We extend the monumental result of Christodoulou-Klainerman on the global nonlinear stability of the Minkowski spacetime to the global nonlinear stability of a class of large dispersive spacetimes. More precisely, we show that any regular future caus
ally geodesically complete, asymptotically flat solution to the Einstein-scalar field system which approaches the Minkowski spacetime sufficiently fast for large times is future globally nonlinearly stable. Combining our main theorem with results of Luk-Oh, Luk-Oh-Yang and Kilgore, we prove that a class of large data spherically symmetric dispersive solutions to the Einstein-scalar field system are globally nonlinearly stable with respect to small non-spherically symmetric perturbations. This in particular gives the first construction of an open set of large asymptotically flat initial data for which the solutions to the Einstein-scalar field system are future causally geodesically complete.
Event definitions in Complex Event Processing systems are constrained by the expressiveness of each systems language. Some systems allow the definition of instantaneous complex events, while others allow the definition of durative complex events. Whi
le there are exceptions that offer both options, they often lack of intervals relations such as those specified by the Allens interval algebra. In this paper, we propose a new logic based temporal phenomena definition language, specifically tailored for Complex Event Processing, that allows the representation of both instantaneous and durative phenomena and the temporal relations between them. Moreover, we demonstrate the expressiveness of our proposed language by employing a maritime use case where we define maritime events of interest. Finally, we analyse the execution semantics of our proposed language for stream processing and introduce the `Phenesthe implementation prototype.
We consider the problem of automatically proving resource bounds. That is, we study how to prove that an integer-valued resource variable is bounded by a given program expression. Automatic resource-bound analysis has recently received significant at
tention because of a number of important applications (e.g., detecting performance bugs, preventing algorithmic-complexity attacks, identifying side-channel vulnerabilities), where the focus has often been on developing precise amortized reasoning techniques to infer the most exact resource usage. While such innovations remain critical, we observe that fully precise amortization is not always necessary to prove a bound of interest. And in fact, by amortizing emph{selectively}, the needed supporting invariants can be simpler, making the invariant inference task more feasible and predictable. We present a framework for selectively-amortized analysis that mixes worst-case and amortized reasoning via a property decomposition and a program transformation. We show that proving bounds in any such decomposition yields a sound resource bound in the original program, and we give an algorithm for selecting a reasonable decomposition.
We establish theorems on the existence and compactness of solutions to the $sigma_2$-Nirenberg problem on the standard sphere $mathbb S^2$. A first significant ingredient, a Liouville type theorem for the associated fully nonlinear Mobius invariant e
lliptic equations, was established in an earlier paper of ours. Our proof of the existence and compactness results requires a number of additional crucial ingredients which we prove in this paper: A Liouville type theorem for the associated fully nonlinear Mobius invariant degenerate elliptic equations, a priori estimates of first and second order derivatives of solutions to the $sigma_2$-Nirenberg problem, and a B^ocher type theorem for the associated fully nonlinear Mobius invariant elliptic equations. Given these results, we are able to complete a fine analysis of a sequence of blow-up solutions to the $sigma_2$-Nirenberg problem. In particular, we prove that there can be at most one blow-up point for such a blow-up sequence of solutions. This, together with a Kazdan-Warner type identity, allows us to prove $L^infty$ a priori estimates for solutions of the $sigma_2$-Nirenberg problem under some simple generic hypothesis. The higher derivative estimates then follow from classical estimates of Nirenberg and Schauder. In turn, the existence of solutions to the $sigma_2$-Nirenberg problem is obtained by an application of the by now standard degree theory for second order fully nonlinear elliptic operators.
In active visual tracking, it is notoriously difficult when distracting objects appear, as distractors often mislead the tracker by occluding the target or bringing a confusing appearance. To address this issue, we propose a mixed cooperative-competi
tive multi-agent game, where a target and multiple distractors form a collaborative team to play against a tracker and make it fail to follow. Through learning in our game, diverse distracting behaviors of the distractors naturally emerge, thereby exposing the trackers weakness, which helps enhance the distraction-robustness of the tracker. For effective learning, we then present a bunch of practical methods, including a reward function for distractors, a cross-modal teacher-student learning strategy, and a recurrent attention mechanism for the tracker. The experimental results show that our tracker performs desired distraction-robust active visual tracking and can be well generalized to unseen environments. We also show that the multi-agent game can be used to adversarially test the robustness of trackers.
