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Relevant bibliographies by topics / Mathematical biology

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Academic literature on the topic 'Mathematical biology'

Author: Grafiati

Published: 4 June 2021

Last updated: 28 July 2024

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Journal articles on the topic "Mathematical biology"

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Griffel, David, and J. D. Murray. "Mathematical Biology." Mathematical Gazette 75, no. 472 (June 1991): 240. http://dx.doi.org/10.2307/3620297.

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Murray, James. "Mathematical Biology." Computer Research and Modeling 3, no. 3 (September 2011): 227–30. http://dx.doi.org/10.20537/2076-7633-2011-3-3-227-230.

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France, J., and J. D. Murray. "Mathematical Biology." Statistician 40, no. 3 (1991): 344. http://dx.doi.org/10.2307/2348289.

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Hoppensteadt, Frank. "Mathematical biology." Scholarpedia 2, no. 6 (2007): 2877. http://dx.doi.org/10.4249/scholarpedia.2877.

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Ermentrout, Bard. "Mathematical biology." Mathematical Biosciences 103, no. 1 (February 1991): 153–55. http://dx.doi.org/10.1016/0025-5564(91)90096-2.

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Yakovlev, Andrei. "Mathematical Biology in Biology Direct." Biology Direct 3, no. 1 (2008): 1. http://dx.doi.org/10.1186/1745-6150-3-1.

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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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Brown, Joel S. "Mathematical evolutionary biology." Mathematical Biosciences 105, no. 2 (July 1991): 243–46. http://dx.doi.org/10.1016/0025-5564(91)90085-w.

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Klyuchko, O. M. "ON THE MATHEMATICAL METHODS IN BIOLOGY AND MEDICINE." Biotechnologia Acta 10, no. 3 (June 2017): 31–40. http://dx.doi.org/10.15407/biotech10.03.031.

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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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Dissertations / Theses on the topic "Mathematical biology"

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Mazzag, Barbara Cathrine. "Mathematical models in biology /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2002. http://uclibs.org/PID/11984.

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Lewis, Matthew. "Laboratory Experiences in Mathematical Biology for Post-Secondary Mathematics Students." DigitalCommons@USU, 2016. https://digitalcommons.usu.edu/etd/5219.

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In addition to the memorization, algorithmic skills and vocabulary which is the default focus in many mathematics classrooms, professional mathematicians are expected to creatively apply known techniques, construct new mathematical approaches and communicate with and about mathematics. We propose that students can learn these professional, higher level skills through Laboratory Experiences in Mathematical Biology (LEMBs) which put students in the role of mathematics researcher creating mathematics to describe and understand biological data. LEMBs are constructed so they require no specialized equipment and can easily be run in the context of a college math class. Students collect data and develop mathematical models to explain the data. In this work examine how LEMBs are designed with the student as the primary focus. We explain how well-designed LEMBs lead students to interact with mathematics at higher levels of cognition while building mathematical skills sought after in both academia and industry. Additionally, we describe the online repository created to assist in the teaching and further development of LEMBs. Since student-centered teaching is foreign to many post-secondary instructors, we provide research-based, pedagogical strategies to ensure student success while maintaining high levels of cognition.

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Li, Yifei. "Nonlinear diffusion in mathematical biology." Thesis, Queensland University of Technology, 2022. https://eprints.qut.edu.au/234381/1/Yifei_Li_Thesis.pdf.

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Reaction-diffusion models with nonlinear diffusion are widely used for studying population dynamics in biology and ecology. Yet, the relationship between nonlinear diffusion mechanisms in populations and the behaviours of individuals is hard to be intuitively interpreted in classical models. To address this problem, we develop a discrete-continuum modelling framework, where the movement of individuals influenced by crowding effects is connected to the nonlinear diffusivity functions in a well-defined continuum limit. Using this framework, we explore the influence of nonlinear diffusion on population extinction, and analyse the existence and stability of travelling waves in continuous equations which model the invasion process.

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Murphy, Ryan John. "Mechanochemical and experimental models in mathematical biology." Thesis, Queensland University of Technology, 2022. https://eprints.qut.edu.au/228428/1/Ryan%20John_Murphy_Thesis.pdf.

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Experiments that probe epithelial tissue dynamics, cell competition, and tumour growth are fundamental to understand processes in developmental biology, cancer progression and treatment. However, interpreting complex biological experiments is challenging. To address this challenge, we develop and use a range of mathematical models. First, we focus on epithelial tissue dynamics. Second, we use real-time cell cycle imaging to reveal the structure of growing tumour spheroids. We then revisit the seminal Greenspan tumour growth model and use statistical analysis to quantitatively connect it to experimental data for the first time to reveal experimental design choices that lead to reliable biological insight.

