5,615 research outputs found
A faster algorithm for packing branchings in digraphs
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We consider the problem of finding an integral (and fractional) packing of branchings in a capacitated digraph with root-set demands. Schrijver described an algorithm that returns a packing with at most m + n(3) + r branchings that makes at most m(m + n3 + r) calls to an oracle that basically computes a minimum cut, where n is the number of vertices, m is the number of arcs and r is the number of root-sets of the input digraph. Leston-Rey and Wakabayashi described an algorithm that returns a packing with at most m + r - 1 branchings but makes a large number of oracle calls. In this work we provide an algorithm, inspired on ideas of Schrijver and in a paper of Gabow and Manu, that returns a packing with at most m+r 1 branchings and makes at most (m+r+2)n oracle calls. Moreover, for the arborescence packing problem our algorithm provides a packing with at most m n + 2 arborescences - thus improving the bound of m of Leston-Rey and Wakabayashi - and makes at most (m - n+5)n oracle calls. (C) 2015 Elsevier B.V. All rights reserved.We consider the problem of finding an integral (and fractional) packing of branchings in a capacitated digraph with root-set demands. Schrijver described an algorithm that returns a packing with at most m + n(3) + r branchings that makes at most m(m + n3194121131CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CNPq [301310/2005-0]CNPq [473867/2010-9, 477692/2012-5]301310/2005-0; 473867/2010-9; 477692/2012-5Wewould like to thank the reviewers for the careful reading of a previous version of this paper and for several suggestions that improved the presentation of the final version. The first author’s research was supported by Bolsa de Produtividade do CNPq P
Some properties of synchrotron radio and inverse-Compton gamma-ray images of supernova remnants
The synchrotron radio maps of supernova remnants (SNRs) in uniform
interstellar medium and interstellar magnetic field (ISMF) are analyzed,
allowing different `sensitivity' of injection efficiency to the shock
obliquity. The very-high energy gamma-ray maps due to inverse Compton process
are also synthesized. The properties of images in these different wavelength
bands are compared, with particular emphasis on the location of the bright
limbs in bilateral SNRs. Recent H.E.S.S. observations of SN 1006 show that the
radio and IC gamma-ray limbs coincide, and we found that this may happen if: i)
injection is isotropic but the variation of the maximum energy of electrons is
rather quick to compensate for differences in magnetic field; ii) obliquity
dependence of injection (either quasi-parallel or quasi-perpendicular) and the
electron maximum energy is strong enough to dominate magnetic field variation.
In the latter case, the obliquity dependence of the injection and the maximum
energy should not be opposite. We argue that the position of the limbs alone
and even their coincidence in radio, X-rays and gamma-rays, as it is discovered
by H.E.S.S. in SN 1006, cannot be conclusive about the dependence of the
electron injection efficiency, the compression/amplification of ISMF and the
electron maximum energy on the obliquity angle.Comment: Accepted for publication in MNRA
-anti-circulant digraphs are -diperfect and BE-diperfect
Let be a digraph. A subset of is a stable set if every pair of
vertices in is non-adjacent in . A collection of disjoint paths
of is a path partition of , if every vertex in
is exactly on a path of . We say that a stable set and a path
partition are orthogonal if each path of contains exactly one
vertex of . A digraph satisfies the -property if for every
maximum stable set of , there exists a path partition such
that and are orthogonal. A digraph is -diperfect
if every induced subdigraph of satisfies the -property. In 1982,
Claude Berge proposed a characterization for -diperfect digraphs in
terms of forbidden anti-directed odd cycles. In 2018, Sambinelli, Silva and Lee
proposed a similar conjecture. A digraph satisfies the Begin-End-property
or BE-property if for every maximum stable set of , there exists a path
partition such that (i) and are orthogonal and
(ii) for each path , either the start or the end of
belongs to . A digraph is BE-diperfect if every induced subdigraph of
satisfies the BE-property. Sambinelli, Silva and Lee proposed a
characterization for BE-diperfect digraphs in terms of forbidden blocking odd
cycles. In this paper, we verified both conjectures for -anti-circulant
digraphs. We also present some structural results for -diperfect and
BE-diperfect digraphs.Comment: arXiv admin note: substantial text overlap with arXiv:2111.1216
Mach-Zehnder Interferometry in a Strongly Driven Superconducting Qubit
We demonstrate Mach-Zehnder-type interferometry in a superconducting flux
qubit. The qubit is a tunable artificial atom, whose ground and excited states
exhibit an avoided crossing. Strongly driving the qubit with harmonic
excitation sweeps it through the avoided crossing two times per period. As the
induced Landau-Zener transitions act as coherent beamsplitters, the accumulated
phase between transitions, which varies with microwave amplitude, results in
quantum interference fringes for n=1...20 photon transitions. The
generalization of optical Mach-Zehnder interferometry, performed in qubit phase
space, provides an alternative means to manipulate and characterize the qubit
in the strongly-driven regime.Comment: 14 pages, 6 figure
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