Canonical general relativity: Matter fields in a general linear frame

Building on the results of previous work, we demonstrate how matter fields are incorporated into the general linear frame approach to general relativity. When considering the Maxwell one-form field, we find that the system that leads naturally to canonical vierbein general relativity has the extrinsic curvature of the Cauchy surface represented by gravitational as well as non-gravitational degrees of freedom. Nevertheless the metric compatibility conditions are undisturbed, and this apparent derivative-coupling is seen to be an effect of working with (possibly orthonormal) linear frames. The formalism is adapted to consider a Dirac Fermion, where we find that a milder form of this apparent derivative-coupling appears.Comment: 13 pages; uses AMS-latex style file

A Spatial Mathematical Model Analysis of the Linkage between Agricultural Trade and Deforestation

Like agricultural trade, deforestation has increased tremendously throughout the past five decades. We analyse the linkage between both factors by applying trade and forest policy scenarios to the global land-use model MAgPIE ("Model of Agricultural Production and its Impact on the Environment"). The model predicts global landuse patterns in a spatially explicit way and uses endogenously derived technological change and land expansion rates. Our study is the first which combines global trade analysis with a spatially explicit mapping of deforestation. By implementing self-sufficiency rates in the regional demand and supply equations, we are able to simulate different trade settings. Our baseline scenario fixes current trade patterns until the year 2045. The three liberalisation scenarios assume a path of increasing trade liberalisation which ends with no trade barriers in 2045 and they differ by applying different forest protection policies. Regions with comparative advantages like Latin America for oilcrops and China for cereals will export more. Whereas, Latin America will buy this competitiveness by converting large parts of its Amazonian rainforest into cropland, China will benefit most due to its decreasing food demand after 2025. In contrast, regions like the Middle East, North Africa and South Asia face the highest increases of imports. Forest protection policies lead to higher technological change rates. In absence of such policies, investments in agricultural Research & Development are the most effective way for protecting the forest.International Relations/Trade, Resource /Energy Economics and Policy,

Shark Declines in the Mediterranean Sea

Summarizes a study of population and biomass trends of large sharks in the Mediterranean, and highlights the risk of some species becoming extinct as a result of unintended capture in fishing gear, targeted shark fishing, and human population pressure

We Do Indeed Reap What We Sow

When violence first broke out in Tunisia in January 2011, few observers would have predicted that waves of unrest would engulf North Africa and the Arab world. When demonstrations swiftly spread to Algeria, Sudan, Egypt, Yemen, Bahrain, and Jordan, observers hastened to place bets on which regime would be the next to fall. That Hosni Mubarak would be felled next came perhaps as no surprise; Egypt had for years been on a knife’s edge, liberalizing and modernizing society while closing all space for political and social participation. Most analysts then turned their attention to Sudan, Yemen, and Bahrain, predicting that surely one of these three would be the next to falter. Yet almost no one expected that Muammar Gaddafi’s Libya would be the next domino in line. Having ruled the country for forty-one years and destroyed all semblance of a free media, of opposition politics, or of civil society, Libya was assumed to be ruthlessly stable

Leaving a Legacy

The ongoing conflict in Somalia, and the complexities that come with finding lasting solutions to a conflict that has raged for decades now, continue to perplex the international community. While a range of previously tried and tested approaches to conflict management are being applied, it is becoming apparent that the international toolkit for responding to conflict situations of such complexity is extremely limited. Indeed, as one international conference after another on Somalia takes place, compacts are signed and funding windows established, old frameworks are abandoned and new ones are forged, and roadmap after roadmap pave the way for further engagement, and as an increasing number of international actors are developing series upon series of strategies for Somalia, the timeframes for engagement are becoming increasingly protracted, and Somali reliance on external actors is being entrenched. Perplexingly little attention is being paid to one core question though: what do the Somali people themselves want

Collective Dynamics of Ride Sharing Systems with Pooled Stops: Sustainability and Reliability

Private cars are responsible for 15% of carbon emissions in the European Union. Ride hailing services like taxis could serve the door-to-door mobility demand of private car users with fewer overall vehicles. If the service combines multiple user trips, it might even reduce the distance driven compared to private cars which becomes ecologically sustainable. Such ride sharing services are particularly sustainable when many users share one vehicle. But connecting the trips of all users yields many small detours. These detours reduce if some users walk a short distance to a neighboring stop. When multiple stops are combined, vehicles drive to fewer stops. Such stop pooling promises to make ride sharing even more sustainable. Some ride sharing services already integrate short user walks into their system. But the effects of stop pooling on ride sharing systems are yet to be understood. Methods from theoretical physics like mean-field theory and agent-based modeling enable a systemic analysis of complex ride sharing systems. This thesis demonstrates that ride sharing may be more sustainable when users accept short walks. With stop pooling, users wait shorter for vehicles and drive shorter because of more direct vehicle routes. In consequence, the user travel time decreases on average despite additional walk time at constant fleet size. Put differently, stop pooling allows to reduce the fleet size at constant travel time. This also reduces the distance driven by all vehicles that is proportional to the fleet size when sufficient users share one vehicle. This result is robust in a data-driven model using taxi trip data from Manhattan (New York City, USA) with fluctuating demand over the day. At constant fleet size the travel time fluctuates with the demand and might deviate a lot from the expected average travel time. Such unreliable travel times might deter users from ride sharing. However, stop pooling reduces the travel time, the more the higher the travel time without walking. Consequently, stop pooling also reduces the fluctuations in the travel time. This effect is particularly large when adapting the maximum allowed walk distance to the current demand. In adaptive stop pooling users walk further at higher demand. Then, the travel time in ride sharing is more reliable when users accept short walks. All in all, this thesis contributes to the fundamental understanding of the collective dynamics of ride sharing and the effect of stop pooling at a systemic level while also explaining underlying mechanisms. The results suggest that ride sharing providers and users benefit from integrating adaptive stop pooling into the service. Based on the results, a framework can be established that roughly adjusts fleet size to demand to ensure that the ride sharing service operates sustainably. Even if this fleet size remains constant throughout the day, adaptive stop pooling keeps the travel time reliable.:1. Introduction 1 1.1. Private Cars are Unsustainable . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2. Potentially More Sustainable Ride Sharing Faces Detours . . . . . . . . . . . . . 2 1.3. Less Detours in Ride Sharing with Walking to Pooled Stops . . . . . . . . . . . . 4 1.4. Physics Methods Help Understanding Ride Sharing . . . . . . . . . . . . . . . . . 5 1.5. Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2. Fundamentals - A Physics Perspective on Ride Sharing 7 2.1. State of Research on Ride Sharing . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1. Ride Sharing Systems are Complex . . . . . . . . . . . . . . . . . . . . . . 8 2.1.2. Measuring Efficiency and Sustainability of Ride Sharing Services . . . . . 8 2.1.3. Ride Sharing might be More Sustainable when Users Accept Short Walks 10 2.1.4. Data-Driven Analysis Yields more Detailed Results . . . . . . . . . . . . . 11 2.1.5. Open Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2. Theoretical Physics Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.1. What is a Complex System? . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.2. Mean-Field Theory Simplifies Complex Systems . . . . . . . . . . . . . . 13 2.2.3. Model Complex Systems Based on Agents, not on Equations . . . . . . . 14 2.2.4. Methods from Statistical Physics to Evaluate Multi-Agent Simulations . . 14 2.2.5. Model Street Networks Using Graph Theory . . . . . . . . . . . . . . . . 20 3. Model for Ride Sharing with Walking to Pooled Stops 25 3.1. Ride Sharing Combines Trips with Similar Directions . . . . . . . . . . . . . . . . 25 3.2. Stop Pooling with Dynamic Stop Locations Maintains Flexibility . . . . . . . . . 26 3.3. Simple Algorithm Assigns Users by Reducing Bus Detour . . . . . . . . . . . . . 28 3.3.1. Standard Ride Sharing Algorithm . . . . . . . . . . . . . . . . . . . . . . 28 3.3.2. Stop Pooling Algorithm at Similar Speed . . . . . . . . . . . . . . . . . . 29 3.4. Basic Setting in Continuous Space . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.4.1. Uniform Request Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.4.2. Heterogeneous Request Distribution . . . . . . . . . . . . . . . . . . . . . 32 3.5. Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.5.1. Relative Distance Driven Measures Ecological Sustainability . . . . . . . . 33 3.5.2. Measure Service Quality by Average User Travel Time . . . . . . . . . . . 34 3.5.3. Further Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.5.4. Bisection Method to Find Minimal Travel Time with Small Effort . . . . 36 3.6. Model Extensions Yield More Detailed Results . . . . . . . . . . . . . . . . . . . 37 3.6.1. Fine-Grained Street Network Enables Short Walk Distances . . . . . . . . 38 iii Contents 3.6.2. Data-Driven Demand is Heterogeneous . . . . . . . . . . . . . . . . . . . . 39 3.6.3. Explicit Stop Times Ensure Penalty For Each Stop . . . . . . . . . . . . . 41 3.6.4. Imbalanced Demand Requires Rebalancing of Buses . . . . . . . . . . . . 42 3.6.5. More Detailed Assignment Algorithm Uses Constraints . . . . . . . . . . 43 4. Quantifying Sustainability of Ride Sharing 45 4.1. Two Mechanisms Influence Ride Sharing Sustainability . . . . . . . . . . . . . . . 46 4.1.1. Pickup Detours Increase Distance Driven . . . . . . . . . . . . . . . . . . 46 4.1.2. Trip Overlap Reduces Distance Driven . . . . . . . . . . . . . . . . . . . . 47 4.2. Distance Driven Reduces with Bus Occupancy . . . . . . . . . . . . . . . . . . . 48 4.3. Ride Sharing is more Sustainable than Private Cars for Sufficient Load . . . . . . 50 4.4. Result is Robust for more Complex Models . . . . . . . . . . . . . . . . . . . . . 52 4.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5. Ride Sharing Sustainability with Stop Pooling 55 5.1. Ride Sharing Trades Sustainability for Travel Time . . . . . . . . . . . . . . . . . 57 5.2. Stop Pooling is more Sustainable at Same Travel Time . . . . . . . . . . . . . . . 58 5.2.1. Roughly Constant Distance Driven Despite Saved Stops . . . . . . . . . . 58 5.2.2. Stop Pooling Reduces Travel Time . . . . . . . . . . . . . . . . . . . . . . 59 5.2.3. Stop Pooling Breaks The Trade-off Between Sustainability And Travel Time 60 5.3. Higher Stop Pooling Effect for High Loads . . . . . . . . . . . . . . . . . . . . . . 61 5.3.1. Stop Pooling Limits Growth of Best Travel Time . . . . . . . . . . . . . . 62 5.3.2. Stop Pooling Breaks Trade-off for Sufficient Load . . . . . . . . . . . . . . 63 5.4. Robust Effect for Simple Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.5. Robust Effect with More Detailed Model . . . . . . . . . . . . . . . . . . . . . . . 66 5.5.1. Load Quantifies Stop Pooling Sustainability . . . . . . . . . . . . . . . . . 67 5.5.2. Already 1.2 Minutes Walk Time might Save 1 Minute Travel Time . . . . 68 5.5.3. Robust Result for Different Parameters . . . . . . . . . . . . . . . . . . . 69 5.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6. Ride Sharing Reliability with Stop Pooling 71 6.1. Unreliable Standard Ride Sharing with Fluctuating Demand . . . . . . . . . . . . 72 6.2. More Reliable Stop Pooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6.3. Robust Effect of Stop Pooling with Limited User Delay . . . . . . . . . . . . . . 77 6.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.5. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 7. Discussion 81 7.1. Results and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.1.1. When is Ride Sharing More Sustainable than Private Cars? . . . . . . . . 81 7.1.2. How Does Stop Pooling Influence Sustainability of Ride Sharing? . . . . . 82 7.1.3. How Does Stop Pooling Influence Reliability of Ride Sharing? . . . . . . . 82 7.2. Limitations of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 7.2.1. Simple Algorithms for Ride Sharing and Stop Pooling . . . . . . . . . . . 82 7.2.2. Integrate Adaptive Stop Pooling into Virtual Bus Stops . . . . . . . . . . 83 7.2.3. Distance Driven as Estimator for Ecological Sustainability . . . . . . . . . 83 7.2.4. Deviations from Load Prediction . . . . . . . . . . . . . . . . . . . . . . . 84 7.2.5. Mean-Field Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7.2.6. Further Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 A. Appendix 87 A.1. Manhattan Street Network Resembles Grid . . . . . . . . . . . . . . . . . . . . . 87 A.2. Computation Details of Bisection Method . . . . . . . . . . . . . . . . . . . . . . 88 A.3. Average Pickup Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 A.4. Robustness of Ride Sharing Sustainability . . . . . . . . . . . . . . . . . . . . . . 90 A.5. Stop Pooling Saves Stops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 A.6. Stop Pooling Effectively Reduces Load . . . . . . . . . . . . . . . . . . . . . . . . 92 A.7. Example Breaking of Trade-off in Simple Model . . . . . . . . . . . . . . . . . . . 93 A.8. Transition in Best Walk Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 A.9. Maximal Trade-off Shift Increases with Load . . . . . . . . . . . . . . . . . . . . 95 A.10.Rebalancing Buses is more Important with Constraint . . . . . . . . . . . . . . . 97 A.11.Breaking of Trade-off in Complex Model . . . . . . . . . . . . . . . . . . . . . . . 98 A.12.More Stop Pooling at Destinations and High Demand . . . . . . . . . . . . . . . 99 A.13.Roughly Constant Wait and Drive Time in Adaptive Stop Pooling . . . . . . . . 100 A.14.Influence of Capacity Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 A.15.Walk Time of Rejected Users . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Bibliography 101 Acknowledgment 116 Statement of Contributions 11