The least eigenvalue of graphs whose complements are unicyclic

A graph in a certain graph class is called minimizing if the least eigenvalue of the adjacency matrix of the graph attains the minimum among all graphs in that class. Bell {\it et al.} have characterized the minimizing graphs in the class of connected graphs of order $n$ and size $m$, whose complements are either disconnected or contain a clique of order at least $n/2$. In this paper we discuss the minimizing graphs of a special class of graphs of order $n$ whose complements are connected and contains exactly one cycle (namely the the class $\mathscr {U}^{c}_{n}$ of graphs whose complements are unicyclic), and characterize the unique minimizing graph in $\mathscr {U}^{c}_{n}$ when $n \geq 20$

Shape transition with temperature of the pear-shaped nuclei in covariant density functional theory

The shape evolutions of the pear-shaped nuclei $^{224}$Ra and even-even $^{144-154}$Ba with temperature are investigated by the finite-temperature relativistic mean field theory with the treatment of pairing correlations by the BCS approach. The free energy surfaces as well as the bulk properties including deformations, pairing gaps, excitation energy, and specific heat for the global minimum are studied. For $^{224}$Ra, three discontinuities found in the specific heat curve indicate the pairing transition at temperature 0.4 MeV, and two shape transitions at temperatures 0.9 and 1.0 MeV, namely one from quadrupole-octupole deformed to quadrupole deformed, and the other from quadrupole deformed to spherical. Furthermore, the gaps at $N=$136 and $Z=$88 are responsible for stabilizing the octupole-deformed global minimum at low temperatures. Similar pairing transition at $T\sim$0.5 MeV and shape transitions at $T$=0.5-2.2 MeV are found for even-even $^{144-154}$Ba. The transition temperatures are roughly proportional to the corresponding deformations at the ground states.Comment: 19 pages, 11 figure

Coexistence curve and molecule number density of AdS topological charged black hole in massive gravity

The coexistence curve and molecule number density of a 4-dimensional AdS topological charged black hole in massive gravity is investigated. We find that the analytic expression of the coexistence curve in the reduced parameter space is dependent on theory parameters. This is very different from the previous results obtained in other modified gravity such as $f(R)$ gravity and Gauss-Bonnet gravity. Besides, we derive the explicit expression of the physical quantity which describes the difference of the number densities of AdS topological charged black hole molecules between the small and large black hole. It is observed that the difference of the molecule number densities is also dependent on theory parameters. Both the expressions of the coexistence curve and the difference of the molecule number densities can be reduced into a form which is similar to a RN-AdS black hole if the mass of graviton $m$ is zero. Moreover, we find the shifted temperature under massive gravity. This can highlight the important role played by the mass of graviton and other parameters in the phase transitions of AdS black holes in massive gravity.Comment: 11 pages, 4 figures. arXiv admin note: text overlap with arXiv:1604.07931, arXiv:1506.03578 by other author

Coupled Self-Organized Hydrodynamics and Navier-Stokes models: local well-posedness and the limit from the Self-Organized Kinetic-fluid models

A coupled system of self-organized hydrodynamics and Navier-Stokes equations (SOH-NS), which models self-propelled particles in a viscous fluid, was recently derived by Degond et al. \cite{DMVY-2017-arXiv}, starting from a micro-macro particle system of Vicsek-Navier-Stokes model, through an intermediate step of a self-organized kinetic-kinetic model by multiple coarse-graining processes. We first transfer SOH-NS into a non-singular system by stereographic projection, then prove the local in time well-posedness of classical solutions by energy method. Furthermore, employing the Hilbert expansion approach, we justify the hydrodynamic limit from the self-organized kinetic-fluid model to macroscopic dynamics. This provides the first analytically rigorous justification of the modeling and asymptotic analysis in \cite{DMVY-2017-arXiv}.Comment: 42 pages. arXiv admin note: text overlap with arXiv:1706.05666 by other author

Constraint on the velocity dependent dark matter annihilation cross section from gamma-ray and kinematic observations of ultrafaint dwarf galaxies

Searching for gamma rays from dwarf spheroidal galaxies (dSphs) is a promising approach to detect dark matter (DM) due to the high DM densities and low baryon components in dSphs. The Fermi-LAT observations from dSphs have set stringent constraints on the velocity independent annihilation cross section. However, the constraints from dSphs may change in velocity dependent annihilation scenarios because of the different velocity dispersions in galaxies. In this work, we study how to set constraints on the velocity dependent annihilation cross section from the combined Fermi-LAT observations of dSphs with the kinematic data. In order to calculate the gamma ray flux from the dSph, the correlation between the DM density profile and velocity dispersion at each position should be taken into account. We study such correlation and the relevant uncertainty from kinematic observations by performing a Jeans analysis. Using the observational results of three ultrafaint dSphs with large J-factors, including Willman 1, Reticulum II, and Triangulum II, we set constraints on the p-wave annihilation cross section in the Galaxy as an example.Comment: 10 pages, 13 figure

