Searcharxiv⌕ Search

arXiv subjects

Jihoon Lee

Publications and source records attributed to Jihoon Lee.

33 records · Page 2Linked to original sources
arXiv2022

Smooth-Swap: A Simple Enhancement for Face-Swapping with Smoothness

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.

cs.CV↗
arXiv2021

Nonlocal adhesion models for two cancer cell phenotypes in a multidimensional bounded domain

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.

math.AP↗
arXiv2021

NNStreamer: Efficient and Agile Development of On-Device AI Systems

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.

cs.LG↗
arXiv2021

Global well-posedness of logarithmic Keller-Segel type systems

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 $χ$, 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.

math.AP↗
arXiv2020

On conormal and oblique derivative problem for elliptic equations with Dini mean oscillation coefficients

We show that weak solutions to conormal derivative problem for elliptic equations in divergence form are continuously differentiable up to the boundary provided that the mean oscillations of the leading coefficients satisfy the Dini condition, the lower order coefficients satisfy certain suitable conditions, and the boundary is locally represented by a $C^1$ function whose derivatives are Dini continuous. We also prove that strong solutions to oblique derivative problem for elliptic equations in nondivergence form are twice continuously differentiable up to the boundary if the mean oscillations of coefficients satisfy the Dini condition and the boundary is locally represented by a $C^1$ function whose derivatives are double Dini continuous. This in particular extends a result of M. V. Safonov (Comm. Partial Differential Equations 20:1349--1367, 1995)

math.AP↗
arXiv2019

Gromov-Hausdorff stability of inertial manifolds under perturbations of the domain and equation

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.

math.DS↗
arXiv2019

Global Well-posedness and Long Time Behaviors of Chemotaxis-Fluid System Modeling Coral Fertilization

We consider generalized models on coral broadcast spawning phenomena involving diffusion, advection, chemotaxis, and reactions when egg and sperm densities are different. We prove the global-in-time existence of the regular solutions of the models as well as their temporal decays in two and three dimensions. We also show that the total masses of egg and sperm density have positive lower bounds as time tends to infinity in three dimensions.

math.AP↗
arXiv2016

Stability of planar traveling waves in a Keller-Segel equation on an infinite strip domain

A simplified model of the tumor angiogenesis can be described by a Keller-Segel equation \cite{FrTe,Le,Pe}. The stability of traveling waves for the one dimensional system has recently been known by \cite{JinLiWa,LiWa}. In this paper we consider the equation on the two dimensional domain $ (x, y) \in \mathbf R \times {\mathbf S^λ}$ for a small parameter $λ>0$ where $ \mathbf S^λ$ is the circle of perimeter $λ$. Then the equation allows a planar traveling wave solution of invading types. We establish the nonlinear stability of the traveling wave solution if the initial perturbation is sufficiently small in a weighted Sobolev space without a chemical diffusion. When the diffusion is present, we show a linear stability. Lastly, we prove that any solution with our front conditions eventually becomes planar under certain regularity conditions. The key ideas are to use the Cole-Hopf transformation and to apply the Poincaré inequality to handle with the two dimensional structure.

math.AP↗
arXiv2016

On the Geometric Regularity Conditions for the 3D Navier-Stokes Equations

We prove geometrically improved version of Prodi-Serrin type blow-up criterion. Let $v$ and $ω$ be the velocity and the vorticity of solutions to the 3D Navier-Stokes equations and denote $\{f\}_+=\max\{f, 0\}$ , $Q_T=\Bbb R^3\times (0, T)$. If $\left\{\left( v \times \fracω{|ω|} \right)\cdot \frac{Λ^βv}{|Λ^βv|}\right\}_+ \in L^{γ, α}_{x,t} (Q_T)$ with $3/γ+2/α\leq 1$ for some $γ>3$ and $1 \leq β\leq 2$, then the local smooth solution $v$ of the Navier-Stokes equations on $(0,T)$ can be continued to $(0, T+δ)$ for some $δ>0$. We also prove localized version of a special case of this. Let $v$ be a suitable weak solution to the Navier-tokes equations in a space-time domain containing $z_0= (x_0, t_0)$, let $Q_{z_0, r}=B_{x_0, r} \times (t_0-r^2, t_0)$ be a parabolic cylinder in the domain. We show that if either $\left\{\left( v \times \fracω{|ω|}\right) \cdot \frac{\nabla \times ω}{|\nabla \times ω|}\right\}_{+} \in L^{γ, α}_{x,t}(Q_{z_0, r})$ with $\frac{3}γ+\frac{2}α \leq 1$, or $\left\{\left(\frac{v}{|v|} \times ω\right) \cdot \frac{\nabla \times ω}{|\nabla \times ω|}\right\}_{+} \in L^{γ, α}_{x,t}(Q_{z_0, r})$ with $\frac{3}γ+\frac{2}α \leq 2$, ($γ\geq 2$, $α\geq 2$), then $z_0$ is a regular point for $v$. This improves previous local regularity criteria for the suitable weak solutions.

math.AP↗
arXiv2015

Global Well-posedness of the Chemotaxis-Navier-Stokes Equations in two dimensions

We consider two dimensional Keller-Segel equations coupled with the Navier-Stokes equations modelled by Tuval et al.[32]. Assuming that the chemotactic sensitivity and oxygen consumption rate are nondecreasing and differentiable, we prove that there is no blow-up in a finite time for solutions with large initial data to chemotaxis-Navier-Stokes equations in two dimensions. In addition, temporal decays of solutions are shown, as time tends to infinity.

math.AP↗
arXiv2013

On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics

In this paper, we establish an optimal blow-up criterion for classical solutions to the incompressible resistive Hall-magnetohydrodynamic equations. We also prove two global-in-time existence results of the classical solutions for small initial data, the smallness conditions of which are given by the suitable Sobolev and the Besov norms respectively. Although the Sobolev space version is already an improvement of the corrresponding result in \cite{Chae-Degond-Liu}, the optimality in terms of the scaling property is achieved via the Besov space estimate. The special property of the energy estimate in terms of $\dot{B}^s_{2,1}$ norm is essential for this result. Contrary to the usual MHD the global well-posedness in the $2\frac12$ dimensional Hall-MHD is wide open.

math.AP↗
arXiv2013

Global existence and temporal decay in Keller-Segel models coupled to fluid equations

We consider a Keller-Segel model coupled to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria for both cases that equations of oxygen concentration is of parabolic or hyperbolic type. We also prove global existence and decay estimate in time under the some smallness conditions of initial data.

math.AP↗
arXiv2012

Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations

We consider a system coupling the parabolic-parabolic Keller-Segel equations to the in- compressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria. For two dimensional Navier-Stokes-Keller-Segel equations, regular solutions constructed locally in time are, in reality, extended globally under some assumptions pertinent to experimental observation in [20] on the consumption rate and chemotactic sensitivity. We also show the existence of global weak solutions in spatially three dimensions with rather restrictive consumption rate and chemotactic sensitivity.

math.AP↗