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An embedded graph uniquely defines cyclic orders of edges incident to the same vertex. The set of all these cyclic orders is called a rotation system.Embeddings with the same rotation system are considered to be equivalent and the corresponding equivalence class of embeddings is called combinatorial embedding (as opposed to the term topological embedding, which refers to the previous ...
Alternatively, if the edges of the graph have positive weights, the minimum weight cycle basis may be constructed in polynomial time. In planar graphs, the set of bounded cycles of an embedding of the graph forms a cycle basis. The minimum weight cycle basis of a planar graph corresponds to the Gomory–Hu tree of the dual graph.
The Hodgkin–Huxley model, or conductance-based model, is a mathematical model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear differential equations that approximates the electrical engineering characteristics of excitable cells such as neurons and muscle cells .
The eukaryotic cell cycle is very complex and is one of the most studied topics, since its misregulation leads to cancers. It is possibly a good example of a mathematical model as it deals with simple calculus but gives valid results. Two research groups [1] [2] have produced several models of the cell cycle simulating several organisms. They ...
The concept of a combinatorial map was introduced informally by J. Edmonds for polyhedral surfaces [2] which are planar graphs.It was given its first definite formal expression under the name "Constellations" by A. Jacques [3] [4] but the concept was already extensively used under the name "rotation" by Gerhard Ringel [5] and J.W.T. Youngs in their famous solution of the Heawood map-coloring ...
Compared to the eukaryotic cell cycle, the prokaryotic cell cycle (known as binary fission) is relatively simple and quick: the chromosome replicates from the origin of replication, a new membrane is assembled, and the cell wall forms a septum which divides the cell into two. [7]
Cell cycle analysis by DNA content measurement is a method that most frequently employs flow cytometry to distinguish cells in different phases of the cell cycle.Before analysis, the cells are usually permeabilised and treated with a fluorescent dye that stains DNA quantitatively, such as propidium iodide (PI) or 4,6-diamidino-2-phenylindole (DAPI).
A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell.