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Multi-arm covariate-adaptive randomization

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Science China Mathematics 2023年第1期66卷 163-190页

作者： Feifang Hu Xiaoqing Ye li-xin zhang Department of Statistics The George Washington UniversityWashingtonDC 20052USA Institute of Statistics and Big Data Renmin University of ChinaBeijing 100872China School of Mathematical Sciences Zhejiang UniversityHangzhou 310058China

Simultaneously investigating multiple treatments in a single study achieves considerable efficiency in contrast to the traditional two-arm trials.Balancing treatment allocation for influential covariates has become increasingly important in today’s clinical trials.The multi-arm covariate-adaptive randomized clinical trial is one of the most powerful tools to incorporate covariate information and multiple treatments in a single study.Pocock and Simon’s procedure has been extended to the multi-arm case.However,the theoretical properties of multi-arm covariate-adaptive randomization have remained largely elusive for decades.In this paper,we propose a general framework for multi-arm covariate-adaptive designs which also includes the two-arm case,and establish the corresponding theory under widely satisfied conditions.The theoretical results provide new insights into the balance properties of covariate-adaptive randomization procedures and make foundations for most existing statistical inferences under two-arm covariate-adaptive randomization.Furthermore,these open a door to study the theoretical properties of statistical inferences for clinical trials based on multi-arm covariateadaptive randomization procedures.

关键词： multiple treatment balancing covariate clinical trial marginal balance Markov chain Hu and Hu’s general procedure Pocock and Simon’s procedure stratified permuted block design

A note on the cluster set of the law of the iterated logarithm under sub-linear expectations

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Probability, Uncertainty and Quantitative Risk 2022年第2期7卷 85-100页

作者： li-xin zhang School of Mathematical Sciences Zhejiang UniversityHangzhou 310027ZhejiangChina

In this note,we establish a compact law of the iterated logarithm under the upper capacity for independent and identically distributed random variables in a sub-linear expectation space.For showing the result,a self-n... 详细信息

关键词： Sub-linear expectation Capacity Compact law of the iterated logarithm

Mesenchymal stem cells,extracellular vesicles,and transcranial magnetic stimulation for ferroptosis after spinal cord injury

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Neural Regeneration Research 2023年第9期18卷 1861-1868页

作者： Qi-Feng Song Qian Cui Ya-Shi Wang li-xin zhang Department of Rehabilitation Shengjing Hospital of China Medical UniversityShenyangLiaoning ProvinceChina

Spinal cord injury is characte rized by diffe rent aetiologies,complex pathogenesis,and diverse pathological changes.Current treatments are not ideal,and prognosis is generally poor.After spinal cord injury,neurons die due to various forms of cell death.Among them,fe rroptosis causes dysfunction after spinal cord injury,and no existing traditional treatments have been indicated to block its occurrence.Meanwhile,emerging therapies using mesenchymal stem cells,extracellular vesicles,and transcranial magnetic stimulation therapy are promising for reve rsing spinal co rd neuronal ferroptosis after spinal cord injury.However,no definitive studies have demonstrated the effectiveness of these approaches.This review summarizes the existing research on the mechanisms of ferroptosis;fe rroptosis after spinal cord injury;treatment of spinal cord injury with mesenchymal stem cells,extracellular vesicles,and transc ranial magnetic stimulation;and treatment of ferroptosis using mesenchymal stem cells,extracellular vesicles,and transc ranial magnetic stimulation.Inhibiting ferroptosis can promote the reversal of neurological dysfunction after spinal cord injury.In addition,mesenchymal stem cells,extracellular vesicles,and transc ranial magnetic stimulation can reve rse adverse outcomes of spinal cord injury and regulate ferroptosis-related fa ctors.Thus,it can be inferred that mesenchymal stem cells,extracellular vesicles,and transcranial magnetic stimulation have the potential to inhibit fe rroptosis after spinal cord injury.This review serves as a reference for future research to confirm these conclusions.

关键词： exosomes extracellular vesicles ferroptosis iron overload lipid peroxidation mesenchymal stem cells miRNAs spinal cord injury stem cells transcranial magnetic stimulation

The Convergence of the Sums of Independent Random Variables Under the Sub-linear Expectations

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Acta Mathematica Sinica,English Series 2020年第3期36卷 224-244页

作者： li xin zhang School of Mathematical Sciences Zhejiang UniversityHangzhou 310027P.R.China

Let {Xn;n≥1} be a sequence of independent random variables on a probability space(Ω,F,P) and Sn=∑k=1n Xk.It is well-known that the almost sure convergence,the convergence in probability and the convergence in distribution of Sn are equivalent.In this paper,we prove similar results for the independent random variables under the sub-linear expectations,and give a group of sufficient and necessary conditions for these convergence.For proving the results,the Levy and Kolmogorov maximal inequalities for independent random variables under the sub-linear expectation are established.As an application of the maximal inequalities,the sufficient and necessary conditions for the central limit theorem of independent and identically distributed random variables are also obtained.

