Search

Given a self-similar iterated function system $\Phi=\{ \phi_i(x)=\rho_i O_i x+t_i \}_{i=1}^m$ acting on $\mathbb{R}^d$, we can generate a parameterised family of iterated function systems by replacing each $t_i$ with a random vector in $\mathbb{R}^d$. In this paper we study whether a Lebesgue typical member of this family will satisfy the strong separation condition. Our main results show that if the similarity dimension of $\Phi$ is sufficiently small, then a Lebesgue typical member of this family will satisfy the strong separation condition., Comment: The main results are covered by Theorem 1.1 in [M. Rams and J. L. V\'ehel, Results on the dimension spectrum for self-conformal measures. Nonlinearity 20 (2007), no.4, 965-973. https://iopscience.iop.org/article/10.1088/0951-7715/20/4/009]

Retrained large language models (LLMs) have become extensively used across various sub-disciplines of natural language processing (NLP). In NLP, text classification problems have garnered considerable focus, but still faced with some limitations related to expensive computational cost, time consumption, and robust performance to unseen classes. With the proposal of chain of thought prompting (CoT), LLMs can be implemented using zero-shot learning (ZSL) with the step by step reasoning prompts, instead of conventional question and answer formats. The zero-shot LLMs in the text classification problems can alleviate these limitations by directly utilizing pretrained models to predict both seen and unseen classes. Our research primarily validates the capability of GPT models in text classification. We focus on effectively utilizing prompt strategies to various text classification scenarios. Besides, we compare the performance of zero shot LLMs with other state of the art text classification methods, including traditional machine learning methods, deep learning methods, and ZSL methods. Experimental results demonstrate that the performance of LLMs underscores their effectiveness as zero-shot text classifiers in three of the four datasets analyzed. The proficiency is especially advantageous for small businesses or teams that may not have extensive knowledge in text classification., Comment: 9 pages, 3 figures, 6 tables

The past few years have witnessed a boom of miniapps, as lightweight applications, miniapps are of great importance in the mobile internet sector. Consequently, the security of miniapps can directly impact compromising the integrity of sensitive data, posing a potential threat to user privacy. However, after a thorough review of the various research efforts in miniapp security, we found that their actions in researching the safety of miniapp web interfaces are limited. This paper proposes a triad threat model focusing on users, servers and attackers to mitigate the security risk of miniapps. By following the principle of least privilege and the direction of permission consistency, we design a novel analysis framework for the security risk assessment of miniapps by this model. Then, we analyzed the correlation between the security risk assessment and the threat model associated with the miniapp. This analysis led to identifying potential scopes and categorisations with security risks. In the case study, we identify nine major categories of vulnerability issues, such as SQL injection, logical vulnerabilities and cross-site scripting. We also assessed a total of 50,628 security risk hazards and provided specific examples., Comment: 9 pages

Manatees are aquatic mammals with voracious appetites. They rely on sea grass as the main food source, and often spend up to eight hours a day grazing. They move slow and frequently stay in group (i.e. aggregations) in shallow water to search for food, making them vulnerable to environment change and other risks. Accurate counting manatee aggregations within a region is not only biologically meaningful in observing their habit, but also crucial for designing safety rules for human boaters, divers, etc., as well as scheduling nursing, intervention, and other plans. In this paper, we propose a deep learning based crowd counting approach to automatically count number of manatees within a region, by using low quality images as input. Because manatees have unique shape and they often stay in shallow water in groups, water surface reflection, occlusion, camouflage etc. making it difficult to accurately count manatee numbers. To address the challenges, we propose to use Anisotropic Gaussian Kernel (AGK), with tunable rotation and variances, to ensure that density functions can maximally capture shapes of individual manatees in different aggregations. After that, we apply AGK kernel to different types of deep neural networks primarily designed for crowd counting, including VGG, SANet, Congested Scene Recognition network (CSRNet), MARUNet etc. to learn manatee densities and calculate number of manatees in the scene. By using generic low quality images extracted from surveillance videos, our experiment results and comparison show that AGK kernel based manatee counting achieves minimum Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). The proposed method works particularly well for counting manatee aggregations in environments with complex background., Comment: 18 pages, 8 figures, 2 tables, 3 algorithms, and it has been accepted for publication in Scientific Reports

We prove an exponential stability result for the small solutions of the Schr{\"o}dinger-Poisson equation on the circle without exterior parameters in Gevrey class. More precisely we prove that for most of the initial data of Gevrey-norm smaller than $\varepsilon$ small enough, the solution of the Schr{\"o}dinger-Poisson equation remains smaller than $2\varepsilon$ for times of order $exp(\alpha |\log \varepsilon|^2 / \log |\log \varepsilon|)$. We stress out that this is the optimal time expected for PDEs as conjectured by Jean Bourgain in [Bou04].

