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Journal articles on the topic 'Mathematical biology'

Author: Grafiati

Published: 4 June 2021

Last updated: 28 July 2024

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1

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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2

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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3

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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4

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

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5

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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6

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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7

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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8

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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9

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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10

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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11

Whitfield, John. "Mathematical biology centre launched." Nature 455, no. 7209 (September 2008): 11. http://dx.doi.org/10.1038/455011a.

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12

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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13

Lakhno, V. D. "Mathematical biology and bioinformatics." Herald of the Russian Academy of Sciences 81, no. 5 (October 2011): 539–45. http://dx.doi.org/10.1134/s1019331611050029.

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14

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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15

Othmer, Hans G. "Mathematical models in biology." Mathematical Biosciences 96, no. 1 (September 1989): 131–33. http://dx.doi.org/10.1016/0025-5564(89)90088-6.

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16

Tomlin, Claire J., and Jeffrey D. Axelrod. "Biology by numbers: mathematical modelling in developmental biology." Nature Reviews Genetics 8, no. 5 (May 2007): 331–40. http://dx.doi.org/10.1038/nrg2098.

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17

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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18

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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19

Hastings, Alan. "Mathematical Models of Population Biology." Ecology 69, no. 4 (August 1988): 1311–12. http://dx.doi.org/10.2307/1941295.

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20

Friedman, Avner. "Conservation laws in mathematical biology." Discrete & Continuous Dynamical Systems - A 32, no. 9 (2012): 3081–97. http://dx.doi.org/10.3934/dcds.2012.32.3081.

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21

Kotvalt, V. "Britton, N.F.: Essential Mathematical Biology." Photosynthetica 41, no. 3 (September 1, 2003): 356. http://dx.doi.org/10.1023/b:phot.0000015523.14609.5a.

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22

Fidelman, Uri. "The Biology of Mathematical Knowledge." Kybernetes 19, no. 2 (February 1990): 34–52. http://dx.doi.org/10.1108/eb005841.

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23

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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24

Bell, Jonathan G. "Mathematical Biology (J. D. Murray)." SIAM Review 32, no. 3 (September 1990): 487–89. http://dx.doi.org/10.1137/1032093.

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25

Robeva, Raina, and Reinhard Laubenbacher. "Mathematical Biology Education: Beyond Calculus." Science 325, no. 5940 (July 30, 2009): 542–43. http://dx.doi.org/10.1126/science.1176016.

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26

Davidson, L. "An introduction to mathematical biology." Development 138, no. 24 (November 22, 2011): 5269–70. http://dx.doi.org/10.1242/dev.066977.

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27

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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28

Chandran, D., W. B. Copeland, S. C. Sleight, and H. M. Sauro. "Mathematical modeling and synthetic biology." Drug Discovery Today: Disease Models 5, no. 4 (December 2008): 299–309. http://dx.doi.org/10.1016/j.ddmod.2009.07.002.

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29

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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30

Golubitsky, Martin, and Ian Stewart. "Symmetry methods in mathematical biology." São Paulo Journal of Mathematical Sciences 9, no. 1 (May 19, 2015): 1–36. http://dx.doi.org/10.1007/s40863-015-0001-9.

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31

Carrillo, José, and Mats Gyllenberg. "Editorial: Year of Mathematical Biology 2018." EMS Newsletter 2017-12, no. 106 (December 6, 2017): 3–4. http://dx.doi.org/10.4171/news/106/1.

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32

Titlyanova, A. A. "Schools on mathematical biology 1973-1992." Computer Research and Modeling 8, no. 2 (April 2016): 411–22. http://dx.doi.org/10.20537/2076-7633-2016-8-2-411-422.

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33

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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34

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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35

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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36

Reed, Michael C. "Mathematical Biology is Good for Mathematics." Notices of the American Mathematical Society 62, no. 10 (November 1, 2015): 1172–76. http://dx.doi.org/10.1090/noti1288.

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37

Ulrich, C. M. "Mathematical Modeling: Epidemiology Meets Systems Biology." Cancer Epidemiology Biomarkers & Prevention 15, no. 5 (May 1, 2006): 827–29. http://dx.doi.org/10.1158/1055-9965.epi-06-0252.

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38

Herzel, Hanspeter, and Nils Blüthgen. "Mathematical models in mammalian cell biology." Genome Biology 9, no. 7 (2008): 316. http://dx.doi.org/10.1186/gb-2008-9-7-316.

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39

Chitnis, N., and T. A. Smith. "Mathematical illiteracy impedes progress in biology." Proceedings of the National Academy of Sciences 109, no. 45 (September 20, 2012): E3055. http://dx.doi.org/10.1073/pnas.1213115109.

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40

Gascuel, Olivier, and Tanja Stadler. "Mathematical and Computational Evolutionary Biology (2013)." Systematic Biology 64, no. 1 (December 12, 2014): 1–2. http://dx.doi.org/10.1093/sysbio/syu086.

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41

Clermont, Gilles, and Sven Zenker. "The inverse problem in mathematical biology." Mathematical Biosciences 260 (February 2015): 11–15. http://dx.doi.org/10.1016/j.mbs.2014.09.001.

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42

Stelling, Jörg. "Mathematical models in microbial systems biology." Current Opinion in Microbiology 7, no. 5 (October 2004): 513–18. http://dx.doi.org/10.1016/j.mib.2004.08.004.

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43

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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44

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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45

Jungck, J. R. "Mathematical Biology Education: Modeling Makes Meaning." Mathematical Modelling of Natural Phenomena 6, no. 6 (2011): 1–21. http://dx.doi.org/10.1051/mmnp/20116601.

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46

Jäger, Willi. "Mathematical Modelling in Chemistry and Biology." Interdisciplinary Science Reviews 11, no. 2 (January 1986): 181–88. http://dx.doi.org/10.1179/isr.1986.11.2.181.

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47

Casti, John, and Karl Sigmund. "Special issue on mathematical biology: Introduction." Applied Mathematics and Computation 32, no. 2-3 (August 1989): 73–74. http://dx.doi.org/10.1016/0096-3003(89)90088-x.

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48

Bakshi, Suruchi, Vijayalakshmi Chelliah, Chao Chen, and Piet H. van der Graaf. "Mathematical Biology Models of Parkinson's Disease." CPT: Pharmacometrics & Systems Pharmacology 8, no. 2 (November 2, 2018): 77–86. http://dx.doi.org/10.1002/psp4.12362.

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49

Shankar, Prabhat, Masatoshi Nishikawa, and Tatsuo Shibata. "2P273 Gain Noise Relation in Adaptation Networks(24. Mathematical biology,Poster)." Seibutsu Butsuri 53, supplement1-2 (2013): S204. http://dx.doi.org/10.2142/biophys.53.s204_2.

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50

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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Abstract:

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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