81,973 research outputs found
On the Triality Theory for a Quartic Polynomial Optimization Problem
This paper presents a detailed proof of the triality theorem for a class of
fourth-order polynomial optimization problems. The method is based on linear
algebra but it solves an open problem on the double-min duality left in 2003.
Results show that the triality theory holds strongly in a tri-duality form if
the primal problem and its canonical dual have the same dimension; otherwise,
both the canonical min-max duality and the double-max duality still hold
strongly, but the double-min duality holds weakly in a symmetrical form. Four
numerical examples are presented to illustrate that this theory can be used to
identify not only the global minimum, but also the largest local minimum and
local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011.
arXiv admin note: substantial text overlap with arXiv:1104.297
The age dependence of halo clustering
We use a very large simulation of the concordance LCDM cosmogony to study the
clustering of dark matter haloes. For haloes less massive than about
1e13Msun/h, the amplitude of the two-point correlation function on large scales
depends strongly on halo formation time. Haloes that assembled at high redshift
are substantially more clustered than those that assembled more recently. The
effect is a smooth function of halo formation time and its amplitude increases
with decreasing halo mass. At 1e11 Msun/h the ``oldest'' 10% of haloes are more
than 5 times more strongly correlated than the ``youngest'' 10%. This
unexpected result is incompatible with the standard excursion set theory for
structure growth, and it contradicts a fundamental assumption of the halo
occupation distribution models often used to study galaxy clustering, namely
that the galaxy content of a halo of given mass is statistically independent of
its larger scale environment.Comment: 5 pages, 5 figures, MNRAS in press. Full resolution pdf file is
avaliable at http://www.mpa-garching.mpg.de/~gaoliang/GSW.pd
Halo assembly bias and its effects on galaxy clustering
The clustering of dark halos depends not only on their mass but also on their
assembly history, a dependence we term `assembly bias'. Using a galaxy
formation model grafted onto the Millennium Simulation of the LCDM cosmogony,
we study how assembly bias affects galaxy clustering. We compare the original
simulation to `shuffled' versions where the galaxy populations are randomly
swapped among halos of similar mass, thus isolating the effects of correlations
between assembly history and environment at fixed mass. Such correlations are
ignored in the halo occupation distribution models often used populate dark
matter simulations with galaxies, but they are significant in our more
realistic simulation. Assembly bias enhances 2-point correlations by 10% for
galaxies with M_bJ-5logh brighter than -17, but suppresses them by a similar
amount for galaxies brighter than -20. When such samples are split by colour,
assembly bias is 5% stronger for red galaxies and 5% weaker for blue ones. Halo
central galaxies are differently affected by assembly bias than are galaxies of
all types. It almost doubles the correlation amplitude for faint red central
galaxies. Shuffling galaxies among halos of fixed formation redshift or
concentration in addition to fixed mass produces biases which are not much
smaller than when mass alone is fixed. Assembly bias must reflect a correlation
of environment with aspects of halo assembly which are not encoded in either of
these parameters. It induces effects which could compromise precision
measurements of cosmological parameters from large galaxy surveys.Comment: 8 pages, 4 figures, accepted for publication in MNRA
Can the Bump be Observed in the Early Afterglow of GRBS with X-Ray Line Emission Features?
Extremely powerful emission lines are observed in the X-ray afterglow of
several GRBs. The energy contained in the illuminating continuum which is
responsible for the line production exceeds 10 erg, much higher than
that of the collimated GRBs. It constrains the models which explain the
production of X-ray emission lines. In this paper, We argue that this energy
can come from a continuous postburst outflow. Focusing on a central engine of
highly magnetized millisecond pulsar or magnetar we find that afterglow can be
affected by the illuminating continuum, and therefore a distinct achromatic
bump may be observed in the early afterglow lightcurves. With the luminosity of
the continuous outflow which produces the line emission, we define the upper
limit of the time when the bump feature appears. We argue that the reason why
the achromatic bumps have not been detected so far is that the bumps should
appear at the time too early to be observed.Comment: 13 pags, 2 tables, appear in v603 n1 pt1 ApJ March 1, 2004 issu
Photoinduced Electron Pairing in a Driven Cavity
We demonstrate how virtual scattering of laser photons inside a cavity via two-photon processes can induce controllable long-range electron interactions in two-dimensional materials. We show that laser light that is red (blue) detuned from the cavity yields attractive (repulsive) interactions whose strength is proportional to the laser intensity. Furthermore, we find that the interactions are not screened effectively except at very low frequencies. For realistic cavity parameters, laser-induced heating of the electrons by inelastic photon scattering is suppressed and coherent electron interactions dominate. When the interactions are attractive, they cause an instability in the Cooper channel at a temperature proportional to the square root of the driving intensity. Our results provide a novel route for engineering electron interactions in a wide range of two-dimensional materials including AB-stacked bilayer graphene and the conducting interface between LaAlO3 and SrTiO3
Combining Models of Approximation with Partial Learning
In Gold's framework of inductive inference, the model of partial learning
requires the learner to output exactly one correct index for the target object
and only the target object infinitely often. Since infinitely many of the
learner's hypotheses may be incorrect, it is not obvious whether a partial
learner can be modifed to "approximate" the target object.
Fulk and Jain (Approximate inference and scientific method. Information and
Computation 114(2):179--191, 1994) introduced a model of approximate learning
of recursive functions. The present work extends their research and solves an
open problem of Fulk and Jain by showing that there is a learner which
approximates and partially identifies every recursive function by outputting a
sequence of hypotheses which, in addition, are also almost all finite variants
of the target function.
The subsequent study is dedicated to the question how these findings
generalise to the learning of r.e. languages from positive data. Here three
variants of approximate learning will be introduced and investigated with
respect to the question whether they can be combined with partial learning.
Following the line of Fulk and Jain's research, further investigations provide
conditions under which partial language learners can eventually output only
finite variants of the target language. The combinabilities of other partial
learning criteria will also be briefly studied.Comment: 28 page
A general maximum entropy principle for self-gravitating perfect fluid
We consider a self-gravitating system consisting of perfect fluid with
spherical symmetry. Using the general expression of entropy density, we
extremize the total entropy under the constraint that the total number of
particles is fixed. We show that extrema of coincides precisely with the
relativistic Tolman-Oppenheimer-Volkoff (TOV) equation of hydrostatic
equilibrium. Furthermore, we apply the maximum entropy principle to a charged
perfect fluid and derive the generalized TOV equation. Our work provides a
strong evidence for the fundamental relationship between general relativity and
ordinary thermodynamics.Comment: 13 pages, no figure. The arguments have been improved so that the
assumption p=p(\rho) is no longer neede
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