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By converting low-frame-rate, low-resolution videos into high-frame-rate, high-resolution ones, space-time video super-resolution techniques can enhance visual experiences and facilitate more efficient information dissemination. We propose a convolutional neural network (CNN) for space-time video super-resolution, namely GIRNet. To generate highly accurate features and thus improve performance, the proposed network integrates a feature-level temporal interpolation module with deformable convolutions and a global spatial-temporal information-based residual convolutional long short-term memory (convLSTM) module. In the feature-level temporal interpolation module, we leverage deformable convolution, which adapts to deformations and scale variations of objects across different scene locations. This presents a more efficient solution than conventional convolution for extracting features from moving objects. Our network effectively uses forward and backward feature information to determine inter-frame offsets, leading to the direct generation of interpolated frame features. In the global spatial-temporal information-based residual convLSTM module, the first convLSTM is used to derive global spatial-temporal information from the input features, and the second convLSTM uses the previously computed global spatial-temporal information feature as its initial cell state. This second convLSTM adopts residual connections to preserve spatial information, thereby enhancing the output features. Experiments on the Vimeo90K dataset show that the proposed method outperforms state-of-the-art techniques in peak signal-to-noise-ratio (by 1.45 dB, 1.14 dB, and 0.02 dB over STARnet, TMNet, and 3DAttGAN, respectively), structural similarity index(by 0.027, 0.023, and 0.006 over STARnet, TMNet, and 3DAttGAN, respectively), and visually.

Unsupervised monocular depth estimation has received widespread attention because of its capability to train without ground truth. In real-world scenarios, the images may be blurry or noisy due to the influence of weather conditions and inherent limitations of the camera. Therefore, it is particularly important to develop a robust depth estimation model. Benefiting from the training strategies of generative networks, generative-based methods often exhibit enhanced robustness. In light of this, we employ a well-converging diffusion model among generative networks for unsupervised monocular depth estimation. Additionally, we propose a hierarchical feature-guided denoising module. This model significantly enriches the model's capacity for learning and interpreting depth distribution by fully leveraging image features to guide the denoising process. Furthermore, we explore the implicit depth within reprojection and design an implicit depth consistency loss. This loss function serves to enhance the performance of the model and ensure the scale consistency of depth within a video sequence. We conduct experiments on the KITTI, Make3D, and our self-collected SIMIT datasets. The results indicate that our approach stands out among generative-based models, while also showcasing remarkable robustness.

In this paper, we consider a sign-changing free boundary problem that comes from the boundary regularity of rotating vortex patches of the two-dimensional incompressible Euler equations. The complete classification of singular points has been obtained through establishing a new Weiss-type monotonicity formula. Upon these results, we prove that only $90^\circ$ corner type of singularity could happen at the boundary of a Lipschitz rotating vortex patch, while the other parts are $C^\infty$ smooth.

Consider the eigenvalue problem of a linear second order elliptic operator: \begin{equation} \nonumber -D\Delta \varphi -2\alpha\nabla m(x)\cdot \nabla\varphi+V(x)\varphi=\lambda\varphi\ \ \hbox{ in }\Omega, \end{equation} complemented by the Dirichlet boundary condition or the following general Robin boundary condition: $$ \frac{\partial\varphi}{\partial n}+\beta(x)\varphi=0 \ \ \hbox{ on }\partial\Omega, $$ where $\Omega\subset\mathbb{R}^N (N\geq1)$ is a bounded smooth domain, $n(x)$ is the unit exterior normal to $\partial\Omega$ at $x\in\partial\Omega$, $D>0$ and $\alpha>0$ are, respectively, the diffusion and advection coefficients, $m\in C^2(\overline\Omega),\,V\in C(\overline\Omega)$, $\beta\in C(\partial\Omega)$ are given functions, and $\beta$ allows to be positive, sign-changing or negative. In \cite{PZZ2019}, the asymptotic behavior of the principal eigenvalue of the above eigenvalue problem as $D\to0$ or $D\to\infty$ was studied. In this paper, when $N\geq2$, under proper conditions on the advection function $m$, we establish the asymptotic behavior of the principal eigenvalue as $\alpha\to\infty$, and when $N=1$, we obtain a complete characterization for such asymptotic behavior provided $m'$ changes sign at most finitely many times. Our results complement or improve those in \cite{BHN2005,CL2008,PZ2018} and also partially answer some questions raised in \cite{BHN2005}., Comment: 36 pages. Comments are welcome

