*Philos Trans A Math Phys Eng Sci ; 380(2226): 20210045, 2022 Jun 27.*

##### RESUMO

In this paper, we construct new, uniformly rotating solutions of the vortex sheet equation bifurcating from circles with constant vorticity amplitude. The proof is accomplished via a Lyapunov-Schmidt reduction and a second-order expansion of the reduced system. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

##### Assuntos

Hidrodinâmica , Matemática*Philos Trans A Math Phys Eng Sci ; 380(2226): 20210057, 2022 Jun 27.*

##### RESUMO

Fluid dynamics is a research area lying at the crossroads of physics and applied mathematics with an ever-expanding range of applications in natural sciences and engineering. However, despite decades of concerted research efforts, this area abounds with many fundamental questions that still remain unanswered. At the heart of these problems often lie mathematical models, usually in the form of partial differential equations, and many of the open questions concern the validity of these models and what can be learned from them about the physical problems. In recent years, significant progress has been made on a number of open problems in this area, often using approaches that transcend traditional discipline boundaries by combining modern methods of modelling, computation and mathematical analysis. The two-part theme issue aims to represent the breadth of these approaches, focusing on problems that are mathematical in nature but help to understand aspects of real physical importance such as fluid dynamical stability, transport, mixing, dissipation and vortex dynamics. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

##### Assuntos

Hidrodinâmica , Física , Matemática , Modelos Teóricos*Elife ; 112022 Apr 04.*

##### RESUMO

Despite efforts to increase gender diversity in science, technology, engineering, mathematics and medicine (STEMM), men continue to hold most tenured and leadership positions. Moreover, the specific population shifts and timelines which may be required to achieve gender parity have not been well delineated. It is obvious that if women are statistically underrepresented in a field, then men must be statistically overrepresented: however, male overrepresentation and related gender-based advantages are rarely mentioned in conversations about gender equality. It is important that actions to address both overrepresentation and underrepresentation are elements of any strategy that seeks to move STEMM fields closer to gender parity.

##### Assuntos

Engenharia , Liderança , Feminino , Humanos , Masculino , Matemática*Sci Rep ; 12(1): 5629, 2022 Apr 04.*

##### RESUMO

When asked to estimate the number of items in the visual field, neurotypical adults are more precise and rapid if the items are clustered into subgroups compared to when they are randomly distributed. It has been suggested that this phenomenon, termed "groupitizing", relies on the recruitment of arithmetical calculation strategies and subitizing. Here the role of arithmetical skills in groupitizing was investigated by measuring the groupitizing effect (or advantage) in a sample of children and adolescents with and without math learning disability (dyscalculia). The results showed that when items were grouped, both groups of participants showed a similar advantage on sensory precision and response time in numerosity estimates. Correlational analyses confirmed a lack of covariation between groupitizing advantage and math scores. Bayesian statistics on sensory precision sustained the frequentist analyses providing decisive evidence in favor of no groups difference on groupitizing advantage magnitude (LBF = - 0.44) and no correlation with math scores (LBF = - 0.57). The results on response times, although less decisive, were again in favor of the null hypothesis. Overall, the results suggest that the link between groupitizing and mathematical abilities cannot be taken for granted, calling for further investigations on the factors underlying this perceptual phenomenon.

##### Assuntos

Discalculia , Adolescente , Adulto , Aptidão , Teorema de Bayes , Criança , Deficiências do Desenvolvimento , Humanos , Matemática*PLoS One ; 17(4): e0266846, 2022.*

