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In computational biology, a Cellular Potts model (CPM, also known as the Glazier-Graner-Hogeweg model) is a computational model of cells and tissues. It is used to simulate individual and collective cell behavior, tissue morphogenesis and cancer development.
Let _ be an outermorphism. We define the adjoint of ¯ to be the outermorphism that satisfies the property ¯ = _ for all vectors and , where is the nondegenerate symmetric bilinear form (scalar product of vectors).
An example of this process is where the anteroposterior axis (the axis drawn between the head and tail end of an embryo) becomes longer as the lateral tissues (those that make up the left and right sides of the embryo) move in towards the dorsal midline (the middle of the back of the animal). [1]
The figure on the right illustrates several ideas about LSM. In the upper left corner is a bounded region with a well-behaved boundary. Below it, the red surface is the graph of a level set function φ {\displaystyle \varphi } determining this shape, and the flat blue region represents the X-Y plane.
Morphogenesis (from the Greek morphê shape and genesis creation, literally "the generation of form") is the biological process that causes a cell, tissue or organism to develop its shape.
Biological thermodynamics (Thermodynamics of biological systems) is a science that explains the nature and general laws of thermodynamic processes occurring in living organisms as nonequilibrium thermodynamic systems that convert the energy of the Sun and food into other types of energy.
A simple configuration in von Neumann's cellular automaton. A binary signal is passed repeatedly around the blue wire loop, using excited and quiescent ordinary transmission states.
The value of λ for the logistic map at r = 4 can be calculated precisely, and its value is λ = log 2 . Although a strict mathematical definition of chaos has not yet been unified, it can be shown that the logistic map with r = 4 is chaotic on [0, 1] according to one well-known definition of chaos . Graph of the invariant measure ρ(x) for r = 4.