Analytic families of quantum hyperbolic invariants

We organize the quantum hyperbolic invariants (QHI) of $3$-manifolds into sequences of rational functions indexed by the odd integers $N\geq 3$ and defined on moduli spaces of geometric structures refining the character varieties. In the case of one-cusped hyperbolic $3$-manifolds $M$ we generalize the QHI and get rational functions $\mathcal{H}_N^{h_f,h_c,k_c}$ depending on a finite set of cohomological data $(h_f,h_c,k_c)$ called {\it weights}. These functions are regular on a determined Abelian covering of degree $N^2$ of a Zariski open subset, canonically associated to $M$, of the geometric component of the variety of augmented $PSL(2,\mathbb{C})$-characters of $M$. New combinatorial ingredients are a weak version of branchings which exists on every triangulation, and state sums over weakly branched triangulations, including a sign correction which eventually fixes the sign ambiguity of the QHI. We describe in detail the invariants of three cusped manifolds, and present the results of numerical computations showing that the functions $\mathcal{H}_N^{h_f,h_c,k_c}$ depend on the weights as $N\rightarrow + \infty$, and recover the volume for some specific choices of the weights.Comment: 54 pages, 21 figures. New section with 3 examples; the results about the reduced invariants are postponed to a separate paper. To appear on Alg. Geom. Topo

Seeing the invisible: from imagined to virtual urban landscapes

Urban ecosystems consist of infrastructure features working together to provide services for inhabitants. Infrastructure functions akin to an ecosystem, having dynamic relationships and interdependencies. However, with age, urban infrastructure can deteriorate and stop functioning. Additional pressures on infrastructure include urbanizing populations and a changing climate that exposes vulnerabilities. To manage the urban infrastructure ecosystem in a modernizing world, urban planners need to integrate a coordinated management plan for these co-located and dependent infrastructure features. To implement such a management practice, an improved method for communicating how these infrastructure features interact is needed. This study aims to define urban infrastructure as a system, identify the systematic barriers preventing implementation of a more coordinated management model, and develop a virtual reality tool to provide visualization of the spatial system dynamics of urban infrastructure. Data was collected from a stakeholder workshop that highlighted a lack of appreciation for the system dynamics of urban infrastructure. An urban ecology VR model was created to highlight the interconnectedness of infrastructure features. VR proved to be useful for communicating spatial information to urban stakeholders about the complexities of infrastructure ecology and the interactions between infrastructure features.https://doi.org/10.1016/j.cities.2019.102559Published versio

Locating and quantifying gas emission sources using remotely obtained concentration data

We describe a method for detecting, locating and quantifying sources of gas emissions to the atmosphere using remotely obtained gas concentration data; the method is applicable to gases of environmental concern. We demonstrate its performance using methane data collected from aircraft. Atmospheric point concentration measurements are modelled as the sum of a spatially and temporally smooth atmospheric background concentration, augmented by concentrations due to local sources. We model source emission rates with a Gaussian mixture model and use a Markov random field to represent the atmospheric background concentration component of the measurements. A Gaussian plume atmospheric eddy dispersion model represents gas dispersion between sources and measurement locations. Initial point estimates of background concentrations and source emission rates are obtained using mixed L2-L1 optimisation over a discretised grid of potential source locations. Subsequent reversible jump Markov chain Monte Carlo inference provides estimated values and uncertainties for the number, emission rates and locations of sources unconstrained by a grid. Source area, atmospheric background concentrations and other model parameters are also estimated. We investigate the performance of the approach first using a synthetic problem, then apply the method to real data collected from an aircraft flying over: a 1600 km^2 area containing two landfills, then a 225 km^2 area containing a gas flare stack

Satellite Navigation for the Age of Autonomy

Global Navigation Satellite Systems (GNSS) brought navigation to the masses. Coupled with smartphones, the blue dot in the palm of our hands has forever changed the way we interact with the world. Looking forward, cyber-physical systems such as self-driving cars and aerial mobility are pushing the limits of what localization technologies including GNSS can provide. This autonomous revolution requires a solution that supports safety-critical operation, centimeter positioning, and cyber-security for millions of users. To meet these demands, we propose a navigation service from Low Earth Orbiting (LEO) satellites which deliver precision in-part through faster motion, higher power signals for added robustness to interference, constellation autonomous integrity monitoring for integrity, and encryption / authentication for resistance to spoofing attacks. This paradigm is enabled by the 'New Space' movement, where highly capable satellites and components are now built on assembly lines and launch costs have decreased by more than tenfold. Such a ubiquitous positioning service enables a consistent and secure standard where trustworthy information can be validated and shared, extending the electronic horizon from sensor line of sight to an entire city. This enables the situational awareness needed for true safe operation to support autonomy at scale.Comment: 11 pages, 8 figures, 2020 IEEE/ION Position, Location and Navigation Symposium (PLANS

Interpreting the yield of transit surveys: Are there groups in the known transiting planets population?

Each transiting planet discovered is characterized by 7 measurable quantities, that may or may not be linked together (planet mass, radius, orbital period, and star mass, radius, effective temperature, and metallicity). Correlations between planet mass and period, surface gravity and period, planet radius and star temperature have been previously observed among the known transiting giant planets. Two classes of planets have been previously identified based on their Safronov number. We use the CoRoTlux code to compare simulated events to the sample of discovered planets and test the statistical significance of these correlations. We first generate a stellar field with planetary companions based on radial velocity discoveries and a planetary evolution model, then apply a detection criterion that includes both statistical and red noise sources. We compare the yield of our simulated survey with the ensemble of 31 well-characterized giant transiting planets, using a multivariate logistic analysis to assess whether the simulated distribution matches the known transiting planets. Our multivariate analysis shows that our simulated sample and observations are consistent to 76%. The mass vs. period correlation for giant planets first observed with radial velocity holds with transiting planets. Our model naturally explains the correlation between planet surface gravity and period and the one between planet radius and stellar effective temperature. Finally, we are also able to reproduce the previously observed apparent bimodal distribution of Safronov numbers in 10% of our simulated cases, although our model predicts a continuous distribution. This shows that the evidence for the existence of two groups of planets with different intrinsic properties is not statistically significant.Comment: 17 page

Occlusion Handling using Semantic Segmentation and Visibility-Based Rendering for Mixed Reality

Real-time occlusion handling is a major problem in outdoor mixed reality system because it requires great computational cost mainly due to the complexity of the scene. Using only segmentation, it is difficult to accurately render a virtual object occluded by complex objects such as trees, bushes etc. In this paper, we propose a novel occlusion handling method for real-time, outdoor, and omni-directional mixed reality system using only the information from a monocular image sequence. We first present a semantic segmentation scheme for predicting the amount of visibility for different type of objects in the scene. We also simultaneously calculate a foreground probability map using depth estimation derived from optical flow. Finally, we combine the segmentation result and the probability map to render the computer generated object and the real scene using a visibility-based rendering method. Our results show great improvement in handling occlusions compared to existing blending based methods

Route Planning in Transportation Networks

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle