Analytical Solution of Transverse Oscillation in Cyclotron Using LP Method

We have carried out an approximate analytical solution to precisely consider the influence of magnetic field on the transverse oscillation of particles in cyclotron. The differential equations of transverse oscillation are solved from the Lindstedt-Poincare method. After careful deduction, the accurate first order analytic solutions are obtained. The analytical solutions are applied to the magnetic field, comes from an isochronous cyclotron with four spiral sectors, the accuracy of these analytical solutions is verified and confirmed from the comparison of numerical method. Finally, we discussed the transverse oscillation at v0=N/2 , using the same analytical solution.Comment: This peper will be published in Chinese Physics

Locality of percolation critical probabilities: uniformly nonamenable case

Let $\{G_n\}_{n=1}^{\infty}$ be a sequence of transitive infinite connected graphs with $\sup\limits_{n\geq 1} p_c(G_n) < 1,$ where each $p_c(G_n)$ is bond percolation critical probability on $G_n.$ Schramm (2008) conjectured that if $G_n$ converges locally to a transitive infinite connected graph $G,$ then $p_c(G_n) \rightarrow p_c(G)$ as $n\rightarrow\infty.$ We prove the conjecture when $G$ satisfies two rough uniformities, and $\{G_n\}_{n=1}^{\infty}$ is uniformly nonamenable

Optimal Puncturing of Polar Codes With a Fixed Information Set

For a given polar code construction, the existing literature on puncturing for polar codes focuses in finding the optimal puncturing pattern, and then re-selecting the information set. This paper devotes itself to find the optimal puncturing pattern when the information set is fixed. Puncturing the coded bits corresponding to the worst quality bit channels, called the worst quality puncturing (WQP), is proposed, which is analyzed to minimize the bit channel quality loss at the punctured positions. Simulation results show that WQP outperforms the best existing puncturing schemes when the information set is fixed.Comment: Polar codes, puncture, quasi-uniform puncturing,worst quality puncturin

K∗0K^{*0} and Σ∗\Sigma^* production in Au+Au collisions at sNN=\sqrt{s_{NN}}= 200 GeV and 62.4 GeV

Applying a quark combination model for the hadronization of Quark Gluon Plasma (QGP) and A Relativistic Transport (ART) model for the subsequent hadronic rescattering process, we investigate the production of $K^{*0}$ and $\Sigma^*$ resonances in central Au+Au collisions at $\sqrt{s_{NN}}=$ 200 GeV and 62.4 GeV. The initial $K^{*0}$ produced via hadronization is higher than the experimental data in the low $p_T$ region and is close to the data at 2-3 GeV/c. We take into account the hadronic rescattering effects which lead to a strong suppression of $K^{*0}$ with low $p_T$, and find that the $p_T$ spectrum of $K^{*0}$ can be well described. According to the suppressed magnitude of $K^{*0}$ yield, the time span of hadronic rescattering stage is estimated to be about 13 fm/c at 200 GeV and 5 fm/c at 62.4 GeV. The $p_T$ spectrum of $\Sigma^*$ directly obtained by quark combination hadronization in central Au+Au collisions at 200 GeV is in well agreement with the experimental data, which shows a weak hadronic rescattering effects. The elliptic flow v2 of $\Sigma^*$ in minimum bias Au+Au collisions at 200 GeV and $p_T$ spectrum of $\Sigma^*$ at lower 62.4 GeV are predicted.Comment: 12 pages, 6 figure

Learning Non-overlapping Convolutional Neural Networks with Multiple Kernels

In this paper, we consider parameter recovery for non-overlapping convolutional neural networks (CNNs) with multiple kernels. We show that when the inputs follow Gaussian distribution and the sample size is sufficiently large, the squared loss of such CNNs is $\mathit{~locally~strongly~convex}$ in a basin of attraction near the global optima for most popular activation functions, like ReLU, Leaky ReLU, Squared ReLU, Sigmoid and Tanh. The required sample complexity is proportional to the dimension of the input and polynomial in the number of kernels and a condition number of the parameters. We also show that tensor methods are able to initialize the parameters to the local strong convex region. Hence, for most smooth activations, gradient descent following tensor initialization is guaranteed to converge to the global optimal with time that is linear in input dimension, logarithmic in precision and polynomial in other factors. To the best of our knowledge, this is the first work that provides recovery guarantees for CNNs with multiple kernels under polynomial sample and computational complexities.Comment: arXiv admin note: text overlap with arXiv:1706.0317

