Hasil untuk "The Bible"

The Tien Mai, Zhi Zhao

Covariance matrices arise naturally in different scientific fields, including finance, genomics, and neuroscience, where they encode dependence structures and reveal essential features of complex multivariate systems. In this work, we introduce a comprehensive Bayesian framework for analyzing heterogeneous covariance data through both classical mixture models and a novel mixture-of-experts Wishart (MoE-Wishart) model. The proposed MoE-Wishart model extends standard Wishart mixtures by allowing mixture weights to depend on predictors through a multinomial logistic gating network. This formulation enables the model to capture complex, nonlinear heterogeneity in covariance structures and to adapt subpopulation membership probabilities to covariate-dependent patterns. To perform inference, we develop an efficient Gibbs-within-Metropolis-Hastings sampling algorithm tailored to the geometry of the Wishart likelihood and the gating network. We additionally derive an Expectation-Maximization algorithm for maximum likelihood estimation in the mixture-of-experts setting. Extensive simulation studies demonstrate that the proposed Bayesian and maximum likelihood estimators achieve accurate subpopulation recovery and estimation under a range of heterogeneous covariance scenarios. Finally, we present an innovative application of our methodology to a challenging dataset: cancer drug sensitivity profiles, illustrating the ability of the MoE-Wishart model to leverage covariance across drug dosages and replicate measurements. Our methods are implemented in the \texttt{R} package \texttt{moewishart} available at https://github.com/zhizuio/moewishart .

Ewa Bednarczuk, The Hung Tran

We consider the saddle point problem where the objective functions are abstract convex with respect to the class of quadratic functions. We propose primal-dual algorithms using the corresponding abstract proximal operator and investigate the convergence under certain restrictions. We test our algorithms by several numerical examples.

Steven Senger, Dung The Tran

We establish a sharp point-sphere incidence bound in finite fields for point sets exhibiting controlled additive structure. Working in the framework of \((4,s)\)-Salem sets, which quantify pseudorandomness via fourth-order additive energy, we prove that if \(P\subset \mathbb{F}_q^d\) is a \((4,s)\)-Salem set with \(s\in \big( \frac{1}{4}, \frac{1}{2} \big]\) and \(|P|\ll q^{ \frac{d}{4s}}\), then for any finite family \(S\) of spheres in \(\mathbb{F}_q^d\), \[ \bigg| I(P,S)-\frac{|P||S| }{q} \bigg| \ll q^{\frac{d}{4}}\,|P|^{1-s}\,|S|^{\frac{3}{4}}. \] This estimate improves the classical point-sphere incidence bounds for arbitrary point sets across a broad parameter range. The proof combines additive energy estimates with a lifting argument that converts point-sphere incidences into point-hyperplane incidences in one higher dimension while preserving the \((4,s)\)-Salem property. As applications, we derive refined bounds for unit distances and sum-product type phenomena, and we extend the method to \((u,s)\)-Salem sets for even moments \(u\ge4\).

Christian T. Petersen

As a matter of course, science has to keep up with the findings. Only generations later, some papers have caused laughter in hindsight. Nonetheless, scholars had to dare to make the best out of their sources. Whilst editions of the Codex Argenteus became even more elaborate by comments and translations, mere grammar and vocabulary studies came into existence. The ‘Neuzeit’ output is connected to names as Grimm and many others. Especially in the past century, publications on Gothic have proliferated, and some text books still found their way to college and university – be it in Europe or America: especially US immigrants with German background have deserved their credits. Nowadays, Bologna-process, PISA-studies and the like have rung the death knell for this very discipline. Sapere aude!

The Tien Mai

Sparse regression problems, where the goal is to identify a small set of relevant predictors, often require modeling not only main effects but also meaningful interactions through other variables. While the pliable lasso has emerged as a powerful frequentist tool for modeling such interactions under strong heredity constraints, it lacks a natural framework for uncertainty quantification and incorporation of prior knowledge. In this paper, we propose a Bayesian pliable lasso that extends this approach by placing sparsity-inducing priors, such as the horseshoe, on both main and interaction effects. The hierarchical prior structure enforces heredity constraints while adaptively shrinking irrelevant coefficients and allowing important effects to persist. We extend this framework to Generalized Linear Models (GLMs) and develop a tailored approach to handle missing responses. To facilitate posterior inference, we develop an efficient Gibbs sampling algorithm based on a reparameterization of the horseshoe prior. Our Bayesian framework yields sparse, interpretable interaction structures, and principled measures of uncertainty. Through simulations and real-data studies, we demonstrate its advantages over existing methods in recovering complex interaction patterns under both complete and incomplete data. Our method is implemented in the package \texttt{hspliable} available on Github.

