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The bootstrap method aims to solve problems by imposing constraints on the space of physical observables, which often follow from physical assumptions such as positivity and symmetry. Here, we employ a bootstrap approach to study interacting electrons in the lowest Landau level by minimizing the energy as a function of the static structure factor subject to a set of constraints, bypassing the need to construct the full many-body wavefunction. This approach rigorously lower bounds the ground state energy, making it complementary to conventional variational upper bounds. We show that the lower bound we obtain is relatively tight, within at most 5\% from the ground state energy computed with exact diagonalization (ED) at small system sizes, and generally gets tighter as we include more constraints. In addition to energetics, our results reproduce the correct power law dependence of the pair correlation function at short distances and the existence of a large entanglement gap in the two-particle entanglement spectra for the Laughlin states at $\nu = 1/3$. We further identify signatures of the composite Fermi liquid state close to half-filling. This shows that the bootstrap approach is capable, in principle, of describing non-trivial gapped topologically ordered, as well as gapless, phases. At the end, we will discuss possible extensions and limitations of this approach. Our work establishes numerical bootstrap as a promising method to study many-body phases in topological bands, paving the way to its application in moir\'e platforms where the energetic competition between fractional quantum anomalous Hall, symmetry broken, and gapless states remains poorly understood., Comment: Total 24 pages. Main text: 16 pages, 7 figures

The generation and manipulation of multipartite entanglement and EPR steering in macroscopic systems not only play a fundamental role in exploring the nature of quantum mechanics, but are also at the core of current developments of various nascent quantum technologies. Here we report a theoretical method using directional injection of quantum squeezing to produce nonreciprocal multipartite entanglement and EPR steering in a three-mode optomechanical system with closed-loop coupling. We show that by directionally applying a two-photon parametric driving field with a phase-matched squeezed vacuum reservoir to an optomechanical resonator, a squeezed optical mode can be introduced for one of its input directions, thereby yielding an asymmetric enhancement of optomechanical interaction and the time-reversal symmetry breaking of the system. Based on this feature, it is found that bipartite and tripartite entanglement and the associated EPR steering of the subsystems can only be generated when the coherent driving field input from the squeezing injection direction, namely, achieving nonreciprocity in such quantum correlations. More excitingly, it is also found that by properly adjusting the squeezing parameter, the overall asymmetry of EPR steering can be stepwise driven from no-way regime, one-way regime to two-way regime. These findings, holding promise for preparing rich types of entangled quantum resources with nonreciprocal correlations, may have potential applications in the area of quantum information processing such as quantum secure direct communication and one-way quantum computing., Comment: 15 pages, 3 figures

Physics-informed neural networks (PINNs) are an emerging technique to solve partial differential equations (PDEs). In this work, we propose a simple but effective PINN approach for the phase-field model of ferroelectric microstructure evolution. This model is a time-dependent, nonlinear, and high-order PDE system of multi-physics, challenging to be solved using a baseline PINN. Considering that the acquisition of steady microstructures is one of the primary focuses in simulations of ferroelectric microstructure evolution, we simplify the time-dependent PDE system to be a static problem. This static problem, however, is ill-posed. To overcome this issue, a term originated from the law of energy dissipation is embedded into the loss function as an extra constraint for the PINN. With this modification, the PINN successfully predicts the steady ferroelectric microstructure without tracking the evolution process. In addition, although the proposed PINN approach cannot tackle the dynamic problem in a straightforward fashion, it is of benefit to the PINN prediction of the evolution process by providing labeled data. These data are crucial because they help the PINN avoid the propagation failure, a common failure mode of PINNs when predicting dynamic behaviors. The above mentioned advantages of the proposed PINN approach are demonstrated through a number of examples.

The cosmic variance on the star formation history may lead to bias to the merger rate density estimation of binary neutron star (BNS) mergers by the compact binary population synthesis. In this paper, we take the advantage of the large boxsize of the Millennium Simulation combined with the semi-analytic galaxy formation model GABE, and the parameterized population binary star evolution (BSE) model to examine how much effect will the cosmic variance introduce on the estimation of merger rate density of BNS mergers. We find that for sub-box size of $100\rm Mpc$ and $200\rm Mpc$, the variance of merger rate density $\sigma_{\rm R}/\rm R$ at different redshift is about $23\%-35\%$ and $13\%-20\%$ respectively. On one hand, as for the variance of the detection rate on BNS mergers with current LIGO-Virgo-KAGRA (LVK) detector network, this value is very small $\lesssim 10\%$, which indicates ignoring the cosmic variance is reasonable for estimating the merger rate density from current LVK observation. On the other hand, with next-generation gravitational wave detectors, it is possible to localize BNS mergers within sub-boxes possessing length of $\rm 40 Mpc$ for source redshift $z_{s}<0.2$. In such a small box, the cosmic variance of the merger rate density is significant, i.e., the value of $\sigma_{\rm R}/\rm R$ is about $\sim 55\%$. This hints that estimating the merger rate density of BNS in different sky areas may provide useful information on the cosmic variance., Comment: 7 pages, 5 figures, Accepted for Publication in ApJ

Ideal $C=1$ Chern bands exhibit a Landau level correspondence: they factorize as a lowest Landau levels and a spinor wavefunction that spans the layer index. We demonstrate that, in single Dirac moir\'e models, the spinor develops generally a Skyrme texture in real space with an associated Berry phase which compensates exactly the magnetic phase of the Landau level. For ideal bands with higher Chern numbers $C>1$, we find that $C$ color Landau levels are carried by $C$ spinors with Skyrme textures. We identify a SU(C) gauge symmetry in the color space of spinors and an emergent non-Abelian connection in real space intimately linked to the Pontryagin winding index of the layer skyrmions. They result in a total real-space Chern number of $-1$, screening the magnetic phase, irrespective of $C$ and of the number of layers. The topologically robust Skyrme texture remains remarkably intact in twisted bilayer graphene, even far from the chiral limit, and for realistic values of corrugation, making it an experimentally testable feature. We verify our predictions at the first magic angle of twisted bilayer, trilayer, and monolayer-bilayer graphene., Comment: 8+13 pages, 6 figures

With the development of deep learning techniques, deep recommendation models also achieve remarkable improvements in terms of recommendation accuracy. However, due to the large number of candidate items in practice and the high cost of preference computation, these methods also suffer from low efficiency of recommendation. The recently proposed tree-based deep recommendation models alleviate the problem by directly learning tree structure and representations under the guidance of recommendation objectives. However, such models have shortcomings. The max-heap assumption in the hierarchical tree, in which the preference for a parent node should be the maximum between the preferences for its children, is difficult to satisfy in their binary classification objectives. To this end, we propose Tree-based Deep Retrieval (TDR for short) for efficient recommendation. In TDR, all the trees generated during the training process are retained to form the forest. When learning the node representation of each tree, we have to satisfy the max-heap assumption as much as possible and mimic beam search behavior over the tree in the training stage. This is achieved by TDR to regard the training task as multi-classification over tree nodes at the same level. However, the number of tree nodes grows exponentially with levels, making us train the preference model with the guidance of the sampled-softmax technique. The experiments are conducted on real-world datasets, validating the effectiveness of the proposed preference model learning method and tree learning method.

