A compactness result for Fano manifolds and K\"ahler Ricci flows

We obtain a compactness result for Fano manifolds and K\"ahler Ricci flows. Comparing to the more general Riemannian versions by Anderson and Hamilton, in this Fano case, the curvature assumption is much weaker and is preserved by the K\"ahler Ricci flows. One assumption is the boundedness of the Ricci potential and the other is the smallness of Perelman's entropy. As one application, we obtain a new local regularity criteria and structure result for K\"ahler Ricci flows. The proof is based on a H\"older estimate for the gradient of harmonic functions, which may be of independent interest

Thinking Outside of the Cereal Box: Breeding Underutilized (Pseudo)Cereals for Improved Human Nutrition.

Cereal grains have historically played a critical role in sustaining the caloric needs of the human population. The major cereal crops, wheat, rice, and maize, are widely cultivated and have been subjected to biofortification to enhance the vitamin and mineral nutrient content of grains. In contrast, grains of several other cereals as well as non-grass pseudocereals are naturally rich in micronutrients, but have yet to be explored for broad-scale cultivation and consumption. This mini review focuses on the micronutrient and phytochemical profiles of a few emerging (pseudo)cereals and examines the current constraints of their integration into the global food system. Prospects of leveraging whole genome sequence information and modern breeding technologies to promote the breeding and accessibility of these crops are also discussed

Isoperimetric inequality under K\"ahler Ricci flow

Let ({\M}, g(t)) be a K\"ahler Ricci flow with positive first Chern class. We prove a uniform isoperimetric inequality for all time. In the process we also prove a Cheng-Yau type log gradient bound for positive harmonic functions on ({\M}, g(t)), and a Poincar\'e inequality without assuming the Ricci curvature is bounded from below.Comment: final version, to appear in Am. J. Mat

R134a flow boiling heat transfer in small diameter tubes

Copyright @ 2007 RT Edwards Inc.Boiling heat transfer in small diameter tubes has been experimentally investigated using R134a as the working fluid. The heat transfer periments were conducted with two stainless steel tubes of internal diameter 4.26 mm and 2.01 mm respectively. Other parameters were varied in the range: mass flux 100 – 500 kg/m2s; pressure 8 – 14 bar; quality up to 0.9; heat flux 13 - 150 kW/m2. The heat transfer coefficient was found to be independent of vapour quality when the quality was less than about 40% to 50% for the 4.26 mm tube and 20% to 30 % for the 2.01 mm tube. Above these quality values, the heat transfer coefficient decreases with vapour quality. Furthermore, at high heat flux values this decrease occurs for the entire quality range. The heat transfer rates were compared with existing correlations.

Entanglement and quantum phase transitions

We examine several well known quantum spin models and categorize behavior of pairwise entanglement at quantum phase transitions. A unified picture on the connection between the entanglement and quantum phase transition is given.Comment: 4 pages, 3 figure

Painterly rendering techniques: A state-of-the-art review of current approaches

In this publication we will look at the different methods presented over the past few decades which attempt to recreate digital paintings. While previous surveys concentrate on the broader subject of non-photorealistic rendering, the focus of this paper is firmly placed on painterly rendering techniques. We compare different methods used to produce different output painting styles such as abstract, colour pencil, watercolour, oriental, oil and pastel. Whereas some methods demand a high level of interaction using a skilled artist, others require simple parameters provided by a user with little or no artistic experience. Many methods attempt to provide more automation with the use of varying forms of reference data. This reference data can range from still photographs, video, 3D polygonal meshes or even 3D point clouds. The techniques presented here endeavour to provide tools and styles that are not traditionally available to an artist. Copyright © 2012 John Wiley & Sons, Ltd

Parallel sparse interpolation using small primes

To interpolate a supersparse polynomial with integer coefficients, two alternative approaches are the Prony-based "big prime" technique, which acts over a single large finite field, or the more recently-proposed "small primes" technique, which reduces the unknown sparse polynomial to many low-degree dense polynomials. While the latter technique has not yet reached the same theoretical efficiency as Prony-based methods, it has an obvious potential for parallelization. We present a heuristic "small primes" interpolation algorithm and report on a low-level C implementation using FLINT and MPI.Comment: Accepted to PASCO 201

Holographic particle localization under multiple scattering

We introduce a novel framework that incorporates multiple scattering for large-scale 3D particle-localization using single-shot in-line holography. Traditional holographic techniques rely on single-scattering models which become inaccurate under high particle-density. We demonstrate that by exploiting multiple-scattering, localization is significantly improved. Both forward and back-scattering are computed by our method under a tractable recursive framework, in which each recursion estimates the next higher-order field within the volume. The inverse scattering is presented as a nonlinear optimization that promotes sparsity, and can be implemented efficiently. We experimentally reconstruct 100 million object voxels from a single 1-megapixel hologram. Our work promises utilization of multiple scattering for versatile large-scale applications