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This paper is devoted to studying the well-posedness, (conditional) conservation of magnetic helicity, inviscid limit and asymptotic stability of the generalized Navier-Stokes-Maxwell equations (NSM) under the Hall effect in two and three dimensions. More precisely, in the viscous case we prove the global well-posedness of NSM for small initial data, which allows us to establish a connection with either the Hall-magnetohydrodynamics (H-MHD) system as the speed of light tends to infinity or NSM without the Hall coefficient as this constant goes to zero. In addition, in the inviscid case the local well-posedness of NSM is also obtained for possibly large initial data. Moreover, under suitable conditions on the initial data and additional assumptions of solutions to NSM in three dimensions, the magnetic helicity is conserved as the electric conductivity goes to infinity. It is different to the case of the fractional H-MHD with critical fractional Laplacian exponents for both the velocity and magnetic fields, where the conservation of magnetic helicity can be provided for smooth initial data without any further conditions on the solution. Furthermore, the asymptotic stability of NSM around a constant magnetic field is established in the case of having a velocity damping term., Comment: arXiv admin note: text overlap with arXiv:2401.14839

In recent years, there has been a significant focus on research related to text-guided image inpainting. However, the task remains challenging due to several constraints, such as ensuring alignment between the image and the text, and maintaining consistency in distribution between corrupted and uncorrupted regions. In this paper, thus, we propose a dual affine transformation generative adversarial network (DAFT-GAN) to maintain the semantic consistency for text-guided inpainting. DAFT-GAN integrates two affine transformation networks to combine text and image features gradually for each decoding block. Moreover, we minimize information leakage of uncorrupted features for fine-grained image generation by encoding corrupted and uncorrupted regions of the masked image separately. Our proposed model outperforms the existing GAN-based models in both qualitative and quantitative assessments with three benchmark datasets (MS-COCO, CUB, and Oxford) for text-guided image inpainting., Comment: ACM MM'2024. 9 pages, 3 tables, 9 figures

We prove that the collection $\mathcal M_{-\infty}$ of backward bounded solutions for a semilinear evolution equation is the graph of an upper hemicontinuous set-valued function from the low Fourier modes to the higher Fourier modes, which is invariant and contains the global attractor. We also show that there exists a limit $\mathcal M_{\infty}$ of finite dimensional Lipschitz manifolds $\mathcal M_t$ generated by the time $t$-maps ($t>0$) from the flat manifold $\mathcal M_0$ with the Hausdorff distance and we find $\mathcal M_{\infty} \subset \mathcal M_{-\infty}$. No spectral gap conditions are assumed.

This paper is devoted to studying the well-posedness, conservation of magnetic helicity, inviscid limit and asymptotic stability of the generalized Navier-Stokes-Maxwell (NSM) equations with the standard Ohm's law in $\mathbb{R}^d$ for $d \in \{2,3\}$. More precisely, the global well-posedness is established in case of fractional Laplacian velocity $(-\Delta)^\alpha v$ with $\alpha = \frac{d}{2}$ for suitable data. In addition, the local well-posedness in the inviscid case is also provided for sufficient smooth data, which allows us to study the inviscid limit of associated positive viscosity solutions in the case $\alpha = 1$, where an explicit bound on the difference is given. Furthermore, in three dimensions if the initial data satisfies futher suitable conditions then magnetic helicity is conserved as the electric conductivity goes to infinity. On the other hand, in the case $\alpha = 0$ the stability near a magnetohydrostatic equilibrium with a constant (or equivalently bounded) magnetic field is also obtained in which nonhomogeneous Sobolev norms of the velocity and electric fields, and for $p \in (2,\infty]$ the $L^p$ norm of the magnetic field converge to zero as time goes to infinity with an implicit rate. In this velocity damping case, the situation is different both in case of the two and a half, and three-dimensional (Hall)-magnetohydrodynamics ((H)-MHD) system, where an explicit rate of convergence in infinite time is computed for both the velocity and magnetic fields in nonhomogeneous Sobolev norms. Therefore, it seems that there is a gap between NSM and MHD in terms of the norm convergence of the magnetic field and the rate of decaying in time, even the latter equations can be proved as a limiting system of the former one in the sense of distributions as the speed of light tends to infinity.

