Ignoring physicochemical mechanisms, the signal dynamics discussed above can be mathematically modelled based on simple uniformly decelerated motion, which is a special case of uniformly accelerated motion, but with a negative acceleration rate (i.e., a deceleration rate).
This question arises because long-range signalling for developmental determination that travels according to a simple, uniformly decelerated type of motion is currently unknown in developmental biology.
Importantly, Hesslow and colleagues have shown in decerebrate ferrets that Purkinje cells with reliable short-latency complex spike responses to the ipsilateral US quite uniformly acquire suppressive simple spike responses with properties that are very similar to behavioral CRs (Hesslow and Ivarsson, 1994, Jirenhed et al., 2007, Wetmore et al., 2014).
The following corollary is related to the simplest uniformly Lipschitzian semigroup defined in Definition 3.2.
The simplest uniformly G1-Lipschitzian semigroup is a semigroup of iterates of a mapping whenever and with.
for each and,, ( 0. The simplest uniformly G3-Lipschitzian semigroup is a semigroup of iterates of a mapping with.
The method of matched asymptotic expansions yields simpler, uniformly valid approximations as series of inverse even powers of ϵ that converge very rapidly for the large values of ϵ(ϵ>40) appropriate for geophysical vortex computations.
Finally, unless empirical evidence suggested otherwise, we kept the simplest (uniformly assigned) values of the parameters and did not try to match empirical data by fine tuning the parameters.
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The known observation sites are either on a 2D grid (including a case of "very non-uniform" grid spacings) or randomly uniformly distributed on a simple 2D region.
