Big Rip in SO(1,1) phantom universe

For the inverse linear potential, the SO(1,1) field behaves as phantom for late time and the Big Rip will occur. The field approaches zero as time approaches the Big Rip, here. For this potential the phantom equation of state takes the late-time minimum $w_\Phi=-3$. We give some discussions that the Big Rip in the SO(1,1) model may be treated as either the transition point of universe from expansion to extract phase or the final state. In the latter picture of the universe, the field has the $T$ symmetry and the scale factor possesses the $CT$ symmetry, for which the SO(1,1) charge $\bar{Q}$ plays a crucial role.Comment: 10 pages, 1 figur

Critical state of phantom universe

The late-time evolution behavior of the autonomous system in the SO(1,1) dark energy model with power-law potential is studied. Big Rip may be a critical point of the autonomous system. This means that such a Big Rip may be considered as the middle state between the expanding and contracting phases of phantom universe. This result is also valid for some special interactions between matter and dark energy.Comment: 6 pages, revtex

Anomalous behavior of trapping in extended dendrimers with a perfect trap

Compact and extended dendrimers are two important classes of dendritic polymers. The impact of the underlying structure of compact dendrimers on dynamical processes has been much studied, yet the relation between the dynamical and structural properties of extended dendrimers remains not well understood. In this paper, we study the trapping problem in extended dendrimers with generation-dependent segment lengths, which is different from that of compact dendrimers where the length of the linear segments is fixed. We first consider a particular case that the deep trap is located at the central node, and derive an exact formula for the average trapping time (ATT) defined as the average of the source-to-trap mean first passage time over all starting points. Then, using the obtained result we deduce a closed-form expression for the ATT to an arbitrary trap node, based on which we further obtain an explicit solution to the ATT corresponding to the trapping issue with the trap uniformly distributed in the polymer systems. We show that the trap location has a substantial influence on the trapping efficiency measured by the ATT, which increases with the shortest distance from the trap to the central node, a phenomenon similar to that for compact dendrimers. In contrast to this resemblance, the leading terms of ATTs for the three trapping problems differ drastically between extended and compact dendrimers, with the trapping processes in the extended dendrimers being less efficient than in compact dendrimers

Extended corona product as an exactly tractable model for weighted heterogeneous networks

Various graph products and operations have been widely used to construct complex networks with common properties of real-life systems. However, current works mainly focus on designing models of binary networks, in spite of the fact that many real networks can be better mimicked by heterogeneous weighted networks. In this paper, we develop a corona product of two weighted graphs, based on which and an observed updating mechanism of edge weight in real networks, we propose a minimal generative model for inhomogeneous weighted networks. We derive analytically relevant properties of the weighted network model, including strength, weight and degree distributions, clustering coefficient, degree correlations and diameter. These properties are in good agreement with those observed in diverse real-world weighted networks. We then determine all the eigenvalues and their corresponding multiplicities of the transition probability matrix for random walks on the weighted networks. Finally, we apply the obtained spectra to derive explicit expressions for mean hitting time of random walks and weighted counting of spanning trees on the weighted networks. Our model is an exactly solvable one, allowing to analytically treat its structural and dynamical properties, which is thus a good test-bed and an ideal substrate network for studying different dynamical processes, in order to explore the impacts of heterogeneous weight distribution on these processes

A Survey of Signed Network Mining in Social Media

Many real-world relations can be represented by signed networks with positive and negative links, as a result of which signed network analysis has attracted increasing attention from multiple disciplines. With the increasing prevalence of social media networks, signed network analysis has evolved from developing and measuring theories to mining tasks. In this article, we present a review of mining signed networks in the context of social media and discuss some promising research directions and new frontiers. We begin by giving basic concepts and unique properties and principles of signed networks. Then we classify and review tasks of signed network mining with representative algorithms. We also delineate some tasks that have not been extensively studied with formal definitions and also propose research directions to expand the field of signed network mining.Comment: 37 page

Magnetic interactions in a proposed diluted magnetic semiconductor (Ba1-x_\text{1-x}Kx_\text{x})(Zn1-y_\text{1-y}Mny_\text{y})2_\text{2}P2_\text{2}

