Brain cells are not spherical. The basal metabolic rate (B) of a spherical cell scales as B approximately r2, where r is the radius of the cell; that of a brain cell scales as B approximately r(d), where r is the characteristic radius of the cell and d is the fractal dimensionality of its contour. The fractal geometry of the cell leads to a 4/5 allometric scaling law for human brain, uniquely e...

We have developed a performance prediction model for non-bonded interaction computations in molecular dynamics simulations, thereby predicting the optimal cell dimension in a linked-list cell method. The model expresses computation time in terms of the number and unit computation time of key operations. The model accurately estimates the number of operations during the simulations with the maxi...

 In this paper, a new homological dimension of modules, copresented dimension, is defined. We study some basic properties of this homological dimension. Some ring extensions are considered, too. For instance, we prove that if $Sgeq R$ is a finite normalizing extension and $S_R$ is a projective module, then for each right $S$-module $M_S$, the copresented dimension of $M_S$ does not exceed the c...

We show that for an algebraic reductive group G , the partition of a double Schubert cell in the flag variety G/B defined by Deodhar, and coming from a Bialynicki-Birula decomposition, is not a stratification in general. We give a counterexample for a group of type Bn, where the closure of some specific cell of dimension 2n has a non-trivial intersection with a cell of dimension 3n − 3.

We consider completely invariant subsets A of weakly expanding piecewise monotonic transformations T on [0, 1]. It is shown that the upper box dimension of A is bounded by the minimum tA of all parameters t for which a t-conformal measure with support A exists. In particular, this implies equality of box dimension and Hausdorff dimension of A.