By Jürgen Jost
ISBN-10: 1447163524
ISBN-13: 9781447163527
ISBN-10: 1447163532
ISBN-13: 9781447163534
Mathematical types can be utilized to satisfy a number of the demanding situations and possibilities provided by means of smooth biology. the outline of organic phenomena calls for quite a number mathematical theories. this can be the case relatively for the rising box of structures biology. Mathematical Methods in Biology and Neurobiology introduces and develops those mathematical constructions and techniques in a scientific demeanour. It studies:
• discrete buildings and graph idea
• stochastic processes
• dynamical structures and partial differential equations
• optimization and the calculus of variations.
The organic purposes variety from molecular to evolutionary and ecological degrees, for example:
• mobile response kinetics and gene regulation
• organic trend formation and chemotaxis
• the biophysics and dynamics of neurons
• the coding of data in neuronal systems
• phylogenetic tree reconstruction
• branching tactics and inhabitants genetics
• optimum source allocation
• sexual recombination
• the interplay of species.
Written by way of the most skilled and profitable authors of complex mathematical textbooks, this booklet stands aside for the big variety of mathematical instruments which are featured. it will likely be precious for graduate scholars and researchers in arithmetic and physics that desire a accomplished assessment and a operating wisdom of the mathematical instruments that may be utilized in biology. it's going to even be invaluable for biologists with a few mathematical historical past that are looking to research extra in regards to the mathematical tools to be had to accommodate organic buildings and data.
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Additional resources for Mathematical Methods in Biology and Neurobiology
Sample text
This makes the systematics amenable to tree representations. Moreover, from the morphological approach underlying cladism that is based on paleontological data, any two species differ in the state of at least one character. 44 2 Discrete Structures 2. Convergence: In the same example, A1 , instead of keeping the state b, assumes the same state b that originated in the species A22 while A21 kept b. Of course, there exist biological examples for either possibility. Snakes have lost the limbs that their ancestors had gained.
Reversion: In the last example, A22 , instead of assuming the new state a , reverts to the ancestral state a. 10 It is a basic principle of cladism that whenever a new species splits off from some line, the remaining part of that line is also classified as a new species. This makes the systematics amenable to tree representations. Moreover, from the morphological approach underlying cladism that is based on paleontological data, any two species differ in the state of at least one character. 44 2 Discrete Structures 2.
This is an undesirable situation in phylogenetic tree reconstruction because the grouping of the four vertices into pairs is ambiguous. However, when we split off a single point from the remaining three, we get i δ (σ) > 0. The simplest example of a metric space admitting no splits at all with i δ (σ) > 0 is given by 5 points x, y, z, w, v with d(x, v) = d(y, z) = d(z, w) = d(y, w) = 2 and the other distances between different points all being one. To describe this metric space somewhat differently, we take the two sets A := {x, v}, B := {y, z, w} and connect each point in A with every point in B by an edge of length 1.
Mathematical Methods in Biology and Neurobiology by Jürgen Jost
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