70,039 research outputs found
Constructions of Strongly Regular Cayley Graphs using Even Index Gauss Sums
In this paper, generalizing the result in \cite{GXY}, we construct strongly
regular Cayley graphs by using union of cyclotomic classes of \F_q and Gauss
sums of index , where is even. In particular, we obtain three
infinite families of strongly regular graphs with new parameters.Comment: 14 page
Quantum phase space with a basis of Wannier functions
A quantum phase space with Wannier basis is constructed: (i) classical phase
space is divided into Planck cells; (ii) a complete set of Wannier functions
are constructed with the combination of Kohn's method and L\"owdin method such
that each Wannier function is localized at a Planck cell. With these Wannier
functions one can map a wave function unitarily onto phase space. Various
examples are used to illustrate our method and compare it to Wigner function.
The advantage of our method is that it can smooth out the oscillations in wave
functions without losing any information and is potentially a better tool in
studying quantum-classical correspondence. In addition, we point out that our
method can be used for time-frequency analysis of signals.Comment: 6 figure
A Practical Framework for Relation Extraction with Noisy Labels Based on Doubly Transitional Loss
Either human annotation or rule based automatic labeling is an effective
method to augment data for relation extraction. However, the inevitable wrong
labeling problem for example by distant supervision may deteriorate the
performance of many existing methods. To address this issue, we introduce a
practical end-to-end deep learning framework, including a standard feature
extractor and a novel noisy classifier with our proposed doubly transitional
mechanism. One transition is basically parameterized by a non-linear
transformation between hidden layers that implicitly represents the conversion
between the true and noisy labels, and it can be readily optimized together
with other model parameters. Another is an explicit probability transition
matrix that captures the direct conversion between labels but needs to be
derived from an EM algorithm. We conduct experiments on the NYT dataset and
SemEval 2018 Task 7. The empirical results show comparable or better
performance over state-of-the-art methods.Comment: 10 page
Multivariate two-sample extended empirical likelihood
Jing (1995) and Liu et al. (2008) studied the two-sample empirical likelihood
and showed it is Bartlett correctable for the univariate and multivariate
cases, respectively. We expand its domain to the full parameter space and
obtain a two-sample extended empirical likelihood which is more accurate and
can also achieve the second-order accuracy of the Bartlett correction.Comment: 10 pages, 2 tables, 1 Figur
Empirical likelihood on the full parameter space
We extend the empirical likelihood of Owen [Ann. Statist. 18 (1990) 90-120]
by partitioning its domain into the collection of its contours and mapping the
contours through a continuous sequence of similarity transformations onto the
full parameter space. The resulting extended empirical likelihood is a natural
generalization of the original empirical likelihood to the full parameter
space; it has the same asymptotic properties and identically shaped contours as
the original empirical likelihood. It can also attain the second order accuracy
of the Bartlett corrected empirical likelihood of DiCiccio, Hall and Romano
[Ann. Statist. 19 (1991) 1053-1061]. A simple first order extended empirical
likelihood is found to be substantially more accurate than the original
empirical likelihood. It is also more accurate than available second order
empirical likelihood methods in most small sample situations and competitive in
accuracy in large sample situations. Importantly, in many one-dimensional
applications this first order extended empirical likelihood is accurate for
sample sizes as small as ten, making it a practical and reliable choice for
small sample empirical likelihood inference.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1143 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Jet Power of Jetted Active Galactic Nuclei: Implication for Evolution and Unification
We construct samples of jetted active galactic nuclei (AGNs) with
low-frequency radio data from the recent released TGSS AD1 catalog at 150 MHz.
With these samples, we compare the properties of jet power for blazars,
radio-loud narrow-line Seyfert 1 galaxies (RL-NLS1s), young radio sources
(YRSs) and radio galaxies. The jet-disk connection, and the unification of
jetted AGNs are explored. On the Eddington ratio --- Eddington-scaled jet power
plane, jetted AGNs can be generally divided into two populations. Low power
radio galaxies, low excitation FR IIs (LEG/FR IIs), and most YRSs show larger
jet power than accretion power, while FSRQs, RL-NLS1s, and high excitation FR
IIs (HEG/FR IIs) are on the contrary. LEG/FR IIs share similar jet power
properties with HEG/FR IIs, while their accretion properties are different with
the latter. These facts suggest an evolutional sequence from HEG/FR IIs, LEG/FR
IIs to FR Is, where the accretion and jet activities get dimmed gradually.
