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This study aims at understanding the role of the tools chosen throughout the processes of solving a non-routine mathematical problem and communicating its solution. In assuming that problem-solving is a synchronous activity of mathematization and expression of mathematical thinking we take our proposed Mathematical Problem Solving with Technology (MPST) model to analyze the processes of solving-and-expressing-problems. Resorting to qualitative methods for data collection and analysis, we report on the case of an 8th grader working on a covariation problem to examine the role that paper-and-pencil and digital tools play in the development of a conceptual model of the situation. We found that the resources used throughout the solving-and-expressing activity influenced the depth of the conceptual model developed, within a process of progressive mathematization. Whereas paper-and-pencil led to the emergence of a conceptual model based on exploring particular cases, the digital transformation of the solution was triggered by the process of communicating its mathematical justification and expanded the previous model. Moreover, the complexity of this activity is evidenced by its multiple sequences of processes. Finally, the integration process seems crucial as the concomitant use of technological and mathematical resources precedes major advancements in the expansion of the conceptual model.

Investigating the research trends within a scientific domain by analyzing semantic information extracted from scientific journals has been a topic of interest in the natural language processing (NLP) field. A research trend evaluation is generally based on the time evolution of the term occurrence or the term topic, but it neglects an important aspect—research publication latency. The average time lag between the research and its publication may vary from one month to more than one year, and it is a characteristic that may have significant impact when assessing research trends, mainly for rapidly evolving scientific areas. To cope with this problem, the present paper is the first work that explicitly considers research publication latency as a parameter in the trend evaluation process. Consequently, we provide a new trend detection methodology that mixes auto-ARIMA prediction with Mann–Kendall trend evaluations. The experimental results in an electronic design automation case study prove the viability of our approach.

We investigated the influence of mental imagery expertise in 15 pen and paper role-players as an expert group compared to the gender-matched control group of computer role-players in the difficult Vandenberg and Kuse mental rotation task. In this task, the participants have to decide which two of four rotated figures match the target figure. The dependent measures were performance speed and accuracy. In our exploratory investigation, we further examined midline frontal theta band activation, parietal alpha band activation, and parietal alpha band asymmetry in EEG as indicator for the chosen rotation strategy. Additionally, we explored the gender influence on performance and EEG activation, although a very small female sample section was given. The expected gender difference concerning performance accuracy was negated by expertise in pen and paper role-playing women, while the gender-specific difference in performance speed was preserved. Moreover, gender differences concerning electro-cortical measures revealed differences in rotation strategy, with women using top-down strategies compared to men, who were using top-down strategies and active inhibition of associative cortical areas. These strategy uses were further moderated by expertise, with higher expertise leading to more pronounced activation patters, especially during successful performance. However, due to the very limited sample size, the findings of this explorative study have to be interpreted cautiously.

In 1923, the Philosophical Transactions published G. I. Taylor’s seminal paper on the stability of what we now call Taylor–Couette flow. In the century since the paper was published, Taylor’s ground-breaking linear stability analysis of fluid flow between two rotating cylinders has had an enormous impact on the field of fluid mechanics. The paper’s influence has extended to general rotating flows, geophysical flows and astrophysical flows, not to mention its significance in firmly establishing several foundational concepts in fluid mechanics that are now broadly accepted. This two-part issue includes review articles and research articles spanning a broad range of contemporary research areas, all rooted in Taylor’s landmark paper. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical Transactions paper (part 1)’.

