Biology and other natural sciences
25 ideas in this subject. The map below lists the main ideas of the subject by area, in teaching order. 1 of its 148 ideas have a page so far.
Start here
- ConceptTopological index
The topological index of an elliptic operator on a closed manifold is an integer built only from topological data. These data are the K-theory class of the principal symbol and the characteristic classes of the manifold. Atiyah and Singer defined it by pushing the symbol class forward along an embedding of the manifold into a Euclidean space. Their index theorem states that it equals the analytic index. In cohomology it is an integral of the Chern character of the symbol times the Todd class.
Map of the subject
General notions 0 of 3
- mathematical biology concept
- population dynamics concept
- population model concept
Single-species population growth 0 of 10
- Malthusian growth model definition
- logistic growth equation definition
- carrying capacity definition
- Gompertz growth model definition
- Allee effect concept
- Ricker model definition
- Beverton–Holt model definition
- Mackey–Glass equation definition
- maximum sustainable yield statement
- metapopulation model of Levins definition
Structured populations and demography 0 of 6
- Leslie matrix definition
- stable age distribution statement
- matrix population model concept
- Euler–Lotka equation statement
- McKendrick–von Foerster equation definition
- mark and recapture estimation definition
Interacting species 0 of 14
- Lotka–Volterra equations definition
- Volterra's principle statement
- competitive Lotka–Volterra equations definition
- generalized Lotka–Volterra equation definition
- competitive exclusion principle statement
- Holling functional response definition
- paradox of enrichment statement
- Nicholson–Bailey model definition
- food web concept
- ecological stability concept
- diversity index definition
- unified neutral theory of biodiversity concept
- Ewens's sampling formula statement
- theory of island biogeography concept
Epidemiology 0 of 12
- compartmental models in epidemiology concept
- SIR model definition
- SIS and SEIR models definition
- Kermack–McKendrick theory statement
- basic reproduction number definition
- next-generation matrix definition
- threshold theorem of epidemiology statement
- final size equation statement
- herd immunity threshold statement
- Reed–Frost model definition
- Ross–Macdonald model of malaria definition
- mathematical modelling of infectious diseases concept
Population genetics 0 of 28
- population genetics concept
- Hardy–Weinberg principle statement
- linkage disequilibrium definition
- genetic drift concept
- Wright–Fisher model definition
- Moran process definition
- effective population size definition
- fixation probability definition
- Kimura's diffusion approximation statement
- Fisher's fundamental theorem of natural selection statement
- Price equation statement
- Hamilton's rule statement
- Fisher's principle statement
- mutation–selection balance statement
- infinite alleles model definition
- infinite sites model definition
- coalescent theory concept
- Kingman's coalescent definition
- Watterson estimator definition
- Tajima's D definition
- Muller's ratchet concept
- quasispecies model definition
- error threshold statement
- fitness landscape concept
- NK model definition
- heritability definition
- breeder's equation statement
- evolutionary graph theory concept
Phylogenetics 0 of 15
- phylogenetic tree definition
- computational phylogenetics concept
- number of rooted binary phylogenetic trees statement
- maximum parsimony definition
- long branch attraction counterexample
- neighbor joining definition
- UPGMA definition
- four-point condition for tree metrics statement
- substitution model definition
- models of DNA evolution concept
- Jukes–Cantor model definition
- Felsenstein's pruning algorithm definition
- Robinson–Foulds metric definition
- phylogenetic network definition
- birth–death model of speciation definition
Sequence analysis and molecular structure 0 of 9
- sequence alignment concept
- Needleman–Wunsch algorithm definition
- Smith–Waterman algorithm definition
- substitution matrix definition
- multiple sequence alignment problem
- Nussinov algorithm definition
- nucleic acid structure prediction problem
- protein folding problem problem
- HP lattice model of proteins definition
Neurons and neural networks 0 of 15
- biological neuron model concept
- Hodgkin–Huxley model definition
- FitzHugh–Nagumo model definition
- Morris–Lecar model definition
- Hindmarsh–Rose model definition
- integrate-and-fire model definition
- cable equation definition
- Goldman equation statement
- Nernst equation statement
- Wilson–Cowan model definition
- Hopfield network definition
- Hebbian learning concept
- Oja's rule statement
- BCM theory definition
- perceptron definition
Biological rhythms and physiology 0 of 8
- Kuramoto model definition
- phase response curve definition
- Windkessel model definition
- multi-compartment model in pharmacokinetics definition
- Keller–Segel model of chemotaxis definition
- French flag model concept
- L-system definition
- phyllotaxis and the golden angle statement
Biochemical kinetics and systems biology 0 of 10
- Michaelis–Menten kinetics statement
- quasi-steady-state approximation statement
- Hill equation definition
- Monod equation definition
- chemostat model definition
- gene regulatory network concept
- Boolean network definition
- biochemical systems theory concept
- metabolic control analysis concept
- flux balance analysis definition
Chemical kinetics and reaction networks 0 of 11
- law of mass action statement
- rate equation definition
- Arrhenius equation statement
- chemical reaction network theory concept
- deficiency zero theorem statement
- global attractor conjecture conjecture
- chemical master equation definition
- Gillespie algorithm definition
- Brusselator example
- Oregonator example
- Belousov–Zhabotinsky reaction example
Chemical graph theory 1 of 7
- chemical graph theory concept
- Topological index definition
- Wiener index definition
- Hosoya index definition
- Randić index definition
- Hückel method definition
- fullerene graph object