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Taxi services are a vital part of urban transportation, and a considerable contributor to traffic congestion and air pollution causing substantial adverse effects on human health. Sharing taxi trips is a possible way of reducing the negative impact of taxi services on cities, but this comes at the expense of passenger discomfort quantifiable in terms of a longer travel time. Due to computational challenges, taxi sharing has traditionally been approached on small scales, such as within airport perimeters, or with dynamical ad hoc heuristics. However, a mathematical framework for the systematic understanding of the tradeoff between collective benefits of sharing and individual passenger discomfort is lacking. Here we introduce the notion of shareability network, which allows us to model the collective benefits of sharing as a function of passenger inconvenience, and to efficiently compute optimal sharing strategies on massive datasets. We apply this framework to a dataset of millions of taxi trips taken in New York City, showing that with increasing but still relatively low passenger discomfort, cumulative trip length can be cut by 40% or more. This benefit comes with reductions in service cost, emissions, and with split fares, hinting toward a wide passenger acceptance of such a shared service. Simulation of a realistic online system demonstrates the feasibility of a shareable taxi service in New York City. Shareability as a function of trip density saturates fast, suggesting effectiveness of the taxi sharing system also in cities with much sparser taxi fleets or when willingness to share is low.carpooling | human mobility | urban computing | maximum matching

The nervous system has a modular architecture with neurons of the same type commonly organized in nonrandom arrays or mosaics. Modularity is essential to parallel processing of sensory information and has provided a key element for brain evolution, but we still know very little of the way neuronal mosaics form during development. Here we have identified the immature elements of two retinal mosaics, the choline acetyltransferase (ChAT) amacrine cells, by their early expression of the homeodomain protein Islet-1, and we show that spatial ordering is an intrinsic property of the two Islet-1 mosaics, dynamically maintained while new elements are inserted into the mosaics. Migrating Islet-1 cells do not show this spatial ordering, indicating that they must move tangentially as they enter the mosaic, under the action of local mechanisms. Clonal territory analysis in X-inactivation transgenic mice confirms the lateral displacement of ChAT amacrine cells away from their clonal columns of origin, and mathematical models show how short-range cellular interactions can guide the assemblage of these mosaics via a simple biological rule. Key words: retina; LIM proteins; Islet-1; X-inactivation transgenic mouse; ChAT amacrine; tangential migration; Voronoi domainsThe retina is one of the best examples of modular organization in neural circuitry. The five main types of retinal neurons are organized into three cell layers. Photoreceptors occupy the outer nuclear layer, bipolar, horizontal, and amacrine cells the inner nuclear layer (I N L), and ganglion cells and displaced amacrine cells the ganglion cell layer (GCL). Each principal class of retinal neurons can be divided f urther into subtypes, which differ in morphology and connectivity as well as biochemical and physiological properties (for review, see Ramon y C ajal, 1892;Rodieck, 1973;Dowling, 1987;Wässle and Boycott, 1991). Within each layer, neurons of the same type are commonly spaced in an orderly manner, forming planar arrays that uniformly tile the retina. Such arrays are known as neuronal mosaics (Wässle and Riemann, 1978) because they bring to mind the regular arrangement of the tesserae of a mosaic.Although the orderly organization of retinal cells is known to be f undamental to the parallel processing of visual information in the retina, little is known of the way neuronal mosaics form during development. Postmitotic retinal neurons migrate to their final positions from the proliferative neuroepithelium, but known markers for retinal mosaics are expressed only after the cells have attained a regular spatial arrangement (Wässle and Riemann, 1978;Mitrofanis et al., 1988;Vaney, 1990;C asini and Brecha, 1991;Wikler and Rakic, 1991;Hutsler and Chalupa, 1995;Scheibe et al., 1995), making it difficult to understand how such regularity comes about.Here we report that the transcription factor Islet-1 is an early marker for cholinergic amacrine cells. Islet-1, a member of the LIM homeodomain family known to be involved in vertebrate and invertebrate development (Thor et al...

Information and communication technologies have opened the way to new solutions for urban mobility that provide better ways to match individuals with on-demand vehicles. However, a fundamental unsolved problem is how best to size and operate a fleet of vehicles, given a certain demand for personal mobility. Previous studies either do not provide a scalable solution or require changes in human attitudes towards mobility. Here we provide a network-based solution to the following 'minimum fleet problem', given a collection of trips (specified by origin, destination and start time), of how to determine the minimum number of vehicles needed to serve all the trips without incurring any delay to the passengers. By introducing the notion of a 'vehicle-sharing network', we present an optimal computationally efficient solution to the problem, as well as a nearly optimal solution amenable to real-time implementation. We test both solutions on a dataset of 150 million taxi trips taken in the city of New York over one year . The real-time implementation of the method with near-optimal service levels allows a 30 per cent reduction in fleet size compared to current taxi operation. Although constraints on driver availability and the existence of abnormal trip demands may lead to a relatively larger optimal value for the fleet size than that predicted here, the fleet size remains robust for a wide range of variations in historical trip demand. These predicted reductions in fleet size follow directly from a reorganization of taxi dispatching that could be implemented with a simple urban app; they do not assume ride sharing, nor require changes to regulations, business models, or human attitudes towards mobility to become effective. Our results could become even more relevant in the years ahead as fleets of networked, self-driving cars become commonplace.

Sharing rides could drastically improve the efficiency of car and taxi transportation. Unleashing such potential, however, requires understanding how urban parameters affect the fraction of individual trips that can be shared, a quantity that we call shareability. Using data on millions of taxi trips in New York City, San Francisco, Singapore, and Vienna, we compute the shareability curves for each city, and find that a natural rescaling collapses them onto a single, universal curve. We explain this scaling law theoretically with a simple model that predicts the potential for ride sharing in any city, using a few basic urban quantities and no adjustable parameters. Accurate extrapolations of this type will help planners, transportation companies, and society at large to shape a sustainable path for urban growth.