To enhance the quality and efficiency of computer-enabled generation of papers for Test for English Majors Band 8 (TEM-8), a paper generation model supported by sparrow search algorithm-genetic algorithm was studied. First, a simplified test paper generation mathematical model was set up after analyzing and studying types and characteristics of TEM-8 tasks. In the model, quantity, type, difficulty, discrimination degree, scores, exposure, and answering time of test questions were taken into consideration. To enhance the optimizing effect of the genetic algorithm for searching test questions, the traditional genetic algorithm was improved by introducing the sparrow search algorithm into the model to achieve a better crossover rate, variance rate, optimization precision, and speed of the genetic algorithm. A new sparrow search-genetic algorithm (SSA-GA) was designed, and the optimizing effect of SSA-GA was verified to be ideal through optimizing six standard test functions. Then, SSA-GA was applied to conduct experimentation with test paper generation, and comparison with traditional genetic algorithms was also made. The values of best and average fitness of SSA-GA were better than those of the traditional genetic algorithm (GA) in the paper generation. Exposure rate and success rate in TEM-8 paper generation of SSA-GA were higher than those of traditional GA in TEM-8 paper generation. Results showed that the studied SSA-GA could implement test paper generation with higher speed and better quality.

Paper waste in the mockups design with regular, irregular, and amorphous patterns is a critical problem in digital printing presses. Paper waste reduction directly impacts production costs, generating business and environmental benefits. This problem can be mapped to the two-dimensional irregular bin-packing problem. In this paper, an iterated local search algorithm using a novel neighborhood structure to detect overlaps between amorphous shapes is introduced. This algorithm is used to solve the paper waste problem, modeled as one 2D irregular bin-packing problem. The experimental results show that this approach works efficiently and effectively to detect and correct the overlaps between regular, irregular, and amorphous figures.

The administration of A/B exams usually involves the use of items. Issues arise when the pre-establishment of a question bank is necessary and the inconsistency in the knowledge points to be tested (in the two exams) reduces the exams &lsquo, fairness&rsquo, These are critical for a large multi-teacher course wherein the teachers are changed such that the course and examination content are altered every few years. However, a fair test with randomly participating students should still be a guaranteed subject with no item pool. Through data-driven decision-making, this study collected data related to a term test for a compulsory general course for empirical assessments, pre-processed the data and used item response theory to statistically estimate the difficulty, discrimination and lower asymptotic for each item in the two exam papers. Binary goal programing was finally used to analyze and balance the fairness of A/B exams without an item pool. As a result, pairs of associated questions in the two exam papers were optimized in terms of their overall balance in three dimensions (as the goals) through the paired exchanges of items. These exam papers guarantee their consistency (in the tested knowledge points) and also ensure the fairness of the term test (a key psychological factor that motivates continued studies). Such an application is novel as the teacher(s) did not have a pre-set question bank and could formulate the fairest strategy for the A/B exam papers. The model can be employed to address similar teaching practice issues.

This paper serves as a conceptualisation of how the principles of Whole Brain® thinking can be used to inform lecturer identity. The objective of this position paper is to engage discourse on the educational professional development of early-career academics in health sciences. It is about laying a scholarly foundation for self-study. As a scholarly community of practice in family medicine we wanted to determine to what extent the literature – theoretical framework – is silent on innovative means to ensure that academics take responsibility for their development, using self-regulated learning and self-empowerment. In our search for literature on theories of professional learning we came across the theory about Whole Brain® thinking. Our action research initiatives revolve around the notion of individuals’ preferences for different modes of thinking. Our preferred modes of thinking inform our teaching practice and lecturer identity. Este documento sirve como una conceptualización de como los principios del pensamiento Whole Brain® pueden usarse para informar la identidad del profesor. El objetivo de este documento de posición es participar en el discurso sobre el desarrollo profesional educativo de los académicos en las primeras carreras de ciencias de la salud. Se trata de sentar una base académica para el autoestudio. Como comunidad académica de práctica en medicina familiar, queríamos determinar en que medida la literatura – el marco teórico – guarda silencio sobre los medios innovadores para garantizar que los académicos asuman la responsabilidad de su desarrollo, utilizando el aprendizaje autorregulado y el autoempoderamiento. En nuestra búsqueda de literatura sobre teorías del aprendizaje profesional nos encontramos con la teoría del pensamiento Whole Brain®. Nuestras iniciativas de investigación-acción giran en torno a la noción de las preferencias de los individuos por diferentes modos de pensamiento. Nuestros modos preferidos de pensamiento informan nuestra práctica docente y nuestra identidad como profesor. O presente artigo busca uma conceitualização sobre como os princípios do pensamento holístico (ou baseado no modelo Whole Brain®) podem ser usados para informar a identidade do professor. O objetivo deste artigo de posição é envolver o discurso sobre o desenvolvimento profissional educacional de acadêmicos em início de carreira nas ciências da saúde; trata-se de estabelecer uma base acadêmica para o autoestudo. Como comunidade de prática em medicina familiar, queríamos determinar até que ponto a literatura – quadro teórico – está silenciosa sobre meios inovadores para garantir que os acadêmicos assumam a responsabilidade por seu desenvolvimento, usando a aprendizagem autorregulada e o autoempoderamento. Na nossa busca por literatura sobre teorias de aprendizagem profissional, encontramos a teoria sobre o pensamento Whole Brain®. Todas as iniciativas estão em torno da noção das preferências individuais por diferentes modos de pensamento; os modos de pensar que preferimos informam a nossa prática de ensino e a identidade docente.

This paper presents a comprehensive study and analysis of the intelligent grouping of papers in adult higher education using a random matrix approach. Using the results of random matrix theory on the eigenvalues of the sample covariance matrix, the energy of each subspace is estimated, and the estimated energy is then used to construct a subspace weighting matrix. The statistical properties of the sample covariance matrix eigenvectors are analyzed using the first-order perturbation approximation, and then, asymptotic results from random matrix theory on the projection of the sample covariance matrix signal subspace to the real signal parametrization are used to obtain the weighting matrix based on the random matrix eigenvectors. Dynamic adjustment according to the fitness of individuals in the population is performed to ensure population diversity, while the combination of the small habitat technique can avoid the algorithm from falling into early convergence. The algorithm introduces chaos theory to optimize the population initialization process and uses the dynamic traversal randomness of chaos to select individuals in the population so that the initial population is close to the desired target solution. The design of the fitness function in the genetic algorithm generally maps the objective function of the problem to the fitness function. A good fitness function can directly reflect the quality of the individuals in the group. Based on the in-depth study of the basic attributes of the test questions and the principles of test paper evaluation, the mathematical model and objective function of intelligent paper grouping are determined by the difficulty, knowledge points, and cognitive level of the test questions as the main constraints, and NCAGA is applied to the intelligent paper grouping method, which better completes the intelligent paper grouping session for the computer system architecture course. In the process of designing the intelligent grouping algorithm, for the situations of premature convergence and convergence to locally optimal solutions that easily occur in the traditional genetic algorithm, this paper adopts the approach of adaptive adjustment of crossover probability and variation probability to improve the algorithm and achieves satisfactory results. Based on extensive business research, this paper completes the requirement analysis of the online practice system based on the intelligent grouping of papers and presents the functional design and database design of the key functional modules in the system in detail. Finally, this paper conducts functional tests on the system and analyses the test results.

Erratum to the paper [Konovalov, Alexander; Smoktunowicz, Agata; Vendramin, Leandro. On skew braces and their ideals. Exp. Math. 30 (2021), no. 1, 95–104. DOI: 10.1080/10586458.2018.1492476.].

Recently, In the year 2020, Altun et al. \cite{AL} introduced the notion of $p$-proximal contractions and discussed about best proximity point results for this class of mappings. Then in the year 2021, Gabeleh and Markin \cite{GB} showed that the best proximity point theorem proved by Altun et al. in \cite{AL} follows from the fixed point theory. In this short note, we show that if the $p$-proximal contraction constant $k, Comment: 3 pages

A simple sticker sensor has been constructed using litmus paper and tests have been conducted to detect the freshness of beef samples. The results show that the sticker sensor can be used to determine the degree of beef freshness, since the color change of the litmus paper and the quality degradation of the beef during storage time had a similar trend, where the decay of the beef could be detected clearly (when the red litmus paper changed to blue). The sticker sensor reacted accurately to the beef’s freshness in terms of pH change due to beef deterioration from pH 5.61 to 6.24 and from pH 5.67 to 6.02 as shown by its color change in real time at room and chiller temperature respectively. Thus, the sticker sensor can be used as an effective tool for monitoring the microbial quality of packaged fresh meat that correlates with the increased pH of the beef, where the total viable count (TVC) of 5 x 106 cfu/g or 6.698 log cfu/g correlates with a pH of 6.24. These levels were reached at 10 hrs and 7 days at room and chiller temperature respectively. This study provides a foundation for developing a simple sensor for beef freshness.

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich., This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively., The paper ‘Zur Dynamik elastisch gekoppelter Punktsysteme’ by Schrödinger (1914) does not seem to have attracted the attention that it deserves. We translate it into English here and we discuss its results in detail, with a view to its possible influence in the modern theories of generalised continua. The clever solution found, in terms of Bessel functions, by Schrödinger of the problem of the vibrations of a linear infinite chain of molecules gives some important methodological hints for contemporary research.

This paper is a corrigendum to the article ``On the ideal theorem for number fields''. The main result of this paper proves to be untrue and is replaced by an estimate of a weighted sum with an improved error term.

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.

We correct a mistake in a lemma in the paper cited in the title and show that it did not affect any of the other results of the paper. To this end, we prove results on linearly disjoint field extensions that do not seem to be commonly known. We give an example to show that a separability assumption in one of these results cannot be dropped (doing so had led to the mistake). Further, we discuss recent generalizations of the original classification of defect extensions.

We introduce our efforts within the project ‘The science of deep specification’ to work out the key formal underpinnings of industrial-scale formal specifications of software and hardware components, anticipating a world where large verified systems are routinely built out of smaller verified components that are also used by many other projects. We identify an important class of specification that has already been used in a few experiments that connect strong component-correctness theorems across the work of different teams. To help popularize the unique advantages of that style, we dub itdeep specification, and we say that it encompasses specifications that arerich,two-sided,formalandlive(terms that we define in the article). Our core team is developing a proof-of-concept system (based on the Coq proof assistant) whose specification and verification work is divided across largely decoupled subteams at our four institutions, encompassing hardware microarchitecture, compilers, operating systems and applications, along with cross-cutting principles and tools for effective specification. We also aim to catalyse interest in the approach, not just by basic researchers but also by users in industry.This article is part of the themed issue ‘Verified trustworthy software systems’.

The purpose of this short note is to present a correction of the proof of the main result given in the paper “Equivalence of the existence of best proximity points and best proximity pairs for cyclic and noncyclic nonexpansive mappings,” Demonstr. Math. 53 (2020), 38–43.

This comment is devoted to the paper “Lie Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Spatially Two-Dimensional Burgers–Huxley Equation” (Symmery, 2020, vol.12, 170), in which several results are either incorrect, or incomplete, or misleading.

We give common generalizations of the Menon-type identities by Sivaramakrishnan (1969) and Li, Kim, Qiao (2019). Our general identities involve arithmetic functions of several variables, and also contain, as special cases, identities for gcd-sum type functions. We point out a new Menon-type identity concerning the lcm function. We present a simple character free approach for the proof., Comment: 14 pages

The first sentence in the abstract should be replaced with the sentence "A sequence $(x_{k})$ is called arithmetically convergent if for each $\varepsilon > 0$ there is an integer $n_{0}$ such that $|x_{m} - x_{}| \geq n_{0}$, where the symbol $< m, n >$ denotes the greatest common divisor of the integers $m$ and $n$".

The main aim of this paper is to perceive some inconsistencies made in the paper “Weyl-almost periodic and asymptotically Weyl-almost periodic properties of solutions to linear and semilinear abstract Volterra integro-differential equations”, recently published in Mathematical Notes of SVFU, as well as to propose alternative solutions for problems considered., №2(102) (2019)

Presented in this paper are the findings of the panel entitled Outlets for undergraduate research as delivered at the Trends in Undergraduate Research in Mathematical Sciences (TURMS) in Chicago on October 27, 2012. We specifically discuss venues and best practices for student papers, posters, and presentations.

