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Calculus of Variations In the paper I On a Non-Newtonian Calculus of Variations i , Delfim F. M. Torres presents, for the first time in the literature, a non-Newtonian calculus of variations that involves the minimization of a function defined by a non-Newtonian integral with a Lagrangian depending on the non-Newtonian derivative. This publication is an editorial for the Special Issue of Axioms "Calculus of Variations, Optimal Control and Mathematical Biology: A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of His 50th birthday". This Special Issue is dedicated to Professor Delfim F. M. Torres on the occasion of his 50th birthday, as recognition of his significant contributions to Mathematics, in particular in the calculus of variations, optimal control, and mathematical biology. [Extracted from the article]

In this paper, we unite concepts from Husserlian phenomenology, the active inference framework in theoretical biology, and category theory in mathematics to develop a comprehensive framework for understanding social action premised on shared goals. We begin with an overview of Husserlian phenomenology, focusing on aspects of inner time-consciousness, namely, retention, primal impression, and protention. We then review active inference as a formal approach to modeling agent behavior based on variational (approximate Bayesian) inference. Expanding upon Husserl's model of time consciousness, we consider collective goal-directed behavior, emphasizing shared protentions among agents and their connection to the shared generative models of active inference. This integrated framework aims to formalize shared goals in terms of shared protentions, and thereby shed light on the emergence of group intentionality. Building on this foundation, we incorporate mathematical tools from category theory, in particular, sheaf and topos theory, to furnish a mathematical image of individual and group interactions within a stochastic environment. Specifically, we employ morphisms between polynomial representations of individual agent models, allowing predictions not only of their own behaviors but also those of other agents and environmental responses. Sheaf and topos theory facilitates the construction of coherent agent worldviews and provides a way of representing consensus or shared understanding. We explore the emergence of shared protentions, bridging the phenomenology of temporal structure, multi-agent active inference systems, and category theory. Shared protentions are highlighted as pivotal for coordination and achieving common objectives. We conclude by acknowledging the intricacies stemming from stochastic systems and uncertainties in realizing shared goals. [ABSTRACT FROM AUTHOR]

Topology is branch of modern mathematics that plays an important role in applications of biology. The aim of this paper is to study DNA sequence mutations using multisets, relations, metric functions, topology and association indices. Moreover, we use association indices to study the similarity between DNA sequences. These different ways of identifying a mutation help biologists to make a decision. A decision of mutation that depends on metrics between two sequences of genes and the topological structure produced by their relationship is presented. [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]

While Luria and Delbrück's seminal work has found its way to some college biology textbooks, it is now largely absent from those in mathematics. This is a significant omission, and we consider it a missed opportunity to present a celebrated conceptual model that provides an authentic and, in many ways, intuitive example of the quantifiable nature of stochasticity. We argue that it is an important topic that could enrich the educational literature in mathematics, from the introductory to advanced levels, opening many doors to undergraduate research. The paper has two main parts. First, we present in detail the mathematical theory behind the Luria–Delbrück model and make suggestions for further readings from the literature. We also give ideas for inclusion in various mathematics courses and for projects that can be used in regular courses, independent projects, or as starting points for student research. Second, we briefly review available hands-on activities as pedagogical ways to facilitate problem posing, problem-based learning, and investigative case-based learning and to expose students to experiments leading to Poisson distributions. These help students with even limited mathematics backgrounds understand the significance of Luria–Delbrück's work for determining mutation rates and its impact on many fields, including cancer chemotherapy, antibiotic resistance, radiation, and environmental screening for mutagens and teratogens. [ABSTRACT FROM AUTHOR]

This study investigates the effects of instruction in genre writing with planning and revising activities (GWPR) on learning. This type of instruction appeared to be successful in promoting learning in several types of education. However, there are few studies on the effects on low achievers. Therefore, two studies were conducted with low-achieving students, each comprising a quasi-experimental study and a small-scale think-aloud study, both of which were embedded in regular education for low-achieving adolescents. The first study took place in biology classes (grade 7, three lessons); the second study was in mathematics classes (grade 10, six lessons). The researchers co-created writing-to-learn tasks with the teachers. The results showed positive effects on learning in mathematics classes as compared with the control group, but not in biology classes. The think-aloud study in the experimental mathematics class condition provided evidence of the learning by writing process. In the experimental biology class condition, such evidence was barely present. The results suggest that the experimental intervention in biology classes was too short for the students to grasp the essentials of learning by writing. This paper also discusses suggestions for further research and pedagogical implications. [ABSTRACT FROM AUTHOR]

The stresses within the soft tissue are not constant for some shell surfaces. They vary with position along the mantle edge. In this paper, we show that elliptical geometry is more convenient to describe this type of surface. Thus, we introduce the elliptical kinematics along an initial curve and construct some accretive surfaces with an elliptical cross-section. In fact, these surfaces are not only curves with an elliptical cross-sectional curve, but also the material points of the surface follow an elliptical trajectory during their formation. This situation can be easily explained through elliptical motion and elliptical quaternion algebra. Then, we investigate the relationship between velocity and eccentricity of the surfaces and compare it to the case of circular motion. Furthermore, we visualize some examples to support the theoretical results through the MAPLE program. [ABSTRACT FROM AUTHOR]

Firstly, the new concepts of G − expansibility, G − almost periodic point, and G − limit shadowing property were introduced according to the concepts of expansibility, almost periodic point, and limit shadowing property in this paper. Secondly, we studied their dynamical relationship between the self-map f and the shift map σ in the inverse limit space under topological group action. The following new results are obtained. Let X , d be a metric G − space and X f , G ¯ , d ¯ , σ be the inverse limit space of X , G , d , f . (1) If the map f : X ⟶ X is an equivalent map, then we have A P G ¯ σ = Lim ← A p G f , f . (2) If the map f : X ⟶ X is an equivalent surjection, then the self-map f is G − expansive if and only if the shift map σ is G ¯ − expansive. (3) If the map f : X ⟶ X is an equivalent surjection, then the self-map f has G − limit shadowing property if and only if the shift map σ has G ¯ − limit shadowing property. The conclusions of this paper generalize the corresponding results given in the study by Li, Niu, and Liang and Li. Most importantly, it provided the theoretical basis and scientific foundation for the application of tracking property in computational mathematics and biological mathematics. [ABSTRACT FROM AUTHOR]

This paper presents the results of the management of a didactic device formulated by a Mathematics male and Biology female teacher from a secondary school in which they sought a codisciplinary study. Based on the Anthropological Theory of the Didactic, the results of an exploratory study that sought to characterize the management of a didactic device for the study of plant growth in secondary school are reported; In particular, we analyze the relevance of mathematical knowledge in its development. The main results indicate that the study enabled the protagonists to be the students: they formulated and answered questions, achieving autonomy and responsibility for the search for information in various media; however, mathematical knowledge did not occupy a prominent place during the study. [ABSTRACT FROM AUTHOR]

In the last few years, graph neural networks (GNNs) have become the standard toolkit for analyzing and learning from data on graphs. This emerging field has witnessed an extensive growth of promising techniques that have been applied with success to computer science, mathematics, biology, physics and chemistry. But for any successful field to become mainstream and reliable, benchmarks must be developed to quantify progress. This led us in March 2020 to release a benchmark framework that i) comprises of a diverse collection of mathematical and real-world graphs, ii) enables fair model comparison with the same parameter budget to identify key architectures, iii) has an open-source, easy-to-use and reproducible code infrastructure, and iv) is flexible for researchers to experiment with new theoretical ideas. As of December 2022, the GitHub repository1 has reached 2,000 stars and 380 forks, which demonstrates the utility of the proposed open-source framework through the wide usage by the GNN community. In this paper, we present an updated version of our benchmark with a concise presentation of the aforementioned framework characteristics, an additional medium-sized molecular dataset AQSOL, similar to the popular ZINC, but with a real-world measured chemical target, and discuss how this framework can be leveraged to explore new GNN designs and insights. As a proof of value of our benchmark, we study the case of graph positional encoding (PE) in GNNs, which was introduced with this benchmark and has since spurred interest of exploring more powerful PE for Transformers and GNNs in a robust experimental setting. [ABSTRACT FROM AUTHOR]

Mathematical biology is a wide field of study with many venues that undergraduate students can access through research. However, the topics of study for these students can be overwhelming, and many topics of study yield either only trivial results or abstract outcomes that are nonintuitive and difficult to understand. We have used natural resource modeling, and more specifically, a partnership between academic researchers and federal scientists, as a bridge between undergraduate research and mathematical biology. Our collaboration is an interdisciplinary team that combines biology, mathematics, and statistics professors with government research scientists. As a team, we have mentored students through opportunities such as a Research Experiences for Undergraduates and other projects. In this article, we provide an overview of how we develop questions for undergraduates and outline two case studies, both of which resulted in peer reviewed journal articles. Last, we describe how we also transfer the results from these undergraduate projects to resource managers so the results may be applied to real world problems. [ABSTRACT FROM AUTHOR]

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The modeling of biological systems has recently gained much attention considering the possibility to describe the time evolution of a biological system by employing differential equations. Different frameworks have been proposed depending on the number of dynamic variables. Ordinary differential equations (ODE) are employed if time is the only dynamic variable; partial differential equations (PDE) are proposed when, in addition to the time variable, space and/or velocity variables are considered. In the context of differential equation models, new frameworks have been proposed where stochastic terms are added to classical deterministic terms. A specific model is proposed when the differential equations are coupled to initial and/or boundary conditions. This editorial article deals with the topic of this special issue, which is devoted to the new developments in the multiscale modeling of complex biological systems with special attention to the interplay between different scholars. [ABSTRACT FROM AUTHOR]

