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for an efficient and systematic search of multistationarity based on the deficiency criterion. First , we search for the kinetic rate constants and steady state concentrations such that the conditions for a saddle ...
and the nonlinear friction. This scaling is the so-called diffusion scaling for kinetic equations; see Bouchut et al. (2000) and Degond et al. (2000) and the references therein. We remark that for the particular ...
obstacles: First , in a cortical column the number of neurons of the same type is small (50–2000 [3]) and hence far from the N → ∞ limit of classic “macroscopic” theories in which fluctuations vanish [14, 36 ...
in strain rates will eventually result in geometrical changes to the organ structure. In order to evaluate whether growth mechanisms allow for stable root growth we therefore reformulate the previously ...
–Bashforth scheme [47] to obtain a second- order accurate explicit approximation (3) where ∇Wij is the gradient of the kernel function and dij is the distance between the i and j particles. The PPE ...
], they are not yet well-developed and generally applicable. However, if we choose the exponential kernel , then we can readily invert the convolution to obtain a second order ODE and thus reduce Eq (7) to an ODE ...
+ f(u), \end{align}$$(1.2) where |$d>0$| is the diffusion coefficient and |$f(u)$| is the nonlinear reaction term. For the fractional order |$\gamma =1$|, (1.2) becomes the classical reaction diffusion ...
Abstract Relaxed random walk (RRW) models of trait evolution introduce branch-specific rate multipliers to modulate the variance of a standard Brownian diffusion process along a phylogeny and more ...
= 60. Diffusion map was run using the following parameters: no_dims = 4, t = 1, and sigma = 1000. Kernel PCA was run with a parameter for computing the “poly” and “gaussian” kernel of 0.1. Only the first ...
-velo we take a different approach, which does not decompose the gene-wise velocity components in the first place but, similarly to velocyto, relies on strongly simplifying assumptions on the kinetic rate ...
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