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We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of nontrivial constant stationary solutions.

In this article, we consider a system of integro-differential equations in L^2(R, R^N), which contains the logarithmic Laplacian in the presence of transport terms. The linear operators associated with the system satisfy the Fredholm property. By virtue of a fixed point technique, we demonstrate the existence of solutions. We emphasize that the discussion is more complicated than that of the scalar situation as there are more cumbersome technicalities to overcome., Comment: arXiv admin note: substantial text overlap with arXiv:2404.09019

In this paper, we consider an integro-differential equation in L^2(R), which involves the logarithmic Laplacian in the presence of a drift term. The linear operator associated with the problem has the Fredholm property. By using a fixed point technique, we establish the existence of solutions.

The article is devoted to the existence of solutions of a certain system of quadratic integral equations in H^1(R, R^N). We show the existence of a perturbed solution by using a fixed point technique in the Sobolev space on the real line.

This short communication addresses the problem of elliptic localization with outlier measurements. Outliers are prevalent in various location-enabled applications, and can significantly compromise the positioning performance if not adequately handled. Instead of following the common trend of using $M$-estimation or adjusting the conventional least squares formulation by integrating extra error variables, we take a different path. Specifically, we explore the worst-case robust approximation criterion to bolster resistance of the elliptic location estimator against outliers. From a geometric standpoint, our method boils down to pinpointing the Chebyshev center of a feasible set, which is defined by the available bistatic ranges with bounded measurement errors. For a practical approach to the associated min-max problem, we convert it into the convex optimization framework of semidefinite programming (SDP). Numerical simulations confirm that our SDP-based technique can outperform a number of existing elliptic localization schemes in terms of positioning accuracy in Gaussian mixture noise.

The mystery behind the bird nest's construction is not well understood. Our study focuses on the stability of a self-supporting nest-like structure. Firstly, we derived a stable/unstable phase boundary for the structure at the fixed coefficient of friction with varying geometrical parameters through force analysis. Structures with a lower height and greater friction coefficient between rods are more stable. The theoretical phase boundary matched the experiment results well. Then we investigate the nest structure's stability under applied weight. Static structures with lower height and more rods (five>four>three) are more stable. Our theory also predicts a transition from plastic phase to elastic phase. These theoretical predictions are all confirmed by experiment. In the experiment, we also find that wet rod structures are more stable than dry ones. The structures can support up to 100 times of it's weight. Finally, we test the nest structure's stability under vibration. When there are no weights applied, we are able to identify the appropriate geometric configuration that can withstand the greatest vibration ($1g$ of vibration acceleration and vibration energy up to $4\times10^{-4}$ times of a rod's maximum potential energy). The critical vibration energy and acceleration depend on the applied weights. They are increased by two and one order of magnitude respectively under proper weight. We also make potential energy analysis to explain the stability of the structure.

Recent progress in the text-driven 3D stylization of a single object has been considerably promoted by CLIP-based methods. However, the stylization of multi-object 3D scenes is still impeded in that the image-text pairs used for pre-training CLIP mostly consist of an object. Meanwhile, the local details of multiple objects may be susceptible to omission due to the existing supervision manner primarily relying on coarse-grained contrast of image-text pairs. To overcome these challenges, we present a novel framework, dubbed TeMO, to parse multi-object 3D scenes and edit their styles under the contrast supervision at multiple levels. We first propose a Decoupled Graph Attention (DGA) module to distinguishably reinforce the features of 3D surface points. Particularly, a cross-modal graph is constructed to align the object points accurately and noun phrases decoupled from the 3D mesh and textual description. Then, we develop a Cross-Grained Contrast (CGC) supervision system, where a fine-grained loss between the words in the textual description and the randomly rendered images are constructed to complement the coarse-grained loss. Extensive experiments show that our method can synthesize high-quality stylized content and outperform the existing methods over a wide range of multi-object 3D meshes. Our code and results will be made publicly available

A fundamental limitation of object detectors is that they suffer from "spatial bias", and in particular perform less satisfactorily when detecting objects near image borders. For a long time, there has been a lack of effective ways to measure and identify spatial bias, and little is known about where it comes from and what degree it is. To this end, we present a new zone evaluation protocol, extending from the traditional evaluation to a more generalized one, which measures the detection performance over zones, yielding a series of Zone Precisions (ZPs). For the first time, we provide numerical results, showing that the object detectors perform quite unevenly across the zones. Surprisingly, the detector's performance in the 96% border zone of the image does not reach the AP value (Average Precision, commonly regarded as the average detection performance in the entire image zone). To better understand spatial bias, a series of heuristic experiments are conducted. Our investigation excludes two intuitive conjectures about spatial bias that the object scale and the absolute positions of objects barely influence the spatial bias. We find that the key lies in the human-imperceptible divergence in data patterns between objects in different zones, thus eventually forming a visible performance gap between the zones. With these findings, we finally discuss a future direction for object detection, namely, spatial disequilibrium problem, aiming at pursuing a balanced detection ability over the entire image zone. By broadly evaluating 10 popular object detectors and 5 detection datasets, we shed light on the spatial bias of object detectors. We hope this work could raise a focus on detection robustness. The source codes, evaluation protocols, and tutorials are publicly available at https://github.com/Zzh-tju/ZoneEval., Comment: Accepted by IEEE TPAMI

We aim at providing the object detection community with an efficient and performant object detector, termed YOLO-MS. The core design is based on a series of investigations on how convolutions with different kernel sizes affect the detection performance of objects at different scales. The outcome is a new strategy that can strongly enhance multi-scale feature representations of real-time object detectors. To verify the effectiveness of our strategy, we build a network architecture, termed YOLO-MS. We train our YOLO-MS on the MS COCO dataset from scratch without relying on any other large-scale datasets, like ImageNet, or pre-trained weights. Without bells and whistles, our YOLO-MS outperforms the recent state-of-the-art real-time object detectors, including YOLO-v7 and RTMDet, when using a comparable number of parameters and FLOPs. Taking the XS version of YOLO-MS as an example, with only 4.5M learnable parameters and 8.7G FLOPs, it can achieve an AP score of 43%+ on MS COCO, which is about 2%+ higher than RTMDet with the same model size. Moreover, our work can also be used as a plug-and-play module for other YOLO models. Typically, our method significantly improves the AP of YOLOv8 from 37%+ to 40%+ with even fewer parameters and FLOPs. Code is available at https://github.com/FishAndWasabi/YOLO-MS.

