addressed from different perspectives. In the present work, the process of design, optimization and verification of a multiple-impact, day-to-day multibody novel model is shown. Specifically, we have decided to focus on a pool/billiard game due to its geometry simplicity. The model involves several balls moving freely and rolling, suffering different kinds of contacts/impacts among them and against the cushions and the cloth. In this system, the proper modelling of both contact and friction forces in the multiple, simultaneous contacts and impacts events is critical to obtain consistent results. In addition, these forces are complicated to model because of its nonlinear behaviour. The different existing approaches when dealing with multiple-contact events are briefly described, along with their most distinctive features. Then, the interactions identified on the model are implemented using several nonlinear contact-force models, following a smooth-based approach and considering friction phenomena, aiming at determining the most suitable set of both contact and friction force models for each of these implemented interactions, which take place simultaneously, thus resulting in a complex system with multiple impacts. Subsequently, the solving method that provides the most accurate results at the minimum computational cost is determined by testing a simple shot. Finally, the different interactions on the model are verified using experimental results and previous works. One of the main goals of this work is to show the some of the issues that arise when dealing with multiple-simultaneous impact multibody systems from a smooth-contact approach, and how researchers can deal with them.