Hyperparameter on-line learning of stochastic resonance based threshold networks

Aiming at training the feed-forward threshold neural network consisting of nondifferentiable activation functions, the approach of noise injection forms a stochastic resonance based threshold network that can be optimized by various gradient-based optimizers. The introduction of injected noise extends the noise level into the parameter space of the designed threshold network, but leads to a highly non-convex optimization landscape of the loss function. Thus, the hyperparameter on-line learning procedure with respective to network weights and noise levels becomes of challenge. It is shown that the Adam optimizer, as an adaptive variant of stochastic gradient descent, manifests its superior learning ability in training the stochastic resonance based threshold network effectively. Experimental results demonstrate the significant improvement of performance of the designed threshold network trained by the Adam optimizer for function approximation and image classification.     

The energy-critical nonlinear wave equation with an inverse-square potential

We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocussing case, we prove that arbitrary initial data in the energy space lead to global solutions that scatter. In the focusing case, we prove scattering below the ground state threshold.     

双掺(Tm3+,Tb3+)LiYF4激光器1.5 μm波长激光阈值分析

由速率方程推出了双掺（Tm^3 ,Tb^3 ）离子准四能级系统的激光阈值解析式，讨论了Tm^3 和Tb^3 离子之间的相互作用。分析了1.5μm波长附近的激光阈值和Tm^3 、Tb^3 离子的掺杂原子数分数及晶体长度的关系。结果表明，对于对应Tm^3 离子^3H4→^3F4跃迁的约1.5μm波长的激光，激活离子Tm^3 的掺杂原子数分数过大时，交叉弛豫作用将使系统阈值迅速增加。Tb^3 离子的加入，一方面能抽空激光下能级，起到降低阈值的作用；另一方面亦减少了激光上能级的寿命，使阈值升高。故Tb^3 离子有最佳掺杂原子数分数。对于Tm原子数分数为y=0.01的Tm:LiYF4晶体，Tb^3 离子的最佳掺杂原子数分数为0.002左右，同时表明，激光阈值与晶体长度有关。最佳晶体长度与Tm^3 、Tb^3 离子的掺杂原子数分数以及晶体的衍射损耗和吸收损耗有关。     

简谐速度噪声及其与势场之间的频率共振

为了描述复杂的噪声环境，考虑了一种具有频率结构的噪声——简谐速度噪声，包括它的产生、关联函数、功率谱以及作为热噪声时的频率特性所导致的一些行为.结果表明：在频谱空间中简谐速度噪声是一种带通噪声，存在一个峰值频率，且噪声带宽由参量Γ控制.当简谐势中的一个布朗粒子受热简谐速度噪声驱动时，粒子能量极大值出现在两种频率相等的情况下.这表明噪声和势场的频率之间存在动力学共振，决定着粒子能量的大小. 关键词： 简谐噪声 简谐速度噪声 功率谱 频率共振     

Simulation of the Action of a Permeable Barrier on an Ideal Incompressible Channel Flow

Plane ideal incompressible flow in a rectangular channel partitioned by a thin permeable barrier (lattice) is considered. In flowing through the lattice the stream suddenly (jumpwise) changes direction and loses energy. The flow is assumed to be vortical; the vorticity is discontinuous on the lattice. A mathematical formulation of the problem for the stream function is proposed in the form of a nonlinear elliptic equation with coefficients discontinuous on the lattice line. A numerical solution is constructed using the finite-element iteration method. The results of the numerical simulation show how the flow velocity profile in the channel can be controlled by means of permeable barriers.     

Nonsensitiveness Regions for Threshold Ellipsoids

The problem is to determine nonsensitiveness regions for threshold ellipsoids within a regular mixed linear model.     

New universality classes in “Percolative” dynamics

We study a site analogue of directed percolation. Random trajectories are generated and their critical behavior is studied. The critical behavior corresponds to that of simple percolation in some of the parameter space, but elsewhere the exponents reveal new universality classes. As a byproduct, we use the model to make an improved estimate of the percolation hull exponents and to calculate the site percolation probability for the square lattice.     

93W合金有关力学参量的综合选评

 对93W合金材料进行了超声测量实验，并结合原有的超声测量结果进行了分析比较，提出了可以直接用冲击波速度关系式的三个系数c₀ 、λ和λ′来对钨合金的有关力学参量，如G₀、K₀、G₀′、K₀′等进行综合选评的方法。得到了一组对93W合金较为合理的力学参量推荐值。     

Nd0.5Ca0.5Mn1-xAlxO3 (x=0,0.03)体系中电荷有序态的超声研究

系统研究了Nd0．5Ca0．5Mn1-xAlxO3(x=0,0．03)单相多晶样品在低温下的电磁性质和超声特性．电阻和磁化率测量表明,Nd0．5Ca0.5O3体系在TCO-257 K处发生了电荷有序相变．超声声速从室温开始随着温度的降低逐渐减小,并在TCO附近达到最小,之后,随着温度的进一步降低,声速急刷增加,同时伴随着一个尖锐的超声衰减峰出现.TCO附近的超声异常表明体系中存在着强烈的电-声子相互作用,该电-声子耦合来源于Mn3 的Jahn-Teller效应．在低温下,出现了另一个超声衰减峰,它的出现归结为反铁磁相与顺磁相之间的相分离现象.随着Al在Mn位的掺入,超声声速的最低点和衰减峰向低温移动,表明体系中的电荷有序态和反铁磁相均被部分抑制,     

光码分多址系统中光学相关接收机判决阈值的分析

介绍了光码分多址系统中常用地址码（一维扩时码、二维码和三维码）的特点，并对它们各自的互相关均值和方差进行了理论分析。基于非相干光码分多址系统中光学相关接收机的基本原理，结合不同的用户地址码，对系统误码率性能进行了分析，得到了接收机最佳判决阈值与地址码基本特性参数和系统同时用户数间的关系。最后，给出了数值仿真结果。结果表明，对于采用特定地址码的光码分多址系统，只有选择合适的接收机判决阈值，系统的误码率性能才能达到最佳。研究结果对光码分多址系统中接收机判决阈值的选取具有一定的参考作用。