A theory of orbit braids

This paper upbuilds the theoretical framework of orbit braids in $M\times I$ by making use of the orbit configuration space $F_G(M,n)$, which enriches the theory of ordinary braids, where $M$ is a connected topological manifold of dimension at least 2 with an effective action of a finite group $G$ and the action of $G$ on $I$ is trivial. Main points of our work include as follows. We introduce the orbit braid group $\mathcal{B}_n^{orb}(M,G)$, and show that it is isomorphic to a group with an additional endowed operation (called the extended fundamental group of $F_G(M,n)$), formed by the homotopy classes of some paths (not necessarily closed paths) in $F_G(M,n)$, which is an essential extension for fundamental groups. The orbit braid group $\mathcal{B}_n^{orb}(M,G)$ is large enough to contain the fundamental group of $F_G(M,n)$ and other various braid groups as its subgroups. Around the central position of $\mathcal{B}_n^{orb}(M,G)$, we obtain five short exact sequences weaved in a commutative diagram. We also analyze the essential relations among various braid groups associated to those configuration spaces $F_G(M,n), F(M/G,n)$, and $F(M,n)$. We finally consider how to give the presentations of orbit braid groups in terms of orbit braids as generators. We carry out our work by choosing $M=\mathbb{C}$ with typical actions of $\mathbb{Z}_p$ and $(\mathbb{Z}_2)^2$. We obtain the presentations of the corresponding orbit braid groups, from which we see that the generalized braid group $Br(B_n)$ actually agrees with an orbit braid group and $Br(D_n)$ is a subgroup of another orbit braid group. In addition, the notion of extended fundamental groups is also defined in a general way in the category of topology and some characteristics extracted from the discussions of orbit braids are given.Comment: 30 pages, minor changes and corrections in section

Hopping conductance and macroscopic quantum tunneling effect in three dimensional Pbx_x(SiO2_2)1−x_{1-x} nanogranular films

We have studied the low-temperature electrical transport properties of Pb$_x$(SiO$_2$)$_{1-x}$ ($x$ being the Pb volume fraction) nanogranular films with thicknesses of $\sim$1000 nm and $x$ spanning the dielectric, transitional, and metallic regions. It is found that the percolation threshold $x_c$ lies between 0.57 and 0.60. For films with $x$$\lesssim$0.50, the resistivities $\rho$ as functions of temperature $T$ obey $\rho\propto\exp(\Delta/k_BT)$ relation ($\Delta$ being the local superconducting gap and the $k_B$ Boltzmann constant) below the superconducting transition temperature $T_c$ ($\sim$7 K) of Pb granules. The value of the gap obtained via this expression is almost identical to that by single electron tunneling spectra measurement. The magnetoresistance is negative below $T_c$ and its absolute value is far larger than that above $T_c$ at a certain field. These observations indicate that single electron hopping (or tunneling), rather than Cooper pair hopping (or tunneling) governs the transport processes below $T_c$. The temperature dependence of resistivities shows reentrant behavior for the 0.50$<$$x$$<$0.57 films. It is found that single electron hopping (or tunneling) also dominates the low-temperature transport process for these films. The reduction of the single electron concentration leads to an enhancement of the resisivity at sufficiently low temperature. For the 0.60$\lesssim$$x$$\lesssim$0.72 films, the resistivities sharply decrease with decreasing temperature just below $T_c$, and then show dissipation effect with further decreasing temperature. Treating the conducting paths composed of Pb particles as nanowires, we have found that the $R(T)$ data below $T_c$ can be well explained by a model that includes both thermally activated phase slips and quantum phase slips.Comment: 8 pages, 6 figure

Perfect state transfer and efficient quantum routing: a discrete-time quantum walk approach

We show a perfect state transfer of an arbitrary unknown two-qubit state can be achieved via a discrete-time quantum walk with various settings of coin flippings, and extend this method to distribution of an arbitrary unknown multi-qubit entangled state between every pair of sites in the multi-dimensional network. Furthermore, we study the routing of quantum information on this network in a quantum walk architecture, which can be used as quantum information processors to communicate between separated qubits.Comment: 6 pages, 2 figure

Quantum security computation on shared secrets

Ouyang et al. proposed an $(n,n)$ threshold quantum secret sharing scheme, where the number of participants is limited to $n=4k+1,k\in Z^+$, and the security evaluation of the scheme was carried out accordingly. In this paper, we propose an $(n,n)$ threshold quantum secret sharing scheme for the number of participants $n$ in any case ( $n\in Z^+$ ). The scheme is based on a quantum circuit, which consists of Clifford group gates and Toffoli gate. We study the properties of the quantum circuit in this paper and use the quantum circuit to analyze the security of the scheme for dishonest participants

Crossing-changeable braids from chromatic configuration spaces

Motivated by the work in [15], this paper deals with the theory of the braids from chromatic configuration spaces. This kind of braids possess the property that some strings of each braid may intersect together and can also be untangled, so they are quite different from the ordinary braids in the sense of Artin. This enriches and extends the theory of ordinary braids.Comment: 17 pages, It has been accepted for publication in SCIENCE CHINA Mathematic

A secret sharing scheme on p^2 -dimensional quantum system

In this paper, we give the mutually unbiased bases on the p^2 -dimensional quantum system where p is an odd prime number, and construct the corresponding unitary transformation based on the properties of these mutually unbiased bases. Then, we construct a (N,N) threshold secret sharing scheme using unitary transformation between these mutually unbiased bases, and analyze the scheme's security by several ways, for example, intercept-and-resend attack, entangle-and-measure attack, Trojan horse attack, and so on. Using our method, we construct a single-particle quantum protocol involving only one qudit, and the method shows much more scalability than other schemes.Comment: 14 page

