749,553 research outputs found
Algebraic structures on graph cohomology
We define algebraic structures on graph cohomology and prove that they
correspond to algebraic structures on the cohomology of the spaces of
imbeddings of S^1 or R into R^n. As a corollary, we deduce the existence of an
infinite number of nontrivial cohomology classes in Imb(S^1,R^n) when n is even
and greater than 3. Finally, we give a new interpretation of the anomaly term
for the Vassiliev invariants in R^3.Comment: Typos corrected, exposition improved. 14 pages, 2 figures. To appear
in J. Knot Theory Ramification
The oriented graph of multi-graftings in the Fuchsian case
We prove the connectedness and calculate the diameter of the oriented graph
of graftings associated to exotic complex projective structures on a compact
surface S with a given holonomy representation of Fuchsian type.
The oriented graph of graftings is the graph whose vertices are the
equivalence classes of marked CP^1-structures on S with a given fixed holonomy,
and there is an oriented edge between two structures if the second is obtained
from the first by grafting.Comment: Improved version. The paper chaged title: from "The oriented graph of
graftings..." to "The oriented graph of multi-graftings...
An Owen-type value for games with two-level communication structures
We introduce an Owen-type value for games with two-level communication structures, being structures where the players are partitioned into a coalition structure such that there exists restricted communication between as well as within the a priori unions of the coalition structure. Both types of communication restrictions are modeled by an undirected communication graph, so there is a communication graph between the unions of the coalition structure as well as a communication graph on the players in every union. We also show that, for particular two-level communication structures, the Owen value and the Aumann-Drèze value for games with coalition structures, the Myerson value for communication graph games and the equal surplus division solution appear as special cases of this new value
Protein Evolution within a Structural Space
Understanding of the evolutionary origins of protein structures represents a
key component of the understanding of molecular evolution as a whole. Here we
seek to elucidate how the features of an underlying protein structural "space"
might impact protein structural evolution. We approach this question using
lattice polymers as a completely characterized model of this space. We develop
a measure of structural comparison of lattice structures that is analgous to
the one used to understand structural similarities between real proteins. We
use this measure of structural relatedness to create a graph of lattice
structures and compare this graph (in which nodes are lattice structures and
edges are defined using structural similarity) to the graph obtained for real
protein structures. We find that the graph obtained from all compact lattice
structures exhibits a distribution of structural neighbors per node consistent
with a random graph. We also find that subgraphs of 3500 nodes chosen either at
random or according to physical constraints also represent random graphs. We
develop a divergent evolution model based on the lattice space which produces
graphs that, within certain parameter regimes, recapitulate the scale-free
behavior observed in similar graphs of real protein structures.Comment: 27 pages, 7 figure
Spatial Logics for Bigraphs
Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, pi-calculus, and Petri nets. Bigraphs are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper-)graph for connections. With the aim of describing bigraphical structures, we introduce a general framework for logics whose terms represent arrows in monoidal categories. We then instantiate the framework to bigraphical structures and obtain a logic that is a natural composition of a place graph logic and a link graph logic. We explore the concepts of separation and sharing in these logics and we prove that they generalise some known spatial logics for trees, graphs and tree contexts
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