Efficient approximation of geodesics is crucial for practical algorithms on manifolds. Here we introduce a class of retractions on submanifolds, induced by a foliation of the ambient manifold. They match the projective retraction to the third order …
Probabilistic models of data sets often exhibit salient geometric structure. Such a phenomenon is summed up in the manifold distribution hypothesis, and can be exploited in probabilistic learning. Here we present normal-bundle bootstrap (NBB), a …
I use three equilibrium concepts in the sciences to study the dynamics of taxi transportation. At the microscopic level, I formalized taxi drivers' decision-making as an income-maximizing optimization, which collectively establishes an economic …
I use in-vehicle Global Positioning System (GPS) data to estimate the supply and demand of street-hail taxis at segment level of a road network, without surveilling the population. To this end, I model taxi demand and supply as non-stationary Poisson …