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The study focuses on the model of houseflies with discrete delay, which is examined both theoretically and numerically. The solution of the delayed system is bounded and positive. The delay is selected as the bifurcation parameter. Stability analysis, local and global Hopf bifurcation are given in theoretical aspect. Through computer simulations, various dynamic behaviors, such as supercritical Hopf bifurcation, are detected. The theoretical analysis and numerical observations in this research are significant contributions to the biomathematics research area. [ABSTRACT FROM AUTHOR]

Over the past two decades, vibrational resonance has garnered significant interest and evolved into a prominent research field. Classical vibrational resonance examines the response of a nonlinear system excited by two signals: a weak, slowly varying characteristic signal, and a fast-varying auxiliary signal. The characteristic signal operates on a much longer time scale than the auxiliary signal. Through the cooperation of the nonlinear system and these two excitations, the faint input can be substantially amplified, showcasing the constructive role of the fast-varying signal. Since its inception, vibrational resonance has been extensively studied across various disciplines, including physics, mathematics, biology, neuroscience, laser science, chemistry, and engineering. Here, we delve into a detailed discussion of vibrational resonance and the most recent advances, beginning with an introduction to characteristic signals commonly used in its study. Furthermore, we compile numerous nonlinear models where vibrational resonance has been observed to enhance readers' understanding and provide a basis for comparison. Subsequently, we present the metrics used to quantify vibrational resonance, as well as offer a theoretical formulation. This encompasses the method of direct separation of motions, linear and nonlinear vibrational resonance, re-scaled vibrational resonance, ultrasensitive vibrational resonance, and the role of noise in vibrational resonance. Later, we showcase two practical applications of vibrational resonance: one in image processing and the other in fault diagnosis. This presentation offers a comprehensive and versatile overview of vibrational resonance, exploring various facets and highlighting promising avenues for future research in both theory and engineering applications. [ABSTRACT FROM AUTHOR]

Integrating scientific disciplines through a transdisciplinary approach is a pivotal component of contemporary learning paradigms, fostering educational experiences that transcend monodisciplinary boundaries and embrace the integration of diverse fields. Addressing this imperative, we collaborated with educators in Indonesia to devise a learning framework that interweaves mathematics, biology, and cultural dimensions by utilizing the context of Tempeh production – a traditional fermented food in Indonesia. This article delineates the intricacies of our pedagogical design, encompassing eight key stages: briefing, contextualization, exploration, action 1 to action 4, and reflection. Furthermore, we present a comprehensive analysis of students' reflective writing, employing thematic analysis across six stages, namely description, feelings, evaluation, analysis, conclusion, and action plan. This initiative seeks to forge connections between scientific disciplines and to furnish students with theoretical knowledge and tangible and pragmatic experiences. [ABSTRACT FROM AUTHOR]

The purpose of this study is to demonstrate clustering methods within a functional data analysis (FDA) framework for identifying subgroups of individuals that may be exhibiting categories of misfit. Person response functions (PRFs) estimated within a FDA framework (FDA-PRFs) provide graphical displays that can aid in the identification of persons that have responded unexpectedly to items comprising an achievement test. Typical person fit statistics are also useful for detecting unexpected response patterns, but they do not provide insight into the underlying behaviors responsible for those responses. However, different responding behaviors tend to produce FDA-PRFs of different shapes, and may provide additional information regarding the reasons for misfit. Functional clustering methods are useful for categorizing respondents into subgroups based on the shapes of their FDA-PRFs. In this study, a small simulation illustrates the potential of clustering FDA-PRFs for identifying persons displaying common types of responding behaviors. The methodology is also applied to data from a high school biology assessment and a mathematics achievement test. Clustering FDA-PRFs offers a promising methodology for operationalizing person fit evaluations in large-scale assessments, and may be a valuable step in person fit assessment when used in conjunction with traditional indices of psychometric quality. [ABSTRACT FROM AUTHOR]

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]

We study, from a probabilistic standpoint, a full randomization of nonhomogeneous second‐order linear difference equations assuming that its data (initial conditions, coefficients, and forcing term) are random variables. Our analysis consists of computing the so‐called first probability density function of the solution, which is a stochastic process, and then analyzing the stability of the solution assuming that all data have an arbitrary joint probability density function. To achieve these goals, we take extensive advantage of the so‐called random variable transformation technique. The theoretical results extend their deterministic counterpart, and then, they have many applications in real‐world problems where uncertainty plays a key role. Our findings are first illustrated by means of several numerical examples, where different simulations are carried out, and, second, by means of a model belonging to biomathematics. [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]

