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We propose a novel statistical inference framework for streaming principal component analysis (PCA) using Oja's algorithm, enabling the construction of confidence intervals for individual entries of the estimated eigenvector. Most existing works on streaming PCA focus on providing sharp sin-squared error guarantees. Recently, there has been some interest in uncertainty quantification for the sin-squared error. However, uncertainty quantification or sharp error guarantees for entries of the estimated eigenvector in the streaming setting remains largely unexplored. We derive a sharp Bernstein-type concentration bound for elements of the estimated vector matching the optimal error rate up to logarithmic factors. We also establish a Central Limit Theorem for a suitably centered and scaled subset of the entries. To efficiently estimate the coordinate-wise variance, we introduce a provably consistent subsampling algorithm that leverages the median-of-means approach, empirically achieving similar accuracy to multiplier bootstrap methods while being significantly more computationally efficient. Numerical experiments demonstrate its effectiveness in providing reliable uncertainty estimates with a fraction of the computational cost of existing methods. 

Oja's algorithm for Streaming Principal Component Analysis (PCA) for n data-points in a d dimensional space achieves the same sin-squared error O(r𝖾𝖿𝖿/n) as the offline algorithm in O(d) space and O(nd) time and a single pass through the datapoints. Here r𝖾𝖿𝖿 is the effective rank (ratio of the trace and the principal eigenvalue of the population covariance matrix Σ). Under this computational budget, we consider the problem of sparse PCA, where the principal eigenvector of Σ is s-sparse, and r𝖾𝖿𝖿 can be large. In this setting, to our knowledge, \textit{there are no known single-pass algorithms} that achieve the minimax error bound in O(d) space and O(nd) time without either requiring strong initialization conditions or assuming further structure (e.g., spiked) of the covariance matrix. We show that a simple single-pass procedure that thresholds the output of Oja's algorithm (the Oja vector) can achieve the minimax error bound under some regularity conditions in O(d) space and O(nd) time. We present a nontrivial and novel analysis of the entries of the unnormalized Oja vector, which involves the projection of a product of independent random matrices on a random initial vector. This is completely different from previous analyses of Oja's algorithm and matrix products, which have been done when the r𝖾𝖿𝖿 is bounded. 

Posterior sampling with the spike-and-slab prior [MB88], a popular multimodal distribution used to model uncertainty in variable selection, is considered the theoretical gold standard method for Bayesian sparse linear regression [CPS09, Roc18]. However, designing provable algorithms for performing this sampling task is notoriously challenging. Existing posterior samplers for Bayesian sparse variable selection tasks either require strong assumptions about the signal-to-noise ratio (SNR) [YWJ16], only work when the measurement count grows at least linearly in the dimension [MW24], or rely on heuristic approximations to the posterior. We give the first provable algorithms for spike-and-slab posterior sampling that apply for any SNR, and use a measurement count sublinear in the problem dimension. Concretely, assume we are given a measurement matrix X∈ℝn×d and noisy observations y=Xθ⋆+ξ of a signal θ⋆ drawn from a spike-and-slab prior π with a Gaussian diffuse density and expected sparsity k, where ξ∼(𝟘n,σ2In). We give a polynomial-time high-accuracy sampler for the posterior π(⋅∣X,y), for any SNR σ−1 > 0, as long as n≥k3⋅polylog(d) and X is drawn from a matrix ensemble satisfying the restricted isometry property. We further give a sampler that runs in near-linear time ≈nd in the same setting, as long as n≥k5⋅polylog(d). To demonstrate the flexibility of our framework, we extend our result to spike-and-slab posterior sampling with Laplace diffuse densities, achieving similar guarantees when σ=O(1k) is bounded. 

Independent Component Analysis (ICA) was introduced in the 1980's as a model for Blind Source Separation (BSS), which refers to the process of recovering the sources underlying a mixture of signals, with little knowledge about the source signals or the mixing process. While there are many sophisticated algorithms for estimation, different methods have different shortcomings. In this paper, we develop a nonparametric score to adaptively pick the right algorithm for ICA with arbitrary Gaussian noise. The novelty of this score stems from the fact that it just assumes a finite second moment of the data and uses the characteristic function to evaluate the quality of the estimated mixing matrix without any knowledge of the parameters of the noise distribution. In addition, we propose some new contrast functions and algorithms that enjoy the same fast computability as existing algorithms like FASTICA and JADE but work in domains where the former may fail. While these also may have weaknesses, our proposed diagnostic, as shown by our simulations, can remedy them. Finally, we propose a theoretical framework to analyze the local and global convergence properties of our algorithms. 