##### RESUMO

Quantum annealing has gained considerable attention because it can be applied to combinatorial optimization problems, which have numerous applications in logistics, scheduling, and finance. In recent years, with the technical development of quantum annealers, research on solving practical combinatorial optimization problems using them has accelerated. However, researchers struggle to find practical combinatorial optimization problems, for which quantum annealers outperform mathematical optimization solvers. Moreover, there are only a few studies that compare the performance of quantum annealers with the state-of-the-art solvers, such as Gurobi and CPLEX. This study determines that quantum annealing demonstrates better performance than the solvers in that the solvers take longer to reach the objective function value of the solution obtained by the quantum annealers for the break minimization problem in a mirrored double round-robin tournament. We also explain the desirable performance of quantum annealing for the sparse interaction between variables and a problem without constraints. In this process, we demonstrate that this problem can be expressed as a 4-regular graph. Through computational experiments, we solve this problem using our quantum annealing approach and two-integer programming approaches, which were performed using the latest quantum annealer D-Wave Advantage, and Gurobi, respectively. Further, we compare the quality of the solutions and the computational time. Quantum annealing was able to determine the exact solution in 0.05 seconds for problems with 20 teams, which is a practical size. In the case of 36 teams, it took 84.8 s for the integer programming method to reach the objective function value, which was obtained by the quantum annealer in 0.05 s. These results not only present the break minimization problem in a mirrored double round-robin tournament as an example of applying quantum annealing to practical optimization problems, but also contribute to find problems that can be effectively solved by quantum annealing.

##### Assuntos

Algoritmos , Teoria Quântica , Matemática*CBE Life Sci Educ ; 21(2): ar26, 2022 Jun.*

##### RESUMO

Large introductory science courses are a particularly important and challenging target for creating inclusive learning environments. In this study, we examined the impact of incorporating learning assistants (LAs) on the learning environment in an introductory biology course taught with two different structures: an in-person lecture with intermittent active-learning components and an online setting taught with a flipped instructional approach. Using a survey that measured sense of belonging in a single class, we found that students in sections with LAs reported greater sense of belonging than students in sections without LAs in both class structures. Further, student focus groups revealed that LAs promoted learning and engagement in the class by answering questions and providing clarity; allowing more use of active- and interactive-learning structures; and serving as accessible, approachable, and immediate sources of help. Student responses also indicated that LAs promoted a sense of belonging in science, technology, engineering, and mathematics (STEM) by decreasing feelings of isolation, serving as inspirational role models, clarifying progression through the STEM educational system, and helping students become more engaged and confident in their STEM-related knowledge and skills. These findings indicate that LAs can support multiple elements of inclusive STEM learning environments.

##### Assuntos

Estudantes , Tecnologia , Biologia/educação , Emoções , Humanos , Matemática , Aprendizagem Baseada em Problemas*Philos Trans A Math Phys Eng Sci ; 380(2225): 20210056, 2022 Jun 13.*

##### RESUMO

Fluid dynamics is a research area lying at the crossroads of physics and applied mathematics with an ever-expanding range of applications in natural sciences and engineering. However, despite decades of concerted research efforts, this area abounds with many fundamental questions that still remain unanswered. At the heart of these problems often lie mathematical models, usually in the form of partial differential equations, and many of the open questions concern the validity of these models and what can be learned from them about the physical problem. In recent years, significant progress has been made on a number of open problems in this area, often using approaches that transcend traditional discipline boundaries by combining modern methods of modelling, computation and mathematical analysis. The two-part theme issue aims to represent the breadth of these approaches, focusing on problems that are mathematical in nature but help to understand aspects of real physical importance such as fluid dynamical stability, transport, mixing, dissipation and vortex dynamics. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.

##### Assuntos

Hidrodinâmica , Modelos Teóricos , Matemática , Física*New Dir Stud Leadersh ; 2022(173): 139-147, 2022 Mar.*

##### RESUMO

Science, Technology, Engineering and Mathematics (STEM) disciplines recognize the need for leadership development, but the lack of a professionally endorsed model has led to a patchwork of programmes across the nation, each with its unique brand of skills development. Leadership programmes in six diverse STEM fields are included.

##### Assuntos

Liderança , Ciência , Engenharia , Humanos , Matemática , Tecnologia*J Theor Biol ; 543: 111107, 2022 Jun 21.*

##### RESUMO

Weber's law states that the ratio of the smallest perceptual change in an input signal and the background signal is constant. The law is observed across the perception of weight, light intensity, and sound intensity and pitch. To explain Weber's law observed in steady-state responses, two models of perception have been proposed, namely the logarithmic and the linear model. This paper argues in favour of the linear model, which requires the sensory system to generate linear input-output relationship over several orders of magnitude. To this end, a four-node motif (FNM) is constructed from first principles whose series provides almost linear relationship between input signal and the output over arbitrary range of input signal. Mathematical analysis into the origin of this quasi-linear relationship shows that the series of coherent type-1 feed-forward loop (C1-FFL) is able to provide perfectly linear input-output relationship over arbitrary range of input signal. FNM also reproduces the neuronal data of numerosity detection study on the monkey. The series of FNM also provides a mechanism for sensitive detection over arbitrary range of input signal when the output has an upper limit. Further, the series of FNM provides a general basis for a class of bow-tie architecture where the number of receptors is much lower than the range of input signal and the "decoded output". Besides (quasi-)linear input-output relationship, another example of this class of bow-tie architecture that the series of FNM is able to produce is absorption spectra of cone opsins of humans. Further, the series of FNM and C1-FFL, both, can compute logarithm over arbitrary range of input signal.

##### Assuntos

Neurônios , Matemática*Pathog Dis ; 80(1)2022 Apr 29.*

##### RESUMO

Racism and bias are pervasive in society-and science, technology, engineering, and mathematics (STEM) fields are not immune to these issues. It is imperative that we educate ourselves and our students about the history and consequences of this bias in STEM, investigate the research showing bias toward marginalized groups, understand how to interpret misuses of science in perpetuating bias, and identify advances and solutions to overcome racism and bias throughout our professional and personal lives. Here, we present one model for teaching a universal course for participants of all professional stages to address these issues and initiate solutions. As very few institutions require students to enroll in courses on racism and bias in STEM or even offer such courses, our curriculum could be used as a blueprint for implementation across institutions. Ultimately, institutions and academic disciplines can incorporate this important material with more region and/or discipline specific studies of bias.

##### Assuntos

Engenharia , Tecnologia , Engenharia/educação , Humanos , Matemática , Poder Psicológico , Estudantes , Tecnologia/educação*Psicothema ; 34(2): 217-225, 2022 05.*

##### RESUMO

BACKGROUND: Academically resilient students are those who exhibit high performance starting from a disadvantaged socioeconomic situation. This study aims to identify the personal, school, and national factors that are associated with that resilience in the European Union (EU). METHOD: The sample comprised 96556 fourth grade students from 21 EU countries participating in TIMSS-2019. Two three-level logistic regression models were specified for the overall sample. RESULTS: The EU has an average of 25.67% resilient students in mathematics and 24.16% in science. Student confidence and having done prior linguistic tasks at school were the variables with the most predictive power after accounting for gender and students' immigrant background. The European countries analyzed largely compensated for the doubly-disadvantaged situation of immigrant students. Those countries with higher proportions of low-performing students had fewer resilient students. CONCLUSIONS: The educational policies in the EU member states are able to largely compensate for unfavorable starting positions; fundamentally, policies of a social nature such as support for immigrant students, families, or schools.

##### Assuntos

Instituições Acadêmicas , Estudantes , Escolaridade , Europa (Continente) , Humanos , Matemática*PLoS One ; 17(4): e0267097, 2022.*

