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We study the counting function of Steklov eigenvalues on compact manifolds with boundary and obtain its upper bound involving the leading term of Weyl's law. Our estimate can be viewed as a weakened version of P\'{o}lya's Conjecture in the Steklov case on general manifolds. As a byproduct, we also obtain a description about the decay behavior of Steklov eigenfunctions near the boundary.

The cloud cover and meteorological parameters serve as fundamental criteria for the qualification of an astronomical observatory working in optical and infrared wavelengths. In this paper, we present a systematic assessment of key meteorological parameters at the Lenghu site. The datasets adopted in this study includes the meteorological parameters collected at the local weather stations at the site and in the Lenghu Town, the sky brightness at the local zenith acquired by the Sky Quality Meters and night sky all-sky images from a digital camera, the ERA5 reanalysis database and global climate monitoring data. From 2019 to 2023, the fractional observable time of photometric condition is 69.70%, 74.97%, 70.26%, 74.27% and 65.12%, respectively. The fractional observing time is inversely correlated with surface air temperature, relative humidity, precipitable water vapor, and dew temperature, demonstrating that the observing conditions are influenced by these meteorological parameters. Large-scale air-sea interactions affect the climate at Lenghu site, which in fact delivers a clue to understand the irregularity of 2023. Specifically, precipitable water vapor at Lenghu site is correlated to both the westerly wind index and the summer North Atlantic Oscillation index, the yearly average temperature of Lenghu site is observed to increase significantly during the occurrence of a strong El Ni\~no event and the relative humidity anomaly at Lenghu site is correlated to the Pacific Decadal Oscillation index. The decrease of fractional observing time in 2023 was due to the ongoing strong El Ni\~no event and relevant global climate change. We underscore the substantial role of global climate change in regulating astronomical observing conditions and the necessity for long-term continuous monitoring of the astronomical meteorological parameters at Lenghu site., Comment: accepted for publication in MNRAS

Wake and force characteristics of an oscillating cylinder in inline steady currents are investigated numerically over a wide parameter space of dimensionless oscillation amplitude ($A^* = 0.01 - 0.50$) and wavelength ($\lambda^* = 0.4 - 25$) at a fixed Reynolds number $Re = 500$. Fundamental issues addressed in this study are the interactions of wakes induced by steady approaching flow and cylinder oscillations and the influences of the governing parameters of $A^$ and $\lambda^$ on such interactions. Whilst the collinear flow is dominated by wakes induced by cylinder oscillation at $\lambda^* \leq 1.5$ and steady current at $\lambda^* \geq 10$, it exhibits characteristics of nonlinear interactions of wakes induced by the cylinder oscillation and steady current at $\lambda^* = 1.5 - 10$, such as the formation of multiple synchronized modes interleaved with desynchronized modes. The synchronized mode varies with both $\lambda^$ and $A^$, forming an inclined Arnold's tongue across $\lambda^-A^$ space. There is a wide variability of the vortex shedding pattern in each synchronized mode. Variations of different hydrodynamic force coefficients with $\lambda^$ and $A^$ are investigated with physical interpretations based on the wake characteristics. The applicability of the Morison equation in predicting inline force fluctuations is examined. We found that the Morison equation shows reasonable accuracy only for a small range of $\lambda^* \leq 1.5$. Beyond this range, its performance deteriorates due to the influence of steady current on wake characteristics., Comment: Under review in JFM

Heat diffusion describes the process by which heat flows from areas with higher temperatures to ones with lower temperatures. This concept was previously adapted to graph structures, whereby heat flows between nodes of a graph depending on the graph topology. Here, we combine the graph heat equation with the stochastic heat equation, which ultimately yields a model for multivariate time signals on a graph. We show theoretically how the model can be used to directly compute the diffusion-based connectivity structure from multivariate signals. Unlike other connectivity measures, our heat model-based approach is inherently multivariate and yields an absolute scaling factor, namely the graph thermal diffusivity, which captures the extent of heat-like graph propagation in the data. On two datasets, we show how the graph thermal diffusivity can be used to characterise Alzheimer's disease (AD). We find that the graph thermal diffusivity is lower for AD patients than healthy controls and correlates with mini mental state examination (MMSE) scores, suggesting structural impairment in patients in line with previous findings., Comment: 4 pages, 1 figure, conference paper