Splicing the shredded paper means the technology that, according the paper, which has been shredded to design a particular algorithm to splice and recover the original paper. This paper introduced the algorithm of splicing the shredded paper based on the matching to texture feature. By means of this algorithm, we modeled for the problem of splicing the shredded paper and solved it. And, we used the algorithm to splice both pieces of English shredded paper and Chinese shredded paper. The recovered paper had proved the accuracy of the algorithm.

Inspired by the article “Anomalous relaxation model based on the fractional derivative with a Prabhakar-like kernel” (Z. Angew. Math. Phys. (2019) 70:42) whose authors Zhao and Sun studied the integro-differential equation with the kernel given by the Prabhakar function $$e^{-\gamma }_{\alpha , \beta }(t, \lambda )$$ , we provide the solution to this equation which is complementary to that obtained up to now. Our solution is valid for effective relaxation times whose admissible range extends the limits given in Zhao and Sun (Z Angew Math Phys 70:42, 2019, Theorem 3.1) to all positive values. For special choices of parameters entering the equation itself and/or characterizing the kernel, the solution comprises to known phenomenological relaxation patterns, e.g., to the Cole–Cole model (if $$\gamma = 1, \beta =1-\alpha $$ ) or to the standard Debye relaxation.

We consider a one-dimensional cutting stock problem (CSP) in which the stock widths are not used to fulfill the order but kept for use in the future for the industrial-use paper production. We present a new model based on the flexible stock allocation and trim loss control to determine the production quantity. We evaluate our approach using a real data and show that we are able to solve industrial-size problems, while also addressing common cutting considerations such as aggregation of orders, multiple stock widths, and cutting different patterns on the same machine. In addition, we compare our model with others, including trim loss minimization problem (TLMP) and cutting stock problem (CSP). The results show that the proposed model outperforms the other two models regarding total flexibility and trim loss ratio.

We argue that, despite the fact that the field of multiscale modelling and simulation has enjoyed significant success within the past decade, it still holds many open questions that are deemed important but so far have barely been explored. We believe that this is at least in part due to the fact that the field has been mainly developed within disciplinary silos. The principal topics that in our view would benefit from a targeted multidisciplinary research effort are related to reaching consensus as to what exactly one means by ‘multiscale modelling’, formulating a generic theory or calculus of multiscale modelling, applying such concepts to the urgent question of validation and verification of multiscale models, and the issue of numerical error propagation in multiscale models. Moreover, we believe that this would, in principle, also lay the foundation for more efficient, well-defined and usable multiscale computing environments. We believe that multidisciplinary research to fill in the gaps is timely, highly relevant, and with substantial potential impact on many scientific disciplines.

The aim of this paper is to study a new equivalent form of the weak maximum principle for a large class of differential operators on Riemannian manifolds. This new form has been inspired by the work of Berestycki, Hamel and Rossi for trace operators, and allows us to shed new light on it and to introduce a new sufficient bounded Khas’minskii type condition for its validity. We show its effectiveness by applying it to obtain some uniqueness results in a geometric setting.

In order to recognize outstanding papers that have been published in Symmetry, the Editorial Board established an annual “Symmetry Best Paper Award”. We are pleased to announce the first “Symmetry Best Paper Award” for 2015. Nominations were selected by the Editorial Board Office, with all research articles published in 2013 and 2014 eligible for consideration. Following review and voting by the Symmetry Best Paper Award Committee, the following three papers have won Symmetry Best Paper Awards for 2015

In this article we argue that in South Africa the current format of legitimised participation and practice in the examination papers for Mathematical Literacy restricts successful apprenticeship in the discipline of scientific mathematics and limits empowered preparation for real-world functioning. The currency of the subject, then, is brought into question. We further argue that the positioning of the subject as a compulsory alternative to Mathematics and the differential distribution of these two subjects to differing groups of learners facilitates the (re)production and sustainment of educational disadvantage. We draw on Dowling’s theoretical constructs of differing domains of mathematical practice and positions and focus analysis on a collection of nationally set exemplar Grade 12 examination papers to identify legitimised forms of participation in the subject. We conclude by arguing for a reconceptualised structure of knowledge and participation in Mathematical Literacy and make preliminary recommendations in this regard.

In his paper "On a construction of semigroups", M. Kolibiar gives a construction for a semigroup $T$ (beginning from a semigroup $S$) which is said to be derived from the semigroup $S$ by a $\theta$-construction. He asserted that every semigroup $T$ can be derived from the factor semigroup $T/\theta (T)$ by a $\theta$-construction, where $\theta (T)$ is the congruence on $T$ defined by: $(a, b)\in \theta (T)$ if and only if $xa=xb$ for all $x\in T$. Unfortunately, the paper contains some incorrect part. In our present paper we give a revision of the paper., Comment: Version v5 differs from the published and the earlier versions in the following: some part of the proof of Theorem 2 are clarified, and some typing errors are corrected

A record mentioned in the paper by Moree (Abh Math Sem Univ Hamburg 77:109–127, 2007) was recently improved on by Akbary and Scholten. However, the record mentioned was not the then record. The then record, due to Gallot (2004), actually slightly improves on that obtained recently by Akbary and Scholten.

In a recent paper (Asker, 2007) [1] a dynamic Cournot oligopoly game is proposed and it is claimed that this model represents competition among firms that exploit a common access natural resource. According to the author’s claim, the feature that relates the model with renewable natural resource harvesting is given by the presence of a particular cost function where the total cost of each fisherman is proportional to the square of the own quantity of harvesting and inversely proportional to the total harvesting quantity. In contrast, the usual function used in the literature on the exploitation of natural resources (such as fisheries) is inversely proportional to the available resource stock, and not to the total harvesting. This, in some sense, assumes exactly the opposite (as the available resource is inversely proportional to the total harvesting). So, we believe that the paper (Asker, 2007) [1] contains an error which is probably due to a misunderstanding or a misreading and misinterpretation of the (well-established) literature on bioeconomic modelling, but nevertheless misleading to researchers interested in bioeconomic modelling. The aim of this short note is to explain the mistake and to summarize the correct derivation and interpretation of the cost function. Our goal is to avoid the propagation of a subtle (but nevertheless misleading) error.

Discussion of "Cross-Covariance Functions for Multivariate Geostatistics" by Genton and Kleiber [arXiv:1507.08017]., Comment: Published at http://dx.doi.org/10.1214/15-STS516 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Software design impacts much of statistical analysis and, as technology changes, dramatically so in recent years, it is exciting to learn how statistical software is adapting and changing. This leads to the collection of papers published here, written by John Chambers, Duncan Temple Lang, Michael Lawrence, Martin Morgan, Yihui Xie, Heike Hofmann and Xiaoyue Cheng., Published in at http://dx.doi.org/10.1214/14-STS481 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

One main focus of teacher education research concentrates on teachers’ pedagogical content knowledge (PCK). It has been shown that teachers’ PCK correlates with teaching effectiveness as well as with students’ achievement gains. Teachers’ PCK should be analyzed as one of the main important components to evaluate professional development programs. On this account, it is necessary to develop standardized measures of biology teachers’ topic-specific PCK that are labor-efficient. This paper presents a study on the development, evaluation, and validation of a paper-and-pencil test to measure biology teachers’ declarative PCK on the topic of blood and the human cardiovascular system. The development of the test was based, among other considerations, on a review of research literature on PCK and an analysis of 50 videotaped biology lessons. The final test instrument was comprised of 15 items distributed across 2 scales. The findings of the main study—with 93 preservice and in-service biology teachers and 12 biologists—confirmed that this measure of biology teachers’ declarative PCK was reliable, objective, and valid. In-service biology teachers scored higher on the test than preservice teachers (effect size Cohen’s d, 0.65) on one hand and, also, than biologists (Cohen’s d, 1.00) on the other hand. Future versions of this test should explore enlarging the scales and measuring procedural aspects of PCK.

