The key quantity of interest here is the Riemannian metric, which characterizes the Riemannian geometry and defines straight lines and derivatives on the manifold.

Work completed at the University of Washington. Work completed at Microsoft Research.

Recent accelerations in multi-modal applications have been made possible with the plethora of image and text data available online.

However, they bring their own set of challenges.

While it possesses many desirable structural properties, the estimation of high-dimensional MI from samples suffers from the curse of dimensionality.

Why Are Some Women Training for Pregnancy Like It's a Marathon? A growing legion of "zero trimester" influencers are convincing followers that healthy pregnancies are a choice--and that raw milk, watching sunsets, and pricey specialized courses can help. Three years ago, Esther Rohr and her husband decided to start thinking about pregnancy. The 26-year-old Oregon-based wedding photographer made small but intentional lifestyle changes--going to bed earlier, drinking more water and less alcohol, dialing in her fitness, loading up on protein, and taking supplements like beef organ capsules and Vitamin D3. They started charging their phones in the kitchen for better sleep and unplugging their Wi-Fi at night, because her research suggested it might affect cellular health. Concerned about their exposure to reproductive toxins, Rohr began the slow, painstaking task of swapping out all their synthetic workout clothes, nonstick pans, and scented personal care products that might contain phthalates or other endocrine-disrupting chemicals. She bought an air purifier and hopes to eventually replace their LED bulbs with incandescents, because she worries they might be affecting her circadian rhythm.