The prospect of future treatment warrants the development of cost-effective screening for Alzheimer's disease (AD). A promising candidate in this regard is electroencephalography (EEG), as it is one of the most economic imaging modalities. Recent efforts in EEG analysis have shifted towards leveraging spatial information, employing novel frameworks such as graph signal processing or graph neural networks. Here, we investigate the importance of spatial information relative to spectral or temporal information by varying the proportion of each dimension for AD classification. To do so, we systematically test various dimension resolution configurations on two routine EEG datasets. Our findings show that spatial information is more important than temporal information and equally valuable as spectral information. On the larger second dataset, substituting spectral with spatial information even led to an increase of 1.1% in accuracy, which emphasises the importance of spatial information for EEG-based AD classification. We argue that our resolution-based feature extraction has the potential to improve AD classification specifically, and multivariate signal classification generally., Comment: 4 pages, 3 figures, conference paper

Hair-thin optical fiber endoscopes have opened up new paradigms for advanced imaging applications in vivo. In certain applications, such as optical coherence tomography (OCT), light-shaping structures may be required on fiber facets to generate needle-like Bessel beams with large depth-of-field, while in others shorter depths of field with high lateral resolutions are preferable. In this paper, we demonstrate a novel method to fabricate light-shaping structures on optical fibres, achieved via bonding encapsulated planar diffractive lenses onto fiber facets. Diffractive metallic structures have the advantages of being simple to design, fabricate and transfer, and our encapsulation approach is scalable to multi-layer stacks. As a demonstration, we design and transfer a Fresnel zone plate and a diffractive axicon onto fiber facets, and show that the latter device generates a needle-like Bessel beam with 350 mu m focal depth. We also evaluate the imaging performance of both devices and show that the axicon fiber is able to maintain focussed images of a USAF resolution target over a 150 mu m distance. Finally, we fabricate a two-layer stack of Fresnel zone plates on a fiber and characterise the modified beam profile and demonstrate good imaging performance. We anticipate our fabrication approach could enable multi-functional complex optical structures (e.g. using plasmonics, polarization control) to be integrated onto fibers for ultra-thin advanced imaging and sensing.

We study polynomial growth holomorphic functions and forms on complete gradient shrinking Ricci solitons. By relating to the spectral data of the $f$-Laplacian, we show that the dimension of the space of polynomial growth holomorphic functions or holomorphic $(p,0)$-forms are finite. In particular, a sharp dimension estimate for the space of linear growth holomorphic functions was obtained. Under some additional curvature assumption, we prove a sharp estimate for the frequency of polynomial growth holomorphic functions, which was used to obtain dimension upper bound as a power function of the polynomial order.

E-commerce platforms usually present an ordered list, mixed with several organic items and an advertisement, in response to each user's page view request. This list, the outcome of ad auction and allocation processes, directly impacts the platform's ad revenue and gross merchandise volume (GMV). Specifically, the ad auction determines which ad is displayed and the corresponding payment, while the ad allocation decides the display positions of the advertisement and organic items. The prevalent methods of segregating the ad auction and allocation into two distinct stages face two problems: 1) Ad auction does not consider externalities, such as the influence of actual display position and context on ad Click-Through Rate (CTR); 2) The ad allocation, which utilizes the auction-winning ad's payment to determine the display position dynamically, fails to maintain incentive compatibility (IC) for the advertisement. For instance, in the auction stage employing the traditional Generalized Second Price (GSP) , even if the winning ad increases its bid, its payment remains unchanged. This implies that the advertisement cannot secure a better position and thus loses the opportunity to achieve higher utility in the subsequent ad allocation stage. Previous research often focused on one of the two stages, neglecting the two-stage problem, which may result in suboptimal outcomes..., Comment: 9 pages, 2 figures, Posting

Multivariate signals, which are measured simultaneously over time and acquired by sensor networks, are becoming increasingly common. The emerging field of graph signal processing (GSP) promises to analyse spectral characteristics of these multivariate signals, while at the same time taking the spatial structure between the time signals into account. A central idea in GSP is the graph Fourier transform, which projects a multivariate signal onto frequency-ordered graph Fourier modes, and can therefore be regarded as a spatial analog of the temporal Fourier transform. This chapter derives and discusses key concepts in GSP, with a specific focus on how the various concepts relate to one another. The experimental section focuses on the role of graph frequency in data classification, with applications to neuroimaging. To address the limited sample size of neurophysiological datasets, we introduce a minimalist simulation framework that can generate arbitrary amounts of data. Using this artificial data, we find that lower graph frequency signals are less suitable for classifying neurophysiological data as compared to higher graph frequency signals. Finally, we introduce a baseline testing framework for GSP. Employing this framework, our results suggest that GSP applications may attenuate spectral characteristics in the signals, highlighting current limitations of GSP for neuroimaging., Comment: 18 pages, 7 figures, book chapter