Reinvestigation of the electron fraction and electron Fermi energy of neutron star

In this work, we reinvestigate the electron fraction $Y_{e}$ and electron Fermi energy $E_{F}(e)$ of neutron stars, based on our previous work of Li et al.(2016), in which we firstly deduced a special solution to $E_{F}(e)$, and then obtained several useful analytical formulae for $Y_{\rm e}$ and matter density $\rho$ within classical models and the relativistic mean field(RMF) theory using numerically fitting. The advantages of this work include the following aspects:(1) The linear functions are substituted for the nonlinear exponential functions used in the previous work. This method may be more simple, and closer to realistic equation of state\,(EoS) of a neutron star(NS), because there are linear or quasi-linear relationships between number fractions of leptons and matter density, which can be seen by solving NS EoS; (2)we introduce a dimensionless variable $\varrho$\,($\varrho=\rho/\rho_0$, $\rho_{0}$ is the standard saturated nuclear density), which greatly reduces the scope of the fitting coefficients;(3)we present numerical errors including absolute and relative deviations between the data and fit. By numerically simulating, we have obtained several analytical formulae for $Y_{e}$ and $\rho$ for both APR98 and RMF models. Combining these analytical formulae with the special solution, we can calculate the value of $E_{\rm F}(e)$ for any given matter density. Since $Y_e$ and $E_{ F}(e)$ are important in assessing cooling rate of a NS and the possibility of kaon/pion condensation in the NS interior, this study could be useful in the future study on the thermal evolution of a NS.Comment: 3 figures, 3 tables , and We welcome any comment you might have about the content, To be published in Astron. Nach

CPOT: Channel Pruning via Optimal Transport

Recent advances in deep neural networks (DNNs) lead to tremendously growing network parameters, making the deployments of DNNs on platforms with limited resources extremely difficult. Therefore, various pruning methods have been developed to compress the deep network architectures and accelerate the inference process. Most of the existing channel pruning methods discard the less important filters according to well-designed filter ranking criteria. However, due to the limited interpretability of deep learning models, designing an appropriate ranking criterion to distinguish redundant filters is difficult. To address such a challenging issue, we propose a new technique of Channel Pruning via Optimal Transport, dubbed CPOT. Specifically, we locate the Wasserstein barycenter for channels of each layer in the deep models, which is the mean of a set of probability distributions under the optimal transport metric. Then, we prune the redundant information located by Wasserstein barycenters. At last, we empirically demonstrate that, for classification tasks, CPOT outperforms the state-of-the-art methods on pruning ResNet-20, ResNet-32, ResNet-56, and ResNet-110. Furthermore, we show that the proposed CPOT technique is good at compressing the StarGAN models by pruning in the more difficult case of image-to-image translation tasks.Comment: 11 page

The inner ∼\sim 40 pc Radial Distribution of the Star formation Rate for a nearby Seyfert 2 galaxy M51

We investigate spatially resolved specific star formation rate (SSFR) in the inner $\sim$ 40 pc for a nearby Seyfert 2 galaxy, M51 (NGC 5194) by analyzing spectra obtained with the \emph{Hubble Space Telescope (HST)} Space Telescope Imaging Spectrograph (STIS). We present 24 radial spectra measured along the STIS long slit in M51, extending \sim 1\arcsec from the nucleus (i.e., -41.5 pc to 39.4 pc). By the simple stellar population synthesis, the stellar contributions in these radial optical spectra are modeled. Excluding some regions with zero young flux fraction near the center (from -6 pc to 2 pc), we find that the mean flux fraction of young stellar populations (younger than 24.5 Myr) is about 9 \%, the mean mass fraction is about 0.09\%. The young stellar populations are not required in the center inner $\sim$ 8 pc in M51, suggesting a possible SSFR suppression in the circumnuclear region ($\sim$ 10 pc) from the feedback of active galactic nuclei (AGNs). The radial distribution of SSFR in M51 is not symmetrical with respect to the long slit in STIS. This unsymmetrical SSFR distribution is possibly due to the unsymmetrical AGN feedback in M51, which is related to its jet.Comment: 9 pages, 4 figures, published in Research in Astron. Astrophy

Measurements of Radon Concentrations Using CR-39 Detectors in China JinPing Underground Laboratory (2015-2016)

Radon background is one of the most critical influences on the ultra-low background and rare-event physical experiments in underground laboratories. To conduct a comprehensive investigation of the radon concentrations in China JinPing underground Laboratory (CJPL), long-term cumulative measurements were carried out using time-integrated passive radon dosimeters containing CR-39 solid-state nuclear track detectors at four sites of CJPL-I. The measurements lasted from May 30,2015 to March 16,2016, a total of 290 days, and the total effective measurement time is 6,953 hours. In the main experiment hall equipped with the ventilation system, the average annual radon concentrations were (55+/-7) Bq m^-3, (58+/-10) Bq^m-3and (53+/-9) Bq m^-3 in three locations respectively. In the storage tunnel without any radon reduction facility, the average annual radon concentrations increased to (345+/-15) Bq m^-3, reflecting the original average annual radon concentration levels in the underground laboratory. Compared with the measured results in the period from 2010 to 2011, the average radon concentration in the main experimental hall was reduced from (86+/-25) Bq m^-3 to (58+/-10) Bq m^-3 due to the well-running ventilation system. Compared with other international underground laboratories, radon concentrations in CJPL-I were at an intermediate level and can meet the demand for low background and rare-event physical experiments