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Bozic, Ivana. "Mathematical Models of Cancer." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10220.

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Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. Here we present mathematical models that begin to address this challenge. First we present a model of accumulation of driver and passenger mutations during tumor progression and derive a formula for the number of driver mutations as a function of the total number of mutations in a tumor. Fitting this formula to recent experimental data, we were able to calculate the selective advantage provided by a typical driver mutation. Second, we performed a quantitative analysis of pancreatic cancer metastasis genetic data. The results of this analysis define a broad time window for detection of pancreatic cancer before metastatic dissemination. Finally, we model the evolution of resistance to targeted cancer therapy. We apply our model to experimental data on the response to panitumumab, targeted therapy against colorectal cancer. Our modeling suggested that cells resistant to therapy were likely present in patients’ tumors prior to the start of therapy.
Mathematics

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Ferrara, Joseph. "A Study of Nonlinear Dynamics in Mathematical Biology." UNF Digital Commons, 2013. http://digitalcommons.unf.edu/etd/448.

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We first discuss some fundamental results such as equilibria, linearization, and stability of nonlinear dynamical systems arising in mathematical modeling. Next we study the dynamics in planar systems such as limit cycles, the Poincaré-Bendixson theorem, and some of its useful consequences. We then study the interaction between two and three different cell populations, and perform stability and bifurcation analysis on the systems. We also analyze the impact of immunotherapy on the tumor cell population numerically.

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Hunt, Gordon S. "Mathematical modelling of pattern formation in developmental biology." Thesis, Heriot-Watt University, 2013. http://hdl.handle.net/10399/2706.

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The transformation from a single cell to the adult form is one of the remarkable wonders of nature. However, the fundamental mechanisms and interactions involved in this metamorphic change still remain elusive. Due to the complexity of the process, researchers have attempted to exploit simpler systems and, in particular, have focussed on the emergence of varied and spectacular patterns in nature. A number of mathematical models have been proposed to study this problem with one of the most well studied and prominent being the novel concept provided by A.M. Turing in 1952. Turing's simple yet elegant idea consisted of a system of interacting chemicals that reacted and di used such that, under certain conditions, spatial patterns can arise from near homogeneity. However, the implicit assumption that cells respond to respective chemical levels, di erentiating accordingly, is an oversimpli cation and may not capture the true extent of the biology. Here, we propose mathematical models that explicitly introduce cell dynamics into pattern formation mechanisms. The models presented are formulated based on Turing's classical mechanism and are used to gain insight into the signi cance and impact that cells may have in biological phenomena. The rst part of this work considers cell di erentiation and incorporates two conceptually di erent cell commitment processes: asymmetric precursor di erentiation and precursor speci cation. A variety of possible feedback mechanisms are considered with the results of direct activator upregulation suggesting a relaxation of the two species Turing Instability requirement of long range inhibition, short range activation. Moreover, the results also suggest that the type of feedback mechanism should be considered to explain observed biological results. In a separate model, cell signalling is investigated using a discrete mathematical model that is derived from Turing's classical continuous framework. Within this, two types of cell signalling are considered, namely autocrine and juxtacrine signalling, with both showing the attainability of a variety of wavelength patterns that are illustrated and explainable through individual cell activity levels of receptor, ligand and inhibitor. Together with the full system, a reduced two species system is investigated that permits a direct comparison to the classical activator-inhibitor model and the results produce pattern formation in systems considering both one and two di usible species together with an autocrine and/or juxtacrine signalling mechanism. Formulating the model in this way shows a greater applicability to biology with fundamental cell signalling and the interactions involved in Turing type patterning described using clear and concise variables.

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Yang, Xige. "MATHEMATICAL MODELS OF PATTERN FORMATION IN CELL BIOLOGY." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1542236214346341.

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Xu, Yiyang. "Topics in population genetics and mathematical evolutionary biology." Thesis, University of Bristol, 2015. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.682366.

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Part A studies the optimal strategies of seed germination problems where the population has a class structure under a fluctuating environment . In particular, a multidimensional age-class model is studied using a dynamical programming method. Numerical results about the so-called optimal stochastic strategy which consists of information about previous environmental states are computed. Comparing the optimal stochastic strategy with the optimal population-based strategy shows that the optimal stochastic strategy is highly effective in genera.l. A potentially useful diffusion approximation for the seed germination problem is also derived with numerical results. For part B, a multi-dimensional Moran model is studied using a diffusion approximation approach. The scaling limit and corresponding governing stochastic partial differential equations (SDEs) are derived. An expansion method is used to approximate the stationary distribution of the SDEs. An approximation formula for the effective migration rate is then derived.

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Buckalew, Richard L. "Mathematical Models in Cell Cycle Biology and Pulmonary Immunity." Ohio University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1395242276.

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Books on the topic "Mathematical biology"

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Shonkwiler, Ronald W., and James Herod. Mathematical Biology. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-70984-0.

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Murray, James D. Mathematical Biology. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-662-08539-4.

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Murray, James D. Mathematical Biology. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-08542-4.

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Murray, J. D., ed. Mathematical Biology. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/b98868.

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Murray, J. D., ed. Mathematical Biology. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/b98869.

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Mathematical biology. 2nd ed. Berlin: Springer-Verlag, 1993.

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Murray, James D. Mathematical Biology. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989.

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Peeyush, Chandra, and Kumar B. V. Rathish, eds. Mathematical biology. Tunbridge Wells, UK: Anshan, 2006.

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Murray, James D. Mathematical Biology. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993.

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1962-, Lewis M., ed. Mathematical biology. Providence, R.I: American Mathematical Society, Institute of Advanced Study, 2009.

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Book chapters on the topic "Mathematical biology"

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Shonkwiler, Ronald W., and James Herod. "Biology, Mathematics, and a Mathematical Biology Laboratory." In Undergraduate Texts in Mathematics, 1–8. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-70984-0_1.

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Yeargers, Edward K., Ronald W. Shonkwiler, and James V. Herod. "Biology, Mathematics, and a Mathematical Biology Laboratory." In An Introduction to the Mathematics of Biology: with Computer Algebra Models, 1–8. Boston, MA: Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4757-1095-3_1.

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Serovajsky, Simon. "Mathematical model in biology." In Mathematical Modelling, 105–28. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003035602-7.

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Ricard, Jacques, and Käty Ricard. "Mathematical Models in Biology." In Philosophy of Mathematics Today, 299–304. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5690-5_17.

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Baker, Alan. "Mathematical Explanation in Biology." In History, Philosophy and Theory of the Life Sciences, 229–47. Dordrecht: Springer Netherlands, 2015. http://dx.doi.org/10.1007/978-94-017-9822-8_10.

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Wang, Lin. "Mathematical Programming." In Encyclopedia of Systems Biology, 1185–86. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_405.

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Henson, Shandelle M., and James L. Hayward. "Mathematical Modeling." In Mathematical Modeling in Biology, 3–28. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003265382-2.

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Murray, James D. "Continuous Population Models for Single Species." In Mathematical Biology, 1–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-662-08539-4_1.

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Murray, James D. "Oscillator Generated Wave Phenomena and Central Pattern Generators." In Mathematical Biology, 254–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-662-08539-4_10.

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Murray, James D. "Biological Waves: Single Species Models." In Mathematical Biology, 274–310. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-662-08539-4_11.

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Conference papers on the topic "Mathematical biology"

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MEJÍA, R. "MATHEMATICAL BIOLOGY: SOME OPPORTUNITIES IN INTEGRATIVE BIOLOGY." In International Symposium on Mathematical and Computational Biology. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814271820_0020.

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ROEDER, INGO. "SYSTEMS STEM CELL BIOLOGY." In International Symposium on Mathematical and Computational Biology. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812708779_0001.

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Lakhno, V. D., M. N. Ustinin, and N. N. Nazipova. "The online journal "Mathematical biology and bioinformatics": ways and prospects." In Mathematical Biology and Bioinformatics. Pushchino: IMPB RAS - Branch of KIAM RAS, 2018. http://dx.doi.org/10.17537/icmbb18.112.

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Juratoni, A., O. Bundău, A. Chevereşan, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "A Mathematical Analysis of a Biology Process." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3497972.

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Nazipova, N. N. "The IMPB RAS is 50 years old. Bioinformatics Laboratory." In Mathematical Biology and Bioinformatics. Pushchino: IMPB RAS - Branch of KIAM RAS, 2022. http://dx.doi.org/10.17537/icmbb22.35.

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Moskalenko, A. V., and S. A. Makhortykh. "On spectral analysis of the regulation of the main cardiac rhythm." In Mathematical Biology and Bioinformatics. Pushchino: IMPB RAS - Branch of KIAM RAS, 2022. http://dx.doi.org/10.17537/icmbb22.13.

