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Graph-based representations are becoming increasingly popular for representing and analyzing video data, especially in object tracking and scene understanding applications. Accordingly, an essential tool in this approach is to generate statistical inferences for graphical time series associated with videos. This paper develops a Kalman-smoothing method for estimating graphs from noisy, cluttered, and incomplete data. The main challenge here is to find and preserve the registration of nodes (salient detected objects) across time frames when the data has noise and clutter due to false and missing nodes. First, we introduce a quotient-space representation of graphs that incorporates temporal registration of nodes, and we use that metric structure to impose a dynamical model on graph evolution. Then, we derive a Kalman smoother, adapted to the quotient space geometry, to estimate dense, smooth trajectories of graphs. We demonstrate this framework using simulated data and actual video graphs extracted from the Multiview Extended Video with Activities (MEVA) dataset. This framework successfully estimates graphs despite the noise, clutter, and missed detections. 

Complex analyses involving multiple, dependent random quantities often lead to graphical models—a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical analyses for graphical data, especially towards generative modeling, one needs mathematical representations and metrics for matching and comparing graphs, and subsequent tools, such as geodesics, means, and covariances. This paper utilizes a quotient structure to develop efficient algorithms for computing these quantities, leading to useful statistical tools, including principal component analysis, statistical testing, and modeling. We demonstrate the efficacy of this framework using datasets taken from several problem areas, including letters, biochemical structures, and social networks. 

Food security will be increasingly challenged by climate change, natural resource degradation, and population growth. Wheat yields, in particular, have already stagnated in many regions and will be further affected by warming temperatures. Despite these challenges, wheat yields can be increased by improving management practices in regions with existing yield gaps. To identify the magnitude and causes of current yield gaps in India, one of the largest wheat producers globally, we produced 30 meter resolution yield maps from 2001 to 2015 across the Indo-Gangetic Plains (IGP), the nation’s main wheat belt. Yield maps were derived using a new method that translates satellite vegetation indices to yield estimates using crop model simulations, bypassing the need for ground calibration data. This is one of the first attempts to apply this method to a smallholder agriculture system, where ground calibration data are rarely available. We find that yields can be increased by 11% on average and up to 32% in the eastern IGP by improving management to current best practices within a given district. Additionally, if current best practices from the highest-yielding state of Punjab are implemented in the eastern IGP, yields could increase by almost 110%. Considering the factors that most influence yields, later sow dates and warmer temperatures are most associated with low yields across the IGP. This suggests that strategies to reduce the negative effects of heat stress, like earlier sowing and planting heat-tolerant wheat varieties, are critical to increasing wheat yields in this globally-important agricultural region.

 

We present Fermi Gamma-ray Burst Monitor (Fermi-GBM) and Swift Burst Alert Telescope (Swift-BAT) searches for gamma-ray/X-ray counterparts to gravitational-wave (GW) candidate events identified during the third observing run of the Advanced LIGO and Advanced Virgo detectors. Using Fermi-GBM onboard triggers and subthreshold gamma-ray burst (GRB) candidates found in the Fermi-GBM ground analyses, the Targeted Search and the Untargeted Search, we investigate whether there are any coincident GRBs associated with the GWs. We also search the Swift-BAT rate data around the GW times to determine whether a GRB counterpart is present. No counterparts are found. Using both the Fermi-GBM Targeted Search and the Swift-BAT search, we calculate flux upper limits and present joint upper limits on the gamma-ray luminosity of each GW. Given these limits, we constrain theoretical models for the emission of gamma rays from binary black hole mergers.