We consider stochastic optimization when one only has access to biased stochastic oracles of the objective and the gradient, and obtaining stochastic gradients with low biases comes at high costs. This setting captures various optimization paradigms, such as conditional stochastic optimization, distributionally robust optimization, shortfall risk optimization, and machine learning paradigms, such as contrastive learning. We examine a family of multi-level Monte Carlo (MLMC) gradient methods that exploit a delicate tradeoff among bias, variance, and oracle cost. We systematically study their total sample and computational complexities for strongly convex, convex, and nonconvex objectives and demonstrate their superiority over the widely used biased stochastic gradient method. When combined with the variance reduction techniques like SPIDER, these MLMC gradient methods can further reduce the complexity in the nonconvex regime. Our results imply that a series of stochastic optimization problems with biased oracles, previously considered to be more challenging, is fundamentally no harder than the classical stochastic optimization with unbiased oracles. We also delineate the boundary conditions under which these problems become more difficult. Moreover, MLMC gradient methods significantly improve the best-known complexities in the literature for conditional stochastic optimization and shortfall risk optimization. Our extensive numerical experiments on distributionally robust optimization, pricing and staffing scheduling problems, and contrastive learning demonstrate the superior performance of MLMC gradient methods., Comment: A preliminary version of this manuscript has appeared in a conference proceeding. Please refer to Yifan Hu, Xin Chen, and Niao He. On the bias-variance-cost tradeoff of stochastic optimization. Advances in Neural Information Processing Systems, 2021

Motivated by distributed selection problems, we formulate a new variant of multi-player multi-armed bandit (MAB) model, which captures stochastic arrival of requests to each arm, as well as the policy of allocating requests to players. The challenge is how to design a distributed learning algorithm such that players select arms according to the optimal arm pulling profile (an arm pulling profile prescribes the number of players at each arm) without communicating to each other. We first design a greedy algorithm, which locates one of the optimal arm pulling profiles with a polynomial computational complexity. We also design an iterative distributed algorithm for players to commit to an optimal arm pulling profile with a constant number of rounds in expectation. We apply the explore then commit (ETC) framework to address the online setting when model parameters are unknown. We design an exploration strategy for players to estimate the optimal arm pulling profile. Since such estimates can be different across different players, it is challenging for players to commit. We then design an iterative distributed algorithm, which guarantees that players can arrive at a consensus on the optimal arm pulling profile in only M rounds. We conduct experiments to validate our algorithm., Comment: 28 pages

Despite the growing prevalence of artificial neural networks in real-world applications, their vulnerability to adversarial attacks remains a significant concern, which motivates us to investigate the robustness of machine learning models. While various heuristics aim to optimize the distributionally robust risk using the $\infty$-Wasserstein metric, such a notion of robustness frequently encounters computation intractability. To tackle the computational challenge, we develop a novel approach to adversarial training that integrates $\phi$-divergence regularization into the distributionally robust risk function. This regularization brings a notable improvement in computation compared with the original formulation. We develop stochastic gradient methods with biased oracles to solve this problem efficiently, achieving the near-optimal sample complexity. Moreover, we establish its regularization effects and demonstrate it is asymptotic equivalence to a regularized empirical risk minimization framework, by considering various scaling regimes of the regularization parameter and robustness level. These regimes yield gradient norm regularization, variance regularization, or a smoothed gradient norm regularization that interpolates between these extremes. We numerically validate our proposed method in supervised learning, reinforcement learning, and contextual learning and showcase its state-of-the-art performance against various adversarial attacks., Comment: 51 pages, 5 figures

Metaphors are common in everyday language, and the identification and understanding of metaphors are facilitated by models to achieve a better understanding of the text. Metaphors are mainly identified and generated by pre-trained models in existing research, but situations, where tenors or vehicles are not included in the metaphor, cannot be handled. The problem can be effectively solved by using Large Language Models (LLMs), but significant room for exploration remains in this early-stage research area. A multi-stage generative heuristic-enhanced prompt framework is proposed in this study to enhance the ability of LLMs to recognize tenors, vehicles, and grounds in Chinese metaphors. In the first stage, a small model is trained to obtain the required confidence score for answer candidate generation. In the second stage, questions are clustered and sampled according to specific rules. Finally, the heuristic-enhanced prompt needed is formed by combining the generated answer candidates and demonstrations. The proposed model achieved 3rd place in Track 1 of Subtask 1, 1st place in Track 2 of Subtask 1, and 1st place in both tracks of Subtask 2 at the NLPCC-2024 Shared Task 9.

Nucleic acids such as mRNA have emerged as a promising therapeutic modality with the capability of addressing a wide range of diseases. Lipid nanoparticles (LNPs) as a delivery platform for nucleic acids were used in the COVID-19 vaccines and have received much attention. While modern manufacturing processes which involve rapidly mixing an organic stream containing the lipids with an aqueous stream containing the nucleic acids are conceptually straightforward, detailed understanding of LNP formation and structure is still limited and scale-up can be challenging. Mathematical and computational methods are a promising avenue for deepening scientific understanding of the LNP formation process and facilitating improved process development and control. This article describes strategies for the mechanistic modeling of LNP formation, starting with strategies to estimate and predict important physicochemical properties of the various species such as diffusivities and solubilities. Subsequently, a framework is outlined for constructing mechanistic models of reactor- and particle-scale processes. Insights gained from the various models are mapped back to product quality attributes and process insights. Lastly, the use of the models to guide development of advanced process control and optimization strategies is discussed., Comment: 67 pages, 10 figures

