The mechanism by which neuronal networks dynamically organize and differentiate during development is a salient issue concerning neurogenesis. This central event reflects a topological order and its metrizability. One important parameter in this process concerns the role of tremor and intrinsic electrical properties of neurons [Llinàs 1988] from a different in the developmental organization of ...

Let V be a valuation domain of rank one with quotient field K. We study the set extensions to rational functions K(X) induced by pseudo-convergent sequences K from topological point view, endowing this either Zariski or constructible topology. In particular, we consider two subspaces prescribed breadth pseudo-limit. give some necessary conditions for space metrizable (under topology) in terms v...

We show that every connected graph can be approximated by a normal tree, up to some arbitrarily small error phrased in terms of neighbourhoods around its ends. The existence such approximate trees has consequences both combinatorial and topological nature. On the side, we spanning tree as soon it locally at each end; i.e., only obstruction for having is an end which none tree. space ?(G), well ...

We investigate the local metrizability of Finsler spaces with $m$-Kropina metric $F = \alpha^{1+m}\beta^{-m}$, where $\beta$ is a closed null 1-form. show that such space Berwald type if and only (pseudo-)Riemannian $\alpha$ 1-form have very specific form in certain coordinates. In particular, when signature Lorentzian, belongs to subclass Kundt class generates corresponding congruence, this ge...