The paper is devoted to investigating the well-posedness, stability and large-time behavior near the hydrostatic balance for the 2D Boussinesq equations with partial dissipation. More precisely, the global well-posedness is obtained in the case of partial viscosity and without thermal diffusion for the initial data belonging to $H^{\delta}(\mathbb{R}^2) \times H^{s}(\mathbb{R}^2)$ for $\delta \in [s-1,s+1]$ if $s \in \mathbb{R}, s > 2$, for $\delta \in (1,s+1]$ if $s \in (0,2]$ and for $\delta \in [0,1]$ if $s = 0$. In addition, if one has either horizontal or vertical thermal diffusion then the stability and large-time behavior are provided in $H^m(\mathbb{R}^2)$, $m \in \mathbb{N}$ and in $\dot{H}^{m-1}(\mathbb{R}^2)$ with $m \in \mathbb{N}$, $m \geq 2$, respectively., Comment: Revised version

A distributed control of vehicle platooning is referred to as distributed consensus (DC) since many autonomous vehicles (AVs) reach a consensus to move as one body with the same velocity and inter-distance. For DC control to be stable, other AVs' real-time position information should be inputted to each AV's controller via vehicle-to-vehicle (V2V) communications. On the other hand, too many V2V links should be simultaneously established and frequently retrained, causing frequent packet loss and longer communication latency. We propose a novel DC algorithm called over-the-air consensus (AirCons), a joint communication-and-control design with two key features to overcome the above limitations. First, exploiting a wireless signal's superposition and broadcasting properties renders all AVs' signals to converge to a specific value proportional to participating AVs' average position without individual V2V channel information. Second, the estimated average position is used to control each AV's dynamics instead of each AV's individual position. Through analytic and numerical studies, the effectiveness of the proposed AirCons designed on the state-of-the-art New Radio architecture is verified by showing a $14.22\%$ control gain compared to the benchmark without the average position., Comment: This work has been submitted to the IEEE for possible publication

We prove the global well-posedness of the 2D incompressible non-resistive MHD equations with a velocity damping term near the non-zero constant background magnetic field. To this end, we newly design a normal mode method of effectively leveraging the anisotropy of the linear propagator that encodes both the partially dissipative nature of the non-resistive MHD system and the stabilizing mechanism of the underlying magnetic field. Isolating new key quantities and estimating them with themselves in an entangling way via the eigenvalue analysis based on Duhamel's formulation, we establish the global well-posedness for any initial data $(v_0,B_0)$ that is sufficiently small in a space rougher than $H^{4}\cap L^1$. This improves the recent work in SIAM J. Math. Anal. 47, 2630-2656 (2015) where the similar result was obtained provided that $(v_0,B_0)$ was small enough in a space strictly embedded in $H^{20}\cap W^{6,1}$.

The quasi-geostrohpic (QG) equation has been used to capture the asymptotic dynamics of the rotating stratified Boussinesq flows in the regime of strong stratification and rapid rotation. In this paper, we establish the invalidity of such approximation when the rotation-stratification ratio is either fixed to be unity or tends to unity sufficiently slowly in the asymptotic regime: the difference between the rotating stratified Boussinesq flow and the corresponding QG flow remains strictly away from zero, independently of the intensities of rotation and stratification. In contrast, we also show that the convergence occurs when the rotation-stratification ratio is fixed to be a number other than unity or converges to unity sufficiently fast. As a corollary, we compute a lower bound of the convergence rate, which blows up as the rotation-stratification ratio goes to unity.

