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In this paper we discuss the types of knowledge used by six middle school students as they engaged with a debugging task designed to integrate ideas from computer science, mathematics and science. Our findings show that the computational thinking practice of debugging is a rich source of opportunities to integrate these different disciplines. The analysis illustrates how the types of knowledge the students did and did not use at each step of the debugging process were related to their ability to succeed at each step. Our work contributes to theory and practice by uncovering implications for studying debugging through two refined frameworks and for designing debugging tasks to support transdisciplinary learning.

The paper discusses a certain type of competitions based on distance interaction of a participant with simulation models of concepts from discrete mathematics and computer science. One of them is the "Construct, Test, Explore" (CTE) competition, developed by the authors, the other is the Olympiad in Discrete Mathematics and Theoretical Informatics (DM&TI). The tasks presented in this paper are generally devoted to the concept of a graph isomorphism. Most of the tasks are verified automatically.

Background: The coronavirus pandemic has caused a shift in how many teaching, learning and research activities are conducted internationally. Lockdowns compelled all education sectors, including higher education (HE), to adopt a variety of online learning practices at short notice. As these changes in practice have implications beyond the pandemic, more needs to be understood about settings across the globe where the move to online may pose particular challenges. This study brings a focus to how lecturers in a college of education in Nigeria responded to the professional demands of lockdowns and developed strategies for managing educational activities that have relevance during and beyond the pandemic itself. Purpose: The aim of the study reported in this paper was to examine lecturers' perceptions of the management of teaching, learning and research activities during a lockdown, drawing out longer term implications. Methods: Data were collected through in-depth, one-to-one interviews with six lecturers from a college of education in Nigeria. Interview data were analysed qualitatively. Findings: Detailed analysis indicated that lecturers' strategies included encouraging students to engage in self-directed learning, as they uploaded learning materials on messaging groups and the college's e-learning platform. However, lecturers felt that the quality of teaching and assessment was compromised by factors including: irregular power supply, poor internet connection, high data costs and some students' limited digital skills. A particular concern was students' lack of interaction on the online platforms, which lecturers perceived to result in a more passive teaching and learning process. Lecturers also experienced difficulties undertaking research activities. A range of strategies and implications for the ongoing management of educational activities was discussed. Conclusions: The study offers insights into how some of the challenges encountered could be addressed to support sustainable online and blended teaching and learning in the longer term, in settings internationally where there are barriers to accessing online teaching and learning. Crucial aspects include strengthening educational technology training for lecturers and students, enhancing e-learning platforms for teaching practical courses, and enabling lecturers to develop beneficial and valuable online resources.

Computing has become essential in modern-day problem-solving, making computational literacy necessary for practicing scientists and engineers. However, K-12 science education has not reflected this computational shift. Integrating computational thinking (CT) into core science courses is an avenue that can build computational literacies in all students. Integrating CT and science involves using computational tools and methods (including programming) to understand scientific phenomena and solve science-based problems. Integrating CT and science is gaining traction, but widespread implementation is still quite limited. Several barriers have limited the integration and implementation of CT in K-12 science education. Most teachers lack experience with computer science, computing, programming, and CT and therefore are ill-prepared to integrate CT into science courses, leading to low self-efficacy and low confidence in integrating CT. This theoretical paper introduces a novel instructional approach for integrating disciplinary science education with CT using unplugged (computer-free) activities. We have grounded our approach in common computational thinking in STEM frameworks but translate this work into an accessible pedagogical strategy. We begin with an overview and critique of current approaches that integrate CT and science. Next, we introduce the "Computational Thinking through Algorithmic Explanations" (CT-AE) instructional approach. We then explain how CT-AE is informed by constructionist writing-to-learn science theory. Based on a pilot implementation with student learning outcomes, we discuss connections to existing literature and future directions.

The International Institute of Knowledge Innovation and Invention (IIKII) is an institute that promotes the exchange of innovations and inventions, and establishes a communication platform for international innovations and researches. In 2019, IIKII cooperated with the Institute of Electrical and Electronics Engineers (IEEE) Tainan Section Sensors Council to hold IEEE conferences such as IEEE ICIASE 2019, IEEE ECBIOS 2019, IEEE ICKII 2019, ICUSA-GAME 2019, and IEEE ECICE 2019. This Special Issue entitled “Selected Papers from IIKII 2019 conferences” aims to select excellent papers from IIKII 2019 conferences, including symmetry in physics, chemistry, biology, mathematics, and computer science, etc. It selected 21 excellent papers from 750 papers presented in IIKII 2019 conferences on the topic of symmetry. The main goals of this Special Issue are to encourage scientists to publish their experimental and theoretical results in as much detail as possible, and to discover new scientific knowledge relevant to the topic of symmetry.

