Non-uniform Berry-Esseen bound by unbounded exchangeable pairs approach

In this paper,a new technique is introduced to obtain non-uniform Berry-Esseen bounds for normal and nonnormal approximations by unbounded exchangeable pairs.This technique does not rely on the concentration inequalities developed by Chen and Shao[4,5]and can be applied to the quadratic forms and the general Curie-Weiss model.

The Berry-Esseen bound for identically distributed random variables by Stein method

In this paper, we obtain the Berry-Esseen bound for identically distributed random variables by Stein method. The results obtained generalize the results of Shao and Su （2006） and Stein （1986）.

Improved Berry-Esseen Bound for Rademacher Sum

Let X=Σ_(i=1)^(n)a_(i)ξ_(i)be a Rademacher sum with Var(X)=1 and Z be a standard normal random variable.This paper concerns the upper bound of|P(X≤x)−P(Z≤x)|for any x∈R.Using the symmetric properties and R software,this paper gets the following improved Berry-Esseen type bound under some conditions,|P(X≤x)−P(Z≤x)|≤P(Z∈(0,a1)),∀x∈R,which is one of the modified conjecture proposed by Nathan K.and Ohad K.

Berry-Esseen bounds for self-normalized sums of locally dependent random variables

The Berry-Esseen bound provides an upper bound on the Kolmogorov distance between a random variable and the normal distribution.In this paper,we establish Berry-Esseen bounds with optimal rates for self-normalized sums of locally dependent random variables,assuming only a second-moment condition.Our proof leverages Stein's method and introduces a novel randomized concentration inequality,which may also be of independent interest for other applications.Our main results have applied to self-normalized sums of m-dependent random variables and graph dependency models.

Berry-Esseen bounds and moderate deviations for the norm, entries and spectral radius of products of positive random matrices

Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.

Uniform Cramer moderate deviations and Berry-Esseen bounds for a supercritical branching process in a random environment

Let{Zn,n≥0}be a supercritical branching process in an independent and identically distributed random environment.We prove Cramer moderate deviations and Berry-Esseen bounds for log(Zn+n0/Zn0)uniformly in n0∈N,which extend the corresponding results by I.Grama,Q.Liu,and M.Miqueu[Stochastic Process.Appl.,2017,127:1255-1281]established for n0=0.The extension is interesting in theory,and is motivated by applications.A new method is developed for the proofs;some conditions of Grama et al.are relaxed in our present setting.An example of application is given in constructing confidence intervals to estimate the criticality parameter in terms of log(Zn+n0/Zn0)and n.

Berry-Esseen bounds and Cramér type large deviations for eigenvalues of random matrices.

We establish Berry-Esseen bounds and Cramér type large deviations for the eigenvalues of Wigner Hermitian matrices in the bulk and at the edge cases. Similar results are also obtained for covariance matrices.

Berry-Esseen Bounds for Self-Normalized Martingales

A Berry–Esseen bound is obtained for self-normalized martingales under the assumption of finite moments.The bound coincides with the classical Berry–Esseenboundforstandardizedmartingales.Anexampleisgiventoshowtheoptimality of the bound.Applications to Student’s statistic and autoregressive process are also discussed.

BERRY-ESSEEN BOUNDS OF ERROR VARIANCE ESTIMATION IN PARTLY LINEAR MODELS

Consider the regression model Y i=x τ iβ+g(t i)+ε i for i=1,…, n. Here (x i, t i) are known and nonrandom design points and ε i are i.i.d. random errors.The family of nonparametric estimates n(·) of g(·) including some known estimates is proposed. Based on the model Y i=x τ i+ n(t i)+ε i, the Berry-Esseen bounds of the distribution of the least-squares estimator of β are investigated.

