Using state space differential geometry for nonlinear blind source separation

Given a time series of multicomponent measurements of an evolving stimulus, nonlinear blind source separation (BSS) seeks to find a "source" time series, comprised of statistically independent combinations of the measured components. In this paper, we seek a source time series with local velocity cross correlations that vanish everywhere in stimulus state space. However, in an earlier paper the local velocity correlation matrix was shown to constitute a metric on state space. Therefore, nonlinear BSS maps onto a problem of differential geometry: given the metric observed in the measurement coordinate system, find another coordinate system in which the metric is diagonal everywhere. We show how to determine if the observed data are separable in this way, and, if they are, we show how to construct the required transformation to the source coordinate system, which is essentially unique except for an unknown rotation that can be found by applying the methods of linear BSS. Thus, the proposed technique solves nonlinear BSS in many situations or, at least, reduces it to linear BSS, without the use of probabilistic, parametric, or iterative procedures. This paper also describes a generalization of this methodology that performs nonlinear independent subspace separation. In every case, the resulting decomposition of the observed data is an intrinsic property of the stimulus' evolution in the sense that it does not depend on the way the observer chooses to view it (e.g., the choice of the observing machine's sensors). In other words, the decomposition is a property of the evolution of the "real" stimulus that is "out there" broadcasting energy to the observer. The technique is illustrated with analytic and numerical examples.Comment: Contains 14 pages and 3 figures. For related papers, see http://www.geocities.com/dlevin2001/ . New version is identical to original version except for URL in the bylin

North American Vegetation Dynamics Observed with Multi-Resolution Satellite Data

North American vegetation has been discovered to be a net carbon sink, with atypical behavior of drawing down more carbon from the atmosphere during the past century. It has been suggested that the Northern Hemisphere will respond favorably to climate warming by enhancing productivity and reducing the impact of fossil fuel emissions into the atmosphere. Many investigations are currently underway to understand and identify mechanisms of storage so they might be actively managed to offset carbon emissions which have detrimental consequences to the functioning of ecosystems and human well being. This paper used a time series of satellite data from multiple sensors at multiple resolutions over the past thlrty years to identify and understand mechanisms of change to vegetation productivity throughout North America. We found that humans had a marked impact to vegetation growth in half of the six selected study regions which cover greater than two million km2. We found climatic influences of increasing temperatures, and longer growing seasons with reduced snow cover in the northern regions of North America with forest fire recovery in the Northern coniferous forests of Canada. The Mid-latitudes had more direct land cover changes induced by humans coupled with climatic influences such as severe drought and altered production strategies of rain-fed agriculture in the upper Midwest, expansion of irrigated agriculture in the lower Midwest, and insect outbreaks followed by subsequent logging in the upper Northeast. Vegetation growth over long time periods (20+ years) in North America appears to be associated with long term climate change but most of the marked changes appear to be associated with climate variability on decadal and shorter time scales along with direct human land cover conversions. Our results document regional land cover land use change and climatic influences that have altered continental scale vegetation dynamics in North America

High Performance Computing Applications in Remote Sensing Studies for Land Cover Dynamics

Global and regional land cover studies require the ability to apply complex models on selected subsets of large amounts of multi-sensor and multi-temporal data sets that have been derived from raw instrument measurements using widely accepted pre-processing algorithms. The computational and storage requirements of most such studies far exceed what is possible on a single workstation environment. We have been pursuing a new approach that couples scalable and open distributed heterogeneous hardware with the development of high performance software for processing, indexing, and organizing remotely sensed data. Hierarchical data management tools are used to ingest raw data, create metadata, and organize the archived data so as to automatically achieve computational load balancing among the available nodes and minimize I/O overheads. We illustrate our approach with four specific examples. The first is the development of the first fast operational scheme for the atmospheric correction of Landsat TM scenes, while the second example focuses on image segmentation using a novel hierarchical connected components algorithm. Retrieval of global BRDF (Bidirectional Reflectance Distribution Function) in the red and near infrared wavelengths using four years (1983 to 1986) of Pathfinder AVHRR Land (PAL) data set is the focus of our third example. The fourth example is the development of a hierarchical data organization scheme that allows on-demand processing and retrieval of regional and global AVHRR data sets. Our results show that substantial improvements in computational times can be achieved by using the high performance computing technology