The recent focus on computational thinking as a key 21st century skill for all students has led to a number of curriculum initiatives to embed it in K-12 classrooms. In this paper, we discuss the key computational thinking constructs, including algorithms, abstraction, and automation. We further discuss how these ideas are related to current educational reforms, such as Common Core and Next Generation Science Standards and provide specific means that would allow teachers to embed these ideas in their K-12 classrooms, including recommendations for instructional technologists and professional development experts for infusing computational thinking into other subjects. In conclusion, we suggest that computational thinking ideas outlined in this paper are key to moving students from merely being technology-literate to using computational tools to solve problems.

"Building Computational Thinkers," a three-year research study, explored how educators and designers can most effectively support the development of computational thinking capacity, and how these learning experiences could be customized to meet the needs of different learners. This research study focused on three specific exhibit design approaches that conveyed problem decomposition content in "The Science Behind Pixar" ("Pixar"), a 13,000 square foot traveling exhibition about the computer science, mathematics, and science behind Pixar's innovative films. Phase One investigated how novice learners could be supported to interact with exhibits and understand problem solving strategies that tackle complex, creative challenges in computer programming. Phase Two investigated the affordances of these exhibits to build capacity, feelings of efficacy, and interest in problem decomposition content in middle and high school youth. The findings in this paper describe the types of scaffolds that can be used to support computational thinking in novice youth, as well as how a combination of exhibit approaches were found to increase youth perceptions, understanding, and beliefs of computer programming. It will also discuss how two exhibit approaches worked particularly well for engaging girls in problem decomposition content.

Abstraction is a key concept in CS, one of the most fundamental ideas underlying CS and its practice. However, teaching this soft concept to novices is a very difficult task, as discussed by many CSE experts. This paper discusses this issue, and suggests a general framework for teaching abstraction in CS to novices, a framework that would fit into most kinds of introductory courses. While this paper leans on some anecdotal evidence to support its claims, it is not an empirical work. Rather, it builds on research literature and experience in underlying some concrete rules that can assist in teaching abstraction.

Reversing is the notion of thinking or working in reverse. Computer science textbooks and tutors recognize it primarily in the form of recursion. However, recursion is only one form of reversing. Reversing appears in the computer science curriculum in many other forms, at various intellectual levels, in a variety of fundamental courses. As such, it is too important a notion to be left unexplored. In this paper we discuss reversing in the context of two theoretical frameworks--as a fundamental idea in computer science, in the context of Schwill's model of fundamental ideas, and as a powerful problem solving means, in the context of Schoenfeld's cognitive model of problem solving. We recognize seven different forms of reversing, and demonstrate the essential role of each in algorithm or proof design. Our focus in the paper is conceptual, yet we briefly note our initial experimental experience, with student difficulties in both the invocation and utilization of reversing. We then discuss cognitive aspects of the teaching of reversing and offer ways to assimilate its awareness and elaborate its fundamental role in computer science. (Contains 1 note.)

Data Structures and Algorithms are a central part of Computer Science. Due to their abstract and dynamic nature, they are a difficult topic to learn for many students. To alleviate these learning difficulties, instructors have turned to algorithm visualizations (AV) and AV systems. Research has shown that especially engaging AVs can have an impact on student learning of DSA topics. Until recently, most AV systems were Java-based systems. But, the popularity of Java has declined and is being supplanted by HTML5 and JavaScript content online. In this paper, we present JSAV: the JavaScript AV development library. JSAV goes beyond traditional AV library support for displaying standard data structures components, to provide functionality to simplify creation of AVs on many engagement levels including interactive exercises. We describe the growing body of content created with JSAV and summarize our three years of experience and research results from using JSAV to build content that supports CS education.

Math self-concept (MSC) is considered an important predictor of the pursuit of science, technology, engineering and math (STEM) fields. Women's underrepresentation in the STEM fields is often attributed to their consistently lower ratings on MSC relative to men. Research in this area typically considers STEM in the aggregate and does not account for variations in MSC that may exist between STEM fields. Further, existing research has not explored whether MSC is an equally important predictor of STEM pursuit for women and men. This paper uses a national sample of male and female entering college students over the past four decades to address how MSC varies across STEM majors over time, and to assess the changing salience of MSC as a predictor of STEM major selection in five fields: biological sciences, computer science, engineering, math/statistics, and physical sciences. Results reveal a pervasive gender gap in MSC in nearly all fields, but also a great deal of variation in MSC among the STEM fields. In addition, the salience of MSC in predicting STEM major selection has generally become weaker over time for women (but not for men). Ultimately, this suggests that women's lower math confidence has become a less powerful explanation for their underrepresentation in STEM fields.

"Personal learning environments" (PLEs) and "personal learning networks" (PLNs) are well-known concepts. A personal learning network "cluster" is a small group of people who regularly interact academically and whose PLNs have a non-empty intersection that includes all the other members. At university level PLN clusters form spontaneously among students and are known to last over an extended period of time. Little is known regarding the workings of these PLN clusters of students. The claim is that these PLN clusters are at the heart of student learning and are aligned with the current trend of a knowledge-pull community of learning. In this paper we investigate the activities and characteristics of PLN clusters in two different fields of study at a South African university, namely mathematics and computer science. We discuss the benefits that these clusters offer, investigate the mashup of activities and tools and we contrast experiences in the two fields of study. It is the commonalities rather than differences that are striking between the two groups of students. Although computer science students lean more towards digital communication, both groups impress with the pride they take in their PLN clusters and are vocal in describing the benefits that these clusters offer.

This paper explores the ways students perceive the transfer of learned knowledge to new situations -- often a surprisingly difficult prospect. The novel aspect compared to the traditional transfer studies is that the learning phase is not a part of the experiment itself. The intention was only to activate acquired knowledge relevant to the transfer target using a short primer immediately prior to the situation where the knowledge was to be applied. Eight volunteer students from either mathematics or computer science curricula were given a task of designing an adder circuit using logic gates: a new context in which to apply knowledge of binary arithmetic and Boolean algebra. The results of a phenomenographic classification of the views presented by the students in their post-experiment interviews are reported. The degree to which the students were conscious of the acquired knowledge they employed and how they applied it in a new context emerged as the differentiating factors.

Stepwise program refinement techniques can be used to simplify program verification. Programs are better understood since their main properties are clearly stated, and verification of rather complex algorithms is reduced to proving simple statements connecting successive program specifications. Additionally, it is easy to analyse similar algorithms and to compare their properties within a single formalization. Usually, formal analysis is not done in the educational setting due to complexity of verification and a lack of tools and procedures to make comparison easy. Verification of an algorithm should not only give a correctness proof, but also better understanding of an algorithm. If the verification is based on a small step program refinement, it can become simple enough to be demonstrated within the university-level computer science curriculum. In this paper we demonstrate this and give a formal analysis of two well- known algorithms (Selection Sort and Heap Sort) using the proof assistant Isabelle/HOL and program refinement techniques.

Abstraction is a major concept in computer science and serves as a powerful tool in software development. Pattern-oriented instruction (POI) is a pedagogical approach that incorporates patterns in an introductory computer science course in order to structure the learning of algorithmic problem solving. This paper examines abstraction processes in the course of solving an algorithmic problem and highlights three distinct, although interrelated, facets of abstraction: pattern recognition, black-boxing, and structure identification. A study that examined the influence of the POI approach on students' abstraction skills is described; students who learned according to the POI approach were compared with students who learned in a traditional manner with regard to analogical reasoning and problem decomposition and solution, as well as verbal expression. The three facets of abstraction were used to analyze students' abstraction skills and their competency in algorithmic problem solving. (Contains 4 figures and 5 tables.)

In this paper, the author aims to offer an elaboration of simple, yet powerful, mathematical patterns through mathematical games. Mathematical games may serve as colorful instructional tools for teachers and textbooks, and may raise students' motivation and intuition. Patterns are fundamental in mathematics and computer science. In the case of games, they may involve integer properties such as parity, primality, and divisibility, as well as invariant properties of repeated actions. The author presents four simply stated, less familiar mathematical games--Co-primes, Interleaved Parity, Proper Divisors, and Powers of 2--and develops the winning strategy for each of the games. Preliminary novice attempts are mentioned, and then instructive strategy developments are presented, through the illumination of underlying mathematical patterns. The author concludes by reflecting on the illuminated patterns and the way they were reached.

Computer science provides with virtual laboratories, places where one can merge real experiments with the formalism of algorithms and mathematics and where, with the advent of multimedia, sounds and movies can also be added. In this paper we present a method, based on principles of formal ontology, allowing one to develop interactive educational tools. The structure of our system starts from general considerations on knowledge itself moving on to formal ontological principles in order to obtain a robust knowledge frame and good awareness of knowledge levels involved during the teaching process. Our system is split into object-knowledge--the knowledge of the phenomenon to be taught--and meta-knowledge--i.e., how to teach it. Using a trip (journey) metaphor, together with the flexibility of semantic graph representations, we define the reference frame and we apply it to a case study related to the Planetary Missions, the subject of our research. This tool is provided with a multimedia interface to show the results of several current missions, but may be implemented with new missions. (Contains 10 figures.)

