Global $C^\infty$ Regularity of the Steady Prandtl Equation
In this paper, we prove the global $C^\infty$ regularity of the Oleinik's solution for the steady Prandtl equation with favorable pressure.
math.AP↗
arXiv subjects
Zhifei Zhang
Publications and source records attributed to Zhifei Zhang.
A Semantic-based Medical Image Fusion Approach
It is necessary for clinicians to comprehensively analyze patient information from different sources. Medical image fusion is a promising approach to providing overall information from medical images of different modalities. However, existing medical image fusion approaches ignore the semantics of images, making the fused image difficult to understand. In this work, we propose a new evaluation index to measure the semantic loss of fused image, and put forward a Fusion W-Net (FW-Net) for multimodal medical image fusion. The experimental results are promising: the fused image generated by our approach greatly reduces the semantic information loss, and has better visual effects in contrast to five state-of-art approaches. Our approach and tool have great potential to be applied in the clinical setting.
eess.IV↗
Well-posedness of the free boundary problem in elastodynamics with mixed stability condition
In this paper, we prove the local well-posedness of the free boundary problem in incompressible elastodynamics under a mixed type stability condition, i.e., for each point of the free boundary, at least one of the Taylor sign condition $-\partial_n p>0$ and the non-collinearity condition holds. This gives an affirmative answer to a problem raised by Trakhinin in [30].
math.AP↗
Linear stability of pipe Poiseuille flow at high Reynolds number regime
In this paper, we prove the linear stability of the pipe Poiseuille flow for general perturbations at high Reynolds number regime. This is a long-standing problem since the experiments of Reynolds in 1883. Our work lays a foundation for the theoretical analysis of hydrodynamic stability of pipe flow, which is one of the oldest yet unsolved problems of fundamental fluid dynamics.
math.AP↗
A new direction to promote the implementation of artificial intelligence in natural clinical settings
Artificial intelligence (AI) researchers claim that they have made great `achievements' in clinical realms. However, clinicians point out the so-called `achievements' have no ability to implement into natural clinical settings. The root cause for this huge gap is that many essential features of natural clinical tasks are overlooked by AI system developers without medical background. In this paper, we propose that the clinical benchmark suite is a novel and promising direction to capture the essential features of the real-world clinical tasks, hence qualifies itself for guiding the development of AI systems, promoting the implementation of AI in real-world clinical practice.
cs.AI↗
Boundary layer separation and local behavior for the Steady Prandtl equation
In the case of favorable pressure gradient, Oleinik proved the global existence of classical solution for the 2-D steady Prandtl equation for a class of positive data. In the case of adverse pressure gradient, an important physical phenomena is the boundary layer separation. In this paper, we prove the boundary layer separation for a large class of Oleinik's data and confirm Goldstein's hypothesis concerning the local behavior of the solution near the separation, which gives a partial answer to open problem 5 proposed by Oleinik and Samokin in \cite{Olei}.
math.AP↗
Image Super-Resolution by Neural Texture Transfer
Due to the significant information loss in low-resolution (LR) images, it has become extremely challenging to further advance the state-of-the-art of single image super-resolution (SISR). Reference-based super-resolution (RefSR), on the other hand, has proven to be promising in recovering high-resolution (HR) details when a reference (Ref) image with similar content as that of the LR input is given. However, the quality of RefSR can degrade severely when Ref is less similar. This paper aims to unleash the potential of RefSR by leveraging more texture details from Ref images with stronger robustness even when irrelevant Ref images are provided. Inspired by the recent work on image stylization, we formulate the RefSR problem as neural texture transfer. We design an end-to-end deep model which enriches HR details by adaptively transferring the texture from Ref images according to their textural similarity. Instead of matching content in the raw pixel space as done by previous methods, our key contribution is a multi-level matching conducted in the neural space. This matching scheme facilitates multi-scale neural transfer that allows the model to benefit more from those semantically related Ref patches, and gracefully degrade to SISR performance on the least relevant Ref inputs. We build a benchmark dataset for the general research of RefSR, which contains Ref images paired with LR inputs with varying levels of similarity. Both quantitative and qualitative evaluations demonstrate the superiority of our method over state-of-the-art.
