Global regularity of axisymmetric incompressible Euler flows with non-trivial swirl in 3d is an outstanding open question. This work establishes that in the presence of uniform rotation, suitably small, localized and axisymmetric initial data lead to
global strong solutions to the rotating 3d Euler equations. The solutions constructed are of Sobolev regularity, have non-vanishing swirl and scatter linearly, thanks to the dispersive effect induced by the rotation. To establish this, we introduce a framework that builds on the symmetries of the problem and precisely captures the anisotropic, dispersive mechanism due to rotation. This enables a fine analysis of the geometry of nonlinear interactions and allows us to propagate sharp decay bounds, which is crucial for the construction of global flows.
This paper investigates the uplink cascaded channel estimation for intelligent-reflecting-surface (IRS)-assisted multi-user multiple-input-single-output systems. We focus on a sub-6 GHz scenario where the channel propagation is not sparse and the num
ber of IRS elements can be larger than the number of BS antennas. A novel channel estimation protocol without the need of on-off amplitude control to avoid the reflection power loss is proposed. In addition, the pilot overhead is substantially reduced by exploiting the common-link structure to decompose the cascaded channel coefficients by the multiplication of the common-link variables and the user-specific variables. However, these two types of variables are highly coupled, which makes them difficult to estimate. To address this issue, we formulate an optimization-based joint channel estimation problem, which only utilizes the covariance of the cascaded channel. Then, we design a low-complexity alternating optimization algorithm with efficient initialization for the non-convex optimization problem, which achieves a local optimum solution. To further enhance the estimation accuracy, we propose a new formulation to optimize the training phase shifting configuration for the proposed protocol, and then solve it using the successive convex approximation algorithm. Comprehensive simulations verify that the proposed algorithm has supreme performance compared to various state-of-the-art baseline schemes.
In the supercritical range of the polytropic indices $gammain(1,frac43)$ we show the existence of smooth radially symmetric self-similar solutions to the gravitational Euler-Poisson system. These solutions exhibit gravitational collapse in the sense
that the density blows-up in finite time. Some of these solutions were numerically found by Yahil in 1983 and they can be thought of as polytropic analogues of the Larson-Penston collapsing solutions in the isothermal case $gamma=1$. They each contain a sonic point, which leads to numerous mathematical difficulties in the existence proof.
In a joint localization and synchronization (JLAS) system comprised of anchor nodes (ANs) and user nodes (UNs), a relative spatiotemporal coordinate is established by the ANs with known positions. It is an essential technique for the moving UNs with
clock offset and skew to resolve the JLAS problem. Existing methods using sequential one-way time-of-arrival (TOA) measurements from the ANs broadcast signals require a good initial guess and have high computational complexity. In this paper, we propose a new closed-form JLAS approach, namely CFJLAS, which achieves optimal solution without initialization, and has low computational complexity. We first linearize the relation between the estimated parameter and the sequential TOA measurement by squaring and differencing the TOA measurement equations. By devising two intermediate variables, we then simplify the problem to finding the solution of a quadratic equation set. Finally, we apply a weighted least squares (WLS) step using the residuals of all the measurements to optimize the estimation. We derive the Cramer-Rao lower bound (CRLB), analyze the estimation error, and show that the estimation accuracy of the CFJLAS reaches CRLB under the small noise condition. The complexity of the CFJLAS is studied and compared with the conventional iterative method. Simulations in the 2D scene verify that the estimation accuracy of the new CFJLAS method in position, velocity, clock offset, and clock skew all reaches CRLB. Compared with the conventional iterative method, which requires a good initial guess to converge to the correct estimation and has growing complexity with more iterations, the proposed new CFJLAS method does not require initialization, always obtains the optimal solution and has constant low computational complexity.
In this paper, we explore a canonical connection between the algebra of $q$-difference operators $widetilde{V}_{q}$, affine Lie algebra and affine vertex algebras associated to certain subalgebra $mathcal{A}$ of the Lie algebra $mathfrak{gl}_{infty}$
. We also introduce and study a category $mathcal{O}$ of $widetilde{V}_{q}$-modules. More precisely, we obtain a realization of $widetilde{V}_{q}$ as a covariant algebra of the affine Lie algebra $widehat{mathcal{A}^{*}}$, where $mathcal{A}^{*}$ is a 1-dimensional central extension of $mathcal{A}$. We prove that restricted $widetilde{V_{q}}$-modules of level $ell_{12}$ correspond to $mathbb{Z}$-equivariant $phi$-coordinated quasi-modules for the vertex algebra $V_{widetilde{mathcal{A}}}(ell_{12},0)$, where $widetilde{mathcal{A}}$ is a generalized affine Lie algebra of $mathcal{A}$. In the end, we show that objects in the category $mathcal{O}$ are restricted $widetilde{V_{q}}$-modules, and we classify simple modules in the category $mathcal{O}$.
