950 research outputs found
Submodular Maximization Meets Streaming: Matchings, Matroids, and More
We study the problem of finding a maximum matching in a graph given by an
input stream listing its edges in some arbitrary order, where the quantity to
be maximized is given by a monotone submodular function on subsets of edges.
This problem, which we call maximum submodular-function matching (MSM), is a
natural generalization of maximum weight matching (MWM), which is in turn a
generalization of maximum cardinality matching (MCM). We give two incomparable
algorithms for this problem with space usage falling in the semi-streaming
range---they store only edges, using working memory---that
achieve approximation ratios of in a single pass and in
passes respectively. The operations of these algorithms
mimic those of Zelke's and McGregor's respective algorithms for MWM; the
novelty lies in the analysis for the MSM setting. In fact we identify a general
framework for MWM algorithms that allows this kind of adaptation to the broader
setting of MSM.
In the sequel, we give generalizations of these results where the
maximization is over "independent sets" in a very general sense. This
generalization captures hypermatchings in hypergraphs as well as independence
in the intersection of multiple matroids.Comment: 18 page
The Anderson-Mott Transition as a Random-Field Problem
The Anderson-Mott transition of disordered interacting electrons is shown to
share many physical and technical features with classical random-field systems.
A renormalization group study of an order parameter field theory for the
Anderson-Mott transition shows that random-field terms appear at one-loop
order. They lead to an upper critical dimension for this model.
For the critical behavior is mean-field like. For an
-expansion yields exponents that coincide with those for the
random-field Ising model. Implications of these results are discussed.Comment: 8pp, REVTeX, db/94/
Order Parameter Description of the Anderson-Mott Transition
An order parameter description of the Anderson-Mott transition (AMT) is
given. We first derive an order parameter field theory for the AMT, and then
present a mean-field solution. It is shown that the mean-field critical
exponents are exact above the upper critical dimension. Renormalization group
methods are then used to show that a random-field like term is generated under
renormalization. This leads to similarities between the AMT and random-field
magnets, and to an upper critical dimension for the AMT. For
, an expansion is used to calculate the critical
exponents. To first order in they are found to coincide with the
exponents for the random-field Ising model. We then discuss a general scaling
theory for the AMT. Some well established scaling relations, such as Wegner's
scaling law, are found to be modified due to random-field effects. New
experiments are proposed to test for random-field aspects of the AMT.Comment: 28pp., REVTeX, no figure
Crystallization of a classical two-dimensional electron system: Positional and orientational orders
Crystallization of a classical two-dimensional one-component plasma
(electrons interacting with the Coulomb repulsion in a uniform neutralizing
positive background) is investigated with a molecular dynamics simulation. The
positional and the orientational correlation functions are calculated for the
first time. We have found an indication that the solid phase has a
quasi-long-range (power-law) positional order along with a long-range
orientational order. This indicates that, although the long-range Coulomb
interaction is outside the scope of Mermin's theorem, the absence of ordinary
crystalline order at finite temperatures applies to the electron system as
well. The `hexatic' phase, which is predicted between the liquid and the solid
phases by the Kosterlitz-Thouless-Halperin-Nelson-Young theory, is also
discussed.Comment: 3 pages, 4 figures; Corrected typos; Double columne
Persistence of a particle in the Matheron-de Marsily velocity field
We show that the longitudinal position of a particle in a
-dimensional layered random velocity field (the Matheron-de Marsily
model) can be identified as a fractional Brownian motion (fBm) characterized by
a variable Hurst exponent for . The
fBm becomes marginal at . Moreover, using the known first-passage
properties of fBm we prove analytically that the disorder averaged persistence
(the probability of no zero crossing of the process upto time ) has a
power law decay for large with an exponent for and
for (with logarithmic correction at ), results that
were earlier derived by Redner based on heuristic arguments and supported by
