1,681 research outputs found
Entire cyclic homology of continuous trace algebras
A central result here is the computation of the entire cyclic homology of
canonical smooth subalgebras of stable continuous trace C*-algebras having
smooth manifolds M as their spectrum. More precisely, the entire cyclic
homology is shown to be canonically isomorphic to the continuous periodic
cyclic homology for these algebras. By an earlier result of the authors, one
concludes that the entire cyclic homology of the algebra is canonically
isomorphic to the twisted de Rham cohomology of M.Comment: 7 pages, Latex2e, minor typos correcte
Crystallographic arrangements: Weyl groupoids and simplicial arrangements
We introduce the simple notion of a "crystallographic arrangement" and prove
a one-to-one correspondence between these arrangements and the connected simply
connected Cartan schemes for which the real roots are a finite root system (up
to equivalence on both sides). We thus obtain a more accessible definition for
this very large subclass of the class of simplicial arrangements for which a
complete classification is known.Comment: 13 page
The dendritic density field of a cortical pyramidal cell
Much is known about the computation in individual neurons in the cortical column. Also, the selective connectivity between many cortical neuron types has been studied in great detail. However, due to the complexity of this microcircuitry its functional role within the cortical column remains a mystery. Some of the wiring behavior between neurons can be interpreted directly from their particular dendritic and axonal shapes. Here, I describe the dendritic density field (DDF) as one key element that remains to be better understood. I sketch an approach to relate DDFs in general to their underlying potential connectivity schemes. As an example, I show how the characteristic shape of a cortical pyramidal cell appears as a direct consequence of connecting inputs arranged in two separate parallel layers
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