The cumulative outcome of bacteria-phytoplankton cell-cell interactions has global-scale consequences that necessitate a more comprehensive understanding of the species that form these relationships, the chemical exchanges that govern them, and the chemical cues that trigger them. However, the diffuse liquid environment supporting these exchanges is inherently difficult to interrogate, which has moved researchers to combine multi-omics analyses, genome mining tools, genetic probes, and mathematical models to gain insight into the species and chemical networks existing around individual phytoplankton cells. Yet, fundamental questions still remain about these micro-scale interactions, creating an opportunity for innovating new methods where biology and chemistry interface with engineering and mathematics. [ABSTRACT FROM AUTHOR]

In the book "The Rise of Chance in Evolutionary Theory: A Pompous Parade of Arithmetic" by Charles H. Pence, the author explores the role of statistics in evolutionary theory. Pence traces the development of mathematical and statistical approaches in understanding natural selection, focusing on key figures such as Francis Galton and R.A. Fisher. The book challenges the idea of a scientific revolution during this period and emphasizes the continuity of ideas and approaches. Pence also discusses the relationship between modeling, abstraction, and generality in studying evolution. Overall, the book provides a valuable contribution to the history and philosophy of biology, as well as to the understanding of the role of mathematics in science. [Extracted from the article]

Graph theory has great deal of application in disciplines like biology, computer science, informatics, engineering, mathematics, social science, linguistics and medicine. Topological indices are created by labeling the chemical structure through numerical parameters. These notations link chemical compounds physicochemical features such as boiling temperature, stability, strain energy etc, to its molecular structure. Different topological features of chemical structure have been explored. One of the molecular graphs topological indices are the connection indices defined on the number of connection between vertices of distance two. In this work, we compute the first Zagreb connection index, second Zagreb connection index, and modified first Zagreb connection index for hexagonal network and non kekulean benzenoid hydrocarbon. [ABSTRACT FROM AUTHOR]

The employment of nonlinear fractional partial differential equations (NLFPDEs) is not limited to branches of mathematics entirely but also applicable in other science fields such as biology, physics and engineering. This paper derives some solitary wave solutions for the space-time fractional symmetric regularized long wave (SRLW) equation by means of the improved P -expansion approach and the F ′ / F -expansion method. We use the definition of the Jumarie's modified Riemann–Liouville derivative to handle the fractional derivatives appearing in this equation. Diverse types of soliton solutions are successfully expressed on the form of rational, hyperbolic, trigonometric, and complex functions. We extract kink wave, internal solitary wave, and solitary wave solutions. The performances of the proposed methods are compared with each other. Moreover, we compare the constructed results with some published solutions. The long behaviors of the obtained solutions are plotted in 2D and 3D figures. The resulting outcomes point out that the used techniques promise to empower us to deal with more NLFPDEs arising in mathematical physics. [ABSTRACT FROM AUTHOR]

Failure to achieve efficacy is among the top, if not the most common reason for clinical trial failures. While there may be many underlying contributors to these failures, selecting the right mechanistic hypothesis, the right dose, or the right patient population are the main culprits. Systems biology is an inter-disciplinary field at the intersection of biology and mathematics that has the growing potential to increase probability of success in clinical trials, delivering a data-driven matching of the right mechanism to the right patient, at the right dose. Moreover, as part of successful selection of targets for a therapeutic area, systems biology is a prime approach to development of combination therapies to combating complex diseases, where single targets have failed to achieve sufficient efficacy in the clinic. Systems biology approaches have become increasingly powerful with the progress in molecular and computational methods and represent a novel innovative tool to tackle the complex mechanisms of human disease biology, linking it to clinical phenotypes and optimizing multiple steps of drug discovery and development. With increasing ability of probing biology at a cellular and organ level with omics technologies, systems biology is here to stay and is positioned to be one of the key pillars of drug discovery and development, predicting and advancing the best therapies that can be combined together for an optimal pharmacological effect in the clinic. Here we describe a systems biology platform with a stepwise approach that starts with characterization of the key pathways contributing to the Mechanism of Disease (MOD) and is followed by identification, design, optimization, and translation into the clinic of the best therapies that are able to reverse disease-related pathological mechanisms through one or multiple Mechanisms of Action (MOA). [ABSTRACT FROM AUTHOR]

