Secure Network Coding Against the Contamination and Eavesdropping Adversaries

In this paper, we propose an algorithm that targets contamination and eavesdropping adversaries. We consider the case when the number of independent packets available to the eavesdropper is less than the multicast capacity of the network. By means of our algorithm every node can verify the integrity of the received packets easily and an eavesdropper is unable to get any meaningful information about the source. We call it practical security if an eavesdropper is unable to get any meaningful information about the source.We show that, by giving up a small amount of overall capacity, our algorithm achieves achieves the practically secure condition at a probability of one. Furthermore, the communication overhead of our algorithm are negligible compared with previous works, since the transmission of the hash values and the code coefficients are both avoided.Comment: 6 pages, 3 figure

An integral test on time dependent local extinction for super-coalescing Brownian motion with Lebesgue initial measure

This paper concerns the almost sure time dependent local extinction behavior for super-coalescing Brownian motion $X$ with $(1+\beta)$-stable branching and Lebesgue initial measure on \bR. We first give a representation of $X$ using excursions of a continuous state branching process and Arratia's coalescing Brownian flow. For any nonnegative, nondecreasing and right continuous function $g$, put \tau:=\sup \{t\geq 0: X_t([-g(t),g(t)])>0 \}. We prove that \bP\{\tau=\infty\}=0 or 1 according as the integral $\int_1^\infty g(t)t^{-1-1/\beta} dt$ is finite or infinite.Comment: 14 page

Branching Particle Systems in Spectrally One-sided Levy Processes

We investigate the branching structure coded by the excursion above zero of a spectrally positive Levy process. The main idea is to identify the level of the Levy excursion as the time and count the number of jumps upcrossing the level. By regarding the size of a jump as the birth site of a particle, we construct a branching particle system in which the particles undergo nonlocal branchings and deterministic spatial motions to the left on the positive half line. A particle is removed from the system as soon as it reaches the origin. Then a measure-valued Borel right Markov process can be defined as the counting measures of the particle system. Its total mass evolves according to a Crump-Mode-Jagers branching process and its support represents the residual life times of those existing particles. A similar result for spectrally negative Levy process is established by a time reversal approach. Properties of the measure-valued processes can be studied via the excursions for the corresponding Levy processes.Comment: 23pages, 2 figure

On the Hadronic Gamma-ray Emission from Tycho's Supernova Remnant

Hadronic gamma-ray emission from supernova remnants (SNRs) is an important tool to test shock acceleration of cosmic ray protons. Tycho is one of nearly a dozen Galactic SNRs which are suggested to emit hadronic gamma-ray emission. Among them, however, it is the only one in which the hadronic emission is proposed to arise from the interaction with low-density (~0.3 cm^{-3}) ambient medium. Here we present an alternative hadronic explanation with a modest conversion efficiency (of order 1%) for this young remnant. With such an efficiency, a normal electron-proton ratio (of order 10^{-2}) is derived from the radio and X-ray synchrotron spectra and an average ambient density that is at least one-order-of-magnitude higher is derived from the hadronic gamma-ray flux. This result is consistent with the multi-band evidence of the presence of dense medium from the north to the east of the Tycho SNR. The SNR-cloud association, in combination with the HI absorption data, helps to constrain the so-far controversial distance to Tycho and leads to an estimate of 2.5 kpc.Comment: 5 pages (including 2 figures), accepted for publication in MNRAS Lette

Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field

We analyze the scaling parameter, extracted from the fidelity for two different ground states, for the one-dimensional quantum Ising model in a transverse field near the critical point. It is found that, in the thermodynamic limit, the scaling parameter is singular, and the derivative of its logarithmic function with respect to the transverse field strength is logarithmically divergent at the critical point. The scaling behavior is confirmed numerically by performing a finite size scaling analysis for systems of different sizes, consistent with the conformal invariance at the critical point. This allows us to extract the correlation length critical exponent, which turns out to be universal in the sense that the correlation length critical exponent does not depend on either the anisotropic parameter or the transverse field strength.Comment: 5 pages, 5 figure

Long-term Optical Observations of the Be/X-ray Binary X Per

We present the optical spectroscopic observations of X Per from 1999 to 2013 with the 2.16m telescope at Xinglong Station and the 2.4m telescope at Lijiang station, National Astronomical Observatories of China. Combining with the public optical photometric data, we find certain epochs of anti-correlations between the optical brightness and the intensity of the H{\alpha} and HeI 6678 lines, which may be attributed to the mass ejections from the Be star. Alternative explanations are however also possible. The variability of FeII 6317 line in the spectra of X Per might be also caused by the shocked waves formed after the mass ejections from the Be star. The X-ray activities of the system might also be connected with the mass ejection events from the Be star. When the ejected materials were transported from the surface of the Be star to the orbit of neutron star, an X-ray flare could be observed in its X-ray light curves. We use the neutron star as a probe to constrain the motion of the ejected material in the circumstellar disk. With the diffusion time of the ejected material from the surface of Be star to the orbit of neutron star, the viscosity parameter {\alpha} of the circumstellar disk is estimated to be 0.39 and 0.28 for the different time, indicating that the disk around Be star may be truncated by the neutron star at the 2:1 resonance radius and Type I X-ray outburst is unlikely to be observed in X Per.Comment: 24 pages, 5 figure, 1 tabl

Measurement of weak static magnetic fields with nitrogen-vacancy color center

We propose a strategy to measure weak static magnetic fields with nitrogen-vacancy color center in diamond. Inspired by avian magnetoreception models, we consider the feasibility of utilizing quantum coherence phenomena to measure weak static magnetic fields. Nitrogen-vacancy (NV) color centers are regarded as the ideal platform to study quantum sciences as a result of its long coherence time up to a millisecond timescale. In high-purity diamond, hyperfine interaction with 13C nuclear spins dominates the decoherence process. In this paper, we numerically simulate the decoherence process between 0 and +1 of the individual NV color center spin in 13C nuclear baths with various of magnitudes of external magnetic fields. By applying Hahn echo into the system, we obtain the coherence of NV color center spin as a function of total evolution time and magnetic field. Furthermore we obtain the high-accuracy relationship between the three decoherence-characteristic timescales, i.e. T_W, T_R, T_2, and magnetic field B. And we draw a conclusion that T_R has the highest sensitivity about magnetic field among the three time-scales. Thus, for a certain NV color center, T_R can be the scale for the magnitude of magnetic field, or rather, the component along the NV electronic spin axis. When measuring an unknown magnetic field, we adjust the NV axis to three mutually orthogonal directions respectively. By this means, we obtain the three components of the magnetic field and thus the magnitude and direction of the actual magnetic field. The accuracy could reach 60 nT/Hz^{1/2},and could be greatly improved by using an ensemble of NV color centers or diamond crystals purified with 12C atoms.Comment: 17 pages, 5 figures, 1 tabl

Finding a Nonnegative Solution to an M-Tensor Equation

We are concerned with the tensor equation with an M-tensor or Z-tensor, which we call the M- tensor equation or Z-tensor equation respectively. We derive a necessary and sufficient condition for a Z (or M)-tensor equation to have nonnegative solutions. We then develop a monotone iterative method to find a nonnegative solution to an M-tensor equation. The method can be regarded as an approximation to Newton's method for solving the equation. At each iteration, we solve a system of linear equations. An advantage of the proposed method is that the coefficient matrices of the linear systems are independent of the iteration. We show that if the initial point is appropriately chosen, then the sequence of iterates generated by the method converges to a nonnegative solution of the M- tensor equation monotonically and linearly. At last, we do numerical experiments to test the proposed methods. The results show the efficiency of the proposed methods

Theory for Spin Selective Andreev Reflection in Vortex Core of Topological Superconductor: Majorana Zero Modes on Spherical Surface and Application to Spin Polarized Scanning Tunneling Microscope Probe

Majorana zero modes (MZMs) have been predicted to exist in the topological insulator (TI)/superconductor (SC) heterostructure. Recent spin polarized scanning tunneling microscope (STM) experiment$^{1}$ has observed spin-polarization dependence of the zero bias differential tunneling conductance at the center of vortex core, which may be attributed to the spin selective Andreev reflection, a novel property of the MZMs theoretically predicted in 1-dimensional nanowire$^{2}$. Here we consider a helical electron system described by a Rashba spin orbit coupling Hamiltonian on a spherical surface with a s-wave superconducting pairing due to proximity effect. We examine in-gap excitations of a pair of vortices with one at the north pole and the other at the south pole. While the MZM is not a spin eigenstate, the spin wavefunction of the MZM at the center of the vortex core, r = 0, is parallel to the magnetic field, and the local Andreev reflection of the MZM is spin selective, namely occurs only when the STM tip has the spin polarization parallel to the magnetic field, similar to the case in 1-dimensional nanowire2. The total local differential tunneling conductance consists of the normal term proportional to the local density of states and an additional term arising from the Andreev reflection. We also discuss the finite size effect, for which the MZM at the north pole is hybridized with the MZM at the south pole. We apply our theory to examine the recently reported spin-polarized STM experiments and show good agreement with the experiments.Comment: 14 pages, 14 figures, 1 table. Comments are welcome

The leptonic CP phase is determined by an equation involving the PMNS matrix elements

Several approximate equalities among the matrix elements of CKM and PMNS imply that hidden symmetries may exist and be common for both quark and neutrino sectors. The CP phase of the CKM matrix ($\delta_{\rm CKM}$) is involved in these equalities and can be investigated when these equalities turn into several equations. As we substitute those experimentally measured values of the three mixing angles into the equations for quarks, it is noted that one of the equations which holds exactly has a solution $\delta_{\rm CKM}=68.95^\circ$. That value accords with $(69.1^{+2.02}_{-3.85})^\circ$ determined from available data. Generalizing the scenario to the lepton sector, the same equality determines the leptonic CP phase $\delta_{\rm PMNS}$ to be $276.10^\circ$. Thus we predict the value of $\delta_{\rm PMNS}$ from the equation. So far there is no direct measurement on $\delta_{\rm PMNS}$ yet, but a recent analysis based on the neutrino oscillation data prefers the phase close to $270^\circ$.Comment: 4 pages, 1 figure. Some references adde