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In this paper, we present an enhanced semi-analytic method for calculating quasinormal excitation factors in the eikonal regime, specifically for Schwarzschild black holes. To achieve improved accuracy in our quasinormal mode computations, we extend the Dolan and Ottewill inverse multipolar expansion technique and incorporate higher-order corrections from the WKB method of Iyer and Will. Our approach is carried out to a higher order than previous methods, thereby reducing the relative error, particularly for lower multipolar numbers. We validate our results by comparing them with those obtained using the Mano, Suzuki, and Takasugi method, demonstrating excellent agreement. A key advantage of our method is its ability to extract quasinormal excitation factors, which are crucial for accurately modeling gravitational wave signals from binary black hole mergers. This advancement provides a useful tool for future gravitational wave studies, enabling better quantification of quasinormal mode excitations and more precise identification of individual modes during black hole ringdowns., Comment: 32 pages, 4 figures, 3 tables, and 2 appendices

Epidermal skin sensors have emerged as a promising approach for continuous and noninvasive monitoring of vital health signals, but to maximize their performance, these sensors must integrate seamlessly with the skin, minimizing impedance while maintaining the skin's natural protective and regulatory functions.In this study, we introduce an imperceptible sweat sensor that achieves this seamless skin integration through interpenetrating networks formed by a porous, ultra-thin, ultra-high molecular weight polyethylene (UHMWPE) nanomembrane. Upon attachment to the skin by van der Waals force, the amphiphilic sweat extrudates infuse into the interconnected nanopores inside the hydrophobic UHWMPE nanomembrane, forming "pseudo skin" nanochannels for continuous sweat perspiration. This integration is further enhanced by the osmotic pressure generated during water evaporation. Leveraging the efficient transport of biomarkers through the "skin" channels within the porous membrane, we developed an organic electrochemical transducer (OECT) cortisol sensor via in-situ synthesis of a molecularly imprinted polymer (MIP) and poly(3,4 ethylenedioxythiophene) (PEDOT) within the nanomembrane. This demonstrates the capability to detect cortisol concentrations from 0.05 to 0.5 {\mu}M for seamless monitoring of stress levels. This work represents a significant advancement in self-adhesive sweat sensors that offer imperceptible and real-time non-invasive health monitoring capabilities.

In this paper, we consider induced subgraphs of the Hamming graph $H(n,3)$. We show that if $U \subseteq \mathbb{Z}_3^n$ and $U$ induces a subgraph of $H(n,3)$ with maximum degree at most $1$ then 1. If $U$ is disjoint from a maximum size independent set of $H(n,3)$ then $|U| \leq 3^{n-1}+1$. Moreover, all such $U$ with size $3^{n-1}+1$ are isomorphic to each other. 2. For $n \geq 6$, there exists such a $U$ with size $|U| = 3^{n-1}+18$ and this is optimal for $n = 6$. 3. If $U \cap \{x, x+e_1, x+2e_1\} \ne \phi$ for all $x \in \mathbb{Z}_3^n$ then $|U| \leq 3^{n-1} + 729$., Comment: 38 pages

The detection of gravitational waves in 2015 ushered in a new era of gravitational wave astronomy capable of probing into the strong field dynamics of black holes and neutron stars. It has opened up an exciting new window for laboratory and space tests of Einstein's theory of classical general relativity. In recent years there are two interesting proposals aimed at revealing the quantum natures of perturbative gravity: 1) theoretical predictions in how graviton noise from the early universe after the vacuum of the gravitational field was strongly squeezed by inflationary expansion; 2) experimental proposals using the quantum entanglement between two masses each in a superposition state. The first proposal invokes the stochastic properties of quantum fields, the second invokes a key concept of quantum information. An equally basic and interesting idea is to ask whether and how gravity might be responsible for a quantum system becoming classical in appearance, known as gravitational decoherence. Decoherence due to gravity is of special interest because gravity is universal. This is an important issue in macroscopic quantum phenomena. To fully appreciate these exciting developments requires a working knowledge in classical GR, QF theory and QI plus some familiarity with stochastic processes, namely, noise in quantum fields. Traditionally a new researcher may be conversant in one or two of these four subjects: GR, QFT, QI, SP, depending on his/her background. This tutorial attempts to provide the necessary connections between them, helping an engaging reader from any one of these four subjects to leapfrog to the frontier of these interdisciplinary research topics. Here we shall treat the three topics listed in the title, save gravitational entanglement, because its nature and implications proclaimed in relation to quantum gravity still contain many controversial elements., Comment: 54 pages, 2 figures