##### RESUMO

Professional development has been identified as an effective way to increase college STEM instructors' use of research-based instructional strategies (RBIS) known to benefit student learning and persistence in STEM. Yet only a few studies relate professional development experiences to later teaching behaviors of higher education instructors. This study of 361 undergraduate mathematics instructors, all of whom participated in multi-day, discipline-based workshops on teaching held in 2010-2019, examined the relationship between such participation and later use of RBIS. We found that instructors' RBIS attitudes, knowledge, and skills strengthened after participating in professional development, and their self-reported use of RBIS became more frequent in the first year after the workshop. Applying the Theory of Planned Behavior as a conceptual framework, we used a structural equation model to test whether this theory could explain the roles of workshop participation and other personal, professional and contextual factors in fostering RBIS use. Findings indicated that, along with workshop participation, prior RBIS experience, class size, and course coordination affected RBIS use. That is, both targeted professional development and elements of the local context for implementation were important in supporting instructors' uptake of RBIS-but, remarkably, both immediate and longer-term outcomes of professional development did not depend on other individual or institutional characteristics. In this study, the large sample size, longitudinal measurement approach, and consistency of the form and quality of professional development make it possible to distinguish the importance of multiple possible influences on instructors' uptake of RBIS. We discuss implications for professional development and for institutional structures that support instructors as they apply what they learned, and we offer suggestions for the use of theory in future research on this topic.

##### Assuntos

Aprendizagem , Estudantes , Atitude , Humanos , Matemática , Ensino*Math Biosci Eng ; 19(5): 5312-5328, 2022 Mar 24.*

##### RESUMO

We consider a two-box model for the administration of a therapeutic substance and discuss two scenarios: First, the substance should have an optimal therapeutic concentration in the central compartment (typically blood) and be degraded in an organ, the peripheral compartment (e.g., the liver). In the other scenario, the concentration in the peripheral compartment should be optimized, with the blood serving only as a means of transport. In either case the corresponding optimal control problem is to determine a dosing schedule, i.e., how to administer the substance as a function u of time to the central compartment so that the concentration of the drug in the central or in the peripheral compartment remains as closely as possible at its optimal therapeutic level. We solve the optimal control problem for the central compartment explicitly by using the calculus of variations and the Laplace transform. We briefly discuss the effect of the approximation of the Dirac delta distribution by a bolus. The optimal control function u for the central compartment satisfies automatically the condition u≥0. But for the peripheral compartment one has to solve an optimal control problem with the non-linear constraint u≥0. This problem does not seem to be widely studied in the current literature in the context of pharmacokinetics. We discuss this question and propose two approximate solutions which are easy to compute. Finally we use Pontryagin's Minimum Principle to deduce the exact solution for the peripheral compartment.

##### Assuntos

Modelos Biológicos , Matemática , Preparações Farmacêuticas*Am Ann Deaf ; 166(5): 621-637, 2022.*

##### RESUMO

Pursuant to the criterion of fluency, two types of mathematical achievement tests were used in the present study: simple subtraction (to measure mathematical fluency) and number series completion (to serve as a nonfluency mathematics test). A cohort of 223 d/Deaf and hard of hearing (d/Dhh) students in grades 3-9 in special education schools took a series of cognitive and mathematical tests. After outlying data were considered, the sample was reduced to 198 students; the findings were consistent with expectations: The numerical magnitude processing did not add significantly to the prediction of mathematical reasoning (nonfluency mathematics) but did make a significant contribution to the prediction of arithmetic computation (fluency mathematics) after demographic variables and general cognitive processing were controlled for. The findings suggest that the effect of numerical magnitude processing on d/Dhh children's mathematical performance can be influenced by mathematical fluency.

##### Assuntos

Perda Auditiva , Pessoas com Deficiência Auditiva , Criança , Perda Auditiva/diagnóstico , Humanos , Matemática , Pessoas com Deficiência Auditiva/psicologia , Instituições Acadêmicas , Estudantes*J Exp Psychol Learn Mem Cogn ; 48(3): 348-374, 2022 Mar.*

