4,032 research outputs found
On the quantum chromatic number of a graph
We investigate the notion of quantum chromatic number of a graph, which is
the minimal number of colours necessary in a protocol in which two separated
provers can convince an interrogator with certainty that they have a colouring
of the graph.
After discussing this notion from first principles, we go on to establish
relations with the clique number and orthogonal representations of the graph.
We also prove several general facts about this graph parameter and find large
separations between the clique number and the quantum chromatic number by
looking at random graphs.
Finally, we show that there can be no separation between classical and
quantum chromatic number if the latter is 2, nor if it is 3 in a restricted
quantum model; on the other hand, we exhibit a graph on 18 vertices and 44
edges with chromatic number 5 and quantum chromatic number 4.Comment: 7 pages, 1 eps figure; revtex4. v2 has some new references; v3 furthe
small improvement
Trades in complex Hadamard matrices
A trade in a complex Hadamard matrix is a set of entries which can be changed
to obtain a different complex Hadamard matrix. We show that in a real Hadamard
matrix of order all trades contain at least entries. We call a trade
rectangular if it consists of a submatrix that can be multiplied by some scalar
to obtain another complex Hadamard matrix. We give a
characterisation of rectangular trades in complex Hadamard matrices of order
and show that they all contain at least entries. We conjecture that all
trades in complex Hadamard matrices contain at least entries.Comment: 9 pages, no figure
Cascade Dynamics of Multiplex Propagation
Random links between otherwise distant nodes can greatly facilitate the
propagation of disease or information, provided contagion can be transmitted by
a single active node. However we show that when the propagation requires
simultaneous exposure to multiple sources of activation, called multiplex
propagation, the effect of random links is just the opposite: it makes the
propagation more difficult to achieve. We calculate analytical and numerically
critical points for a threshold model in several classes of complex networks,
including an empirical social network.Comment: 4 pages, 5 figures, for similar work visit http://hsd.soc.cornell.edu
and http://www.imedea.uib.es/physdep
Growth and form of the mound in Gale Crater, Mars: Slope wind enhanced erosion and transport
Ancient sediments provide archives of climate and habitability on Mars. Gale Crater, the landing site for the Mars Science Laboratory (MSL), hosts a 5-km-high sedimentary mound (Mount Sharp/Aeolis Mons). Hypotheses for mound formation include evaporitic, lacustrine, fluviodeltaic, and aeolian processes, but the origin and original extent of Galeâs mound is unknown. Here we show new measurements of sedimentary strata within the mound that indicate âŒ3° outward dips oriented radially away from the mound center, inconsistent with the first three hypotheses. Moreover, although mounds are widely considered to be erosional remnants of a once crater-filling unit, we find that the Gale moundâs current form is close to its maximal extent. Instead we propose that the moundâs structure, stratigraphy, and current shape can be explained by growth in place near the center of the crater mediated by wind-topography feedbacks. Our model shows how sediment can initially accrete near the crater center far from crater-wall katabatic winds, until the increasing relief of the resulting mound generates mound-flank slope winds strong enough to erode the mound. The slope wind enhanced erosion and transport (SWEET) hypothesis indicates mound formation dominantly by aeolian deposition with limited organic carbon preservation potential, and a relatively limited role for lacustrine and fluvial activity. Morphodynamic feedbacks between wind and topography are widely applicable to a range of sedimentary and ice mounds across the Martian surface, and possibly other planets
Identifying communities by influence dynamics in social networks
Communities are not static; they evolve, split and merge, appear and
disappear, i.e. they are product of dynamical processes that govern the
evolution of the network. A good algorithm for community detection should not
only quantify the topology of the network, but incorporate the dynamical
processes that take place on the network. We present a novel algorithm for
community detection that combines network structure with processes that support
creation and/or evolution of communities. The algorithm does not embrace the
universal approach but instead tries to focus on social networks and model
dynamic social interactions that occur on those networks. It identifies
leaders, and communities that form around those leaders. It naturally supports
overlapping communities by associating each node with a membership vector that
