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Zhiren Wang

Publications and source records attributed to Zhiren Wang.

At least 19 recordsLinked to original sources
arXiv2026

Smooth projections of self-similar measures

We prove a Furstenberg-type criterion for a given orthogonal projection of a self-similar measure to be absolutely continuous, with quantified regularity. It requires exponential mixing of the rotational part at a rate that is sufficiently fast compared with an orbit relative analogue of its dimension. Using Ramanujan sets of irrational rotations in \(\mathrm{SO}(3)\) constructed by Lubotzky, Phillips and Sarnak (1986, 1987), we obtain explicit applications. In particular, we exhibit singular self-similar measures whose every line projection is absolutely continuous, measures of arbitrarily small Fourier dimension with smooth projections in all but a fully explicit exceptional set of directions, and a non-trivial example of a self-similar measure that is Salem with a $C^2 _0$ density.

math.DS↗
arXiv2026

Performance of Conventional EEG Biomarkers Across Different Clinical Phases of Major Depressive Disorder: A Comprehensive Evaluation

While EEG features differentiate Major Depressive Disorder (MDD) from healthy controls (HC), their clinical utility as biomarkers depends on a monotonic trajectory across the disease spectrum, from the acute (AC) phase to the maintenance (MA) phase and finally to the healthy baseline. However, the progression of the MA phase remains poorly understood in traditional marker analysis. Analyzing EEG data from 74 individuals (24 AC, 23 MA, and 27 HC), this study provides a comprehensive evaluation of classic ERP and resting-state indices across AC, MA, and HC groups. Our results demonstrate that almost no conventional metrics strictly satisfy the criterion of monotonic progression, likely due to profound inter-individual heterogeneity. These findings highlight the inherent limitations of group-level feature extraction and provide critical insights for developing future paradigms and algorithms to identify neurobiological markers with genuine clinical utility.

q-bio.NC↗
arXiv2026

CRCC: Contrast-Based Robust Cross-Subject and Cross-Site Representation Learning for EEG

EEG-based neural decoding models often fail to generalize across acquisition sites due to structured, site-dependent biases implicitly exploited during training. We reformulate cross-site clinical EEG learning as a bias-factorized generalization problem, in which domain shifts arise from multiple interacting sources. We identify three fundamental bias factors and propose a general training framework that mitigates their influence through data standardization and representation-level constraints. We construct a standardized multi-site EEG benchmark for Major Depressive Disorder and introduce CRCC, a two-stage training paradigm combining encoder-decoder pretraining with joint fine-tuning via cross-subject/site contrastive learning and site-adversarial optimization. CRCC consistently outperforms state-of-the-art baselines and achieves a 10.7 percentage-point improvement in balanced accuracy under strict zero-shot site transfer, demonstrating robust generalization to unseen environments.

q-bio.NC↗
arXiv2025

Effective equidistribution for some one parameter unipotent flows

We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of $\operatorname{SL}_2(\mathbb R)$ in arithmetic quotients of $\operatorname{SL}_2(\mathbb C)$ and $\operatorname{SL}_2(\mathbb R)\times\operatorname{SL}_2(\mathbb R)$. The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.

math.NT↗
arXiv2025

Effective equidistribution in rank 2 homogeneous spaces and values of quadratic forms

We establish effective equidistribution theorems, with a polynomial error rate, for orbits of unipotent subgroups in quotients of quasi-split, almost simple Linear algebraic groups of absolute rank 2. As an application, inspired by the results of Eskin, Margulis and Mozes, we establish quantitative results regarding the distribution of values of an indefinite ternary quadratic form at integer points, giving in particular an effective and quantitative proof of the Oppenheim Conjecture.

math.DS↗
arXiv2025

Differences in Neurovascular Coupling in Patients with Major Depressive Disorder: Evidence from Simultaneous Resting-State EEG-fNIRS

Neurovascular coupling (NVC) refers to the process by which local neural activity, through energy consumption, induces changes in regional cerebral blood flow to meet the metabolic demands of neurons. Event-related studies have shown that the hemodynamic response typically lags behind neural activation by 4-6 seconds. However, little is known about how NVC is altered in patients with major depressive disorder (MDD) and throughout the recovery process. In this study, we employed simultaneous resting-state electroencephalography (rsEEG) and functional near-infrared spectroscopy (fNIRS) to monitor neural and hemodynamic signals. Twelve patients with MDD during the acute phase, ten patients in the maintenance or consolidation phase, and six healthy controls were involved. We calculated the differences in coherence and temporal delay between spontaneous peak electrophysiological activity and hemodynamic responses across groups during the resting state in the prefrontal cortex (PFC). We found that the neural activity and its subsequent correlation with hemodynamic responses were significantly higher in patients during the maintenance phase. The rise time from the lowest to the highest point of correlation was shorter in healthy individuals than in patients in the acute phase, and gradually recovered during remission. By leveraging wearable neuroimaging techniques, this study reveals alterations in neurovascular coupling in depression and offers novel multimodal insights into potential biomarkers for MDD and its recovery process.

