23,816 research outputs found
Application of artificial intelligence for Euler solutions clustering
International audienceResults of Euler deconvolution strongly depend on the selection of viable solutions. Synthetic calculations using multiple causative sources show that Euler solutions cluster in the vicinity of causative bodies even when they do not group densely about the perimeter of the bodies. We have developed a clustering technique to serve as a tool for selecting appropriate solutions. The clustering technique uses a methodology based on artificial intelligence, and it was originally designed to classify large data sets. It is based on a geometrical approach to study object concentration in a finite metric space of any dimension. The method uses a formal definition of cluster and includes free parameters that search for clusters of given properties. Tests on synthetic and real data showed that the clustering technique successfully outlines causative bodies more accurately than other methods used to discriminate Euler solutions. In complex field cases, such as the magnetic field in the Gulf of Saint Malo region (Brittany, France), the method provides dense clusters, which more clearly outline possible causative sources. In particular, it allows one to trace offshore the main inland tectonic structures and to study their interrelationships in the Gulf of Saint Malo. The clusters provide solutions associated with particular bodies, or parts of bodies, allowing the analysis of different clusters of Euler solutions separately. This may allow computation of average parameters for individual causative bodies. Those measurements of the anomalous field that yield clusters also form dense clusters themselves. Application of this clustering technique thus outlines areas where the influence of different causative sources is more prominent. This allows one to focus on these areas for more detailed study, using different window sizes, structural indices, etc
Clustered Graph Coloring and Layered Treewidth
A graph coloring has bounded clustering if each monochromatic component has
bounded size. This paper studies clustered coloring, where the number of colors
depends on an excluded complete bipartite subgraph. This is a much weaker
assumption than previous works, where typically the number of colors depends on
an excluded minor. This paper focuses on graph classes with bounded layered
treewidth, which include planar graphs, graphs of bounded Euler genus, graphs
embeddable on a fixed surface with a bounded number of crossings per edge,
amongst other examples. Our main theorem says that for fixed integers ,
every graph with layered treewidth at most and with no subgraph
is -colorable with bounded clustering. In the case, which
corresponds to graphs of bounded maximum degree, we obtain polynomial bounds on
the clustering. This greatly improves a corresponding result of Esperet and
Joret for graphs of bounded genus. The case implies that every graph with
a drawing on a fixed surface with a bounded number of crossings per edge is
5-colorable with bounded clustering. Our main theorem is also a critical
component in two companion papers that study clustered coloring of graphs with
no -subgraph and excluding a fixed minor, odd minor or topological
minor
Non-linear dark energy clustering
We consider a dark energy fluid with arbitrary sound speed and equation of
state and discuss the effect of its clustering on the cold dark matter
distribution at the non-linear level. We write the continuity, Euler and
Poisson equations for the system in the Newtonian approximation. Then, using
the time renormalization group method to resum perturbative corrections at all
orders, we compute the total clustering power spectrum and matter power
spectrum. At the linear level, a sound speed of dark energy different from that
of light modifies the power spectrum on observationally interesting scales,
such as those relevant for baryonic acoustic oscillations. We show that the
effect of varying the sound speed of dark energy on the non-linear corrections
to the matter power spectrum is below the per cent level, and therefore these
corrections can be well modelled by their counterpart in cosmological scenarios
with smooth dark energy. We also show that the non-linear effects on the matter
growth index can be as large as 10-15 per cent for small scales.Comment: 33 pages, 7 figures. Improved presentation. References added. Matches
published version in JCA
Fluctuations in ballistic transport from Euler hydrodynamics
We propose a general formalism, within large deviation theory, giving access
to the exact statistics of fluctuations of ballistically transported conserved
quantities in homogeneous, stationary states. The formalism is expected to
apply to any system with an Euler hydrodynamic description, classical or
quantum, integrable or not, in or out of equilibrium. We express the exact
scaled cumulant generating function (or full counting statistics) for any
(quasi-)local conserved quantity in terms of the flux Jacobian. We show that
the "extended fluctuation relations" of Bernard and Doyon follow from the
linearity of the hydrodynamic equations, forming a marker of "freeness" much
like the absence of hydrodynamic diffusion does. We show how an extension of
the formalism gives exact exponential behaviours of spatio-temporal two-point
functions of twist fields, with applications to order-parameter dynamical
correlations in arbitrary homogeneous, stationary state. We explain in what
situations the large deviation principle at the basis of the results fail, and
discuss how this connects with nonlinear fluctuating hydrodynamics. Applying
the formalism to conformal hydrodynamics, we evaluate the exact cumulants of
energy transport in quantum critical systems of arbitrary dimension at low but
nonzero temperatures, observing a phase transition for Lorentz boosts at the
sound velocity.Comment: 27+22 pages, one figur
Defective and Clustered Graph Colouring
Consider the following two ways to colour the vertices of a graph where the
requirement that adjacent vertices get distinct colours is relaxed. A colouring
has "defect" if each monochromatic component has maximum degree at most
. A colouring has "clustering" if each monochromatic component has at
most vertices. This paper surveys research on these types of colourings,
where the first priority is to minimise the number of colours, with small
defect or small clustering as a secondary goal. List colouring variants are
also considered. The following graph classes are studied: outerplanar graphs,
planar graphs, graphs embeddable in surfaces, graphs with given maximum degree,
graphs with given maximum average degree, graphs excluding a given subgraph,
graphs with linear crossing number, linklessly or knotlessly embeddable graphs,
graphs with given Colin de Verdi\`ere parameter, graphs with given
circumference, graphs excluding a fixed graph as an immersion, graphs with
given thickness, graphs with given stack- or queue-number, graphs excluding
as a minor, graphs excluding as a minor, and graphs excluding
an arbitrary graph as a minor. Several open problems are discussed.Comment: This is a preliminary version of a dynamic survey to be published in
the Electronic Journal of Combinatoric
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