Graph neural networks (GNN) are increasingly used to classify EEG for tasks such as emotion recognition, motor imagery and neurological diseases and disorders. A wide range of methods have been proposed to design GNN-based classifiers. Therefore, there is a need for a systematic review and categorisation of these approaches. We exhaustively search the published literature on this topic and derive several categories for comparison. These categories highlight the similarities and differences among the methods. The results suggest a prevalence of spectral graph convolutional layers over spatial. Additionally, we identify standard forms of node features, with the most popular being the raw EEG signal and differential entropy. Our results summarise the emerging trends in GNN-based approaches for EEG classification. Finally, we discuss several promising research directions, such as exploring the potential of transfer learning methods and appropriate modelling of cross-frequency interactions., Comment: 14 pages, 3 figures

IC3 is a famous bit-level framework for safety verification. By incorporating datapath abstraction, a notable enhancement in the efficiency of hardware verification can be achieved. However, datapath abstraction entails a coarse level of abstraction where all datapath operations are approximated as uninterpreted functions. This level of abstraction, albeit useful, can lead to an increased computational burden during the verification process as it necessitates extensive exploration of redundant abstract state space. In this paper, we introduce a novel approach called datapath propagation. Our method involves leveraging concrete constant values to iteratively compute the outcomes of relevant datapath operations and their associated uninterpreted functions. Meanwhile, we generate potentially useful datapath propagation lemmas in abstract state space and tighten the datapath abstraction. With this technique, the abstract state space can be reduced, and the verification efficiency is significantly improved. We implemented the proposed approach and conducted extensive experiments. The results show promising improvements of our approach compared to the state-of-the-art verifiers.

Crowding is widely regarded as one of the most important risk factors in designing portfolio strategies. In this paper, we analyze stock crowding using network analysis of fund holdings, which is used to compute crowding scores for stocks. These scores are used to construct costless long-short portfolios, computed in a distribution-free (model-free) way and without using any numerical optimization, with desirable properties of hedge portfolios. More specifically, these long-short portfolios provide protection for both small and large market price fluctuations, due to their negative correlation with the market and positive convexity as a function of market returns. By adding our long-short portfolio to a baseline portfolio such as a traditional 60/40 portfolio, our method provides an alternative way to hedge portfolio risk including tail risk, which does not require costly option-based strategies or complex numerical optimization. The total cost of such hedging amounts to the total cost of rebalancing the hedge portfolio., Comment: 8 pages, 6 figures

Reducing noises and enhancing signal-to-noise ratios (SNRs) have become critical for designing third-generation gravitational-wave (GW) detectors with a GW strain of less than $10^{-23}$/$\rm \sqrt{Hz}$. In this paper, we propose a potential third-generation GW detector based on autocorrelative weak-value amplification (AWVA) for GW detection with a strain of $h_g =$ $4 \times 10^{-25}$/$\rm \sqrt{Hz}$. In our scheme, a GW event induces a phase difference $\Delta \phi$ by passing through an 11-bounce delay line, 10-km arm-length, zero-area Sagnac interferometer illuminated with a 1064-nm laser. Subsequently, $\Delta \phi$ is amplified as the parameter of post-selection by choosing the appropriate pre-selected state and coupling strength in AWVA. In particular, we theoretically investigate the AWVA measurements for GW detection within the frequency band of 200 Hz $\leq$ $f_g$ $\leq$ 800 Hz, considering Gaussian noises with negative-decibel SNRs. The peak response of the AWVA sensitivity $\kappa(f_g)$ occurs at frequency $f_{g, max}$ = 500 Hz, which falls within the frequency band of interest of the current third-generation GW detectors. Our simulation results indicate that AWVA can demonstrate a measurable sensitivity of $\Theta(f_g)$ within the frequency band of interest. Moreover, the robustness of WVA shows promising potential in mitigating the effects of Gaussian noises., Comment: 21 pages, 6 figures