q-bio.NC↗
arXiv2025

Spectral gaps and Fourier decay for self-conformal measures in the plane

Let $Φ$ be a $C^ω(\mathbb{C})$ self-conformal IFS on the plane, satisfying some mild non-linearity and irreducibility conditions. We prove a uniform spectral gap estimate for the transfer operator corresponding to the derivative cocycle and every given self-conformal measure. Building on this result, we establish polynomial Fourier decay for any such measure. Our technique is based on a refinement of a method of Oh-Winter (2017) where we do not require separation from the IFS or the Federer property for the underlying measure.

math.DS↗
arXiv2024

Month-long-lifetime microwave spectral holes in an erbium-doped scheelite crystal at millikelvin temperature

Rare-earth-ion (REI) ensembles in crystals have remarkable optical and spin properties characterized by narrow homogeneous linewidths relative to the inhomogeneous ensemble broadening. This makes it possible to precisely tailor the ensemble spectral density and therefore the absorption profile by applying narrow-linewidth radiation to transfer population into auxiliary levels, a process broadly known as spectral hole burning (SHB). REI-doped crystals find applications in information processing, both classical (pattern recognition, filtering, spectral analysis) and quantum (photon storage), all protocols requiring suitable ensemble preparation by SHB as a first step. In Er$^{3+}$-doped materials, the longest reported hole lifetime is one minute, and longer lifetimes are desirable. Here, we report SHB and accumulated echo measurements in a scheelite crystal of CaWO$_4$ by pumping the electron spin transition of Er$^{3+}$ ions at microwave frequencies and millikelvin temperatures, with nuclear spin states of neighboring $^{183}$W atoms serving as the auxiliary levels. The lifetime of the holes and accumulated echoes rises steeply as the sample temperature is decreased, exceeding a month at 10 mK. Our results demonstrate that millikelvin temperatures can be beneficial for signal processing applications requiring long spectral hole lifetimes.

quant-ph↗
arXiv2024

Polynomial Fourier decay and a cocycle version of Dolgopyat's method for self conformal measures

We show that every self conformal measure with respect to a $C^2 (\mathbb{R})$ IFS $Φ$ has polynomial Fourier decay under some mild and natural non-linearity conditions. In particular, every such measure has polynomial decay if $Φ$ is $C^ω(\mathbb{R})$ and contains a non-affine map. A key ingredient in our argument is a cocycle version of Dolgopyat's method, that does not require the cylinder covering of the attractor to be a Markov partition. It is used to obtain spectral gap-type estimates for the transfer operator, which in turn imply a renewal theorem with an exponential error term in the spirit of Li (2022).

math.DS↗
arXiv2024

Arbitrarily slow decay in the logarithmically averaged Sarnak conjecture

In 2017 Tao proposed a variant Sarnak's Möbius disjointness conjecture with logarithmic averaging: For any zero entropy dynamical system $(X,T)$, $\frac{1}{\log N} \sum_{n=1} ^N \frac{f(T^n x) μ(n)}{n}= o(1)$ for every $f\in \mathcal{C}(X)$ and every $x\in X$. We construct examples showing that this $o(1)$ can go to zero arbitrarily slowly. Nonetheless, all of our examples satisfy the conjecture.

math.DS↗
arXiv2024

Boundary actions by higher-rank lattices: Classification and embedding in low dimensions, local rigidity, smooth factors

We study actions by lattices in higher-rank (semi)simple Lie groups on compact manifolds. By classifying certain measures invariant under a related higher-rank abelian action (the diagonal action on the suspension space) we deduce a number of new rigidity results related to standard projective actions (i.e. boundary actions) by such groups. Specifically, in low dimensions we show all actions (with infinite image) are conjugate to boundary actions. We also show standard boundary actions (e.g. projective actions on generalized flag varieties) are local rigid and classify all smooth actions that are topological factors of such actions. Finally, for volume-preserving actions in low dimensions (with infinite image) we provide a mechanism to detect the presence of "blow-ups" for the action by studying measures that are $P$-invariant but not $G$-invariant for the suspension action.

math.DS↗
arXiv2024

A Bi-Pyramid Multimodal Fusion Method for the Diagnosis of Bipolar Disorders

Previous research on the diagnosis of Bipolar disorder has mainly focused on resting-state functional magnetic resonance imaging. However, their accuracy can not meet the requirements of clinical diagnosis. Efficient multimodal fusion strategies have great potential for applications in multimodal data and can further improve the performance of medical diagnosis models. In this work, we utilize both sMRI and fMRI data and propose a novel multimodal diagnosis model for bipolar disorder. The proposed Patch Pyramid Feature Extraction Module extracts sMRI features, and the spatio-temporal pyramid structure extracts the fMRI features. Finally, they are fused by a fusion module to output diagnosis results with a classifier. Extensive experiments show that our proposed method outperforms others in balanced accuracy from 0.657 to 0.732 on the OpenfMRI dataset, and achieves the state of the art.