THE BERRY-ESSEEN BOUND AND LIL PP CM STATISTIC TESTING UNIFORM DISTRIBUTION ON SPHERE ABOUT DIMENSION AND SAMPLE SIZE

Cheng[1] gave the limit distribution of weighted PP Cramer-Von Mises test statistic when dimension and sample size tend to infinity simultaneously under the underlying distribution being uniform distribution on SP-1 = {a: ||a|| = 1, a SP-1 }; this limit distribution is standard normal distribution N(0, 1). In this paper, we give the Berry- Esseen bound of this statistic converging to normal distribution and the law of iterated logarithm.

The Berry-Esseen bound for studentized U-statistics

We establish the Berry-Esseen bound O(n-δ#2) for a studentized U-statistic under the assumption of existence of the (2 + δ)-th moment.

Chiral bound states in a staggered array of coupled resonators

We study the chiral bound states in a coupled-resonator array with staggered hopping strengths,which interacts with a two-level small atom through a single coupling point or two adjacent ones.In addition to the two typical bound states found above and below the energy bands,this system presents an extraordinary chiral bound state located within the energy gap.We use the chirality to quantify the breaking of the mirror symmetry.We find that the chirality value undergoes continuous changes by tuning the coupling strengths.The preferred direction of the chirality is controlled not only by the competition between the intracell and the intercell hoppings in the coupled-resonator array,but also by the coherence between the two coupling points.In the case with one coupling point,the chirality values varies monotonously with difference between the intracell hopping and the intercell hoppings.While in the case with two coupling points,due to the coherence between the two coupling points the perfect chiral states can be obtained.

Theoretical investigation of excited dipole bound states of alkali-containing diatomic anions

Information about electronic excited states of molecular anions plays an important role in investigating electron attachment and detachment processes.Here we present a high-level theoretical study of the electronic structures of 12 alkali-metal-containing diatomic anions MX-(MX = LiH,LiF,LiCl,NaF,NaCl,NaBr,RbCl,KCl,KBr,RbI,KI and CsI).The equation-of-motion electron-attachment coupled-cluster singles and doubles(EOM-EA-CCSD) method is used to calculate the electron binding energies(EBEs) of 10 electronic excited states of each of the 12 molecule anions.With addition of different s-/p-/d-type diffusion functions in the basis set,we have identified possible excited dipole bound states(DBSs) of each anion.With the investigation of EBEs on the 12 MXs with dipole moment(DM) up to 12.1 D,we evaluate the dependence of the number of anionic excited DBSs on molecular DM.The results indicate that there are at least two or three DBSs of anions with a molecular DM larger than 7 D and a molecule with DM > 10 D can sustain a π-DBS of the anion.Our study has some implications for the excited DBS electronic states of alkali-metal-containing diatomic molecules.

Comparison of the Minimum Bounding Rectangle and Minimum Circumscribed Ellipse of Rain Cells from TRMM

Based on the TRMM dataset, this paper compares the applicability of the improved MCE(minimum circumscribed ellipse), MBR(minimum bounding rectangle), and DIA(direct indexing area) methods for rain cell fitting. These three methods can reflect the geometric characteristics of clouds and apply geometric parameters to estimate the real dimensions of rain cells. The MCE method shows a major advantage in identifying the circumference of rain cells. The circumference of rain cells identified by MCE in most samples is smaller than that identified by DIA and MBR, and more similar to the observed rain cells. The area of rain cells identified by MBR is relatively robust. For rain cells composed of many pixels(N> 20), the overall performance is better than that of MCE, but the contribution of MBR to the best identification results,which have the shortest circumference and the smallest area, is less than that of MCE. The DIA method is best suited to small rain cells with a circumference of less than 100 km and an area of less than 120 km^(2), but the overall performance is mediocre. The MCE method tends to achieve the highest success at any angle, whereas there are fewer “best identification”results from DIA or MBR and more of the worst ones in the along-track direction and cross-track direction. Through this comprehensive comparison, we conclude that MCE can obtain the best fitting results with the shortest circumference and the smallest area on behalf of the high filling effect for all sizes of rain cells.

