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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 ...
Cell-based models are mathematical models that represent biological cells as discrete entities. Within the field of computational biology they are often simply called agent-based models [1] of which they are a specific application and they are used for simulating the biomechanics of multicellular structures such as tissues. to study the influence of these behaviors on how tissues are organised ...
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In graph theory, a branch of mathematics, a cycle basis of an undirected graph is a set of simple cycles that forms a basis of the cycle space of the graph. That is, it is a minimal set of cycles that allows every even-degree subgraph to be expressed as a symmetric difference of basis cycles.
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 ...
The G 1 phase, gap 1 phase, or growth 1 phase, is the first of four phases of the cell cycle that takes place in eukaryotic cell division. In this part of interphase , the cell synthesizes mRNA and proteins in preparation for subsequent steps leading to mitosis.
The state of each cell in a totalistic cellular automaton is represented by a number (usually an integer value drawn from a finite set), and the value of a cell at time t depends only on the sum of the values of the cells in its neighborhood (possibly including the cell itself) at time t − 1.
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 ...