cs.CV↗
Landscape of Big Medical Data: A Pragmatic Survey on Prioritized Tasks
Big medical data poses great challenges to life scientists, clinicians, computer scientists, and engineers. In this paper, a group of life scientists, clinicians, computer scientists and engineers sit together to discuss several fundamental issues. First, what are the unique characteristics of big medical data different from those of the other domains? Second, what are the prioritized tasks in clinician research and practices utilizing big medical data? And do we have enough publicly available data sets for performing those tasks? Third, do the state-of-the-practice and state-of-the-art algorithms perform good jobs? Fourth, are there any benchmarks for measuring algorithms and systems for big medical data? Fifth, what are the performance gaps of state-of-the-practice and state-of-the-art systems handling big medical data currently or in future? Finally but not least, are we, life scientists, clinicians, computer scientists and engineers, ready for working together? We believe answering the above issues will help define and shape the landscape of big medical data.
cs.CY↗
Beyond Inferring Class Representatives: User-Level Privacy Leakage From Federated Learning
Federated learning, i.e., a mobile edge computing framework for deep learning, is a recent advance in privacy-preserving machine learning, where the model is trained in a decentralized manner by the clients, i.e., data curators, preventing the server from directly accessing those private data from the clients. This learning mechanism significantly challenges the attack from the server side. Although the state-of-the-art attacking techniques that incorporated the advance of Generative adversarial networks (GANs) could construct class representatives of the global data distribution among all clients, it is still challenging to distinguishably attack a specific client (i.e., user-level privacy leakage), which is a stronger privacy threat to precisely recover the private data from a specific client. This paper gives the first attempt to explore user-level privacy leakage against the federated learning by the attack from a malicious server. We propose a framework incorporating GAN with a multi-task discriminator, which simultaneously discriminates category, reality, and client identity of input samples. The novel discrimination on client identity enables the generator to recover user specified private data. Unlike existing works that tend to interfere the training process of the federated learning, the proposed method works "invisibly" on the server side. The experimental results demonstrate the effectiveness of the proposed attacking approach and the superior to the state-of-the-art.
cs.LG↗
Long time behavior of Alfvén waves in a flowing plasma: mathematical analysis on the generation of the magnetic island
In this paper, we consider the generation of magnetic island for the linearized MHD equations around the steady flowing plasma with velocity field $U_s=(u(y),0)$ and magnetic field $H_s=(b(y),0)$ in the finite channel.
math.AP↗
Linear inviscid damping for the $β$-plane equation
In this paper, we study the linear inviscid damping for the linearized $β$-plane equation around shear flows. We develop a new method to give the explicit decay rate of the velocity for a class of monotone shear flows. This method is based on the space-time estimate and the vector field method in sprit of the wave equation. For general shear flows including the Sinus flow, we also prove the linear damping by establishing the limiting absorption principle, which is based on the compactness method introduced by Wei-Zhang-Zhao in \cite{WZZ2}. The main difficulty is that the Rayleigh-Kuo equation has more singular points due to the Coriolis effects so that the compactness argument becomes more involved and delicate.
math.AP↗
Transition threshold for the 2-D Couette flow in a finite channel
In this paper, we study the transition threshold problem for the 2-D Navier-Stokes equations around the Couette flow $(y,0)$ at large Reynolds number $Re$ in a finite channel. We develop a systematic method to establish the resolvent estimates of the linearized operator and space-time estimates of the linearized Navier-Stokes equations. In particular, three kinds of important effects: enhanced dissipation, inviscid damping and boundary layer, are integrated into the space-time estimates in a sharp form. As an application, we prove that if the initial velocity $v_0$ satisfies $\|v_0-(y, 0)\|_{H^2}\le cRe^{-\frac 12}$ for some small $c$ independent of $Re$, then the solution of the 2-D Navier-Stokes equations remains within $O(Re^{-\frac 12})$ of the Couette flow for any time.
math.AP↗
Reference-Conditioned Super-Resolution by Neural Texture Transfer
With the recent advancement in deep learning, we have witnessed a great progress in single image super-resolution. However, due to the significant information loss of the image downscaling process, it has become extremely challenging to further advance the state-of-the-art, especially for large upscaling factors. This paper explores a new research direction in super resolution, called reference-conditioned super-resolution, in which a reference image containing desired high-resolution texture details is provided besides the low-resolution image. We focus on transferring the high-resolution texture from reference images to the super-resolution process without the constraint of content similarity between reference and target images, which is a key difference from previous example-based methods. Inspired by recent work on image stylization, we address the problem via neural texture transfer. We design an end-to-end trainable deep model which generates detail enriched results by adaptively fusing the content from the low-resolution image with the texture patterns from the reference image. We create a benchmark dataset for the general research of reference-based super-resolution, which contains reference images paired with low-resolution inputs with varying degrees of similarity. Both objective and subjective evaluations demonstrate the great potential of using reference images as well as the superiority of our results over other state-of-the-art methods.
