arXiv subjects

Zhou Zhou

Publications and source records attributed to Zhou Zhou.

At least 19 recordsLinked to original sources

arXiv2026

Existence of Relaxed Equilibrium for Time-Inconsistent Mean Field Games: A Set-Valued Fixed Point Approach

This paper studies the existence of relaxed equilibria for finite-horizon continuous-time time-inconsistent mean field games. We work directly on the product space of relaxed feedback policies and population flows. The policy component is endowed with the stable topology of Young measures, while the population component is restricted to a compact convex set of Wasserstein-continuous flows with uniform moment and time-regularity bounds. For every policy-flow pair, we establish uniform Sobolev and H\"older estimates for the associated auxiliary value function and prove its stability under Young-measure convergence of policies and uniform Wasserstein convergence of population flows. We also establish continuity of the induced population-flow map. The latter requires a duality argument for the Fokker-Planck equations because Young-measure convergence yields only weak-$*$ convergence of the controlled drifts. We then construct a set-valued best-response/consistency map with nonempty compact convex values and apply the Kakutani-Fan-Glicksberg fixed-point theorem. The resulting fixed point satisfies both the equilibrium response condition of the intra-personal game and the mean field consistency condition, , thereby establishing the existence of a relaxed equilibrium

math.OC↗

arXiv2026

Recursive Multiple Change Point Detection of Nonstationary Time Series: Instability Tests, Estimation and Confidence Intervals

We develop bootstrap-assisted robust binary segmentation (BARBS), a recursive binary segmentation method for multiple change point detection under general nonstationary temporal dynamics. A novel Gaussian multiplier bootstrap for the CUSUM statistics is proposed, offering robustness to complex dependence structures. Through meticulous calibration of the critical values at each stage of the recursion, BARBS ensures control of the Type I error under the null hypothesis of no change points. When change points are present, BARBS identifies the correct number of changes with a prespecified probability, and the resulting change point location estimators attain the same uniform consistency rate as classical binary segmentation. Building on this, we introduce second-stage refined estimators that achieve the optimal individual localization rate, and establish their asymptotic distributions and nearly optimal uniform localization rates under both fixed and vanishing jump magnitudes. Extensive numerical experiments across various settings confirm the robustness and superior performance of BARBS relative to existing approaches. To illustrate the practical relevance of the proposed methodology, we analyze U.S. inflation data, yielding change points that align with several documented macroeconomic episodes.

stat.ME↗

arXiv2026

Testing for Serial Independence via Auto Hilbert-Schmidt Independence Criterion

We develop a Hilbert--Schmidt independence criterion (HSIC)-based framework for testing serial independence in strictly stationary time series. The proposed auto Hilbert--Schmidt independence criterion (AutoHSIC) measures dependence between an observation and its lagged counterpart, providing a kernel-based approach to detecting nonlinear serial dependence. The empirical AutoHSIC statistic is a lagged U-statistic constructed from overlapping observations, and hence inherits temporal dependence even under the i.i.d. null. Its asymptotic analysis therefore differs from standard i.i.d. HSIC theory and must account for degeneracy under the null. We establish the limiting behaviour of the resulting single-lag and portmanteau tests under the null and under fixed alternatives. Since the limiting null distribution is non-pivotal, we develop a wild bootstrap procedure for critical value approximation and prove its asymptotic validity. The framework is further extended to residual-based model diagnostics, where parameter estimation affects the null distribution. Simulations and empirical applications illustrate its ability to detect nonlinear serial dependence in multivariate, functional and matrix time series.

stat.ME↗

arXiv2026

Simultaneous Inference for Nonlinear Time Series, a Sieve M-regression Approach

This paper studies simultaneous inference of conditional distributions in nonlinear time series from a sieve M-regression perspective. Existing literature on sieve M-regression has primarily focused on pointwise asymptotics, leaving the development of uncertainty quantification over the entire predictor space unexplored. We address this gap by establishing a uniform Bahadur representation for the sieve M-estimator, accommodating dependent data and a growing number of sieve basis functions. A novel high-dimensional empirical process theory is developed for temporally dependent data, and a specifically designed M-decomposition method is utilized to control high-dimensional complexities. Building on this representation, we develop a convex Gaussian approximation to characterize the asymptotic behavior of the estimator and construct valid simultaneous confidence regions (SCRs). To facilitate practical implementation, we introduce a self-convolved bootstrap algorithm that accurately approximates the distribution of the maximal deviation. Our inferential framework is supported by rigorous error bounds and validated through numerical simulations and real data applications.

