arXiv subjects

Ruda Zhang

Publications and source records attributed to Ruda Zhang.

21 records · Page 2Linked to original sources

arXiv2020

Newton retraction as approximate geodesics on submanifolds

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 and thus match the exponential map to the second order. In particular, we show that Newton retraction (NR) is always stabler than the popular approach known as oblique projection or orthographic retraction: per Kantorovich-type convergence theorems, the superlinear convergence regions of NR include those of the latter. We also show that NR always has a lower computational cost. The preferable properties of NR are useful for optimization, sampling, and many other statistical problems on manifolds.

math.NA↗

arXiv2020

Environmental Economics and Uncertainty: Review and a Machine Learning Outlook

Economic assessment in environmental science concerns the measurement or valuation of environmental impacts, adaptation, and vulnerability. Integrated assessment modeling is a unifying framework of environmental economics, which attempts to combine key elements of physical, ecological, and socioeconomic systems. Uncertainty characterization in integrated assessment varies by component models: uncertainties associated with mechanistic physical models are often assessed with an ensemble of simulations or Monte Carlo sampling, while uncertainties associated with impact models are evaluated by conjecture or econometric analysis. Manifold sampling is a machine learning technique that constructs a joint probability model of all relevant variables which may be concentrated on a low-dimensional geometric structure. Compared with traditional density estimation methods, manifold sampling is more efficient especially when the data is generated by a few latent variables. The manifold-constrained joint probability model helps answer policy-making questions from prediction, to response, and prevention. Manifold sampling is applied to assess risk of offshore drilling in the Gulf of Mexico.

econ.GN↗

arXiv2019

Demand, Supply, and Performance of Street-Hail Taxi

Travel decisions are fundamental to understanding human mobility, urban economy, and sustainability, but measuring it is challenging and controversial. Previous studies of taxis are limited to taxi stands or hail markets at aggregate spatial units. Here we estimate the dynamic demand and supply of taxis in New York City (NYC) at street segment level, using in-vehicle Global Positioning System (GPS) data which preserve individual privacy. To this end, we model taxi demand and supply as non-stationary Poisson random fields on the road network, and pickups result from income-maximizing drivers searching for impatient passengers. With 868 million trip records of all 13,237 licensed taxis in NYC in 2009 - 2013, we show that while taxi demand are almost the same in 2011 and 2012, it declined about 2% in spring 2013, possibly caused by transportation network companies (TNCs) and fare raise. Contrary to common impression, street-hail taxis out-perform TNCs such as Uber in high-demand locations, suggesting a taxi/TNC regulation change to reduce congestion and pollution. We show that our demand estimates are stable at different supply levels and across years, a property not observed in existing matching functions. We also validate that taxi pickups can be modeled as Poisson processes. Our method is thus simple, feasible, and reliable in estimating street-hail taxi activities at a high spatial resolution; it helps quantify the ongoing discussion on congestion charges to taxis and TNCs.

physics.soc-ph↗