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 $w$, where $w\geq 2$ 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 pzp_z-wave pairing in quasi one dimensional A2_2Cr3_3As3_3 superconductors

We construct minimum effective models to investigate the pairing symmetry in the newly discovered quasi-one-dimensional superconductor K$_2$Cr$_3$As$_3$. We show that a minimum three-band model based on the $d_{z^2}$, $d_{xy}$ and $d_{x^2-y^2}$ 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 $p_z$-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 $k_z=0$ plane on the Fermi surfaces.Comment: 10 pages plus two appendix, 12 figures; Published version by Phys. Rev.

Experimental consequences of pzp_z-wave spin triplet superconductivity in A2_2Cr3_3As3_3

The experimental observable properties of the triplet $p_z$-wave pairing state, proposed by Wu {\em et al.} [arXiv:1503.06707] in quasi-one dimensional A$_2$Cr$_3$As$_3$ materials, are theoretically investigated. This pairing state is characterized by the line nodes on the $k_z=0$ 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 ($T\ll T_c$) show powerlaw behaviors and are consistent available experiments. Particularly, the superfluid density determined by the $p_z$-wave pairing state in this quasi-one dimensional system is anisotropic: the in-plane superfluid density varies as $\Delta\rho_{\parallel}\sim T$ but the out-plane one varies as $\Delta\rho_{\perp}\sim T^3$ at low temperature. The anisotropic upper critical field reported in experiment is consistent with the $S_z=0$ (i.e., $(\uparrow\downarrow+\downarrow\uparrow)$) $p_z$-wave pairing state. We also suggest the phase-sensitive dc-SQUID measurements to pin down the triplet $p_z$-wave pairing state.Comment: 5 pages, 5 figures, + supplemental materials, Fig.3 is update

Further factorization of xn−1x^n-1 over a finite field

Let $\Bbb F_q$ be a finite field with $q$ elements and $n$ a positive integer. Mart\'inez, Vergara and Oliveira \cite{MVO} explicitly factorized $x^{n} - 1$ over $\Bbb F_q$ under the condition of $rad(n)|(q-1)$. In this paper, suppose that $rad(n)\nmid (q-1)$ and $rad(n)|(q^w-1)$, where $w$ is a prime, we explicitly factorize $x^{n}-1$ into irreducible factors in $\Bbb F_q[x]$ and count the number of its irreducible factors