7 research outputs found
On the spectral distribution of large weighted random regular graphs
McKay proved that the limiting spectral measures of the ensembles of
-regular graphs with vertices converge to Kesten's measure as
. In this paper we explore the case of weighted graphs. More
precisely, given a large -regular graph we assign random weights, drawn from
some distribution , to its edges. We study the relationship
between and the associated limiting spectral distribution
obtained by averaging over the weighted graphs. Among other results, we
establish the existence of a unique `eigendistribution', i.e., a weight
distribution such that the associated limiting spectral
distribution is a rescaling of . Initial investigations suggested
that the eigendistribution was the semi-circle distribution, which by Wigner's
Law is the limiting spectral measure for real symmetric matrices. We prove this
is not the case, though the deviation between the eigendistribution and the
semi-circular density is small (the first seven moments agree, and the
difference in each higher moment is ). Our analysis uses
combinatorial results about closed acyclic walks in large trees, which may be
of independent interest.Comment: Version 1.0, 19 page
The Phase-I Trigger Readout Electronics Upgrade of the ATLAS Liquid Argon Calorimeters
The Phase-I trigger readout electronics upgrade of the ATLAS Liquid Argon
calorimeters enhances the physics reach of the experiment during the upcoming
operation at increasing Large Hadron Collider luminosities. The new system,
installed during the second Large Hadron Collider Long Shutdown, increases the
trigger readout granularity by up to a factor of ten as well as its precision
and range. Consequently, the background rejection at trigger level is improved
through enhanced filtering algorithms utilizing the additional information for
topological discrimination of electromagnetic and hadronic shower shapes. This
paper presents the final designs of the new electronic elements, their custom
electronic devices, the procedures used to validate their proper functioning,
and the performance achieved during the commissioning of this system.Comment: 56 pages, 41 figures, 6 table
The Phase-I trigger readout electronics upgrade of the ATLAS Liquid Argon calorimeters
International audienceThe Phase-I trigger readout electronics upgrade of the ATLAS Liquid Argon calorimeters enhances the physics reach of the experiment during the upcoming operation at increasing Large Hadron Collider luminosities. The new system, installed during the second Large Hadron Collider Long Shutdown, increases the trigger readout granularity by up to a factor of ten as well as its precision and range. Consequently, the background rejection at trigger level is improved through enhanced filtering algorithms utilizing the additional information for topological discrimination of electromagnetic and hadronic shower shapes. This paper presents the final designs of the new electronic elements, their custom electronic devices, the procedures used to validate their proper functioning, and the performance achieved during the commissioning of this system
The Phase-I Trigger Readout Electronics Upgrade of the ATLAS Liquid Argon Calorimeters
The Phase-I trigger readout electronics upgrade of the ATLAS Liquid Argon calorimeters enhances the physics reach of the experiment during the upcoming operation at increasing Large Hadron Collider luminosities. The new system, installed during the second Large Hadron Collider Long Shutdown, increases the trigger readout granularity by up to a factor of ten as well as its precision and range. Consequently, the background rejection at trigger level is improved through enhanced filtering algorithms utilizing the additional information for topological discrimination of electromagnetic and hadronic shower shapes. This paper presents the final designs of the new electronic elements, their custom electronic devices, the procedures used to validate their proper functioning, and the performance achieved during the commissioning of this system