A scaling relation between merger rate of galaxies and their close pair count

We study how to measure the galaxy merger rate from the observed close pair count. Using a high-resolution N-body/SPH cosmological simulation, we find an accurate scaling relation between galaxy pair counts and merger rates down to a stellar mass ratio of about 1:30. The relation explicitly accounts for the dependence on redshift (or time), on pair separation, and on mass of the two galaxies in a pair. With this relation, one can easily obtain the mean merger timescale for a close pair of galaxies. The use of virial masses, instead of stellar masses, is motivated by the fact that the dynamical friction time scale is mainly determined by the dark matter surrounding central and satellite galaxies. This fact can also minimize the error induced by uncertainties in modeling star formation in the simulation. Since the virial mass can be read from the well-established relation between the virial masses and the stellar masses in observation, our scaling relation can be easily applied to observations to obtain the merger rate and merger time scale. For major merger pairs (1:1-1:4) of galaxies above a stellar mass of 4*10^10 M_sun/h at z=0.1, it takes about 0.31 Gyr to merge for pairs within a projected distance of 20 kpc/h with stellar mass ratio of 1:1, while the time taken goes up to 1.6 Gyr for mergers with stellar mass ratio of 1:4. Our results indicate that a single timescale usually used in literature is not accurate to describe mergers with the stellar mass ratio spanning even a narrow range from 1:1 to 1:4.Comment: accepted for publication in Ap

The multidimensional dependence of halo bias in the eye of a machine: a tale of halo structure, assembly and environment

We develop a novel approach in exploring the joint dependence of halo bias on multiple halo properties using Gaussian process regression. Using a $\Lambda$CDM $N$-body simulation, we carry out a comprehensive study of the joint bias dependence on halo structure, formation history and environment. We show that the bias is a multivariate function of halo properties that falls into three regimes. For massive haloes, halo mass explains the majority of bias variation. For early-forming haloes, bias depends sensitively on the recent mass accretion history. For low-mass and late-forming haloes, bias depends more on the structure of a halo such as its shape and spin. Our framework enables us to convincingly prove that $V_\mathrm{max}/V_\mathrm{vir}$ is a lossy proxy of formation time for bias modelling, whereas the mass, spin, shape and formation time variables are non-redundant with respect to each other. Combining mass and formation time largely accounts for the mass accretion history dependence of bias. Combining all the internal halo properties fully accounts for the density profile dependence inside haloes, and predicts the clustering variation of individual haloes to a $20\%$ level at $\sim 10\mathrm{Mpc}h^{-1}$. When an environmental density is measured outside $1\mathrm{Mpc}h^{-1}$ from the halo centre, it outperforms and largely accounts for the bias dependence on the internal halo structure, explaining the bias variation above a level of $30\%$.Comment: MNRAS accepte

A note on a predator–prey model with modified Leslie–Gower and Holling-type II schemes with stochastic perturbation

AbstractIn this paper, we show there is a stationary distribution of a predator–prey model with modified Leslie–Gower and Holling-type II schemes with stochastic perturbation and it has ergodic property

An Empirical Study of Evaluation Index System and Measure Method on City’s Soft Power: 17 Cities in Shandong Province

Based on the research of city’s soft power at home and abroad, the current study was intended to build an evaluation index system and analyzed the city’s soft power of 17cities in Shandong Province in 2010. Both the qualitative and quantitative methods were adopted. Frequency statistical method was used to build the evaluation index system of city’s soft power, and AHP and CRITIC methods were used to determine index weight. By using the evaluation system, data from Shandong 2010 statistic yearbook and SPSS18.0, the researchers analyzed the soft power of 17 cities in Shandong province, and finally constructed a measure model for city’s soft power. Results indicated that this model is practically viable and consistent with the real situation of the soft power of 17cities in Shandong Province. It is the researchers hope that this measure model would provide reference for government’s decision-making in the development of promoting urbanization

Single-Loop Full R Joints of Multi-Mode Omnidirectional Ground Mobile Robot

In order to solve the problem of loss of locomotion ability due to overturning and instability during the movement of a mobile robot, a multi-mode omnidirectional ground mobile robot with a deformable structure is proposed. Single-loop is used as the unit, and the three-direction geometric deformation can be realized by controlling its R joints in time sharing. The 4-RRRRRR parallel mobile robot formed by two closed-loops orthogonally has four different rolling modes, and each mode can be switched between each other. Once the robot is overturned and unstable during the movement, it can be deformed into other modes and continue to move. After the description of the robot, the DOF (degree-of-freedom) is calculated based on the screw theory. Gait planning and locomotion feasibility analysis indicate that the robot can realize four locomotion modes and their mutual switching. Finally, the simulations and prototype experiments are presented to verify the feasibility of the different locomotion modes and the ability of the obstacle crossing

Information Bottleneck-Inspired Type Based Multiple Access for Remote Estimation in IoT Systems

Type-based multiple access (TBMA) is a semantics-aware multiple access protocol for remote inference. In TBMA, codewords are reused across transmitting sensors, with each codeword being assigned to a different observation value. Existing TBMA protocols are based on fixed shared codebooks and on conventional maximum-likelihood or Bayesian decoders, which require knowledge of the distributions of observations and channels. In this letter, we propose a novel design principle for TBMA based on the information bottleneck (IB). In the proposed IB-TBMA protocol, the shared codebook is jointly optimized with a decoder based on artificial neural networks (ANNs), so as to adapt to source, observations, and channel statistics based on data only. We also introduce the Compressed IB-TBMA (CIB-TBMA) protocol, which improves IB-TBMA by enabling a reduction in the number of codewords via an IB-inspired clustering phase. Numerical results demonstrate the importance of a joint design of codebook and neural decoder, and validate the benefits of codebook compression.Comment: 5 pages, 3 figures, accepted by IEEE Signal Processing Letters (SPL