BEM for simulation of a 2D elastic body with randomly distributed circular inclusions

Based on our 2D BEM software THBEM2 which can be applied to the simulation of an elastic body with randomly distributed identical circular holes, a scheme of BEM for the simulation of elastic bodies with randomly distributed circular inclusions is proposed. The numerical examples given show that the boundary element method is more accurate and more effective than the finite element method for such a problem. The scheme presented can also be successfully used to estimate the effective elastic properties of composite materials. Project supported by the National Natural Science Foundation of China (No. 19772025).     

Free-Space QKD with Modulating Retroreflectors Based on the B92 Protocol

Free-space quantum key distribution (QKD) has attracted considerable attention due to its lower channel loss and link flexibility. It allows two participants share theoretical unconditional secure keys, and can potentially be applied to air-to-ground quantum communication to establish a global quantum network. Free-space QKD using modulating retro-reflectors (MRR-QKD) significantly reduces the pointing requirement and simplifies the structure of the mobile terminal, therefore making it suitable for lightweight aircraft such as unmanned aerial vehicle and Cubesat, etc. Based on intensity modulation of two non-orthogonal states and the B92 protocol, we proposed a scheme to improve the previous work (Optics Express 2018, 26, 11331). Our scheme simplifies the optical structure and shows more robustness in equipment imperfection. The analysis and simulation show that the number of multiple quantum well modulators needed in our scheme decreases from eight to three with similar performance. Additionally, while the previous scheme cannot work due to low modulator extinction ratio or high optical misalignment, our scheme can still operate.     

Non-anticipative representations of Banach space valued gaussian processes with respect to brownian motion

Necessary and sufficient conditions are found for the equivalence of the measures associated with (i) a Banach space valued Gaussian process, with mean 0, and (ii) a Bach space valued Brownian motion. The notion of a non-anticipative representation of (i) with respect to (ii) is defined and in the case of equivalence of the measures it is shown that such a representation exists and has an explicit stochastic integral form which is invertible. Theorems of Ershov on absolute continuity of measures associated with diffusion processes are extended to Banach space. Applications to infinite-dimensional filtering are considered.     

Tests for standardized generalized variances of multivariate normal populations of possibly different dimensions

In many practical problems, one needs to compare variabilities of several multidimensional populations. The concept of standardized generalized variance (SGV) is introduced as an extension of the concept of GV. Considering multivariate normal populations of possibly different dimensions and general covariance matrices, LRTs are derived for SGVs. The criteria turn out to be elegant multivariate analogs to those for tests for variances in the univariate cases. The null and nonnull distributions of the test criteria are deducdd in computable forms in terms of Special Functions, e.g., Pincherle'sH-function, by exploiting the theory of calculus of residues (Mathai and Saxena,Ann. Math. Statist.40, 1439–1448).     

Multivariate Liouville distributions

A random vector (X₁, …, X_n), with positive components, has a Liouville distribution if its joint probability density function is of the formf(x₁ + … + x_n)x₁^a₁.1 … x_n^a_n.1 with thea_i all positive. Examples of these are the Dirichlet and inverted Dirichlet distributions. In this paper, a comprehensive treatment of the Liouville distributions is provided. The results pertain to stochastic representations, transformation properties, complete neutrality, marginal and conditional distributions, regression functions, and total positivity and reverse rule properties. Further, these topics are utilized in various characterizations of the Dirichlet and inverted Dirichlet distributions. Matrix analogs of the Liouville distributions are also treated, and many of the results obtained in the vector setting are extended appropriately.     

不完全边值问题的极小二乘解及其稳定性

定义了一类在部分边界上函数值为0函数的Sobolev空间，并用以讨论部分边界缺乏边值的二阶散度型椭圆型微分方程与其最小范数极小二乘解的稳定性．     

Variational Bayesian Inference for Nonlinear Hawkes Process with Gaussian Process Self-Effects

Traditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and derive an inference algorithm by performing inference on an aggregated sum of Gaussian Processes. Approximate Bayesian inference is achieved via data augmentation, and we describe a mean-field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from different domains and compare it to previously reported results.     

Discrimination of Excited States of Acetylacetone through Theoretical Molecular-Frame Photoelectron Angular Distributions

Photoelectron angular distribution (PAD) in the laboratory frame for randomly oriented molecules is typically described by a single anisotropy parameter, the so-called asymmetry parameter. However, especially from a theoretical perspective, it is more natural to consider molecular photoionization by using a molecular frame. The molecular frame PADs (MFPADs) may be used to extract information about the electronic structure of the system studied. In the last decade, significant experimental efforts have been directed to MFPAD measurements. MFPADs are highly characterizing signatures of the final ionic states. In particular, they are very sensitive to the nature of the final state, which is embodied in the corresponding Dyson orbital. In our previous work on acetylacetone, a prototype system for studying intra-molecular hydrogen bond interactions, we followed the dynamics of the excited states involved in the photoexcitation–deexcitation process of this molecule. It remains to be explored the possibility of discriminating between different excited states through the MFPAD profiles. The calculation of MFPADs to differentiate excited states can pave the way to the possibility of a clear discrimination for all the cases where the recognition of excited states is otherwise intricate.     

Third order residual distribution schemes for the Navier–Stokes equations

We construct a third order multidimensional upwind residual distribution scheme for the system of the Navier–Stokes equations. The underlying approximation is obtained using standard P² Lagrange finite elements. To discretise the inviscid component of the equations, each element is divided in sub-elements over which we compute a high order residual defined as the integral of the inviscid fluxes on the boundary of the sub-element. The residuals are distributed to the nodes of each sub-element in a multi-dimensional upwind way. To obtain a discretisation of the viscous terms consistent with this multi-dimensional upwind approach, we make use of a Petrov–Galerkin analogy. The analogy allows to find a family of test functions which can be used to obtain a weak approximation of the viscous terms. The performance of this high-order method is tested on flows with high and low Reynolds number.