Poleward water vapor transport in the midlatitudes mainly occurs in meandering filaments of intense water vapor transport, spanning thousands of kilometers long and hundreds of kilometers wide and drifting eastward. The water vapor filaments are known as atmospheric rivers (ARs). They can cause extreme wind gusts, intense precipitation, and flooding along densely populated coastal regions. Many recent studies about ARs focused on the statistical analyses of ARs, but a process-level understanding of ARs remains elusive. Here we show that ARs are streams of air with enhanced vapor kinetic energy (VKE) and derive a governing equation for Integrated VKE (IVKE) to understand what contributes to the evolution of ARs. We find that ARs grow mainly because of potential energy conversion to kinetic energy, decay largely owing to condensation and turbulence, and the eastward drift is primarily due to horizontal advection of VKE. Our VKE framework complements the integrated vapor transport framework, which is popular for identifying ARs but lacks a prognostic equation for understanding the physical processes.

One-bit sampling has emerged as a promising technique in multiple-input multiple-output (MIMO) radar systems due to its ability to significantly reduce data volume and processing requirements. Nevertheless, current detection methods have not adequately addressed the impact of colored noise, which is frequently encountered in real scenarios. In this paper, we present a novel detection method that accounts for colored noise in MIMO radar systems. Specifically, we derive Rao's test by computing the derivative of the likelihood function with respect to the target reflectivity parameter and the Fisher information matrix, resulting in a detector that takes the form of a weighted matched filter. To ensure the constant false alarm rate (CFAR) property, we also consider noise covariance uncertainty and examine its effect on the probability of false alarm. The detection probability is also studied analytically. Simulation results demonstrate that the proposed detector provides considerable performance gains in the presence of colored noise.

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

Self-supervised frameworks for representation learning have recently stirred up interest among the remote sensing community, given their potential to mitigate the high labeling costs associated with curating large satellite image datasets. In the realm of multimodal data fusion, while the often used contrastive learning methods can help bridging the domain gap between different sensor types, they rely on data augmentations techniques that require expertise and careful design, especially for multispectral remote sensing data. A possible but rather scarcely studied way to circumvent these limitations is to use a masked image modelling based pretraining strategy. In this paper, we introduce Fus-MAE, a self-supervised learning framework based on masked autoencoders that uses cross-attention to perform early and feature-level data fusion between synthetic aperture radar and multispectral optical data - two modalities with a significant domain gap. Our empirical findings demonstrate that Fus-MAE can effectively compete with contrastive learning strategies tailored for SAR-optical data fusion and outperforms other masked-autoencoders frameworks trained on a larger corpus.

In this paper, we explore the challenges associated with biomarker identification for diagnosis purpose in biomedical experiments, and propose a novel approach to handle the above challenging scenario via the generalization of the Dantzig selector. To improve the efficiency of the regularization method, we introduce a transformation from an inherent nonlinear programming due to its nonlinear link function into a linear programming framework. We illustrate the use of of our method on an experiment with binary response, showing superior performance on biomarker identification studies when compared to their conventional analysis. Our proposed method does not merely serve as a variable/biomarker selection tool, its ranking of variable importance provides valuable reference information for practitioners to reach informed decisions regarding the prioritization of factors for further investigations.

The Cholinergic Pathways Hyperintensities Scale (CHIPS) is a visual rating scale used to assess the extent of cholinergic white matter hyperintensities in T2-FLAIR images, serving as an indicator of dementia severity. However, the manual selection of four specific slices for rating throughout the entire brain is a time-consuming process. Our goal was to develop a deep learning-based model capable of automatically identifying the four slices relevant to CHIPS. To achieve this, we trained a 4-class slice classification model (BSCA) using the ADNI T2-FLAIR dataset (N=150) with the assistance of ResNet. Subsequently, we tested the model's performance on a local dataset (N=30). The results demonstrated the efficacy of our model, with an accuracy of 99.82% and an F1-score of 99.83%. This achievement highlights the potential impact of BSCA as an automatic screening tool, streamlining the selection of four specific T2-FLAIR slices that encompass white matter landmarks along the cholinergic pathways. Clinicians can leverage this tool to assess the risk of clinical dementia development efficiently., Comment: 8 pages, 2 figures, 2 tables

