Stress–strain curves capture the mechanical behavior of materials but are computationally expensive to generate using crystal-plasticity finite-element (CPFE) models, due to the profound nonlinearity of the response, and its relationship to crystallographic orientation. We propose an AI-driven framework for predicting bilinear approximate stress–strain curves of metallic alloys using supervised machine learning models. We evaluate its performance on three representative materials: aluminum (Al), nickel (Ni), and copper (Cu), commonly used in aerospace engineering. Trained on just 100 fully resolved CPFE curves per material, our model accurately reconstructs entire curves using features extracted after only a single CPFE step, effectively leading to orders of magnitude speedup with respect to CPFE simulation for predicting stress-strain curves of new orientations unseen by the AI model. The resulting predictions achieve a mean absolute error fraction of around 1.53% for nickel, 1.43% for aluminum, and 2.86% for copper, while producing orientation-specific stress–strain curves several times faster than conventional CPFE simulations.

The m-out-of-n bootstrap—proposed by \cite{bickel1992resampling}—approximates the distribution of a statistic by repeatedly drawing $m$ subsamples ($m \ll n$) without replacement from an original sample of size n; it is now routinely used for robust inference with heavy-tailed data, bandwidth selection, and other large-sample applications. Despite this broad applicability across econometrics, biostatistics, and machine-learning workflows, rigorous parameter-free guarantees for the soundness of the m-out-of-n bootstrap when estimating sample quantiles have remained elusive. This paper establishes such guarantees by analysing the estimator of sample quantiles obtained from m-out-of-n resampling of a dataset of length n. We first prove a central limit theorem for a fully data-driven version of the estimator that holds under a mild moment condition and involves no unknown nuisance parameters. We then show that the moment assumption is essentially tight by constructing a counter-example in which the CLT fails. Strengthening the assumptions slightly, we derive an Edgeworth expansion that delivers exact convergence rates and, as a corollary, a Berry–Esséen bound on the bootstrap approximation error. Finally, we illustrate the scope of our results by obtaining parameter-free asymptotic distributions for practical statistics, including the quantiles for random walk MH, and rewards of ergodic MDP's, thereby demonstrating the usefulness of our theory in modern estimation and learning tasks.

Fake reviews are having a devastating negative influence on online shopping sites. The proliferation of fake reviews is exacerbated by the presence of SockFarms, companies that create and operate huge sets of sockpuppet accounts to promote their customers’ products by posting fake reviews. Our proposed SockAttack algorithm allows such companies to optimize their actions to maximize profits. We show that SockAttack compromises the F1-score of four well-known review fraud detection engines on real-world datasets (up to 27.1% more than baselines). We then propose a defense algorithm called SockDef and show that it mitigates the impact of SockAttack (up to 69.2% with respect to F1-score).

Probabilistic principal component analysis (PPCA) is currently one of the most used statistical tools to reduce the ambient dimension of the data. From multidimensional scaling to the imputation of missing data, PPCA has a broad spectrum of applications ranging from science and engineering to quantitative finance.\\ Despite this wide applicability in various fields, hardly any theoretical guarantees exist to justify the soundness of the maximal likelihood (ML) solution for this model. In fact, it is well known that the maximum likelihood estimation (MLE) can only recover the true model parameters up to a rotation. The main obstruction is posed by the inherent identifiability nature of the PPCA model resulting from the rotational symmetry of the parameterization. To resolve this ambiguity, we propose a novel approach using quotient topological spaces and in particular, we show that the maximum likelihood solution is consistent in an appropriate quotient Euclidean space. Furthermore, our consistency results encompass a more general class of estimators beyond the MLE. Strong consistency of the ML estimate and consequently strong covariance estimation of the PPCA model have also been established under a compactness assumption.

We show that a simple single-pass semi-streaming variant of the Pivot algorithm for Correlation Clustering gives a (3+eps)-approximation using O(n/eps) words of memory. This is a slight improvement over the recent results of Cambus, Kuhn, Lindy, Pai, and Uitto, who gave a (3+eps)-approximation using O(n log n) words of memory, and Behnezhad, Charikar, Ma, and Tan, who gave a 5-approximation using O(n) words of memory. One of the main contributions of our paper is that the algorithm and its analysis are simple and easy to understand.