37,368 research outputs found
Improved Lower Bounds for Testing Triangle-freeness in Boolean Functions via Fast Matrix Multiplication
Understanding the query complexity for testing linear-invariant properties
has been a central open problem in the study of algebraic property testing.
Triangle-freeness in Boolean functions is a simple property whose testing
complexity is unknown. Three Boolean functions , and are said to be triangle free if there is no such that . This property
is known to be strongly testable (Green 2005), but the number of queries needed
is upper-bounded only by a tower of twos whose height is polynomial in 1 /
\epsislon, where \epsislon is the distance between the tested function
triple and triangle-freeness, i.e., the minimum fraction of function values
that need to be modified to make the triple triangle free. A lower bound of for any one-sided tester was given by Bhattacharyya and
Xie (2010). In this work we improve this bound to .
Interestingly, we prove this by way of a combinatorial construction called
\emph{uniquely solvable puzzles} that was at the heart of Coppersmith and
Winograd's renowned matrix multiplication algorithm
Excitation function of initial temperature of heavy flavor quarkonium emission source in high energy collisions
The transverse momentum spectra of , , and produced in proton-proton (+), proton-antiproton
(+), proton-lead (+Pb), gold-gold (Au+Au), and lead-lead (Pb+Pb)
collisions over a wide energy range are analyzed by the (two-component) Erlang
distribution, the Hagedorn function (the inverse power-law), and the
Tsallis-Levy function. The initial temperature is obtained from the color
string percolation model due to the fit by the (two-component) Erlang
distribution in the framework of multisource thermal model. The excitation
functions of some parameters such as the mean transverse momentum and initial
temperature increase from dozens of GeV to above 10 TeV. The mean transverse
momentum and initial temperature decrease (increase slightly or do not change
obviously) with the increase of rapidity (centrality). Meanwhile, the mean
transverse momentum of is larger than that of
and , and the initial temperature for
emission is higher than that for and emission, which shows
a mass-dependent behavior.Comment: 26 pages, 12 figures. Advances in High Energy Physics, accepte
The Algorithmic Complexity of Bondage and Reinforcement Problems in bipartite graphs
Let be a graph. A subset is a dominating set if
every vertex not in is adjacent to a vertex in . The domination number
of , denoted by , is the smallest cardinality of a dominating set
of . The bondage number of a nonempty graph is the smallest number of
edges whose removal from results in a graph with domination number larger
than . The reinforcement number of is the smallest number of
edges whose addition to results in a graph with smaller domination number
than . In 2012, Hu and Xu proved that the decision problems for the
bondage, the total bondage, the reinforcement and the total reinforcement
numbers are all NP-hard in general graphs. In this paper, we improve these
results to bipartite graphs.Comment: 13 pages, 4 figures. arXiv admin note: substantial text overlap with
arXiv:1109.1657; and text overlap with arXiv:1204.4010 by other author
Energy dependent kinetic freeze-out temperature and transverse flow velocity in high energy collisions
Transverse momentum spectra of negative and positive pions produced at
mid-(pseudo)rapidity in inelastic or non-single-diffractive proton-proton
collisions and in central nucleus-nucleus collisions over an energy range from
a few GeV to above 10 TeV are analyzed by a (two-component) blast-wave model
with Boltzmann-Gibbs statistics and with Tsallis statistics respectively. The
model results are in similarly well agreement with the experimental data
measured by a few productive collaborations who work at the Heavy Ion
Synchrotron (SIS), Super Proton Synchrotron (SPS), Relativistic Heavy Ion
Collider (RHIC), and Large Hadron Collider (LHC), respectively. The energy
dependent kinetic freeze-out temperature and transverse flow velocity are
obtained and analyzed. Both the quantities have quick increase from the SIS to
SPS, and slight increase or approximate invariability from the top RHIC to LHC.
Around the energy bridge from the SPS to RHIC, the considered quantities in
proton-proton collisions obtained by the blast-wave model with Boltzmann-Gibbs
statistics show more complex energy dependent behavior comparing with the
results in other three cases.Comment: 16 pages, 4 figures. The European Physical Journal A, accepted. arXiv
admin note: text overlap with arXiv:1805.0334
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