Entropy of a semigroup of maps from a set-valued view

In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bi\'s. Some examples with positive or zero Hausdorff metric entropy are given. Moreover, some notions of chaos are also well generalized for finitely generated semigroups from a set-valued view.Comment: 13 pages, 0 figure

The Fundamental Plane Relation of Early-Type Galaxies: Environmental Dependence

Using a sample of 70,793 early-type galaxies from SDSS DR7, we study the environmental dependence of the fundamental plane relation. With the help of the galaxy group catalogue based on SDSS DR7, we calculate the fundamental planes in different dark matter halo mass bins for central and satellite galaxies respectively. We find the environmental dependence of the fundamental plane coefficients are similar in $g$, $r$, $i$ and $z$ bands. The environmental dependence for central and satellite galaxies is significantly different. While the fundamental plane coefficients of centrals vary systematically with the halo mass, those of satellites are similar in different halo mass bins. The discrepancy between centrals and satellites are significant in small halos, but negligible in the largest halo mass bins. These results remain the same when we only keep red galaxies, or galaxies with $b/a>0.6$, or galaxies in a specific radius range in the sample. After the correction of the sky background, results are still similar. We suggest that the different environmental effects of the halo mass on centrals and satellites may arise from the different quenching processes of them.Comment: 14 pages, 5 Figures, 3 Tables. Accepted by RA

Unicyclic signed graphs with maximal energy

Let $x_1, x_2, \dots, x_n$ be the eigenvalues of a signed graph $\Gamma$ of order $n$. The energy of $\Gamma$ is defined as $E(\Gamma)=\sum^{n}_{j=1}|x_j|.$ Let $\mathcal{P}_n^4$ be obtained by connecting a vertex of the negative circle $(C_4,{\overline{\sigma}})$ with a terminal vertex of the path $P_{n-4}$. In this paper, we show that for $n=4,6$ and $n \geq 8,$ $\mathcal{P}_n^4$ has the maximal energy among all connected unicyclic $n$-vertex signed graphs, except the cycles $C_5^+, C_7^+.

Non-perturbative Theory of Pauli Spin Blockade

Pauli spin blockade (PSB) is a significant physical effect in double quantum dot (DQD) systems. In this paper, we start from the fundamental quantum model of the DQD with the electron-electron interaction being considered, and then systematically study the PSB effect in DQD by using a recently developed non-perturbative method, the hierarchical equations of motion (HEOM) approach. The physical picture of the PSB is elucidated explicitly and the gate voltage manipulation is described minutely, which are both qualitatively consistent with the experimental measurements. When dotdot exchange interaction is involved, the PSB effect may be lifted by the strong antiferromagnetic exchange coupling.Comment: 10 pages, 8 figure

Design of a Low-cost Miniature Robot to Assist the COVID-19 Nasopharyngeal Swab Sampling

Nasopharyngeal (NP) swab sampling is an effective approach for the diagnosis of coronavirus disease 2019 (COVID-19). Medical staffs carrying out the task of collecting NP specimens are in close contact with the suspected patient, thereby posing a high risk of cross-infection. We propose a low-cost miniature robot that can be easily assembled and remotely controlled. The system includes an active end-effector, a passive positioning arm, and a detachable swab gripper with integrated force sensing capability. The cost of the materials for building this robot is 55 USD and the total weight of the functional part is 0.23kg. The design of the force sensing swab gripper was justified using Finite Element (FE) modeling and the performances of the robot were validated with a simulation phantom and three pig noses. FE analysis indicated a 0.5mm magnitude displacement of the gripper's sensing beam, which meets the ideal detecting range of the optoelectronic sensor. Studies on both the phantom and the pig nose demonstrated the successful operation of the robot during the collection task. The average forces were found to be 0.35N and 0.85N, respectively. It is concluded that the proposed robot is promising and could be further developed to be used in vivo.Comment: 5 pages, 8 figure

Deep Ranking Model by Large Adaptive Margin Learning for Person Re-identification

Person re-identification aims to match images of the same person across disjoint camera views, which is a challenging problem in video surveillance. The major challenge of this task lies in how to preserve the similarity of the same person against large variations caused by complex backgrounds, mutual occlusions and different illuminations, while discriminating the different individuals. In this paper, we present a novel deep ranking model with feature learning and fusion by learning a large adaptive margin between the intra-class distance and inter-class distance to solve the person re-identification problem. Specifically, we organize the training images into a batch of pairwise samples. Treating these pairwise samples as inputs, we build a novel part-based deep convolutional neural network (CNN) to learn the layered feature representations by preserving a large adaptive margin. As a result, the final learned model can effectively find out the matched target to the anchor image among a number of candidates in the gallery image set by learning discriminative and stable feature representations. Overcoming the weaknesses of conventional fixed-margin loss functions, our adaptive margin loss function is more appropriate for the dynamic feature space. On four benchmark datasets, PRID2011, Market1501, CUHK01 and 3DPeS, we extensively conduct comparative evaluations to demonstrate the advantages of the proposed method over the state-of-the-art approaches in person re-identification.Comment: Accepted to Pattern Recognitio

