Almost Sure Convergence of Proximal Stochastic Accelerated Gradient Methods

Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.

Almost Sure Convergence and Complete Convergence for the Weighted Sums of Martingale Differences

Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.

Almost sure central limit theory for products of sums of partial sums

Consider a sequence of i.i.d.positive random variables.An universal result in almost sure limit theorem for products of sums of partial sums is established.We will show that the almost sure limit theorem holds under a fairly general condition on the weight dk= k-1 exp（lnβk）,0≤β〈1.And in a sense,our results have reached the optimal form.

ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.

Almost sure stability condition of weakly coupled linear nonautonomous random systems

In this study, the sufficient condition of almost sure stability of twodimensional oscillating systems under parametric excitations is investigated. The systems considered are assumed to be composed of two weakly coupled subsystems. The driving actions are considered to be stationary stochastic processes satisfying ergodic properties. The properties of quadratic forms are used in conjunction with the bounds for the eigenvalues to obtain, in a closed form, the sufficient condition for the almost sure stability of the systems.

Almost sure limit theorem for the maximum of a class of quasi-stationary sequences

This paper investigates the problem of almost sure limit theorem for the maximum of quasi-stationary sequence based on the result of Turkman and Walker. We prove an almost sure limit theorem for the maximum of a class of quasi-stationary sequence under weak dependence conditions of D （uk, un） and αtm,ln = 0 （（log log n）-（1＋ε））.

A Note on the Almost Sure Central Limit Theorem in the Joint Version for the Maxima and Partial Sums of Certain Stationary Gaussian Sequences

Considering a sequence of standardized stationary Gaussian random variables, a universal result in the almost sure central limit theorem for maxima and partial sum is established. Our result generalizes and improves that on the almost sure central limit theory previously obtained by Marcin Dudzinski [1]. Our result reaches the optimal form.

Almost sure exponential stability of neutral stochastic delayed cellular neural networks

In this paper, almost sure exponential stability of neutral delayed cellular neural networks which are in the noised environment is studied by decomposing the state space to sub-regions in view of the saturation linearity of output functions of neurons of the cellular neural networks. Some algebraic criteria are obtained and easily verified. Some examples are given to illustrate the correctness of the results obtained.

An Almost Sure Central Limit Theorem for Weighted Sums of Mixing Sequences

In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather arbitrary weight sequences. This extends the earlier work on mixing random variables

Almost sure T-stability and convergence for random iterative algorithms

The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of C-weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed points for this kind of random operators and the almost sure T-stability and convergence for these two kinds of random iterative algorithms are proved.

Almost Sure Convergence of Weighted Sums of NA Sequences

For double arrays of constants {a ni, 1≤i≤k n, n≥1} and NA r.v. 's {X n, n≥1}, conditions for almost sure convergence of are given. Both casesk n ↑ ∞ andk n=∞ are treated. A Marcinkiewicz-type theorem for i. d. NA sequences is obtained as a special case.

ALMOST SURE GLOBAL WELL-POSEDNESS FOR THE FOURTH-ORDER NONLINEAR SCHR?DINGER EQUATION WITH LARGE INITIAL DATA

We consider the fourth-order nonlinear Schr?dinger equation(4NLS)(i?t+εΔ+Δ2)u=c1um+c2(?u)um-1+c3(?u)2um-2,and establish the conditional almost sure global well-posedness for random initial data in Hs(Rd)for s∈(sc-1/2,sc],when d≥3 and m≥5,where sc:=d/2-2/(m-1)is the scaling critical regularity of 4NLS with the second order derivative nonlinearities.Our proof relies on the nonlinear estimates in a new M-norm and the stability theory in the probabilistic setting.Similar supercritical global well-posedness results also hold for d=2,m≥4 and d≥3,3≤m<5.

A Note on the Almost Sure Central Limit Theorem for Partial Sums of ρ^(−)-Mixing Sequences

Let be a strictly stationary sequence of ρ?-mixing random variables. We proved the almost sure central limit theorem, containing the general weight sequences, for the partial sums , where , . The result generalizes and improves the previous results.

An extended state observer with adjustable bandwidth for measurement noise

In this paper,a bandwidth-adjustable extended state observer(ABESO)is proposed for the systems with measurement noise.It is known that increasing the bandwidth of the observer improves the tracking speed but tolerates noise,which conflicts with observation accuracy.Therefore,we introduce a bandwidth scaling factor such that ABESO is formulated to a 2-degree-of-freedom system.The observer gain is determined and the bandwidth scaling factor adjusts the bandwidth according to the tracking error.When the tracking error decreases,the bandwidth decreases to suppress the noise,otherwise the bandwidth does not change.It is proven that the error dynamics are bounded and converge in finite time.The relationship between the upper bound of the estimation error and the scaling factor is given.When the scaling factor is less than 1,the ABESO has higher estimation accuracy than the linear extended state observer(LESO).Simulations of an uncertain nonlinear system with compound disturbances show that the proposed ABESO can successfully estimate the total disturbance in noisy environments.The mean error of total disturbance of ABESO is 15.28% lower than that of LESO.

