Learning Interpretable Dynamics from Images of a Freely Rotating 3D Rigid Body

In many real-world settings, image observations of freely rotating 3D rigid bodies, such as satellites, may be available when low-dimensional measurements are not. However, the high-dimensionality of image data precludes the use of classical estimation techniques to learn the dynamics and a lack of interpretability reduces the usefulness of standard deep learning methods. In this work, we present a physics-informed neural network model to estimate and predict 3D rotational dynamics from image sequences. We achieve this using a multi-stage prediction pipeline that maps individual images to a latent representation homeomorphic to $\mathbf{SO}(3)$, computes angular velocities from latent pairs, and predicts future latent states using the Hamiltonian equations of motion with a learned representation of the Hamiltonian. We demonstrate the efficacy of our approach on a new rotating rigid-body dataset with sequences of rotating cubes and rectangular prisms with uniform and non-uniform density.Comment: 8 pages, 7 figure

An expert-based system to predict population survival rate from health data

This work was supported by the Office of Naval Research Marine Mammal Biology Program [grant number N00014-17-1-2868].Timely detection and understanding of causes for population decline are essential for effective wildlife management and conservation. Assessing trends in population size has been the standard approach but we propose that monitoring population health could prove more effective. We collated data from seven bottlenose dolphin (Tursiops truncatus) populations in southeastern U.S. to develop the Veterinary Expert System for Outcome Prediction (VESOP), which estimates survival probability using a suite of health measures identified by experts as indices for inflammatory, metabolic, pulmonary, and neuroendocrine systems. VESOP was implemented using logistic regression within a Bayesian analysis framework, and parameters were fit using records from five of the sites that had a robust stranding network and frequent photographic identification (photo-ID) surveys to document definitive survival outcomes. We also conducted capture-mark-recapture (CMR) analyses of photo-ID data to obtain separate estimates of population survival rates for comparison with VESOP survival estimates. VESOP analyses found multiple measures of health, particularly markers of inflammation, were predictive of 1- and 2-year individual survival. The highest mortality risk one year following health assessment related to low alkaline phosphatase, with an odds ratio of 10.2 (95% CI 3.41-26.8), while 2-year mortality was most influenced by elevated globulin (9.60; 95% CI 3.88-22.4); both are markers of inflammation. The VESOP model predicted population-level survival rates that correlated with estimated survival rates from CMR analyses for the same populations (1-year Pearson's r = 0.99; p = 1.52e-05, 2-year r = 0.94; p = 0.001). While our proposed approach will not detect acute mortality threats that are largely independent of animal health, such as harmful algal blooms, it is applicable for detecting chronic health conditions that increase mortality risk. Random sampling of the population is important and advancement in remote sampling methods could facilitate more random selection of subjects, obtainment of larger sample sizes, and extension of the approach to other wildlife species.Publisher PDFPeer reviewe

Learning to Predict 3D Rotational Dynamics from Images of a Rigid Body with Unknown Mass Distribution

In many real-world settings, image observations of freely rotating 3D rigid bodies may be available when low-dimensional measurements are not. However, the high-dimensionality of image data precludes the use of classical estimation techniques to learn the dynamics. The usefulness of standard deep learning methods is also limited, because an image of a rigid body reveals nothing about the distribution of mass inside the body, which, together with initial angular velocity, is what determines how the body will rotate. We present a physics-based neural network model to estimate and predict 3D rotational dynamics from image sequences. We achieve this using a multi-stage prediction pipeline that maps individual images to a latent representation homeomorphic to SO(3), computes angular velocities from latent pairs, and predicts future latent states using the Hamiltonian equations of motion. We demonstrate the efficacy of our approach on new rotating rigid-body datasets of sequences of synthetic images of rotating objects, including cubes, prisms and satellites, with unknown uniform and non-uniform mass distributions. Our model outperforms competing baselines on our datasets, producing better qualitative predictions and reducing the error observed for the state-of-the-art Hamiltonian Generative Network by a factor of 2

Principal components analyses on males from within a season: winter (A), summer (C).

<p>Within a season, there is no significant correlation (Spearman rank) between ∑POPs in blubber (μg/g lipid) and the PC1 scores, which are responsible for 22.7% (winter, B) and 20.6% (summer, D) of the total variance in the gene expression profiles. Symbols: red—Barataria Bay, blue—Chandeleur Sound, brown—Mississippi Sound.</p

Hierarchical cluster of probes mapping to the KEGG pathway “Metabolism of xenobiotics by cytochrome p450”.

<p>Heat map color is relative to the median intensity for each probe: red is increased, blue is decreased, log₂ scale.</p

Two-dimensional hierarchical cluster analysis of 391 probes differentially expressed in 29 samples collected from spring and summer 2010 (pre- and post-oiling) (p<0.01, fold change ≥1.5).

<p>Spring Chandeleur Sound (boxed) animals cluster with the summer expression profiles. Heat map color is relative to the median intensity for each probe: red is increased, blue is decreased, log₂ scale.</p

Location of biopsy samples collected from Barataria Bay (BB), Chandeleur Sound (CS), and Mississippi Sound (MS), in the northern Gulf of Mexico.

<p>Location of biopsy samples collected from Barataria Bay (BB), Chandeleur Sound (CS), and Mississippi Sound (MS), in the northern Gulf of Mexico.</p

Samples included in microarray analysis.

<p>*pre oil-exposure</p><p>** possible exposure; all others post-exposure</p><p>Samples included in microarray analysis.</p

Seasonal Variation in the Skin Transcriptome of Common Bottlenose Dolphins (<i>Tursiops truncatus - Fig 2 </i>) from the Northern Gulf of Mexico

<p>A. Principal component analysis on all 94 microarrays shows complete separation of winter samples from all others, with no apparent segregation according to location. B. Unsupervised hierarchical cluster analysis of the normalized array data similarly shows complete separation of winter samples from the warmer seasons.</p