Recycling Randomness with Structure for Sublinear time Kernel Expansions

We propose a scheme for recycling Gaussian random vectors into structured matrices to approximate various kernel functions in sublinear time via random embeddings. Our framework includes the Fastfood construction as a special case, but also extends to Circulant, Toeplitz and Hankel matrices, and the broader family of structured matrices that are characterized by the concept of low-displacement rank. We introduce notions of coherence and graph-theoretic structural constants that control the approximation quality, and prove unbiasedness and low-variance properties of random feature maps that arise within our framework. For the case of low-displacement matrices, we show how the degree of structure and randomness can be controlled to reduce statistical variance at the cost of increased computation and storage requirements. Empirical results strongly support our theory and justify the use of a broader family of structured matrices for scaling up kernel methods using random features

A Framework for Consistency Algorithms

We present a framework that provides deterministic consistency algorithms for given memory models. Such an algorithm checks whether the executions of a shared-memory concurrent program are consistent under the axioms defined by a model. For memory models like SC and TSO, checking consistency is NP-complete. Our framework shows, that despite the hardness, fast deterministic consistency algorithms can be obtained by employing tools from fine-grained complexity. The framework is based on a universal consistency problem which can be instantiated by different memory models. We construct an algorithm for the problem running in time ?^*(2^k), where k is the number of write accesses in the execution that is checked for consistency. Each instance of the framework then admits an ?^*(2^k)-time consistency algorithm. By applying the framework, we obtain corresponding consistency algorithms for SC, TSO, PSO, and RMO. Moreover, we show that the obtained algorithms for SC, TSO, and PSO are optimal in the fine-grained sense: there is no consistency algorithm for these running in time 2^{o(k)} unless the exponential time hypothesis fails

Cloud cover determination in polar regions from satellite imagery

A definition is undertaken of the spectral and spatial characteristics of clouds and surface conditions in the polar regions, and to the creation of calibrated, geometrically correct data sets suitable for quantitative analysis. Ways are explored in which this information can be applied to cloud classifications as new methods or as extensions to existing classification schemes. A methodology is developed that uses automated techniques to merge Advanced Very High Resolution Radiometer (AVHRR) and Scanning Multichannel Microwave Radiometer (SMMR) data, and to apply first-order calibration and zenith angle corrections to the AVHRR imagery. Cloud cover and surface types are manually interpreted, and manual methods are used to define relatively pure training areas to describe the textural and multispectral characteristics of clouds over several surface conditions. The effects of viewing angle and bidirectional reflectance differences are studied for several classes, and the effectiveness of some key components of existing classification schemes is tested

Investigation of relationship between hydrologic time series and sunspot numbers, The

April 1968.Includes bibliographical references (page 19)