Knowledge Distillation (KD) has been validated as an effective model compression technique for learning compact object detectors. Existing state-of-the-art KD methods for object detection are mostly based on feature imitation. In this paper, we present a general and effective prediction mimicking distillation scheme, called CrossKD, which delivers the intermediate features of the student's detection head to the teacher's detection head. The resulting cross-head predictions are then forced to mimic the teacher's predictions. This manner relieves the student's head from receiving contradictory supervision signals from the annotations and the teacher's predictions, greatly improving the student's detection performance. Moreover, as mimicking the teacher's predictions is the target of KD, CrossKD offers more task-oriented information in contrast with feature imitation. On MS COCO, with only prediction mimicking losses applied, our CrossKD boosts the average precision of GFL ResNet-50 with 1x training schedule from 40.2 to 43.7, outperforming all existing KD methods. In addition, our method also works well when distilling detectors with heterogeneous backbones. Code is available at https://github.com/jbwang1997/CrossKD.

This paper introduces a computational framework to reconstruct and forecast a partially observed state that evolves according to an unknown or expensive-to-simulate dynamical system. Our reduced-order autodifferentiable ensemble Kalman filters (ROAD-EnKFs) learn a latent low-dimensional surrogate model for the dynamics and a decoder that maps from the latent space to the state space. The learned dynamics and decoder are then used within an ensemble Kalman filter to reconstruct and forecast the state. Numerical experiments show that if the state dynamics exhibit a hidden low-dimensional structure, ROAD-EnKFs achieve higher accuracy at lower computational cost compared to existing methods. If such structure is not expressed in the latent state dynamics, ROAD-EnKFs achieve similar accuracy at lower cost, making them a promising approach for surrogate state reconstruction and forecasting.

Semantic objects are unevenly distributed over images. In this paper, we study the spatial disequilibrium problem of modern object detectors and propose to quantify this ``spatial bias'' by measuring the detection performance over zones. Our analysis surprisingly shows that the spatial imbalance of objects has a great impact on the detection performance, limiting the robustness of detection applications. This motivates us to design a more generalized measurement, termed Spatial equilibrium Precision (SP), to better characterize the detection performance of object detectors. Furthermore, we also present a spatial equilibrium label assignment (SELA) to alleviate the spatial disequilibrium problem by injecting the prior spatial weight into the optimization process of detectors. Extensive experiments on PASCAL VOC, MS COCO, and 3 application datasets on face mask/fruit/helmet images demonstrate the advantages of our method. Our findings challenge the conventional sense of object detectors and show the indispensability of spatial equilibrium. We hope these discoveries would stimulate the community to rethink how an excellent object detector should be. All the source code, evaluation protocols, and the tutorials are publicly available at https://github.com/Zzh-tju/ZoneEval, Comment: Our source codes are publicly available at https://github.com/Zzh-tju/ZoneEval

Purpose: This study aims to develop a novel approach to extracting and measuring uncertain biomedical knowledge from scientific statements. Design/methodology/approach: Taking cardiovascular research publications in China as a sample, we extracted the SPO triples as knowledge unit and the hedging/conflicting uncertainties as the knowledge context. We introduced Information Entropy and Uncertainty Rate as potential metrics to quantity the uncertainty of biomedical knowledge claims represented at different levels, such as the SPO triples (micro level), as well as the semantic type pairs (micro-level). Findings: The results indicated that while the number of scientific publications and total SPO triples showed a liner growth, the novel SPO triples occurring per year remained stable. After examining the frequency of uncertain cue words in different part of scientific statements, we found hedging words tend to appear in conclusive and purposeful sentences, whereas conflicting terms often appear in background and act as the premise (e.g., unsettled scientific issues) of the work to be investigated. Practical implications: Our approach identified major uncertain knowledge areas, such as diagnostic biomarkers, genetic characteristics, and pharmacologic therapies surrounding cardiovascular diseases in China. These areas are suggested to be prioritized in which new hypotheses need to be verified, and disputes, conflicts, as well as contradictions to be settled further.

Data assimilation is concerned with sequentially estimating a temporally-evolving state. This task, which arises in a wide range of scientific and engineering applications, is particularly challenging when the state is high-dimensional and the state-space dynamics are unknown. This paper introduces a machine learning framework for learning dynamical systems in data assimilation. Our auto-differentiable ensemble Kalman filters (AD-EnKFs) blend ensemble Kalman filters for state recovery with machine learning tools for learning the dynamics. In doing so, AD-EnKFs leverage the ability of ensemble Kalman filters to scale to high-dimensional states and the power of automatic differentiation to train high-dimensional surrogate models for the dynamics. Numerical results using the Lorenz-96 model show that AD-EnKFs outperform existing methods that use expectation-maximization or particle filters to merge data assimilation and machine learning. In addition, AD-EnKFs are easy to implement and require minimal tuning.