Ricci Curvature of the Internet Topology

Analysis of Internet topologies has shown that the Internet topology has negative curvature, measured by Gromov's "thin triangle condition", which is tightly related to core congestion and route reliability. In this work we analyze the discrete Ricci curvature of the Internet, defined by Ollivier, Lin, etc. Ricci curvature measures whether local distances diverge or converge. It is a more local measure which allows us to understand the distribution of curvatures in the network. We show by various Internet data sets that the distribution of Ricci cuvature is spread out, suggesting the network topology to be non-homogenous. We also show that the Ricci curvature has interesting connections to both local measures such as node degree and clustering coefficient, global measures such as betweenness centrality and network connectivity, as well as auxilary attributes such as geographical distances. These observations add to the richness of geometric structures in complex network theory.Comment: 9 pages, 16 figures. To be appear on INFOCOM 201

Greedy routing with guaranteed delivery using Ricci flows

Greedy forwarding with geographical locations in a wireless sensor network may fail at a local minimum. In this paper we propose to use conformal mapping to compute a new embedding of the sensor nodes in the plane such that greedy forwarding with the virtual coordinates guarantees delivery. In particular, we extract a planar triangulation of the sensor network with non-triangular faces as holes, by either using the nodes ’ location or using a landmark-based scheme without node location. The conformal map is computed with Ricci flow such that all the non-triangular faces are mapped to perfect circles. Thus greedy forwarding will never get stuck at an intermediate node. The computation of the conformal map and the virtual coordinates is performed at a preprocessing phase and can be implemented by local gossip-style computation. The method applies to both unit disk graph models and quasi-unit disk graph models. Simulation results are presented for these scenarios

Hydrological evaluation of open-access precipitation and air temperature datasets using SWAT in a poorly gauged basin in Ethiopia

Precipitation and air temperature are key drivers of watershed models. Currently there are many open-access gridded precipitation and air temperature datasets at different spatial and temporal resolutions over global or quasi-global scale. Motivated by the scarcity and substantial temporal and spatial gaps in ground measurements in Africa, this study evaluated the performance of three open-access precipitation datasets (i.e. CHIRPS (Climate Hazards Group InfraRed Precipitation with Station data), TRMM (Tropical Rainfall Measuring Mission) and CFSR (Climate Forecast System Reanalysis)) and one air temperature dataset (CFSR) in driving Soil and Water Assessment Tool (SWAT) model in simulation of daily and monthly streamflow in the upper Gilgel Abay Basin, Ethiopia. The “best” available measurements of precipitation and air temperature from sparse gauge stations were also used to drive SWAT model and the results were compared with those using open-access datasets. After a comprehensive comparison of a total of eight model scenarios with different combinations of precipitation and air temperature inputs, we draw the following conclusions: (1) using measured precipitation from even sparse available stations consistently yielded better performance in streamflow simulation than using all three open-access precipitation datasets; (2) using CFSR air temperature yielded almost identical performance in streamflow simulation to using measured air temperature from gauge stations; (3) among the three open-access precipitation, overall CHIRPS yielded best performance. These results suggested that the CHIRPS precipitation available at high spatial resolution (0.05°) together with CFSR air temperature can be a promising alternative open-access data source for streamflow simulation in this data-scarce area in the case of limited access to desirable gauge data

Resilient Routing for Sensor Networks Using Hyperbolic Embedding of Universal Covering Space

Abstract—We study how to characterize the families of paths between any two nodes s, t in a sensor network with holes. Two paths that can be deformed to one another through local changes are called homotopy equivalent. Two paths that pass around holes in different ways have different homotopy types. With a distributed algorithm we compute an embedding of the network in hyperbolic space by using Ricci flow such that paths of different homotopy types are mapped naturally to paths connecting s with different images of t. Greedy routing to a particular image is guaranteed with success to find a path with a given homotopy type. This leads to simple greedy routing algorithms that are resilient to both local link dynamics and large scale jamming attacks and improve load balancing over previous greedy routing algorithms. I