Gravity-Inspired Graph Autoencoders for Directed Link Prediction

Graph autoencoders (AE) and variational autoencoders (VAE) recently emerged as powerful node embedding methods. In particular, graph AE and VAE were successfully leveraged to tackle the challenging link prediction problem, aiming at figuring out whether some pairs of nodes from a graph are connected by unobserved edges. However, these models focus on undirected graphs and therefore ignore the potential direction of the link, which is limiting for numerous real-life applications. In this paper, we extend the graph AE and VAE frameworks to address link prediction in directed graphs. We present a new gravity-inspired decoder scheme that can effectively reconstruct directed graphs from a node embedding. We empirically evaluate our method on three different directed link prediction tasks, for which standard graph AE and VAE perform poorly. We achieve competitive results on three real-world graphs, outperforming several popular baselines.Comment: ACM International Conference on Information and Knowledge Management (CIKM 2019

The century of the incomplete revolution: searching for general relativistic quantum field theory

In fundamental physics, this has been the century of quantum mechanics and general relativity. It has also been the century of the long search for a conceptual framework capable of embracing the astonishing features of the world that have been revealed by these two ``first pieces of a conceptual revolution''. I discuss the general requirements on the mathematics and some specific developments towards the construction of such a framework. Examples of covariant constructions of (simple) generally relativistic quantum field theories have been obtained as topological quantum field theories, in nonperturbative zero-dimensional string theory and its higher dimensional generalizations, and as spin foam models. A canonical construction of a general relativistic quantum field theory is provided by loop quantum gravity. Remarkably, all these diverse approaches have turn out to be related, suggesting an intriguing general picture of general relativistic quantum physics.Comment: To appear in the Journal of Mathematical Physics 2000 Special Issu

A proposal for analyzing the classical limit of kinematic loop gravity

We analyze the classical limit of kinematic loop quantum gravity in which the diffeomorphism and hamiltonian constraints are ignored. We show that there are no quantum states in which the primary variables of the loop approach, namely the SU(2) holonomies along {\em all} possible loops, approximate their classical counterparts. At most a countable number of loops must be specified. To preserve spatial covariance, we choose this set of loops to be based on physical lattices specified by the quasi-classical states themselves. We construct ``macroscopic'' operators based on such lattices and propose that these operators be used to analyze the classical limit. Thus, our aim is to approximate classical data using states in which appropriate macroscopic operators have low quantum fluctuations. Although, in principle, the holonomies of `large' loops on these lattices could be used to analyze the classical limit, we argue that it may be simpler to base the analysis on an alternate set of ``flux'' based operators. We explicitly construct candidate quasi-classical states in 2 spatial dimensions and indicate how these constructions may generalize to 3d. We discuss the less robust aspects of our proposal with a view towards possible modifications. Finally, we show that our proposal also applies to the diffeomorphism invariant Rovelli model which couples a matter reference system to the Hussain Kucha{\v r} model.Comment: Replaced with substantially revised versio

The ACIGA Data Analysis programme

The Data Analysis programme of the Australian Consortium for Interferometric Gravitational Astronomy (ACIGA) was set up in 1998 by the first author to complement the then existing ACIGA programmes working on suspension systems, lasers and optics, and detector configurations. The ACIGA Data Analysis programme continues to contribute significantly in the field; we present an overview of our activities.Comment: 10 pages, 0 figures, accepted, Classical and Quantum Gravity, (Proceedings of the 5th Edoardo Amaldi Conference on Gravitational Waves, Tirrenia, Pisa, Italy, 6-11 July 2003

