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This paper addresses the open problem of conducting change-point analysis for interval-valued time series data using the maximum likelihood estimation (MLE) framework. Motivated by financial time series, we analyze data that includes daily opening (O), up (U), low (L), and closing (C) values, rather than just a closing value as traditionally used. To tackle this, we propose a fundamental model based on stochastic differential equations, which also serves as a transformation of other widely used models, such as the log-transformed geometric Brownian motion model. We derive the joint distribution for these interval-valued observations using the reflection principle and Girsanov's theorem. The MLE is obtained by optimizing the log-likelihood function through first and second-order derivative calculations, utilizing the Newton-Raphson algorithm. We further propose a novel parametric bootstrap method to compute confidence intervals, addressing challenges related to temporal dependency and interval-based data relationships. The performance of the model is evaluated through extensive simulations and real data analysis using S&P500 returns during the 2022 Russo-Ukrainian War. The results demonstrate that the proposed OULC model consistently outperforms the traditional OC model, offering more accurate and reliable change-point detection and parameter estimates.

In this paper, we study a very general stochastic variational inequality(SVI) having jumps, random coefficients, delay, and path dependence, in infinite dimensions. Well-posedness in terms of the existence and uniqueness of a solution is established, and a stochastic averaging principle on strong convergence of a time-explosion SVI to an averaged equation is obtained, both under non-Lipschitz conditions. We illustrate our results on general but concrete examples of finite dimension and infinite dimension respectively, which cover large classes of particle systems with electro-static repulsion, nonlinear stochastic partial differential equations with jumps, semilinear stochastic partial differential equations (especially stochastic reaction-diffusion equations) with delays, and others.

Continuous data assimilation (CDA) is a method that continuously integrates observational data into a dynamical system to improve model accuracy in real-time. The AOT algorithm is one of the most widely used methods in CDA due to its efficiency in incorporating observational data to enhance model accuracy. However, no research to date has evaluated the performance of the AOT algorithm compared to the most widely used DA method, the ensemble Kalman filter (EnKF). Hence, in this paper, we conduct an extensive numerical examination to evaluate and compare these two algorithms for CDA problems with measurement error, addressing this gap. By analyzing the one-dimensional Kuramoto-Sivashinsky equation and the two-dimensional Navier-Stokes equation, which are central to many applications and representative in CDA problems, we found a significant computational advantage of the AOT algorithm.

Genuine multipartite nonlocality and nonlocality arising in networks composed of several independent sources have been separately investigated. While some genuinely entangled states cannot be verified by violating a single Bell-type inequality, a quantum network consisting of different sources allows for the certification of the non-classicality of all sources. In this paper, we propose the first method to verify both types of nonlocality simultaneously in a single experiment. We consider a quantum network comprising a bipartite source and a tripartite source. We demonstrate that there are quantum correlations cannot be simulated if the tripartite source distributes biseparable systems while the bipartite source distributes even stronger-than-quantum systems. These correlations can be used to verify both the genuine multipartite nonlocality of generalized Greenberger-Horne-Zeilinger states and the full network nonlocality that is stronger than all the existing results. Experimentally, we observe both types of nonlocality in a high fidelity photonic quantum network by violating a single network Bell inequality., Comment: 7 pages, 3 figures

Markov random fields (MRFs) are invaluable tools across diverse fields, and spatiotemporal MRFs (STMRFs) amplify their effectiveness by integrating spatial and temporal dimensions. However, modeling spatiotemporal data introduces additional hurdles, including dynamic spatial dimensions and partial observations, prevalent in scenarios like disease spread analysis and environmental monitoring. Tracking high-dimensional targets with complex spatiotemporal interactions over extended periods poses significant challenges in accuracy, efficiency, and computational feasibility. To tackle these obstacles, we introduce the variable target MRF scalable particle filter (VT-MRF-SPF), a fully online learning algorithm designed for high-dimensional target tracking over STMRFs with varying dimensions under partial observation. We rigorously guarantee algorithm performance, explicitly indicating overcoming the curse of dimensionality. Additionally, we provide practical guidelines for tuning graphical parameters, leading to superior performance in extensive examinations., Comment: 70 pages

Since synchrotron polarization fluctuations are related to the fundamental properties of the magnetic field, we propose the polarization intensity variance to measure the Galactic interstellar medium (ISM) magnetization. We confirm the method's applicability by comparing it with the polarization angle dispersion and its reliability by measuring the underlying Alfv\'enic Mach number of MHD turbulence. With the finding of the power-law relation of $\mathcal{A} \propto M_{\rm A}^{2}$ between polarization intensity variance $\mathcal{A}$ and Alfv\'enic Mach number $M_{\rm A}$, we apply the new technique to the Canadian Galactic Plane Survey (CGPS) data, achieving Alfv\'enic Mach number of the Galactic ISM. Our results show that the low-latitude Galactic ISM is dominated by sub-Alf\'enic turbulence, with $M_{\rm A}$ approximately between 0.5 and 1.0., Comment: 10 pages, 5 figures, and 2 tables. Accepted for publication in ApJ

The COVID-19 pandemic has changed human life. To mitigate the pandemic's impacts, different regions implemented various policies to contain COVID-19 and residents showed diverse responses. These human responses in turn shaped the uneven spatial-temporal spread of COVID-19. Consequently, the human-pandemic interaction is complex, dynamic, and interconnected. Delineating the reciprocal effects between human society and the pandemic is imperative for mitigating risks from future epidemics. Geospatial big data acquired through mobile applications and sensor networks have facilitated near-real-time tracking and assessment of human responses to the pandemic, enabling a surge in researching human-pandemic interactions. However, these investigations involve inconsistent data sources, human activity indicators, relationship detection models, and analysis methods, leading to a fragmented understanding of human-pandemic dynamics. To assess the current state of human-pandemic interactions research, we conducted a synthesis study based on 67 selected publications between March 2020 and January 2023. We extracted key information from each article across six categories, e.g., research area and time, data, methodological framework, and results and conclusions. Results reveal that regression models were predominant in relationship detection, featured in 67.16% of papers. Only two papers employed spatial-temporal models, notably underrepresented in the existing literature. Studies examining the effects of policies and human mobility on the pandemic's health impacts were the most prevalent, each comprising 12 articles (17.91%). Only 3 papers (4.48%) delved into bidirectional interactions between human responses and the COVID-19 spread. These findings shed light on the need for future research to spatially and temporally model the long-term, bidirectional causal relationships within human-pandemic systems.

Expander graphs are fundamental in both computer science and mathematics, with a wide array of applications. With quantum technology reshaping our world, quantum expanders have emerged, finding numerous uses in quantum information theory. The classical expander mixing lemma plays a central role in graph theory, offering essential insights into edge distribution within graphs and aiding in the analysis of diverse network properties and algorithms. This paper establishes the quantum analogue of the classical expander mixing lemma and its converse for quantum expanders.

Binary neural networks utilize 1-bit quantized weights and activations to reduce both the model's storage demands and computational burden. However, advanced binary architectures still incorporate millions of inefficient and nonhardware-friendly full-precision multiplication operations. A&B BNN is proposed to directly remove part of the multiplication operations in a traditional BNN and replace the rest with an equal number of bit operations, introducing the mask layer and the quantized RPReLU structure based on the normalizer-free network architecture. The mask layer can be removed during inference by leveraging the intrinsic characteristics of BNN with straightforward mathematical transformations to avoid the associated multiplication operations. The quantized RPReLU structure enables more efficient bit operations by constraining its slope to be integer powers of 2. Experimental results achieved 92.30%, 69.35%, and 66.89% on the CIFAR-10, CIFAR-100, and ImageNet datasets, respectively, which are competitive with the state-of-the-art. Ablation studies have verified the efficacy of the quantized RPReLU structure, leading to a 1.14% enhancement on the ImageNet compared to using a fixed slope RLeakyReLU. The proposed add&bit-operation-only BNN offers an innovative approach for hardware-friendly network architecture., Comment: CVPR 2024 Accepted

In this paper, we study a broad class of McKean-Vlasov stochastic variational inequalities (MVSVIs), where both the drift coefficient $b$ and the diffusion coefficient $\sigma$ depend on time $t$, the state $X_t$ and its distribution $\mu_t$. We establish the strong well-posedness, when $b$ is superlinear growth and locally Lipschitz continuous, and $\sigma$ is locally H\"older continuous, both with respect to $X_t$ and $\mu_t$. Additionally, we present the first propagation of chaos result for MVSVIs.

In this paper, we establish propagation of chaos (POC) for doubly mean reflected backward stochastic differential equations (MRBSDEs). MRBSDEs differentiate the typical RBSDEs in that the constraint is not on the paths of the solution but on its law. This unique property has garnered significant attention since the inception of MRBSDEs. Rather than directly investigating these equations, we focus on approximating them by interacting particle systems (IPS). We propose two sets of IPS having mean-field Skorokhod problems, capturing the dynamics of IPS reflected in a mean-field way. As the dimension of the IPS tends to infinity, the POC phenomenon emerges, indicating that the system converges to a limit with independent particles, where each solves the MRBSDE. Beyond establishing the first POC result for doubly MRBSDEs, we achieve distinct convergence speeds under different scenarios.

In the last decade, it was understood that quantum networks involving several independent sources of entanglement which are distributed and measured by several parties allowed for completely novel forms of nonclassical quantum correlations, when entangled measurements are performed. Here, we experimentally obtain quantum correlations in a triangle network structure, and provide solid evidence of its nonlocality. Specifically, we first obtain the elegant distribution proposed in (Entropy 21, 325) by performing a six-photon experiment. Then, we justify its nonlocality based on machine learning tools to estimate the distance of the experimentally obtained correlation to the local set, and through the violation of a family of conjectured inequalities tailored for the triangle network.

Diverse non-pharmacological interventions (NPIs), serving as the primary approach for COVID-19 control prior to pharmaceutical interventions, showed heterogeneous spatiotemporal effects on pandemic management. Investigating the dynamic compounding impacts of NPIs on pandemic spread is imperative. However, the challenges posed by data availability of high-dimensional human behaviors and the complexity of modeling changing and interrelated factors are substantial. To address these challenges, this study analyzed social media data, COVID-19 case rates, Apple mobility data, and the stringency of stay-at-home policies in the United States throughout the year 2020, aiming to (1) uncover the spatiotemporal variations in NPIs during the COVID-19 pandemic utilizing geospatial big data; (2) develop a statistical machine learning model that incorporates spatiotemporal dependencies and temporal lag effects for the detection of relationships; (3) dissect the impacts of NPIs on the pandemic across space and time. Three indices were computed based on Twitter (currently known as X) data: the Negative and Positive Sentiments Adjusted by Demographics (N-SAD and P-SAD) and the Ratio Adjusted by Demographics (RAD), representing negative sentiment, positive sentiment, and public awareness of COVID-19, respectively. The Multivariate Bayesian Structural Time Series Time Lagged model (MBSTS-TL) was proposed to investigate the effects of NPIs, accounting for spatial dependencies and temporal lag effects. The developed MBSTS-TL model exhibited a high degree of accuracy. Determinants of COVID-19 health impacts transitioned from an emphasis on human mobility during the initial outbreak period to a combination of human mobility and stay-at-home policies during the rapid spread phase, and ultimately to the compound of human mobility, stay-at-home policies, and public awareness of COVID-19.

Mathematical models in ecology and epidemiology must be consistent with observed data in order to generate reliable knowledge and evidence-based policy. Metapopulation systems, which consist of a network of connected sub-populations, pose technical challenges in statistical inference due to nonlinear, stochastic interactions. Numerical difficulties encountered in conducting inference can obstruct the core scientific questions concerning the link between the mathematical models and the data. Recently, an algorithm has been developed which enables effective likelihood-based inference for the high-dimensional partially observed stochastic dynamic models arising in metapopulation systems. The COVID-19 pandemic provides a situation where mathematical models and their policy implications were widely visible, and we use the new inferential technology to revisit an influential metapopulation model used to inform basic epidemiological understanding early in the pandemic. Our methods support self-critical data analysis, enabling us to identify and address model limitations, and leading to a new model with substantially improved statistical fit and parameter identifiability. Our results suggest that the lockdown initiated on January 23, 2020 in China was more effective than previously thought. We proceed to recommend statistical analysis standards for future metapopulation system modeling.