The rapid rate of expansion of the disciplines of biotechnology, genomics, and bioinformatics emphasizes the increased interdependency between computer science and biology, with mathematics serving as the bridge between these disciplines. This paper demonstrates this inter-relationship within the context of a computational model for a biological process. We designed and implemented a lesson plan for an interdisciplinary science course that examines the evolutionary process from biological, mathematical, and computer science perspectives. The observations obtained from this lesson can be used to augment studies in mathematics with emphasis on arithmetic functions, probability, and generating series.

This paper describes a "learning community" designed for sophomore computer science majors who are simultaneously studying discrete mathematics. The learning community consists of three courses: Discrete Mathematics, Data Structures and an Integrative Seminar/Lab. The seminar functions as a link that integrates the two disciplines. Participation in the seminar enables students to study and appreciate the mutually beneficial relationship that exists between mathematics and computer science--a relationship that students often fail to see. Through carefully planned experimentation, students investigate how mathematics is used to formalize computer science, and how computer science can be used as a tool to explore mathematics.

More than 53,000 citations from 609 dissertations published at The Ohio State University between 1998-2012 representing four science disciplines--civil engineering, computer science, mathematics and physics--were examined to determine what, if any, preferences or trends exist. This case study seeks to identify whether or not researcher preferences have changed over time when determining which citation categories are cited in their dissertation. These results revealed that books, articles, and conference papers continue to rank highest in popularity among researchers, however, some shifts have occurred among categories across all four disciplines. When comparing overall rankings, web pages have clearly shown an increase in popularity jumping from 9th place in 1998 to 4th place in 2012. Most surprising, is the decline in usage of theses and dissertations from 6th place (1998) to 8th place (2012) even though improved electronic access has increased availability during the 15-year period.

Purpose — The aims of this article are to describe the current status, usage, and acceptance of domestic preprint servers in mainland China by investigating three integrated preprint servers in mainland China. These are the Qiji e-print archive (Qiji), the Chinese Preprint Server (CPS), Chinese Science Papers Online (CSPO)., Design/methodology/approach — This research gives a quantitative analysis of the submission numbers to three preprint servers, the subject distribution and citations. An investigation of university websites and their policies was also carried out. Findings — Preprint submissions have a strong correlation with official promotion and policies. The preprints communication pattern in mainland China concentrates on the disciplines of physics, mathematics and computer science which reflects international preprint communication behaviour. As yet the domestic preprint servers in mainland China attract little attention from excellent scholars and have a low impact on scientific communication. Research limitations/implications — No author survey was conducted. Originality/value — This is the first paper to characterize the usage and acceptance of domestic preprint servers in mainland China using a quantitative method. [ABSTRACT FROM AUTHOR]

Four liberal arts college programs are described that use a variety of interdisciplinary and innovative approaches to bring technological, computer, scientific, mathematical, and physics literacy for both students and faculty. (MSE)

The concept and nature of proof in mathematics is examined, and the emerging role of computers in this area is reviewed. The issue is seen to force mathematicians and philosophers to reexamine their assumptions about mathematics and how it is done. (MP)

This paper describes the implementation of a STEM scholarship program which utilized a holistic approach to providing a multi-dimensional student support system. The program has been successful in encouraging and supporting women in Applied Mathematics and Computer Science by offering a diverse suite of extracurricular opportunities, actively engaging them in organized events, research projects, and participation in STEM communities, and helping them achieve higher GPAs and shorter times to graduation. The supported women also benefitted from close mentoring relationships with the faculty mentors. The program emphasized the development of empowering settings for women's engagement and achievement, which act to sustain and expand interest in mathematics and computing, and thereby help them to see themselves as future professionals in the field. [ABSTRACT FROM AUTHOR]

The paper describes a two-week summer course for gifted students which successfully develops mathematical program solving, promotes understanding of advanced mathematical concepts, and allows students to learn a great deal of programing. (CL)

