Geodesics in Heat

We introduce the heat method for computing the shortest geodesic distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The method represents a significant breakthrough in the practical computation of distance on a wide variety of geometric domains, since the resulting linear systems can be prefactored once and subsequently solved in near-linear time. In practice, distance can be updated via the heat method an order of magnitude faster than with state-of-the-art methods while maintaining a comparable level of accuracy. We provide numerical evidence that the method converges to the exact geodesic distance in the limit of refinement; we also explore smoothed approximations of distance suitable for applications where more regularity is required

Major John Bradford Homestead archaeological collections report

This report describes a collections management project undertaken on archaeological finds excavated at the Major John Bradford Homestead in 1972 and 1973. One of the chief goals of the project were to clean all artifacts that had not been processed after sorting the materials that had been processed and labeled and to reunite them with their provenience groups. The next goal was to catalogue all of the finds and to re-bag and re-box all of the materials in archivally appropriate bags and acid-free boxes and to provide a box inventory keyed to the catalogue so that future researchers or exhibit designers could readily locate objects of interest. A further goal was to provide a narrative about the excavations and to make suggestions about how to interpret the archaeological evidence and to suggest potential future research. All of these goals were met and are detailed in this report

Chiron: A Robust Recommendation System with Graph Regularizer

Recommendation systems have been widely used by commercial service providers for giving suggestions to users. Collaborative filtering (CF) systems, one of the most popular recommendation systems, utilize the history of behaviors of the aggregate user-base to provide individual recommendations and are effective when almost all users faithfully express their opinions. However, they are vulnerable to malicious users biasing their inputs in order to change the overall ratings of a specific group of items. CF systems largely fall into two categories - neighborhood-based and (matrix) factorization-based - and the presence of adversarial input can influence recommendations in both categories, leading to instabilities in estimation and prediction. Although the robustness of different collaborative filtering algorithms has been extensively studied, designing an efficient system that is immune to manipulation remains a significant challenge. In this work we propose a novel "hybrid" recommendation system with an adaptive graph-based user/item similarity-regularization - "Chiron". Chiron ties the performance benefits of dimensionality reduction (through factorization) with the advantage of neighborhood clustering (through regularization). We demonstrate, using extensive comparative experiments, that Chiron is resistant to manipulation by large and lethal attacks

Fourier PCA and Robust Tensor Decomposition

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a pair of tensors sharing the same vectors in rank-$1$ decompositions. Our main application is the first provably polynomial-time algorithm for underdetermined ICA, i.e., learning an $n \times m$ matrix $A$ from observations $y=Ax$ where $x$ is drawn from an unknown product distribution with arbitrary non-Gaussian components. The number of component distributions $m$ can be arbitrarily higher than the dimension $n$ and the columns of $A$ only need to satisfy a natural and efficiently verifiable nondegeneracy condition. As a second application, we give an alternative algorithm for learning mixtures of spherical Gaussians with linearly independent means. These results also hold in the presence of Gaussian noise.Comment: Extensively revised; details added; minor errors corrected; exposition improve

Nonparametric Regression on a Graph

The 'Signal plus Noise' model for nonparametric regression can be extended to the case of observations taken at the vertices of a graph. This model includes many familiar regression problems. This article discusses the use of the edges of a graph to measure roughness in penalized regression. Distance between estimate and observation is measured at every vertex in the L2 norm, and roughness is penalized on every edge in the L1 norm. Thus the ideas of total variation penalization can be extended to a graph. The resulting minimization problem presents special computational challenges, so we describe a new and fast algorithm and demonstrate its use with examples. The examples include image analysis, a simulation applicable to discrete spatial variation, and classification. In our examples, penalized regression improves upon kernel smoothing in terms of identifying local extreme values on planar graphs. In all examples we use fully automatic procedures for setting the smoothing parameters. Supplemental materials are available online. © 2011 American Statistical Association

Negative Link Prediction in Social Media

Signed network analysis has attracted increasing attention in recent years. This is in part because research on signed network analysis suggests that negative links have added value in the analytical process. A major impediment in their effective use is that most social media sites do not enable users to specify them explicitly. In other words, a gap exists between the importance of negative links and their availability in real data sets. Therefore, it is natural to explore whether one can predict negative links automatically from the commonly available social network data. In this paper, we investigate the novel problem of negative link prediction with only positive links and content-centric interactions in social media. We make a number of important observations about negative links, and propose a principled framework NeLP, which can exploit positive links and content-centric interactions to predict negative links. Our experimental results on real-world social networks demonstrate that the proposed NeLP framework can accurately predict negative links with positive links and content-centric interactions. Our detailed experiments also illustrate the relative importance of various factors to the effectiveness of the proposed framework

Organic Pollutants and Ocean Fronts Across the Atlantic Ocean: A Review

Little is known about the effect of ocean fronts on pollutants dynamics, particularly organic pollutants. Since fronts are associated with convergent currents and productive fishing grounds, any possible convergence of pollutants at fronts would raise concerns. The focus here is on relatively persistent organic pollutants, POPs, as non-persistent organic pollutants are rarely found in the open ocean. Results from recent cruises in the Atlantic Ocean are examined for POP distributions across ocean fronts in (i) the Canary Current; (ii) the Gulf Stream; and (iii) the Amazon and Rio de la Plata Plumes. Few studies achieved a spatial resolution of 10–20 km, while most had 100–300 km between adjacent stations. The majority of the well-resolved studies measured perfluorinated compounds (PFCs), which seem particularly well suited for frontal resolution. In the NE Atlantic, concentrations of PFCs sharply decreased between SW Europe and NW Africa upon crossing the Canary Current Front at 24–27°N. In the Western Atlantic, the PFC concentrations sharply increased upon entering the Amazon River Plume and Rio de la Plata Plume. In the NW Atlantic, concentrations of several pollutants such as polycyclic aromatic hydrocarbons are very high in Rhode Island Sound, decreasing to below detection limit in the open ocean. The more persistent and already phased-out polychlorinated biphenyls (PCBs) displayed elevated concentrations in the Gulf Stream and Rhode Island Sound, thereby highlighting the importance of ocean fronts, along-front currents, and cross-frontal transport for the dispersal of PCBs

Long Wavelength VCSELs and VCSEL-Based Processing of Microwave Signals

We address the challenge of decreasing the size, cost and power consumption for practical applications of next generation microwave photonics systems by using long-wavelength vertical cavity surface emitting lasers. Several demonstrations of new concepts of microwave photonics devices are presented and discussed

Long-term variability of sea surface temperature in Taiwan Strait

Long-term variability of sea surface temperature (SST) in the Taiwan Strait was studied from the U.K. Met Office Hadley Centre climatological data set HadISST1. In 1957–2011, three epochs were identified. The first epoch of cooling SST lasted through 1976. The regime shift of 1976–1977 led to an extremely rapid warming of 2.1 °C in 22 years. Another regime shift occurred in 1998–1999, resulting in a 1.0 °C cooling by 2011. The cross-frontal gradient between the China Coastal Current and offshore Taiwan Strait waters has abruptly decreased in 1992 and remained low through 2011. The long-term warming of SST increased towards the East China Sea, where the SST warming in 1957–2011 was about three times that in the South China Sea. The long-term warming was strongly enhanced in winter, with the maximum warming of 3.8 °C in February. The wintertime amplification of long-term warming has resulted in a decrease of the north–south SST range from 5 to 4 °C and a decrease in the amplitude of seasonal cycle of SST from 11 to 8 °C

Transverse instabilities of multiple vortex chains in superconductor-ferromagnet bilayers

Using scanning tunneling microscopy and Ginzburg-Landau simulations we explore vortex configurations in magnetically coupled NbSe$_2$-Permalloy superconductor-ferromagnet bilayer. The Permalloy film with stripe domain structure induces periodic local magnetic induction in the superconductor creating a series of pinning-antipinning channels for externally added magnetic flux quanta. Such laterally confined Abrikosov vortices form quasi-1D arrays (chains). The transitions between multichain states occur through propagation of kinks at the intermediate fields. At high fields we show that the system becomes non-linear due to a change in both the number of vortices and the confining potential. The longitudinal instabilities of the resulting vortex structures lead to vortices `levitating' in the anti-pinning channels.Comment: accepted in PRB-Rapid