Cascade ranking is widely used for large-scale top-k selection problems in online advertising and recommendation systems, and learning-to-rank is an important way to optimize the models in cascade ranking. Previous works on learning-to-rank usually focus on letting the model learn the complete order or top-k order, and adopt the corresponding rank metrics (e.g. OPA and NDCG@k) as optimization targets. However, these targets can not adapt to various cascade ranking scenarios with varying data complexities and model capabilities; and the existing metric-driven methods such as the Lambda framework can only optimize a rough upper bound of limited metrics, potentially resulting in sub-optimal and performance misalignment. To address these issues, we propose a novel perspective on optimizing cascade ranking systems by highlighting the adaptability of optimization targets to data complexities and model capabilities. Concretely, we employ multi-task learning to adaptively combine the optimization of relaxed and full targets, which refers to metrics Recall@m@k and OPA respectively. We also introduce permutation matrix to represent the rank metrics and employ differentiable sorting techniques to relax hard permutation matrix with controllable approximate error bound. This enables us to optimize both the relaxed and full targets directly and more appropriately. We named this method as Adaptive Neural Ranking Framework (abbreviated as ARF). Furthermore, we give a specific practice under ARF. We use the NeuralSort to obtain the relaxed permutation matrix and draw on the variant of the uncertainty weight method in multi-task learning to optimize the proposed losses jointly. Experiments on a total of 4 public and industrial benchmarks show the effectiveness and generalization of our method, and online experiment shows that our method has significant application value., Comment: 12 pages, Accepted by www2024

The recent observations of a stable molecular condensate emerging from a condensate of bosonic atoms and related "super-chemical" dynamics have raised an intriguing set of questions. Here we provide a microscopic understanding of this unexpected stability and dynamics in atom-molecule superfluids; we show one essential element behind these phenomena is an extremely narrow Feshbach resonance in $^{133}$Cs at 19.849G. Comparing theory and experiment we demonstrate how this narrow resonance enables the dynamical creation of a large closed-channel molecular fraction superfluid, appearing in the vicinity of unitarity. Theoretically the observed superchemistry (\textit{i.e.}, Bose enhanced reactions of atoms and molecules), is found to be assisted by the formation of Cooper-like pairs of bosonic atoms that have opposite momenta. Importantly, this narrow resonance opens the possibility to explore the quantum critical point of a molecular Bose superfluid and related phenomena which would not be possible near a more typically broad Feshbach resonance., Comment: 14 pages, 8 figures; close to the published version

The polar Kerr effect and the closely related anomalous charge Hall effect are among the most distinguishing signatures of the superconducting state in Sr$_2$RuO$_4$, as well as in several other compounds. These effects are often thought to be derived from chiral superconducting pairing, and different mechanisms have been invoked for the explanation. However, the intrinsic mechanisms proposed previously often involve unrealistically strong interband Cooper pairing. In this study we show that, even without interband pairing, nonunitary superconducting states can support intrinsic anomalous charge Hall effect, thanks to the quantum geometric properties of the Bloch electrons. The key here is to have a normal-state spin Hall effect, for which a nonzero spin-orbit coupling is essential. A finite charge Hall effect then naturally arises at the onset of a spin-polarized nonunitary superconducting pairing. It depends on both the spin polarization and the normal-state electron Berry curvature, the latter of which is the imaginary part of the quantum geometric tensor of the Bloch states. Applying our results to the weakly-paired Sr$_2$RuO$_4$ we conclude that, if the reported Kerr effect is of intrinsic origin, the superconducting state is most likely nonunitary and has odd-parity. Our theory may be generalized to other superconductors that exhibit polar Kerr effect., Comment: 7+7 pages

In this paper we introduce two notions of fractal sumset properties. A compact set $K\subset\mathbb{R}^d$ is said to have the Hausdorff sumset property (HSP) if for any $\ell\in\mathbb{N}_{\ge 2}$ there exist compact sets $K_1, K_2,\ldots, K_\ell$ such that $K_1+K_2+\cdots+K_\ell\subset K$ and $\dim_H K_i=\dim_H K$ for all $1\le i\le \ell$. Analogously, if we replace the Hausdorff dimension by the packing dimension in the definition of HSP, then the compact set $K\subset\mathbb{R}^d$ is said to have the packing sumset property (PSP). We show that the HSP fails for certain homogeneous self-similar sets satisfying the strong separation condition, while the PSP holds for all homogeneous self-similar sets in $\mathbb{R}^d$., Comment: 11 pages, final version