Background: Finding duplicates is an important phase of systematic review. However, no consensus regarding the methods to find duplicates has been provided. This study aims to describe a pragmatic strategy of combining auto- and hand-searching duplicates in systematic review and to evaluate the prevalence and characteristics of duplicates. Methods and Findings: Literatures regarding portal vein thrombosis (PVT) and Budd-Chiari syndrome (BCS) were searched by the PubMed, EMBASE, and Cochrane library databases. Duplicates included one index paper and one or more redundant papers. They were divided into type-I (duplicates among different databases) and type-II (duplicate publications in different journals/issues) duplicates. For type-I duplicates, reference items were further compared between index and redundant papers. Of 10936 papers regarding PVT, 2399 and 1307 were identified as auto- and hand-searched duplicates, respectively. The prevalence of auto- and hand-searched redundant papers was 11.0% (1201/10936) and 6.1% (665/10936), respectively. They included 3431 type-I and 275 type-II duplicates. Of 11403 papers regarding BCS, 3275 and 2064 were identified as auto- and hand-searched duplicates, respectively. The prevalence of auto- and hand-searched redundant papers was 14.4% (1640/11403) and 9.1% (1039/11403), respectively. They included 5053 type-I and 286 type-II duplicates. Most of type-I duplicates were identified by auto-searching method (69.5%, 2385/3431 in PVT literatures; 64.6%, 3263/5053 in BCS literatures). Nearly all type-II duplicates were identified by hand-searching method (94.9%, 261/275 in PVT literatures; 95.8%, 274/286 in BCS literatures). Compared with those identified by auto-searching method, type-I duplicates identified by hand-searching method had a significantly higher prevalence of wrong items (47/2385 versus 498/1046, p<0.0001 in PVT literatures; 30/3263 versus 778/1790, p<0.0001 in BCS literatures). Most of wrong items originated from EMBASE database. Conclusion: Given the inadequacy of a single strategy of auto-searching method, a combined strategy of auto- and hand-searching methods should be employed to find duplicates in systematic review. [ABSTRACT FROM AUTHOR]

: In computational science literature including, e.g., bioinformatics, computational statistics or machine learning, most published articles are devoted to the development of “new methods”, while comparison studies are generally appreciated by readers but surprisingly given poor consideration by many journals. This paper stresses the importance of neutral comparison studies for the objective evaluation of existing methods and the establishment of standards by drawing parallels with clinical research. The goal of the paper is twofold. Firstly, we present a survey of recent computational papers on supervised classification published in seven high-ranking computational science journals. The aim is to provide an up-to-date picture of current scientific practice with respect to the comparison of methods in both articles presenting new methods and articles focusing on the comparison study itself. Secondly, based on the results of our survey we critically discuss the necessity, impact and limitations of neutral comparison studies in computational sciences. We define three reasonable criteria a comparison study has to fulfill in order to be considered as neutral, and explicate general considerations on the individual components of a “tidy neutral comparison study”. R codes for completely replicating our statistical analyses and figures are available from the companion website http://www.ibe.med.uni-muenchen.de/organisation/mitarbeiter/020_professuren/boulesteix/plea2013. [ABSTRACT FROM AUTHOR]

Algebraic topology studies topological spaces with the help of tools from abstract algebra. The main focus of this paper is to show that many concepts from algebraic topology can be conveniently expressed in terms of (normal) factor graphs. As an application, we give an alternative proof of a classical duality result of Kramers and Wannier, which expresses the partition function of the 2-D Ising model at a low temperature in terms of the partition function of the 2-D Ising model at a high temperature. Moreover, we discuss analogous results for the 3-D Ising model and the Potts model. [ABSTRACT FROM AUTHOR]

Programming is an interdisciplinary practice with applications in both mathematics and computer science. Mathematics concerns rigor, abstraction, and generalization. Computer science predominantly concerns efficiency, concreteness, and physicality. This makes programming a medium for problem solving that mediates between mathematics and computer science in intriguing ways. Behind programming practices is computational thinking (CT), a mode of thinking involved in formulating and solving problems so that the solutions could be represented and carried out by computing means. In this paper, CT is seen as a boundary object connecting mathematics and computer science in a school problem-solving context. In particular, we examine and analyse middle school students' work upon engaging in mathematical problem solving-in a programming environment, taking CT as a boundary object embedded in the block-based programming environment, Scratch. The analysis is guided by observing boundary crossing features of CT in the students' artefacts produced in Scratch while solving mathematical problems related to symmetry and arithmetic sequence. The findings of this study open up new dimensions to explore CT as a boundary object in integrated STEM pedagogy. [ABSTRACT FROM AUTHOR]

In 2019, the Department of Mathematics and Statistics at Maynooth University commenced a project which sought to address, through the provision of mathematics learning supports, the issues of poor engagement and retention of computer science students studying mathematics. In this paper, we present preliminary engagement and performance data along with interviews conducted with eight students. We discuss how the quantitative data seemed to indicate that computer science students were engaging at similar levels to their peers, but several factors, including the quality of this engagement and their mathematical backgrounds may explain their poor exam performance. It also emerged that, while students were largely negative about their experiences in large lectures and their awareness of the relevance of mathematics to computer science, they were generally positive about smaller teaching situations such as tutorials, mathematics support drop-in and opportunities to work with their peers. [ABSTRACT FROM AUTHOR]