New molecular genetic algorithms, as tools for the visualization and analysis of big data, have made it possible not only to illustrate the internal structure of DNA molecules within their parameters but also to explore the field of chaos theory, particularly to display processes and signals close to chaotic ones. This provides a new perspective on the problem of determining criteria for borderline states between order and chaos. This article demonstrates the differences between chaotic and quasi-chaotic signals when visualized with molecular genetic algorithms. It presents examples of molecular genetic mappings of signals generated using various pseudorandom noise generators, as well as acoustic signals. This article considers structural and integral (folded) mappings as one-dimensional and two-dimensional projections of the pattern. The authors illustrate the internal structure of the reconstructed signal mappings in spaces of fractional dimensionality, which is considered as a visualization of the entropy structure based on functional mappings in spaces of the fractional dimension. As a result of this research, it was found that the use of molecular genetic algorithms for visualizing information signals makes it possible to identify the so-called entropy structure of these signals. At the same time, the entropy structure of chaotic signals is absent. [ABSTRACT FROM AUTHOR]

Mathematical modelling and simulation in biophysics and its applications in terms of both theoretical and biological/physical/ecological point of view arise in a number of research problems ranging from physical and chemical processes to biomathematics and life science. As known, the modeling of a biophysical system requires the analysis of the different interactions occurring among the different components of the system. This editorial article deals with the topic of this special issue, which is devoted to the new developments in the modelling and simulation in biophysical applications with special attention to the interplay between different scholars. [ABSTRACT FROM AUTHOR]

Previous studies have shown that fractional derivative operators have become an integral part of modeling natural and physical phenomena. During the progress and evolution of these operators, it has become clear to researchers that each of these operators has special capacities for investigating phenomena in engineering sciences, physics, biological mathematics, etc. Fixed point theory and its famous contractions have always served as useful tools in these studies. In this regard, in this work, we considered the Hilfer-type fractional operator to study the proposed integrodifferential equation. We have used the capabilities of measure theory and fixed point techniques to provide the required space to guarantee the existence of the solution. The Schauder and Arzela-Ascoli theorems play a fundamental role in the existence of solutions. Finally, we provided two examples with some graphical and numerical simulation to make our results more objective. [ABSTRACT FROM AUTHOR]

Background: Although a large body of research has identified challenges faced by women in STEM fields and strategies to improve the experience for women in STEM, little of this research has examined which strategies undergraduate women would recommend to their peers. In the current study, undergraduate women in STEM fields (N = 89) wrote letters to younger women in STEM about their experiences. The participants were recruited from a small public liberal arts college and a large public research institution in the United States. Participants were juniors and seniors majoring in engineering, mathematics, computer science, physics, biological or biomedical sciences, and chemistry. Results: Using thematic analysis, we identified seven types of advice. The participants shared advice about improving academically, forming communities, finding family support, and seeking out women role models. They also provided general words of encouragement and reassured women that everyone struggles, and failure is not indicative of their potential. In some cases, the letters were consistent with themes from prior research; however, other influences that have been studied by quantitative research were not prominent in women's own advice to their fellow students. For example, although the letters focused on communal themes such as building community, they did not focus on the communal goal of helping others through their careers. Additionally, they highlighted the role of family, which has been relatively neglected in prior work. Conclusions: The present research highlights which empirically supported theories about retention and success in STEM are reflected in students' advice to others. These letters also provide insight into which obstacles and solutions were most salient for women students looking back on their undergraduate STEM careers. The women's letters provide a rich understanding of how women navigate STEM fields and what they would tell future students about persisting in those fields. [ABSTRACT FROM AUTHOR]

The expansion of mitochondrial DNA molecules with deletions has been associated with aging, particularly in skeletal muscle fibers; its mechanism has remained unclear for three decades. Previous accounts have assigned a replicative advantage (RA) to mitochondrial DNA containing deletion mutations, but there is also evidence that cells can selectively remove defective mitochondrial DNA. Here we present a spatial model that, without an RA, but instead through a combination of enhanced density for mutants and noise, produces a wave of expanding mutations with speeds consistent with experimental data. A standard model based on RA yields waves that are too fast. Weprovide a formula that predicts that wave speed drops with copy number, consonant with experimental data. Crucially, our model yields traveling waves of mutants even if mutants are preferentially eliminated. Additionally, we predict that mutant loads observed in single-cell experiments can be produced by de novo mutation rates that are drastically lower than previously thought for neutral models. Given this exemplar of how spatial structure (multiple linked mtDNA populations), noise, and density affect muscle cell aging, we introduce the mechanism of stochastic survival of the densest (SSD), an alternative to RA, that may underpin other evolutionary phenomena. [ABSTRACT FROM AUTHOR]

Mathematical modelling is a discipline pledged to identify problems, which may arise from virtually any branch of the human knowledge, and formalise them in the language of mathematics by developing suitable methodologies of investigation. To pursue its goals, modelling must build connections with other mathematical sciences and, in particular, with numerics. Three major examples of the efficiency of such combination are industrial mathematics, mathematical biology and biomechanics. At first sight, industrial mathematics is a branch of applied mathematics focusing on problems that come from industry and it aims at determining solutions relevant to manufacturing. Some relevant examples are petroleum engineering, hydrogeology, and the description of sand dynamics in the neighbourhood of railways in desert zones. On the other hand, the adoption of mathematics to formalise problems of biological relevance has attracted scientists working on population dynamics, epidemiology and related fields. Moreover, a strong impact has been given by the combination of modelling with the mechanics of biological tissues, thereby giving rise to biomechanics. Few examples in this respect are the mechanics of cell motion and migration, which relate to kinetic theories, the mechanics of the interactions between cells and the extracellular matrix, the conversion of mechanical signals into chemical stimuli, and "mathematical oncology". Since it is not possible to present a theoretical corpus of all that, the aim of the present special issue is to put together a list of outstanding scientific papers giving clear connections among nonlinear mechanics, industrial mathematics, biomathematics, biomechanics and kinetic theories, in different fields of interest. This special issue of IJNLM is the Festschrift celebrating the 60th birthday of Luigi Preziosi, whose research is a recognised example of how mechanics may be the fuel for interesting applied mathematics. [ABSTRACT FROM AUTHOR]

The applied mathematics program was quite flexible and Emilia was able to choose co-advisors from two different departments for her PhD. The student that introduced Emilia to the REU program had the biggest influence on her career, exposing Emilia to a completely new field that she otherwise wouldn't have known about. In Emilia's PhD program, coursework needed to be completed first before diving into research, and Emilia felt as though if she couldn't do well in the classes, would she be able to make it through the program at all?. [Extracted from the article]

This contribution belongs to a larger empirical study that focuses on issues related to the implementation of inquiry-based learning and formative assessment in science and mathematics education, while it also refers to the issue of STEM education. Here, we discuss the two topics from the perspective of professional preparation of primary school teachers. We employ an educational tool called Concept Cartoons and perceive it as a common diagnostic tool for investigating modes of reasoning about general statements in arithmetic, geometry and biology. The presented qualitative exploratory empirical study maps and codes various kinds of reasoning that can be identified with the tool and investigates possibilities of a joint coding procedure. As a result, it provides a conversion table between various modes of reasoning in the three subject domains. The arisen code categories cover the field of generic examples, including the initial stages so that they can be used for scaffolding the process of learning the foundations of deductive reasoning. The joint approach to reasoning in mathematics and biology shows how argumentation and formative assessment can be understood equally and developed simultaneously in both school subjects. It helps us to see how the two school subjects can be integrated didactically. [ABSTRACT FROM AUTHOR]

No gene has garnered more interest than p53 since its discovery over 40 years ago. In the last two decades, thanks to seminal work from Uri Alon and Ghalit Lahav, p53 has defined a truly synergistic topic in the field of mathematical biology, with a rich body of research connecting mathematic endeavour with experimental design and data. In this review we survey and distill the extensive literature of mathematical models of p53. Specifically, we focus on models which seek to reproduce the oscillatory dynamics of p53 in response to DNA damage. We review the standard modelling approaches used in the field categorising them into three types: time delay models, spatial models and coupled negative-positive feedback models, providing sample model equations and simulation results which show clear oscillatory dynamics. We discuss the interplay between mathematics and biology and show how one informs the other; the deep connections between the two disciplines has helped to develop our understanding of this complex gene and paint a picture of its dynamical response. Although yet more is to be elucidated, we offer the current state-of-the-art understanding of p53 response to DNA damage. [ABSTRACT FROM AUTHOR]

Models are essential in science and therefore in scientific literacy. Therefore, pupils need to attain competency in the appropriate use of models. This so-called model–methodical competence distinguishes between model competence (the conceptual part) and modelling competence (the procedural part), wherefrom a definition follows a general overview of the concept of models in this article. Based on this, modelling processes enable the promotion of the modelling competence. In this context, two established approaches mainly applied in other disciplines (biology and mathematics) and a survey among chemistry teachers and employees of chemistry education departments (N = 98) form the starting point for developing a chemistry modelling process. The article concludes with a description of the developed modelling process, which by its design, provides an opportunity to develop students' modelling competence. [ABSTRACT FROM AUTHOR]