This paper deals with a parabolic-elliptic chemotaxis-consumption system with tensor-valued sensitivity $S(x,n,c)$ under no-flux boundary conditions for $n$ and Robin-type boundary conditions for $c$. The global existence of bounded classical solutions is established in dimension two under general assumptions on tensor-valued sensitivity $S$. One of main steps is to show that $\nabla c(\cdot,t)$ becomes tiny in $L^{2}(B_{r}(x)\cap \Omega)$ for every $x\in\overline{\Omega}$ and $t$ when $r$ is sufficiently small, which seems to be of independent interest. On the other hand, in the case of scalar-valued sensitivity $S=\chi(x,n,c)\mathbb{I}$, there exists a bounded classical solution globally in time for two and higher dimensions provided the domain is a ball with radius $R$ and all given data are radial. The result of the radial case covers scalar-valued sensitivity $\chi$ that can be singular at $c=0$.

Face-swapping models have been drawing attention for their compelling generation quality, but their complex architectures and loss functions often require careful tuning for successful training. We propose a new face-swapping model called `Smooth-Swap', which excludes complex handcrafted designs and allows fast and stable training. The main idea of Smooth-Swap is to build smooth identity embedding that can provide stable gradients for identity change. Unlike the one used in previous models trained for a purely discriminative task, the proposed embedding is trained with a supervised contrastive loss promoting a smoother space. With improved smoothness, Smooth-Swap suffices to be composed of a generic U-Net-based generator and three basic loss functions, a far simpler design compared with the previous models. Extensive experiments on face-swapping benchmarks (FFHQ, FaceForensics++) and face images in the wild show that our model is also quantitatively and qualitatively comparable or even superior to the existing methods., Comment: CVPR 2022 (Oral)

We propose NNStreamer, a software system that handles neural networks as filters of stream pipelines, applying the stream processing paradigm to deep neural network applications. A new trend with the wide-spread of deep neural network applications is on-device AI. It is to process neural networks on mobile devices or edge/IoT devices instead of cloud servers. Emerging privacy issues, data transmission costs, and operational costs signify the need for on-device AI, especially if we deploy a massive number of devices. NNStreamer efficiently handles neural networks with complex data stream pipelines on devices, significantly improving the overall performance with minimal efforts. Besides, NNStreamer simplifies implementations and allows reusing off-the-shelf media filters directly, which reduces developmental costs significantly. We are already deploying NNStreamer for a wide range of products and platforms, including the Galaxy series and various consumer electronic devices. The experimental results suggest a reduction in developmental costs and enhanced performance of pipeline architectures and NNStreamer. It is an open-source project incubated by Linux Foundation AI, available to the public and applicable to various hardware and software platforms., Comment: IEEE/ACM ICSE 2021 SEIP (preprint)

We consider a class of logarithmic Keller-Segel type systems modeling the spatio-temporal behavior of either chemotactic cells or criminal activities in spatial dimensions two and higher. Under certain assumptions on parameter values and given functions, the existence of classical solutions is established globally in time, provided that initial data are sufficiently regular. In particular, we enlarge the range of chemotatic sensitivity $\chi$, compared to known results, in case that spatial dimensions are between two and eight. In addition, we provide new type of small initial data to obtain global classical solution, which is also applicable to the urban crime model. We discuss long-time asymptotic behaviors of solutions as well., Comment: 21 pages

Cell-cell adhesion is an inherently nonlocal phenomenon. Numerous partial differential equation models with nonlocal term have been recently presented to describe this phenomenon, yet the mathematical properties of nonlocal adhesion model are not well understood. Here we consider a model with two kinds of nonlocal cell-cell adhesion, satisfying no-flux conditions in a multidimensional bounded domain. We show global-in-time well-posedness of the solution to this model and obtain the uniform boundedness of solution.

In this paper, we study the Gromov-Hausdorff stability and continuous dependence of the inertial manifolds under perturbations of the domain and equation. More precisely, we use the Gromov-Hausdorff distances between two inertial manifolds and two dynamical systems to consider the continuous dependence of the inertial manifolds and the stability of the dynamical systems on inertial manifolds induced by the reaction diffusion equations under perturbations of the domain and equation.