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If a graph is embedded on a closed surface , the complement of the union of the points and arcs associated with the vertices and edges of is a family of regions (or faces). [3] A 2-cell embedding , cellular embedding or map is an embedding in which every face is homeomorphic to an open disk. [ 4 ]
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 ...
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 signals have a split of 30 seconds and a cycle length of 60 second. With this information, it is a simple matter of iteration of equations (1) for all the cells and time steps. Figure 3 and Table 1 shows the spatial and temporal distribution of density for the case of offset=0 seconds.
Cell synchronization is a process by which cells in a culture at different stages of the cell cycle are brought to the same phase. Cell synchrony is a vital process in the study of cells progressing through the cell cycle as it allows population-wide data to be collected rather than relying solely on single-cell experiments.
The hyper phosphorylation of Rb is considered the late G1 restriction point, after which the cell cannot go backwards in the cell cycle. At this point, E2F 1-3 proteins bind to DNA and transcribe Cyclin A and Cdc 6. [11] Cyclin-dependent kinase inhibitor 1B (CDKN1B), also known as p27, binds to and prevents the activation of CyclinE:Cdk2 by ...
Every graph has a cycle basis in which every cycle is an induced cycle. In a 3-vertex-connected graph, there always exists a basis consisting of peripheral cycles, cycles whose removal does not separate the remaining graph. [4] [5] In any graph other than one formed by adding one edge to a cycle, a peripheral cycle must be an induced cycle.
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.