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With more satellite and model precipitation data becoming available, new analytical methods are needed that can take advantage of emerging data patterns to make well informed predictions in many hydrological applications. We propose a new strategy where we extract precipitation variability patterns and use correlation map to build the resulting density map that serves as an input to centroidal Voronoi tessellation construction that optimizes placement of precipitation gauges. We provide results of numerical experiments based on the data from the Alto-Adige region in Northern Italy and Oklahoma and compare them against actual gauge locations. This method provides an automated way for choosing new gauge locations and can be generalized to include physical constraints and to tackle other types of resource allocation problems.

Image segmentation algorithms often depend on appearance models that characterize the distribution of pixel values in different image regions. We describe a novel approach for estimating appearance models directly from an image, without explicit consideration of the pixels that make up each region. Our approach is based on algebraic expressions that relate local image statistics to the appearance models of spatially coherent regions. We describe two algorithms that can use the aforementioned algebraic expressions for estimating appearance models. The first algorithm is based on solving a system of linear and quadratic equations. The second algorithm is a spectral method based on an eigenvector computation. We present experimental results that demonstrate the proposed methods work well in practice and lead to effective image segmentation algorithms.

Pediatric obstructive sleep apnea affects an estimated 1-5% of elementaryschool aged children and can lead to other detrimental health problems. Swift diagnosis and treatment are critical to a child's growth and development, but the variability of symptoms and the complexity of the available data make this a challenge. We take a first step in streamlining the process by focusing on inexpensive data from questionnaires and craniofacial measurements. We apply correlation networks, the Mapper algorithm from topological data analysis, and singular value decomposition in a process of exploratory data analysis. We then apply a variety of supervised and unsupervised learning techniques from statistics, machine learning, and topology, ranging from support vector machines to Bayesian classifiers and manifold learning. Finally, we analyze the results of each of these methods and discuss the implications for a multi-data-sourced algorithm moving forward.

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