Lattice Boltzmann Model for The Volume-Averaged Navier-Stokes Equations

A numerical method, based on the discrete lattice Boltzmann equation, is presented for solving the volume-averaged Navier-Stokes equations. With a modified equilibrium distribution and an additional forcing term, the volume-averaged Navier-Stokes equations can be recovered from the lattice Boltzmann equation in the limit of small Mach number by the Chapman-Enskog analysis and Taylor expansion. Due to its advantages such as explicit solver and inherent parallelism, the method appears to be more competitive with traditional numerical techniques. Numerical simulations show that the proposed model can accurately reproduce both the linear and nonlinear drag effects of porosity in the fluid flow through porous media.Comment: 9 pages, 2 figure

ViP-CNN: Visual Phrase Guided Convolutional Neural Network

As the intermediate level task connecting image captioning and object detection, visual relationship detection started to catch researchers' attention because of its descriptive power and clear structure. It detects the objects and captures their pair-wise interactions with a subject-predicate-object triplet, e.g. person-ride-horse. In this paper, each visual relationship is considered as a phrase with three components. We formulate the visual relationship detection as three inter-connected recognition problems and propose a Visual Phrase guided Convolutional Neural Network (ViP-CNN) to address them simultaneously. In ViP-CNN, we present a Phrase-guided Message Passing Structure (PMPS) to establish the connection among relationship components and help the model consider the three problems jointly. Corresponding non-maximum suppression method and model training strategy are also proposed. Experimental results show that our ViP-CNN outperforms the state-of-art method both in speed and accuracy. We further pretrain ViP-CNN on our cleansed Visual Genome Relationship dataset, which is found to perform better than the pretraining on the ImageNet for this task.Comment: 10 pages, 5 figures, accepted by CVPR 201

Dynamical topology and statistical properties of spatiotemporal chaos

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a large extent, the location and movement of these topologically special points determine the qualitative structure of the disordered states. We analyze numerically statistical properties of the topologically special points in one-dimensional spatiotemporal chaos. The probability distribution functions for the number of point, the lifespan, and the distance covered during their lifetime are obtained from numerical simulations. Mathematically, we establish a probabilistic model to describe the dynamics of these topologically special points. In despite of the different definitions in different spatiotemporal chaos, the dynamics of these special points can be described in a uniform approach.Comment: 6 pages, 5 figure

Approximating Word Ranking and Negative Sampling for Word Embedding

CBOW (Continuous Bag-Of-Words) is one of the most commonly used techniques to generate word embeddings in various NLP tasks. However, it fails to reach the optimal performance due to uniform involvements of positive words and a simple sampling distribution of negative words. To resolve these issues, we propose OptRank to optimize word ranking and approximate negative sampling for bettering word embedding. Specifically, we first formalize word embedding as a ranking problem. Then, we weigh the positive words by their ranks such that highly ranked words have more importance, and adopt a dynamic sampling strategy to select informative negative words. In addition, an approximation method is designed to efficiently compute word ranks. Empirical experiments show that OptRank consistently outperforms its counterparts on a benchmark dataset with different sampling scales, especially when the sampled subset is small. The code and datasets can be obtained from https://github.com/ouououououou/OptRank