Virtual Reality (VR) can support effective and scalable training of psychomotor skills in manufacturing. However, many industry training modules offer experiences that are close-ended and do not allow for human error. We aim to address this gap in VR training tools for psychomotor skills training by exploring an open-ended approach to the system design. We designed a VR training simulation prototype to perform open-ended practice of drilling using a 3-axis milling machine. The simulation employs near "end-to-end" instruction through a safety module, a setup and drilling tutorial, open-ended practice complete with warnings of mistakes and failures, and a function to assess the geometries and locations of drilled holes against an engineering drawing. We developed and conducted a user study within an undergraduate-level introductory fabrication course to investigate the impact of open-ended VR practice on learning outcomes. Study results reveal positive trends, with the VR group successfully completing the machining task of drilling at a higher rate (75% vs 64%), with fewer mistakes (1.75 vs 2.14 score), and in less time (17.67 mins vs 21.57 mins) compared to the control group. We discuss our findings and limitations and implications for the design of open-ended VR training systems for learning psychomotor skills., Comment: 10 pages, 4 figures, 9 tables

With the emerging environment-aware applications, ubiquitous sensing is expected to play a key role in future networks. In this paper, we study a 3-dimensional (3D) multi-target localization system where multiple intelligent reflecting surfaces (IRSs) are applied to create virtual line-of-sight (LoS) links that bypass the base station (BS) and targets. To fully unveil the fundamental limit of IRS for sensing, we first study a single-target-single-IRS case and propose a novel \textit{two-stage localization protocol} by controlling the on/off state of IRS. To be specific, in the IRS-off stage, we derive the Cram\'{e}r-Rao bound (CRB) of the azimuth/elevation direction-of-arrival (DoA) of the BS-target link and design a DoA estimator based on the MUSIC algorithm. In the IRS-on stage, the CRB of the azimuth/elevation DoA of the IRS-target link is derived and a simple DoA estimator based on the on-grid IRS beam scanning method is proposed. Particularly, the impact of echo signals reflected by IRS from different paths on sensing performance is analyzed. Moreover, we prove that the single-beam of the IRS is not capable of sensing, but it can be achieved with \textit{multi-beam}. Based on the two obtained DoAs, the 3D single-target location is constructed. We then extend to the multi-target-multi-IRS case and propose an \textit{IRS-adaptive sensing protocol} by controlling the on/off state of multiple IRSs, and a multi-target localization algorithm is developed. Simulation results demonstrate the effectiveness of our scheme and show that sub-meter-level positioning accuracy can be achieved., Comment: This paper has been submitted to IEEE journal for possible publication

To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the thresholding functions of these nonconvex regularizers may not have closed-form expressions and thus iterations are needed, which increases the computational loads. To solve this issue, we devise a framework to generate sparsity-inducing regularizers with closed-form thresholding functions. These regularizers are applied to low-tubal-rank tensor completion, and efficient algorithms based on the alternating direction method of multipliers are developed. Furthermore, convergence of our methods is analyzed and it is proved that the generated sequences are bounded and any limit point is a stationary point. Experimental results using synthetic and real-world datasets show that the proposed algorithms outperform the state-of-the-art methods in terms of restoration performance.

This paper presents a novel loss function referred to as hybrid ordinary-Welsch (HOW) and a new sparsity-inducing regularizer associated with HOW. We theoretically show that the regularizer is quasiconvex and that the corresponding Moreau envelope is convex. Moreover, the closed-form solution to its Moreau envelope, namely, the proximity operator, is derived. Compared with nonconvex regularizers like the lp-norm with 0

Applying half-quadratic optimization to loss functions can yield the corresponding regularizers, while these regularizers are usually not sparsity-inducing regularizers (SIRs). To solve this problem, we devise a framework to generate an SIR with closed-form proximity operator. Besides, we specify our framework using several commonly-used loss functions, and produce the corresponding SIRs, which are then adopted as nonconvex rank surrogates for low-rank matrix completion. Furthermore, algorithms based on the alternating direction method of multipliers are developed. Extensive numerical results show the effectiveness of our methods in terms of recovery performance and runtime.

