Journal articles: 'Mathematical biology in general'

1

Maini, P. K. "Essential Mathematical Biology." Mathematical Medicine and Biology 20, no. 2 (June 1, 2003): 225–26. http://dx.doi.org/10.1093/imammb/20.2.225.

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Logan, J. David, Elizabeth S. Allman, and John A. Rhodes. "Mathematical Models in Biology." American Mathematical Monthly 112, no. 9 (November 1, 2005): 847. http://dx.doi.org/10.2307/30037621.

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Sanft, Rebecca, and Anne Walter. "Experimenting with Mathematical Biology." PRIMUS 26, no. 1 (July 9, 2015): 83–103. http://dx.doi.org/10.1080/10511970.2015.1064050.

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Deem, Michael W. "Mathematical adventures in biology." Physics Today 60, no. 1 (January 1, 2007): 42–47. http://dx.doi.org/10.1063/1.2709558.

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Vasieva, Olga, Manan'Iarivo Rasolonjanahary, and Bakhtier Vasiev. "Mathematical modelling in developmental biology." REPRODUCTION 145, no. 6 (June 2013): R175—R184. http://dx.doi.org/10.1530/rep-12-0081.

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In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.

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Laubenbacher, Reinhard. "Algebraic Methods in Mathematical Biology." Bulletin of Mathematical Biology 73, no. 4 (March 12, 2011): 701–5. http://dx.doi.org/10.1007/s11538-011-9643-7.

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Kraikivski, Pavel. "Mathematical Modeling in Systems Biology." Entropy 25, no. 10 (September 25, 2023): 1380. http://dx.doi.org/10.3390/e25101380.

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Ali Lashari, Abid, and Faiz Ahmad. "False mathematical reasoning in biology." Journal of Theoretical Biology 307 (August 2012): 211. http://dx.doi.org/10.1016/j.jtbi.2012.05.006.

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Shelah, Saharon, and Lutz Strüngmann. "Infinite combinatorics in mathematical biology." Biosystems 204 (June 2021): 104392. http://dx.doi.org/10.1016/j.biosystems.2021.104392.

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Krumbeck, Yvonne, Tim Rogers, and George Constable. "An Invitation to Stochastic Mathematical Biology." Notices of the American Mathematical Society 68, no. 11 (December 1, 2021): 1. http://dx.doi.org/10.1090/noti2381.

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Anikonov, Yu E. "An inverse problem of mathematical biology." Siberian Mathematical Journal 33, no. 3 (1992): 385–88. http://dx.doi.org/10.1007/bf00970885.

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Friedman, Avner. "Free boundary problems in biology." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2050 (September 13, 2015): 20140368. http://dx.doi.org/10.1098/rsta.2014.0368.

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In this paper, I review several free boundary problems that arise in the mathematical modelling of biological processes. The biological topics are quite diverse: cancer, wound healing, biofilms, granulomas and atherosclerosis. For each of these topics, I describe the biological background and the mathematical model, and then proceed to state mathematical results, including existence and uniqueness theorems, stability and asymptotic limits, and the behaviour of the free boundary. I also suggest, for each of the topics, open mathematical problems.

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Kiefer, J. "Quantitative mathematical models in radiation biology." Radiation and Environmental Biophysics 27, no. 3 (September 1988): 219–32. http://dx.doi.org/10.1007/bf01210839.

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López-Ruiz, Ricardo. "Mathematical Biology: Modeling, Analysis, and Simulations." Mathematics 10, no. 20 (October 20, 2022): 3892. http://dx.doi.org/10.3390/math10203892.

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Mathematical biology has been an area of wide interest during the recent decades, as the modeling of complicated biological processes has enabled the creation of analytical and computational approaches to many different bio-inspired problems originating from different branches such as population dynamics, molecular dynamics in cells, neuronal and heart diseases, the cardiovascular system, genetics, etc [...]

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Kočinac, Ljubiša D. R. "Advances in General Topology and Its Application." Axioms 12, no. 6 (June 11, 2023): 579. http://dx.doi.org/10.3390/axioms12060579.

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In recent years, mathematical and, in particular, topological models and methods have been used extensively in real-world problems related to economics, engineering, biology, computer science, medical science, social science, etc [...]

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Friedman, Avner. "PDE problems arising in mathematical biology." Networks & Heterogeneous Media 7, no. 4 (2012): 691–703. http://dx.doi.org/10.3934/nhm.2012.7.691.

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López Pouso, Rodrigo, and Ignacio Márquez Albés. "General existence principles for Stieltjes differential equations with applications to mathematical biology." Journal of Differential Equations 264, no. 8 (April 2018): 5388–407. http://dx.doi.org/10.1016/j.jde.2018.01.006.

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Henson, Shandelle M., Fred Brauer, and Carlos Castillo-Chavez. "Mathematical Models in Population Biology and Epidemiology." American Mathematical Monthly 110, no. 3 (March 2003): 254. http://dx.doi.org/10.2307/3647954.

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Gadbail, Amol R., and Shailesh Gondivkar. "Scope of Mathematical Biology in Cancer Research." Journal of Contemporary Dental Practice 19, no. 9 (2018): 1035–36. http://dx.doi.org/10.5005/jp-journals-10024-2376.

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20

Freedman, H. I. "G. J. Butler's research in mathematical biology." Rocky Mountain Journal of Mathematics 20, no. 4 (December 1990): 839–45. http://dx.doi.org/10.1216/rmjm/1181073045.

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Kllogjeri, Qamil, and Pellumb Kllogjer. "Mathematical biology: a powerful science for progress." MOJ Biology and Medicine 7, no. 1 (February 11, 2022): 20–25. http://dx.doi.org/10.15406/mojbm.2022.07.00160.

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This paper is about mathematical biology as a new fast growing and cooperative field of the two sciences: biology and mathematics. The challenge is that more quantitative becomes the biology science, wider and deeper becomes the application of mathematics in this science, hence more exciting results will be in the global scope. Many experiments in biology need quantification in order to make measurements, to discover and estimate the influence of different factors in the phenomenon under study, and draw right conclusions. An example is the estimation of the total number of choices a fly faces while travelling through the apparatus for fractionating the flies. The combinations of the successive choices result with a great number. Comparative experiments estimate differences in response between treatments or between the two groups involved in the experiment. There are many cases where the comparisons are biased, no matter how precise the measurements are done, because of the way a group is partitioned into two subgroups. The biologist needs to know all the possible partitions and the respective numbers of comparisons, make them part of the experiment and find out which partition gives the lowest error. In this paper our intention is to help biologists and researchers with few formulas that can be used for calculations in different experiments.

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Britton, N. F. "Review: Mathematical Models in Biology: An Introduction." Mathematical Medicine and Biology: A Journal of the IMA 22, no. 3 (September 1, 2005): 289–90. http://dx.doi.org/10.1093/imammb/dqi008.

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23

EDELSTEINKESHET, L. "J.D. Murray, Mathematical Biology, Springer-Verlag (1989)." Bulletin of Mathematical Biology 52, no. 6 (1990): 797–802. http://dx.doi.org/10.1016/s0092-8240(05)80386-6.

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Buiatti, M. "Mathematical modeling in biology: A critical assessment." Il Nuovo Cimento D 20, no. 1 (January 1998): 79–89. http://dx.doi.org/10.1007/bf03036040.

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Kemp, A. W., and J. Mazumdar. "An Introduction to Mathematical Physiology and Biology." Biometrics 47, no. 1 (March 1991): 349. http://dx.doi.org/10.2307/2532530.

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26

Brown, Jeremy M., and Robert C. Thomson. "Evaluating Model Performance in Evolutionary Biology." Annual Review of Ecology, Evolution, and Systematics 49, no. 1 (November 2, 2018): 95–114. http://dx.doi.org/10.1146/annurev-ecolsys-110617-062249.

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Many fields of evolutionary biology now depend on stochastic mathematical models. These models are valuable for their ability to formalize predictions in the face of uncertainty and provide a quantitative framework for testing hypotheses. However, no mathematical model will fully capture biological complexity. Instead, these models attempt to capture the important features of biological systems using relatively simple mathematical principles. These simplifications can allow us to focus on differences that are meaningful, while ignoring those that are not. However, simplification also requires assumptions, and to the extent that these are wrong, so is our ability to predict or compare. Here, we discuss approaches for evaluating the performance of evolutionary models in light of their assumptions by comparing them against reality. We highlight general approaches, how they are applied, and remaining opportunities. Absolute tests of fit, even when not explicitly framed as such, are fundamental to progress in understanding evolution.

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McNAB, W. BRUCE. "A General Framework Illustrating an Approach to Quantitative Microbial Food Safety Risk Assessment." Journal of Food Protection 61, no. 9 (September 1, 1998): 1216–28. http://dx.doi.org/10.4315/0362-028x-61.9.1216.

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Hazard analysis critical control point (HACCP), risk assessment, predictive microbiology, and dose-response modeling have been recognized as important tools for the assessment and management of health risks posed by food-borne pathogens. Unfortunately, the biology of both the food chain and food poisoning is complex and dynamic. Therefore, mathematical modeling of microbial risk from food production through to consumption and illness is difficult. Nevertheless, previous authors have made impressive progress in modeling specific pathogen-food-consumer combinations. In this study a framework for a Monte Carlo model of a generic food system was developed. It links together food ingredients, batch processing, cross contamination, microbial growth, cooking, recontamination, consumption, human exposure to pathogens, the dose-response relationship, and the biologic and economic impact components of such risks. This framework is presented to illustrate one potential approach to quantitative risk assessment for microbial food safety. It requires refinement with appropriate distributions and mathematical relationships before it can be applied to a specific pathogen-food-consumer situation.

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Kimmel, Marek. "Evolution and cancer: a mathematical biology approach." Biology Direct 5, no. 1 (2010): 29. http://dx.doi.org/10.1186/1745-6150-5-29.

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Jungck, John R., Holly Gaff, and Anton E. Weisstein. "Mathematical Manipulative Models: In Defense of “Beanbag Biology”." CBE—Life Sciences Education 9, no. 3 (September 2010): 201–11. http://dx.doi.org/10.1187/cbe.10-03-0040.

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Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process—1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets—we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project ( http://bioquest.org/esteem ) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount ). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.

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Varga, Zoltán. "Applications of mathematical systems theory in population biology." Periodica Mathematica Hungarica 56, no. 1 (March 2008): 157–68. http://dx.doi.org/10.1007/s10998-008-5157-0.

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Kaur, Jaspreet. "Inclusion of mathematics in biological concepts at the senior secondary level in Indian education system." Assimilation: Indonesian Journal of Biology Education 6, no. 2 (September 30, 2023): 117–32. http://dx.doi.org/10.17509/aijbe.v6i2.62077.

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The students who study biology often develop fear from mathematical concepts and tend to avoid the pages of biology textbook where mathematical details are included. The students often perceive Mathematics and Biology as two separate disciplines of study. One of the main reasons for this perception is that biology textbooks do not include relevant mathematical details in biological concepts. Moreover, biology teachers often have little or no mathematical academic background while mathematics is taught by teachers with least or no interest in biology. This often leads to the lack of understanding among students that both subjects are actually linked to each other. So, the students study them in parallel and there are hardly any cross talks between these two subjects. But, the myth is debunked later when biology students reach the undergraduate and postgraduate level wherein they are expected to apply the mathematical skills to understand the biological concepts. So, if the realization is sparked at an early stage during schooling years that both Mathematics and Biology are related to each other, then the ‘Maths phobia’ among Biology students can be easily overcome. In this article, illustrative examples have been presented with detailed explanation wherein the biology students can appreciate mathematical concepts efficiently in a teaching-learning environment at the senior secondary level.

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Ledder, Glenn. "An Experimental Approach to Mathematical Modeling in Biology∗." PRIMUS 18, no. 1 (January 17, 2008): 119–38. http://dx.doi.org/10.1080/10511970701753423.

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Chiel, Hillel J., Jeffrey M. McManus, and Kendrick M. Shaw. "From Biology to Mathematical Models and Back: Teaching Modeling to Biology Students, and Biology to Math and Engineering Students." CBE—Life Sciences Education 9, no. 3 (September 2010): 248–65. http://dx.doi.org/10.1187/cbe.10-03-0022.