LEG/FR IIs are the transitional objects that accretion processes have switched
off, while jets are still active. After correcting the contribution from radio
core of blazars, the unification between blazars and radio galaxies is
confirmed with the jet power distributions. The unification involved RL-NLS1s
is more complicated than the simple scenarios of black hole growth or
orientation effect. In addition, our results manifest that low synchrotron
peaked BL Lacs (LBLs) contain two distinct groups on the distribution of jet
power, with one group similar with FSRQs and the other similar with
intermediate synchrotron peaked BL Lacs. The LBLs with higher jet powers might
be the aligned counterparts of LEG/FR IIs.Comment: 16 pages, 11 figures, 1 table, accepted by Ap
The Radio/Gamma Connection of Blazars from High to Low Radio Frequencies
We construct a large sample of gamma-ray blazars with low-frequency radio
data using the recent released TGSS AD1 catalog at 150 MHz. The radio/gamma
connections of blazars are compared from 143 GHz to 150 MHz. The radio flux
density at all radio frequencies shows strong correlation with gamma-ray flux
for blazars, as well as for the two subclasses, FSRQs and BL Lacs. But the
correlations get worse from high to low radio frequencies, which indicates that
the low-frequency radio emission is the mixture of extended and core components
for blazars. In addition, we find that the correlation between 150 MHz radio
flux density and gamma-ray flux is more significant for BL Lacs than that for
FSRQs. The slope for the luminosity correlation between radio and gamma-ray
also get flatter than unity at 150 MHz. These results indicate that the core
dominance at 150 MHz for BL Lacs is larger than that for FSRQs. We also compare
the radio luminosity from direct TGSS observation and the extended radiation at
150 MHz for blazars. The results show that the ratio between core and extended
component at 150 MHz is about 1:1 on average.Comment: 10 pages, 6 figures, 2 tables, accepted by Ap
Triplet -wave pairing in quasi one dimensional ACrAs superconductors
We construct minimum effective models to investigate the pairing symmetry in
the newly discovered quasi-one-dimensional superconductor KCrAs. We
show that a minimum three-band model based on the , and
orbitals of one Cr sublattice can capture the band structures
near Fermi surfaces. In both weak and strong coupling limits, the standard
random phase approximation (RPA) and mean-field solutions consistently yield
the triplet -wave pairing as the leading pairing symmetry for physically
realistic parameters. The triplet pairing is driven by the ferromagnetic
fluctuations within the sublattice. The gap function of the pairing state
possesses line gap nodes on the plane on the Fermi surfaces.Comment: 10 pages plus two appendix, 12 figures; Published version by Phys.
Rev.
Experimental consequences of -wave spin triplet superconductivity in ACrAs
The experimental observable properties of the triplet -wave pairing
state, proposed by Wu {\em et al.} [arXiv:1503.06707] in quasi-one dimensional
ACrAs materials, are theoretically investigated. This pairing state
is characterized by the line nodes on the plane on the Fermi surfaces.
Based on the three-band tight binding model, we obtain the specific heat,
superfluid density, Knight shift and spin relaxation rate and find that all
these properties at low temperature () show powerlaw behaviors and
are consistent available experiments. Particularly, the superfluid density
determined by the -wave pairing state in this quasi-one dimensional system
is anisotropic: the in-plane superfluid density varies as
but the out-plane one varies as
at low temperature. The anisotropic upper critical
field reported in experiment is consistent with the (i.e.,
) -wave pairing state. We also
suggest the phase-sensitive dc-SQUID measurements to pin down the triplet
-wave pairing state.Comment: 5 pages, 5 figures, + supplemental materials, Fig.3 is update
Further factorization of over a finite field
Let be a finite field with elements and a positive
integer. Mart\'inez, Vergara and Oliveira \cite{MVO} explicitly factorized
over under the condition of . In this
paper, suppose that and , where is a
prime, we explicitly factorize into irreducible factors in and count the number of its irreducible factors
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