50,272 research outputs found
Statistical Self-Similar Properties of Complex Networks
It has been shown that many complex networks shared distinctive features,
which differ in many ways from the random and the regular networks. Although
these features capture important characteristics of complex networks, their
applicability depends on the type of networks. To unravel ubiquitous
characteristics that complex networks may have in common, we adopt the
clustering coefficient as the probability measure, and present a systematic
analysis of various types of complex networks from the perspective of
statistical self-similarity. We find that the probability distribution of the
clustering coefficient is best characterized by the multifractal; moreover, the
support of the measure had a fractal dimension. These two features enable us to
describe complex networks in a unified way; at the same time, offer unforeseen
possibilities to comprehend complex networks.Comment: 11 pages, 4 figure
A non-hyponormal operator generating Stieltjes moment sequences
A linear operator in a complex Hilbert space \hh for which the set
\dzn{S} of its -vectors is dense in \hh and is a Stieltjes moment sequence for every f \in \dzn{S}
is said to generate Stieltjes moment sequences. It is shown that there exists a
closed non-hyponormal operator which generates Stieltjes moment sequences.
What is more, \dzn{S} is a core of any power of . This is
established with the help of a weighted shift on a directed tree with one
branching vertex. The main tool in the construction comes from the theory of
indeterminate Stieltjes moment sequences. As a consequence, it is shown that
there exists a non-hyponormal composition operator in an -space (over a
-finite measure space) which is injective, paranormal and which
generates Stieltjes moment sequences. In contrast to the case of abstract
Hilbert space operators, composition operators which are formally normal and
which generate Stieltjes moment sequences are always subnormal (in fact
normal). The independence assertion of Barry Simon's theorem which
parameterizes von Neumann extensions of a closed real symmetric operator with
deficiency indices is shown to be false
Stability boundaries of roll and square convection in binary fluid mixtures with positive separation ratio
Rayleigh-B\'{e}nard convection in horizontal layers of binary fluid mixtures
heated from below with realistic horizontal boundary conditions is studied
theoretically using multi-mode Galerkin expansions. For positive separation
ratios the main difference between the mixtures and pure fluids lies in the
existence of stable three dimensional patterns near onset in a wide range of
the parameter space. We evaluated the stationary solutions of roll, crossroll,
and square convection and we determined the location of the stability
boundaries for many parameter combinations thereby obtaining the Busse balloon
for roll and square patterns.Comment: 19 pages + 15 figures, accepted by Journal of Fluid Mechanic
Track clustering with a quantum annealer for primary vertex reconstruction at hadron colliders
Clustering of charged particle tracks along the beam axis is the first step
in reconstructing the positions of hadronic interactions, also known as primary
vertices, at hadron collider experiments. We use a 2036 qubit D-Wave quantum
annealer to perform track clustering in a limited capacity on artificial events
where the positions of primary vertices and tracks resemble those measured by
the Compact Muon Solenoid experiment at the Large Hadron Collider. The
algorithm, which is not a classical-quantum hybrid but relies entirely on
quantum annealing, is tested on a variety of event topologies from 2 primary
vertices and 10 tracks up to 5 primary vertices and 15 tracks. It is
benchmarked against simulated annealing executed on a commercial CPU
constrained to the same processor time per anneal as time in the physical
annealer, and performance is found to be comparable for small numbers of
vertices with an intriguing advantage noted for 2 vertices and 16 tracks
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