We use the Phoenix simulations to study the mass assembly history and internal structures of cluster dark matter haloes ($M_{200} \gtrsim 5\times 10^{14} h^{-1}{\rm M}_\odot$). We confirm that cluster haloes grow inside-out, similar to galactic haloes. Major merger events dominate the growth of the internal region and minor mergers/diffuse accretion shape the outskirts. However, compared to galactic haloes, cluster haloes tend to have a younger and more actively evolving inner region. On average, the majority of mass (> 80%) in the inner region ($R< 0.1 r_{200}$) of Phoenix haloes is accreted after $z = 3$, while for galactic haloes, most mass in the central region has already been accreted before $z=6$. The density profiles of cluster haloes are less stable than those of galactic haloes over different radii. The enclosed mass within $50$ or $150$ kpc of all Phoenix haloes evolves substantially in the past ${\sim} 7$ Gyr, while galactic haloes remained stable during the same period. We suggest that the relatively younger and more active state explains the various observations of cluster haloes, especially in central regions., Comment: 12 pages, 11 figures, accepted for publication in MNRAS

Inductive relation prediction (IRP) -- where entities can be different during training and inference -- has shown great power for completing evolving knowledge graphs. Existing works mainly focus on using graph neural networks (GNNs) to learn the representation of the subgraph induced from the target link, which can be seen as an implicit rule-mining process to measure the plausibility of the target link. However, these methods cannot differentiate the target link and other links during message passing, hence the final subgraph representation will contain irrelevant rule information to the target link, which reduces the reasoning performance and severely hinders the applications for real-world scenarios. To tackle this problem, we propose a novel \textit{single-source edge-wise} GNN model to learn the \textbf{R}ule-induc\textbf{E}d \textbf{S}ubgraph represen\textbf{T}ations (\textbf{REST}), which encodes relevant rules and eliminates irrelevant rules within the subgraph. Specifically, we propose a \textit{single-source} initialization approach to initialize edge features only for the target link, which guarantees the relevance of mined rules and target link. Then we propose several RNN-based functions for \textit{edge-wise} message passing to model the sequential property of mined rules. REST is a simple and effective approach with theoretical support to learn the \textit{rule-induced subgraph representation}. Moreover, REST does not need node labeling, which significantly accelerates the subgraph preprocessing time by up to \textbf{11.66$\times$}. Experiments on inductive relation prediction benchmarks demonstrate the effectiveness of our REST. Our code is available at https://github.com/smart-lty/REST.

The recent Segment Anything Model (SAM) 2 has demonstrated remarkable foundational competence in semantic segmentation, with its memory mechanism and mask decoder further addressing challenges in video tracking and object occlusion, thereby achieving superior results in interactive segmentation for both images and videos. Building upon our previous empirical studies, we further explore the zero-shot segmentation performance of SAM 2 in robot-assisted surgery based on prompts, alongside its robustness against real-world corruption. For static images, we employ two forms of prompts: 1-point and bounding box, while for video sequences, the 1-point prompt is applied to the initial frame. Through extensive experimentation on the MICCAI EndoVis 2017 and EndoVis 2018 benchmarks, SAM 2, when utilizing bounding box prompts, outperforms state-of-the-art (SOTA) methods in comparative evaluations. The results with point prompts also exhibit a substantial enhancement over SAM's capabilities, nearing or even surpassing existing unprompted SOTA methodologies. Besides, SAM 2 demonstrates improved inference speed and less performance degradation against various image corruption. Although slightly unsatisfactory results remain in specific edges or regions, SAM 2's robust adaptability to 1-point prompts underscores its potential for downstream surgical tasks with limited prompt requirements., Comment: Empirical study. Previous work "SAM Meets Robotic Surgery" is accessible at: arXiv:2308.07156

Modern artificial intelligence (AI) systems are powered by foundation models. This paper presents a new set of foundation models, called Llama 3. It is a herd of language models that natively support multilinguality, coding, reasoning, and tool usage. Our largest model is a dense Transformer with 405B parameters and a context window of up to 128K tokens. This paper presents an extensive empirical evaluation of Llama 3. We find that Llama 3 delivers comparable quality to leading language models such as GPT-4 on a plethora of tasks. We publicly release Llama 3, including pre-trained and post-trained versions of the 405B parameter language model and our Llama Guard 3 model for input and output safety. The paper also presents the results of experiments in which we integrate image, video, and speech capabilities into Llama 3 via a compositional approach. We observe this approach performs competitively with the state-of-the-art on image, video, and speech recognition tasks. The resulting models are not yet being broadly released as they are still under development.

For a graph $G$, let $\mu_k(G):=\min~\{\max_{x\in S}d_G(x):~S\in \mathcal{S}_k\}$, where $\mathcal{S}_k$ is the set consisting of all independent sets $\{u_1,\ldots,u_k\}$ of $G$ such that some vertex, say $u_i$ ($1\leq i\leq k$), is at distance two from every other vertex in it. A graph $G$ is $1$-tough if for each cut set $S\subseteq V(G)$, $G-S$ has at most $|S|$ components. Recently, Shi and Shan \cite{Shi} conjectured that for each integer $k\geq 4$, being $2k$-connected is sufficient for $1$-tough $(P_2\cup kP_1)$-free graphs to be hamiltonian, which was confirmed by Xu et al. \cite{Xu} and Ota and Sanka \cite{Ota2}, respectively. In this article, we generalize the above results through the following Fan-type theorem: Let $k$ be an integer with $k\geq 2$ and let $G$ be a $1$-tough and $k$-connected $(P_2\cup kP_1)$-free graph with $\mu_{k+1}(G)\geq\frac{7k-6}{5}$, then $G$ is hamiltonian or the Petersen graph., Comment: 19 pages, 4 figures

We present an extragalactic HI 21-cm absorption lines catalog from a blind search at z $\leq$ 0.35, using drift-scan data collected in 1616.9 hours by the ongoing Commensal Radio Astronomy FasT Survey (CRAFTS) and FAST All Sky HI Survey (FASHI), which spans a sky area of 7456.8 deg$^{2}$ and covers 84,533 radio sources with a flux density greater than 12 mJy. 14 previously identified HI absorbers and 20 newly discovered HI absorbers were detected, comprising 14 associated systems, 11 intervening systems, and 9 systems with undetermined classifications. We fit HI profiles with multi-component Gaussian functions and calculate the redshift, width, flux density, optical depth, and HI column densities for each source. Through spectral stacking, the mean peak optical path, mean velocity-integrated optical path $\langle \tau\rangle$, mean FWHM and mean HI column density $\langle$ N$_{HI}\rangle$ are measured to be 0.46 and 0.34; 25.85 km/s and 4.62 km/s; 39.80 km/s and 8.95 km/s; 0.470 and 0.085 T$_{s} \times$ 10$^{20}$cm$^{-2}$K$^{-1}$, for the associated and intervening samples, respectively. Statistical analysis also reveals that associated systems tend to be hosted by red (g$-$r$>$0.7) galaxies at lower redshifts, whereas galaxies hosting intervening HI absorption are typically found at higher redshifts and are of a bluer (g$-$r$\leq$0.7) type. Additionally, it has been demonstrated that associated HI 21-cm absorptions connected to compact radio sources display higher N$_{HI}$ values compared to those linked with extended radio sources., Comment: 28 pages, 39 figures, 5 tables

Hyperspectral image classification, a task that assigns pre-defined classes to each pixel in a hyperspectral image of remote sensing scenes, often faces challenges due to the neglect of correlations between spectrally similar pixels. This oversight can lead to inaccurate edge definitions and difficulties in managing minor spectral variations in contiguous areas. To address these issues, we introduce the novel Dual-stage Spectral Supertoken Classifier (DSTC), inspired by superpixel concepts. DSTC employs spectrum-derivative-based pixel clustering to group pixels with similar spectral characteristics into spectral supertokens. By projecting the classification of these tokens onto the image space, we achieve pixel-level results that maintain regional classification consistency and precise boundary. Moreover, recognizing the diversity within tokens, we propose a class-proportion-based soft label. This label adaptively assigns weights to different categories based on their prevalence, effectively managing data distribution imbalances and enhancing classification performance. Comprehensive experiments on WHU-OHS, IP, KSC, and UP datasets corroborate the robust classification capabilities of DSTC and the effectiveness of its individual components. Code will be publicly available at https://github.com/laprf/DSTC., Comment: Accepted by ECCV 2024

Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Notably, Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations, have become a popular paradigm. With these models being usually characterized by intuition-driven design or highly intricate components, placing them within the theoretical analysis framework to distill the core concepts, helps understand the key principles that drive the functionality better and guide further development. Given this surge in interest, this article provides a comprehensive summary of the theoretical foundations and breakthroughs concerning the approximation and learning behaviors intrinsic to prevalent graph learning models. Encompassing discussions on fundamental aspects such as expressiveness power, generalization, optimization, and unique phenomena such as over-smoothing and over-squashing, this piece delves into the theoretical foundations and frontier driving the evolution of graph learning. In addition, this article also presents several challenges and further initiates discussions on possible solutions., Comment: 35pages,273references. Github link: https://github.com/minehly/awesome-paper-for-graph-learning-theory

The increasing complexity of modern very-large-scale integration (VLSI) design highlights the significance of Electronic Design Automation (EDA) technologies. Chip placement is a critical step in the EDA workflow, which positions chip modules on the canvas with the goal of optimizing performance, power, and area (PPA) metrics of final chip designs. Recent advances have demonstrated the great potential of AI-based algorithms in enhancing chip placement. However, due to the lengthy workflow of chip design, the evaluations of these algorithms often focus on intermediate surrogate metrics, which are easy to compute but frequently reveal a substantial misalignment with the end-to-end performance (i.e., the final design PPA). To address this challenge, we introduce ChiPBench, which can effectively facilitate research in chip placement within the AI community. ChiPBench is a comprehensive benchmark specifically designed to evaluate the effectiveness of existing AI-based chip placement algorithms in improving final design PPA metrics. Specifically, we have gathered 20 circuits from various domains (e.g., CPU, GPU, and microcontrollers). These designs are compiled by executing the workflow from the verilog source code, which preserves necessary physical implementation kits, enabling evaluations for the placement algorithms on their impacts on the final design PPA. We executed six state-of-the-art AI-based chip placement algorithms on these designs and plugged the results of each single-point algorithm into the physical implementation workflow to obtain the final PPA results. Experimental results show that even if intermediate metric of a single-point algorithm is dominant, while the final PPA results are unsatisfactory. We believe that our benchmark will serve as an effective evaluation framework to bridge the gap between academia and industry., Comment: A comprehensive benchmark for AI-based chip placement algorithms using end-to-end performance metrics

Interpolation-based techniques become popular in recent years, as they can improve the scalability of existing verification techniques due to their inherent modularity and local reasoning capabilities. Synthesizing Craig interpolants is the cornerstone of these techniques. In this paper, we investigate nonlinear Craig interpolant synthesis for two polynomial formulas of the general form, essentially corresponding to the underlying mathematical problem to separate two disjoint semialgebraic sets. By combining the homogenization approach with existing techniques, we prove the existence of a novel class of non-polynomial interpolants called semialgebraic interpolants. These semialgebraic interpolants subsume polynomial interpolants as a special case. To the best of our knowledge, this is the first existence result of this kind. Furthermore, we provide complete sum-of-squares characterizations for both polynomial and semialgebraic interpolants, which can be efficiently solved as semidefinite programs. Examples are provided to demonstrate the effectiveness and efficiency of our approach., Comment: 21 pages (with appendix); accepted by the 26th International Symposium on Formal Methods (FM2024)

Speech-to-text (S2T) generation systems frequently face challenges in low-resource scenarios, primarily due to the lack of extensive labeled datasets. One emerging solution is constructing virtual training samples by interpolating inputs and labels, which has notably enhanced system generalization in other domains. Despite its potential, this technique's application in S2T tasks has remained under-explored. In this paper, we delve into the utility of interpolation augmentation, guided by several pivotal questions. Our findings reveal that employing an appropriate strategy in interpolation augmentation significantly enhances performance across diverse tasks, architectures, and data scales, offering a promising avenue for more robust S2T systems in resource-constrained settings., Comment: ACL 2024 Findings

Contemporary AI applications leverage large language models (LLMs) to harness their knowledge and reasoning abilities for natural language processing tasks. This approach shares similarities with the concept of oracle Turing machines (OTMs). To capture the broader potential of these computations, including those not yet realized, we propose an extension to OTMs: the LLM-oracle machine (LLM-OM), by employing a cluster of LLMs as the oracle. Each LLM acts as a black box, capable of answering queries within its expertise, albeit with a delay. We introduce four variants of the LLM-OM: basic, augmented, fault-avoidance, and $\epsilon$-fault. The first two are commonly observed in existing AI applications. The latter two are specifically designed to address the challenges of LLM hallucinations, biases, and inconsistencies, aiming to ensure reliable outcomes., Comment: 6 pages

