52 research outputs found
A Central Partition of Molecular Conformational Space.III. Combinatorial Determination of the Volume Spanned by a Molecular System
In the first work of this series [physics/0204035] it was shown that the
conformational space of a molecule could be described to a fair degree of
accuracy by means of a central hyperplane arrangement. The hyperplanes divide
the espace into a hierarchical set of cells that can be encoded by the face
lattice poset of the arrangement. The model however, lacked explicit rotational
symmetry which made impossible to distinguish rotated structures in
conformational space. This problem was solved in a second work
[physics/0404052] by sorting the elementary 3D components of the molecular
system into a set of morphological classes that can be properly oriented in a
standard 3D reference frame. This also made possible to find a solution to the
problem that is being adressed in the present work: for a molecular system
immersed in a heat bath we want to enumerate the subset of cells in
conformational space that are visited by the molecule in its thermal wandering.
If each visited cell is a vertex on a graph with edges to the adjacent cells,
here it is explained how such graph can be built
A second look at the toric h-polynomial of a cubical complex
We provide an explicit formula for the toric -contribution of each cubical
shelling component, and a new combinatorial model to prove Clara Chan's result
on the non-negativity of these contributions. Our model allows for a variant of
the Gessel-Shapiro result on the -polynomial of the cubical lattice, this
variant may be shown by simple inclusion-exclusion. We establish an isomorphism
between our model and Chan's model and provide a reinterpretation in terms of
noncrossing partitions. By discovering another variant of the Gessel-Shapiro
result in the work of Denise and Simion, we find evidence that the toric
-polynomials of cubes are related to the Morgan-Voyce polynomials via
Viennot's combinatorial theory of orthogonal polynomials.Comment: Minor correction
Invariant Peano curves of expanding Thurston maps
We consider Thurston maps, i.e., branched covering maps
that are postcritically finite. In addition, we assume that is expanding in
a suitable sense. It is shown that each sufficiently high iterate of
is semi-conjugate to , where is equal to the
degree of . More precisely, for such an we construct a Peano curve
(onto), such that
(for all ).Comment: 63 pages, 12 figure
Quantum Symmetries and Strong Haagerup Inequalities
In this paper, we consider families of operators in
a tracial C-probability space , whose joint
-distribution is invariant under free complexification and the action of
the hyperoctahedral quantum groups . We prove a strong
form of Haagerup's inequality for the non-self-adjoint operator algebra
generated by , which generalizes the
strong Haagerup inequalities for -free R-diagonal families obtained by
Kemp-Speicher \cite{KeSp}. As an application of our result, we show that
always has the metric approximation property (MAP). We also apply
our techniques to study the reduced C-algebra of the free unitary
quantum group . We show that the non-self-adjoint subalgebra generated by the matrix elements of the fundamental corepresentation of
has the MAP. Additionally, we prove a strong Haagerup inequality for
, which improves on the estimates given by Vergnioux's property
RD \cite{Ve}
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