关键词： Sub-linear expectation capacity independence Levy maximal inequality central limit theorem

lindeberg's central limit theorems for martingale-like sequences under sub-linear expectations

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Science China Mathematics 2021年第6期64卷 1263-1290页

作者： li-xin zhang School of Mathematical Sciences Zhejiang UniversityHangzhou 310027China

The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem and the functional central limit theorem are obtained for martingale-like random variables under the sub-linear expectation.As applications,the lindeberg's central limit theorem is obtained for independent but not necessarily identically distributed random variables,and a new proof of the Lévy characterization of a GBrownian motion without using stochastic calculus is given.For proving the results,Rosenthal's inequality and the exponential inequality for the martingale-like random variables are established.

关键词： capacity central limit theorem functional central limit theorem martingale difference sub-linear expectation

Precise Asymptotics in Chung's Law of the Iterated Logarithm

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Acta Mathematica Sinica,English Series 2008年第4期24卷 631-646页

作者： li xin zhang Department of Mathematics Zhejiang University Hangzhou 310027 P. R. China

Let X, X1, X2,... be i.i.d, random variables with mean zero and positive, finite variance σ^2, and set Sn = X1 ＋... ＋ Xn, n≥1. The author proves that, if EX^2I{｜X｜≥t} = 0（（log log t）^-1） as t→∞, then for any a〉-1 and b〉 -1,lim ε↑1/√1＋a（1/√1＋a-ε）b＋1 ∑n=1^∞（logn）^a（loglogn）^b/nP{max κ≤n｜Sκ｜≤√σ^2π^2n/8loglogn（ε＋an）}=4/π（1/2（1＋a）^3/2）^b＋1 Г（b＋1）,whenever an = o（1/log log n）. The author obtains the sufficient and necessary conditions for this kind of results to hold.

关键词： the law of the iterated logarithm Chung＇s law of the iterated logarithm small deviation,i.i.d random variables

Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes

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Acta Mathematica Sinica,English Series 2006年第1期22卷 143-156页

作者： Yun Xia li li xin zhang Zhejiang University of Finance and Economics Hangzhou 310012 P. R. China Department of Mathematics Zhejiang University Hangzhou 310028 P. R. China

In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai＋kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞） is an absolutely solutely summable sequence of real numbers.

关键词： Moving-average process ψ-mixing Negative association The law of the iterated logarithm

A theoretical study of step edge geometry on sapphire(0001) and its effect on ZnO nucleation

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Frontiers of physics 2019年第2期14卷 105-112页

作者： Ping Yang li-xin zhang School of Physics Nankai UniversityTianjin 300071china

Step-edge-induced nucleation plays a key role in controlling the growth of novel nanostructures and low-dimensional mat erials. However, it is difficult to experimentally determine the step edge structures of complex metal oxides. In this work, we present a detailed theoretical study of the stability of stoichiometTic steps on sapphire(OOOl). Based on first-principles calculations and excess charge computation by Finnis1 approach, a pair of non-polar step edges are determined to be the most stable. By studying the adsorption characteristics of ZnO and combining previous works, we successfully explained how growth temperature and deposition rate affect the in-plane orientation of ZnO grown on sapphire(OOOl). The knowledge on the step edge structures and nucleation patterns would benefit the study on step-edge-guided nanostruc ture grow th.

关键词： stepped sapphire surface first-principles excess charge step-edge-induced nucleation

Precise Rates in the Law of Iterated Logarithm for the Moment of I.I.D. Random Variables

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Acta Mathematica Sinica,English Series 2006年第3期22卷 781-792页

作者： Ye JIANG li xin zhang College of Business and Administration Zhejiang University of Technology Department of Mathematics Zhejiang University

Let{X,Xn;n≥1} be a sequence of i,i.d, random variables, E X = 0, E X^2 = σ^2 〈 ∞.Set Sn=X1＋X2＋…＋Xn,Mn=max k≤n│Sk│,n≥1.Let an=O（1/loglogn）.In this paper,we prove that,for b〉-1,lim ε→0 →^2（b＋1）∑n=1^∞ （loglogn）^b/nlogn n^1/2 E{Mn-σ（ε＋an）√2nloglogn}＋σ2^-b/（b＋1）（2b＋3）E│N│^2b＋3∑k=0^∞ （-1）k/（2k＋1）^2b＋3 holds if and only if EX=0 and EX^2=σ^2〈∞.

关键词： the law of iterated logarithm strong approximation truncation method i.i.d random variables