Exploring the nature of visual fixations on other pedestrians

How we look at other people may affect conclusions drawn about the effect of changes in lighting when this task needs to be done after dark. This paper reports further analysis of the distance and duration of fixation on other pedestrians, updating a previous review by considering a greater number of fixations and by examining the influence on these of other characteristics such as the relative direction of travel. This analysis provides further support for a tendency to fixate others at a distance of 15 m and for a duration of 500 ms

Bayesian Exponential Random Graph Models with Nodal Random Effects

We extend the well-known and widely used Exponential Random Graph Model (ERGM) by including nodal random effects to compensate for heterogeneity in the nodes of a network. The Bayesian framework for ERGMs proposed by Caimo and Friel (2011) yields the basis of our modelling algorithm. A central question in network models is the question of model selection and following the Bayesian paradigm we focus on estimating Bayes factors. To do so we develop an approximate but feasible calculation of the Bayes factor which allows one to pursue model selection. Two data examples and a small simulation study illustrate our mixed model approach and the corresponding model selection.Comment: 23 pages, 9 figures, 3 table

Atmospheric velocity fields in tepid main sequence stars

The line profiles of the stars with v sin i below a few km/s can reveal direct signatures of local velocity fields (e.g. convection) in stellar atmospheres. This effect is well established in cool main sequence stars, and has been detected and studied in three A stars. This paper reports observations of main sequence B, A and F stars with two goals: (1) to identify additional stars having sufficiently low values of v sin i to search for spectral line profile signatures of local velocity fields, and (2) to explore how the signatures of the local velocity fields in the atmosphere depend on stellar parameters such as effective temperature T_eff and peculiarity type. For stars having T_eff below about 10000 K, we always detect local atmospheric velocity fields indirectly through a non-zero microturbulence parameter, but not for hotter stars. Among the A and F stars in our sample having the sharpest lines, direct tracers of atmospheric velocity fields are found in six new stars. The velocity field signatures identified include asymmetric excess line wing absorption, deeper in the blue line wing than in the red; line profiles of strong lines that are poorly fit by computed profiles; and strong lines that are broader than they should be for the v sin i values deduced from weak lines. These effects are found in both normal and Am stars, but seem stronger in Am stars. These data still have not been satisfactorily explained by models of atmospheric convection, including numerical simulations.Comment: Acepted for publication by Astronomy and Astrophysic

Annual Carbon Emissions from Deforestation in the Amazon Basin between 2000 and 2010

Funding for Open Access provided by the UMD Libraries Open Access Publishing Fund.Reducing emissions from deforestation and forest degradation (REDD+) is considered one of the most cost-effective strategies for mitigating climate change. However, historical deforestation and emission rates―critical inputs for setting reference emission levels for REDD+―are poorly understood. Here we use multi-source, time-series satellite data to quantify carbon emissions from deforestation in the Amazon basin on a year-to-year basis between 2000 and 2010.We first derive annual deforestation indicators by using the Moderate Resolution Imaging Spectroradiometer Vegetation Continuous Fields (MODIS VCF) product. MODIS indicators are calibrated by using a large sample of Landsat data to generate accurate deforestation rates, which are subsequently combined with a spatially explicit biomass dataset to calculate committed annual carbon emissions. Across the study area, the average deforestation and associated carbon emissions were estimated to be 1.59 ± 0.25M ha•yr−1 and 0.18 ± 0.07 Pg C•yr−1 respectively, with substantially different trends and inter-annual variability in different regions. Deforestation in the Brazilian Amazon increased between 2001 and 2004 and declined substantially afterwards, whereas deforestation in the Bolivian Amazon, the Colombian Amazon, and the Peruvian Amazon increased over the study period. The average carbon density of lost forests after 2005 was 130 Mg C•ha−1, ~11%lower than the average carbon density of remaining forests in year 2010 (144 Mg C•ha−1). Moreover, the average carbon density of cleared forests increased at a rate of 7 Mg C•ha−1•yr−1 from 2005 to 2010, suggesting that deforestation has been progressively encroaching into high-biomass lands in the Amazon basin. Spatially explicit, annual deforestation and emission estimates like the ones derived in this study are useful for setting baselines for REDD+ and other emission mitigation programs, and for evaluating the performance of such efforts