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We propose in this paper Periodic Interaction Primitives - a probabilistic framework that can be used to learn compact models of periodic behavior. Our approach extends existing formulations of Interaction Primitives to periodic movement regimes, i.e., walking. We show that this model is particularly well-suited for learning data-driven, customized models of human walking, which can then be used for generating predictions over future states or for inferring latent, biomechanical variables. We also demonstrate how the same framework can be used to learn controllers for a robotic prosthesis using an imitation learning approach. Results in experiments with human participants indicate that Periodic Interaction Primitives efficiently generate predictions and ankle angle control signals for a robotic prosthetic ankle, with MAE of 2.21 degrees in 0.0008s per inference. Performance degrades gracefully in the presence of noise or sensor fall outs. Compared to alternatives, this algorithm functions 20 times faster and performed 4.5 times more accurately on test subjects. 

Introduced predators currently threaten endemic animals on Madagascar through predation, facilitation of human-led hunts, competition, and disease transmission, but the antiquity and past consequences of these introductions are poorly known. We use directly radiocarbon dated bones of introduced dogs ( Canis familiaris ) to test whether dogs could have aided human-led hunts of the island’s extinct megafauna. We compare carbon and nitrogen isotope data from the bone collagen of dogs and endemic “fosa” ( Cryptoprocta spp.) in central and southwestern Madagascar to test for competition between introduced and endemic predators. The distinct isotopic niches of dogs and fosa suggest that any past antagonistic relationship between these predators did not follow from predation or competition for shared prey. Radiocarbon dates confirm that dogs have been present on Madagascar for over a millennium and suggest that they at least briefly co-occurred with the island’s extinct megafauna, which included giant lemurs, elephant birds, and pygmy hippopotamuses. Today, dogs share a mutualism with pastoralists who also occasionally hunt endemic vertebrates, and similar behavior is reflected in deposits at several Malagasy paleontological sites that contain dog and livestock bones along with butchered bones of extinct megafauna and extant lemurs. Dogs on Madagascar have had a wide range of diets during the past millennium, but relatively high stable carbon isotope values suggest few individuals relied primarily on forest bushmeat. Our newly generated data suggest that dogs were part of a suite of animal introductions beginning over a millennium ago that coincided with widespread landscape transformation and megafaunal extinction.