Approximate Message Passing (AMP) algorithms have seen widespread use across a variety of applications. However, the precise forms for their Onsager corrections and state evolutions depend on properties underlying random matrix ensemble, limiting extent to which AMP derived white noise may be applicable data matrices that arise in practice. In this work, we study more general W satisfy orthogonal rotational invariance law, where spectral distribution is different from semicircle...

Objective: To analyse the 3D-Flair MRI manifestations of inner ear, vestibular function status, and their correlation with hearing treatment outcomes in patients severe sudden sensorineural loss (SSNHL), to explore potential prognostic indicators for deafness. Methods: The clinical data adult unilateral profound were retrospectively analyzed Otorhinolaryngology Department Shandong Provincial ENT Hospital from March 2018 August 2020. Patients categorized based on results ear into two groups:...

In this article, we study the existence and multiplicity of solutions quasilinear Dirac-Poisson system $$\displaylines{ i\sum^3_{k=1}\alpha_k\partial_k u-a\beta u-\omega u-\phi u =h(x,|u|)u ,\quad x\in\mathbb{R}^3,\cr -\Delta\phi-\varepsilon^4\Delta_4\phi=u^2,\quad x\in\mathbb{R}^3, }$$ where \(\partial_k=\partial/\partial x_k\), \(k=1,2,3\); \(a>0\) is a constant, \(\alpha_1, \alpha_2, \alpha_3\) \(\beta\) are \(4\times 4\) Pauli-Dirac matrices; operator $\Delta_4$ 4-Laplacian operator,...

Numerous studies have been devoted to uncovering the characteristics of resident density and urban mobility with multisource geospatial big data. However, little attention has paid internal diversity residents such as their occupations, which is a crucial aspect vibrancy. This study aims investigate variation between individual interactive influences built environment factors on occupation mixture index (OMI) novel GeoDetector-based indicator. first integrated application (App) use patterns...

Abstract We study a class of Approximate Message Passing (AMP) algorithms for symmetric and rectangular spiked random matrix models with orthogonally invariant noise. The AMP iterates have fixed dimension $K \geq 1$, multivariate non-linearity is applied in each iteration, the algorithm spectrally initialized $K$ super-critical sample eigenvectors. derive forms Onsager debiasing coefficients corresponding state evolution, which depend on free cumulants noise spectral distribution. This...

To date, the pathogenesis of Ménière's disease (MD) remains unclear. This study aims to investigate possible relationship between potential immune system-related genes and sporadic MD. The whole RNA-sequencing (RNA-seq) technology was used analyse transcriptome peripheral blood mononuclear cells three MD patients control individuals. Of 366 differentially expressed (DEGs), 154 were up-regulated 212 down-regulated (|log2 fold change| > 1 P < 0·05). Gene ontology (GO) enrichment analysis...

Mobile phone data is a typical type of big with great potential to explore human mobility and individual portrait identification. Previous studies in population classifications mobile only focused on spatiotemporal patterns their clusters. In this study, novel analytical framework an integration spatial non-spatial behavior, through smart APP (applications) usage preference, was proposed portray citizens’ occupations Guangzhou center data. An occupation mixture index (OMI) assess the...

To report eight cases of inferior vestibular neuritis, in order to raise awareness this new subtype neuritis.We retrospectively analysed 216 patients (104 males and 112 females; age range 10-64 years; mean 38.4 years) with full clinical documentation who had attended our hospital's vertigo clinic between May 2007 December 2008. All underwent systematic investigation, including hearing tests, radiology, caloric testing evoked myogenic potential testing.Of were diagnosed as based on...

We analyze a new spectral graph matching algorithm, GRAph Matching by Pairwise eigen-Alignments (GRAMPA), for recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs. Extending exact recovery guarantees established in companion paper Gaussian weights, this work, we prove universality of these general correlated Wigner model. In particular, Erdős-Rényi graphs with edge correlation coefficient $1-σ^2$ and average degree at least...

Graph matching aims at finding the vertex correspondence between two unlabeled graphs that maximizes total edge weight correlation. This amounts to solving a computationally intractable quadratic assignment problem. In this paper we propose new spectral method, GRAph Matching by Pairwise eigen-Alignments (GRAMPA). Departing from prior approaches only compare top eigenvectors, or eigenvectors of same order, GRAMPA first constructs similarity matrix as weighted sum outer products all pairs...

We consider the Sherrington–Kirkpatrick model of spin glasses with ferromagnetically biased couplings. For a specific choice couplings mean, resulting Gibbs measure is equivalent to Bayesian posterior for high-dimensional estimation problem known as "${\mathbb{Z}}_{2}$ synchronization." Statistical physics suggests compute expectation respect this (the mean in synchronization problem), by minimizing so-called Thouless–Anderson–Palmer (TAP) free energy, instead field (MF) energy. prove that...

Abstract Fine-mapping aims to identify causal variants for phenotypes. Bayesian fine-mapping algorithms (e.g.: SuSiE, FINEMAP, ABF, and COJO-ABF) are widely used, but assessing posterior probability calibration remains challenging in real data, where model misspecification likely exists, true unknown. We introduce Replication Failure Rate (RFR), a metric assess consistency by down-sampling. FINEMAP COJO-ABF show high RFR, indicating potential under-conservative mis-calibration. Simulations...

We study estimation in the linear model <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$y=A \beta ^{\star} +\epsilon $ </tex-math></inline-formula> , a Bayesian setting where notation="LaTeX">$ has an entrywise i.i.d. prior and design notation="LaTeX">$A$ is rotationally-invariant law. In large system limit as dimension sample size increase proportionally, set of related conjectures have been postulated...

We study the sample covariance matrix for real-valued data with general population covariance, as well MANOVA-type estimators in variance components models under null hypotheses of global sphericity. In limit dimensions increase proportionally, asymptotic spectra such may have multiple disjoint intervals support, possibly intersecting negative half line. show that distribution extremal eigenvalue at each regular edge support has a GOE Tracy–Widom limit. Our proof extends comparison argument...

Abstract We study the nonconvex optimization landscape for maximum likelihood estimation in discrete orbit recovery model with Gaussian noise. This is a statistical motivated by applications molecular microscopy and image processing, where each measurement of an unknown object subject to independent random rotation from known rotational group. Equivalently, it mixture centers belong group orbit. show that fundamental properties depend on signal‐to‐noise ratio structure. At low noise, this...

We study mean-field variational Bayesian inference using the TAP approach, for Z2-synchronization as a prototypical example of high-dimensional model. show that any signal strength λ>1 (the weak-recovery threshold), there exists unique local minimizer free energy functional near mean Bayes posterior law. Furthermore, in neighborhood this is strongly convex. Consequently, natural-gradient/mirror-descent algorithm achieves linear convergence to from initialization, which may be obtained by...

We study the eigenvalue distributions of Conjugate Kernel and Neural Tangent associated to multi-layer feedforward neural networks. In an asymptotic regime where network width is increasing linearly in sample size, under random initialization weights, for input samples satisfying a notion approximate pairwise orthogonality, we show that CK NTK converge deterministic limits. The limit described by iterating Marcenko-Pastur map across hidden layers. equivalent linear combination matrices...

Abstract When the dimension of data is comparable to or larger than number samples, principal components analysis (PCA) may exhibit problematic high-dimensional noise. In this work, we propose an empirical Bayes PCA method that reduces noise by estimating a joint prior distribution for components. EB-PCA based on classical Kiefer–Wolfowitz non-parametric maximum likelihood estimator estimation, distributional results derived from random matrix theory sample PCs and iterative refinement using...