89 research outputs found
Colorings of simplicial complexes and vector bundles over Davis-Januszkiewicz spaces
We show that coloring properties of a simplicial complex K are reflected by
splitting properties of a bundle over the associated Davis-Januszkiewicz space
whose Chern classes are given by the elementary symmetric polynomials in the
generators of the Stanley-Reisner algebra of K.Comment: 8 page
On the integral cohomology of smooth toric varieties
Let be a smooth, not necessarily compact toric variety. We show
that a certain complex, defined in terms of the fan , computes the
integral cohomology of , including the module structure over the
homology of the torus. In some cases we can also give the product. As a
corollary we obtain that the cycle map from Chow groups to integral Borel-Moore
homology is split injective for smooth toric varieties. Another result is that
the differential algebra of singular cochains on the Borel construction of
is formal.Comment: 10 page
Graph products of spheres, associative graded algebras and Hilbert series
Given a finite, simple, vertex-weighted graph, we construct a graded
associative (non-commutative) algebra, whose generators correspond to vertices
and whose ideal of relations has generators that are graded commutators
corresponding to edges. We show that the Hilbert series of this algebra is the
inverse of the clique polynomial of the graph. Using this result it easy to
recognize if the ideal is inert, from which strong results on the algebra
follow. Non-commutative Grobner bases play an important role in our proof.
There is an interesting application to toric topology. This algebra arises
naturally from a partial product of spheres, which is a special case of a
generalized moment-angle complex. We apply our result to the loop-space
homology of this space.Comment: 19 pages, v3: elaborated on connections to related work, added more
citations, to appear in Mathematische Zeitschrif
Dense active matter model of motion patterns in confluent cell monolayers
Epithelial cell monolayers show remarkable displacement and velocity
correlations over distances of ten or more cell sizes that are reminiscent of
supercooled liquids and active nematics. We show that many observed features
can be described within the framework of dense active matter, and argue that
persistent uncoordinated cell motility coupled to the collective elastic modes
of the cell sheet is sufficient to produce swirl-like correlations. We obtain
this result using both continuum active linear elasticity and a normal modes
formalism, and validate analytical predictions with numerical simulations of
two agent-based cell models, soft elastic particles and the self-propelled
Voronoi model together with in-vitro experiments of confluent corneal
epithelial cell sheets. Simulations and normal mode analysis perfectly match
when tissue-level reorganisation occurs on times longer than the persistence
time of cell motility. Our analytical model quantitatively matches measured
velocity correlation functions over more than a decade with a single fitting
parameter.Comment: updated version accepted for publication in Nat. Com
Active wetting of epithelial tissues
Development, regeneration and cancer involve drastic transitions in tissue
morphology. In analogy with the behavior of inert fluids, some of these
transitions have been interpreted as wetting transitions. The validity and
scope of this analogy are unclear, however, because the active cellular forces
that drive tissue wetting have been neither measured nor theoretically
accounted for. Here we show that the transition between 2D epithelial
monolayers and 3D spheroidal aggregates can be understood as an active wetting
transition whose physics differs fundamentally from that of passive wetting
phenomena. By combining an active polar fluid model with measurements of
physical forces as a function of tissue size, contractility, cell-cell and
cell-substrate adhesion, and substrate stiffness, we show that the wetting
transition results from the competition between traction forces and contractile
intercellular stresses. This competition defines a new intrinsic lengthscale
that gives rise to a critical size for the wetting transition in tissues, a
striking feature that has no counterpart in classical wetting. Finally, we show
that active shape fluctuations are dynamically amplified during tissue
dewetting. Overall, we conclude that tissue spreading constitutes a prominent
example of active wetting --- a novel physical scenario that may explain
morphological transitions during tissue morphogenesis and tumor progression
Dinosaur peptides suggest mechanisms of protein survival
Eleven collagen peptide sequences recovered from chemical extracts of dinosaur bones were mapped onto molecular models of the vertebrate collagen fibril derived from extant taxa. The dinosaur peptides localized to fibril regions protected by the close packing of collagen molecules, and contained few acidic amino acids. Four peptides mapped to collagen regions crucial for cell-collagen interactions and tissue development. Dinosaur peptides were not represented in more exposed parts of the collagen fibril or regions mediating intermolecular cross-linking. Thus functionally significant regions of collagen fibrils that are physically shielded within the fibril may be preferentially preserved in fossils. These results show empirically that structure-function relationships at the molecular level could contribute to selective preservation in fossilized vertebrate remains across geological time, suggest a ‘preservation motif’, and bolster current concepts linking collagen structure to biological function. This non-random distribution supports the hypothesis that the peptides are produced by the extinct organisms and suggests a chemical mechanism for survival
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