M-estmators including the Welsch and Cauchy have been widely adopted for robustness against outliers, but they also down-weigh the uncontaminated data. To address this issue, we devise a framework to generate a class of nonconvex functions which only down-weigh outlier-corrupted observations. Our framework is then applied to the Welsch, Cauchy and $\ell_p$-norm functions to produce the corresponding robust loss functions. Targeting on the application of robust matrix completion, efficient algorithms based on these functions are developed and their convergence is analyzed. Finally, extensive numerical results demonstrate that the proposed methods are superior to the competitors in terms of recovery accuracy and runtime.

In this paper we study quantum field theory in impulsive plane wave spacetimes. We first analyze the geodesics and the formation of conjugate planes in these spacetimes. The behaviors of the world function and the van Vleck determinant near conjugate plane are also considered. For the quantum field, we work out the mode functions, their Bogoliubov transformations, and the construction of the Wightman functions. By examining the Wightman function near and on the conjugate plane, we show how the twofold and fourfold singularity structure of the Wigthman function arise when crossing this plane. Lastly, we come to the stochastic gravity noise kernel which is also the correlation function of the stress energy tensor of the quantum field. Its explicit form is given in terms of the world function and the van Vleck determinant. We investigate its limits for small and large geodesic distances. The leading divergent term of the noise kernel on the conjugate plane are expressed in terms of derivatives of delta functions. Similar to that of the Wightman functions, we also examine how the singularity structure of the noise kernel near the lightcone changes when crossing the conjugate plane., Comment: 33 pages

We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex} has uncovered the limitations of the widely used $\ell_1$-norm in learning sparse graphs under this model: empirically, the number of nonzero entries in the solution grows with the regularization parameter of the $\ell_1$-norm; theoretically, a large regularization parameter leads to a fully connected (densest) graph. To overcome these challenges, we propose a graph Laplacian estimation method incorporating the $\ell_0$-norm constraint. An efficient gradient projection algorithm is developed to solve the resulting optimization problem, characterized by sparsity and Laplacian constraints. Through numerical experiments with synthetic and financial time-series datasets, we demonstrate the effectiveness of the proposed method in network topology inference.

This study explores traffic patterns on Taiwanese highways during consecutive holidays and focuses on understanding Taiwanese highway traffic behavior. We propose a prediction-based detection method for finding highway traffic anomalies using reconciled ordinary least squares (OLS) forecasts and bootstrap prediction intervals. Two fundamental features of traffic flow time series -- namely, seasonality and spatial autocorrelation -- are captured by adding Fourier terms in OLS models, spatial aggregation (as a hierarchical structure mimicking the geographical division in regions, cities, and stations), and a reconciliation step. Our approach, although simple, is able to model complex traffic datasets with reasonable accuracy. Being based on OLS, it is efficient and permits avoiding the computational burden of more complex methods. Analyses of Taiwan's consecutive holidays in 2019, 2020, and 2021 (73 days) showed strong variations in anomalies across different directions and highways. Specifically, we detected some areas and highways comprising a high number of traffic anomalies (north direction-central and southern regions-highways No. 1 and 3, south direction-southern region-highway No.3), and others with generally normal traffic (east and west direction). These results could provide important decision-support information to traffic authorities.

The target sensing/localization performance is fundamentally limited by the line-of-sight link and severe signal attenuation over long distances. This paper considers a challenging scenario where the direct link between the base station (BS) and the target is blocked due to the surrounding blockages and leverages the intelligent reflecting surface (IRS) with some active sensors, termed as \textit{semi-passive IRS}, for localization. To be specific, the active sensors receive echo signals reflected by the target and apply signal processing techniques to estimate the target location. We consider the joint time-of-arrival (ToA) and direction-of-arrival (DoA) estimation for localization and derive the corresponding Cram\'{e}r-Rao bound (CRB), and then a simple ToA/DoA estimator without iteration is proposed. In particular, the relationships of the CRB for ToA/DoA with the number of frames for IRS beam adjustments, number of IRS reflecting elements, and number of sensors are theoretically analyzed and demystified. Simulation results show that the proposed semi-passive IRS architecture provides sub-meter level positioning accuracy even over a long localization range from the BS to the target and also demonstrate a significant localization accuracy improvement compared to the fully passive IRS architecture., Comment: The paper has been submitted to IEEE journal for possible publication