Rotating Black Hole Shadow in Perfect Fluid Dark Matter

We study analytically the shadow cast by the rotating black hole in the perfect fluid dark matter. The apparent shape of the shadow depends upon the black hole spin $a$ and the perfect fluid dark matter intensity parameter $k$ ($k>0$). In general, the shadow is a perfect circle in the non-rotating case ($a=0$) and a deformed one in the rotating case ($a\neq 0$). The deformation gets more and more significant with the increasing $a$, similar to the Schwarzschild and Kerr black holes. In addition, there exists a reflection point $k_0$. When $k<k_0$, the size of the shadow decreases with the increasing $k$ and the distortion increases with the increasing $k$. When $k>k_0$, the size of the shadow increases with the increasing $k$ and the distortion decreases with the increasing $k$. Furthermore, the energy emission rate of the black hole in the perfect fluid dark matter increases with the increasing $k$ and the peak of the emission shifts to higher frequencies. Finally, we propose that to observe the effect of the black hole spin $a$ and the perfect fluid dark matter intensity $k$ on the shadow of the black hole Sgr A$^{*}$ at the center of the Milky Way, highly improved techniques would be necessary for the development of future astronomical instruments.Comment: 9 pages, 3 figures. arXiv admin note: text overlap with arXiv:1806.09415, arXiv:1804.0811

The Mutual Inclusion in a Nonlocal Competitive Lotka Volterra System

We investigate the traveling front solutions of a nonlocal Lotka Volterra system to illustrate the outcome of the competition between two species. The existence of the front solution is obtained through a new monotone iteration scheme, the uniqueness of the front solution corresponding to each propagation speed is proved by sliding domain method adapted to nonlocal systems, and the asymptotic decay rate of the fronts with critical and noncritical wave speeds is derived by a new method, which is different from the single equation case. The results demonstrate that in the long run, two weakly competing species can co-exist.Comment: Need further update

Kerr-Anti-De-Sitter/De-Sitter Black Hole In Perfect Fluid Dark Matter Background

We obtain the Kerr-anti-de-sitter (Kerr-AdS) and Kerr-de-sitter (Kerr-dS) black hole (BH) solutions to the Einstein field equation in the perfect fluid dark matter background using the Newman-Janis method and Mathematica package. We discuss in detail the black hole properties and obtain the following main results: (i) From the horizon equation $g_{rr}=0$, we derive the relation between the perfect fluid dark matter parameter $\alpha$ and the cosmological constant $\Lambda$ when the cosmological horizon $r_{\Lambda}$ exists. For $\Lambda=0$, we find that $\alpha$ is in the range $00$ and $-7.18M<\alpha<0$ for $\alpha<0$. For positive cosmological constant $\Lambda$ (Kerr-AdS BH), $\alpha_{max}$ decreases if $\alpha>0$, and $\alpha_{min}$ increases if $\alpha<0$. For negative cosmological constant $-\Lambda$ (Kerr-dS BH), $\alpha_{max}$ increases if $\alpha>0$ and $\alpha_{min}$ decreases if $\alpha<0$; (ii) An ergosphere exists between the event horizon and the outer static limit surface. The size of the ergosphere evolves oppositely for $\alpha>0$ and $\alpha<0$, while decreasing with the increasing $\mid\alpha\mid$. When there is sufficient dark matter around the black hole, the black hole spacetime changes remarkably; (iii) The singularity of these black holes is the same as that of rotational black holes. In addition, we study the geodesic motion using the Hamilton-Jacobi formalism and find that when $\alpha$ is in the above ranges for $\Lambda=0$, stable orbits exist. Furthermore, the rotational velocity of the black hole in the equatorial plane has different behaviour for different $\alpha$ and the black hole spin $a$. It is asymptotically flat and independent of $\alpha$ if $\alpha>0$ while is asymptotically flat only when $\alpha$ is close to zero if $\alpha<0$.Comment: 22 pages, 4 figure

n-point functions at finite temperature

We study $n$-point functions at finite temperature in the closed time path formalism. With the help of two basic column vectors and their dual partners we derive a compact decomposition of the time-ordered $n$-point functions with $2^n$ components in terms of $2^{n-1} -1$ independent retarded/advanced $n$-point functions. This representation greatly simplifies calculations in the real-time formalism.Comment: Revtex, 14pages, no figur