Graph neural network (GNN) models are increasingly being used for the classification of electroencephalography (EEG) data. However, GNN-based diagnosis of neurological disorders, such as Alzheimer's disease (AD), remains a relatively unexplored area of research. Previous studies have relied on functional connectivity methods to infer brain graph structures and used simple GNN architectures for the diagnosis of AD. In this work, we propose a novel adaptive gated graph convolutional network (AGGCN) that can provide explainable predictions. AGGCN adaptively learns graph structures by combining convolution-based node feature enhancement with a correlation-based measure of power spectral density similarity. Furthermore, the gated graph convolution can dynamically weigh the contribution of various spatial scales. The proposed model achieves high accuracy in both eyes-closed and eyes-open conditions, indicating the stability of learned representations. Finally, we demonstrate that the proposed AGGCN model generates consistent explanations of its predictions that might be relevant for further study of AD-related alterations of brain networks., Comment: 16 pages, 16 figures

Video instance segmentation (VIS) aims at segmenting and tracking objects in videos. Prior methods typically generate frame-level or clip-level object instances first and then associate them by either additional tracking heads or complex instance matching algorithms. This explicit instance association approach increases system complexity and fails to fully exploit temporal cues in videos. In this paper, we design a simple, fast and yet effective query-based framework for online VIS. Relying on an instance query and proposal propagation mechanism with several specially developed components, this framework can perform accurate instance association implicitly. Specifically, we generate frame-level object instances based on a set of instance query-proposal pairs propagated from previous frames. This instance query-proposal pair is learned to bind with one specific object across frames through conscientiously developed strategies. When using such a pair to predict an object instance on the current frame, not only the generated instance is automatically associated with its precursors on previous frames, but the model gets a good prior for predicting the same object. In this way, we naturally achieve implicit instance association in parallel with segmentation and elegantly take advantage of temporal clues in videos. To show the effectiveness of our method InsPro, we evaluate it on two popular VIS benchmarks, i.e., YouTube-VIS 2019 and YouTube-VIS 2021. Without bells-and-whistles, our InsPro with ResNet-50 backbone achieves 43.2 AP and 37.6 AP on these two benchmarks respectively, outperforming all other online VIS methods., Comment: NeurIPS 2022

Although various methods have been proposed for multi-label classification, most approaches still follow the feature learning mechanism of the single-label (multi-class) classification, namely, learning a shared image feature to classify multiple labels. However, we find this One-shared-Feature-for-Multiple-Labels (OFML) mechanism is not conducive to learning discriminative label features and makes the model non-robustness. For the first time, we mathematically prove that the inferiority of the OFML mechanism is that the optimal learned image feature cannot maintain high similarities with multiple classifiers simultaneously in the context of minimizing cross-entropy loss. To address the limitations of the OFML mechanism, we introduce the One-specific-Feature-for-One-Label (OFOL) mechanism and propose a novel disentangled label feature learning (DLFL) framework to learn a disentangled representation for each label. The specificity of the framework lies in a feature disentangle module, which contains learnable semantic queries and a Semantic Spatial Cross-Attention (SSCA) module. Specifically, learnable semantic queries maintain semantic consistency between different images of the same label. The SSCA module localizes the label-related spatial regions and aggregates located region features into the corresponding label feature to achieve feature disentanglement. We achieve state-of-the-art performance on eight datasets of three tasks, \ie, multi-label classification, pedestrian attribute recognition, and continual multi-label learning., Comment: 17 pages, 9 figures

Video object detection has been an important yet challenging topic in computer vision. Traditional methods mainly focus on designing the image-level or box-level feature propagation strategies to exploit temporal information. This paper argues that with a more effective and efficient feature propagation framework, video object detectors can gain improvement in terms of both accuracy and speed. For this purpose, this paper studies object-level feature propagation, and proposes an object query propagation (QueryProp) framework for high-performance video object detection. The proposed QueryProp contains two propagation strategies: 1) query propagation is performed from sparse key frames to dense non-key frames to reduce the redundant computation on non-key frames; 2) query propagation is performed from previous key frames to the current key frame to improve feature representation by temporal context modeling. To further facilitate query propagation, an adaptive propagation gate is designed to achieve flexible key frame selection. We conduct extensive experiments on the ImageNet VID dataset. QueryProp achieves comparable accuracy with state-of-the-art methods and strikes a decent accuracy/speed trade-off. Code is available at https://github.com/hf1995/QueryProp., Comment: This paper is accepted to AAAI2022