Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms

In this paper, we focus on the construction of structure preserving algorithms for Birkhoffian systems, based on existing symplectic schemes for the Hamiltonian equations. The key of the method is to seek an invertible transformation which drives the Birkhoffian equations reduce to the Hamiltonian equations. When there exists such a transformation,applying the corresponding inverse map to symplectic discretization of the Hamiltonian equations, then resulting difference schemes are verified to be Birkhoffian symplectic for the original Birkhoffian equations. To illustrate the operation process of the method, we construct several desirable algorithms for the linear damped oscillator and the single pendulum with linear dissipation respectively. All of them exhibit excellent numerical behavior, especially in preserving conserved quantities.     

Type II quantum algorithms

We review and analyze the hybrid quantum-classical NMR computing methodology referred to as Type II quantum computing. We show that all such algorithms considered so far within this paradigm are equivalent to some classical lattice Boltzmann scheme. We derive a sufficient and necessary constraint on the unitary operator representing the quantum mechanical part of the computation which ensures that the model reproduces the Boltzmann approximation of a lattice-gas model satisfying semi-detailed balance. Models which do not satisfy this constraint represent new lattice Boltzmann schemes which cannot be formulated as the average over some underlying lattice-gas. We conclude the paper with some discussion of the strengths, weaknesses and possible future direction of Type II quantum computing.     

量子计算算法介绍

量子计算机利用量子力学原理进行计算,具有量子并行计算的优势,能够超越经典计算1990年中期,量子算法取得突破,舒尔(Shor)构造了大数质因子的量子算法,葛洛沃(Grover)构造了无序数据库的量子搜索算法,引起了人们对量子计算的重视,极大地推动了量子计算的研究.文章简单介绍了几个典型的量子算法以及量子算法研究的一些新进展.     

New algorithms for one-loop integrals

New algorithms are presented for evaluating the scalar one loop integrals for three- and four-point functions for arbitrary masses and external momenta. These formulations are useful both for analytic integration and for numerical evaluation in a computer program. The expressions are very compact and provide for an easy isolation of asymptotic behaviour and potential numerical problems. The tensor integrals have also been rewritten according to new algorithms, making it very easy to express amplitudes in terms of scalar loop integrals.     

Optimized third-order force-gradient symplectic algorithms

With the natural splitting of a Hamiltonian system into kinetic energy and potential energy,we construct two new optimal thirdorder force-gradient symplectic algorithms in each of which the norm of fourth-order truncation errors is minimized.They are both not explicitly superior to their no-optimal counterparts in the numerical stability and the topology structure-preserving,but they are in the accuracy of energy on classical problems and in one of the energy eigenvalues for one-dimensional time-independent Schrdinger equations.In particular,they are much better than the optimal third-order non-gradient symplectic method.They also have an advantage over the fourth-order non-gradient symplectic integrator.     

Nonparametric algorithms for vector optimization

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 5–10, September, 1995.     

Structure-preserving algorithms for Birkhoffian systems

We propose a new approach to construct structure-preserving algorithms for Birkhoffian systems. First, the Pfaff–Birkhoff variational principle is discretized, and based on the discrete variational principle the discrete Birkhoffian equations are obtained. Then, taking the discrete equations as an algorithm, the corresponding discrete flow is proved to be symplectic. That means the algorithm preserves the symplectic structure of Birkhoffian systems. Simulation results of the given example indicate that structure-preserving algorithms obtained by this method have great advantage in conserving conserved quantities.     

流体力学拉氏守恒滑移线算法设计

本文在Wilkins滑移线算法的基础上, 设计了从区网格边人工黏性对主点施加算法. 结合拉氏“相容性格式”, 通过定义“接触力”和“接触力做功”, 利用局部修正内能的方法设计了总能量守恒的流体力学拉氏格式. 该修正方法可保证对称性、守恒性; 提高数值模拟分辨率.     

Quantum games via search algorithms

We build new quantum games, similar to the spin flip game, where as a novelty the players perform measurements on a quantum system associated to a continuous time search algorithm. The measurements collapse the wave function into one of the two possible states. These games are characterized by a continuous space of strategies and the selection of a particular strategy is determined by the moments when the players measure.     

