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1.
We derive a test problem for evaluating the ability of time-steppingmethods to preserve the statistical properties of systems inmolecular dynamics. We consider a family of deterministic systemsconsisting of a finite number of particles interacting on acompact interval. The particles are given random initial conditionsand interact through instantaneous energy- and momentum-conservingcollisions. As the number of particles, the particle density,and the mean particle speed go to infinity, the trajectory ofa tracer particle is shown to converge to a stationary Gaussianstochastic process. We approximate this system by one describedby a system of ordinary differential equations and provide numericalevidence that it converges to the same stochastic process. Wesimulate the latter system with a variety of numerical integrators,including the symplectic Euler method, a fourth-order Runge-Kuttamethod, and an energyconserving step-and-project method. Weassess the methods' ability to recapture the system's limitingstatistics and observe that symplectic Euler performs significantlybetter than the others for comparable computational expense. 相似文献
2.
Pierre Gaspard 《Journal of statistical physics》2004,117(3-4):599-615
A concept of time-reversed entropy per unit time is introduced in analogy with the entropy per unit time by Shannon, Kolmogorov, and Sinai. This time-reversed entropy per unit time characterizes the dynamical randomness of a stochastic process backward in time, while the standard entropy per unit time characterizes the dynamical randomness forward in time. The difference between the time-reversed and standard entropies per unit time is shown to give the entropy production of Markovian processes in nonequilibrium steady states. 相似文献
3.
4.
Noga Alon Oded Goldreich Johan Hstad Ren Peralta 《Random Structures and Algorithms》1992,3(3):289-304
We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1)) (log log n + k/2 + log k + log 1/?), where ? is the statistical difference between the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by Naor and Naor (our size bound is better as long as ? < 1/(k log n)). An additional advantage of our constructions is their simplicity. 相似文献
5.
Synthesis and characterization of a series of Polysulfone (PSF)-Polyester (PEs) block copolymers were studied.The degree of randomness (B) of these block eopolymers was calculated from the intensities of their proton signals in ~1H NMR spectra and lies in the region of 0相似文献
6.
J. E. Komosiński 《Isotopes in environmental and health studies》2013,49(5):199-201
Studies on the workability of precise seeders by means of labelling methods has been possible due to the solution of the following problems: labelling of seeds, radiation collimation of labelled seeds being sown, elaboration of measuring and registering systems as well as processing systems of a measuring signal. The developed method allows for precise, quick and fully objective evaluation of the studied seeders to be done under natural conditions. 相似文献
7.
Lianet Contreras Rodríguez Evaristo Jos Madarro-Cap
Carlos Miguel Legn-Prez
Omar Rojas Guillermo Sosa-Gmez 《Entropy (Basel, Switzerland)》2021,23(5)
Entropy makes it possible to measure the uncertainty about an information source from the distribution of its output symbols. It is known that the maximum Shannon’s entropy of a discrete source of information is reached when its symbols follow a Uniform distribution. In cryptography, these sources have great applications since they allow for the highest security standards to be reached. In this work, the most effective estimator is selected to estimate entropy in short samples of bytes and bits with maximum entropy. For this, 18 estimators were compared. Results concerning the comparisons published in the literature between these estimators are discussed. The most suitable estimator is determined experimentally, based on its bias, the mean square error short samples of bytes and bits. 相似文献
8.
Stochastic Configuration Network (SCN) has a powerful capability for regression and classification analysis. Traditionally, it is quite challenging to correctly determine an appropriate architecture for a neural network so that the trained model can achieve excellent performance for both learning and generalization. Compared with the known randomized learning algorithms for single hidden layer feed-forward neural networks, such as Randomized Radial Basis Function (RBF) Networks and Random Vector Functional-link (RVFL), the SCN randomly assigns the input weights and biases of the hidden nodes in a supervisory mechanism. Since the parameters in the hidden layers are randomly generated in uniform distribution, hypothetically, there is optimal randomness. Heavy-tailed distribution has shown optimal randomness in an unknown environment for finding some targets. Therefore, in this research, the authors used heavy-tailed distributions to randomly initialize weights and biases to see if the new SCN models can achieve better performance than the original SCN. Heavy-tailed distributions, such as Lévy distribution, Cauchy distribution, and Weibull distribution, have been used. Since some mixed distributions show heavy-tailed properties, the mixed Gaussian and Laplace distributions were also studied in this research work. Experimental results showed improved performance for SCN with heavy-tailed distributions. For the regression model, SCN-Lévy, SCN-Mixture, SCN-Cauchy, and SCN-Weibull used less hidden nodes to achieve similar performance with SCN. For the classification model, SCN-Mixture, SCN-Lévy, and SCN-Cauchy have higher test accuracy of 91.5%, 91.7% and 92.4%, respectively. Both are higher than the test accuracy of the original SCN. 相似文献
9.
基于模糊随机广义可靠性分析向随机可靠性分析的转换,提出了模糊随机广义失效概率计算的自适应重要抽样法,该方法利用模拟退火智能优化,在模拟的过程中逐步逼近模糊随机广义设计点,并在模拟过程中自适应地构造重要抽样函数,从而使得模糊随机失效概率的计算效率和精度大为提高。与传统的重要抽样法相比,本文方法无需首先求解失效模式的设计点。对非线性失效区和复杂等价概率密度函数,由于模拟退火智能优化在寻找设计点时比诸如一次二阶矩法(FOSM)更为有效,因而所提方法适合非线性失效区和复杂等价概率密度函数情况下的广义可靠性分析。另外,随着重要抽样密度函数逐步向最优值的自动调整,抽取的样本数逐渐增大,使后续构建的重要抽样函数更能体现对广义失效概率贡献的重要程度,并使失效概率的计算更加准确。文中算例证明了所提方法的合理性。 相似文献
10.
Christopher J. May Jeffrey C. Schank Sanjay Joshi Jonathan Tran R. J. Taylor I‐Esha Scott 《Complexity》2006,12(1):53-66
Biorobotic research continually demonstrates that behavior and cognition can be the emergent products of (1) embodied agents that are (2) dynamically embedded within an environment and (3) equipped with simple sensorimotor rules. Thigmotaxis is an orientation response to contact manifested in infant rats by wall following, corner burrowing, and group aggregation. Orientation responses have been long thought to be mediated only by sensory or central processes. Here we show that a random control architecture in a morphologically similar robot embedded in a scaled environment can reproduce thigmotaxic behaviors seen in infant rats. We conclude that (1) and (2) may play a larger role than previously thought in the generation of complex behaviors. © 2006 Wiley Periodicals, Inc. Complexity 12: 53–66, 2006 相似文献