Coulomb-assisted nonlocal electron transport between two pairs of Majorana bound states in a superconducting island

We investigate the nonlocal transport modulated by Coulomb interactions in devices comprising two interacting Majorana wires,where both nanowires are in proximity to a mesoscopic superconducting(SC)island.Each Majorana bound state(MBS)is coupled to one lead via a quantum dot with resonant levels.In this device,the nonlocal correlations can be induced in the absence of Majorana energy splitting.We find that the negative differential conductance and giant current noise cross correlation could be induced,due to the interplay between nonlocality of MBSs and dynamical Coulomb blockade effect.This feature may provide a signature for the existence of the MBSs.

MINIMIZERS OF L^(2)-SUBCRITICAL VARIATIONAL PROBLEMS WITH SPATIALLY DECAYING NONLINEARITIES IN BOUNDED DOMAINS

This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.

Holevo bound independent of weight matrices for estimating two parameters of a qubit

Holevo bound plays an important role in quantum metrology as it sets the ultimate limit for multi-parameter estimations,which can be asymptotically achieved.Except for some trivial cases,the Holevo bound is implicitly defined and formulated with the help of weight matrices.Here we report the first instance of an intrinsic Holevo bound,namely,without any reference to weight matrices,in a nontrivial case.Specifically,we prove that the Holevo bound for estimating two parameters of a qubit is equivalent to the joint constraint imposed by two quantum Cramér–Rao bounds corresponding to symmetric and right logarithmic derivatives.This weightless form of Holevo bound enables us to determine the precise range of independent entries of the mean-square error matrix,i.e.,two variances and one covariance that quantify the precisions of the estimation,as illustrated by different estimation models.Our result sheds some new light on the relations between the Holevo bound and quantum Cramer–Rao bounds.Possible generalizations are discussed.

随机环境上临界分枝过程的非一致Berry-Esseen不等式

设{Z_(n),n≥0}为独立同分布随机环境ξ=(ξ_(n))下的分枝过程。在Cramér条件及与其等价的Bernstein条件下,利用Wn的非退化性,对于一致的n_(0)∈N,证明了log(Z_(n+n_(0))/Z_(n_(0)))带有指数衰减速率的非一致BerryEsseen不等式,其中W_(n)=Z_(n)/(E_(ξ)Z_(n))为非负鞅。该结果把log(Z_(n+n_(0))/Z_(n_(0)))已有的Berry-Esseen不等式推广到了非一致情形。

Iterative physical optics method based on efficient occlusion judgment with bounding volume hierarchy technology

This paper builds a binary tree for the target based on the bounding volume hierarchy technology,thereby achieving strict acceleration of the shadow judgment process and reducing the computational complexity from the original O(N^(3))to O(N^(2)logN).Numerical results show that the proposed method is more efficient than the traditional method.It is verified in multiple examples that the proposed method can complete the convergence of the current.Moreover,the proposed method avoids the error of judging the lit-shadow relationship based on the normal vector,which is beneficial to current iteration and convergence.Compared with the brute force method,the current method can improve the simulation efficiency by 2 orders of magnitude.The proposed method is more suitable for scattering problems in electrically large cavities and complex scenarios.

Interface state-based bound states in continuum and below-continuum-resonance modes with high-Q factors in the rotational periodic system

We have introduced a new approach to calculate the orbital angular momentum(OAM)of bound states in continuum(BICs)and below-continuum-resonance(BCR)modes in the rotational periodic system nested inside and outside by transforming the Bloch wave number from the translational periodic system.We extensively classify and study these BICs and BCR modes,which exhibit high-quality(high-Q)factors,in different regions relative to the interface of the system.These BICs and BCR modes with a high-Q factor have been studied in detail based on distinctive structural parameters and scattering theory.The outcomes of this research break the periodic limitation of interface state-based BICs,and realize more and higher symmetry interface state-based BICs and BCR modes.Moreover,we can control the region where light is captured by adjusting the frequency,and show that the Q factor of BICs is more closely related to the ordinal number of rings and the rotational symmetry number of the system.