Where does the physics of extreme gravitational collapse reside?

The gravitational collapse of massive stars serves to manifest the most severe deviations of general relativity with respect to Newtonian gravity: the formation of horizons and spacetime singularities. Both features have proven to be catalysts of deep physical developments, especially when combined with the principles of quantum mechanics. Nonetheless, it is seldom remarked that it is hardly possible to combine all these developments into a unified theoretical model, while maintaining reasonable prospects for the independent experimental corroboration of its different parts. In this paper we review the current theoretical understanding of the physics of gravitational collapse in order to highlight this tension, stating the position that the standard view on evaporating black holes stands for. This serves as the motivation for the discussion of a recent proposal that offers the opposite perspective, represented by a set of geometries that regularize the classical singular behavior and present modifications of the near-horizon Schwarzschild geometry as the result of the propagation of non-perturbative ultraviolet effects originated in regions of high curvature. We present an extensive exploration of the necessary steps on the explicit construction of these geometries, and discuss how this proposal could change our present understanding of astrophysical black holes and even offer the possibility of detecting genuine ultraviolet effects on future gravitational wave experiments.Comment: 43 pages, 1 figure. Review article with new results on the black to white hole transition. Prepared for the special issue "Open Questions in Black Hole Physics" edited by Gonzalo J. Olm

Spacetime Singularities

We present here an overview of our basic understanding and recent developments on spacetime singularities in the Einstein theory of gravity. Several issues related to physical significance and implications of singularities are discussed. The nature and existence of singularities are considered which indicate the formation of super ultra-dense regions in the universe as predicted by the general theory of relativity. Such singularities develop during the gravitational collapse of massive stars and in cosmology at the origin of the universe. Possible astrophysical implications of the occurrence of singularities in the spacetime universe are indicated. We discuss in some detail the profound and key fundamental issues that the singularities give rise to, such as the cosmic censorship and predictability in the universe, naked singularities in gravitational collapse and their relevance in black hole physics today, and their astrophysical implications in modern relativistic astrophysics and cosmology.Comment: 45 pages, LaTex; Invited Review article for the `Springer Handbook of Spacetime' (eds A. Ashtekar and V. Petkov

Dense 3D Object Reconstruction from a Single Depth View

In this paper, we propose a novel approach, 3D-RecGAN++, which reconstructs the complete 3D structure of a given object from a single arbitrary depth view using generative adversarial networks. Unlike existing work which typically requires multiple views of the same object or class labels to recover the full 3D geometry, the proposed 3D-RecGAN++ only takes the voxel grid representation of a depth view of the object as input, and is able to generate the complete 3D occupancy grid with a high resolution of 256^3 by recovering the occluded/missing regions. The key idea is to combine the generative capabilities of autoencoders and the conditional Generative Adversarial Networks (GAN) framework, to infer accurate and fine-grained 3D structures of objects in high-dimensional voxel space. Extensive experiments on large synthetic datasets and real-world Kinect datasets show that the proposed 3D-RecGAN++ significantly outperforms the state of the art in single view 3D object reconstruction, and is able to reconstruct unseen types of objects.Comment: TPAMI 2018. Code and data are available at: https://github.com/Yang7879/3D-RecGAN-extended. This article extends from arXiv:1708.0796

Computing the Partial Word Avoidability Indices of Ternary Patterns

We study pattern avoidance in the context of partial words. The problem of classifying the avoidable binary patterns has been solved, so we move on to ternary and more general patterns. Our results, which are based on morphisms (iterated or not), determine all the ternary patterns' avoidability indices or at least give bounds for them

Active Image-based Modeling with a Toy Drone

Image-based modeling techniques can now generate photo-realistic 3D models from images. But it is up to users to provide high quality images with good coverage and view overlap, which makes the data capturing process tedious and time consuming. We seek to automate data capturing for image-based modeling. The core of our system is an iterative linear method to solve the multi-view stereo (MVS) problem quickly and plan the Next-Best-View (NBV) effectively. Our fast MVS algorithm enables online model reconstruction and quality assessment to determine the NBVs on the fly. We test our system with a toy unmanned aerial vehicle (UAV) in simulated, indoor and outdoor experiments. Results show that our system improves the efficiency of data acquisition and ensures the completeness of the final model.Comment: To be published on International Conference on Robotics and Automation 2018, Brisbane, Australia. Project Page: https://huangrui815.github.io/active-image-based-modeling/ The author's personal page: http://www.sfu.ca/~rha55

Redundant Array Configurations for 21 cm Cosmology

Realizing the potential of 21 cm tomography to statistically probe the intergalactic medium before and during the Epoch of Reionization requires large telescopes and precise control of systematics. Next-generation telescopes are now being designed and built to meet these challenges, drawing lessons from first-generation experiments that showed the benefits of densely packed, highly redundant arrays--in which the same mode on the sky is sampled by many antenna pairs--for achieving high sensitivity, precise calibration, and robust foreground mitigation. In this work, we focus on the Hydrogen Epoch of Reionization Array (HERA) as an interferometer with a dense, redundant core designed following these lessons to be optimized for 21 cm cosmology. We show how modestly supplementing or modifying a compact design like HERA's can still deliver high sensitivity while enhancing strategies for calibration and foreground mitigation. In particular, we compare the imaging capability of several array configurations, both instantaneously (to address instrumental and ionospheric effects) and with rotation synthesis (for foreground removal). We also examine the effects that configuration has on calibratability using instantaneous redundancy. We find that improved imaging with sub-aperture sampling via "off-grid" antennas and increased angular resolution via far-flung "outrigger" antennas is possible with a redundantly calibratable array configuration.Comment: 19 pages, 11 figures. Revised to match the accepted ApJ versio

Underwater Exploration and Mapping

This paper analyzes the open challenges of exploring and mapping in the underwater realm with the goal of identifying research opportunities that will enable an Autonomous Underwater Vehicle (AUV) to robustly explore different environments. A taxonomy of environments based on their 3D structure is presented together with an analysis on how that influences the camera placement. The difference between exploration and coverage is presented and how they dictate different motion strategies. Loop closure, while critical for the accuracy of the resulting map, proves to be particularly challenging due to the limited field of view and the sensitivity to viewing direction. Experimental results of enforcing loop closures in underwater caves demonstrate a novel navigation strategy. Dense 3D mapping, both online and offline, as well as other sensor configurations are discussed following the presented taxonomy. Experimental results from field trials illustrate the above analysis.acceptedVersio

Statistical Mechanics of thermalized ribbons and sheets

In this dissertation, we study the thermal behavior of two-dimensional sheets and ribbons. We study the effects of thermal fluctuations on the crumpling transition of elastic sheets. Existing two-dimensional sheets have a crumpling temperature which is very high and the crumpling transition has not been observed experimentally. We propose a mechanism using which one can tune this crumpling transition by changing the shape and geometry of \u3ethe sheet. We perform extensive molecular dynamics simulations by perforating the sheet with a dense array of holes and find that the critical temperature is a function of the removed area. Lastly, we look at clamped thermalized ribbons and study thermalized Euler buckling. Again, we perform molecular dynamics simulations by clamping one end and allowing the other end to slide to get the projected thermal length of the ribbon. We compress this system and observe a distinct two-state dynamics of the center of mass along with thermalized Euler buckling