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Romanov, M. S., and V. B. Masterov. "Analysis of Steller's Sea Eagle reproduction efficiency on Sakhalin Island using Generalized Linear Mixed Models (GLMM)." In Mathematical Biology and Bioinformatics. Pushchino: IMPB RAS - Branch of KIAM RAS, 2022. http://dx.doi.org/10.17537/icmbb22.47.

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Lelekov, A. S., and A. V. Shiryaev. "Dynamics of the macromolecular composition of microalgae culture in natural light conditions. Model." In Mathematical Biology and Bioinformatics. Pushchino: IMPB RAS - Branch of KIAM RAS, 2022. http://dx.doi.org/10.17537/icmbb22.5.

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Khanina, L. G., M. V. Bobrovsky, V. E. Smirnov, K. V. Ivashchenko, A. I. Zhuravleva, and I. V. Zhmaylov. "Effects of mass windthrow in broad-leaved forest on characteristics of sandy and loamy soils." In Mathematical Biology and Bioinformatics. Pushchino: IMPB RAS - Branch of KIAM RAS, 2022. http://dx.doi.org/10.17537/icmbb22.50.

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Furletova, E. I. "Aho-Corasick automaton minimization. Application to the computation of pattern occurrences P-value." In Mathematical Biology and Bioinformatics. Pushchino: IMPB RAS - Branch of KIAM RAS, 2022. http://dx.doi.org/10.17537/icmbb22.54.

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Reports on the topic "Mathematical biology"

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Chakraborty, Srijani. Promises and Challenges of Systems Biology. Nature Library, October 2020. http://dx.doi.org/10.47496/nl.blog.09.

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Modern systems biology is essentially interdisciplinary, tying molecular biology, the omics, bioinformatics and non-biological disciplines like computer science, engineering, physics, and mathematics together.

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Tucker Blackmon, Angelicque. Formative External Evaluation and Data Analysis Report Year Three: Building Opportunities for STEM Success. Innovative Learning Center, LLC, August 2020. http://dx.doi.org/10.52012/mlfk2041.

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Williams, Thomas. Cell Biology Board Game: Cell Survival (School Version). University of Dundee, 2022. http://dx.doi.org/10.20933/100001270.

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Cells are the smallest units of life. The environment around cells is always changing. Cells need to adapt to survive. This curriculum linked game and lesson plan introduces the world of cells to pupils 8-13. But can they keep their cells alive? This is a guide to how the cell survival resources can be used in a lesson and can be adapted as the teacher sees fit to do so. This lesson is aimed at 8-13 year olds, and fits into an hour long session. The Cell Survival Game has been adapted for both home use and for use in the classroom, and is accompanied by a series of videos. Learning Outcomes – Cells are the smallest unit of life – There are many different types of cells, and some examples of cell types – Cells experience many dangers, and some examples of dangers – How cells notice and defend themselves against dangers Links to the Curriculum – Health and Wellbeing: I am developing my understanding of the human body – Languages: I can find specific information in a straight forward text (book and instructions) to learn new things, I discover new words and phrases (relating to cells) – Mathematics: I am developing a sense of size and amount (by using the dice), I am exploring number processes (addition and subtraction) and understand they represent quantities (steps to finish line), I am learning about measurements (cell sizes) and am exploring patterns (of cell defences against dangers) – Science: I am learning about biodiversity (different types of microbes), body systems, cells and how they work. – Technology: I am learning about new technologies (used to understand how cells work).

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Bilousova, Liudmyla I., Liudmyla E. Gryzun, Daria H. Sherstiuk, and Ekaterina O. Shmeltser. Cloud-based complex of computer transdisciplinary models in the context of holistic educational approach. [б. в.], September 2019. http://dx.doi.org/10.31812/123456789/3259.

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The paper represents the authors’ cloud-based complex of computer dynamic models and their transdisciplinary facilities. Proper theoretical background for the complex design is elaborated and the process of the computer models development is covered. The models in the complex are grouped in the sections according to the curriculum subjects (Physics, Algebra, Geometry, Biology, Geography, and Informatics). Each of the sections includes proper models along with their description and transdisciplinary didactic support. The paper also presents recommendations as for using of the complex to provide holistic learning of Mathematics, Science and Informatics at secondary school. The prospects of further research are outlined.

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Computational Biology: Development in the Field of Medicine. Science Repository, April 2021. http://dx.doi.org/10.31487/sr.blog.31.

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Computational biology involves the development and application of analytical-data and theoretical methods, computational simulation techniques, and mathematical modeling to the study of biological, behavioral, ecological, and social systems.

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