Programmable networks for quantum algorithms

The implementation of a quantum computer requires the realization of a large number of N-qubit unitary operations which represent the possible oracles or which are part of the quantum algorithm. Until now there have been no standard ways to uniformly generate whole classes of N-qubit gates. We develop a method to generate arbitrary controlled phase-shift operations with a single network of one-qubit and two-qubit operations. This kind of network can be adapted to various physical implementations of quantum computing and is suitable to realize the Deutsch-Jozsa algorithm as well as Grover's search algorithm.     

More efficient Brownian dynamics algorithms

We examine the relative efficiencies of three- algorithms for performing Brownian Dynamics simulations without many-body hydrodynamics. We compare the conventional Brownian Dynamics algorithm of Ermak (CBD), Smart Monte Carlo (SMC) which incorporates Boltzmann sampling into essentially a CBD procedure, and the Stochastic Runge Kutta (SRK) method. We show, using the repulsive potential φ(r) = ε(σ/r) ⁿ , where n = 36 and 72, that the SRK algorithm gives the most accurate short-time dynamics for the mean-square displacements. The SRK algorithm static and dynamical properties converge better with a reducing time step to the exact values, than those generated by the CBD algorithm; giving efficiency gains typically of a factor of 3–4. Both CBD and SMC have the incorrect sign for the first correction term to the mean square displacement in a time step, whereas the SRK algorithm gives essentially the exact solution to order Δt ², where Δt is the simulation time step. In fact, these correction terms are almost equal and opposite in sign. Expressions for these terms were derived in terms of the average interaction energy per particle. The force, shear and bulk stress autocorrelation functions were calculated. The average energy per particle and time correlation functions at short time have values in excess of the exact values, while the corresponding quantities for SRK are below this. This difference in behaviour can be traced back to the extent of compliance of the particle trajectories with the exact expansion of the Smoluchowski equation. The accuracy, at a given value of the time step, of the stochastic algorithms can significantly depend on the form of the interaction potential between particles. It is also demonstrated that the long time limits of various correlation functions are fairly insensitive to a particular scheme (SRK or CBD) used in the simulations. All the correlation functions have a stretched exponential region at intermediate to long times, and the values of the exponents on density and force law steepness have been determined.     

图像增强算法综述

图像增强算法能够提高图像整体和局部的对比度,突出图像的细节信息,使增强后的图像更符合人眼的视觉特性且易于机器识别,在军事和民用领域具有广泛的应用。本文从图像增强算法的原理出发,归纳总结了近年来应用比较广泛的4类图像增强算法及其改进算法,包括直方图均衡图像增强算法、小波变换图像增强算法、偏微分方程图像增强算法和基于Retinex理论的图像增强算法。结合人眼视觉特性、噪声抑制、亮度保持和信息熵最大化等图像增强的改进算法,在保证增强图像具有较高对比度的前提下,可进一步提升图像的质量。实现了9种较为典型的图像增强算法,采用主观和客观的评价方法对增强效果进行了对比,分析了不同增强算法的优缺点,并给出了这些算法的计算时间。对这些算法的深入研究能够推动图像增强技术向更高水平发展,从而使图像增强技术在多个学科领域发挥重要作用。     

Efficient subpixel image registration algorithms

Three new algorithms for 2D translation image registration to within a small fraction of a pixel that use nonlinear optimization and matrix-multiply discrete Fourier transforms are compared. These algorithms can achieve registration with an accuracy equivalent to that of the conventional fast Fourier transform upsampling approach in a small fraction of the computation time and with greatly reduced memory requirements. Their accuracy and computation time are compared for the purpose of evaluating a translation-invariant error metric.     

Determining reflections for beam propagation algorithms

Reflections occur whenever different waveguide sections are concatenated. In this paper, we will give approximate formulas for determining the reflection coefficient. Starting with generalized transmission line equations we will derive general formulas where suitable approximations are introduced. These approximations allow the determination of the reflections with low numerical effort. The expressions were implemented in an FD-BPM algorithm to determine the field distribution in waveguide devices. For an application in CAD systems the reflection coefficient of the fundamental mode was computed with the approximate formulas. Numerical results were obtained for various concatenations of different waveguide sections. A comparison with the method of lines, a semi-analytic algorithm, shows a good agreement.     

Quantum algorithms in one-way quantum computation

Cluster states are the fundamental resource for the one-way model of quantum computation. In this paper we show the realization of a two-photon four-qubit cluster state. The qubits are encoded in the polarization and the linear momentum of the particles. By using this state we realized two important quantum algorithms, namely the Grover’s search and the Deutsch’s algorithm.