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Skip to Search Results- 4Mathematical ecology
- 3Advection-diffusion
- 2Aggregation-diffusion
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- 2Existence theorems
- 2Non-local advection
- 4Biological Sciences, Department of
- 4Biological Sciences, Department of/Journal Articles (Biological Sciences)
- 4Mathematical and Statistical Sciences, Department of
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2019-05-04
We identify seven-tone (heptatonic) scales as a sequence of minor and major thirds, where we use a zero to indicate a minor third and a one for a major third. Each proper seven-tone scale is then represented by a {0,1}-sequence of length seven. On these {0,1}-sequences we define group operations...
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Detecting minimum energy states and multi-stability in nonlocal advection–diffusion models for interacting species
Download2022-06-13
Valeria Giunta, Thomas Hillen, Mark A. Lewis, Jonathan R. Potts
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations, these emergent patterns sometimes appear as local minimisers of a corresponding energy functional. Here we give methods for determining the...
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2023-06-06
Applied Functional Analysis is a branch of mathematics that lies at the intersection of pure mathematics and practical applications to real world problems. It explores the deep an intricate structures of function spaces, often infinite dimensional, and the mappings between them. This text...
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2021-01-01
Valeria Giunta, Thomas Hillen, Mark A. Lewis, Jonathan R. Potts
Non-local advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has been increasing attention on modelling non-local advection mathematically. These often take the form of partial...
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2021-06-11
Valeria Giunta, Thomas Hillen, Mark A. Lewis, Jonathan R. Potts
Non-local advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has been increasing attention on modelling non-local advection mathematically. These often take the form of partial...
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2023-01-30
Thomas Hillen, Alexandra Shyntar
Cancer stem cells (CSCs) are pluripotent cancer cells, which are less sensitive to treatments, and which can generate new tumors once transplanted into a healthy tissue environment. They have been identified in many cancers and they are the driving force of cancer growth and metastasis....
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The “edge effect” phenomenon: deriving population abundance patterns from individual animal movement decisions
Download2016-01-01
Jonathan R. Potts, Thomas Hillen, Mark A. Lewis
Edge effects have been observed in a vast spectrum of animal populations. They occur where two conjoining habitats interact to create ecological phenomena that are not present in either habitat separately. On the individuallevel, an edge effect is a change in behavioral tendency on or near the...