Stochastic representation of solution to nonlocal-in-time diffusion

The aim of this paper is to give a stochastic representation for the solution to a natural extension of the Caputo-type evolution equation. The nonlocal-in-time operator is defined by a hypersingular integral with a (possibly time-dependent) kernel function, and it results in a model which serves a bridge between normal diffusion and anomalous diffusion. We derive the stochastic representation for the weak solution of the nonlocal-in-time problem in case of nonsmooth data. We do so by starting from an auxiliary Caputo-type evolution equation with a specific forcing term. Numerical simulations are also provided to support our theoretical results.Comment: 31 pages, 12 figures, submitte

Revisiting 1-Dimensional Double-Barrier Tunneling in Quantum Mechanics

This paper revisited quantum tunneling dynamics through a square double-barrier potential. We emphasized the similarity of tunneling dynamics through double-barrier and that of optical Fabry--P$\acute{e}$rot (FP) interferometer. Based on this similarity, we showed that the well-known resonant tunneling can also be interpreted as a result of matter multi-wave interference, analogous to that of FP interferometer. From this analogy, we also got an analytical finesse formula of double-barrier. Compared with that obtained numerically for a specific barrier configuration, we found that this formula works well for resonances at "deep tunneling region". Besides that, we also calculated standing wave spectrum inside the well of double barriers and phase time of double-barrier tunneling. The wave number spectrums of standing wave and phase time show another points of view on resonance. From semi-numerical calculations, we interpreted the peak of phase time at resonance as resonance life time, which coincides at least in order of magnitude with that obtained from uncertainty principle. Not to our surprise, phase time of double-barrier tunneling also saturates at long barrier length limit $l\rightarrow\infty$ as that of tunneling through a single barrier, and the limits are the same.Comment: 14 pages, 18 figure

Final State Interactions in D→PPD \to PP decays

The two-body nonleptonic charmed meson decays into two pseudoscalar mesons are studied using one-particle-exchange method. The effects of the final state interactions are analyzed through the strong phases extracted from the experimental data.Comment: 15 pages, 7 figure

2-walk-regular dihedrants from group-divisible designs

In this note, we construct bipartite 2-walk-regular graphs with exactly 6 distinct eigenvalues as incidence graphs of group-divisible designs with the dual property. For many of them, we show that they are 2-arc-transitive dihedrants. We note that many of these graphs are not described in Du et al. [7, Theorem1.2], in which they classify the connected 2-arc transitive dihedrants

Hidden Broad-line Regions in Seyfert 2 Galaxies: from the spectropolarimetric perspective

The hidden broad-line regions (BLRs) in Seyfert 2 galaxies, which display broad emission lines (BELs) in their polarized spectra, are a key piece of evidence in support of the unified model for active galactic nuclei (AGNs). However, the detailed kinematics and geometry of hidden BLRs are still not fully understood. The virial factor obtained from reverberation mapping of type 1 AGNs may be a useful diagnostic of the nature of hidden BLRs in type 2 objects. In order to understand the hidden BLRs, we compile six type 2 objects from the literature with polarized BELs and dynamical measurements of black hole masses. All of them contain pseudobulges. We estimate their virial factors, and find the average value is 0.60 and the standard deviation is 0.69, which agree well with the value of type 1 AGNs with pseudobulges. This study demonstrates that (1) the geometry and kinematics of BLR are similar in type 1 and type 2 AGNs of the same bulge type (pseudobulges), and (2) the small values of virial factors in Seyfert 2 galaxies suggest that, similar to type 1 AGNs, BLRs tend to be very thick disks in type 2 objects.Comment: 6 pages, 2 figures, 2 tables, accepted for publication in The Astrophysical Journal Letter

Weak CS Emission in an Extremely Metal-poor Galaxy DDO 70

In most galaxies like the Milky Way, stars form in clouds of molecular gas. Unlike the CO emission that traces the bulk of molecular gas, the rotational transitions of HCN and CS molecules mainly probe the dense phase of molecular gas, which has a tight and almost linear relation with the far-infrared luminosity and star formation rate. However, it is unclear if dense molecular gas exists at very low metallicity, and if exists, how it is related to star formation. In this work, we report ALMA observations of the CS $J$=5$\rightarrow$4 emission line of DDO~70, a nearby gas-rich dwarf galaxy with $\sim7\%$ solar metallicity. We did not detect CS emission from all regions with strong CO emission. After stacking all CS spectra from CO-bright clumps, we find no more than a marginal detection of CS $J$=5$\rightarrow$4 transition, at a signal-to-noise ratio of $\sim 3.3$. This 3-$\sigma$ upper limit deviates from the $L^\prime_{\rm CS}$-$L_{\rm IR}$ and $L^\prime_{\rm CS}$-SFR relationships found in local star forming galaxies and dense clumps in the Milky Way, implying weaker CS emission at given IR luminosity and SFR. We discuss the possible mechanisms that suppress CS emission at low metallicity.Comment: 5 pages, 4 figures. Accepted for publication in MNRAS Letter

