Learning representations for graphs plays a critical role in a wide spectrum of downstream applications. In this paper, we summarize the limitations of the prior works in three folds: representation space, modeling dynamics and modeling uncertainty.
To bridge this gap, we propose to learn dynamic graph representation in hyperbolic space, for the first time, which aims to infer stochastic node representations. Working with hyperbolic space, we present a novel Hyperbolic Variational Graph Neural Network, referred to as HVGNN. In particular, to model the dynamics, we introduce a Temporal GNN (TGNN) based on a theoretically grounded time encoding approach. To model the uncertainty, we devise a hyperbolic graph variational autoencoder built upon the proposed TGNN to generate stochastic node representations of hyperbolic normal distributions. Furthermore, we introduce a reparameterisable sampling algorithm for the hyperbolic normal distribution to enable the gradient-based learning of HVGNN. Extensive experiments show that HVGNN outperforms state-of-the-art baselines on real-world datasets.
We investigate the shadows and photon spheres of the four-dimensional Gauss-Bonnet black hole with the static and infalling spherical accretions. We show that for both cases, the shadow and photon sphere are always present. The radii of the shadow an
d photon sphere are independent of the profiles of accretion for a fixed Gauss-Bonnet constant, implying that the shadow is a signature of the spacetime geometry and it is hardly influenced by accretion in this case. Because of the Doppler effect, the shadow of the infalling accretion is found to be darker than that of the static one. We also investigate the effect of the Gauss-Bonnet constant on the shadow and photon sphere, and find that the larger the Gauss-Bonnet constant is, the smaller the radii of the shadow and photon sphere will be. In particular, the observed specific intensity increases with the increasing of the Gauss-Bonnet constant.
By using the conserved currents associated to the diffeomorphism invariance, we study dynamical holographic systems and the relation between thermodynamical and dynamical stability of such systems. The case with fixed space-time backgrounds is discus
sed first, where a generalized free energy is defined with the property of monotonic decreasing in dynamic processes. It is then shown that the (absolute) thermodynamical stability implies the dynamical stability, while the linear dynamical stability implies the thermodynamical (meta-)stability. The case with full back-reaction is much more complicated. With the help of conserved currents associated to the diffeomorphism invariance induced by a preferred vector field, we propose a thermodynamic form of the bulk space-time dynamics with a preferred temperature of the event horizon, where a monotonically decreasing quantity can be defined as well. In both cases, our analyses help to clarify some aspects of the far-from-equilibrium holographic physics.
Social network alignment, aligning different social networks on their common users, is receiving dramatic attention from both academic and industry. All existing studies consider the social network to be static and neglect its inherent dynamics. In f
act, the dynamics of social networks contain the discriminative pattern of an individual, which can be leveraged to facilitate social network alignment. Hence, we for the first time propose to study the problem of aligning dynamic social networks. Towards this end, we propose a novel Dynamic social Network Alignment (DNA) framework, a unified optimization approach over deep neural architectures, to unfold the fruitful dynamics to perform alignment. However, it faces tremendous challenges in both modeling and optimization: (1) To model the intra-network dynamics, we explore the local dynamics of the latent pattern in friending evolvement and the global consistency of the representation similarity with neighbors. We design a novel deep neural architecture to obtain the dual embedding capturing local dynamics and global consistency for each user. (2) To model the inter-network alignment, we exploit the underlying identity of an individual from the dual embedding in each dynamic social network. We design a unified optimization approach interplaying proposed deep neural architectures to construct a common subspace of identity embeddings. (3) To address this optimization problem, we design an effective alternating algorithm with solid theoretical guarantees.We conduct extensive experiments on real-world datasets and show that the proposed DNA framework substantially outperforms the state-of-the-art methods.
The strong cosmic censorship has recently been put into question for the charged black holes in de Sitter space. We have performed the full non-linear evolution of the massless charged scalar field minimally coupled to the Einstein-Maxwell system in
de Sitter space, and found that the non-linear effect can restore the strong cosmic censorship, making it as strong as ever.
We initiate the investigation of the zero temperature holographic superfluids with two competing orders, where besides the vacuum phase, two one band superfluid phases, the coexistent superfluid phase has also been found in the AdS soliton background
for the first time. We construct the complete phase diagram in the $e-mu$ plane by numerics, which is consistent with our qualitative analysis. Furthermore, we calculate the corresponding optical conductivity and sound speed by the linear response theory. The onset of pole of optical conductivity at $omega=0$ indicates that the spontaneous breaking phase always represents the superfluid phase, and the residue of pole is increased with the chemical potential, which is consistent with the fact that the particle density is essentially the superfluid density for zero temperature superfluids. In addition, the resulting sound speed demonstrates the non-smoothness at the critical points as the order parameter of condensate, which indicates that the phase transitions can also be identified by the behavior of sound speed. Moreover, as expected from the boundary conformal field theory, the sound speed saturates to $frac{1}{sqrt{2}}$ at the large chemical potential limit for our two band holographic superfluid model.
Reissner-Nordstrom Anti-de Sitter (RNAdS) black holes are unstable against the charged scalar field perturbations due to the well-known superradiance phenomenon. We present the time domain analysis of charged scalar field perturbations in the RNAdS b
lack hole background in general dimensions. We show that the instabilities of charged scalar field can be explicitly illustrated from the time profiles of evolving scalar field. By using the Prony method to fit the time evolution data, we confirm the mode that dominates the long time behavior of scalar field is in accordance with the quasinormal mode from the frequency domain analysis. The superradiance origin of the instability can also be demonstrated by comparing the real part of the dominant mode with the superradiant condition of charged scalar field. It is shown that all the unstable modes are superradiant, which is consistent with the analytical result in the frequency domain analysis. Furthermore, we also confirm there exists the rapid exponential growing modes in the RNAdS case, which makes the RNAdS black hole a good test ground to investigate the nonlinear evolution of superradiant instability.
It has been proved that the charged stringy black holes are stable under the perturbations of massive charged scalar fields. However, superradiant instability can be generated by adding the mirror-like boundary condition to the composed system of cha
rged stringy black hole and scalar field. The unstable boxed quasinormal modes have been calculated by using both analytical and numerical method. In this paper, we further provide a time domain analysis by performing a long time evolution of charged scalar field configuration in the background of the charged stringy black hole with the mirror-like boundary condition imposed. We have used the ingoing Eddington-Finkelstein coordinates to derive the evolution equation, and adopted Pseudo-spectral method and the forth-order Runge-Kutta method to evolve the scalar field with the initial Gaussian wave packet. It is shown by our numerical scheme that Fourier transforming the evolution data coincides well with the unstable modes computed from frequency domain analysis. The existence of the rapid growth mode makes the charged stringy black hole a good test ground to study the nonlinear development of superradiant instability.
