A bound on the Wasserstein-2 distance between linear combinations of independent random variables

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ${?}^2\left({\mathbb{N}}^1\right)$. We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent.     

Dependency distance: A new perspective on syntactic patterns in natural languages

Dependency distance, measured by the linear distance between two syntactically related words in a sentence, is generally held as an important index of memory burden and an indicator of syntactic difficulty. Since this constraint of memory is common for all human beings, there may well be a universal preference for dependency distance minimization (DDM) for the sake of reducing memory burden. This human-driven language universal is supported by big data analyses of various corpora that consistently report shorter overall dependency distance in natural languages than in artificial random languages and long-tailed distributions featuring a majority of short dependencies and a minority of long ones. Human languages, as complex systems, seem to have evolved to come up with diverse syntactic patterns under the universal pressure for dependency distance minimization. However, there always exist a small number of long-distance dependencies in natural languages, which may reflect some other biological or functional constraints. Language system may adapt itself to these sporadic long-distance dependencies. It is these universal constraints that have shaped such a rich diversity of syntactic patterns in human languages.     

基于飞秒激光模间拍频法的大尺寸测距方法

本文基于飞秒激光模间拍频法实现多波长相位式绝对距离测量, 通过改变光频梳重复频率合成波长扩大测距量程, 并采用监测臂和双快门切换系统补偿和消除由电路产生的相位差单向漂移和大幅抖动. 实验中以20倍重复频率的拍频进行测量, 在30 min内相位测量的标准偏差为0.022°; 与双频激光干涉仪比对1125 mm行程内位移测量结果, 测距精度优于50 μm; 实验验证了合成波长方法扩大量程方案的可行性, 获得的测距重复性优于3 μm, 该系统理论上可扩展量程至7.5 km.     

Localization microscopy (SPDM) facilitates high precision control of lithographically produced nanostructures

Nanoscale resolution in material sciences is usually restricted to scanning electron beam microscopes. Here we present a procedure that allows single molecule resolution of the sample surface with visible light. Highlighting the performance we used electron beam lithography to generate highly regular nanostructures consisting of interconnected cubes. The samples were labeled with Alexa 647 dyes. The spatial organization of the dyes on nanostructured surfaces was localized with single molecule resolution using localization microscopy. This succeeded also in an absolute spatial calibration of the localization method applied (spectral precision distance microscopy/SPDM). The findings will contribute to the field of product control for industrial applications and long-term fluorescence imaging.     

基于小波高频距离像的红外小目标检测

针对远距离复杂背景下红外小目标检测问题,本文提出了一种基于小波高频距离像的方法。该方法首先将处理空间变换到小波域,通过分析残留背景、目标和噪声系数在高频子带的差异,定义基于邻域均值的子带系数表达形式,构造高频子带系数的中心向量,对小波高频图像进行综合形成距离像,得到红外复杂背景的抑制结果。在此基础上,利用恒虚警率算法将单帧背景抑制图像分割成候选目标、残留背景和噪声像素点。最后,在时间域基于目标运动的相关性,利用管道滤波实现红外小目标的最终检测。仿真实验结果表明,相对于经典算法,本文方法可以实现对红外复杂背景的有效抑制,增强目标信号的强度,准确稳定的从红外复杂背景中检测出小目标。     

Computing the distribution of the Robinson-Foulds distance

With the exponential growth of genome databases, the importance of phylogenetics has increased dramatically over the past years. Studying phylogenetic trees enables us not only to understand how genes, genomes, and species evolve, but also helps us predict how they might change in future. One of the crucial aspects of phylogenetics is the comparison of two or more phylogenetic trees. There are different metrics for computing the dissimilarity between a pair of trees. The Robinson-Foulds (RF) distance is one of the widely used metrics on the space of labeled trees. The distribution of the RF distance from a given tree has been studied before, but the fastest known algorithm for computing this distribution is a slow, albeit polynomial-time, O(l⁵) algorithm. In this paper, we modify the dynamic programming algorithm for computing the distribution of this distance for a given tree by leveraging the number-theoretic transform (NTT), and improve the running time from O(l⁵) to O(l³ log l), where l is the number of tips of the tree. In addition to its practical usefulness, our method represents a theoretical novelty, as it is, to our knowledge, one of the rare applications of the number-theoretic transform for solving a computational biology problem.