Random Sampling of Bandlimited Graph Signals from Local Measurements

The random sampling on graph signals is one of the fundamental topics in graph signal processing. In this letter, we consider the random sampling of k-bandlimited signals from the local measurements and show that no more than O(klogk) measurements with replacement are sufficient for the accurate and stable recovery of any k-bandlimited graph signals. We propose two random sampling strategies based on the minimum measurements, i.e., the optimal sampling and the estimated sampling. The geodesic distance between vertices is introduced to design the sampling probability distribution. Numerical experiments are included to show the effectiveness of the proposed methods

Latest Observational Constraints to the Ghost Dark Energy Model by Using Markov Chain Monte Carlo Approach

Recently, the vacuum energy of the QCD ghost in a time-dependent background is proposed as a kind of dark energy candidate to explain the acceleration of the universe. In this model, the energy density of the dark energy is proportional to the Hubble parameter $H$, which is the Hawking temperature on the Hubble horizon of the Friedmann-Robertson-Walker (FRW) universe. In this paper, we perform a constraint on the ghost dark energy model with and without bulk viscosity, by using the Markov Chain Monte Carlo (MCMC) method and the combined latest observational data from the type Ia supernova compilations including Union2.1(580) and Union2(557), cosmic microwave background, baryon acoustic oscillation, and the observational Hubble parameter data.Comment: 12 pages, 4 figure

Hidden Tree Structure is a Key to the Emergence of Scaling in the World Wide Web

Preferential attachment is the most popular explanation for the emergence of scaling behavior in the World Wide Web, but this explanation has been challenged by the global information hypothesis, the existence of linear preference and the emergence of new big internet companies in the real world. We notice that most websites have an obvious feature that their pages are organized as a tree (namely hidden tree) and hence propose a new model that introduces a hidden tree structure into the Erd\H{o}s-R\'e}yi model by adding a new rule: when one node connects to another, it should also connect to all nodes in the path between these two nodes in the hidden tree. The experimental results show that the degree distribution of the generated graphs would obey power law distributions and have variable high clustering coefficients and variable small average lengths of shortest paths. The proposed model provides an alternative explanation to the emergence of scaling in the World Wide Web without the above-mentioned difficulties, and also explains the "preferential attachment" phenomenon.Comment: 4 Pages, 7 Figure

Ultrasonic frogs show extraordinary sex differences in auditory frequency sensitivity

Acoustic communication plays an important role in the reproductive behavior of anurans. Males of concave-eared torrent frog (_Odorrana tormota_) have ultrasonic communication capacity 1, 2, but it is unknown whether females communicate with ultrasound. Here we show that _O. tormota_ exhibits great sex differences in the auditory frequency sensitivity. Acoustic playback experiments demonstrated that the male's advertisement calls evoke gravid females' positive phonotaxis and vocal responses, whereas ultrasonic components of the male's calls (frequencies above 20 kHz) do not elicit female phonotaxis or vocalization. The behavioral study was complemented by electrophysiological recordings from the auditory midbrain and by laser Doppler vibrometer measurements of the tympanic membrane's response to acoustic stimuli. These measurements revealed that females have an upper frequency limit up to 16 kHz (threshold 107 dB SPL) and no ultrasound sensitivity, unlike males which have an upper frequency limit of up to 35 kHz (87 dB SPL). Single units in the female auditory midbrain have the best excitatory frequencies (BEFs) peaked around 5 kHz, corresponding to the fundamental frequency (F0) of male's most calls, whereas the male auditory midbrain units have BEFs mostly above 8 kHz, largely consistent with the F0 of female courtship calls. Females have a frequency sensitive bandwidth (10 dB above threshold) ranged from 2 to 6 kHz, narrower than that males have (5-20 kHz). The velocity amplitude of the tympanic membranes peaked around 5 kHz in females, whereas 7 kHz in males. The results suggest that the frog species O. tormota is an example of a vertebrate, which demonstrates well phonotaxis and extraordinary sex differences in hearing

Thermodynamic of the Ghost Dark Energy Universe

Recently, the vacuum energy of the QCD ghost in a time-dependent background is proposed as a kind of dark energy candidate to explain the acceleration of the Universe. In this model, the energy density of the dark energy is proportional to the Hubble parameter $H$, which is the Hawking temperature on the Hubble horizon of the Friedmann-Robertson-Walker (FRW) Universe. In this paper, we generalized this model and choice the Hawking temperature on the so-called trapping horizon, which will coincides with the Hubble temperature in the context of flat FRW Universe dominated by the dark energy component. We study the thermodynamics of Universe with this kind of dark energy and find that the entropy-area relation is modified, namely, there is an another new term besides the area term.Comment: 8 pages, no figure

Probing AGN Inner Structure with X-ray Obscured Type 1 AGN

Using the X-ray-selected active galactic nuclei (AGN) from the XMM-XXL north survey and the SDSS Baryon Oscillation Spectroscopic Survey (BOSS) spectroscopic follow-up of them, we compare the properties of X-ray unobscured and obscured broad-line AGN (BLAGN1 and BLAGN2; $N_\textrm{H}$below and above $10^{21.5}$ cm$^{-2}$), including their X-ray luminosity $L_X$, black hole mass, Eddington ratio $\lambda_{\textrm{Edd}}$, optical continuum and line features. We find that BLAGN2 have systematically larger broad line widths and hence apparently higher (lower) $M_{\textrm{BH}}$ ($\lambda_{\textrm{Edd}}$) than BLAGN1. We also find that the X-ray obscuration in BLAGN tends to coincide with optical dust extinction, which is optically thinner than that in narrow-line AGN (NLAGN) and likely partial-covering to the broad line region. All the results can be explained in the framework of a multi-component, clumpy torus model by interpreting BLAGN2 as an intermediate type between BLAGN1 and NLAGN in terms of an intermediate inclination angle.Comment: 21 pages, 12 figures, published in MNRA