The body composition determination is carried out through measurement methods that require the use of specialized equipment that is difficult to acquire and manipulate. Therefore, different authors have developed mathematical models for its calculation. The target of this review was to analyze the work carried out on mathematical models of body composition variables from different anthropometric measurements, answering the following questions: what is the corporal variable that the model predicts?, what are the input variables for model development?, how is the patients typification in each model?, what data analysis method has been used?, and how has been the model evaluated? The search was limited to journals found in repositories in the areas of Medicine, Nursing, Biochemistry, Biology, Health, Pharmacology, Immunology, Engineering, and Mathematics. Four hundred and twenty-four articles were found, which were reduced to 30 by applying the systematic literature review process. The analyzed studies are oriented to the prediction of variables related to body fat mass. The evaluation results found for fat-free mass, fat mass and metabolic rate differ according to the comparison technique and the body segments analyzed. The evaluation is mainly based on the intraclass correlation, the Pearson correlation and the coefficient of determination (r²), and they present a good correlation for the population under study. [ABSTRACT FROM AUTHOR]

Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning—specifically deep learning—techniques have shown their capabilities in approximating dynamics from data, but a shortcoming of traditional deep learning is that there is little insight into the underlying mapping beyond its numerical output for a given input. This limits their utility in analysis beyond simple prediction. Simultaneously, a number of strategies exist which identify models based on a fixed dictionary of basis functions, but most either require some intuition or insight about the system, or are susceptible to overfitting or a lack of parsimony. Here, we present a novel approach that combines the flexibility and accuracy of deep learning approaches with the utility of symbolic solutions: a deep neural network that generates a symbolic expression for the governing equations. We first describe the architecture for our model and then show the accuracy of our algorithm across a range of classical dynamical systems. [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]

Cybernetics covers many traditional disciplines, including technology, philosophy, biology, mathematics, and social sciences. So, studying and understanding cybernetics systems and their management are essential concepts in all aspects of life. But, as far as we know, a perfect and profound discussion about the topic of cybernetic systems is rare. In order to address the emerging challenges of the information society, this paper will cover recent developments in the development of cybernetic systems with particular reference to management applications. Selected articles were analyzed in 7 main groups: historical evolution of cybernetics systems, system dynamics, dialogic design science, complexity theory, artificial intelligence, cybernetics, and management optimization). In order to advance research and development, the study showed the multi- and trans-disciplinary nature of cybernetics, systems, and the management sciences. According to the findings of our analysis, most papers were released in 2007. We also found that the IEEE Journals had the largest number of published articles. It suggests that the researchers' attention to research in this field has diminished over time. Also, the results showed that cybernetics might render a conceptual-philosophical aid and a functional instrument in control and managerial planning. [ABSTRACT FROM AUTHOR]

The interrelationship between predator populations and prey populations is a central problem in biology and mathematics. Setting up appropriate predator–prey models to portray the development law of predator populations and prey populations has aroused widespread interest in many scholars. In this work, we propose a new fractional order predator–prey system involving Michaelis–Menten-type functional response and both unequal delays. Utilizing the contraction mapping theorem, we prove the existence and uniqueness of the solution to the considered fractional order predator–prey system. By virtue of some mathematical analysis techniques, nonnegativeness of the solution to the involved fractional order predator–prey system is analyzed. By constructing a suitable function, the boundedness of the solution to the considered fractional order predator–prey system is explored. Making use of Laplace transform, we derive the characteristic equation of the involved fractional order predator–prey system, then by means of the stability principle and the bifurcation theory of fractional order dynamical system, a series of novel delay-independent stability criteria and bifurcation conditions ensuring the stability of the equilibrium point and the creation of Hopf bifurcation of the considered fractional order predator–prey system, are built. The global stability of the involved fractional order predator–prey system is analyzed in detail. The role of time delay in controlling the stability and the creation of Hopf bifurcation is revealed. To check the legitimacy of the derived key results, software simulation results are effectively presented. The obtained results in this work are completely novel and play a significant role in maintaining ecological balance. [ABSTRACT FROM AUTHOR]

