The fundamental germ is a generalization of π1, first defined for laminations which arise through group actions [4]. In this paper, the fundamental germ is extended to any lamination having a dense leaf admitting a smooth structure. In addition, an amplification of the fundamental germ called the mother germ is constructed, which is, unlike the fundamental germ, a topological invariant. The fun...

The macaque lateral geniculate nucleus (LGN) exhibits an intricate lamination pattern, which changes midway through the nucleus at a point coincident with small gaps due to the blind spot in the retina. We present a three-dimensional model of morphogenesis in which local cell interactions cause a wave of development of neuronal receptive fields to propagate through the nucleus and establish two...

We study the space of all continuous fuzzy-valued functions  from a space $X$ into the space of fuzzy numbers $(mathbb{E}sp{1},dsb{infty})$  endowed with the pointwise convergence topology.   Our results generalize the classical ones for  continuous real-valued functions.   The field of applications of this approach seems to be large, since the classical case  allows many known devices to be fi...

Classical invariant theory has died and been resurrected many times. Its golden age in the last century was marked with the flowering of unsurpassed computational ability, and the explicit determination of the invariants of most of the elementary polynomials. The computational approach is commonly acknowledged to have been dealt a death-blow by Hilbert’s celebrated Basis Theorem, an existential...

Powerset structures of extensional fuzzy sets in sets with similarity relations are investigated. It is proved that extensional fuzzy sets have powerset structures which are powerset theories in the category of sets with similarity relations, and some of these powerset theories are defined also by algebraic theories (monads). Between Zadeh's fuzzy powerset theory and the classical powerset theo...