##### RESUMO

We investigated the role of working memory in symbolic and spatial algebra and related tasks across five experiments. Each experiment combined a processing task (expression evaluation, arithmetic, coordinate plane, geometry, or mental rotation) with verbal and spatial memory loads in a dual-task design. Spatial memory was compromised in the presence of more difficult processing tasks, and verbal memory was only compromised in the presence of algebraic tasks. The latter was related to the demands of retaining quantities associated with variables in verbal memory. We suggest that both verbal and spatial working memory retention engage domain-general attention, but that their maintenance mechanisms differ. Verbal memory has attention-based and rehearsal-based mechanisms, and thus sustaining verbal information over a short period is less attention-demanding than holding spatial information. We suggest that effects of a memory load on processing (e.g., x = 6) depend on whether use of maintenance strategies are possible for the specific memory load while carrying out processing. In all, our results indicate that algebraic tasks use domain-general attention and include verbal processing of algebraic variables (i.e., information conveyed in x, y). We discuss the implications for algebra learning and working memory theories. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

##### Assuntos

Memória de Curto Prazo , Memória Espacial , Humanos , Matemática*PLoS One ; 17(4): e0266920, 2022.*

##### RESUMO

The approximate number system (a) views number as an imprecise signal that (b) functions equivalently regardless of a number's initial presentation. These features do not readily account for exact readings when a task calls for them. While profiting from insights in areas neighboring the number cognition literature, we propose that linguistic-pragmatic and cultural pressures operate on a number's upper bound in order to provide exact readings. With respect to (a), Experimental Pragmatic findings indicate that numbers appear to be semantically lower-bounded (Eleven candidates are coming means at least eleven) but fluid at its upper-bound; exactly readings emerge as a consequence of an additional pragmatic process that solidifies the upper bound. With respect to (b), studies from cognitive anthropology underline how symbolic representations of number are distinct from written codes. Here, we investigate a novel hypothesis proposing that symbolic expressions of number (such as "11") explicitly provide exactly readings unlike verbal (oral and written) ones, which engender at least readings. We then employ a Numerical Magnitude Task (NMT), in which French-speaking participants determine whether a presented number is lesser or greater than a benchmark (12) in one of three presentation conditions: i) Symbolic/Hindu-Arabic (e.g. "11" via screen), ii) Oral (e.g. "/'on.zÉ/" via headphones), or; iii) spelled-out-in-Letters (e.g. "onze" via screen). Participants also carry out a Number Identification Task (NIT) so that each participant's recognition speed per number can be removed from their NMT times. We report that decision reaction times to "onze" take longer to process (and prompt more errors) than "treize" whereas "11" and "13" are comparable. One prediction was not supported: Decision times to the critical oral forms ("/'on.zÉ/" and "[tÊÌ¥ÉËzÉÌ]") were comparable, making these outcomes resonate with those in the Symbolic condition.

##### Assuntos

Cognição , Resolução de Problemas , Humanos , Matemática , Tempo de Reação , Reconhecimento Psicológico*Acta Psychol (Amst) ; 226: 103576, 2022 Jun.*

##### RESUMO

Facets of fine motor skills (FMS) and finger gnosia have been reported to predict young children's numerical competencies, possibly by affecting early finger counting experiences. Furthermore, neuronal connections between areas involved in finger motor movement, finger gnosia, and numerical processing have been posited. In this study, FMS and finger gnosia were investigated as predictors for preschool children's performance in numerical tasks. Preschool children (N = 153) completed FMS tasks measuring finger agility and finger dexterity as well as a non-motor finger gnosia task. Furthermore, children completed numerical tasks that involved finger use (i.e., finger counting and finger montring), and tasks that did not (i.e., picture-aided calculation and number line estimation). To control for possible confounding influences of domain general skills, we included measures of reasoning and spatial working memory. We found associations between FMS and both finger counting and calculation, but not finger montring. In contrast, finger gnosia was only associated with finger montring, but not finger counting and calculation. Surprisingly, there were no associations between FMS or finger gnosia with number line estimation. Findings highlight that the relationship between finger gnosia, FMS, and numerical skills is specific to task requirements. Possible implications are discussed.

