From time to timescape - Einstein's unfinished revolution

I argue that Einstein overlooked an important aspect of the relativity of time in never quite realizing his quest to embody Mach's principle in his theory of gravity. As a step towards that goal, I broaden the Strong Equivalence Principle to a new principle of physics, the Cosmological Equivalence Principle, to account for the role of the evolving average regional density of the universe in the synchronisation of clocks and the relative calibration of inertial frames. In a universe dominated by voids of the size observed in large-scale structure surveys, the density contrasts of expanding regions are strong enough that a relative deceleration of the background between voids and the environment of galaxies, typically of order 10^{-10} m/s^2, must be accounted for. As a result one finds a universe whose present age varies by billions of years according to the position of the observer: a timescape. This model universe is observationally viable: it passes three critical independent tests, and makes additional predictions. Dark energy is revealed as a mis-identification of gravitational energy gradients and the resulting variance in clock rates. Understanding the biggest mystery in cosmology therefore involves a paradigm shift, but in an unexpected direction: the conceptual understanding of time and energy in Einstein's own theory is incomplete.Comment: 13 pages, 3 figures; A runner-up in the 2008 FQXi Essay Contest on the Nature of Time; Int. J. Mod. Phys. D 18, in pres

Deep Video Generation, Prediction and Completion of Human Action Sequences

Current deep learning results on video generation are limited while there are only a few first results on video prediction and no relevant significant results on video completion. This is due to the severe ill-posedness inherent in these three problems. In this paper, we focus on human action videos, and propose a general, two-stage deep framework to generate human action videos with no constraints or arbitrary number of constraints, which uniformly address the three problems: video generation given no input frames, video prediction given the first few frames, and video completion given the first and last frames. To make the problem tractable, in the first stage we train a deep generative model that generates a human pose sequence from random noise. In the second stage, a skeleton-to-image network is trained, which is used to generate a human action video given the complete human pose sequence generated in the first stage. By introducing the two-stage strategy, we sidestep the original ill-posed problems while producing for the first time high-quality video generation/prediction/completion results of much longer duration. We present quantitative and qualitative evaluation to show that our two-stage approach outperforms state-of-the-art methods in video generation, prediction and video completion. Our video result demonstration can be viewed at https://iamacewhite.github.io/supp/index.htmlComment: Under review for CVPR 2018. Haoye and Chunyan have equal contributio

A variational approach to stable principal component pursuit

We introduce a new convex formulation for stable principal component pursuit (SPCP) to decompose noisy signals into low-rank and sparse representations. For numerical solutions of our SPCP formulation, we first develop a convex variational framework and then accelerate it with quasi-Newton methods. We show, via synthetic and real data experiments, that our approach offers advantages over the classical SPCP formulations in scalability and practical parameter selection.Comment: 10 pages, 5 figure

Time-dependent radio emission from evolving jets

We investigated the time-dependent radiative and dynamical properties of light supersonic jets launched into an external medium, using hydrodynamic simulations and numerical radiative transfer calculations. These involved various structural models for the ambient media, with density profiles appropriate for galactic and extragalactic systems. The radiative transfer formulation took full account of emission, absorption, re-emission, Faraday rotation and Faraday conversion explicitly. High time-resolution intensity maps were generated, frame-by-frame, to track the spatial hydrodynamical and radiative properties of the evolving jets. Intensity light curves were computed via integrating spatially over the emission maps. We apply the models to jets in active galactic nuclei (AGN). From the jet simulations and the time-dependent emission calculations we derived empirical relations for the emission intensity and size for jets at various evolutionary stages. The temporal properties of jet emission are not solely consequences of intrinsic variations in the hydrodynamics and thermal properties of the jet. They also depend on the interaction between the jet and the ambient medium. The interpretation of radio jet morphology therefore needs to take account of environmental factors. Our calculations have also shown that the environmental interactions can affect specific emitting features, such as internal shocks and hotspots. Quantification of the temporal evolution and spatial distribution of these bright features, together with the derived relations between jet size and emission, would enable us to set constraints on the hydrodynamics of AGN and the structure of the ambient medium.Comment: 16 pages, 18 figures, MNRAS in press

Reproducing formulas for generalized translation invariant systems on locally compact abelian groups

In this paper we connect the well established discrete frame theory of generalized shift invariant systems to a continuous frame theory. To do so, we let $\Gamma_j$, $j \in J$, be a countable family of closed, co-compact subgroups of a second countable locally compact abelian group $G$ and study systems of the form $\cup_{j \in J}\{g_{j,p}(\cdot - \gamma)\}_{\gamma \in \Gamma_j, p \in P_j}$ with generators $g_{j,p}$ in $L^2(G)$ and with each $P_j$ being a countable or an uncountable index set. We refer to systems of this form as generalized translation invariant (GTI) systems. Many of the familiar transforms, e.g., the wavelet, shearlet and Gabor transform, both their discrete and continuous variants, are GTI systems. Under a technical $\alpha$ local integrability condition ($\alpha$-LIC) we characterize when GTI systems constitute tight and dual frames that yield reproducing formulas for $L^2(G)$. This generalizes results on generalized shift invariant systems, where each $P_j$ is assumed to be countable and each $\Gamma_j$ is a uniform lattice in $G$, to the case of uncountably many generators and (not necessarily discrete) closed, co-compact subgroups. Furthermore, even in the case of uniform lattices $\Gamma_j$, our characterizations improve known results since the class of GTI systems satisfying the $\alpha$-LIC is strictly larger than the class of GTI systems satisfying the previously used local integrability condition. As an application of our characterization results, we obtain new characterizations of translation invariant continuous frames and Gabor frames for $L^2(G)$. In addition, we will see that the admissibility conditions for the continuous and discrete wavelet and Gabor transform in $L^2(\mathbb{R}^n)$ are special cases of the same general characterizing equations.Comment: Minor changes (v2). To appear in Trans. Amer. Math. So

Modelling Load Balancing and Carrier Aggregation in Mobile Networks

In this paper, we study the performance of multicarrier mobile networks. Specifically, we analyze the flow-level performance of two inter-carrier load balancing schemes and the gain engendered by Carrier Aggregation (CA). CA is one of the most important features of HSPA+ and LTE-A networks; it allows devices to be served simultaneously by several carriers. We propose two load balancing schemes, namely Join the Fastest Queue (JFQ) and Volume Balancing (VB), that allow the traffic of CA and non-CA users to be distributed over the aggregated carriers. We then evaluate the performance of these schemes by means of analytical modeling. We show that the proposed schemes achieve quasi-ideal load balancing. We also investigate the impact of mixing traffic of CA and non-CA users in the same cell and show that performance is practically insensitive to the traffic mix.Comment: 8 pages, 6 figures, submitted to WiOpt201