cs.CV↗
Transition threshold for the 3D Couette flow in Sobolev space
In this paper, we study the transition threshold of the 3D Couette flow in Sobolev space at high Reynolds number $\text{Re}$. It was proved that if the initial velocity $v_0$ satisfies $\|v_0-(y,0,0)\|_{H^2}\le c_0\text{Re}^{-1}$, then the solution of the 3D Navier-Stokes equations is global in time and does not transition away from the Couette flow. This result confirms the transition threshold conjecture in physical literatures.
math.AP↗
Well-posedness of the free boundary problem in incompressible elastodynamics
In this paper, we prove the local well-posedness of the free boundary problem in incompressible elastodynamics under a natural stability condition, which ensures that the evolution equation describing the free boundary is strictly hyperbolic. Our result gives a rigorous confirmation that the elasticity has a stabilizing effect on the Rayleigh-Taylor instability.
math.AP↗
Decoupled Learning for Conditional Adversarial Networks
Incorporating encoding-decoding nets with adversarial nets has been widely adopted in image generation tasks. We observe that the state-of-the-art achievements were obtained by carefully balancing the reconstruction loss and adversarial loss, and such balance shifts with different network structures, datasets, and training strategies. Empirical studies have demonstrated that an inappropriate weight between the two losses may cause instability, and it is tricky to search for the optimal setting, especially when lacking prior knowledge on the data and network. This paper gives the first attempt to relax the need of manual balancing by proposing the concept of \textit{decoupled learning}, where a novel network structure is designed that explicitly disentangles the backpropagation paths of the two losses. Experimental results demonstrate the effectiveness, robustness, and generality of the proposed method. The other contribution of the paper is the design of a new evaluation metric to measure the image quality of generative models. We propose the so-called \textit{normalized relative discriminative score} (NRDS), which introduces the idea of relative comparison, rather than providing absolute estimates like existing metrics.
cs.CV↗
Pseudospectral bound and transition threshold for the 3D Kolmogorov flow
In this paper, we establish the pseudospectral bound for the linearized operator of the Navier-Stokes equations around the 3D Kolmogorov flow. Using the pseudospectral bound and the wave operator method introduced in [LWZ], we prove the sharp enhanced dissipation rate for the linearized Navier-Stokes equations. As an application, we prove that if the initial velocity satisfies $\big\| U_0-\big(k_f^{-2}\sin(k_fy),0,0\big)\big\|_{H^2}\le cν^{\frac{7}{4}}$ ($ν$ the viscosity coefficient) and $k_f\in (0,1)$, then the solution does not transition away from the Kolmogorov flow.
math.AP↗
r-BTN: Cross-domain Face Composite and Synthesis from Limited Facial Patches
We start by asking an interesting yet challenging question, "If an eyewitness can only recall the eye features of the suspect, such that the forensic artist can only produce a sketch of the eyes (e.g., the top-left sketch shown in Fig. 1), can advanced computer vision techniques help generate the whole face image?" A more generalized question is that if a large proportion (e.g., more than 50%) of the face/sketch is missing, can a realistic whole face sketch/image still be estimated. Existing face completion and generation methods either do not conduct domain transfer learning or can not handle large missing area. For example, the inpainting approach tends to blur the generated region when the missing area is large (i.e., more than 50%). In this paper, we exploit the potential of deep learning networks in filling large missing region (e.g., as high as 95% missing) and generating realistic faces with high-fidelity in cross domains. We propose the recursive generation by bidirectional transformation networks (r-BTN) that recursively generates a whole face/sketch from a small sketch/face patch. The large missing area and the cross domain challenge make it difficult to generate satisfactory results using a unidirectional cross-domain learning structure. On the other hand, a forward and backward bidirectional learning between the face and sketch domains would enable recursive estimation of the missing region in an incremental manner (Fig. 1) and yield appealing results. r-BTN also adopts an adversarial constraint to encourage the generation of realistic faces/sketches. Extensive experiments have been conducted to demonstrate the superior performance from r-BTN as compared to existing potential solutions.
cs.CV↗