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We describe the development of a course to teach modeling and mathematical analysis skills to students of biology and to teach biology to students with strong backgrounds in mathematics, physics, or engineering. The two groups of students have different ways of learning material and often have strong negative feelings toward the area of knowledge that they find difficult. To give students a sense of mastery in each area, several complementary approaches are used in the course: 1) a “live” textbook that allows students to explore models and mathematical processes interactively; 2) benchmark problems providing key skills on which students make continuous progress; 3) assignment of students to teams of two throughout the semester; 4) regular one-on-one interactions with instructors throughout the semester; and 5) a term project in which students reconstruct, analyze, extend, and then write in detail about a recently published biological model. Based on student evaluations and comments, an attitude survey, and the quality of the students' term papers, the course has significantly increased the ability and willingness of biology students to use mathematical concepts and modeling tools to understand biological systems, and it has significantly enhanced engineering students' appreciation of biology.

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Martins, A. M., P. Vera-Licona, and R. Laubenbacher. "'Model your genes the mathematical way'--a mathematical biology workshop for secondary school teachers." Teaching Mathematics and its Applications 27, no. 2 (April 24, 2008): 91–101. http://dx.doi.org/10.1093/teamat/hrn003.

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Robeva, Raina, Robin Davies, Terrell Hodge, and Alexander Enyedi. "Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics." CBE—Life Sciences Education 9, no. 3 (September 2010): 227–40. http://dx.doi.org/10.1187/cbe.10-03-0019.

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We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

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de Pillis, Lisette, and Stephen C. Adolph. "Mathematical Biology at an Undergraduate Liberal Arts College." CBE—Life Sciences Education 9, no. 4 (December 2010): 417–21. http://dx.doi.org/10.1187/cbe.10-08-0099.

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Chyba, Monique, and Benedetto Piccoli. "Special issue on mathematical methods in systems biology." Networks & Heterogeneous Media 14, no. 1 (2019): ⅰ—ⅱ. http://dx.doi.org/10.3934/nhm.20191i.

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38

Maciá, Enrique. "Aperiodic crystals in biology." Journal of Physics: Condensed Matter 34, no. 12 (January 5, 2022): 123001. http://dx.doi.org/10.1088/1361-648x/ac443d.

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Abstract Biological systems display a broad palette of hierarchically ordered designs spanning over many orders of magnitude in size. Remarkably enough, periodic order, which profusely shows up in non-living ordered compounds, plays a quite subsidiary role in most biological structures, which can be appropriately described in terms of the more general aperiodic crystal notion instead. In this topical review I shall illustrate this issue by considering several representative examples, including botanical phyllotaxis, the geometry of cell patterns in tissues, the morphology of sea urchins, or the symmetry principles underlying virus architectures. In doing so, we will realize that albeit the currently adopted quasicrystal notion is not general enough to properly account for the rich structural features one usually finds in biological arrangements of matter, several mathematical tools and fundamental notions belonging to the aperiodic crystals science toolkit can provide a useful modeling framework to this end.

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Andersen, Janet. "Enriching the Teaching of Biology with Mathematical Concepts." American Biology Teacher 69, no. 4 (April 1, 2007): 205–9. http://dx.doi.org/10.2307/4452139.

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Andersen, Janet. "Enriching the Teaching of Biology with Mathematical Concepts." American Biology Teacher 69, no. 4 (April 2007): 205–9. http://dx.doi.org/10.1662/0002-7685(2007)69[205:ettobw]2.0.co;2.

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41

MAINI, P. "Bulletin of mathematical biology?facts, figures and comparisons*1." Bulletin of Mathematical Biology 66, no. 4 (July 2004): 595–603. http://dx.doi.org/10.1016/j.bulm.2004.03.003.

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42

Nikolova, Iveta. "On stochastic models in biology and medicine." Asian-European Journal of Mathematics 13, no. 08 (May 21, 2020): 2050168. http://dx.doi.org/10.1142/s1793557120501685.

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Stochastic models along with deterministic models are successfully used for mathematical description of biological processes. They apply knowledge from probability theory and mathematical statistics to analyze specific characteristics of living systems. The paper is devoted to some stochastic models of various phenomena in biology and medicine. Basic concepts and definitions used in classical probability models are considered and illustrated by several examples with solutions. The stochastic kinetic modeling approach is described. A new kinetic model of autoimmune disease is presented. It is a system of nonlinear partial integro-differential equations supplemented by corresponding initial conditions. The modeling problem is solved computationally.

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43

Masomi, Hayatullah. "The Application of Mathematical Series in Sciences." Journal of Mathematics and Statistics Studies 4, no. 4 (November 8, 2023): 76–83. http://dx.doi.org/10.32996/jmss.2023.4.4.8.

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Mathematical series and sequences are crucial in scientific disciplines to identify patterns, make predictions, and deduce mathematical correlations between variables. Chemistry, biology and physics rely heavily on mathematical series to model complex systems, make precise predictions, and identify fundamental principles of chemical and biological processes. The study used a qualitative approach to identify mathematical series used in scientific research and evaluate their application in chemistry and biology. A comprehensive literature review was conducted to gather pertinent papers and articles from credible scientific databases, followed by a thematic analysis strategy to examine the content. The findings of the study revealed that mathematical series are widely used in various fields, including chemistry, biology, and physics. The Taylor series, power series expansion, Fibonacci series, power series and binomial series are some of the most commonly used series. They approximate functions, express reaction rates, solve linear equations, depict spiral patterns, study population growth, and analyze genetics and molecular biology. They are crucial tools in physics, quantum mechanics, and natural phenomena description.

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King, P. "Mathematical models in population biology and epidemiology [Book Reviews]." IEEE Engineering in Medicine and Biology Magazine 20, no. 4 (July 2001): 101. http://dx.doi.org/10.1109/memb.2001.940057.

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Olsen, Christian Haargaard, Johnny T. Ottesen, Ralph C. Smith, and Mette S. Olufsen. "Parameter subset selection techniques for problems in mathematical biology." Biological Cybernetics 113, no. 1-2 (October 30, 2018): 121–38. http://dx.doi.org/10.1007/s00422-018-0784-8.

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Adler, Fred. "Essential Mathematical Biology Essential Mathematical Biology Nicholas F. Britton Springer-Verlag, New York, 2003. $34.95 (335 pp.). ISBN 1-85233-536-X." Physics Today 57, no. 3 (March 2004): 80–82. http://dx.doi.org/10.1063/1.1712507.

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Bloomfield, Victor. "An Introduction to Mathematical Physiology and Biology. J. Mazumdar." Quarterly Review of Biology 65, no. 4 (December 1990): 535. http://dx.doi.org/10.1086/417038.

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Getz, Wayne M. "Nonlinear Dynamics, Mathematical Biology, and Social Science.Joshua M. Epstein." Quarterly Review of Biology 73, no. 4 (December 1998): 554–57. http://dx.doi.org/10.1086/420538.

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Benigni, R., and A. Giuliani. "Quantitative modeling and biology: the multivariate approach." American Journal of Physiology-Regulatory, Integrative and Comparative Physiology 266, no. 5 (May 1, 1994): R1697—R1704. http://dx.doi.org/10.1152/ajpregu.1994.266.5.r1697.

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Even though elegant examples of mathematical modeling of biological problems exist, such approaches still remain outside the domain of most biologists. It is proposed that, for a wider and more systematic use of mathematical models in biology, the soft modeling approaches, which are applicable to phenomena with a limited level of definition, should be investigated and preferred. In particular, multivariate data analysis (MDA) is indicated as an important tool toward fulfilling this goal. This paper reviews the general principles of MDA and examines in detail principal component analysis and cluster analysis, which are two of the most important MDA techniques. A number of applications to real biological problems are presented. These examples show how the construction of classifications corresponds to the generation of new knowledge and new concepts, which are hierarchically on a higher level than the initial information. This new form of knowledge is obtained without superimposing a priori theories on the data. It is demonstrated how the MDA can lead to the identification of biological systems; also shown is their ability to describe multiple scale phenomena, a typical feature of biological systems. Moreover, the multivariate analyses provide new descriptors for a given biological system; these descriptors are quantitative, thus allowing the system to be described in a "metric space," where it then becomes possible to use any other mathematical tool.

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Eveson, S. P. "An Integral Equation Arising from a Problem in Mathematical Biology." Bulletin of the London Mathematical Society 23, no. 3 (May 1991): 293–99. http://dx.doi.org/10.1112/blms/23.3.293.

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Journal articles on the topic 'Mathematical biology in general'

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