math.ST↗

arXiv2026

Structured Single-photon Metasource

Structured quantum light is crucial for high-dimensional quantum information processing, yet its direct generation from quantum emitters remains challenging due to their intrinsic locality and omnidirectional radiation. Metasurfaces have been adopted for quantum-light wavefront shaping, typically in cascaded or stacked configurations that suffer from low efficiency and limited resolution. Here, we demonstrate a semiconductor metasource that directly embodies single quantum dots in a nonlocal GaAs metasurface. Spontaneous emission from quantum dot is efficiently funneled into an extended quasi-bound-state-in-the-continuum mode while sustaining strong mode-emitter overlap. A lateral core-barrier heterostructure tunes mode volume and spatial distribution to balance Purcell enhancement and holographic resolution. Using spatially modulated geometric phase, our compact metasource enables deterministic generation of diverse single-photon radiation patterns, including orbital-angular-momentum beams and holographic images. Our work brings versatile single-photon wavefront control into the nanoscale cavity quantum electrodynamics regime, offering a scalable route toward integrated sources of structured quantum light.

physics.optics↗

arXiv2026

Equilibrium under Time-Inconsistency: A New Existence Theory by Vanishing Entropy Regularization

This paper develops a framework for establishing the existence of solutions to the equilibrium Hamilton-Jacobi-Bellman (EHJB) equation arising in time-inconsistent stochastic control problems. The time-inconsistency in our setting arises from the initial-time dependence such as the non-exponential discounting. The classical approach typically relates the existence of equilibrium to the classical solution of the EHJB, whose existence is still an open problem under general model assumptions. We resolve this challenge by building on a vanishing entropy regularization approach. Using fixed-point arguments, we first establish the existence of classical solutions to the exploratory equilibrium Hamilton-Jacobi-Bellman Equation (EEHJB) by deriving a series of delicate PDE estimates for the solution and its derivatives. Building on these estimates for the solution of the EEHJB and its derivatives, we then conduct a rigorous convergence analysis under suitable norms as the entropy regularization vanishes. Our main result shows that solutions of the EEHJB converge to a strong solution of the original EHJB, corresponding to the limit of the regularized equilibria. This convergence yields a verification argument ensuring that the limiting relaxed equilibrium indeed constitutes an equilibrium for the original time-inconsistent control problem. We thus establish the well-posedness of the EHJB and the existence of equilibria in diffusion models under time-inconsistency, without resorting to conventional stringent regularity assumptions of the EHJB.

math.OC↗

arXiv2026

A Formal Framework for Predicting Distributed System Performance under Faults (Extended Version)

Today's distributed systems operate in complex environments that inevitably involve faults and even adversarial behaviors. Predicting their performance under such environments directly from formal designs remains a longstanding challenge. We present the first formal framework that systematically enables performance prediction of distributed systems across diverse faulty scenarios. Our framework features a fault injector together with a wide range of faults, reusable as a library, and model compositions that integrate the system and the fault injector into a unified model suitable for statistical analysis of performance properties such as throughput and latency. We formalize the framework in Maude and implement it as an automated tool, PERF. Applied to representative distributed systems, PERF accurately predicts system performance under varying fault settings, with estimations from formal designs consistent with evaluations on real deployments.

cs.DC↗

arXiv2026

Beyond Pixels: Vector-to-Graph Transformation for Reliable Schematic Auditing

Multimodal Large Language Models (MLLMs) have shown remarkable progress in visual understanding, yet they suffer from a critical limitation: structural blindness. Even state-of-the-art models fail to capture topology and symbolic logic in engineering schematics, as their pixel-driven paradigm discards the explicit vector-defined relations needed for reasoning. To overcome this, we propose a Vector-to-Graph (V2G) pipeline that converts CAD diagrams into property graphs where nodes represent components and edges encode connectivity, making structural dependencies explicit and machine-auditable. On a diagnostic benchmark of electrical compliance checks, V2G yields large accuracy gains across all error categories, while leading MLLMs remain near chance level. These results highlight the systemic inadequacy of pixel-based methods and demonstrate that structure-aware representations provide a reliable path toward practical deployment of multimodal AI in engineering domains. To facilitate further research, we release our benchmark and implementation at https://github.com/gm-embodied/V2G-Audit.

cs.AI↗

arXiv2026

Optimal Underreporting and Competitive Equilibrium

This paper develops a dynamic insurance market model comprising two competing insurance companies and a continuum of insureds, and examines the interaction between strategic underreporting by the insureds and competitive pricing between the insurance companies under a Bonus-Malus System (BMS) framework. For the first time in an oligopolistic setting, we establish the existence and uniqueness of the insureds' optimal reporting barrier, as well as its continuous dependence on the BMS premiums. For the 2-class BMS case, we prove the existence of Nash equilibrium premium strategies and conduct an extensive sensitivity analysis on the impact of the model parameters on the equilibrium premiums.

q-fin.MF↗

arXiv2026

Mean-Field Games Under Model Uncertainty

We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within an uncertainty set. Unlike in classical MFGs, model uncertainty renders the population distribution flow stochastic. This leads us to consider strategies that depend on both individual states and the realized distribution of the population. Our main results establish the asymptotic relationship between $N$-agent games and MFGs: every MFG equilibrium constitutes an $\varepsilon$-Nash equilibrium for sufficiently large populations, and conversely, limits of $N$-agent equilibria are MFG equilibria. We also prove the existence of equilibria for finite-agent games and construct a solvable mean-field example with closed-form solutions.

math.OC↗

arXiv2025

Deciphering the lattice vibrational behaviors of CuInP2S6 by angle-resolved polarized Raman scattering

The layered van der Waals (vdW) ferroelectric CuInP2S6 (CIPS) exhibits unique cation hopping-driven phenomena that bring about unconventional properties with intriguing mechanisms and hold promises for advanced applications in nanoelectronics. However, an explicit analysis of its lattice dynamics and vibrational symmetries, pivotal for understanding the material's peculiar ferroelectric and ferroionic behaviors, remains incomplete. Here, we employ angle-resolved polarized Raman spectroscopy in concert with first-principles calculations to systematically unravel the anisotropic lattice vibrations of CIPS single crystals. By analyzing the polarization-dependent Raman intensities, we determine the symmetry assignments and Raman tensors of all major vibrational modes, revealing good agreement with theoretical predictions. Furthermore, we demonstrate the utility of Raman spectroscopy as a sensitive and non-invasive probe for structural and ferroelectric order evolution, by examining temperature-driven phase transitions and thickness-dependent polarization suppression in CIPS. Our findings establish a foundational framework for correlating lattice dynamics with functional properties in CIPS and provide a methodological blueprint for studying other vdW ferroelectrics.

cond-mat.mtrl-sci↗

arXiv2025

Continuous-time reinforcement learning for optimal switching over multiple regimes

This paper studies the continuous-time reinforcement learning (RL) for optimal switching problems across multiple regimes. We consider a type of exploratory formulation under entropy regularization where the agent randomizes both the timing of switches and the selection of regimes through the generator matrix of an associated continuous-time finite-state Markov chain. We establish the well-posedness of the associated system of Hamilton-Jacobi-Bellman (HJB) equations and provide a characterization of the optimal policy. The policy improvement and the convergence of the policy iterations are rigorously established by analyzing the system of equations. We also show that the value function in the exploratory formulation converges to the one in the classical formulation as the temperature parameter vanishes. Finally, a model-free reinforcement learning algorithm is devised and implemented by invoking the policy evaluation based on the martingale characterization. Our numerical examples with financial applications illustrate the effectiveness and efficiency of the proposed RL algorithm.

math.OC↗

arXiv2025

Three-Class Emotion Classification for Audiovisual Scenes Based on Ensemble Learning Scheme

Emotion recognition plays a pivotal role in enhancing human-computer interaction, particularly in movie recommendation systems where understanding emotional content is essential. While multimodal approaches combining audio and video have demonstrated effectiveness, their reliance on high-performance graphical computing limits deployment on resource-constrained devices such as personal computers or home audiovisual systems. To address this limitation, this study proposes a novel audio-only ensemble learning framework capable of classifying movie scenes into three emotional categories: Good, Neutral, and Bad. The model integrates ten support vector machines and six neural networks within a stacking ensemble architecture to enhance classification performance. A tailored data preprocessing pipeline, including feature extraction, outlier handling, and feature engineering, is designed to optimize emotional information from audio inputs. Experiments on a simulated dataset achieve 67% accuracy, while a real-world dataset collected from 15 diverse films yields an impressive 86% accuracy. These results underscore the potential of audio-based, lightweight emotion recognition methods for broader consumer-level applications, offering both computational efficiency and robust classification capabilities.

cs.SD↗

arXiv2025

Stackelberg stopping games

We study a Stackelberg variant of the classical discrete-time Dynkin game, in which Player 1 (the leader) commits to a stopping strategy first and Player 2 (the follower) responds optimally. This leader-follower structure induces an optimal control problem for the leader and gives rise to intrinsic time-inconsistency. We first clarify notions of precommitment and equilibrium strategies in the Stackelberg setting, and contrast them with the Nash equilibrium in the standard Dynkin game using a finite-horizon example. We then consider an infinite-horizon framework with a time-homogeneous Markov process on a general Polish state space. We characterize the leader's value function under randomized precommitment strategies and show that randomized exact equilibrium strategies may fail to exist via a counterexample. Motivated by this nonexistence phenomenon, we introduce an entropy-regularized Stackelberg stopping game. The regularization induces a continuous response rule and yields the existence of randomized regular equilibria. We further show that these regular equilibria induce epsilon-equilibria for the original Stackelberg stopping game when the regularization parameter is sufficiently small. In the finite-state setting, we also establish a limiting result as the regularization parameter converges to zero.