Combinatorial optimization (CO) is one of the most fundamental mathematical models in real-world applications. Traditional CO solvers, such as Branch-and-Bound (B&B) solvers, heavily rely on expert-designed heuristics, which are reliable but require substantial manual tuning. Recent studies have leveraged deep learning (DL) models as an alternative to capture rich feature patterns for improved performance on GPU machines. Nonetheless, the drawbacks of high training and inference costs, as well as limited interpretability, severely hinder the adoption of DL methods in real-world applications. To address these challenges, we propose a novel deep symbolic optimization learning framework that combines their advantages. Specifically, we focus on the node selection module within B&B solvers -- namely, deep symbolic optimization for node selection (Dso4NS). With data-driven approaches, Dso4NS guides the search for mathematical expressions within the high-dimensional discrete symbolic space and then incorporates the highest-performing mathematical expressions into a solver. The data-driven model captures the rich feature information in the input data and generates symbolic expressions, while the expressions deployed in solvers enable fast inference with high interpretability. Experiments demonstrate the effectiveness of Dso4NS in learning high-quality expressions, outperforming existing approaches on a CPU machine. Encouragingly, the learned CPU-based policies consistently achieve performance comparable to state-of-the-art GPU-based approaches.

Accurate flux density calibration is essential for precise analysis and interpretation of observations across different observation modes and instruments. In this research, we firstly introduce the flux calibration model incorporated in HIFAST pipeline, designed for processing HI 21-cm spectra. Furthermore, we investigate different calibration techniques and assess the dependence of the gain parameter on the time and environmental factors. A comparison is carried out in various observation modes (e.g. tracking and scanning modes) to determine the flux density gain ($G$), revealing insignificant discrepancies in $G$ among different methods. Long-term monitoring data shows a linear correlation between $G$ and atmospheric temperature. After subtracting the $G$--Temperature dependence, the dispersion of $G$ is reduced to $<$3% over a one-year time scale. The stability of the receiver response of FAST is considered sufficient to facilitate HI observations that can accommodate a moderate error in flux calibration (e.g., $>\sim5\%$) when utilizing a constant $G$ for calibration purposes. Our study will serve as a useful addition to the results provided by Jiang et al. (2020). Detailed measurement of $G$ for the 19 beams of FAST, covering the frequency range 1000 MHz -- 1500 MHz can be found on the HIFAST homepage: https://hifast.readthedocs.io/fluxgain., Comment: 14 pages, 15 figures, accepted by RAA

Recent advancements in Retrieval-Augmented Generation have significantly enhanced code completion at the repository level. Various RAG-based code completion systems are proposed based on different design choices. For instance, gaining more effectiveness at the cost of repeating the retrieval-generation process multiple times. However, the indiscriminate use of retrieval in current methods reveals issues in both efficiency and effectiveness, as a considerable portion of retrievals are unnecessary and may introduce unhelpful or even harmful suggestions to code language models. To address these challenges, we introduce CARD, a lightweight critique method designed to provide insights into the necessity of retrievals and select the optimal answer from multiple predictions. CARD can seamlessly integrate into any RAG-based code completion system. Our evaluation shows that CARD saves 21% to 46% times of retrieval for Line completion, 14% to 40% times of retrieval for API completion, and 6% to 46.5% times of retrieval for function completion respectively, while improving the accuracy. CARD reduces latency ranging from 16% to 83%. CARD is generalizable to different LMs, retrievers, and programming languages. It is lightweight with training in few seconds and inference in few milliseconds.

Image-text matching (ITM) is a fundamental problem in computer vision. The key issue lies in jointly learning the visual and textual representation to estimate their similarity accurately. Most existing methods focus on feature enhancement within modality or feature interaction across modalities, which, however, neglects the contextual information of the object representation based on the inter-object relationships that match the corresponding sentences with rich contextual semantics. In this paper, we propose a Hybrid-modal Interaction with multiple Relational Enhancements (termed \textit{Hire}) for image-text matching, which correlates the intra- and inter-modal semantics between objects and words with implicit and explicit relationship modelling. In particular, the explicit intra-modal spatial-semantic graph-based reasoning network is designed to improve the contextual representation of visual objects with salient spatial and semantic relational connectivities, guided by the explicit relationships of the objects' spatial positions and their scene graph. We use implicit relationship modelling for potential relationship interactions before explicit modelling to improve the fault tolerance of explicit relationship detection. Then the visual and textual semantic representations are refined jointly via inter-modal interactive attention and cross-modal alignment. To correlate the context of objects with the textual context, we further refine the visual semantic representation via cross-level object-sentence and word-image-based interactive attention. Extensive experiments validate that the proposed hybrid-modal interaction with implicit and explicit modelling is more beneficial for image-text matching. And the proposed \textit{Hire} obtains new state-of-the-art results on MS-COCO and Flickr30K benchmarks., Comment: 22pages, 5 Figures, 6 tables, the extension of CMSEI in WACV23, and submitted to ACM TIST. arXiv admin note: text overlap with arXiv:2210.08908

With the exceptional sensitivity of the Five-hundred-meter Aperture Spherical radio Telescope (FAST), we conducted observations of the neutral hydrogen (HI) in the circumgalactic medium of Andromeda's (M31) satellite galaxies, specifically Andromeda II, NGC 205, and NGC 185. Initially, three drift scans were executed for these satellites, with a detection limit of $4\times10^{18}$ cm$^{-2}$ ( approximately $1.88\times10^3 M_{\odot}$ of HI mass), followed by a more in-depth scan of a specific region. We discovered a C-shaped HI arc structure sharing a position and line-of-sight velocity similar to a stellar ring structure around Andromeda II, hinting at a potential connection with Andromeda II. In the context of NGC 205, we identified two mass concentrations in the northeast direction, which could be indicative of tidal streams resulting from the interaction between this galaxy and M31. These new lumps discovered could be very helpful in solving the missing interstellar medium (ISM) problem for NGC 205. Observations regarding NGC 185 are consistent with previous studies, and we did not detect any additional HI material around this galaxy. These observational results enhance our understanding of the evolution of these satellite galaxies and provide insight into their historical interactions with the galaxy M31., Comment: 9 pages, 7 figures, accepted by RAA

GitHub issue resolving recently has attracted significant attention from academia and industry. SWE-bench is proposed to measure the performance in resolving issues. In this paper, we propose CodeR, which adopts a multi-agent framework and pre-defined task graphs to Repair & Resolve reported bugs and add new features within code Repository. On SWE-bench lite, CodeR is able to solve 28.33% of issues, when submitting only once for each issue. We examine the performance impact of each design of CodeR and offer insights to advance this research direction., Comment: https://github.com/NL2Code/CodeR

Purpose: Reliability for Nerve Fiber Layer Reflectance Using Spectral Domain Optical Coherence Tomography (OCT) Methods: The study utilized OCT to scan participants with a cubic 6x6 mm disc scan. NFL reflectance were normalized by the average of bands below NFL and summarized. We selected several reference bands, including the pigment epithelium complex (PPEC), the band between NFL and Bruch's membrane (Post-NFL), and the top 50% of pixels with higher values were selected from the Post-NFL band by Post-NFL-Bright. Especially, we also included NFL attenuation coefficient (AC), which was equivalent to NFL reflectance normalized by all pixels below NFL. An experiment was designed to test the NFL reflectance against different levels of attenuation using neutral density filter (NDF). We also evaluated the within-visit and between-visit repeatability using a clinical dataset with normal and glaucoma eyes. Results: The experiment enrolled 20 healthy participants. The clinical dataset selected 22 normal and 55 glaucoma eyes with at least two visits form functional and structural OCT (FSOCT) study. The experiment showed that NFL reflectance normalized PPEC Max and Post-NFL-Bright had lowest dependence, slope=-0.77 and -1.34 dB/optical density on NDF levels, respectively. The clinical data showed that the NFL reflectance metrics normalized by Post-NFL-Bright or Post-NFL-Mean metrics had a trend of better repeatability and reproducibility than others, but the trend was not significant. All metrics demonstrated similar diagnostic accuracy (0.82-0.87), but Post-NFL-Bright provide the best result. Conclusions: The NFL reflectance normalized by the maximum in PPEC had less dependence of the global attenuation followed by Post-NFL-Bright, PPEC/Mean, Post-NFL-Mean and NFL/AC. But NFL reflectance normalized by Post-NFL-Bright had better result in two datasets., Comment: 13 pages

Fine urban change segmentation using multi-temporal remote sensing images is essential for understanding human-environment interactions in urban areas. Although there have been advances in high-quality land cover datasets that reveal the physical features of urban landscapes, the lack of fine-grained land use datasets hinders a deeper understanding of how human activities are distributed across the landscape and the impact of these activities on the environment, thus constraining proper technique development. To address this, we introduce FUSU, the first fine-grained land use change segmentation dataset for Fine-grained Urban Semantic Understanding. FUSU features the most detailed land use classification system to date, with 17 classes and 30 billion pixels of annotations. It includes bi-temporal high-resolution satellite images with 0.2-0.5 m ground sample distance and monthly optical and radar satellite time series, covering 847 km^2 across five urban areas in the southern and northern of China with different geographical features. The fine-grained land use pixel-wise annotations and high spatial-temporal resolution data provide a robust foundation for developing proper deep learning models to provide contextual insights on human activities and urbanization. To fully leverage FUSU, we propose a unified time-series architecture for both change detection and segmentation. We benchmark FUSU on various methods for several tasks. Dataset and code are available at: https://github.com/yuanshuai0914/FUSU.

We study the existence and structure of $d$-polytopes for which the number $f_1$ of edges is small compared to the number $f_0$ of vertices. Our results are more elegantly expressed in terms of the excess degree of the polytope, defined as $2f_1-df_0$. We show that the excess degree of a $d$-polytope cannot lie in the range $[d+3,2d-7]$, complementing the known result that values in the range $[1,d-3]$ are impossible. In particular, many pairs $(f_0,f_1)$ are not realised by any polytope. For $d$-polytopes with excess degree $d-2$, strong structural results are known; we establish comparable results for excess degrees $d$, $d+2$, and $2d-6$. Frequently, in polytopes with low excess degree, say at most $2d-6$, the nonsimple vertices all have the same degree and they form either a face or a missing face. We show that excess degree $d+1$ is possible only for $d=3,5$, or $7$, complementing the known result that an excess degree $d-1$ is possible only for $d=3$ or $5$., Comment: 23 pages, 3 figures

Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is desirable when applied to high-dimensional data with low-dimensional structures. The kernel max-sliced (KMS) Wasserstein distance is developed for this purpose by finding an optimal nonlinear mapping that reduces data into $1$ dimensions before computing the Wasserstein distance. However, its theoretical properties have not yet been fully developed. In this paper, we provide sharp finite-sample guarantees under milder technical assumptions compared with state-of-the-art for the KMS $p$-Wasserstein distance between two empirical distributions with $n$ samples for general $p\in[1,\infty)$. Algorithm-wise, we show that computing the KMS $2$-Wasserstein distance is NP-hard, and then we further propose a semidefinite relaxation (SDR) formulation (which can be solved efficiently in polynomial time) and provide a relaxation gap for the SDP solution. We provide numerical examples to demonstrate the good performance of our scheme for high-dimensional two-sample testing., Comment: 34 pages, 7 figures, 4 tables

Quantum geometry is a fundamental concept to characterize the local properties of quantum states. It is recently demonstrated that saturating certain quantum geometric bounds allows a topological Chern band to share many essential features with the lowest Landau level, facilitating fractionalized phases in moir\'e flat bands. In this work, we systematically extend the consequence and universality of saturated geometric bounds to arbitrary Landau levels by introducing a set of single-particle states, which we term as ``generalized Landau levels''. These generalized Landau levels exhibit exactly quantized values of integrated trace of quantum metric determined by their corresponding Landau level indices, regardless of the nonuniformity of their quantum geometric quantities. We derive all geometric quantities for individual and multiple generalized Landau levels, discuss their relations, and understand them in light of the theory of holomorphic curves and moving frames. We further propose a model by superposing few generalized Landau levels which is supposed to capture a large portion of the single-particle Hilbert space of a generic Chern band analogous to the first Landau level. Using this model, we employ exact diagonalization to identify a single-particle geometric criterion for permitting the non-Abelian Moore-Read phase, which is potentially useful for future engineering of moir\'e materials and beyond. We use a double twisted bilayer graphene model with only adjacent layer hopping term to show the existence of first generalized Landau level type narrow band and zero-field Moore-Read state at the second magic angle which serves as a promising starting point for more detailed future studies. We expect that generalized Landau levels will serve as a systematic tool for analyzing topological Chern bands and fractionalized phases therein., Comment: 40 pages, 11 figures

Understanding the nature of brittle failure in ferroelectric materials is essential, but difficult due to the complex interaction between mechanical and electrical concentrated fields near the crack tip. In this work, an extended phase-field model incorporating multiple order parameters is constructed to analyze the coupled evolution of fracture and domain behavior in ferroelectric materials. The strain gradient is incorporated into the governing equations to evaluate the impact of the flexoelectric effect during the crack propagation process. Our advanced phase-field model demonstrated that, with the consideration of the flexoelectric effect, both the crack extension rate and crack path are related to the initial polarization direction. This phenomenon is associated with the eigenstrain induced by the flexoelectric effect. This study provides in-depth insight into the fracture behavior of ferroelectric materials. The developed model framework can also be employed to investigate electromechanical coupling failures in more complex ferroelectric structures.