Spectrum sensing in cognitive radio necessitates effective monitoring of wide bandwidths, which requires high-rate sampling. Traditional spectrum sensing methods employing high-precision analog-to-digital converters (ADCs) result in increased power consumption and expensive hardware costs. In this paper, we explore blind spectrum sensing utilizing one-bit ADCs. We derive a closed-form detector based on Rao's test and demonstrate its equivalence with the second-order eigenvalue-moment-ratio test. Furthermore, a near-exact distribution based on the moment-based method, and an approximate distribution in the low signal-to-noise ratio (SNR) regime with the use of the central limit theorem, are obtained. Theoretical analysis is then performed and our results show that the performance loss of the proposed detector is approximately $2$ dB ($\pi/2$) compared to detectors employing $\infty$-bit ADCs when SNR is low. This loss can be compensated for by using approximately $2.47$ ($\pi^2/4$) times more samples. In addition, we unveil that the efficiency of incoherent accumulation in one-bit detection is the square root of that of coherent accumulation. Simulation results corroborate the correctness of our theoretical calculations.

This article considers the problem of source localization (SL) using possibly unreliable time-of-arrival (TOA) based range measurements. Adopting the strategy of statistical robustification, we formulate TOA SL as minimization of a versatile loss that possesses resistance against the occurrence of outliers. We then present an alternating direction method of multipliers (ADMM) to tackle the nonconvex optimization problem in a computationally attractive iterative manner. Moreover, we prove that the solution obtained by the proposed ADMM will correspond to a Karush-Kuhn-Tucker point of the formulation when the algorithm converges, and discuss reasonable assumptions about the robust loss function under which the approach can be theoretically guaranteed to be convergent. Numerical investigations demonstrate the superiority of our method over many existing TOA SL schemes in terms of positioning accuracy and computational simplicity. In particular, the proposed ADMM achieves estimation results with mean square error performance closer to the Cram\'{e}r-Rao lower bound than its competitors in our simulations of impulsive noise environments., Comment: Should you have any questions regarding this contribution, please don't hesitate to reach out to me via email at w.x.xiong@outlook.com

With the continuous maturation and expansion of neural network technology, deep neural networks have been widely utilized as the fundamental building blocks of deep learning in a variety of applications, including speech recognition, machine translation, image processing, and the creation of recommendation systems. Therefore, many real-world complex problems can be solved by the deep learning techniques. As is known, traditional news recommendation systems mostly employ techniques based on collaborative filtering and deep learning, but the performance of these algorithms is constrained by the sparsity of the data and the scalability of the approaches. In this paper, we propose a recommendation model using granular neural network model to recommend news to appropriate channels by analyzing the properties of news. Specifically, a specified neural network serves as the foundation for the granular neural network that the model is considered to be build. Different information granularities are attributed to various types of news material, and different information granularities are released between networks in various ways. When processing data, granular output is created, which is compared to the interval values pre-set on various platforms and used to quantify the analysis's effectiveness. The analysis results could help the media to match the proper news in depth, maximize the public attention of the news and the utilization of media resources.

Classifying the same event reported by different countries is of significant importance for public opinion control and intelligence gathering. Due to the diverse types of news, relying solely on transla-tors would be costly and inefficient, while depending solely on translation systems would incur considerable performance overheads in invoking translation interfaces and storing translated texts. To address this issue, we mainly focus on the clustering problem of cross-lingual news. To be specific, we use a combination of sentence vector representations of news headlines in a mixed semantic space and the topic probability distributions of news content to represent a news article. In the training of cross-lingual models, we employ knowledge distillation techniques to fit two semantic spaces into a mixed semantic space. We abandon traditional static clustering methods like K-Means and AGNES in favor of the incremental clustering algorithm Single-Pass, which we further modify to better suit cross-lingual news clustering scenarios. Our main contributions are as follows: (1) We adopt the English standard BERT as the teacher model and XLM-Roberta as the student model, training a cross-lingual model through knowledge distillation that can represent sentence-level bilingual texts in both Chinese and English. (2) We use the LDA topic model to represent news as a combina-tion of cross-lingual vectors for headlines and topic probability distributions for con-tent, introducing concepts such as topic similarity to address the cross-lingual issue in news content representation. (3) We adapt the Single-Pass clustering algorithm for the news context to make it more applicable. Our optimizations of Single-Pass include ad-justing the distance algorithm between samples and clusters, adding cluster merging operations, and incorporating a news time parameter.