Compositional Distributional Semantics with Long Short Term Memory

We are proposing an extension of the recursive neural network that makes use of a variant of the long short-term memory architecture. The extension allows information low in parse trees to be stored in a memory register (the `memory cell') and used much later higher up in the parse tree. This provides a solution to the vanishing gradient problem and allows the network to capture long range dependencies. Experimental results show that our composition outperformed the traditional neural-network composition on the Stanford Sentiment Treebank.Comment: 10 pages, 7 figure

3D Human Activity Recognition with Reconfigurable Convolutional Neural Networks

Human activity understanding with 3D/depth sensors has received increasing attention in multimedia processing and interactions. This work targets on developing a novel deep model for automatic activity recognition from RGB-D videos. We represent each human activity as an ensemble of cubic-like video segments, and learn to discover the temporal structures for a category of activities, i.e. how the activities to be decomposed in terms of classification. Our model can be regarded as a structured deep architecture, as it extends the convolutional neural networks (CNNs) by incorporating structure alternatives. Specifically, we build the network consisting of 3D convolutions and max-pooling operators over the video segments, and introduce the latent variables in each convolutional layer manipulating the activation of neurons. Our model thus advances existing approaches in two aspects: (i) it acts directly on the raw inputs (grayscale-depth data) to conduct recognition instead of relying on hand-crafted features, and (ii) the model structure can be dynamically adjusted accounting for the temporal variations of human activities, i.e. the network configuration is allowed to be partially activated during inference. For model training, we propose an EM-type optimization method that iteratively (i) discovers the latent structure by determining the decomposed actions for each training example, and (ii) learns the network parameters by using the back-propagation algorithm. Our approach is validated in challenging scenarios, and outperforms state-of-the-art methods. A large human activity database of RGB-D videos is presented in addition.Comment: This manuscript has 10 pages with 9 figures, and a preliminary version was published in ACM MM'14 conferenc

Structure-preserving mesh coupling based on the Buffa-Christiansen complex

The state of the art for mesh coupling at nonconforming interfaces is presented and reviewed. Mesh coupling is frequently applied to the modeling and simulation of motion in electromagnetic actuators and machines. The paper exploits Whitney elements to present the main ideas. Both interpolation- and projection-based methods are considered. In addition to accuracy and efficiency, we emphasize the question whether the schemes preserve the structure of the de Rham complex, which underlies Maxwell's equations. As a new contribution, a structure-preserving projection method is presented, in which Lagrange multiplier spaces are chosen from the Buffa-Christiansen complex. Its performance is compared with a straightforward interpolation based on Whitney and de Rham maps, and with Galerkin projection.Comment: 17 pages, 7 figures. Some figures are omitted due to a restricted copyright. Full paper to appear in Mathematics of Computatio

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology