15,345 research outputs found
Recognizing well-parenthesized expressions in the streaming model
Motivated by a concrete problem and with the goal of understanding the sense
in which the complexity of streaming algorithms is related to the complexity of
formal languages, we investigate the problem Dyck(s) of checking matching
parentheses, with different types of parenthesis.
We present a one-pass randomized streaming algorithm for Dyck(2) with space
\Order(\sqrt{n}\log n), time per letter \polylog (n), and one-sided error.
We prove that this one-pass algorithm is optimal, up to a \polylog n factor,
even when two-sided error is allowed. For the lower bound, we prove a direct
sum result on hard instances by following the "information cost" approach, but
with a few twists. Indeed, we play a subtle game between public and private
coins. This mixture between public and private coins results from a balancing
act between the direct sum result and a combinatorial lower bound for the base
case.
Surprisingly, the space requirement shrinks drastically if we have access to
the input stream in reverse. We present a two-pass randomized streaming
algorithm for Dyck(2) with space \Order((\log n)^2), time \polylog (n) and
one-sided error, where the second pass is in the reverse direction. Both
algorithms can be extended to Dyck(s) since this problem is reducible to
Dyck(2) for a suitable notion of reduction in the streaming model.Comment: 20 pages, 5 figure
Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
We develop the Density Matrix Renormalization Group (DMRG) technique for
numerically studying incompressible fractional quantum Hall (FQH) states on the
sphere. We calculate accurate estimates for ground state energies and
excitationgaps at FQH filling fractions \nu=1/3 and \nu=5/2 for systems that
are almost twice as large as the largest ever studied by exact diagonalization.
We establish, by carefully comparing with existing numerical results on smaller
systems, that DMRG is a highly effective numerical tool for studying
incompressible FQH states.Comment: 5 pages, 4 figure
Schwinger Mechanism for Gluon Pair Production in the Presence of Arbitrary Time Dependent Chromo-Electric Field
We study Schwinger mechanism for gluon pair production in the presence of
arbitrary time-dependent chromo-electric background field with
arbitrary color index =1,2,...8 in SU(3) by directly evaluating the path
integral. We obtain an exact expression for the probability of non-perturbative
gluon pair production per unit time per unit volume and per unit transverse
momentum from arbitrary . We show that the
tadpole (or single gluon) effective action does not contribute to the
non-perturbative gluon pair production rate . We find
that the exact result for non-perturbative gluon pair production is independent
of all the time derivatives where
and has the same functional dependence on two casimir invariants
and as the constant
chromo-electric field result with the replacement: . This
result may be relevant to study the production of a non-perturbative
quark-gluon plasma at RHIC and LHC.Comment: 13 pages latex, Published in European Physical Journal
Production and Equilibration of the Quark-Gluon Plasma with Chromoelectric Field and Minijets
Production and equilibration of quark-gluon plasma are studied within the
color flux-tube model, at the RHIC and LHC energies. Non-Abelian relativistic
transport equations for quarks, antiquarks and gluons, are solved in the
extended phase space which includes coordinates, momenta and color. Before the
chromoelectric field is formed, hard and semihard partons are produced via
minijets which provide the initial conditions necessary to solve the transport
equations. The model predicts that in spite of the vast difference between the
RHIC and LHC incident energies, once the local equilibrium is reached, the
energy densities, the number densities and the temperatures at the two machines
may not be very different from each other. The minijet input significantly
alters the evolution of the deconfined matter, unless the color field is too
strong. For the input parameters used here the equilibration time is estimated
to be fm at RHIC and fm at LHC, measured from the instant
when the two colliding nuclei have just passed through each other. The
temperature at equilibration is found to be MeV at RHIC and MeV at LHC.Comment: version to appear in Phys. Rev. C; discussion enlarged to include
comparison with other models; conclusions unchanged; 14 single-spaced pages +
8 ps figure
Fractional statistic
We improve Haldane's formula which gives the number of configurations for
particles on states in a fractional statistic defined by the coupling
. Although nothing is changed in the thermodynamic limit, the new
formula makes sense for finite with integer and A
geometrical interpretation of fractional statistic is given in terms of
''composite particles''.Comment: flatex hald.tex, 3 files Submitted to: Phys. Rev.
Large zero-field cooled exchange-bias in bulk Mn2PtGa
We report a large exchange-bias (EB) effect after zero-field cooling the new
tetragonal Heusler compound Mn2PtGa from the paramagnetic state. The
first-principle calculation and the magnetic measurements reveal that Mn2PtGa
orders ferrimagnetically with some ferromagnetic (FM) inclusions. We show that
ferrimagnetic (FI) ordering is essential to isothermally induce the exchange
anisotropy needed for the zero-field cooled (ZFC) EB during the virgin
magnetization process. The complex magnetic behavior at low temperatures is
characterized by the coexistence of a field induced irreversible magnetic
behavior and a spin-glass-like phase. The field induced irreversibility
originates from an unusual first-order FI to antiferromagnetic transition,
whereas, the spin-glass like state forms due to the existence of anti-site
disorder intrinsic to the material.Comment: 5 pages, 4 figures, supplementary material included in a separate
file; accepted for publication in PR
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