Salient object detection segments attractive objects in scenes. RGB and thermal modalities provide complementary information and scribble annotations alleviate large amounts of human labor. Based on the above facts, we propose a scribble-supervised RGB-T salient object detection model. By a four-step solution (expansion, prediction, aggregation, and supervision), label-sparse challenge of scribble-supervised method is solved. To expand scribble annotations, we collect the superpixels that foreground scribbles pass through in RGB and thermal images, respectively. The expanded multi-modal labels provide the coarse object boundary. To further polish the expanded labels, we propose a prediction module to alleviate the sharpness of boundary. To play the complementary roles of two modalities, we combine the two into aggregated pseudo labels. Supervised by scribble annotations and pseudo labels, our model achieves the state-of-the-art performance on the relabeled RGBT-S dataset. Furthermore, the model is applied to RGB-D and video scribble-supervised applications, achieving consistently excellent performance., Comment: ICME2023

Crowd counting aims to estimate the number of persons in a scene. Most state-of-the-art crowd counting methods based on color images can't work well in poor illumination conditions due to invisible objects. With the widespread use of infrared cameras, crowd counting based on color and thermal images is studied. Existing methods only achieve multi-modal fusion without count objective constraint. To better excavate multi-modal information, we use count-guided multi-modal fusion and modal-guided count enhancement to achieve the impressive performance. The proposed count-guided multi-modal fusion module utilizes a multi-scale token transformer to interact two-modal information under the guidance of count information and perceive different scales from the token perspective. The proposed modal-guided count enhancement module employs multi-scale deformable transformer decoder structure to enhance one modality feature and count information by the other modality. Experiment in public RGBT-CC dataset shows that our method refreshes the state-of-the-art results. https://github.com/liuzywen/RGBTCC

In this paper, we are concerned with two SIS epidemic reaction-diffusion models with mass action infection mechanism of the form $SI$, and study the spatial profile of population distribution as the movement rate of the infected individuals is restricted to be small. For the model with a constant total population number, our results show that the susceptible population always converges to a positive constant which is indeed the minimum of the associated risk function, and the infected population either concentrates at the isolated highest-risk points or aggregates only on the highest-risk intervals once the highest-risk locations contain at least one interval. In sharp contrast, for the model with a varying total population number which is caused by the recruitment of the susceptible individuals and death of the infected individuals, our results reveal that the susceptible population converges to a positive function which is non-constant unless the associated risk function is constant, and the infected population may concentrate only at some isolated highest-risk points, or aggregate at least in a neighborhood of the highest-risk locations or occupy the whole habitat, depending on the behavior of the associated risk function and even its smoothness at the highest-risk locations. Numerical simulations are performed to support and complement our theoretical findings., Comment: All comments are welcomed. 29 pages,16 figures

Goppa, in the 1970s, discovered the relation between algebraic geometry and codes, which led to the family of Goppa codes. As one of the most interesting subclasses of linear codes, the family of Goppa codes is often chosen as a key in the McEliece cryptosystem. Knowledge of the number of inequivalent binary Goppa codes for fixed parameters may facilitate in the evaluation of the security of such a cryptosystem. Let $n\geq5$ be an odd prime number, let $q=2^n$ and let $r\geq3$ be a positive integer satisfying $\gcd(r,n)=1$. The purpose of this paper is to establish an upper bound on the number of inequivalent extended irreducible binary Goppa codes of length $q+1$ and degree $r$.A potential mathematical object for this purpose is to count the number of orbits of the projective semi-linear group ${\rm PGL}_2(\mathbb{F}_q)\rtimes{\rm Gal}(\mathbb{F}_{q^r}/\mathbb{F}_2)$ on the set $\mathcal{I}_r$ of all monic irreducible polynomials of degree $r$ over the finite field $\mathbb{F}_q$. An explicit formula for the number of orbits of ${\rm PGL}_2(\mathbb{F}_q)\rtimes{\rm Gal}(\mathbb{F}_{q^r}/\mathbb{F}_2)$ on $\mathcal{I}_r$ is given, and consequently, an upper bound for the number of inequivalent extended irreducible binary Goppa codes of length $q+1$ and degree $r$ is derived. Our main result naturally contains the main results of Ryan (IEEE-TIT 2015), Huang and Yue (IEEE-TIT, 2022) and, Chen and Zhang (IEEE-TIT, 2022), which considered the cases $r=4$, $r=6$ and $\gcd(r,q^3-q)=1$ respectively., Comment: arXiv admin note: substantial text overlap with arXiv:2203.15346

The family of Goppa codes is one of the most interesting subclasses of linear codes. As the McEliece cryptosystem often chooses a random Goppa code as its key,knowledge of the number of inequivalent Goppa codes for fixed parameters may facilitate in the evaluation of the security of such a cryptosystem. In this paper we present a new approach to give an upper bound on the number of inequivalent extended irreducible binary Goppa codes. To be more specific, let $n>3$ be an odd prime number and $q=2^n$; let $r\geq3$ be a positive integer satisfying $\gcd(r,n)=1$ and $\gcd\big(r,q(q^2-1)\big)=1$. We obtain an upper bound for the number of inequivalent extended irreducible binary Goppa codes of length $q+1$ and degree $r$., Comment: This paper is already accepted by IEEE Transactions on Information Theory on March 3, 2022