describes node's involvement in each community. This way, in addition to
overlapping communities, we can identify nodes that are good followers to their
leader, and also nodes with no clear community involvement that serve as a
proxy between several communities and are equally as important. We run the
algorithm for several real social networks which we believe represent a good
fraction of the wide body of social networks and discuss the results including
other possible applications.Comment: 10 pages, 6 figure
Stratospheric Data Analysis System (STRATAN)
A state of the art stratospheric analyses using a coupled stratosphere/troposphere data assimilation system is produced. These analyses can be applied to stratospheric studies of all types. Of importance to this effort is the application of the Stratospheric Data Analysis System (STRATAN) to constituent transport and chemistry problems
Sampling properties of random graphs: the degree distribution
We discuss two sampling schemes for selecting random subnets from a network:
Random sampling and connectivity dependent sampling, and investigate how the
degree distribution of a node in the network is affected by the two types of
sampling. Here we derive a necessary and sufficient condition that guarantees
that the degree distribution of the subnet and the true network belong to the
same family of probability distributions. For completely random sampling of
nodes we find that this condition is fulfilled by classical random graphs; for
the vast majority of networks this condition will, however, not be met. We
furthermore discuss the case where the probability of sampling a node depends
on the degree of a node and we find that even classical random graphs are no
longer closed under this sampling regime. We conclude by relating the results
to real {\it E.coli} protein interaction network data.Comment: accepted for publication in Phys.Rev.
Reciprocal and dynamic polarization of planar cell polarity core components and myosin
Citation: Newman-Smith, E., Kourakis, M. J., Reeves, W., Veeman, M., & Smith, W. C. (2015). Reciprocal and dynamic polarization of planar cell polarity core components and myosin. eLife, 2015(4). doi:10.7554/eLife.05361The Ciona notochord displays PCP-dependent polarity, with anterior localization of Prickle (Pk) and Strabismus (Stbm). We report that a myosin is polarized anteriorly in these cells and strongly colocalize with Stbm. Disruption of the actin/myosin machinery with cytochalasin or blebbistatin disrupts polarization of Pk and Stbm, but not of myosin complexes, suggesting a PCP-independent aspect of myosin localization. Washout of cytochalasin restored Pk polarization, but not if done in the presence of blebbistatin, suggesting an active role for myosin in core PCP protein localization. On the other hand, in the pk mutant line aimless myosin polarization in approximately one third of the cells, indicating a reciprocal action of core PCP signaling on myosin localization. Our results indicate a complex relationship between the actomyosin cytoskeleton and core PCP components in which myosin is not simply a downstream target of PCP signaling, but also required for PCP protein localization. © 2015, eLife. All rights reserved
Interfacial mixing in heteroepitaxial growth
We investigate the growth of a film of some element B on a substrate made of
another substrance A in a model of molecular beam epitaxy. A vertical exchange
mechanism allows the A-atoms to stay on the growing surface with a certain
probability. Using kinetic Monte Carlo simulations as well as scaling
arguments, the incorporation of the A's into the growing B-layer is
investigated. Moreover we develop a rate equation theory for this process. In
the limit of perfect layer-by-layer growth, the density of A-atoms decays in
the B-film like the inverse squared distance from the interface. The power law
is cut off exponentially at a characteristic thickness of the interdiffusion
zone that depends on the rate of exchange of a B-adatom with an A-atom in the
surface and on the system size. Kinetic roughening changes the exponents. Then
the thickness of the interdiffusion zone is determined by the diffusion length.Comment: 11 pages, 11 figure
Random Geometric Graphs
We analyse graphs in which each vertex is assigned random coordinates in a
geometric space of arbitrary dimensionality and only edges between adjacent
points are present. The critical connectivity is found numerically by examining
the size of the largest cluster. We derive an analytical expression for the
cluster coefficient which shows that the graphs are distinctly different from
standard random graphs, even for infinite dimensionality. Insights relevant for
graph bi-partitioning are included.Comment: 16 pages, 10 figures. Minor changes. Added reference
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