Deep reinforcement learning (DRL) algorithms can suffer from modeling errors between the simulation and the real world. Many studies use adversarial learning to generate perturbation during training process to model the discrepancy and improve the robustness of DRL. However, most of these approaches use a fixed parameter to control the intensity of the adversarial perturbation, which can lead to a trade-off between average performance and robustness. In fact, finding the optimal parameter of the perturbation is challenging, as excessive perturbations may destabilize training and compromise agent performance, while insufficient perturbations may not impart enough information to enhance robustness. To keep the training stable while improving robustness, we propose a simple but effective method, namely, Adaptive Adversarial Perturbation (A2P), which can dynamically select appropriate adversarial perturbations for each sample. Specifically, we propose an adaptive adversarial coefficient framework to adjust the effect of the adversarial perturbation during training. By designing a metric for the current intensity of the perturbation, our method can calculate the suitable perturbation levels based on the current relative performance. The appealing feature of our method is that it is simple to deploy in real-world applications and does not require accessing the simulator in advance. The experiments in MuJoCo show that our method can improve the training stability and learn a robust policy when migrated to different test environments. The code is available at https://github.com/Lqm00/A2P-SAC.

This paper is devoted to the problem of minimizing a sum of rational functions over a basic semialgebraic set. We provide a hierarchy of sum of squares (SOS) relaxations that is dual to the generalized moment problem approach due to Bugarin, Henrion, and Lasserre. The investigation of the dual SOS aspect offers two benefits: 1) it allows us to conduct a convergence rate analysis for the hierarchy; 2) it leads to a sign symmetry adapted hierarchy consisting of block-diagonal semidefinite relaxations. When the problem possesses correlative sparsity as well as sign symmetries, we propose sparse semidefinite relaxations by exploiting both structures. Various numerical experiments are performed to demonstrate the efficiency of our approach. Finally, an application to maximizing sums of generalized Rayleigh quotients is presented., Comment: 25 pages, 9 tables

Batched sparse (BATS) code is a network coding solution for multi-hop wireless networks with packet loss. Achieving a close-to-optimal rate relies on an optimal degree distribution. Technical challenges arise from the sensitivity of this distribution to the often empirically obtained rank distribution at the destination node. Specifically, if the empirical distribution overestimates the channel, BATS codes experience a significant rate degradation, leading to unstable rates across different runs and hence unpredictable transmission costs. Confronting this unresolved obstacle, we introduce a formulation for distributionally robust optimization in degree optimization. Deploying the resulting degree distribution resolves the instability of empirical rank distributions, ensuring a close-to-optimal rate, and unleashing the potential of applying BATS codes in real-world scenarios., Comment: 8 pages, accepted by 2024 IEEE International Symposium on Information Theory

We introduce a high-fidelity neural implicit dense visual Simultaneous Localization and Mapping (SLAM) system, termed DF-SLAM. In our work, we employ dictionary factors for scene representation, encoding the geometry and appearance information of the scene as a combination of basis and coefficient factors. Compared to neural implicit dense visual SLAM methods that directly encode scene information as features, our method exhibits superior scene detail reconstruction capabilities and more efficient memory usage, while our model size is insensitive to the size of the scene map, making our method more suitable for large-scale scenes. Additionally, we employ feature integration rendering to accelerate color rendering speed while ensuring color rendering quality, further enhancing the real-time performance of our neural SLAM method. Extensive experiments on synthetic and real-world datasets demonstrate that our method is competitive with existing state-of-the-art neural implicit SLAM methods in terms of real-time performance, localization accuracy, and scene reconstruction quality. Our source code is available at https://github.com/funcdecl/DF-SLAM.

In this paper, we propose a novel visual Semantic-Spatial Self-Highlighting Network (termed 3SHNet) for high-precision, high-efficiency and high-generalization image-sentence retrieval. 3SHNet highlights the salient identification of prominent objects and their spatial locations within the visual modality, thus allowing the integration of visual semantics-spatial interactions and maintaining independence between two modalities. This integration effectively combines object regions with the corresponding semantic and position layouts derived from segmentation to enhance the visual representation. And the modality-independence guarantees efficiency and generalization. Additionally, 3SHNet utilizes the structured contextual visual scene information from segmentation to conduct the local (region-based) or global (grid-based) guidance and achieve accurate hybrid-level retrieval. Extensive experiments conducted on MS-COCO and Flickr30K benchmarks substantiate the superior performances, inference efficiency and generalization of the proposed 3SHNet when juxtaposed with contemporary state-of-the-art methodologies. Specifically, on the larger MS-COCO 5K test set, we achieve 16.3%, 24.8%, and 18.3% improvements in terms of rSum score, respectively, compared with the state-of-the-art methods using different image representations, while maintaining optimal retrieval efficiency. Moreover, our performance on cross-dataset generalization improves by 18.6%. Data and code are available at https://github.com/XuriGe1995/3SHNet., Comment: Accepted Information Processing and Management (IP&M), 10 pages, 9 figures and 8 tables

Cutting planes (cuts) play an important role in solving mixed-integer linear programs (MILPs), which formulate many important real-world applications. Cut selection heavily depends on (P1) which cuts to prefer and (P2) how many cuts to select. Although modern MILP solvers tackle (P1)-(P2) by human-designed heuristics, machine learning carries the potential to learn more effective heuristics. However, many existing learning-based methods learn which cuts to prefer, neglecting the importance of learning how many cuts to select. Moreover, we observe that (P3) what order of selected cuts to prefer significantly impacts the efficiency of MILP solvers as well. To address these challenges, we propose a novel hierarchical sequence/set model (HEM) to learn cut selection policies. Specifically, HEM is a bi-level model: (1) a higher-level module that learns how many cuts to select, (2) and a lower-level module -- that formulates the cut selection as a sequence/set to sequence learning problem -- to learn policies selecting an ordered subset with the cardinality determined by the higher-level module. To the best of our knowledge, HEM is the first data-driven methodology that well tackles (P1)-(P3) simultaneously. Experiments demonstrate that HEM significantly improves the efficiency of solving MILPs on eleven challenging MILP benchmarks, including two Huawei's real problems., Comment: arXiv admin note: substantial text overlap with arXiv:2302.00244