Inclined cables used in bridges or other infrastructures are vulnerable to unsteady wind-induced loads producing moderate- to large-amplitude vibration that may result in damage or failure of the cables, resulting in catastrophic failure of the structure they secure. In the present study, wind-induced response of an inclined smooth cable was studied through wind tunnel measurements using a flexible cable model for a better understanding of the vibration characteristics of structural cables in atmospheric boundary layer wind. For this purpose, in-plane and out-of-plane responses of a sagged and a non-sagged flexible cable were recorded by four accelerometers. Four cases with different yaw and inclination angles of a cable with approximate sag ratios of 1/10 were studied to investigate the wind directionality effect on its excitation mode(s) and response amplitude. Cable tension was also measured during all experiments to assess the correlation of wind speed, excitation vibration mode, and natural frequency of the cable with change in cable tension. Additionally, two inclined cables with no sag were tested to determine the influence of sag of a cable on its vibration characteristics. In the second part of this study, a series of finite element analyses were conducted to predict the wind-induced aerodynamic damping of an inclined bridge cable. Experimental results showed that excitation mode(s) of a cable depend on wind speed, inclination angle, and sag ratio and cable tension. First, second, and third vibration modes were observed at a low wind speed for different test cases, whereas higher vibration modes were observed to contribute to the cable response at high wind speeds. Moreover, it was seen that the cable tension significantly increased with wind speed resulting in increased value of the excited natural frequency. Numerical results obtained through finite element analysis of an inclined full-scale cable showed that the criteria that are based on section models can underestimate the critical reduced velocity for dry cable galloping. 

A computational approach based on a k-ω delayed detached eddy simulation model for predicting aerodynamic loads on a smooth circular cylinder is verified against experiments. Comparisons with experiments are performed for flow over a rigidly mounted (static) cylinder and for an elastically-mounted rigid cylinder oscillating in the transverse direction due to vortex-induced vibration (VIV). For the static cases, measurement data from the literature is used to validate the predictions for normally incident flow. New experiments are conducted as a part of this study for yawed flow, where the cylinder axis is inclined with respect to the inflow velocity at the desired yaw angle, β = 30◦. Good agreement is observed between the predictions and measurements for mean and rms surface pressure. Three yawed flow cases (β = 15◦, 30◦, & 45◦) are simulated and the results are found to be independent of β (independence principle) when the flow speed normal to the cylinder axis is selected as the reference velocity scale. Dynamic (VIV) simulations for an elastically-mounted rigid cylinder are performed by coupling the flow solver with a solid dynamics solver where the cylinder motion is modeled as a mass–spring–damper system. The simulations accurately predict the displacement amplitude and unsteady loading over a wide range of reduced velocity, including the region where ‘‘lock-in’’ (synchronization) occurs. VIV simulations are performed at two yaw angles, β = 0◦ and 45◦ and the independence principle is found to be valid over the range of reduced velocities tested with a slightly higher discrepancy when the vortex shedding frequency is close to the natural frequency of the system. 

Abstract The Gravitational-Wave Transient Catalog (GWTC) is a collection of short-duration (transient) gravitational-wave signals identified by the LIGO–Virgo–KAGRA Collaboration in gravitational-wave data produced by the eponymous detectors. The catalog provides information about the identified candidates, such as the arrival time and amplitude of the signal and properties of the signal’s source as inferred from the observational data. GWTC is the data release of this dataset, and version 4.0 extends the catalog to include observations made during the first part of the fourth LIGO–Virgo–KAGRA observing run up until 2024 January 31. This Letter marks an introduction to a collection of articles related to this version of the catalog, GWTC-4.0. The collection of articles accompanying the catalog provides documentation of the methods used to analyze the data, summaries of the catalog of events, observational measurements drawn from the population, and detailed discussions of selected candidates.