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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.

This paper provides a unified perspective of iterative ensemble Kalman methods, a family of derivative-free algorithms for parameter reconstruction and other related tasks. We identify, compare and develop three subfamilies of ensemble methods that differ in the objective they seek to minimize and the derivative-based optimization scheme they approximate through the ensemble. Our work emphasizes two principles for the derivation and analysis of iterative ensemble Kalman methods: statistical linearization and continuum limits. Following these guiding principles, we introduce new iterative ensemble Kalman methods that show promising numerical performance in Bayesian inverse problems, data assimilation and machine learning tasks.

This paper suggests a framework for the learning of discretizations of expensive forward models in Bayesian inverse problems. The main idea is to incorporate the parameters governing the discretization as part of the unknown to be estimated within the Bayesian machinery. We numerically show that in a variety of inverse problems arising in mechanical engineering, signal processing and the geosciences, the observations contain useful information to guide the choice of discretization.

The voting rules of the European Council (EU) under the Treaty of Lisbon became effective on 1 November 2014. Kurz \& Napel (2015) showed that the dimension of this voting system is between $7$ and $13,368$. The lower bound $7$ actually sets a new world record for the dimension of the real-world voting bodies. In this article, by finding a new way to represent the union of two weighted games as an intersection of certain weighted games (Theorem 1), we greatly reduce the upper bound $13,368$ to just $25$. We also consider what will happen to our upper bound and Kurz \& Napel's lower bound if the United Kingdom is no longer a member of the European Union Council.

On the basis of detrended fluctuation analysis (DFA), we propose a new bivariate linear regression model. This new model provides estimators of multi-scale regression coefficients to measure the dependence between variables and corresponding variables of interest with multi-scales. Numerical tests are performed to illustrate that the proposed DFA-based regression estimators are capable of accurately depicting the dependence between the variables of interest and can be used to identify different dependence at different time scales. We apply this model to analyze the PM2.5 series of three adjacent cities (Beijing, Tianjin, and Baoding) in Northern China. The estimated regression coefficients confirmed the dependence of PM2.5 among the three cities and illustrated that each city has different influence on the others at different seasons and at different time scales. Two statistics based on the scale-dependent $t$-statistic and the partial detrended cross-correlation coefficient are used to demonstrate the significance of the dependence. Three new scale-dependent evaluation indices show that the new DFA-based bivariate regression model can provide rich information on studied variables., Comment: This is a pre-print of an article published in Scientific Reports. The final authenticated version is available online at: https://www.nature.com/articles/s41598-018-25822-w

We introduce hybrid fractals as a class of fractals constructed by gluing several fractal pieces in a specific manner and study energy forms and Laplacians on them. We consider in particular a hybrid based on the $3$-level Sierpinski gasket, for which we construct explicitly an energy form with the property that it does not "capture" the $3$-level Sierpinski gasket structure. This characteristic type of energy forms that "miss" parts of the structure of the underlying space are investigated in the more general framework of finitely ramified cell structures. The spectrum of the associated Laplacian and its asymptotic behavior in two different hybrids is analyzed theoretically and numerically. A website with further numerical data analysis is available at http://www.math.cornell.edu/~harry970804/., Comment: 41 pages, 25 figures, 4 tables

Place recognition is one of the most fundamental topics in computer vision and robotics communities, where the task is to accurately and efficiently recognize the location of a given query image. Despite years of wisdom accumulated in this field, place recognition still remains an open problem due to the various ways in which the appearance of real-world places may differ. This paper presents an overview of the place recognition literature. Since condition invariant and viewpoint invariant features are essential factors to long-term robust visual place recognition system, We start with traditional image description methodology developed in the past, which exploit techniques from image retrieval field. Recently, the rapid advances of related fields such as object detection and image classification have inspired a new technique to improve visual place recognition system, i.e., convolutional neural networks (CNNs). Thus we then introduce recent progress of visual place recognition system based on CNNs to automatically learn better image representations for places. Eventually, we close with discussions and future work of place recognition., Comment: Applied Sciences (2018)