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A sequence of random variables is called exchangeable if its joint distribution is invariant under permutations. The original formulation of de Finetti's theorem says that any exchangeable sequence of $\{0,1\}$-valued random variables can be thought of as a mixture of independent and identically distributed sequences in a certain precise mathematical sense. Interpreting this statement from a convex analytic perspective, Hewitt and Savage obtained the same conclusion for more general state spaces under some topological conditions. The main contribution of this paper is in providing a new framework that explains the theorem purely as a consequence of the underlying distribution of the random variables, with no topological conditions (beyond Hausdorffness) on the state space being necessary if the distribution is Radon. We also show that it is consistent with the axioms of ZFC that de Finetti's theorem holds for all sequences of exchangeable random variables taking values in any complete metric space. The framework we use is based on nonstandard analysis. We have provided a self-contained introduction to nonstandard analysis as an appendix, thus rendering measure theoretic probability and point-set topology as the only prerequisites for this paper. Our introduction aims to develop some new ideologies that might be of interest to mathematicians, philosophers, and mathematics educators alike. Our technical tools come from nonstandard topological measure theory, in which a highlight is a new generalization of Prokhorov's theorem. Modulo such technical tools, our proof relies on properties of the empirical measures induced by hyperfinitely many identically distributed random variables -- a feature that allows us to establish de Finetti's theorem in the generality that we seek while still retaining the combinatorial intuition of proofs of simpler versions of de Finetti's theorem.

LoRa backscatter (LB) communication systems can be considered as a potential candidate for ultra low power wide area networks (LPWAN) because of their low cost and low power consumption. In this paper, we comprehensively analyze LB modulation from various aspects, i.e., temporal, spectral, and error performance characteristics. First, we propose a signal model for LB signals that accounts for the limited number of loads in the tag. Then, we investigate the spectral properties of LB signals, obtaining a closed-form expression for the power spectrum. Finally, we derived the symbol error rate (SER) of LB with two decoders, i.e., the maximum likelihood (ML) and fast Fourier transform (FFT) decoders, in both additive white Gaussian noise (AWGN) and double Nakagami-m fading channels. The spectral analysis shows that out-of-band emissions for LB satisfy the European Telecommunications Standards Institute (ETSI) regulation only when considering a relatively large number of loads. For the error performance, unlike conventional LoRa, the FFT decoder is not optimal. Nevertheless, the ML decoder can achieve a performance similar to conventional LoRa with a moderate number of loads.

In this paper, we propose a novel Kalman Filter (KF)-based uplink (UL) joint communication and sensing (JCAS) scheme, which can significantly reduce the range and location estimation errors due to the clock asynchronism between the base station (BS) and user equipment (UE). Clock asynchronism causes time-varying time offset (TO) and carrier frequency offset (CFO), leading to major challenges in uplink sensing. Unlike existing technologies, our scheme does not require knowing the location of the UE in advance, and retains the linearity of the sensing parameter estimation problem. We first estimate the angle-of-arrivals (AoAs) of multipaths and use them to spatially filter the CSI. Then, we propose a KF-based CSI enhancer that exploits the estimation of Doppler with CFO as the prior information to significantly suppress the time-varying noise-like TO terms in spatially filtered CSIs. Subsequently, we can estimate the accurate ranges of UE and the scatterers based on the KF-enhanced CSI. Finally, we identify the UE's AoA and range estimation and locate UE, then locate the dumb scatterers using the bi-static system. Simulation results validate the proposed scheme. The localization root mean square error of the proposed method is about 20 dB lower than the benchmarking scheme.

The increasingly crowded spectrum has spurred the design of joint radar-communications systems that share hardware resources and efficiently use the radio frequency spectrum. We study a general spectral coexistence scenario, wherein the channels and transmit signals of both radar and communications systems are unknown at the receiver. In this dual-blind deconvolution (DBD) problem, a common receiver admits a multi-carrier wireless communications signal that is overlaid with the radar signal reflected off multiple targets. The communications and radar channels are represented by continuous-valued range-time and Doppler velocities of multiple transmission paths and multiple targets. We exploit the sparsity of both channels to solve the highly ill-posed DBD problem by casting it into a sum of multivariate atomic norms (SoMAN) minimization. We devise a semidefinite program to estimate the unknown target and communications parameters using the theories of positive-hyperoctant trigonometric polynomials (PhTP). Our theoretical analyses show that the minimum number of samples required for near-perfect recovery is dependent on the logarithm of the maximum of number of radar targets and communications paths rather than their sum. We show that our SoMAN method and PhTP formulations are also applicable to more general scenarios such as unsynchronized transmission, the presence of noise, and multiple emitters. Numerical experiments demonstrate great performance enhancements during parameter recovery under different scenarios.

Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data dependence structure. Before applying such methods, we need to decide whether the data are elliptically distributed. Currently existing tests either focus exclusively on spherical distributions, or rely on bootstrap to determine the null distribution, or require specific forms of the alternative distribution. In this paper, we introduce a general nonparametric test for elliptical distribution based on kernel embedding of the probability measure that embodies the two properties that characterize an elliptical distribution: namely, after centering and rescaling, (1) the direction and length of the random vector are independent, and (2) the directional vector is uniformly distributed on the unit sphere. We derive the null asymptotic distribution of the test statistic via von-Mises expansion, develop the sample-level procedure to determine the rejection region, and establish the consistency and validity of the proposed test. We apply our test to a SENIC dataset with and without a transformation aimed to achieve ellipticity.

Integrated Sensing and Communication (ISAC) is an emerging technology that integrates wireless sensing and communication into a single system, transforming many applications, including cooperative mobile robotics. However, in scenarios where radio communications are unavailable, alternative approaches are needed. In this paper, we propose a new optical ISAC (OISAC) scheme for cooperative mobile robots by integrating camera sensing and screen-camera communication (SCC). Unlike previous throughput-oriented SCC designs that work with stationary SCC links, our OISAC scheme is designed for real-time control of mobile robots. It addresses new problems such as image blur and long image display delay. As a case study, we consider the leader-follower formation control problem, an essential part of cooperative mobile robotics. The proposed OISAC scheme enables the follower robot to simultaneously acquire the information shared by the leader and sense the relative pose to the leader using only RGB images captured by its onboard camera. We then design a new control law that can leverage all the information acquired by the camera to achieve stable and accurate formations. We design and conduct real-world experiments involving uniform and nonuniform motions to evaluate the proposed system and demonstrate the advantages of applying OISAC over a benchmark approach that uses extended Kalman filtering (EKF) to estimate the leader's states. Our results show that the proposed OISAC-augmented leader-follower formation system achieves better performance in terms of accuracy, stability, and robustness.

Empirical evidence demonstrates that citations received by scholarly publications follow a pattern of preferential attachment, resulting in a power-law distribution. Such asymmetry has sparked significant debate regarding the use of citations for research evaluation. However, a consensus has yet to be established concerning the historical trends in citation concentration. Are citations becoming more concentrated in a small number of articles? Or have recent geopolitical and technical changes in science led to more decentralized distributions? This ongoing debate stems from a lack of technical clarity in measuring inequality. Given the variations in citation practices across disciplines and over time, it is crucial to account for multiple factors that can influence the findings. This article explores how reference-based and citation-based approaches, uncited articles, citation inflation, the expansion of bibliometric databases, disciplinary differences, and self-citations affect the evolution of citation concentration. Our results indicate a decreasing trend in citation concentration, primarily driven by a decline in uncited articles, which, in turn, can be attributed to the growing significance of Asia and Europe. On the whole, our findings clarify current debates on citation concentration and show that, contrary to a widely-held belief, citations are increasingly scattered.

This article focuses on the near-field effect in terahertz (THz) communications and sensing systems. By equipping with extremely large-scale antenna arrays (ELAAs), the near-field region in THz systems can be possibly extended to hundreds of meters in proximity to THz transceivers, which necessitates the consideration of near-field effect in the THz band both for the communications and sensing. We first review the main characteristics of the near-field region in the THz bands. The signal propagation in the near-field region is characterized by spherical waves rather than planar waves in the far-field region. This distinction introduces a new distance dimension to the communication and sensing channels, which brings new opportunities and challenges for both THz communications and sensing. More particularly, 1) For THz communications, the near-field effect enables a new mechanism for beamforming, namely, beamfocusing, in the focusing region. Furthermore, in THz multiple-input and multiple-output (MIMO) systems, the near-field effect can be exploited to combat the multiplexing gain degradation caused by the sparse THz channels. To address the near-field beam split effect caused by the conventional frequency-independent hybrid beamforming architecture in THz wideband communications, we propose a pair of wideband beamforming optimization approaches by a new hybrid beamforming architecture based on true-time-delayers (TTDs). 2) For THz sensing, joint angle and distance sensing can be achieved in the near-field region. Additionally, the near-field beam split becomes a beneficial effect for enhancing the sensing performance by focusing on multiple possible target locations rather than a drawback encountered in communications. Finally, several topics for future research are discussed.

A community reveals the features and connections of its members that are different from those in other communities in a network. Detecting communities is of great significance in network analysis. Despite the classical spectral clustering and statistical inference methods, we notice a significant development of deep learning techniques for community detection in recent years with their advantages in handling high dimensional network data. Hence, a comprehensive overview of community detection's latest progress through deep learning is timely to both academics and practitioners. This survey devises and proposes a new taxonomy covering different categories of the state-of-the-art methods, including deep learning-based models upon deep neural networks, deep nonnegative matrix factorization and deep sparse filtering. The main category, i.e., deep neural networks, is further divided into convolutional networks, graph attention networks, generative adversarial networks and autoencoders. The survey also summarizes the popular benchmark data sets, model evaluation metrics, and open-source implementations to address experimentation settings. We then discuss the practical applications of community detection in various domains and point to implementation scenarios. Finally, we outline future directions by suggesting challenging topics in this fast-growing deep learning field.

Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.