Statistically and Computationally Efficient Estimating Equations for Large Spatial Datasets

For Gaussian process models, likelihood-based methods are often difficult to use with large irregularly spaced spatial datasets, because exact calculations of the likelihood for n observations require O(n³) operations and O(n²) memory. Various approximation methods have been developed to address the computational difficulties. In this article, we propose new, unbiased estimating equations (EE) based on score equation approximations that are both computationally and statistically efficient. We replace the inverse covariance matrix that appears in the score equations by a sparse matrix to approximate the quadratic forms, then set the resulting quadratic forms equal to their expected values to obtain unbiased EE. The sparse matrix is constructed by a sparse inverse Cholesky approach to approximate the inverse covariance matrix. The statistical efficiency of the resulting unbiased EE is evaluated both in theory and by numerical studies. Our methods are applied to nearly 90,000 satellite-based measurements of water vapor levels over a region in the Southeast Pacific Ocean.     

速度追踪问题中鞍点系统的新分裂迭代

 有限元离散一类速度追踪问题后得到具有鞍点结构的线性系统,针对该鞍点系统,本文提出了一种新的分裂迭代技术.证明了新的分裂迭代方法的无条件收敛性,详细分析了新的分裂预条件子对应的预处理矩阵的谱性质.数值结果验证了对于大范围的网格参数和正则参数,新的分裂预条件子在求解有限元离散速度追踪问题得到的鞍点系统时的可行性和有效性.     

Relationships between different types of initial conditions for simultaneous root finding methods

The construction of initial conditions of an iterative method is one of the most important problems in solving nonlinear equations. In this paper, we obtain relationships between different types of initial conditions that guarantee the convergence of iterative methods for simultaneously finding all zeros of a polynomial. In particular, we show that any local convergence theorem for a simultaneous method can be converted into a convergence theorem with computationally verifiable initial conditions which is of practical importance. Thus, we propose a new approach for obtaining semilocal convergence results for simultaneous methods via local convergence results.     

The haplotype assembly model with genotype information and iterative local-exhaustive search algorithm

The minimum error correction (MEC) model for haplotype reconstruction is efficient only when the error rate in SNP fragments is low. In order to improve reconstruction rate, additional genotype information is added into MEC model as an extension to MEC model. In this paper, we first establish a new mathematical model for haplotype assembly problem with genotype information. Several properties of the mathematical model are proved. Then an iterative local-exhaustive search algorithm is proposed based on the model and its properties. The main idea is to find the optimal pair among 2(l-1) (l denotes the number of heterozygous sites of a genotype) haplotype pairs by performing local exhaustive search for the promising haplotype pair step by step. By experiments and comparison, extensive numerical results on real data and simulated data indicate that our algorithm outperforms the other algorithms in terms of efficiency and robustness.     

Iterative two-step strategy for C2-C4′ linked poly-oxazole synthesis using Suzuki-Miyaura cross-coupling reaction

An iterative method for the synthesis of C2-C4′ linked poly-oxazoles has been developed. This efficient two-step repetitive process includes TBS-iodine exchange reaction and Suzuki-Miyaura cross-coupling reaction with oxazolylboronate 8, which allows appending a bis-oxazole moiety per each iteration. The synthesis of bis-, tris-, tetrakis-, pentakis-, and hexakis-oxazoles (10, 14, 22, 18, and 24) was achieved starting from the common intermediate 7 in 1-5 steps.     

透射光栅测量的解谱方法

对透射光栅谱仪配Ｘ射线ＣＣＤ的软Ｘ射线谱测量系统ＴＧ－ＸＣＣＤ进行了简要描述,提出了正交函数展开法用于透射光栅谱仪配Ｘ射线ＣＣＤ测量的谱回推。将正交展开法用于激光打击金盘靶的软Ｘ射线谱回推,并与迭代法的解谱结果进行了比较。结果基本一致,不对此测量系统进行了误差分析。     

轴对称收敛型电子枪设计方法再讨论

 对轴对称收敛型电子枪设计方法进行了整理分析,就阴极半锥角的初始值对迭代综合法的收敛性能所产生的影响进行了讨论,针对低压缩比条件下原来的Vaughan公式失效的问题进行了分析,给出了更为合理的初始值计算公式。采用修正后的公式和迭代综合法对电子枪进行设计,在高压缩比情况下的设计结果与采用原来Vaughan方法的结果完全一致;而对于低压缩比的情况,也得到了合理的设计,从而解决了原来的Vaughan方法在低压缩比情况下失效的问题,扩大了迭代综合法的应用范围。     

非对称空间外差光谱仪自适应频率跟踪处理方法

非对称空间外差光谱技术是一种新型的超高分辨率遥感探测技术,要求后期的数据处理技术也具有相应的超高准确度.从数字信号处理的角度,提出了一种自适应的频率跟踪处理方法,根据信号的空间频率来插值补偿信号的相位偏移,并且递归迭代出最接近真实值的相位信息.经仿真实验对比验证表明,在噪声干扰强度不大的条件下,相较于传统傅里叶变换方法,本文算法对信号频率和相位提取的准确度提高了约100倍以上,能够有效降低非对称空间外差光谱技术的系统误差.     

Effect of conduction band nonprabolicity on the Rashba spin splitting of AlGaN/GaN QWs

By using the perturbation expansion method and self-consistent iterative method, we evaluate the effect of the conduction band nonprabolicity on the wave vector (k_t) dependent Rashba coefficient (α) and nonlinear Rashba spin splitting (ΔE) in the Al_0.5Ga_0.5N/GaN quantum well (QW). The effective mass (energy) under the first order approximation m_t1 (E_k1) is in proximity to the iterative result m_tp (E_kp) and m_t1>m_tp, E_k1<E_kp, showing the higher order contributions to m_t (E_k) are small. The sign of the nonparabolic correction to E_k is just opposite to that of the correction to m_t. The increase of α and ΔE due to the conduction band nonparabolicity reaches about 3% at k_t=1 nm⁻¹. Around the left heterointerface, the probability density is high and E_k0>E_kp>E_k1, so α₀<α_p<α₁, ΔE₀<ΔE_p<ΔE₁. With increasing k_t, α decreases, and ΔE increases slowly. For small k_t, α₀ (ΔE₀), α₁ (ΔE₁) and α_p (ΔE_p) are nearly the same. While for large k_t, the difference between α₀ and α₁ (α_p) increases rapidly, but the difference between ΔE₀ and ΔE₁ (ΔE_p) increases slowly.     

Iterative method to compute the Fermat points and Fermat distances of multiquarks

The multiquark confining potential is proportional to the total distance of the fundamental strings linking the quarks and antiquarks. We address the computation of the total string distance and of the Fermat points where the different strings meet. For a meson the distance is trivially the quark–antiquark distance. For a baryon the problem was solved geometrically from the onset by Fermat and by Torricelli, it can be determined just with a rule and a compass, and we briefly review it. However we also show that for tetraquarks, pentaquarks, hexaquarks, etc., the geometrical solution is much more complicated. Here we provide an iterative method, converging fast to the correct Fermat points and the total distances, relevant for the multiquark potentials.