Solving systems of linear equations is a critical component of nearly all scientific computing methods.Traditional algorithms that rely on synchronization become prohibitively expensive in computing paradigms where communication is costly, such as heterogeneous hardware, edge computing, and unreliable environments.In this paper, we introduce an s-step Approximate Conjugate Directions (s-ACD) method and develop resiliency measures that can address a variety of different data error scenarios.This method leverages a Conjugate Gradient (CG) approach locally while using Conjugate Directions (CD) globally to achieve asynchronicity.We demonstrate with numerical experiments that s-ACD admits scaling with respect to the condition number that is comparable with CG on the tested 2D Poisson problem.Furthermore, through the addition of resiliency measures, our method is able to cope with data errors, allowing it to be used effectively in unreliable environments.

Being able to detect and recognize human activities is essential for several applications, including personal assistive robotics. In this paper, we perform detection and recognition of unstructured human activity in unstructured environments. We use a RGBD sensor (Microsoft Kinect) as the input sensor, and compute a set of features based on human pose and motion, as well as based on image and point-cloud information. Our algorithm is based on a hierarchical maximum entropy Markov model (MEMM), which considers a person's activity as composed of a set of sub-activities. We infer the two-layered graph structure using a dynamic programming approach. We test our algorithm on detecting and recognizing twelve different activities performed by four people in different environments, such as a kitchen, a living room, an office, etc., and achieve good performance even when the person was not seen before in the training set.1

We present here an efficient algorithm to compute the Principal Component Analysis (PCA) of a large image set consisting of images and, for each image, the set of its uniform rotations in the plane. We do this by pointing out the block circulant structure of the covariance matrix and utilizing that structure to compute its eigenvectors. We also demonstrate the advantages of this algorithm over similar ones with numerical experiments. Although it is useful in many settings, we illustrate the specific application of the algorithm to the problem of cryo-electron microscopy.