A mathematical model to analyze the self-purification potential of organic matter in reservoirs was developed, seeking to constitute a potential water management tool for easy application. Therefore, it was considered the input of organic matter into the watercourse, its sedimentation, decomposition and its output downstream, as well as the oxygen input through the flow and through re-oxygenation, its consumption by microbial activity and its downstream exit. The model was validated using data of Tietê river and applied using data of Salto Grande reservoir, both located at São Paulo State, Brazil, considering different scenarios of biochemical oxygen demand (BOD), dissolved oxygen (DO), water inlet flow and reservoir water volume. The results show that organic matter is decomposed faster in the first 12 hours of water travel; moreover, self-purification efficiency is better with a greater volume of water in the reservoir. The model is quite representative to study different self-purification scenarios in dammed areas, concluding that the developed model, being tested and improved, can already contribute to the management of reservoirs, with the advantage of having a simple application. [ABSTRACT FROM AUTHOR]

For the sake of development of modern sciences, there has been a tendency in education to make use of integration processes between sciences. Interdisciplinary integration and coordination is one of the characteristic features of the learning process which is an interconnected and fully integrated discipline. Creating interdisciplinary integration, focusing on strengthening student knowledge and skills, teaching Computer Science in relationship with other disciplines, such as mathematics, physics, biology and others, is an area of interest. This method of teaching requires instructors to be fluent not only in their own discipline, but also in other disciplines. The method of interdisciplinary relationship can be widely used in the teaching of Computer Science in relation to the course of Physics, and this opportunity is one of the actual problems. For the purpose of fulfilling this task, curriculums of both disciplines have been researched and analyzed. Certain topics from the Physics course are reminded students as a refresh to reinforce the knowledge once again, and then on the basis of this knowledge, Computer Science topics are taught, which helps consciously master the new knowledge and increase cognitive activity of students. In this study, to solve physics problems we have employed the programming language C ++, which is a universal language with a wide range of capabilities. This article justifies actuality of the issue, gives background on the existing work, and presents goals and tasks of this research, as well as methodological basics, scientific novelty, and theoretical and practical importance of this work. Experiments have been conducted with the key points emerging from the context have been presented in the conclusion section. In conclusion, one of the ways to improve the teaching of Computer Science is the use of interdisciplinary relationships in the educational process. These interdisciplinary relationships play an important role for students in acquisition of scientific, theoretical and practical knowledge and skills. These relationships can be a prerequisite for a comprehensive approach to education. [ABSTRACT FROM AUTHOR]

The purpose of this study was to evaluate the preliminary outcomes of a learning community intervention (LC), which was based on the performance pyramid theoretical model of student supports. The LC integrated college algebra into biology course work. We used a quasi-experimental design to compare LC students to separate General Biology I and College Algebra course control groups on respective measures of biology and algebra course knowledge, and an assessment of perceived performance pyramid supports. Participants included 198 students (LC, n = 22; biology control, n = 52; mathematics control, n = 124) at a Historically Black University in the Southern United States. An analysis of covariance (ANCOVA) indicated that the LC students had significantly greater performance from pre- to post-test on a measure of biology course knowledge (Cohen's d = 0.76) compared to the biology control group. An ANCOVA indicated that the LC and mathematics control students performed similarly on a measure of algebra course knowledge. Group differences from a multivariate analysis of covariance on perceived performance pyramid supports were mostly statistically non-significant. Overall, the LC increased biology course performance. Implications for improving biology course performance and better assessment of students' perceptions of support for academic success are discussed. [ABSTRACT FROM AUTHOR]

A review of works devoted to the theory of stable matchings or, more generally, of stable networks of contracts is given. A set (network) of contracts is called stable if no coalition has an available contract that gives all coalition members strictly more than the proposed set. In a special case, this concept was introduced in 1962 by Gale and Shapley and has since gone a long way in its development both theoretically (theorems, structures, and algorithms) and in the field of applications in economics, physics, biology, and mathematics. [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]

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]

Background: Gut microbiota is involved in the development of liver diseases such as fibrosis. We and others identified that selected sets of gut bacterial DNA and bacteria translocate to tissues, notably the liver, to establish a non-infectious tissue microbiota composed of microbial DNA and a low frequency live bacteria. However, the precise set of bacterial DNA, and thereby the corresponding taxa associated with the early stages of fibrosis need to be identified. Furthermore, to overcome the impact of different group size and patient origins we adapted innovative statistical approaches. Liver samples with low liver fibrosis scores (F0, F1, F2), to study the early stages of the disease, were collected from Romania(n = 36), Austria(n = 10), Italy(n = 19), and Spain(n = 17). The 16S rRNA gene was sequenced. We considered the frequency, sparsity, unbalanced sample size between cohorts to identify taxonomic profiles and statistical differences. Results: Multivariate analyses, including adapted spectral clustering with L1-penalty fair-discriminant strategies, and predicted metagenomics were used to identify that 50% of liver taxa associated with the early stage fibrosis were Enterobacteriaceae, Pseudomonadaceae, Xanthobacteriaceae and Burkholderiaceae. The Flavobacteriaceae and Xanthobacteriaceae discriminated between F0 and F1. Predicted metagenomics analysis identified that the preQ0 biosynthesis and the potential pathways involving glucoryranose and glycogen degradation were negatively associated with liver fibrosis F1-F2 vs F0. Conclusions: Without demonstrating causality, our results suggest first a role of bacterial translocation to the liver in the progression of fibrosis, notably at the earliest stages. Second, our statistical approach can identify microbial signatures and overcome issues regarding sample size differences, the impact of environment, and sets of analyses. Trial registration: TirguMECCH ROLIVER Prospective Cohort for the Identification of Liver Microbiota, registration 4065/2014. Registered 01 01 2014. [ABSTRACT FROM AUTHOR]

Entropy is a thermodynamic function in physics that measures the randomness and disorder of molecules in a particular system or process based on the diversity of configurations that molecules might take. Distance-based entropy is used to address a wide range of problems in the domains of mathematics, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines. We explain the basic applications of distance-based entropy to chemical phenomena. These applications include signal processing, structural studies on crystals, molecular ensembles, and quantifying the chemical and electrical structures of molecules. In this study, we examine the characterisation of polyphenylenes and boron ( B 12 ) using a line of symmetry. Our ability to quickly ascertain the valences of each atom, and the total number of atom bonds is made possible by the symmetrical chemical structures of polyphenylenes and boron B 12 . By constructing these structures with degree-based indices, namely the K Banhatti indices, R e Z G 1 -index, R e Z G 2 -index, and R e Z G 3 -index, we are able to determine their respective entropies. [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]

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]

Quantitative abilities and techniques are vital in modern biological sciences from lab calculations and classical hypothesis testing to the growth of 'omics' and big data. Long before the employability at Higher Education can be considered, the transition between Secondary and Higher Education must be. Students doing biological sciences degrees at a UK university were surveyed to ascertain the factors that prepared students best for the quantitative nature of a biological sciences degree. Student perceptions of biological sciences as a quantitative subject altered once they began their degree's. Students who studied mathematics post-16 felt more prepared for the quantitative nature of their biological sciences degree while Secondary level biology does not prepare. Post-16 mathematics is only an entry requirement for 1of 49 biological sciences courses across the UK's Russell Group universities. Most students do not feel prepared by their Secondary Education for the quantitative nature of a biological sciences degree and Higher Education Institutions do not ask for quantitative qualifications. This study highlights the lack of preparedness perceived by students and the potential discord in this field between Secondary and Higher Education. [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]

In mathematical biology, there is a great deal of interest in producing continuum models by scaling discrete agent-based models governed by local stochastic rules. We discuss a particular example of this approach: a model for the proliferation of neural crest cells that can help us understand the development of Hirschprung’s disease, a potentially-fatal condition in which the enteric nervous system of a new-born child does not extend all the way through the intestine and colon. Our starting point is a discrete-state, continuous-time Markov chain model proposed by Hywood et al. (2013a) for the location of the neural crest cells that make up the enteric nervous system. Hywood et al. (2013a) scaled their model to derive an approximate second order partial differential equation describing how the limiting expected number of neural crest cells evolve in space and time. In contrast, we exploit the relationship between the above-mentioned Markov chain model and the well-known Yule-Furry process to derive the exact form of the scaled version of the process. Furthermore, we provide expressions for other features of the domain agent occupancy process, such as the variance of the marginal occupancy at a particular site, the distribution of the number of agents that are yet to reach a given site and a stochastic description of the process itself. [ABSTRACT FROM AUTHOR]

This year we celebrate the 200th anniversary of Gregor Mendel's birth. Mendel was not recognized for his scientific work during his lifetime. It was not until 16 long years after his death that his work was rediscovered to lay the foundations for a new field – genetics. Mendel›s contribution lay not only in his own experiments and their results, but above all in the methodological innovation that consisted in the use of mathematics and statistics in biological research, which was something completely new for the then purely descriptive biological sciences. Interestingly, Mendel's motivation was not to expand human knowledge. Mendel, as he himself stated in the introduction to his work, was interested in the principles of heredity so that he could breed better and better ornamental plants. This desire for improvement was also reflected in his other research activities in the field of beekeeping or meteorology. Although he never had a university degree, Mendel was a very popular teacher. He was the head of one of the largest and richest monasteries in Moravia. His life and work, his followers and the builders of his legacy, the history of medical genetics in our country, as well as the contributions of Mendelian genetics to modern medicine are discussed in our review. [ABSTRACT FROM AUTHOR]

Contemporary scientific knowledge is built on both methodological and epistemological reductionism. The discovery of the limitations of the reductionist paradigm in the mathematical treatment of certain physical phenomena originated the notion of complexity, both as a pattern and process. After clarifying some very general terms and ideas on biological evolution and biological complexity, the article will tackle to seek to summarize the debate on biological complexity and discuss the difference between complexities of living and inert matter. Some examples of the major successes of mathematics applied to biological problems will follow; the notion of an intrinsic limitation in the application of mathematics to biological complexity as a global, relational, and historical phenomenon at the individual and species level will also be advanced. [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]

The Gierer–Meinhardt system occurs in morphogenesis, where the development of an organism from a single cell is modelled. One of the steps in the development is the formation of spatial patterns of the cell structure, starting from an almost homogeneous cell distribution. Turing proposed different activator–inhibitor systems with varying diffusion rates in his pioneering work, which could trigger the emergence of such cell structures. Mathematically, one describes these activator–inhibitor systems as coupled systems of reaction-diffusion equations with different diffusion coefficients and highly nonlinear interaction. One famous example of these systems is the Gierer–Meinhardt system. These systems usually are not of monotone type, such that one has to apply other techniques. The purpose of this article is to study the stochastic reaction-diffusion Gierer–Meinhardt system with homogeneous Neumann boundary conditions on a one or two-dimensional bounded spatial domain. To be more precise, we perturb the original Gierer–Meinhardt system by an infinite-dimensional Wiener process and show under which conditions on the Wiener process and the initial conditions, a solution exists. In dimension one, we even show the pathwise uniqueness. In dimension two, uniqueness is still an open question. [ABSTRACT FROM AUTHOR]

The integration of biology with mathematics and computer science mandates the training of students capable of comfortably navigating among these fields. We address this formidable pedagogical challenge with the creation of transdisciplinary modules that guide students toward solving realistic problems with methods from different disciplines. Knowledge is gradually integrated as the same topic is revisited in biology, mathematics, and computer science courses. We illustrate this process with a module on the homeostasis and dynamic regulation of red blood cell production, which was first implemented in an introductory biology course and will be revisited in the mathematics and computer science curricula. [ABSTRACT FROM AUTHOR]

There are many perceived benefits to undergraduate student research; however, students may not have a full understanding of the research process prior to engaging in a project. In this paper, we analyze the impact of an undergraduate research workshop on students' understanding of academic research as well as the impact on their self-efficacy for conducting research through an analysis of the 2018 and 2019 Intercollegiate Biomathematics Alliance Cross-Institutional Research Experience (CURE) workshops. Students were asked to complete a survey at the start and end of the three-day workshop, which included both Likert-type scale questions as well as free response questions addressing their understanding of research and effective collaboration in conducting research, their perceived role in conducting research, and their perception of their own skills specific to biomathematics research. We observed improved self-efficacy in specific research skills where students had not already indicated a high level of self-efficacy prior to the workshop. Additionally, student responses indicated a shift in perception of research from solving a particular problem to contributing to a field by discovering or creating new knowledge. Other shifts in student perceptions are discussed in the paper as well as recommendations for the workshop organizers. [ABSTRACT FROM AUTHOR]

This article describes the authors' experiences developing and implementing an innovative curriculum connecting mathematics and the biological sciences. It describes the original plan, the modifications that were necessary, and some advice to readers who might want to develop comparable programs. [ABSTRACT FROM AUTHOR]

Emmanuele DiBenedetto passed away in May 2021, after battling cancer for fifteen months. I have had the unique privilege to collaborate and discuss Mathematics with him, almost up to his final days. Here I briefly present his life and those mathematical results of his, which I consider most familiar with. [ABSTRACT FROM AUTHOR]

