Improved linear multi-step methods for stochastic ordinary differential equations

We consider linear multi-step methods for stochastic ordinary differential equations and study their convergence properties for problems with small noise or additive noise. We present schemes where the drift part is approximated by well-known methods for deterministic ordinary differential equations. In previous work, we considered Maruyama-type schemes, where only the increments of the driving Wiener process are used to discretize the diffusion part. Here, we suggest the improvement of the discretization of the diffusion part by also taking into account mixed classical-stochastic integrals. We show that the relation of the applied step sizes to the smallness of the noise is essential in deciding whether the new methods are worthwhile. Simulation results illustrate the theoretical findings.     

基于Bootstrap法的动态修正贝叶斯精度评估

针对工程实际中所普遍存在的小子样条件下,研究具有多阶段试验信息时的参数估计问题,提出一种结合Bootstrap方法与动态修正贝叶斯估计方法对精度评估中的弹点散布方差进行估计的方案.     

Exact L 2 Small Balls of Gaussian Processes

We prove a comparison theorem extending Li(6) and develop a complex-analytic approach to treat L ² small ball probabilities of Gaussian processes. We demonstrate the techniques for the m-times integrated Brownian motions and in examples where one can not apply Li comparison theorem.     

Ar-buffer-assisted deposition of Cu13 on Cu(1 1 1) surfaces

In this paper, the deposition of Cu₁₃ onto Cu(1 1 1) surface through argon buffer layers was investigated by molecular dynamics (MD) simulations. The interactions between Cu-Cu, Cu-Ar, and Ar-Ar were described by Finnis-Sinclair (FS) tight-binding potential and L-J potential, respectively. The impact energy was chosen to be 2-6 eV/atom in order to compare with experimental results. It was observed that with Ar-buffer layers, the Cu cluster deposited on the surface may retain its free cluster symmetry (I_h). Whereas, on originally bare Cu surface, the deposited Cu cluster lost its original symmetry completely and was recrystalized to have the same fcc structure as the substrate. The Ar-buffer dissipates most of the translational energy of the incident cluster. Therefore, it prevents the cluster from being overheated upon impinging. Furthermore, the interaction between Ar and Cu benefits the confinement of the cluster structure. Our study shows that with Ar-buffer layers, the lateral spread of deposited clusters is 20% smaller than that on the bare Cu surface. This is consistent with the experimental findings.     

Duality in algebra and topology

We apply ideas from commutative algebra, and Morita theory to algebraic topology using ring spectra. This allows us to prove new duality results in algebra and topology, and to view (1) Poincaré duality for manifolds, (2) Gorenstein duality for commutative rings, (3) Benson–Carlson duality for cohomology rings of finite groups, (4) Poincaré duality for groups and (5) Gross–Hopkins duality in chromatic stable homotopy theory as examples of a single phenomenon.     

Measuring small wavelength differences by heterodyne interferometry and optical activity of chiral crystal

The optical activity of a chiral crystal and common-path heterodyne interferometry are used in a simple measurement technique that was developed to measure small wavelength differences. When circularly polarized heterodyne light passes through a chiral crystal, the plane of polarization rotates. The phase difference between the right- and left-circular lights is directly proportional to the angle of rotation. The rotation angle depends strongly on the wavelength. The phase difference can be accurately detected and substituted into specially derived equations to estimate wavelength variations. The feasibility of this method was demonstrated and the wavelength sensitivity was about 0.00812 nm. This method provides the advantages of a simple structure, ease of operations, a large wavelength measurement range and high sensitivity.     

Data-driven preventive maintenance for a heterogeneous machine portfolio

We describe a data-driven approach to optimize periodic maintenance policies for a heterogeneous portfolio with different machine profiles. When insufficient data are available per profile to assess failure intensities and costs accurately, we pool the data of all machine profiles and evaluate the effect of (observable) machine characteristics by calibrating appropriate statistical models. This reduces maintenance costs compared to a stratified approach that splits the data into subsets per profile and a uniform approach that treats all profiles the same.     

结合区域提取和改进卷积神经网络的水下小目标检测

针对水下小目标信息量有限而难以提取有效特征导致的检测性能不佳问题,提出了一种结合区域提取和融合Hu矩特征的改进卷积神经网络水下小目标检测方法。该方法包含区域提取和分类两个步骤。首先以马尔可夫随机场分割算法为基础进行区域提取,对潜在目标定位的同时降低伪目标对后续分类的干扰;然后提取潜在目标区域的Hu矩特征并融入卷积神经网络,形成一种形状特征表征能力更强的改进卷积神经网络用于分类。声呐实测数据处理结果表明,该方法可以有效提升对水下小目标的发现概率和正确报警率,与其他目标检测方法相比,该方法具有更好的检测性能和泛化性。     

Spontaneous Formation of RNA Strands,Peptidyl RNA,and Cofactors

How the biochemical machinery evolved from simple precursors is an open question. Here we show that ribonucleotides and amino acids condense to peptidyl RNAs in the absence of enzymes under conditions established for genetic copying. Untemplated formation of RNA strands that can encode genetic information, formation of peptidyl chains linked to RNA, and formation of the cofactors NAD⁺, FAD, and ATP all occur under the same conditions. In the peptidyl RNAs, the peptide chains are phosphoramidate‐linked to a ribonucleotide. Peptidyl RNAs with long peptide chains were selected from an initial pool when a lipophilic phase simulating the interior of membranes was offered, and free peptides were released upon acidification. Our results show that key molecules of genetics, catalysis, and metabolism can emerge under the same conditions, without a mineral surface, without an enzyme, and without the need for chemical pre‐activation.     

Incorporation of graphene oxide nanosheets into boronate‐functionalized polymeric monolith to enhance the electrochromatographic separation of small molecules

Graphene oxide (GO) nanosheets were incorporated into an organic polymer monolith containing 3‐acrylamidophenylboronic acid (AAPBA) and pentaerythritol triacrylate (PETA) to form a novel monolithic stationary phase for CEC. The effects of the mass ratio of AAPBA/PETA, the amount of GO, and the volume of porogen on the morphology, permeability and pore properties of the prepared poly(AAPBA‐GO‐PETA) monoliths were investigated. A series of test compounds including amides, alkylbenzenes, polycyclic aromatics, phenols, and anilines were used to evaluate and compare the separation performances of the poly(AAPBA‐GO‐PETA) and the parent poly(AAPBA‐co‐PETA) monoliths. The results indicated that incorporation of GO into monolithic column exhibited much higher resolutions (>1.5) and column efficiency (62 000 ～ 110 000 plates/m for toluene, DMF, formamide, and thiourea) than the poly(AAPBA‐co‐PETA). The successful application in isocratic separation of peptides suggests the potential of the GO incorporated monolithic column in complex sample analysis. In addition, the reproducibility and stability of the prepared poly(AAPBA‐GO‐PETA) monolith was assessed. The run‐to‐run, column‐to‐column and batch‐to‐batch reproducibilities of this monolith for alkylbenzenes’ retention were satisfactory with the RSDs less than 1.8% (n = 5), 3.7% and 5.6% (n = 3), respectively, indicating the effectiveness and practicability of the proposed method.