Geodesics are of fundamental interest in mathematics, physics, computer science, and many other subjects. The so-called leapfrog algorithm was proposed in [L. Noakes, J. Aust. Math. Soc., 65 (1998), pp. 37--50] (but not named there as such) to find geodesics joining two given points x0 and x1 on a path-connected complete Riemannian manifold. The basic idea is to choose some junctions between x0 and x1 that can be joined by geodesics locally and then adjust these junctions. It was proved that the sequence of piecewise geodesics\{γk} k≥1 generated by this algorithm converges to a geodesic joining x0 and x1. The present paper investigates leapfrog's convergence rate τi,n of ith junction depending on the manifold M. A relationship is found with the maximal root λn of a polynomial of degree n-3, where n (n >3) is the number of geodesic segments. That is, the minimal τi,n is upper bounded by λn(1+c+), where c+ is a sufficiently small positive constant depending on the curvature of the manifold M. Moreover, we show that λn increases as n increases. These results are illustrated by implementing leapfrog on two Riemannian manifolds: the unit 2-sphere and the manifold of all 2 × 2 symmetric positive definite matrices. [ABSTRACT FROM AUTHOR]

A discussion on who should teach computer literacy in academe is presented. Computer science can be described as an experimental science with the computer as the laboratory but computer science is an interdisciplinary area. Defining a computer scientist is difficult. (MLW)

The mathematicians who developed the computer-aided proof to the Four-Color Conjecture discuss the ramifications of their work and the use of computers in working on the proof of theorems in the future. (MP)

Linear codes generated by component functions of perfect nonlinear (PN for short) and almost perfect nonlinear (APN for short) functions and the first-order Reed-Muller codes have been an object of intensive study in coding theory. The objective of this paper is to investigate some binary shortened codes of two families of linear codes from APN functions and some $p$ -ary shortened codes associated with PN functions. The weight distributions of these shortened codes and the parameters of their duals are determined. The parameters of these binary codes and $p$ -ary codes are flexible. Many of the codes presented in this paper are optimal or almost optimal. The results of this paper show that the shortening technique is very promising for constructing good codes. [ABSTRACT FROM AUTHOR]

Bibliographic analysis has been a very powerful tool in evaluating the effective contributions of a researcher and determining his/her future research potential. The lack of an absolute quantification of the author’s scientific contributions by the existing measurement system hampers the decision-making process. In this paper, a new metric system, Absolute index (Ab-index), has been proposed that allows a more objective comparison of the contributions of a researcher. The Ab-index takes into account the impact of research findings while keeping in mind the physical and intellectual contributions of the author(s) in accomplishing the task. The Ab-index and h-index were calculated for 10 highly cited geneticists and molecular biologist and 10 young researchers of biological sciences and compared for their relationship to the researchers input as a primary author. This is the first report of a measuring method clarifying the contributions of the first author, corresponding author, and other co-authors and the sharing of credit in a logical ratio. A java application has been developed for the easy calculation of the Ab-index. It can be used as a yardstick for comparing the credibility of different scientists competing for the same resources while the Productivity index (Pr-index), which is the rate of change in the Ab-index per year, can be used for comparing scientists of different age groups. The Ab-index has clear advantage over other popular metric systems in comparing scientific credibility of young scientists. The sum of the Ab-indices earned by individual researchers of an institute per year can be referred to as Pr-index of the institute. [ABSTRACT FROM AUTHOR]

Diagnosability is a fundamental consideration when designing an interconnected network. The PMC and MM ∗ fault diagnosis models are the two most commonly used models. Both the g -good-neighbour diagnosability and g -extra diagnosability of an interconnection network have been two of the hot topics in the intersectional research areas of Graph theory and Computer Science, which become increasingly attractive for new solutions to real-world problems. However, there are still some problems in the transformation from the concepts of Computer Science to that of mathematics. In this paper, we systematically study such problems and give a strict proof from concepts to mathematical conclusions. In the terms of results, we not only give the relationship between g -good-neighbour diagnosabilities of the network under PMC model and MM ∗ model, but also between g -extra diagnosabilities of the network under PMC and MM ∗ models. To apply our results, we give an application on the enhanced hypercube in the end and derive a lemma explaining whether these are 3-cycles in enhanced hypercubes and how many common neighbours for two vertices of enhanced hypercubes under different values of k in the meantime. [ABSTRACT FROM AUTHOR]

