Invariant analysis and explicit solutions of the time fractional nonlinear perturbed Burgers equation

The Lie group analysis method is performed for the nonlinear perturbed Burgers equation and the time fractional nonlinear perturbed Burgers equation. All of the point symmetries of the equations are constructed. In view of the point symmetries, the vector fields of the equations are constructed. Subsequently, the symmetry reductions are investigated. In particular, some novel exact and explicit solutions are obtained

Group analysis and conservation laws of an integrable Kadomtsev–Petviashvili equation

In this paper, an integrable KP equation is studied using symmetry and conservation laws. First, on the basis of various cases of coefficients, we construct the infinitesimal generators. For the special case, we get the corresponding geometry vector fields, and then from known soliton solutions we derive new soliton solutions. In addition, the explicit power series solutions are derived. Lastly, nonlinear self-adjointness and conservation laws are constructed with symmetries

Selective-Stereo: Adaptive Frequency Information Selection for Stereo Matching

Stereo matching methods based on iterative optimization, like RAFT-Stereo and IGEV-Stereo, have evolved into a cornerstone in the field of stereo matching. However, these methods struggle to simultaneously capture high-frequency information in edges and low-frequency information in smooth regions due to the fixed receptive field. As a result, they tend to lose details, blur edges, and produce false matches in textureless areas. In this paper, we propose Selective Recurrent Unit (SRU), a novel iterative update operator for stereo matching. The SRU module can adaptively fuse hidden disparity information at multiple frequencies for edge and smooth regions. To perform adaptive fusion, we introduce a new Contextual Spatial Attention (CSA) module to generate attention maps as fusion weights. The SRU empowers the network to aggregate hidden disparity information across multiple frequencies, mitigating the risk of vital hidden disparity information loss during iterative processes. To verify SRU's universality, we apply it to representative iterative stereo matching methods, collectively referred to as Selective-Stereo. Our Selective-Stereo ranks $1^{st}$ on KITTI 2012, KITTI 2015, ETH3D, and Middlebury leaderboards among all published methods. Code is available at https://github.com/Windsrain/Selective-Stereo.Comment: Accepted to CVPR 202

Accurate and Efficient Stereo Matching via Attention Concatenation Volume

Stereo matching is a fundamental building block for many vision and robotics applications. An informative and concise cost volume representation is vital for stereo matching of high accuracy and efficiency. In this paper, we present a novel cost volume construction method, named attention concatenation volume (ACV), which generates attention weights from correlation clues to suppress redundant information and enhance matching-related information in the concatenation volume. The ACV can be seamlessly embedded into most stereo matching networks, the resulting networks can use a more lightweight aggregation network and meanwhile achieve higher accuracy. We further design a fast version of ACV to enable real-time performance, named Fast-ACV, which generates high likelihood disparity hypotheses and the corresponding attention weights from low-resolution correlation clues to significantly reduce computational and memory cost and meanwhile maintain a satisfactory accuracy. The core idea of our Fast-ACV is volume attention propagation (VAP) which can automatically select accurate correlation values from an upsampled correlation volume and propagate these accurate values to the surroundings pixels with ambiguous correlation clues. Furthermore, we design a highly accurate network ACVNet and a real-time network Fast-ACVNet based on our ACV and Fast-ACV respectively, which achieve the state-of-the-art performance on several benchmarks (i.e., our ACVNet ranks the 2nd on KITTI 2015 and Scene Flow, and the 3rd on KITTI 2012 and ETH3D among all the published methods; our Fast-ACVNet outperforms almost all state-of-the-art real-time methods on Scene Flow, KITTI 2012 and 2015 and meanwhile has better generalization ability)Comment: Accepted to TPAMI 2023. arXiv admin note: substantial text overlap with arXiv:2203.0214

Group analysis, nonlinear self-adjointness, conservation laws, and soliton solutions for the mKdV systems

We study the symmetry groups, conservation laws, solitons, and singular solitary waves of some versions of systems of the modified KdV equations

New Initiation Modes for Directed Carbonylative C-C Bond Activation:Rhodium-Catalyzed (3+1+2) Cycloadditions of Aminomethylcyclopropanes

Under carbonylative conditions, neutral Rh­(I)-systems modified with weak donor ligands (AsPh₃ or 1,4-oxathiane) undergo N-Cbz, N-benzoyl, or N-Ts directed insertion into the proximal C–C bond of amino­methyl­cyclo­propanes to generate rhodacyclo­pentanone intermediates. These are trapped by N-tethered alkenes to provide complex perhydroisoindoles

A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions

In this paper, a (2+1)-dimensional sine-Gordon equation and a sinh-Gordon equation are derived from the well-known AKNS system. Based on the Hirota bilinear method and Lie symmetry analysis, kink wave solutions and travelingwave solutions of the (2+1)-dimensional sine-Gordon equation are constructed. The traveling wave solutions of the (2+1)-dimensional sinh-Gordon equation can also be provided in a similar manner. Meanwhile, conservation laws are derived

Continual Learning in Predictive Autoscaling

Predictive Autoscaling is used to forecast the workloads of servers and prepare the resources in advance to ensure service level objectives (SLOs) in dynamic cloud environments. However, in practice, its prediction task often suffers from performance degradation under abnormal traffics caused by external events (such as sales promotional activities and applications re-configurations), for which a common solution is to re-train the model with data of a long historical period, but at the expense of high computational and storage costs. To better address this problem, we propose a replay-based continual learning method, i.e., Density-based Memory Selection and Hint-based Network Learning Model (DMSHM), using only a small part of the historical log to achieve accurate predictions. First, we discover the phenomenon of sample overlap when applying replay-based continual learning in prediction tasks. In order to surmount this challenge and effectively integrate new sample distribution, we propose a density-based sample selection strategy that utilizes kernel density estimation to calculate sample density as a reference to compute sample weight, and employs weight sampling to construct a new memory set. Then we implement hint-based network learning based on hint representation to optimize the parameters. Finally, we conduct experiments on public and industrial datasets to demonstrate that our proposed method outperforms state-of-the-art continual learning methods in terms of memory capacity and prediction accuracy. Furthermore, we demonstrate remarkable practicability of DMSHM in real industrial applications

Prompt-augmented Temporal Point Process for Streaming Event Sequence

Neural Temporal Point Processes (TPPs) are the prevalent paradigm for modeling continuous-time event sequences, such as user activities on the web and financial transactions. In real-world applications, event data is typically received in a \emph{streaming} manner, where the distribution of patterns may shift over time. Additionally, \emph{privacy and memory constraints} are commonly observed in practical scenarios, further compounding the challenges. Therefore, the continuous monitoring of a TPP to learn the streaming event sequence is an important yet under-explored problem. Our work paper addresses this challenge by adopting Continual Learning (CL), which makes the model capable of continuously learning a sequence of tasks without catastrophic forgetting under realistic constraints. Correspondingly, we propose a simple yet effective framework, PromptTPP\footnote{Our code is available at {\small \url{ https://github.com/yanyanSann/PromptTPP}}}, by integrating the base TPP with a continuous-time retrieval prompt pool. The prompts, small learnable parameters, are stored in a memory space and jointly optimized with the base TPP, ensuring that the model learns event streams sequentially without buffering past examples or task-specific attributes. We present a novel and realistic experimental setup for modeling event streams, where PromptTPP consistently achieves state-of-the-art performance across three real user behavior datasets.Comment: NeurIPS 2023 camera ready versio