1,923 research outputs found
Silent MST approximation for tiny memory
In network distributed computing, minimum spanning tree (MST) is one of the
key problems, and silent self-stabilization one of the most demanding
fault-tolerance properties. For this problem and this model, a polynomial-time
algorithm with memory is known for the state model. This is
memory optimal for weights in the classic range (where
is the size of the network). In this paper, we go below this
memory, using approximation and parametrized complexity.
More specifically, our contributions are two-fold. We introduce a second
parameter~, which is the space needed to encode a weight, and we design a
silent polynomial-time self-stabilizing algorithm, with space . In turn, this allows us to get an approximation algorithm for the problem,
with a trade-off between the approximation ratio of the solution and the space
used. For polynomial weights, this trade-off goes smoothly from memory for an -approximation, to memory for exact solutions,
with for example memory for a 2-approximation
Role of current quark mass dependent multi-quark interactions in low lying meson mass spectra
We call attention to a class of current-quark mass dependent multi-quark
interaction terms which break explicitly the chiral and
symmetries. They complete the set of effective quark interactions that
contribute at the same order in as the 't Hooft flavor determinant
interaction and the eight quark interactions in the phase of spontaneously
broken chiral symmetry. The classification scheme matches the counting
rules based on arguments set by the scale of spontaneous chiral symmetry
breaking. Together with the leading in four quark Nambu-Jona-Lasinio
Lagrangian and current quark mass matrix, the model is apt to account for the
correct empirical ordering and magnitude of the splitting of states in the low
lying mass spectra of spin zero mesons. The new terms turn out to be essential
for the ordering in the pseudoscalar sector and for the scalars.Comment: 6 pages, 1 figure, prepared for the proceedings of the workshop
"Excited QCD 2013", 03-09 February 2013 in Bjelasnica Mountain, Sarajevo,
Bosni
The phase diagram in the SU(3) Nambu-Jona-Lasinio model with 't Hooft and eight-quark interactions
It is shown that the endpoint of the first order transition line which merges
into a crossover regime in the phase diagram of the Nambu--Jona-Lasinio model,
extended to include the six-quark 't Hooft and eight-quark interaction
Lagrangians, is pushed towards vanishing chemical potential and higher
temperatures with increasing strength of the OZI-violating eight-quark
interactions. We clarify a connection between the location of the endpoint in
the phase diagram and the mechanism of chiral symmetry breaking at the quark
level. Constraints on the coupling strengths based on groundstate stability and
physical considerations are explained.Comment: 5 pages, 3 figures, prepared for the proceedings of Hadron 2009 -
XIII International Conference on Hadron Spectroscopy, November 29 - December
4, Florida State University (USA
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