Economic and environmental benefits of automated electric vehicle ride-hailing services in New York City.

A precise, scalable, and computationally efficient mathematical framework is proposed for region-wide autonomous electric vehicle (AEV) fleet management, sizing and infrastructure planning for urban ride-hailing services. A comprehensive techno-economic analysis in New York City is conducted not only to calculate the societal costs but also to quantify the environmental and health benefits resulting from reduced emissions. The results reveal that strategic fleet management can reduce fleet size and unnecessary cruising mileage by up to 40% and 70%, respectively. This alleviates traffic congestion, saves travel time, and further reduces fleet sizes. Besides, neither large-battery-size AEVs nor high-power charging infrastructure is necessary to achieve efficient service. This effectively alleviates financial and operational burdens on fleet operators and power systems. Moreover, the reduced travel time and emissions resulting from efficient fleet autonomy create an economic value that exceeds the total capital investment and operational costs of fleet services.

Hopfield Neural Network Flow: A Geometric Viewpoint.

We provide gradient flow interpretations for the continuous-time continuous-state Hopfield neural network (HNN). The ordinary and stochastic differential equations associated with the HNN were introduced in the literature as analog optimizers and were reported to exhibit good performance in numerical experiments. In this work, we point out that the deterministic HNN can be transcribed into Amari's natural gradient descent, and thereby uncover the explicit relation between the underlying Riemannian metric and the activation functions. By exploiting an equivalence between the natural gradient descent and the mirror descent, we show how the choice of activation function governs the geometry of the HNN dynamics. For the stochastic HNN, we show that the so-called "diffusion machine," while not a gradient flow itself, induces a gradient flow when lifted in the space of probability measures. We characterize this infinite-dimensional flow as the gradient descent of certain free energy with respect to a Wasserstein metric that depends on the geodesic distance on the ground manifold. Furthermore, we demonstrate how this gradient flow interpretation can be used for fast computation via recently developed proximal algorithms.