In the digital education landscape, cross-modal retrieval (CMR) from multimodal educational slides represents a significant challenge, particularly because of the complex nature of academic content, which includes images, diagrams, equations, and tables across various subjects such as mathematics and biology. Current CMR systems are primarily designed for "(natural) image to text" interactions (or vice versa) and inadequately address real-world educational scenarios. This study presents EduCross, a novel framework devised to enhance CMR within multimodal educational slides, which is a domain in which traditional retrieval systems fall short. Recognizing the imperative for a system that is tailored to the educational context, EduCross integrates dual adversarial bipartite hypergraph learning, harnessing the capabilities of generative adversarial networks with figure-text dual channels. This powerful combination facilitates robust bidirectional mapping, allowing for the precise association of figures with their descriptive spoken language segments and ensuring a comprehensive CMR experience. Specifically, we develop framelet-based deep bipartite hypergraph neural networks that effectively manage the high-order relationships between diverse educational content types and various types of slide figures. Our experimental results underscore the superior performance of EduCross, demonstrating its effectiveness through the use of the real Multimodal Lecture Presentations dataset that mirrors authentic educational settings. These outcomes highlight the significant advancements of EduCross over existing methods, marking a leap forward in the accurate retrieval of multimodal educational content. • A novel dual adversarial bipartite hypergraph learning method for cross-modal retrieval. • Novel framelet-based deep bipartite hypergraph neural networks are developed. • EduCross combines adversarial learning with bipartite hypergraph learning. • EduCross achieves SOTA results on the real-world multimodal educational slide dataset. [ABSTRACT FROM AUTHOR]

The information contained in DNA is encoded in a double helix formed by two antiparallel and complementary sequences of nucleotides, which are stabilized by hydrogen bonds. At physiological conditions, each nucleobase possesses three main characteristics; molecular structure, functional group, and orientation in the double helix. These properties produce steric constraints that allow only complementary interactions between nucleobase pairs to form double or triple hydrogen bonds. In this work, a mathematical model is proposed to describe the pairing interactions between nucleobases according to their physicochemical properties (structure, functional group and orientation). The results suggest that stable hydrogen bonds derived from nucleobase interactions can be represented by a set of 4 hermitian matrices and a Clifford Algebra C l (4 , 0). Moreover, it is shown that the allowed interactions between pairs of nucleobases enable the formulation of an exclusion principle between the states of the observables. Finally, the mathematical representation of the hydrogen bonding between complementary nucleobases suggests a preferential orientation (chirality), which could be associated with the major groove in the double helix structure of B-DNA. • Hydrogen bonds in DNA arise from the interaction between physicochemical properties. • Pairing specificity in nucleobases exhibits an exclusion principle. • Matrices representing hydrogen bonds in DNA show chirality (right or left). [ABSTRACT FROM AUTHOR]

In this paper, we deal with a new approximation of a diffusive predator–prey model with Leslie–Gower term and social behavior for the prey subject to Neumann boundary conditions. A new approach for a predator–prey interaction in the presence of prey social behavior has been considered. Our main topic in this work is to study the influence of the prey's herd shape on the predator–prey interaction in the presence of Leslie–Gower term. First of all, we examine briefly the system without spatial diffusion. By analyzing the distribution of the eigenvalues associated with the constant equilibria, the local stability of the equilibrium points and the existence of Hopf bifurcation have been investigated. Then, the spatiotemporal dynamics introduced by self‐diffusion was determined, where the existence of the positive solution, Hopf bifurcation, Turing‐driven instability, and Turing–Hopf bifurcation point have been derived. Further, the effect of the prey's herd shape rate on the prey and predator equilibrium densities as well as on the Hopf bifurcating points has been discussed. Finally, by using the normal form theory on the center manifold, the direction and stability of the bifurcating periodic solutions have also been obtained. To illustrate the theoretical results, some graphical representations are given. [ABSTRACT FROM AUTHOR]

The application of mathematics to fields such as biology, medicine, and biotechnology has resulted in quantitative relations, and mathematical biology, an interdisciplinary branch, has emerged. The considered models of cell/tissue growth are determined by cross‐reaction‐diffusion equations with possible transitions between malignant cells with different growth rates or healthy cells. For the considered models, the exact solutions in the explicit form were not obtained in the existing literature to our knowledge. Our main aim is to fill this gap by revealing their exact solutions. The obtained results have a major role in the literature so that the considered models are seen in a large scale of applications. [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]