An Analysis of Planarity in Face-Routing

In this report we investigate the limits of routing according to left- or right-hand rule (LHR). Using LHR, a node upon receipt of a message will forward to the neighbour that sits next in counter-clockwise order in the network graph. When used to recover from greedy routing failures, LHR guarantees success if implemented over planar graphs. This is often referred to as face or geographic routing. In the current body of knowledge it is known that if planarity is violated then LHR is guaranteed only to eventually return to the point of origin. Our work seeks to understand why a non-planar environment stops LHR from making delivery guarantees. Our investigation begins with an analysis to enumerate all node con gurations that cause intersections. A trace over each con guration reveals that LHR is able to recover from all but a single case, the `umbrella' con guration so named for its appearance. We use this information to propose the Prohibitive Link Detection Protocol (PDLP) that can guarantee delivery over non-planar graphs using standard face-routing techniques. As the name implies, the protocol detects and circumvents the `bad' links that hamper LHR. The goal of this work is to maintain routing guarantees while disturbing the network graph as little as possible. In doing so, a new starting point emerges from which to build rich distributed protocols in the spirit of protocols such as CLDP and GDSTR

Degenerate Stars and Gravitational Collapse in AdS/CFT

We construct composite CFT operators from a large number of fermionic primary fields corresponding to states that are holographically dual to a zero temperature Fermi gas in AdS space. We identify a large N regime in which the fermions behave as free particles. In the hydrodynamic limit the Fermi gas forms a degenerate star with a radius determined by the Fermi level, and a mass and angular momentum that exactly matches the boundary calculations. Next we consider an interacting regime, and calculate the effect of the gravitational back-reaction on the radius and the mass of the star using the Tolman-Oppenheimer-Volkoff equations. Ignoring other interactions, we determine the "Chandrasekhar limit" beyond which the degenerate star (presumably) undergoes gravitational collapse towards a black hole. This is interpreted on the boundary as a high density phase transition from a cold baryonic phase to a hot deconfined phase.Comment: 75 page

Unsupervised Monocular Depth Reconstruction of Non-Rigid Scenes

Monocular depth reconstruction of complex and dynamic scenes is a highly challenging problem. While for rigid scenes learning-based methods have been offering promising results even in unsupervised cases, there exists little to no literature addressing the same for dynamic and deformable scenes. In this work, we present an unsupervised monocular framework for dense depth estimation of dynamic scenes, which jointly reconstructs rigid and non-rigid parts without explicitly modelling the camera motion. Using dense correspondences, we derive a training objective that aims to opportunistically preserve pairwise distances between reconstructed 3D points. In this process, the dense depth map is learned implicitly using the as-rigid-as-possible hypothesis. Our method provides promising results, demonstrating its capability of reconstructing 3D from challenging videos of non-rigid scenes. Furthermore, the proposed method also provides unsupervised motion segmentation results as an auxiliary output