Efficient Bayesian Inference for Multivariate Factor Stochastic Volatility Models

We discuss efficient Bayesian estimation of dynamic covariance matrices in multivariate time series through a factor stochastic volatility model. In particular, we propose two interweaving strategies to substantially accelerate convergence and mixing of standard MCMC approaches. Similar to marginal data augmentation techniques, the proposed acceleration procedures exploit nonidentifiability issues which frequently arise in factor models. Our new interweaving strategies are easy to implement and come at almost no extra computational cost; nevertheless, they can boost estimation efficiency by several orders of magnitude as is shown in extensive simulation studies. To conclude, the application of our algorithm to a 26-dimensional exchange rate dataset illustrates the superior performance of the new approach for real-world data. Supplementary materials for this article are available online.     

Interweaving Markov Chain Monte Carlo Strategies for Efficient Estimation of Dynamic Linear Models

In dynamic linear models (DLMs) with unknown fixed parameters, a standard Markov chain Monte Carlo (MCMC) sampling strategy is to alternate sampling of latent states conditional on fixed parameters and sampling of fixed parameters conditional on latent states. In some regions of the parameter space, this standard data augmentation (DA) algorithm can be inefficient. To improve efficiency, we apply the interweaving strategies of Yu and Meng to DLMs. For this, we introduce three novel alternative DAs for DLMs: the scaled errors, wrongly scaled errors, and wrongly scaled disturbances. With the latent states and the less well known scaled disturbances, this yields five unique DAs to employ in MCMC algorithms. Each DA implies a unique MCMC sampling strategy and they can be combined into interweaving and alternating strategies that improve MCMC efficiency. We assess these strategies using the local level model and demonstrate that several strategies improve efficiency relative to the standard approach and the most efficient strategy interweaves the scaled errors and scaled disturbances. Supplementary materials are available online for this article.     

传递对准中测量延迟的补偿方法

采用“速度 姿态”匹配方式，提出了一种解决传递对准中主惯导数据测量延迟现象的方法。该方法将主惯导数据测量延迟时间扩展为卡尔曼滤波器的一个状态变量，并同时考虑了测量延迟时间对速度和姿态测量量的影响。在主惯导数据存在测量延迟的情况下，推导了速度、姿态测量方程，最后对提出的方法进行了仿真。仿真结果表明，该方法可以加快滤波器的收敛速度，提高传递对准的对准精度。     

Flow and heat transfer over a backward-facing step with a cylinder mounted near its top corner

A study was made to see if it is possible to enhance the heat transfer in the downstream region of a backward-facing step, where heat transfer is normally deteriorated, by the insertion of a cylinder near the top corner of the step. Cylinder size and streamwise position of the cylinder were kept constant but the cross-stream position of the cylinder was changed in three steps. Results of the heat transfer experiment, flow visualization, and measurement of the averaged and fluctuating flow fields were reported. When the cylinder was mounted at a position, a little higher than the top surface of the step, a jet-like flow pattern emerged in the averaged velocity profile beneath the cylinder and the recirculating flow was intensified. Therefore, the velocity of recirculating flow near the wall is increased at some streamwise positions. Additionally, the velocity fluctuation was intensified not only in the shear layer between the jet-like flow and the recirculating flow regions but also in the near wall region, resulting in the effective augmentation of heat transfer in this case. Therefore, it is concluded that the mounting of a cylinder is effective in the enhancement of deteriorated heat transfer in the recirculating flow region, if its is mounted in a proper position.     

Parallel and fast sequential algorithms for undirected edge connectivity augmentation

1 ,E₂,..., such that ⋃_i≤τE_i optmially increases the connectivity by τ, for any integer τ. The main result of the paper is that this sequence of edge sets can be divided into O(n) groups such that within one group, all E_i are basically the same. Using this result, we improve on the running time of edge connectivity augmentation, as well as we give the first parallel (RNC) augmentation algorithm. We also present new efficient subroutines for finding the so-called extreme sets and the cactus representation of min-cuts required in our algorithms. Augmenting the connectivity of hypergraphs with ordinary edges is known to be structurally harder than that of ordinary graphs. In a weaker version when one exceptional hyperedge is allowed in the augmenting edge set, we derive similar results as for ordinary graphs. Received November 1995 / Revised version received July 1998 Published online March 16, 1999     

Two-Connected Augmentation Problems in Planar Graphs

Given a weighted undirected graph G and a subgraph S of G, we consider the problem of adding a minimum-weight set of edges of G to S so that the resulting subgraph satisfies specified (edge or vertex) connectivity requirements between pairs of nodes of S. This has important applications in upgrading telecommunication networks to be invulnerable to link or node failures. We give a polynomial algorithm for this problem when S is connected, nodes are required to be at most 2-connected, and G is planar. Applications to network design and multicommodity cut problems are also discussed.     

A note on mixed graphs and directed splitting off

We give counterexamples to two conjectures of Bill Jackson in Some remarks on arc-connectivity, vertex splitting, and orientation in graphs and digraphs (Journal of Graph Theory 12 (3):429–436, 1988) concerning orientations of mixed graphs and splitting off in digraphs, and prove the first conjecture in the (di-) Eulerian case(s). Beside that we solve a degree constrained non-uniform directed augmentation problem for di-Eulerian mixed graphs. © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 213–221, 1998     

Prediction and Construction of Energetic Materials Based on Machine Learning Methods

Energetic materials (EMs) are the core materials of weapons and equipment. Achieving precise molecular design and efficient green synthesis of EMs has long been one of the primary concerns of researchers around the world. Traditionally, advanced materials were discovered through a trial-and-error processes, which required long research and development (R&D) cycles and high costs. In recent years, the machine learning (ML) method has matured into a tool that compliments and aids experimental studies for predicting and designing advanced EMs. This paper reviews the critical process of ML methods to discover and predict EMs, including data preparation, feature extraction, model construction, and model performance evaluation. The main ideas and basic steps of applying ML methods are analyzed and outlined. The state-of-the-art research about ML applications in property prediction and inverse material design of EMs is further summarized. Finally, the existing challenges and the strategies for coping with challenges in the further applications of the ML methods are proposed.     

Comparing roadsoils pollution patterns extracted by MOLMAP and classical three-way decomposition methods

A recent approach based on self-organizing maps (SOMs) to extract patterns from three-way data, named MOLMAP, was applied in a four-seasons study on soil pollution and its results compared with three different conventional approaches: Parallel factor analysis (PARAFAC), matrix augmented principal components analysis (MA-PCA) and Procrustes rotation. Each sampling season comprised 92 roadsoil samples and 12 analytical variables (Cd, Co, Cu, Cr, Fe, Mn, Ni, Pb, Zn, loss on ignition, pH and humidity). It was found that all techniques yielded highly similar results as the samples became organized in two major groups, each with a differentiated pollution pattern. This confirmed MOLMAP as a reliable option to handle environmental three-way datasets and to extract accurate pollution patterns.     

Augmenting a graph of minimum degree 2 to have two disjoint total dominating sets

A total dominating set of a graph is a set of vertices such that every vertex is adjacent to a vertex in the set. We show that given a graph of order n with minimum degree at least 2, one can add at most edges such that the resulting graph has two disjoint total dominating sets, and this bound is best possible.