Pseudorandom States, Non-Cloning Theorems and Quantum Money

We propose the concept of pseudorandom states and study their constructions, properties, and applications. Under the assumption that quantum-secure one-way functions exist, we present concrete and efficient constructions of pseudorandom states. The non-cloning theorem plays a central role in our study---it motivates the proper definition and characterizes one of the important properties of pseudorandom quantum states. Namely, there is no efficient quantum algorithm that can create more copies of the state from a given number of pseudorandom states. As the main application, we prove that any family of pseudorandom states naturally gives rise to a private-key quantum money scheme.Comment: 20 page

Strangeness S=−1S=-1 hyperon-nucleon interactions: chiral effective field theory vs. lattice QCD

Hyperon-nucleon interactions serve as basic inputs to studies of hypernuclear physics and dense (neutron) stars. Unfortunately, a precise understanding of these important quantities have lagged far behind that of the nucleon-nucleon interaction due to lack of high precision experimental data. Historically, hyperon-nucleon interactions are either formulated in quark models or meson exchange models. In recent years, lattice QCD simulations and chiral effective field theory approaches start to offer new insights from first principles. In the present work, we contrast the state of art lattice QCD simulations with the latest chiral hyperon-nucleon forces and show that the leading order relativistic chiral results can already describe the lattice QCD data reasonably well. Given the fact that the lattice QCD simulations are performed with pion masses ranging from the (almost) physical point to 700 MeV, such studies provide a highly non-trivial check on both the chiral effective field theory approaches as well as lattice QCD simulations. Nevertheless more precise lattice QCD simulations are eagerly needed to refine our understanding of hyperon-nucleon interactions.Comment: 13 pages, 5 figure

Encoding Complexity of Network Coding with Two Simple Multicast Sessions

The encoding complexity of network coding for single multicast networks has been intensively studied from several aspects: e.g., the time complexity, the required number of encoding links, and the required field size for a linear code solution. However, these issues as well as the solvability are less understood for networks with multiple multicast sessions. Recently, Wang and Shroff showed that the solvability of networks with two unit-rate multicast sessions (2-URMS) can be decided in polynomial time. In this paper, we prove that for the 2-URMS networks: $1)$ the solvability can be determined with time $O(|E|)$; $2)$ a solution can be constructed with time $O(|E|)$; $3)$ an optimal solution can be obtained in polynomial time; $4)$ the number of encoding links required to achieve a solution is upper-bounded by $\max\{3,2N-2\}$; and $5)$ the field size required to achieve a linear solution is upper-bounded by $\max\{2,\lfloor\sqrt{2N-7/4}+1/2\rfloor\}$, where $|E|$ is the number of links and $N$ is the number of sinks of the underlying network. Both bounds are shown to be tight

Symmetry Analysis of ZnSe(100) Surface in Air By Second Harmonic Generation

Polarized and azimuthal dependencies of optical second harmonics generation (SHG) at the surface of noncentrosymmetric semiconductor crystals have been measured on polished surfaces of ZnSe(100), using a fundamental wavelength of 1.06$\mu m$. The SHG intensity patterns were analyzed for all four combination of p- and s-polarized incidence and output, considering both the bulk and surface optical nonlinearities in the electric dipole approximation. We found that the measurement using $S_{in}-S_{out}$ is particularly useful in determining the symmetry of the oxdized layer interface, which would lower the effective symmetry of the surface from $C_{4v}$ to $C_{2v}.$ We also have shown that the [011] and [0$\bar{1}$1] directions can be distinguished through the analysis of p-incident and p-output confugration.Comment: 21 pages, 5 figure

On the Solvability of 3s/nt Sum-Network---A Region Decomposition and Weak Decentralized Code Method

We study the network coding problem of sum-networks with 3 sources and n terminals (3s/nt sum-network), for an arbitrary positive integer n, and derive a sufficient and necessary condition for the solvability of a family of so-called terminal-separable sum-network. Both the condition of terminal-separable and the solvability of a terminal-separable sum-network can be decided in polynomial time. Consequently, we give another necessary and sufficient condition, which yields a faster (O(|E|) time) algorithm than that of Shenvi and Dey ([18], (O(|E|^3) time), to determine the solvability of the 3s/3t sum-network. To obtain the results, we further develop the region decomposition method in [22], [23] and generalize the decentralized coding method in [21]. Our methods provide new efficient tools for multiple source multiple sink network coding problems.Comment: 41 pages. arXiv admin note: text overlap with arXiv:1401.394