Loop Quantum Gravity

The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a mathematically well-defined, non-perturbative and background independent quantization of general relativity, with its conventional matter couplings. The research in loop quantum gravity forms today a vast area, ranging from mathematical foundations to physical applications. Among the most significative results obtained are: (i) The computation of the physical spectra of geometrical quantities such as area and volume; which yields quantitative predictions on Planck-scale physics. (ii) A derivation of the Bekenstein-Hawking black hole entropy formula. (iii) An intriguing physical picture of the microstructure of quantum physical space, characterized by a polymer-like Planck scale discreteness. This discreteness emerges naturally from the quantum theory and provides a mathematically well-defined realization of Wheeler's intuition of a spacetime ``foam''. Long standing open problems within the approach (lack of a scalar product, overcompleteness of the loop basis, implementation of reality conditions) have been fully solved. The weak part of the approach is the treatment of the dynamics: at present there exist several proposals, which are intensely debated. Here, I provide a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.Comment: Review paper written for the electronic journal `Living Reviews'. 34 page

Gels under stress: the origins of delayed collapse

Attractive colloidal particles can form a disordered elastic solid or gel when quenched into a two-phase region, if the volume fraction is sufficiently large. When the interactions are comparable to thermal energies the stress-bearing network within the gel restructures over time as individual particle bonds break and reform. Typically, under gravity such weak gels show a prolonged period of either no or very slow settling, followed by a sudden and rapid collapse - a phenomenon known as delayed collapse. The link between local bond breaking events and the macroscopic process of delayed collapse is not well understood. Here we summarize the main features of delayed collapse and discuss the microscopic processes which cause it. We present a plausible model which connects the kinetics of bond breaking to gel collapse and test the model by exploring the effect of an applied external force on the stability of a gel.Comment: Accepted version: 10 pages, 7 figure

Clusters and the Cosmic Web

We discuss the intimate relationship between the filamentary features and the rare dense compact cluster nodes in this network, via the large scale tidal field going along with them, following the cosmic web theory developed Bond et al. The Megaparsec scale tidal shear pattern is responsible for the contraction of matter into filaments, and its link with the cluster locations can be understood through the implied quadrupolar mass distribution in which the clusters are to be found at the sites of the overdense patches. We present a new technique for tracing the cosmic web, identifying planar walls, elongated filaments and cluster nodes in the galaxy distribution. This will allow the practical exploitation of the concept of the cosmic web towards identifying and tracing the locations of the gaseous WHIM. These methods, the Delaunay Tessellation Field Estimator (DTFE) and the Morphology Multiscale Filter (MMF) find their basis in computational geometry and visualization.Comment: 13 pages, 6 figures, appeared in proceedings workshop "Measuring the Diffuse Intergalactic Medium", eds. J-W. den Herder and N. Yamasaki, Hayama, Japan, October 2005. For version with high-res figures see http://www.astro.rug.nl/~weygaert/weywhim05.pd

On the determination of Jupiter's satellite-dependent Love numbers from Juno gravity data

The Juno gravity experiment, among the nine instruments onboard the spacecraft, is aimed at studying the interior structure of Jupiter to gain insight into its formation. Doppler data collected during the first two gravity-dedicated orbits completed by Juno around the gas giant have already provided a measurement of Jupiter's gravity field with outstanding accuracy, answering crucial questions about its interior composition. The large dataset that will be collected throughout the remaining phases of the mission until the end in July 2021 might allow to determine Jupiter's response to the satellite-dependent tidal perturbation raised by its moons, and even to separate the static and dynamic effects. We report on numerical simulations performed over the full science mission to assess the sensitivity of Juno gravity measurements to satellite-dependent tides on Jupiter. We assumed a realistic simulation scenario that is coherent with the result of data analysis from the first gravity passes. Furthermore, we implemented a satellite-dependent tidal model within the dynamical model used to fit the simulated Doppler data. The formal uncertainties resulting from the covariance analysis show that Juno is indeed sensitive to satellite-dependent tides on Jupiter raised by the inner Galilean satellites (the static Love numbers of degree and order 2 of Io, Europa and Ganymede can be determined respectively to 0.28%, 4.6% and 5.3% at 1 sigma). This unprecedented determination, that will be carried out towards the end of the mission, could further constrain the interior structure of the planet, allowing to discern among interior models and improving existing theories of planetary tidal response