Curriculum Adversarial Training

Recently, deep learning has been applied to many security-sensitive applications, such as facial authentication. The existence of adversarial examples hinders such applications. The state-of-the-art result on defense shows that adversarial training can be applied to train a robust model on MNIST against adversarial examples; but it fails to achieve a high empirical worst-case accuracy on a more complex task, such as CIFAR-10 and SVHN. In our work, we propose curriculum adversarial training (CAT) to resolve this issue. The basic idea is to develop a curriculum of adversarial examples generated by attacks with a wide range of strengths. With two techniques to mitigate the forgetting and the generalization issues, we demonstrate that CAT can improve the prior art's empirical worst-case accuracy by a large margin of 25% on CIFAR-10 and 35% on SVHN. At the same, the model's performance on non-adversarial inputs is comparable to the state-of-the-art models.Comment: IJCAI 201

Pressure of Degenerate and Relativistic electrons in a superhigh magnetic field

Based on our previous work, we deduce a general formula for pressure of degenerate and relativistic electrons,Pe, which is suitable for superhigh magnetic fields, discuss the quantization of Landau levels of electrons, and consider the quantum electrodynam-ic(QED) effects on the equations of states (EOSs) for different matter systems. The main conclusions are as follows:Pe is related to the magnetic field B, matter density ?, and electron fraction Ye ; the stronger the magnetic field, the higher the electron pressure becomes; the high electron pressure could be caused by high Fermi energy of electrons in a superhigh magnetic field; compared with a common radio pulsar, a magnetar could be a more compact oblate spheroid-like deformed neutron star due to the anisotropic total pressure; and an increase in the maximum mass of a magnetar is expected because of the positive contribution of the magnetic field energy to the EOS of the star.Comment: 26 Papers, 5 Figures, Published in Modern Physics Letters A ., Vol.28, No.36, p.1350138 (2013

Probing the Neutrino Mass Hierarchy beyond Λ\LambdaCDM Model

Taking the neutrino oscillation data into consideration, a dimensionless parameter $\Delta = (m_3-m_1)/(m_3+m_1)$ is adopted to parameterize the three neutrino mass eigenstates and the normal (positive $\Delta$) or inverted (negative $\Delta$) mass hierarchies in three typical cosmological models. Using the currently available cosmic observational data, several Markov Chain Monte Carlo chains are obtained with uniform priors on the free parameters at first. Applying importance sampling the results are compared with three new priors, i.e., logarithmic prior on $|\Delta|$, linear and logarithmic priors on $\Sigma m_\nu$. It turns out that the three new priors increase the upper limits of neutrino mass, but do not change the tendency towards different model's preference for different hierarchies, i.e., the normal hierarchy tends to be favored by $\Lambda$CDM and $w$CDM, which, however, disappears in the $w_0 w_a$CDM model. In addition, the almost symmetrical contours in the $w-\Delta$, $w_0-\Delta$, $w_a-\Delta$ planes indicate that the normal and inverted hierarchy have strong degeneracy. Finally, we perform a Bayesian model comparison analysis, finding that flat linear prior on $\Delta$ and $w_0 w_a$CDM are the most preferred prior and model, respectively.Comment: 14 pages, 8 figures, accept to publish in JCAP. Revised to match the final typ

Resonance spectrum of a bulk fermion on branes

It is known that there are two mechanisms for localizing a bulk fermion on a brane, one is the well-known Yukawa coupling and the other is the new coupling proposed in [Phys. Rev. D 89, 086001 (2014)]. In this paper, we investigate localization and resonance spectrum of a bulk fermion on the same branes with the two localization mechanisms. It is found that both the two mechanisms can result in a volcano-like effective potential of the fermion Kaluza-Klein modes. The left-chiral fermion zero mode can be localized on the brane and there exist some discrete massive fermion Kaluza-Klein modes that quasilocalized on the brane (also called fermion resonances). The number of the fermion resonances increases linearly with the coupling parameter.Comment: 14 pages, 18 figure