Federated learning involves training machine learning models over devices or data silos, such as edge processors or data warehouses, while keeping the data local. Training in heterogeneous and potentially massive networks introduces bias into the sys
tem, which is originated from the non-IID data and the low participation rate in reality. In this paper, we propose Elastic Federated Learning (EFL), an unbiased algorithm to tackle the heterogeneity in the system, which makes the most informative parameters less volatile during training, and utilizes the incomplete local updates. It is an efficient and effective algorithm that compresses both upstream and downstream communications. Theoretically, the algorithm has convergence guarantee when training on the non-IID data at the low participation rate. Empirical experiments corroborate the competitive performance of EFL framework on the robustness and the efficiency.
Computer systems such as storage systems normally require transparent white-box algorithms that are interpretable for human experts. In this work, we propose a learning-aided heuristic design method, which automatically generates human-readable strat
egies from Deep Reinforcement Learning (DRL) agents. This method benefits from the power of deep learning but avoids the shortcoming of its black-box property. Besides the white-box advantage, experiments in our storage productions resource allocation scenario also show that this solution outperforms the systems default settings and the elaborately handcrafted strategy by human experts.
Inspired by investigations of Bose-Einstein condensates (BECs) produced in the Cold Atom Laboratory (CAL) aboard the International Space Station, we present a study of thermodynamic properties of shell-shaped BECs. Within the context of a spherically
symmetric `bubble trap potential, we study the evolution of the system from small filled spheres to hollow, large, thin shells via the tuning of trap parameters. We analyze the bubble trap spectrum and states, and track the distinct changes in spectra between radial and angular modes across the evolution. This separation of the excitation spectrum provides a basis for quantifying dimensional cross-over to quasi-2D physics at a given temperature. Using the spectral data, for a range of trap parameters, we compute the critical temperature for a fixed number of particles to form a BEC. For a set of initial temperatures, we also evaluate the change in temperature that would occur in adiabatic expansion from small filled sphere to large thin shell were the trap to be dynamically tuned. We show that the system cools during this expansion but that the decrease in critical temperature occurs more rapidly, thus resulting in depletion of any initial condensate. We contrast our spectral methods with standard semiclassical treatments, which we find must be used with caution in the thin-shell limit. With regards to interactions, using energetic considerations and corroborated through Bogoliubov treatments, we demonstrate that they would be less important for thin shells due to reduced density but vortex physics would become more predominant. Finally, we apply our treatments to traps that realistically model CAL experiments and borrow from the thermodynamic insights found in the idealized bubble case during adiabatic expansion.
Single-image super-resolution (SR) and multi-frame SR are two ways to super resolve low-resolution images. Single-Image SR generally handles each image independently, but ignores the temporal information implied in continuing frames. Multi-frame SR i
s able to model the temporal dependency via capturing motion information. However, it relies on neighbouring frames which are not always available in the real world. Meanwhile, slight camera shake easily causes heavy motion blur on long-distance-shot low-resolution images. To address these problems, a Blind Motion Deblurring Super-Reslution Networks, BMDSRNet, is proposed to learn dynamic spatio-temporal information from single static motion-blurred images. Motion-blurred images are the accumulation over time during the exposure of cameras, while the proposed BMDSRNet learns the reverse process and uses three-streams to learn Bidirectional spatio-temporal information based on well designed reconstruction loss functions to recover clean high-resolution images. Extensive experiments demonstrate that the proposed BMDSRNet outperforms recent state-of-the-art methods, and has the ability to simultaneously deal with image deblurring and SR.
Rain is a common natural phenomenon. Taking images in the rain however often results in degraded quality of images, thus compromises the performance of many computer vision systems. Most existing de-rain algorithms use only one single input image and
aim to recover a clean image. Few work has exploited stereo images. Moreover, even for single image based monocular deraining, many current methods fail to complete the task satisfactorily because they mostly rely on per pixel loss functions and ignore semantic information. In this paper, we present a Paired Rain Removal Network (PRRNet), which exploits both stereo images and semantic information. Specifically, we develop a Semantic-Aware Deraining Module (SADM) which solves both tasks of semantic segmentation and deraining of scenes, and a Semantic-Fusion Network (SFNet) and a View-Fusion Network (VFNet) which fuse semantic information and multi-view information respectively. In addition, we also introduce an Enhanced Paired Rain Removal Network (EPRRNet) which exploits semantic prior to remove rain streaks from stereo images. We first use a coarse deraining network to reduce the rain streaks on the input images, and then adopt a pre-trained semantic segmentation network to extract semantic features from the coarse derained image. Finally, a parallel stereo deraining network fuses semantic and multi-view information to restore finer results. We also propose new stereo based rainy datasets for benchmarking. Experiments on both monocular and the newly proposed stereo rainy datasets demonstrate that the proposed method achieves the state-of-the-art performance.
