Limit Cycle Bifurcations from Centers of Symmetric Hamiltonian Systems Perturbing by Cubic Polynomials

In this paper, we consider some cubic near-Hamiltonian systems obtained from perturbing the symmetric cubic Hamiltonian system with two symmetric singular points by cubic polynomials. First, following Han [2012] we develop a method to study the analytical property of the Melnikov function near the origin for near-Hamiltonian system having the origin as its elementary center or nilpotent center. Based on the method, a computationally efficient algorithm is established to systematically compute the coefficients of Melnikov function. Then, we consider the symmetric singular points and present the conditions for one of them to be elementary center or nilpotent center. Under the condition for the singular point to be a center, we obtain the normal form of the Hamiltonian systems near the center. Moreover, perturbing the symmetric cubic Hamiltonian systems by cubic polynomials, we consider limit cycles bifurcating from the center using the algorithm to compute the coefficients of Melnikov function. Finally, perturbing the symmetric hamiltonian system by symmetric cubic polynomials, we consider the number of limit cycles near one of the symmetric centers of the symmetric near-Hamiltonian system, which is same to that of another center

Probabilistic teleportation of unknown two-particle state via POVM

We propose a scheme for probabilistic teleportation of unknown two-particle state with partly entangled four-particle state via POVM. In this scheme the teleportation of unknown two-particle state can be realized with certain probability by performing two Bell state measurements, a proper POVM and a unitary transformation.Comment: 5 pages, no figur

DecideNet: Counting Varying Density Crowds Through Attention Guided Detection and Density Estimation

In real-world crowd counting applications, the crowd densities vary greatly in spatial and temporal domains. A detection based counting method will estimate crowds accurately in low density scenes, while its reliability in congested areas is downgraded. A regression based approach, on the other hand, captures the general density information in crowded regions. Without knowing the location of each person, it tends to overestimate the count in low density areas. Thus, exclusively using either one of them is not sufficient to handle all kinds of scenes with varying densities. To address this issue, a novel end-to-end crowd counting framework, named DecideNet (DEteCtIon and Density Estimation Network) is proposed. It can adaptively decide the appropriate counting mode for different locations on the image based on its real density conditions. DecideNet starts with estimating the crowd density by generating detection and regression based density maps separately. To capture inevitable variation in densities, it incorporates an attention module, meant to adaptively assess the reliability of the two types of estimations. The final crowd counts are obtained with the guidance of the attention module to adopt suitable estimations from the two kinds of density maps. Experimental results show that our method achieves state-of-the-art performance on three challenging crowd counting datasets.Comment: CVPR 201

Effects of spin imbalance on the electric-field driven quantum dissipationless spin current in pp-doped Semiconductors

It was proposed recently by Murakami et al. [Science \textbf{301}, 1348(2003)] that in a large class of $p$-doped semiconductors, an applied electric field can drive a quantum dissipationless spin current in the direction perpendicular to the electric field. In this paper we investigate the effects of spin imbalance on this intrinsic $spin$ Hall effect. We show that in a real sample with boundaries, due to the presence of spin imbalance near the edges of the sample, the spin Hall conductivity is not a constant but a sensitively $position$-$dependent$ quantity, and due to this fact, in order to take the effects of spin imbalance properly into account, a microscopic calculation of both the quantum dissipationless spin Hall current and the spin accumulation on an equal footing is thus required. Based on such a microscopic calculation, a detailed discussion of the effects of spin imbalance on the intrinsic spin Hall effect in thin slabs of $p$-doped semiconductors are presented.Comment: 8 pages, 2 figures, An extended version with detailed calculations To appear in Phys. Rev.

The Effects of Halo Assembly Bias on Self-Calibration in Galaxy Cluster Surveys

Self-calibration techniques for analyzing galaxy cluster counts utilize the abundance and the clustering amplitude of dark matter halos. These properties simultaneously constrain cosmological parameters and the cluster observable-mass relation. It was recently discovered that the clustering amplitude of halos depends not only on the halo mass, but also on various secondary variables, such as the halo formation time and the concentration; these dependences are collectively termed assembly bias. Applying modified Fisher matrix formalism, we explore whether these secondary variables have a significant impact on the study of dark energy properties using the self-calibration technique in current (SDSS) and the near future (DES, SPT, and LSST) cluster surveys. The impact of the secondary dependence is determined by (1) the scatter in the observable-mass relation and (2) the correlation between observable and secondary variables. We find that for optical surveys, the secondary dependence does not significantly influence an SDSS-like survey; however, it may affect a DES-like survey (given the high scatter currently expected from optical clusters) and an LSST-like survey (even for low scatter values and low correlations). For an SZ survey such as SPT, the impact of secondary dependence is insignificant if the scatter is 20% or lower but can be enhanced by the potential high scatter values introduced by a highly correlated background. Accurate modeling of the assembly bias is necessary for cluster self-calibration in the era of precision cosmology.Comment: 13 pages, 5 figures, replaced to match published versio

Consistency of shared reference frames should be reexamined

In a recent Letter [G. Chiribella et al., Phys. Rev. Lett. 98, 120501 (2007)], four protocols were proposed to secretly transmit a reference frame. Here We point out that in these protocols an eavesdropper can change the transmitted reference frame without being detected, which means the consistency of the shared reference frames should be reexamined. The way to check the above consistency is discussed. It is shown that this problem is quite different from that in previous protocols of quantum cryptography.Comment: 3 pages, 1 figure, comments are welcom

A strong constitutive ethylene-response phenotype conferred on Arabidopsis plants containing null mutations in the ethylene receptors ETR1 and ERS1

Background: The ethylene receptor family of Arabidopsis consists of five members, falling into two subfamilies. Subfamily 1 is composed of ETR1 and ERS1, and subfamily 2 is composed of ETR2, ERS2, and EIN4. Although mutations have been isolated in the genes encoding all five family members, the only previous insertion allele of ERS1 (ers1-2) is a partial loss-of-function mutation based on our analysis. The purpose of this study was to determine the extent of signaling mediated by subfamily-1 ethylene receptors through isolation and characterization of null mutations. Results: We isolated new T-DNA insertion alleles of subfamily 1 members ERS1 and ETR1 (ers1-3 and etr1-9, respectively), both of which are null mutations based on molecular, biochemical, and genetic analyses. Single mutants show an ethylene response similar to wild type, although both mutants are slightly hypersensitive to ethylene. Double mutants of ers1-3 with etr1-9, as well as with the previously isolated etr1-7, display a constitutive ethylene-response phenotype more pronounced than that observed with any previously characterized combination of ethylene receptor mutations. Dark-grown etr1-9;ers1-3 and etr1-7;ers1-3 seedlings display a constitutive triple-response phenotype. Light-grown etr1-9;ers1-3 and etr1-7;ers1-3 plants are dwarfed, largely sterile, exhibit premature leaf senescence, and develop novel filamentous structures at the base of the flower. A reduced level of ethylene response was still uncovered in the double mutants, indicating that subfamily 2 receptors can independently contribute to signaling, with evidence suggesting that this is due to their interaction with the Raf-like kinase CTR1. Conclusion: Our results are consistent with the ethylene receptors acting as redundant negative regulators of ethylene signaling, but with subfamily 1 receptors playing the predominant role. Loss of a single member of subfamily 1 is largely compensated for by the activity of the other member, but loss of both subfamily members results in a strong constitutive ethylene-response phenotype. The role of subfamily 1 members is greater than previously suspected and analysis of the double mutant null for both ETR1 and ERS1 uncovers novel roles for the receptors not previously characterized