SURE算法在核磁共振信号去噪中的实现

核磁共振产生的回波信号幅度比较低,容易受到噪声干扰.如何有效提高低场核磁共振回波信号的信噪比一直是核磁共振技术研究的关键课题之一.本文讨论了一种基于小波变换的Stein无偏风险估计(SURE)算法,从相关系数图版中确定尺度因子和分解层次,依据噪声在不同分解层次上的差异取不同的阈值对回波信号去噪.该算法与传统的模极大值法和空域相关法相比,能获得更高的信噪比,为储层流体分析提供更准确的孔隙度信息.

基于SURE小波阈值消噪和MCEEMD-HHT的低频振荡分析

为解决低频振荡分析中广域量测系统存在量测噪声影响和应用希尔伯特黄变换(Hilbert-Huang transform,HHT)进行模态辨识中的模态混叠和伪分量问题,提出基于Stein的无偏似然估计(Stein unbiased risk estimate,SURE)小波阈值消噪和改进的补充集合经验模态分解希尔伯特黄变换(modified complementary ensemble empirical mode decomposition and Hilbert-Huang transform,MCEEMD-HHT)的低频振荡分析方法。首先,对含较强噪声的电网量测低频振荡信号,采用SURE小波阈值消噪实现信号预处理。其次,引入排列熵算法改进CEEMD形成MCEEMD,有效抑制经验模态分解中的模态混叠和伪分量现象。最后,对MCEEMD分解得到的低频振荡真实模态进行HHT分析。通过复合信号测试、IEEE四机两区域系统仿真以及实测北美电网数据分析,验证了所提方法在电力系统低频振荡分析中的有效性。此外,与快速傅里叶变换(fast Fourier transform,FFT)、Prony算法分析进行对比可知,所提方法在模态参数的提取方面表现得更为准确,且无需人为定价。

腹腔镜下行全子宫切除术中举宫杯联合LigaSure的临床应用价值

目的:探讨举宫杯及Liga Sure在腹腔镜全子宫切除术(TLH)的应用价值。方法:将2007年1月至2010年12月在我院实施腹腔镜全子宫切除术324例患者分为两组。I组用举宫杯及Liga Sure完成手术,II组用简易举宫器及单极电凝。比较分析两组手术时间、出血量、下推膀胱时间、术后并发症等情况。结果:I组、II组各有1例中转开腹。I组手术时间、下推膀胱时间明显少于II组(P<0.05)。出血量及环切阴道时间亦明显少于II组(P<0.05)。结论:举宫杯及Liga Sure在腹腔镜全子宫切除术中安全、有效、手术时间短、出血少、并发症少,极大降低了手术难度,在有条件的医院值得推广。

基于SURE估计的图像块稀疏收缩去噪算法

针对图像过完备稀疏收缩去噪的阈值选取问题,根据图像的常规稀疏模型,提出一种基于SURE无偏估计的自适应阈值选择算法。在一阶可导收缩函数的基础上,推导阈值选择的优化目标函数,证明该函数是关于阈值的凸函数,利用黄金分割法搜索其全局最小值。仿真结果表明,该算法选择的阈值接近峰值信噪比阈值曲线的极大值点,将该算法应用于图像的块稀疏模型,可取得比常规稀疏模型更好的去噪效果。

LigaSure与钳夹法在单发肝癌切除术中的比较

目的比较Liga Sure与钳夹法在单发肝癌切除术中的应用价值。方法 2014年6-11月,回顾性分析我科60例单发肝癌患者资料,30例应用Liga Sure,30例应用钳夹法,比较2组手术时间、断肝时间、肝断面处理时间、术中出血量,术前和术后第1、3、5天血清丙氨酸氨基转移酶（ALT）、总胆红素（TBIL）的变化,术后并发症发生情况。结果与钳夹组相比,Liga Sure组手术时间长[（130.7±27.0）min vs.（115.2±27.8）min,t=2.106,P=0.044],断肝时间长[（25.6±12.1）min vs.（15.1±7.2）min,t=3.703,P=0.001],但肝断面处理时间短[（11.9±2.7）min vs.（16.4±7.3）min,t=-2.281,P=0.007],术中失血量少[（145.0±130.2）ml vs.（233.3±164.7）ml,t=-2.150,P=0.040],差异均有统计学意义。2组术前和术后第1、3、5天ALT和TBIL及术后并发症发生率差异无统计学意义。结论与钳夹法比较,Liga Sure行肝癌切除术虽断肝时间长,但肝断面处理时间短,术中出血量少,更具有优势。