This special issue is devoted to ‘‘Selected Papers from the 4th International Conference on Bioinspired Systems and Cognitive Signal Processing.” This peer-reviewed special issue is one product of the International Conference on Bioinspired systems and Signal Processing (Biosignals 2011), as part of the International Joint Conference on Biomedical Engineering Systems and Technologies, Biostec (http://www.biosignals.biostec.org/BIOSIGNALS2011/home.asp), which was held in Rome, during 26–29 January 2011. This issue was promoted by the IEEE Technical Committee of Biomedical Signal Processing (IEE TC-BSP). The goal of this special issue is to convey mainly several messages which arose from this prestigious and intense conference. The major focus in this meeting was biomedical signal processing, where several areas of interest to the researchers in this field were comprehensively covered. This issue is therefore to report some highlighted contributions by a number of prominent researchers in the related field. Interested readers will find in this special issue papers that belong broadly to the areas of neuroscience, cardiovascular signals, behaviour, body movement, and modelling. These areas have been spanned by a number of articles in computational modelling and intelligence, neuroimaging, neuromarketing, body movement and gait analysis, brain-computer interfacing, electrocardiography and analysis of cardiovascular signals, neurocomputing and retinal image matching technique. What follows is a brief editorial review of the topics covered by the published papers in this special issue.

This note concerns the paper "On the controllability of a coupled system of two Korteweg–de Vries equations" by Micu et al. [2]. They study a nonlinear coupled system of two Korteweg–de Vries equations and prove that the system is controllable by using four boundary controls. Here, we prove that in some cases it is possible to get the controllablity of the system by using only two controls. This can be done depending on both the spatial domain and the control time.

We correct the proof of Theorem 3.8 in [GP2].

International audience; In a previous paper, we have described the construction of an automaton from a rational expression which has the property that the automaton built from an expression which is itself computed from a co-deterministic automaton by the state elimination method is co-deterministic. It turned out that the definition on which the construction is based was inappropriate, and thus the proof of the property was flawed. We give here the correct definition of the broken derived terms of an expression which allow to define the automaton and the detailed full proof of the property.

The purpose of this article is to analyse how students use inscriptions as tools for thinking and learning in mathematical problem-solving activities. The empirical context is that of learning about geometric series in a small group setting. What has been analysed is how students made use of inscriptions, self-made as well as those provided by text books and teachers, and the role these inscriptions played in the coordination of students’ learning/communication. Through the use of inscriptions (made on the chalkboard and with paper and pencil), the students externalised their thinking while engaging in mathematical reasoning on the topic of geometric series. The inscriptions were significant as anchor points for arguments in the ongoing discussions. Three main issues are highlighted: (a) how the inscriptions used contribute to the process of appropriation, (b) how the students use inscriptions to externalise and clarify their ideas and attempts at meaning-making, and (c) how the inscriptions are conducive to closing the gap between the original problem as given in the text book and the mathematisation necessary. It is argued that inscriptions, through their material nature, play a decisive role in learning mathematical reasoning. This study is an attempt to document and analyse how students are using inscriptions in reasoning and learning about geometric series. Following a sociocultural perspective on learning and development (Rogoff, 1990; Saljo, 2005; Wertsch, 1998), it is important to study students’ actions and use of artifacts in problem-solving settings to gain insight into how they appropriate mathematical concepts and modes of reasoning. The focus of the present study is on how students rely on and use the specific type of cultural tools that we refer to as inscriptions when engaging in mathematical problem solving. Inscriptions are understood as artifacts such as graphs, drawings, and mathematical symbols used for cognitive, communicative, mathematical, and problem-solving purposes in interactional settings1. The inscriptions may appear in text books, they may be made by the teacher for instructional purposes, or they may be self-made by learners while engaging in problem solving.