Quantum steering ellipsoid visualizes the set of all qubit states that can be steered by measuring on another correlated qubit in the Bloch picture. Together with local reduced states, it provides a faithful geometric characterization of the underlying two-qubit state so that almost all nonclassical state features can be reflected in its geometric properties. Consequently, the various types of quantum ellipsoids with different geometric properties form an ellipsoid zoo, which, in this work, is experimentally verified via measurements on many polarization-path photonic states. By generating two-qubit states with high fidelity, the corresponding ellipsoids are constructed to certify the presence of entanglement, one-way Einstein-Podolsky-Rosen steering, discord, and steering incompleteness. It is also experimentally verified that the steering ellipsoid can be reconstructed from using the twelve vertices of the icosahedron as measurement directions. Our results aid progress in applying the quantum steering ellipsoid to reveal nonclassical features of the multi-qubit system., Comment: Several references are added and the presentation is close to the publication version

Structural investigations conducted using transmission electron microscopy (TEM) on LuH2 synthesized under atmospheric pressure (AP-LuH2) and nitrogen-doped LuH2 synthesized under high pressure (HP-LuH2) have revealed numerous microstructural phenomena. Both materials show a clear superstructure modulation with wave vector, q^* = 1/4 (2-20), and this modulation can be well interpreted by the displacements of Lu atoms. Further investigations on the nitrogen-doped HP-LuH2 materials reveal the appearance of high-density antiphase boundaries, in particular, domain walls of a few atomic layer thickness without structural modulation can be observed, suggesting possible interface properties could be detected in this system. In-situ TEM observations of AP-LuH2 suggest that no evident structural phase transition occurs between 94 K and 673 K., Comment: 8 pages, 7 figures

Itinerant ferromagnetism at room temperature is a key ingredient for spin transport and manipulation. Here, we report the realization of nearly-room-temperature itinerant ferromagnetism in Co doped Fe5GeTe2 thin flakes. The ferromagnetic transition temperature TC (323 K - 337 K) is almost unchanged when thickness is down to 12 nm and is still about 284 K at 2 nm (bilayer thickness). Theoretical calculations further indicate that the ferromagnetism persists in monolayer Fe4CoGeTe2. In addition to the robust ferromagnetism down to the ultrathin limit, Fe4CoGeTe2 exhibits an unusual temperature- and thickness-dependent intrinsic anomalous Hall effect. We propose that it could be ascribed to the dependence of band structure on thickness that changes the Berry curvature near the Fermi energy level subtly. The nearly-room-temperature ferromagnetism and tunable anomalous Hall effect in atomically thin Fe4CoGeTe2 provide opportunities to understand the exotic transport properties of two-dimensional van der Waals magnetic materials and explore their potential applications in spintronics., Comment: 28 pages, 4 figures, 1 table

In this article, we investigate three classes of equations: the McKean-Vlasov stochastic differential equation (MVSDE), the MVSDE with a subdifferential operator referred to as the McKean-Vlasov stochastic variational inequality (MVSVI), and the coupled forward-backward MVSVI. The latter class encompasses the FBSDE with reflection in a convex domain as a special case. We establish the well-posedness, in terms of the existence and uniqueness of a strong solution, for these three classes in their general forms. Importantly, we consider stochastic coefficients with locally Holder continuity and employ different strategies to achieve that for each class.

In recent years, analysis methods for quantum states based on randomized measurements have been investigated extensively. Still, in the experimental implementations these methods were typically used for characterizing strongly entangled states and not to analyze the different families of multiparticle or weakly entangled states. In this work, we experimentally prepare various entangled states with path-polarization hyper-entangled photon pairs, and study their entanglement properties using the full toolbox of randomized measurements. First, we successfully characterize the correlations of a series of GHZ-W mixed states using the second moments of the random outcomes, and demonstrate the advantages of this method by comparing it with the well-known three-tangle and squared concurrence. Second, we generate bound entangled chessboard states of two three-dimensional systems and verify their weak entanglement with a criterion derived from moments of randomized measurements., Comment: 10 pages, 6 figures, Comments are welcome

In this paper, we study the mean reflected stochastic differential equations driven by G- Brownian motion, where the constraint depends on the distribution of the solution rather than on its paths. Well-posedness is achieved by first investigating the Skorokhod problem with mean reflection under the G-expectation. Two approaches to constructing the solution are introduced, both offering insights into desired properties and aiding in the application of the contraction mapping method. Additionally, a new technique is proposed to prove the first propagation of chaos result for mean reflected G-SDEs, overcoming challenges posed by the nonlinearity of G- expectation and the non-deterministic nature of the quadratic variation of G-Brownian motion.