Scene Text Recognition with Sliding Convolutional Character Models

Scene text recognition has attracted great interests from the computer vision and pattern recognition community in recent years. State-of-the-art methods use concolutional neural networks (CNNs), recurrent neural networks with long short-term memory (RNN-LSTM) or the combination of them. In this paper, we investigate the intrinsic characteristics of text recognition, and inspired by human cognition mechanisms in reading texts, we propose a scene text recognition method with character models on convolutional feature map. The method simultaneously detects and recognizes characters by sliding the text line image with character models, which are learned end-to-end on text line images labeled with text transcripts. The character classifier outputs on the sliding windows are normalized and decoded with Connectionist Temporal Classification (CTC) based algorithm. Compared to previous methods, our method has a number of appealing properties: (1) It avoids the difficulty of character segmentation which hinders the performance of segmentation-based recognition methods; (2) The model can be trained simply and efficiently because it avoids gradient vanishing/exploding in training RNN-LSTM based models; (3) It bases on character models trained free of lexicon, and can recognize unknown words. (4) The recognition process is highly parallel and enables fast recognition. Our experiments on several challenging English and Chinese benchmarks, including the IIIT-5K, SVT, ICDAR03/13 and TRW15 datasets, demonstrate that the proposed method yields superior or comparable performance to state-of-the-art methods while the model size is relatively small.Comment: 10 pages,4 figure

An X-ray periodicity of ∼\sim1.8 hours in a narrow-line Seyfert 1 galaxy Mrk 766

In the narrow-line Seyfert 1 galaxy Mrk 766, a Quasi-Periodic Oscillation (QPO) signal with a period of $\sim6450$ s is detected in the \emph{XMM-Newton} data collected on 2005 May 31. This QPO signal is highly statistical significant at the confidence level at $\sim5\sigma$ with the quality factor of $Q=f/\Delta f>13.6$. The X-ray intensity changed by a factor of 3 with root mean square fractional variability of $14.3\%$. Furthermore, this QPO signal presents in the data of all three EPIC detectors and two RGS cameras and its frequency follows the $f_{\rm QPO}$-$M_{\rm BH}$ relation spanning from stellar-mass to supermassive black holes. Interestingly, a possible QPO signal with a period of $\sim4200$ s had been reported in the literature. The frequency ratio of these two QPO signals is $\sim$ 3:2. Our result is also in support of the hypothesis that the QPO signals can be just transient. The spectral analysis reveals that the contribution of the soft excess component below $\sim$ 1 keV is different between epochs with and without QPO, this property as well as the former frequency-ratio are well detected in X-ray BH binaries, which may have shed some lights on the physical origin of our event.Comment: 7 pages, 5 figures, 1 table. Accepted for publication in Ap

Zitterbewegung effect in spin-orbit coupled spin-1 ultracold atoms

The Zitterbewegung effect in spin-orbit coupled spin-1 cold atoms is investigated in the presence of the Zeeman field and a harmonic trap. It is shown that the Zeeman field and the harmonic trap have significant effect on the Zitterbewegung oscillatory behaviors. The external Zeeman field could suppress or enhance the Zitterbewegung amplitude and change the frequencies of oscillation. A much slowly damping Zitterbewegung oscillation can be achieved by adjusting both the linear and quadratic Zeeman field. Multi-frequency Zitterbewegung oscillation can be induced by the applied Zeeman field. In the presence of the harmonic trap, the subpackets corresponding to different eigenenergies would always keep coherent, resulting in the persistent Zitterbewegung oscillations. The Zitterbewegung oscillation would display very complicated and irregular oscillation characteristics due to the coexistence of different frequencies of the Zitterbewegung oscillation. Numerical results show that, the Zitterbewegung effect is robust even in the presence of interaction between atoms.Comment: 9 pages, 8 figure

Charm quarks in medium and their contribution to di-electron spectra in relativistic heavy ion collisions

We study the dynamics of charm quarks in the partonic medium and its implication to the di-electron spectra in high energy heavy ion collisions. The charm quarks traversing a thermal medium is simulated by the relativistic Langevin equation for elastic scatterings of charm quarks by thermal partons in an expanding fireball. The transport coefficients of charm quarks are calculated by the in-medium T-matrix method, where a static heavy quark potential is used with parameters fitted by the lattice QCD results. The di-electron invariant mass spectra are computed in most central collisions and are compared to the STAR data. The angular correlations of di-electrons are almost the same in $p+p$ and Au+Au collisions in the mass range $1.1<M<2.5~\mathrm{GeV/c^2}$ with the back-to-back feature. This means that the angular correlation is intact even with medium interaction at the RHIC energy.Comment: Revtex 4, 10 pages, 7 figures. Accepted version to PR

SCAN: Sliding Convolutional Attention Network for Scene Text Recognition

Scene text recognition has drawn great attentions in the community of computer vision and artificial intelligence due to its challenges and wide applications. State-of-the-art recurrent neural networks (RNN) based models map an input sequence to a variable length output sequence, but are usually applied in a black box manner and lack of transparency for further improvement, and the maintaining of the entire past hidden states prevents parallel computation in a sequence. In this paper, we investigate the intrinsic characteristics of text recognition, and inspired by human cognition mechanisms in reading texts, we propose a scene text recognition method with sliding convolutional attention network (SCAN). Similar to the eye movement during reading, the process of SCAN can be viewed as an alternation between saccades and visual fixations. Compared to the previous recurrent models, computations over all elements of SCAN can be fully parallelized during training. Experimental results on several challenging benchmarks, including the IIIT5k, SVT and ICDAR 2003/2013 datasets, demonstrate the superiority of SCAN over state-of-the-art methods in terms of both the model interpretability and performance