Generalizing to longer sentences is important for recent Transformer-based language models. Besides algorithms manipulating explicit position features, the success of Transformers without position encodings (NoPE) provides a new way to overcome the challenge. In this paper, we study the length generalization property of NoPE. We find that although NoPE can extend to longer sequences than the commonly used explicit position encodings, it still has a limited context length. We identify a connection between the failure of NoPE's generalization and the distraction of attention distributions. We propose a parameter-efficient tuning for searching attention heads' best temperature hyper-parameters, which substantially expands NoPE's context size. Experiments on long sequence language modeling, the synthetic passkey retrieval task and real-world long context tasks show that NoPE can achieve competitive performances with state-of-the-art length generalization algorithms. The source code is publicly accessible

We present a statistical study of the properties of diffuse HI in ten nearby galaxies, comparing the HI detected by the single-dish telescope FAST (FEASTS program) and the interferometer VLA (THINGS program), respectively. The THINGS' observation missed HI with a median of 23% due to the short-spacing problem of interferometry and limited sensitivity. We extract the diffuse HI by subtracting the dense HI, which is obtained from the THINGS data with a uniform flux-density threshold, from the total HI detected by FAST. Among the sample, the median diffuse-HI fraction is 34%, and more diffuse HI is found in galaxies exhibiting more prominent tidal-interaction signatures. The diffuse HI we detected seems to be distributed in disk-like layers within a typical thickness of $1\,\text{kpc}$, different from the more halo-like diffuse HI detected around NGC 4631 in a previous study. Most of the diffuse HI is cospatial with the dense HI and has a typical column density of $10^{17.7}$-$10^{20.1}\,\text{cm}^{-2}$. The diffuse and dense HI exhibits a similar rotational motion, but the former lags by a median of 25% in at least the inner disks, and its velocity dispersions are typically twice as high. Based on a simplified estimation of circum-galactic medium properties and assuming pressure equilibrium, the volume density of diffuse HI appears to be constant within each individual galaxy, implying its role as a cooling interface. Comparing with existing models, these results are consistent with a possible link between tidal interactions, the formation of diffuse HI, and gas accretion., Comment: 45 pages, 23 figures. In press at ApJ. Data will be released at the FEASTS site upon publication

Multimodal video sentiment analysis aims to integrate multiple modal information to analyze the opinions and attitudes of speakers. Most previous work focuses on exploring the semantic interactions of intra- and inter-modality. However, these works ignore the reliability of multimodality, i.e., modalities tend to contain noise, semantic ambiguity, missing modalities, etc. In addition, previous multimodal approaches treat different modalities equally, largely ignoring their different contributions. Furthermore, existing multimodal sentiment analysis methods directly regress sentiment scores without considering ordinal relationships within sentiment categories, with limited performance. To address the aforementioned problems, we propose a trustworthy multimodal sentiment ordinal network (TMSON) to improve performance in sentiment analysis. Specifically, we first devise a unimodal feature extractor for each modality to obtain modality-specific features. Then, an uncertainty distribution estimation network is customized, which estimates the unimodal uncertainty distributions. Next, Bayesian fusion is performed on the learned unimodal distributions to obtain multimodal distributions for sentiment prediction. Finally, an ordinal-aware sentiment space is constructed, where ordinal regression is used to constrain the multimodal distributions. Our proposed TMSON outperforms baselines on multimodal sentiment analysis tasks, and empirical results demonstrate that TMSON is capable of reducing uncertainty to obtain more robust predictions., Comment: 14 pages, 9 figures, Accepted by IEEE Transactions on Circuits and Systems for Video Technology

In recent years, there has been significant attention given to the robustness assessment of neural networks. Robustness plays a critical role in ensuring reliable operation of artificial intelligence (AI) systems in complex and uncertain environments. Deep learning's robustness problem is particularly significant, highlighted by the discovery of adversarial attacks on image classification models. Researchers have dedicated efforts to evaluate robustness in diverse perturbation conditions for image recognition tasks. Robustness assessment encompasses two main techniques: robustness verification/ certification for deliberate adversarial attacks and robustness testing for random data corruptions. In this survey, we present a detailed examination of both adversarial robustness (AR) and corruption robustness (CR) in neural network assessment. Analyzing current research papers and standards, we provide an extensive overview of robustness assessment in image recognition. Three essential aspects are analyzed: concepts, metrics, and assessment methods. We investigate the perturbation metrics and range representations used to measure the degree of perturbations on images, as well as the robustness metrics specifically for the robustness conditions of classification models. The strengths and limitations of the existing methods are also discussed, and some potential directions for future research are provided., Comment: Corrected typos and grammatical errors in Section 5

Heart rate is an important physiological indicator of human health status. Existing remote heart rate measurement methods typically involve facial detection followed by signal extraction from the region of interest (ROI). These SOTA methods have three serious problems: (a) inaccuracies even failures in detection caused by environmental influences or subject movement; (b) failures for special patients such as infants and burn victims; (c) privacy leakage issues resulting from collecting face video. To address these issues, we regard the remote heart rate measurement as the process of analyzing the spatiotemporal characteristics of the optical flow signal in the video. We apply chaos theory to computer vision tasks for the first time, thus designing a brain-inspired framework. Firstly, using an artificial primary visual cortex model to extract the skin in the videos, and then calculate heart rate by time-frequency analysis on all pixels. Our method achieves Robust Skin Tracking for Heart Rate measurement, called HR-RST. The experimental results show that HR-RST overcomes the difficulty of environmental influences and effectively tracks the subject movement. Moreover, the method could extend to other body parts. Consequently, the method can be applied to special patients and effectively protect individual privacy, offering an innovative solution., Comment: 8 pages, 10 figures

This paper studies shift operators which arises from extractions of solutions for Lasserre's hierarchy. First, we establish a connection between multiplication operators and shift operators. More importantly, we derive new positive semidefinite conditions of rank-one moment sequences via shift operators, and utilize these conditions to strengthen Lasserre's hierarchy for real and complex polynomial optimization. Furthermore, we integrate the strengthening technique with correlative sparsity and sign symmetries present in polynomial optimization problems. Extensive numerical experiments show that our strengthening technique can significantly improve the bound (especially for complex polynomial optimization) and allows to achieve global optimality at lower relaxation orders, thus providing substantial computational savings and considerable speedup., Comment: 17 pages, 9 tables