##### Assuntos

Dedos , Destreza Motora , Pré-Escolar , Humanos , Matemática , Destreza Motora/fisiologia , Resolução de Problemas*CBE Life Sci Educ ; 21(2): ar27, 2022 Jun.*

##### RESUMO

Mentoring relationships can be important for promoting the success and persistence of undergraduates, particularly for students from historically underrepresented groups in science, technology, engineering, and mathematics (STEM) disciplines. While mentoring is often cited as important for attracting and retaining students from underrepresented groups in STEM, little is known about the differential mentoring processes that can result from similar and dissimilar mentor-protégé pairs. The present study tests the process-oriented mentorship model (POMM) regarding how mentor-protégé similarities and the moderating role of contact frequency influence mentorship quality and STEM research career persistence intentions among faculty-mentored Hispanic STEM majors in their senior year of college. The results indicate that mentor-protégé similarity matters. Specifically, higher levels of mentor-protégé psychological similarity were related to higher levels of psychosocial support and relationship satisfaction. Hispanic students with a Hispanic faculty mentor reported engaging in more coauthoring opportunities than peers with non-Hispanic mentors. Among those with higher contact frequency, students with same-gender mentors had higher levels of relationship satisfaction than peers with different-gender mentors; however, there were no differences among those with low contact frequency. Additionally, protégés who reported coauthoring support were more likely to also report commitment to pursuing a STEM research career.

##### Assuntos

Tutoria , Mentores , Humanos , Matemática , Tutoria/métodos , Mentores/psicologia , Estudantes/psicologia , Tecnologia*Sci Rep ; 12(1): 3894, 2022 03 31.*

##### RESUMO

The numerical understanding of cichlids and stingrays was examined regarding addition and subtraction abilities within the number space of one to five. Experiments were conducted as two-alternative forced-choice experiments, using a delayed matching to sample technique. On each trial, fish had to perform either an addition or subtraction, based on the presentation of two-dimensional objects in two distinct colors, with the color signaling a particular arithmetic process. Six cichlids and four stingrays successfully completed training and recognized specific colors as symbols for addition and subtraction. Cichlids needed more sessions than stingrays to reach the learning criterion. Transfer tests showed that learning was independent of straightforward symbol memorization. Individuals did not just learn to pick the highest or lowest number presented based on the respective color; instead, learning was specific to adding or subtracting 'one'. Although group results were significant for both species in all tests, individual results varied. Addition was learned more easily than subtraction by both species. While cichlids learned faster than stingrays, and more cichlids than stingrays learned the task, individual performance of stingrays exceeded that of cichlids. Previous studies have provided ample evidence that fish have numerical abilities on par with those of other vertebrate and invertebrate species tested, a result that is further supported by the findings of the current study.

##### Assuntos

Ciclídeos , Rajidae , Animais , Aprendizagem , Matemática*PLoS One ; 17(4): e0264059, 2022.*

##### RESUMO

It is well established that there is a national problem surrounding the equitable participation in and completion of science, technology, engineering, and mathematics (STEM) higher education programs. Persons excluded because of their ethnicity or race (PEERs) experience lower course performance, major retention, sense of belonging, and degree completion. It is unclear though how pervasive these issues are across an institution, from the individual instructor, course, and discipline perspectives. Examining over six years of institutional data from a large-enrollment, research-intensive, minority-serving university, we present an analysis of racial opportunity gaps between PEERs and non-PEERs to identify the consistency of these issues. From this analysis, we find that there is considerable variability as to whether a given course section taught by a single instructor does or does not exhibit opportunity gaps, although encouragingly we did identify exemplar instructors, course-instructor pairs, courses, and departments that consistently had no significant gaps observed. We also identified significant variation across course-instructor pairs within a department, and found that certain STEM disciplines were much more likely to have courses that exhibited opportunity gaps relative to others. Across nearly all disciplines though, it is clear that these gaps are more pervasive in the lower division curriculum. This work highlights a means to identify the extent of inequity in STEM success across a university by leveraging institutional data. These findings also lay the groundwork for future studies that will enable the intentional design of STEM education reform by leveraging beneficial practices used by instructors and departments assigning equitable grades.