Siamese network based trackers formulate the visual tracking task as a similarity matching problem. Almost all popular Siamese trackers realize the similarity learning via convolutional feature cross-correlation between a target branch and a search b
ranch. However, since the size of target feature region needs to be pre-fixed, these cross-correlation base methods suffer from either reserving much adverse background information or missing a great deal of foreground information. Moreover, the global matching between the target and search region also largely neglects the target structure and part-level information. In this paper, to solve the above issues, we propose a simple target-aware Siamese graph attention network for general object tracking. We propose to establish part-to-part correspondence between the target and the search region with a complete bipartite graph, and apply the graph attention mechanism to propagate target information from the template feature to the search feature. Further, instead of using the pre-fixed region cropping for template-feature-area selection, we investigate a target-aware area selection mechanism to fit the size and aspect ratio variations of different objects. Experiments on challenging benchmarks including GOT-10k, UAV123, OTB-100 and LaSOT demonstrate that the proposed SiamGAT outperforms many state-of-the-art trackers and achieves leading performance. Code is available at: https://git.io/SiamGAT
Compared with the progress made on human activity classification, much less success has been achieved on human interaction understanding (HIU). Apart from the latter task is much more challenging, the main cause is that recent approaches learn human
interactive relations via shallow graphical models, which is inadequate to model complicated human interactions. In this paper, we propose a consistency-aware graph network, which combines the representative ability of graph network and the consistency-aware reasoning to facilitate the HIU task. Our network consists of three components, a backbone CNN to extract image features, a factor graph network to learn third-order interactive relations among participants, and a consistency-aware reasoning module to enforce labeling and grouping consistencies. Our key observation is that the consistency-aware-reasoning bias for HIU can be embedded into an energy function, minimizing which delivers consistent predictions. An efficient mean-field inference algorithm is proposed, such that all modules of our network could be trained jointly in an end-to-end manner. Experimental results show that our approach achieves leading performance on three benchmarks.
In this paper we study the dynamics of an incompressible viscous fluid evolving in an open-top container in two dimensions. The fluid mechanics are dictated by the Navier-Stokes equations. The upper boundary of the fluid is free and evolves within th
e container. The fluid is acted upon by a uniform gravitational field, and capillary forces are accounted for along the free boundary. The triple-phase interfaces where the fluid, air above the vessel, and solid vessel wall come in contact are called contact points, and the angles formed at the contact point are called contact angles. The model that we consider integrates boundary conditions that allow for full motion of the contact points and angles. Equilibrium configurations consist of quiescent fluid within a domain whose upper boundary is given as the graph of a function minimizing a gravity-capillary energy functional, subject to a fixed mass constraint. The equilibrium contact angles can take on any values between $0$ and $pi$ depending on the choice of capillary parameters. The main thrust of the paper is the development of a scheme of a priori estimates that show that solutions emanating from data sufficiently close to the equilibrium exist globally in time and decay to equilibrium at an exponential rate.
While it is well known that constant rotation induces linear dispersive effects in various fluid models, we study here its effect on long time nonlinear dynamics in the inviscid setting. More precisely, we investigate stability in the 3d rotating Eul
er equations in $mathbb{R}^3$ with a fixed speed of rotation. We show that for any $M>0$, axisymmetric initial data of sufficiently small size $varepsilon$ lead to solutions that exist for a long time at least $varepsilon^{-M}$ and disperse. This is a manifestation of the stabilizing effect of rotation, regardless of its speed. To achieve this we develop an anisotropic framework that naturally builds on the available symmetries. This allows for a precise quantification and control of the geometry of nonlinear interactions, while at the same time giving enough information to obtain dispersive decay via adapted linear dispersive estimates.
We first determine the automorphism group of the twisted Heisenberg-Virasoro vertex operator algebra $V_{mathcal{L}}(ell_{123},0)$.Then, for any integer $t>1$, we introduce a new Lie algebra $mathcal{L}_{t}$, and show that $sigma_{t}$-twisted $V_{mat
hcal{L}}(ell_{123},0)$($ell_{2}=0$)-modules are in one-to-one correspondence with restricted $mathcal{L}_{t}$-modules of level $ell_{13}$, where $sigma_{t}$ is an order $t$ automorphism of $V_{mathcal{L}}(ell_{123},0)$. At the end, we give a complete list of irreducible $sigma_{t}$-twisted $V_{mathcal{L}}(ell_{123},0)$($ell_{2}=0$)-modules.