Fractional variants of distance-based parameters have application in the fields of sensor networking, robot navigation, and integer programming problems. Complex networks are exceptional networks which exhibit significant topological features and have become quintessential research area in the field of computer science, biology, and mathematics. Owing to the possibility that many real-world systems can be intelligently modeled and represented as complex networks to examine, administer and comprehend the useful information from these real-world networks. In this paper, local fractional strong metric dimension of certain complex networks is computed. Building blocks of complex networks are considered as the symmetric networks such as cyclic networks C n , circulant networks C n 1,2 , mobious ladder networks M 2 n , and generalized prism networks G m n . In this regard, it is shown that LSFMD of C n n ≥ 3 and G m n n ≥ 6 is 1 when n is even and n / n − 1 when n is odd, whereas LSFMD of M 2 n is 1 when n is odd and n / n − 1 when n is even. Also, LSFMD of C n 1,2 is n / 2 ⌈ m + 1 / 2 ⌉ where n ≥ 6 and m = ⌈ n − 5 / 4 ⌉. [ABSTRACT FROM AUTHOR]

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK. [ABSTRACT FROM AUTHOR]

Graph theory is the most powerful tools in the mathematics and computer science, also study of descriptors in quantitative structure property relationship (QSPR) and quantitative structure activity relationship (QSAR) studies in the chemistry science. The eccentricity based topological indices are very important for QSPR/QSAR studies, and these values have been studied for different graph types in many articles recently. In this paper, some eccentricity based topological indices of two convex polytopes Qn and Rn are computed. [ABSTRACT FROM AUTHOR]

The problem of counting independent sets of a graph G is not only mathematically relevant and interesting, but also has many applications in physics, mathematics, and theoretical computer science. In this paper, a novel method for counting independent sets on grid-like structures is presented. It starts by explaining the recurrences used by the method to count independent sets on basic topologies of graphs. The method is extended to process grid-like structures of quadratic faces. The proposal has a lower time complexity than the required on the leading and current method based on the transfer matrix for counting independent sets on grids. [ABSTRACT FROM AUTHOR]

The paper initially develops the semi-Jordan curve theorem on the digital plane with the Marcus-Wyse topology, i.e., M W -topological plane or ( Z 2 , γ) for brevity. We first prove that while every simple closed M W -curve is semi-open in ( Z 2 , γ) , it may not be semi-closed. Given a simple closed M W -curve with l elements, denoted by S C γ l , after establishing a continuous analog of S C γ l denoted by A (S C γ l) , we initially show that A (S C γ l) is both semi-open and semi-closed in ( R 2 , U) , where ( R 2 , U) is the 2 -dimensional real plane R 2 with the usual topology U . Furthermore, we find a condition for A (S C γ l) to separate ( R 2 , U) into exactly two non-empty components, compared to a typical Jordan curve theorem on ( R 2 , U). Since not every S C γ l always separates ( Z 2 , γ) into two nonempty components, we find a condition for S C γ l , l ≠ 4 , to separate ( Z 2 , γ) into exactly two components. The semi-Jordan curve theorem on the M W -topological plane plays an important role in applied topology such as digital topology, mathematical morphology as well as computer science. [ABSTRACT FROM AUTHOR]

The law of importation is an important property of fuzzy implication functions because of its interesting applications in approximate reasoning and image processing. In this paper, as a continuation of the paper [S. Massanet, D. Ruiz-Aguilera, and J. Torrens, “Characterization of a class of fuzzy implication functions satisfying the law of importation with respect to a fixed uninorm—Part I,” IEEE Trans. Fuzz Syst. , to be published.], the characterization of all fuzzy implication functions that satisfy the law of importation with respect to a given uninorm $U$ , and having an $\alpha$ -section that is a continuous fuzzy negation is given for the cases when the uninorm $U$ lies in one of the most used classes of uninorms. As the case when the uninorm $U$ is in ${\mathcal U}_{\min }$ was already solved in [S. Massanet, D. Ruiz-Aguilera, and J. Torrens, “Characterization of a class of fuzzy implication functions satisfying the law of importation with respect to a fixed uninorm—Part I,” IEEE Trans. Fuzz Syst., to be published.], this paper focuses in the cases when $U$ is an idempotent uninorm, a representable uninorm, or a uninorm continuous in the open unit square. [ABSTRACT FROM AUTHOR]

Maximum distance separable (MDS) codes are very important in both theory and practice. There is a classical construction of a family of $[{2^{m}+1, 2u-1, 2^{m}-2u+3}]$ MDS codes for $1 \leq u \leq 2^{m-1}$ , which are cyclic, reversible and BCH codes over ${\mathrm {GF}}(2^{m})$. The objective of this paper is to study the quaternary subfield subcodes and quaternary subfield codes of a subfamily of the MDS codes for even $m$. A family of quaternary cyclic codes is obtained. These quaternary codes are distance-optimal in some cases and very good in general. Furthermore, two infinite families of 3-designs from these quaternary codes and their duals are presented. [ABSTRACT FROM AUTHOR]

With the untimely passing of Patrick Dehornoy in September 2019, the world of mathematics lost a brilliant scholar who made profound contributions to set theory, algebra, topology, and even computer science and cryptography. And I lost a dear friend and a strong influence in the direction of my own research in mathematics. In this paper, I will concentrate on his remarkable discovery that the braid groups are left-orderable, and its consequences, and its strong influence on my own research. I'll begin by describing how I learned of his work. [ABSTRACT FROM AUTHOR]

A k-plex of order n is an ${n} \times {n}$ matrix on n symbols, where every row contains k distinct symbols, every column contains k distinct symbols, and every symbol occurs exactly k times. Yi et al. (2019) introduced 3-plex codes which are 2-erasure codes (2-erasure tolerant array codes) derived from 3-plexes. In this paper, we generalize 3-plex codes to k-plex codes. We introduce the notion of a “strong” k-plex which implies the derived k-plex code is 2-erasure tolerant. Moreover, k-plex codes derived from strong $k$ -plexes have a straightforward algorithm for reconstruction. These general k-plex codes offer greater flexibility when choosing a suitable code for a storage system, enabling the operator to better optimize the unavoidable trade-offs involved. Blackburn asked for the maximum number of entries in an ${n} \times {n}$ partial Latin square on n symbols in which if distinct cells $({i},{j})$ and $({i}',{j}')$ contain the same symbol, then the cells $({i}',{j})$ and $({i},{j}')$ are empty. A “strong” k-plex satisfies the Blackburn property (along with two other properties related to erasure coding). We investigate the necessary conditions for the existence of Blackburn k-plexes (and hence necessary conditions for the existence of strong k-plexes). We show that any Blackburn k-plex has order ${n} \geq \lceil (\sqrt {2}+1){k}-2 \rceil $. We describe how to construct strong k-plexes of order n when $k \in \{2,3,4,5\}$ for all possible orders n, and we give a simple construction of strong k-plexes of order ${k}^{2}$ for $k \geq 2$. [ABSTRACT FROM AUTHOR]

Boolean functions, coding theory and $t$ -designs have close connections and interesting interplay. A standard approach to constructing $t$ -designs is the use of linear codes with certain regularity. The Assmus-Mattson Theorem and the automorphism groups are two ways for proving that a code has sufficient regularity for supporting $t$ -designs. However, some linear codes hold $t$ -designs, although they do not satisfy the conditions in the Assmus-Mattson Theorem and do not admit a $t$ -transitive or $t$ -homogeneous group as a subgroup of their automorphisms. The major objective of this paper is to develop a theory for explaining such codes and obtaining such new codes and hence new $t$ -designs. To this end, a general theory for punctured and shortened codes of linear codes supporting $t$ -designs is established, a generalized Assmus-Mattson theorem is developed, and a link between 2-designs and differentially $\delta $ -uniform functions and 2-designs is built. With these general results, binary codes with new parameters and explicit weight distributions are obtained, new 2-designs and Steiner system $S(2, 4, 2^{n})$ are produced in this paper. [ABSTRACT FROM AUTHOR]

In 1979 Haralick famously introduced a method for analyzing the texture of an image: a set of statistics extracted from the co-occurrence matrix. In this paper we investigate novel sets of texture descriptors extracted from the co-occurrence matrix; in addition, we compare and combine different strategies for extending these descriptors. The following approaches are compared: the standard approach proposed by Haralick, two methods that consider the co-occurrence matrix as a three-dimensional shape, a gray-level run-length set of features and the direct use of the co-occurrence matrix projected onto a lower dimensional subspace by principal component analysis. Texture descriptors are extracted from the co-occurrence matrix evaluated at multiple scales. Moreover, the descriptors are extracted not only from the entire co-occurrence matrix but also from subwindows. The resulting texture descriptors are used to train a support vector machine and ensembles. Results show that our novel extraction methods improve the performance of standard methods. We validate our approach across six medical datasets representing different image classification problems using the Wilcoxon signed rank test. The source code used for the approaches tested in this paper will be available at: http://www.dei.unipd.it/wdyn/?IDsezione=3314&IDgruppo_pass=124&preview=. [ABSTRACT FROM AUTHOR]