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A k-deformed Model of Growing Complex Networks with Fitness
Abstract: The Barab\'asi-Bianconi (BB) fitness model can be solved by a mapping between
the original network growth model to an idealized bosonic gas. The well-known
transition to Bose-Einstein condensation in the latter then corresponds to the
emergence of "super-hubs" in the network model. Motivated by the preservation
of the scale-free property, thermodynamic stability and self-duality, we
generalize the original extensive mapping of the BB fitness model by using the
nonextensive Kaniadakis k-distribution. Through numerical simulation and
mean-field calculations we show that deviations from extensivity do not
compromise qualitative features of the phase transition. Analysis of the
critical temperature yields a monotonically decreasing dependence on the
nonextensive parameter k.
Statistical Mechanics (cond-mat.stat-mech)
[cond-mat.stat-mech]
[cond-mat.stat-mech] for this version)
Submission history
From: Massimo Stella []
[v1] Sat, 12 Apr :11 GMTAll papers
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Violations of Lorentz invariance in the neutrino sector: an improved
analysis of anomalous threshold constraints
(DESY, LMU and MPP),
(SISSA and INFN Trieste),
(University of New Hampshire)
Abstract: Recently there has been a renewed activity in the physics of violations of
Lorentz invariance in the neutrino sector. Flavor dependent Lorentz violation,
which generically changes the pattern of neutrino oscillations, is extremely
tightly constrained by oscillation experiments. Flavor independent Lorentz
violation, which does not introduce new oscillation phenomena, is much more
weakly constrained with constraints coming from time of flight and anomalous
threshold analyses. We use a simplified rotationally invariant model to
investigate the effects of finite baselines and energy dependent dispersion on
anomalous reaction rates in long baseline experiments and show numerically that
anomalous reactions do not necessarily cut off the spectrum quite as sharply as
currently assumed. We also present a revised analysis of how anomalous
reactions can be used to cast constraints from the observed atmospheric high
energy neutrinos and the expected cosmogenic ones.
High Energy Physics - Phenomenology (hep-ph)
Journal&reference:
Report&number:
DESY 11-172, LMU-ASC 20/13, MPP-
[hep-ph] for this version)
Submission history
From: Luca Maccione []
Tue, 4 Oct :55 GMT
Tue, 20 Mar :59 GMT
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, 15 April 2015, Pages
Unitary groups and spectral sets, , , , a University of Central Florida, Department of Mathematics, 4000 Central Florida Blvd., P.O. Box 161364, Orlando, FL , USAb University of Iowa, Department of Mathematics, 14 MacLean Hall, Iowa City, IA , USAWe study spectral theory for bounded Borel subsets of RR and in particular finite unions of intervals. For Hilbert space, we take L2L2 of the union of the intervals. This yields a boundary value problem arising from the minimal operator D=12πiddx with domain consisting of C&C& functions vanishing at the endpoints. We offer a detailed interplay between geometric configurations of unions of intervals and a spectral theory for the corresponding self-adjoint extensions of DD and for the associated unitary groups of local translations. While motivated by scattering theory and quantum graphs, our present focus is on the Fuglede-spectral pair problem. Stated more generally, this problem asks for a determination of those bounded Borel sets Ω   in RkRk such that L2(Ω)L2(Ω) has an orthogonal basis of Fourier frequencies (spectrum), i.e., a total set of orthogonal complex exponentials restricted to Ω. In the general case, we characterize Borel sets Ω   having this spectral property in terms of a unitary representation of (R,+)(R,+) acting by local translations. The case of k=1k=1 is of special interest, hence the interval-configurations. We give a characterization of those geometric interval-configurations which allow Fourier spectra directly in terms of the self-adjoint extensions of the minimal operator DD. This allows for a direct and explicit interplay between geometry and spectra.MSCprimary, 47B25, 47B15, 47B32, 47B40, 43A70, 34K08; secondary, 35P25, 58J50KeywordsFuglede conjecture; Self-adjoint extensions; Unitary one-parameter groups
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