DFacTo: Distributed Factorization of Tensors

We present a technique for significantly speeding up Alternating Least Squares (ALS) and Gradient Descent (GD), two widely used algorithms for tensor factorization. By exploiting properties of the Khatri-Rao product, we show how to efficiently address a computationally challenging sub-step of both algorithms. Our algorithm, DFacTo, only requires two sparse matrix-vector products and is easy to parallelize. DFacTo is not only scalable but also on average 4 to 10 times faster than competing algorithms on a variety of datasets. For instance, DFacTo only takes 480 seconds on 4 machines to perform one iteration of the ALS algorithm and 1,143 seconds to perform one iteration of the GD algorithm on a 6.5 million x 2.5 million x 1.5 million dimensional tensor with 1.2 billion non-zero entries.Comment: Under review for NIPS 201

New Numerical Mid-ocean Ridge Models for Interactions Between Plate-driving and Resistant Force

Evidence for asymmetric plate growth, variable crustal thickness, and non-uniform spreading rates is ubiquitous on the seafloor. However, conventional numerical modeling approaches are often incapable of explaining the non-uniform growth of oceanic lithosphere. Noting that plate-boundary forces can dynamically determine plate speed by finding a balance against the resistance to extension at ridge axes and at lithosphere-asthenosphere boundary, I introduce plate-boundary forces instead of kinematics to drive plate motions in numerical models for mid-ocean ridges. I construct such models using FLAC, an open-source finite element code for geodynamic simulations. My mid-ocean ridge models tested three different boundary conditions: Prescribed velocities, zero boundary force, and constant non-zero boundary force. All three types of boundary conditions can produce faulting styles consistent with the previous studies but mean plate speeds respond differently to different boundary condition types. Mean plate speed is almost constant in the kinematic and zero boundary force models. The constant non-zero force boundary conditions make plates move at 1.8 cm/yr of mean speed, but plate speed changes over time by more than 1 cm/yr. These model results suggest that even if far-field plate-driving forces are nearly constant, non-uniform seafloor growth can result. However, further investigation is necessary for reducing numerical noise and extracting mean plate speed with greater confidence

The Welfare Effect of Organic Milk

This study analyzes the demands for organic and conventional milk at both brand level and commodity level adopting the multi-stage demand approach. The study also measures the consumer benefits from organic milk introduction and finds the welfare effect significant.Demand and Price Analysis,