Multifractal Analysis of Multiple Ergodic Averages

In this paper we present a complete solution to the problem of multifractal analysis of multiple ergodic averages in the case of symbolic dynamics for functions of two variables depending on the first coordinate.Comment: 5 pages, to appear in Comptes Rendus Mathematiqu

Interbasin Water Transfers and Water Scarcity in a Changing World: A Solution or a Pipedream?

The world is increasingly forced to face the challenge of how to ensure access to adequate water resources for expanding populations and economies, whilst maintaining healthy freshwater ecosystems and the vital services they provide. Now the growing impacts of climate change are exacerbating the problem of water scarcity in key regions of the world. One popular way for governments to distribute water more evenly across the landscape is to transfer it from areas with perceived surpluses, to those with shortages.While there is a long history of water transfers from ancient times, as many societies reach the limits of locally renewable water supplies increasingly large quantities of water are being moved over long distances, from one river basin to another. Since the beginning of dam building that marked the last half of the 1900s more that 364 large-scale interbasin water transfer schemes (IBTs) have been established that transfer around 400 km³ of water per year (Shiklomanov 1999). IBTs are now widely touted as the quick fix solution to meeting escalating water demands. One estimate suggests that the total number of largescale water transfer schemes may rise to between 760 and 1 240 by 2020 to transfer up to 800 km³ of water per year (Shiklomanov 1999).The wide range of IBT projects in place, or proposed, has provoked the preparation of this review, including seven case studies from around the globe. It builds on previous assessments and examines the costs and benefits of large scale IBTs. This report assesses related, emerging issues in sustaining water resources and ecosystems, namely the virtual water trade, expanding use of desalination, and climate change adaptation. It is based on WWF's 2007 publication "Pipedreams? Interbasin water transfers and water shortages".The report concludes that while IBTs can potentially solve water supply issues in regions of water shortage - they come with significant costs. Large scale IBTs are typically very high cost, and thus economically risky, and they usually also come with significant social and environmental costs; usually for both the river basin providing and the river basin receiving the water

Optical Flow At Occlusion Boundaries And In Occlusion Regions

Optical flow is an important research area in the Computer Vision field, with the estimation of optical flow at occlusion still an open problem. Traditional approaches to this problem have either used additional terms in a regularization calculation (the flow still tends to “bleed” across occlusion boundaries) or a local least squares calculation that attempted to minimize the influence of two adjacent differently moving regions on the optical flow at points close to both regions (the flow still tends to be “corrupted” by the two regions). Ideally, optical flow for two adjacent differently moving regions should be distinct right up to the occlusion boundary. A recent approach to calculate optical flow at occlusion is to combining boundary and region segmentation with the optical flow computation. Based on the work of Sundberg et al. Arbelaez et al. and Brox et al., we implement a motion gradient (mg) edge map algorithm which detects motion information in closed regions in the image sequences. Here we utilize the motion gradient as an additional local cue in the globalized probability of a boundary (gPb) as a new boundary detector to produce a gPb + mg contour map. The next step is to apply the Ultrametric Contour Map (UCM) mechanism, which is a framework to compute closed contours in a hierarchical region tree to produce a hierarchical edge map which indicates possible boundaries, including occlusion boundaries. We implemented Sundberg et al.’s work to detect occlusion boundaries using optical flow, but, unlike Sundberg et al., we compute and display optical flow everywhere. The Sundberg et al. optical flow was generated by Brox et al’s method. They used a least squares calcula- tion on the brox flow at pixels around an occlusion boundary to determine whether a boundary computed by the gPb − UCM library developed by UC Berkeley is occluding or occluded. We extended their least squares idea to 1st and 2nd order optical flow models to generate dense opti- cal flow inside each closed region. Finally, we analyze our optical flow fields both qualitatively and quantitatively. In particular, for quantitative analysis, we use warping error, as the correct flow is unknown. We show improved results over those of Sundberg et al., note a number of shortcomings in Sundberg et al.’s approach and point to areas of future research

A Neural Network Based Strategy for Robot Navigation in Dynamic Environments

This thesis studies the problem of robot navigation in the presence of unexpected environmental changes, which include unknown static obstacles and moving objects with unknown trajectories. Throughout this work, neural networks, as a new technique, are used to develop the functional components, which constitute the proposed navigation strategy. The neural network based navigation strategy we propose follows a two-level hierarchy and operates by integrating three network components (planner, navigator and predictor). At the higher level, the planner generates a nominal path from the initial position to the goal among the fixed known obstacles. At the lower level, the navigator incorporates the predictor to refine the coarse path by taking into account unexpected environment changes to achieve on line real-time guidance. During this research, three neural network components were developed. The path planner was developed first by using a three-layer feedforward network to optimize the cost (collision penalty) function of a path. The first version of the navigator - Navigator-1 - was then implemented using a multilayer feedforward network in which steering commands for static obstacle avoidance were generated by directly converting sensor reading through the network. To enable the navigator to handle moving objects with unknown trajectories, on-line motion prediction was introduced. The predictor was developed using an Elman recurrent net. Following that, an enhanced version of the Navigator-1 - Navigator-2 - was developed using a structured network in which three sub-nets were used - two of the sub-nets were used to realise dynamic obstacle avoidance and static obstacle avoidance respectively, and the third sub-net was used to make final steering decision by reconciling the results from those two sub-nets. Finally, the overall navigation strategy was implemented in a simulation system. Simulations showed encouraging results. It demonstrates that the neural network based strategy is capable of achieving adaptive navigation in the presence of unexpected environmental changes