cs.CV↗
arXiv2023

Fundamental Physics Opportunities with the Next-Generation Event Horizon Telescope

The Event Horizon Telescope (EHT) Collaboration recently published the first images of the supermassive black holes in the cores of the Messier 87 and Milky Way galaxies. These observations have provided a new means to study supermassive black holes and probe physical processes occurring in the strong-field regime. We review the prospects of future observations and theoretical studies of supermassive black hole systems with the next-generation Event Horizon Telescope (ngEHT), which will greatly enhance the capabilities of the existing EHT array. These enhancements will open up several previously inaccessible avenues of investigation, thereby providing important new insights into the properties of supermassive black holes and their environments. This review describes the current state of knowledge for five key science cases, summarising the unique challenges and opportunities for fundamental physics investigations that the ngEHT will enable.

astro-ph.HE↗
arXiv2023

Single electron-spin-resonance detection by microwave photon counting

Electron spin resonance (ESR) spectroscopy is the method of choice for characterizing paramagnetic impurities, with applications ranging from chemistry to quantum computing, but it gives access only to ensemble-averaged quantities due to its limited signal-to-noise ratio. Single-electron-spin sensitivity has however been reached using spin-dependent photoluminescence, transport measurements, and scanning-probe techniques. These methods are system-specific or sensitive only in a small detection volume, so that practical single spin detection remains an open challenge. Here, we demonstrate single electron magnetic resonance by spin fluorescence detection, using a microwave photon counter at cryogenic temperatures. We detect individual paramagnetic erbium ions in a scheelite crystal coupled to a high-quality factor planar superconducting resonator to enhance their radiative decay rate, with a signal-to-noise ratio of 1.9 in one second integration time. The fluorescence signal shows anti-bunching, proving that it comes from individual emitters. Coherence times up to 3 ms are measured, limited by the spin radiative lifetime. The method has the potential to apply to arbitrary paramagnetic species with long enough non-radiative relaxation time, and allows single-spin detection in a volume as large as the resonator magnetic mode volume ( 10 um^3 in the present experiment), orders of magnitude larger than other single-spin detection techniques. As such, it may find applications in magnetic resonance and quantum computing.

quant-ph↗
arXiv2023

Constraining the Existence of Axion Clouds in M87* with Closure Trace Analyses

Black holes can amplify incoming bosonic waves via rotational superradiance, inducing bound states of ultralight bosons around them. This phenomenon has the potential to confine the parameter spaces of new bosons. Axions and axion-like particles (ALPs) are candidate beyond-standard-model particles that can form such clouds around supermassive black holes (SMBHs) and impact the polarization signal in a similar fashion to Faraday rotation via axion-photon coupling. Prior efforts have used polarized images from the Event Horizon Telescope (EHT) M87 2017 observations to limit the dimensionless axion-photon coupling to previously unexplored regions. However, with the novel calibration-insensitive quantities, closure traces and conjugate closure trace products, it is possible to constrain the existence of axion clouds while avoiding the dominant sources of systematic uncertainties, e.g., station gains and polarization leakages. We utilize a simple geometric model for the polarization map of M87* to fit the model parameters with both simulated and real data sets and reach a comparable level of constraint in the accuracy with which an axion cloud may be excluded in M87. Future applications of our approach include subsequent M87* and Sgr A* observations by EHT and next-generation EHT (ngEHT) are expected to produce stronger constraints across a wider range of axion and ALP masses. Because it does not require imaging, closure trace analyses may be applied to target AGN for which imaging is marginal, extending the number of SMBHs from which axion limits may be obtained significantly.

astro-ph.HE↗
arXiv2023

Multi-Dimension-Embedding-Aware Modality Fusion Transformer for Psychiatric Disorder Clasification

Deep learning approaches, together with neuroimaging techniques, play an important role in psychiatric disorders classification. Previous studies on psychiatric disorders diagnosis mainly focus on using functional connectivity matrices of resting-state functional magnetic resonance imaging (rs-fMRI) as input, which still needs to fully utilize the rich temporal information of the time series of rs-fMRI data. In this work, we proposed a multi-dimension-embedding-aware modality fusion transformer (MFFormer) for schizophrenia and bipolar disorder classification using rs-fMRI and T1 weighted structural MRI (T1w sMRI). Concretely, to fully utilize the temporal information of rs-fMRI and spatial information of sMRI, we constructed a deep learning architecture that takes as input 2D time series of rs-fMRI and 3D volumes T1w. Furthermore, to promote intra-modality attention and information fusion across different modalities, a fusion transformer module (FTM) is designed through extensive self-attention of hybrid feature maps of multi-modality. In addition, a dimension-up and dimension-down strategy is suggested to properly align feature maps of multi-dimensional from different modalities. Experimental results on our private and public OpenfMRI datasets show that our proposed MFFormer performs better than that using a single modality or multi-modality MRI on schizophrenia and bipolar disorder diagnosis.

eess.IV↗