math.OC↗

arXiv2025

Simultaneous Sieve Estimation and Inference for Time-Varying Nonlinear Time Series Regression

In this paper, we investigate time-varying nonlinear time series regression for a broad class of locally stationary time series. First, we propose sieve nonparametric estimators for the time-varying regression functions that achieve uniform consistency. Second, we develop a unified simultaneous inferential theory to conduct both structural and exact form tests on these functions. Additionally, we introduce a multiplier bootstrap procedure for practical implementation. Our methodology and theory require only mild assumptions on the regression functions, allow for unbounded domain support, and effectively address the issue of identifiability for practical interpretation. Technically, we establish sieve approximation theory for 2-D functions in unbounded domains, prove two Gaussian approximation results for affine forms of high-dimensional locally stationary time series, and calculate critical values for the maxima of the Gaussian random field arising from locally stationary time series, which may be of independent interest. Numerical simulations and two data analyses support our results, and we have developed an $\mathtt{R}$ package, $\mathtt{SIMle}$, to facilitate implementation.

stat.ME↗

arXiv2025

Wasserstein and Convex Gaussian Approximations for Non-stationary Time Series of Diverging Dimensionality

In high-dimensional time series analysis, Gaussian approximation (GA) schemes under various distance measures or on various collections of subsets of the Euclidean space play a fundamental role in a wide range of statistical inference problems. To date, most GA results for high-dimensional time series are established on hyper-rectangles and their equivalence. In this paper, by considering the 2-Wasserstein distance and the collection of all convex sets, we establish a general GA theory for a broad class of high-dimensional non-stationary (HDNS) time series, extending the scope of problems that can be addressed in HDNS time series analysis. For HDNS time series of sufficiently weak dependence and light tail, the GA rates established in this paper are either nearly optimal with respect to the dimensionality and time series length, or they are nearly identical to the corresponding best-known GA rates established for independent data. A multiplier bootstrap procedure is utilized and theoretically justified to implement our GA theory. We demonstrate by two previously undiscussed time series applications the use of the GA theory and the bootstrap procedure as unified tools for a wide range of statistical inference problems in HDNS time series analysis.

math.ST↗

arXiv2025

Uncertainty quantification of synchrosqueezing transform under complicated nonstationary noise

We propose a bootstrapping framework to quantify uncertainty in time-frequency representations (TFRs) generated by the short-time Fourier transform (STFT) and the STFT-based synchrosqueezing transform (SST) for oscillatory signals with time-varying amplitude and frequency contaminated by complex nonstationary noise. To this end, we leverage a recent high-dimensional Gaussian approximation technique to establish a sequential Gaussian approximation for nonstationary processes under mild assumptions. This result is of independent interest and provides a theoretical basis for characterizing the approximate Gaussianity of STFT-induced TFRs as random fields. Building on this foundation, we establish the robustness of SST-based signal decomposition in the presence of nonstationary noise. Furthermore, assuming locally stationary noise, we develop a Gaussian autoregressive bootstrap for uncertainty quantification of SST-based TFRs and provide theoretical justification. We validate the proposed methods with simulations and illustrate their practical utility by analyzing spindle activity in electroencephalogram recordings. Our work bridges time-frequency analysis in signal processing and nonlinear spectral analysis of time series in statistics.

stat.ME↗

arXiv2025

MuGrid-v2: A novel scintillator detector for multidisciplinary applications

Muography, traditionally recognized as a potent instrument for imaging the internal structure of gigantic objects, has initialized various interdisciplinary applications. As the financial and labor costs of muography detector development hinder their massive applications, we develop a novel muon detector called MuGrid by coupling a monolithic plastic scintillator with the light guide array in order to achieve competitive spatial resolution while substantially reducing production costs. For a prototype detector in 30 cm $\times$ 30 cm, the intrinsic spatial resolution has been optimized toward a millimeter scale. An outdoor field muography experiment was conducted to monitor two buildings for validation purposes. The test successfully resolved the geometric influence of architectural features based on the attenuation of muon flux in a good agreement between experimental results and the simulation prediction.

physics.ins-det↗