numerical simulations (S. Redner, Phys. Rev. E {\bf 56}, 4967 (1997)).Comment: 4 pages Revtex, 1 .eps figure included, to appear in PRE Rapid
Communicatio
Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices
We present the number of dimers on the Sierpinski gasket
at stage with dimension equal to two, three, four or five, where one of
the outmost vertices is not covered when the number of vertices is an
odd number. The entropy of absorption of diatomic molecules per site, defined
as , is calculated to be
exactly for . The numbers of dimers on the generalized
Sierpinski gasket with and are also obtained
exactly. Their entropies are equal to , , ,
respectively. The upper and lower bounds for the entropy are derived in terms
of the results at a certain stage for with . As the
difference between these bounds converges quickly to zero as the calculated
stage increases, the numerical value of with can be
evaluated with more than a hundred significant figures accurate.Comment: 35 pages, 20 figures and 1 tabl
Random Exchange Quantum Heisenberg Chains
The one-dimensional quantum Heisenberg model with random bonds is
studied for and . The specific heat and the zero-field
susceptibility are calculated by using high-temperature series expansions and
quantum transfer matrix method. The susceptibility shows a Curie-like
temperature dependence at low temperatures as well as at high temperatures. The
numerical results for the specific heat suggest that there are anomalously many
low-lying excitations. The qualitative nature of these excitations is discussed
based on the exact diagonalization of finite size systems.Comment: 13 pages, RevTex, 12 figures available on request ([email protected]
Enhanced stability of the square lattice of a classical bilayer Wigner crystal
The stability and melting transition of a single layer and a bilayer crystal
consisting of charged particles interacting through a Coulomb or a screened
Coulomb potential is studied using the Monte-Carlo technique. A new melting
criterion is formulated which we show to be universal for bilayer as well as
for single layer crystals in the case of (screened) Coulomb, Lennard--Jones and
1/r^{12} repulsive inter-particle interactions. The melting temperature for the
five different lattice structures of the bilayer Wigner crystal is obtained,
and a phase diagram is constructed as a function of the interlayer distance. We
found the surprising result that the square lattice has a substantial larger
melting temperature as compared to the other lattice structures. This is a
consequence of the specific topology of the defects which are created with
increasing temperature and which have a larger energy as compared to the
defects in e.g. a hexagonal lattice.Comment: Accepted for publication in Physical Review
Thermodynamics of Random Ferromagnetic Antiferromagnetic Spin-1/2 Chains
Using the quantum Monte Carlo Loop algorithm, we calculate the temperature
dependence of the uniform susceptibility, the specific heat, the correlation
length, the generalized staggered susceptibility and magnetization of a
spin-1/2 chain with random antiferromagnetic and ferromagnetic couplings, down
to very low temperatures. Our data show a consistent scaling behavior in all
the quantities and support strongly the conjecture drawn from the approximate
real-space renormalization group treatment.A statistical analysis scheme is
developed which will be useful for the search of scaling behavior in numerical
and experimental data of random spin chains.Comment: 13 pages, 13 figures, RevTe
Radiative β decay of the free neutron
The theory of quantum electrodynamics predicts that the β decay of the neutron into a proton, electron, and antineutrino is accompanied by a continuous spectrum of emitted photons described as inner bremsstrahlung. While this phenomenon has been observed in nuclear β decay and electron-capture decay for many years, it has only been recently observed in free-neutron decay. We present a detailed discussion of an experiment in which the radiative decay mode of the free neutron was observed. In this experiment, the branching ratio for this rare decay was determined by recording photons that were correlated with both the electron and proton emitted in neutron decay. We determined the branching ratio for photons with energy between 15 and 340 keV to be (3.09±0.32)×10-3 (68% level of confidence), where the uncertainty is dominated by systematic effects. This value for the branching ratio is consistent with theoretical predictions. The characteristic energy spectrum of the radiated photons, which differs from the uncorrelated background spectrum, is also consistent with the theoretical spectrum
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