By using first-principles electronic structure calculations, we have studied the magnetic interactions in a proposed BaZn$_2$P$_2$-based diluted magnetic semiconductor (DMS). For a typical compound Ba(Zn$_{0.944}$Mn$_{0.056}$)$_2$P$_2$ with only spin doping, due to the superexchange interaction between Mn atoms and the lack of itinerant carriers, the short-range antiferromagnetic coupling dominates. Partially substituting K atoms for Ba atoms, which introduces itinerant hole carriers into the $p$ orbitals of P atoms so as to link distant Mn moments with the spin-polarized hole carriers via the $p$-$d$ hybridization between P and Mn atoms, is very crucial for the appearance of ferromagnetism in the compound. Furthermore, applying hydrostatic pressure first enhances and then decreases the ferromagnetic coupling in (Ba$_{0.75}$K$_{0.25}$)(Zn$_{0.944}$Mn$_{0.056}$)$_2$P$_2$ at a turning point around 15 GPa, which results from the combined effects of the pressure-induced variations of electron delocalization and $p$-$d$ hybridization. Compared with the BaZn$_2$As$_2$-based DMS, the substitution of P for As can modulate the magnetic coupling effectively. Both the results for BaZn$_2$P$_2$-based and BaZn$_2$As$_2$-based DMSs demonstrate that the robust antiferromagnetic (AFM) coupling between the nearest Mn-Mn pairs bridged by anions is harmful to improving the performance of this II-II-V based DMS materials.Comment: 7 pages, 6 figures, 1 table; Accepted by Chinese Physics B (2018

Reconciling the light component and all-particle cosmic ray energy spectra at the knee

The knee phenomenon of the cosmic ray spectrum, which plays an important role in studying the acceleration mechanism of cosmic rays, is still an unsolved mystery. We try to reconcile the knee spectra measured by ARGO-YBJ and Tibet-III. A simple broken power-law model fails to explain the experimental data. Therefore a modified broken power-law model with non-linear acceleration effects is adopted, which can describe the sharp knee structure. This model predicts that heavy elements dominate at the knee.Comment: 5 pages, 5 figure

The power-law expansion universe and dark energy evolution

In order to depict the transition from deceleration to acceleration expansion of the universe we use a power-law expansion scale factor, $a\sim t^{n_0+bt^m}$, with $n_0$, $b$ and $m$ three parameters determined by $H_0$, $q_0$ and $z_T$. For the spatially flat, isotropic and homogeneous universe, such a scale factor leads to the results that the dark energy density is slowly changing currently, and predicts the equation of state $w_X$ changes from $w_X>-1$ to $w_X<-1$.Comment: 10 pages, 2 figure

The power-law expansion universe and the late-time behavior

Using the SNe Ia data we determine the three parameters in the power-law expanding universe model with time-dependent power \cite{W}. Inputting $H_0$ and $t_0$, then we find the $\dot{a}-t$ evolution curve with $m=5.0$ and $q_0=-0.90$ can fit very well to that from SNe observation data. The model predicts the transition redshift $z\simeq0.38$. The dark energy deduced from this model have phantom property but the universe doesn't encounter the Big Rip singularity. Assuming that this model with the three parameters is valid for the future universe, then we predict that the total energy density of the universe is decreasing and will soon reach its minimum.Comment: 10 pages, 5 figure

Triplet Distillation for Deep Face Recognition

Convolutional neural networks (CNNs) have achieved a great success in face recognition, which unfortunately comes at the cost of massive computation and storage consumption. Many compact face recognition networks are thus proposed to resolve this problem. Triplet loss is effective to further improve the performance of those compact models. However, it normally employs a fixed margin to all the samples, which neglects the informative similarity structures between different identities. In this paper, we propose an enhanced version of triplet loss, named triplet distillation, which exploits the capability of a teacher model to transfer the similarity information to a small model by adaptively varying the margin between positive and negative pairs. Experiments on LFW, AgeDB, and CPLFW datasets show the merits of our method compared to the original triplet loss.Comment: 5 pages, 2 tables, accpeted by ICML 2019 ODML-CDNNR Worksho