A bound on the Wasserstein-2 distance between linear combinations of independent random variables

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ${?}^2\left({\mathbb{N}}^1\right)$. We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent.     

On uniform propagation of chaos

In this paper we obtain a time-uniform propagation estimate for a system of interacting diffusion processes. Using a well defined metric function h , our result guarantees a time-uniform estimate for the convergence of a class of interacting stochastic differential equations towards their mean field limit, under conditions that ensure that the decay associated to the internal dynamics term dominates the interaction and noise terms. Our result should have diverse applications, particularly in neuroscience, and allows for models more elaborate than the one of Wilson and Cowan. In particular, the internal dynamics need not be that of linear decay.     

Development and assessment of an intrusive polynomial chaos expansion-based continuous adjoint method for shape optimization under uncertainties

This article contributes to the development of methods for shape optimization under uncertainties, associated with the flow conditions, based on intrusive Polynomial Chaos Expansion (iPCE) and continuous adjoint. The iPCE to the Navier–Stokes equations for laminar flows of incompressible fluids is developed to compute statistical moments of the Quantity of Interest which are, then, compared with those obtained through the Monte Carlo method. The optimization is carried out using a continuous adjoint-enabled, gradient-based loop. Two different formulations for the continuous adjoint to the iPCE PDEs are derived, programmed, and verified. Intrusive PCE methods for the computation of the statistical moments require mathematical development, derivation of a new system of governing equations and their numerical solution. The development is presented for a chaos order of two and two uncertain variables and can be used as a guide to those willing to extend this development to a different set of uncertain variables or chaos order. The developed method and software, programmed in OpenFOAM, is applied to two optimization problems pertaining to the flow around isolated airfoils with uncertain farfield conditions.     

Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry

We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.     

一种基于混沌振子的DSSS信号盲检测方法

直接序列扩频通信是一种具有强保密性和抗干扰性的先进通信体制,对DSSS信号的检测具有重要作用。将非线性科学中的混沌理论应用于DSSS信号的盲检测,结合DSSS信号特征研究了一种利用混沌振子进行检测的方法。首先分析了洛伦兹混沌振子检测周期信号的原理和DSSS信号模型,然后构造出了一个基于混沌振子阵列的盲检测系统,可实现对低信噪比条件下对DSSS信号的盲检测。最后,通过计算机仿真结果表明了该方法的有效性,且性能优于过去的一些算法。     

临界布尔网络的函数泛化问题研究

布尔网络是研究基因调控网络的一种非常重要的模型,通过时序数据推理基因之间的调控关系是研究网络动态行为和干预策略的基础.现有的预测研究主要集中在基因之间的调控关系,而对调控基因与目标基因之间的布尔函数的作用方式研究甚少.由于基因调控网络是一种处于有序和无序之间的临界网络,本文研究了众数规则、基于偏斜和基于互信息的三种泛化方法对临界布尔网络的稳态分布距离和灵敏度误差的影响.结果表明合理的泛化能够明显提高预测网络的稳态分布距离和灵敏度误差指标.三种泛化方法中,基于互信息的泛化方法的总体性能最好.     

混合激励与应变超晶格系统沟道运动的临界特征

从势和场的观点出发讨论了带电粒子在应变超晶格中的运动行为.在经典力学框架内和偶极近似下,引入正弦平方势,把粒子运动方程化为具有阻尼项和混合激励项的广义摆方程.利用Melnikov方法讨论了系统的临界性质与混沌行为.结果表明,系统的混沌行为与它的参数有关,适当调节参数,就可以原则上保证系统的稳定性.     

白噪声激励下双稳态压电发电系统的响应分析

研究了白噪声激励下双稳态压电发电系统的响应特性。首先利用蒙特-卡罗法模拟高斯白噪声;然后利用数值模拟和实验的方法分别分析了噪声强度、负载阻抗和初始值对系统响应特性的影响。得到了噪声强度的增加会减少双稳态系统两个稳定平衡点之间的跳跃时间。通过给出大幅运动的吸引域说明初始值会影响系统的运动状态,从而影响输出功率,当电阻为19.1kΩ时,输出功率最大。     

基于混沌粒子群算法的多目标调度优化研究

针对当前车间调度多目标优化研究存在收敛速度慢、精度低的问题,提出了混沌多目标粒子群优化算法。在算法中,设计了一种新的叠加Logistic扰动的Tent混沌映射算子,通过该算子周期性地更新种群以保证种群的多样性;对收缩粒子群算法进行了扩展使其能够快速收敛到Pareto前沿。通过标准测试问题与实际应用对所提方法进行了验证,实验结果显示混沌多目标粒子群优化算法无论在收敛速度还是在优化精度上都优于其它典型多目标进化算法。     

Maximum entropy principle and coherent harmonic generation using a single-pass free-electron laser

Single-pass free-electron lasers constitute an example of systems with long-range interactions. The light-particle interplay leading to the power growth and successive relaxation towards a quasi-stationary state is governed by the Vlasov equation. A maximum entropy principle inspired to Lynden-Bell's theory of “violent relaxation" for the Vlasov equation can be invoked to analytically characterize the behaviour of the saturated system. In particular, we here concentrate on the case of coherent harmonic generation obtained from an externally seeded free-electron laser and provide a simple strategy to predict the laser intensity as well as the final electron-beam energy distribution.