The Tien Mai

In high-dimensional statistics, the Lasso is a cornerstone method for simultaneous variable selection and parameter estimation. However, its reliance on the squared loss function renders it highly sensitive to outliers and heavy-tailed noise, potentially leading to unreliable model selection and biased estimates. To address this limitation, we introduce the Exponential Lasso, a novel robust method that integrates an exponential-type loss function within the Lasso framework. This loss function is designed to achieve a smooth trade-off between statistical efficiency under Gaussian noise and robustness against data contamination. Unlike other methods that cap the influence of large residuals, the exponential loss smoothly redescends, effectively downweighting the impact of extreme outliers while preserving near-quadratic behavior for small errors. We establish theoretical guarantees showing that the Exponential Lasso achieves strong statistical convergence rates, matching the classical Lasso under ideal conditions while maintaining its robustness in the presence of heavy-tailed contamination. Computationally, the estimator is optimized efficiently via a Majorization-Minimization (MM) algorithm that iteratively solves a series of weighted Lasso subproblems. Numerical experiments demonstrate that the proposed method is highly competitive, outperforming the classical Lasso in contaminated settings and maintaining strong performance even under Gaussian noise. Our method is implemented in the \texttt{R} package \texttt{heavylasso} available on Github: https://github.com/tienmt/heavylasso

The Anh Bui

We establish fractional Leibniz rules in weighted settings for nonnegative self-adjoint operators on spaces of homogeneous type. Using a unified method that avoids Fourier transforms, we prove bilinear estimates for spectral multiplier on weighted Hardy, Besov and Triebel-Lizorkin spaces. Our approach is flexible and applies beyond the Euclidean setting-covering, for instance, nilpotent Lie groups, Grushin operators, and Hermite expansions-thus extending classical Kato-Ponce inequalities. The framework also yields new weighted bilinear estimates including fractional Leibniz rules for Hermite, Laguerre, and Bessel operator, with applications to scattering formulas and related PDE models.

The Tien Mai

Quantile regression, a robust method for estimating conditional quantiles, has advanced significantly in fields such as econometrics, statistics, and machine learning. In high-dimensional settings, where the number of covariates exceeds sample size, penalized methods like lasso have been developed to address sparsity challenges. Bayesian methods, initially connected to quantile regression via the asymmetric Laplace likelihood, have also evolved, though issues with posterior variance have led to new approaches, including pseudo/score likelihoods. This paper presents a novel probabilistic machine learning approach for high-dimensional quantile prediction. It uses a pseudo-Bayesian framework with a scaled Student-t prior and Langevin Monte Carlo for efficient computation. The method demonstrates strong theoretical guarantees, through PAC-Bayes bounds, that establish non-asymptotic oracle inequalities, showing minimax-optimal prediction error and adaptability to unknown sparsity. Its effectiveness is validated through simulations and real-world data, where it performs competitively against established frequentist and Bayesian techniques.

The Tien Mai

The problem of estimating a matrix based on a set of its observed entries is commonly referred to as the matrix completion problem. In this work, we specifically address the scenario of binary observations, often termed as 1-bit matrix completion. While numerous studies have explored Bayesian and frequentist methods for real-value matrix completion, there has been a lack of theoretical exploration regarding Bayesian approaches in 1-bit matrix completion. We tackle this gap by considering a general, non-uniform sampling scheme and providing theoretical assurances on the efficacy of the fractional posterior. Our contributions include obtaining concentration results for the fractional posterior and demonstrating its effectiveness in recovering the underlying parameter matrix. We accomplish this using two distinct types of prior distributions: low-rank factorization priors and a spectral scaled Student prior, with the latter requiring fewer assumptions. Importantly, our results exhibit an adaptive nature by not mandating prior knowledge of the rank of the parameter matrix. Our findings are comparable to those found in the frequentist literature, yet demand fewer restrictive assumptions.

The Tien Mai

Reduced rank regression (RRR) is a widely employed model for investigating the linear association between multiple response variables and a set of predictors. While RRR has been extensively explored in various works, the focus has predominantly been on continuous response variables, overlooking other types of outcomes. This study shifts its attention to the Bayesian perspective of generalized linear models (GLM) within the RRR framework. In this work, we relax the requirement for the link function of the generalized linear model to be canonical. We examine the properties of fractional posteriors in GLM within the RRR context, where a fractional power of the likelihood is utilized. By employing a spectral scaled Student prior distribution, we establish consistency and concentration results for the fractional posterior. Our results highlight adaptability, as they do not necessitate prior knowledge of the rank of the parameter matrix. These results are in line with those found in frequentist literature. Additionally, an examination of model mis-specification is undertaken, underscoring the effectiveness of our approach in such scenarios.

Paul D. Wheatley

The abundance of ritual descriptions in the Gospel of Mark suggests a discourse about ritual between the narrator and early audiences of the Gospel. The prominence of the ritual of baptism at the beginning (Mark 1:9–11) and anointing at the end (16:1–8), and the recurrence of themes introduced in Jesus’s baptism at turning points in the Gospel (9:2–8; 10:38–39; 15:38–39) suggest broader ritual—and specifically baptismal—significance in the narrative. Recent changes helpfully differentiate narrative- and performance-critical interpretive approaches as text-oriented (narrative) and audience-oriented (performance), but these hermeneutical methods also work in concert. This article combines cognitive studies of narrative immersion with observations about the role of ritual in group identity formation and the impartation of religious traditions to analyze the narration of ritual acts in Mark. Giving attention to the use of internal focalization and description of bodily movements in ritual narrations, this article argues that depictions of rituals in Mark involve the audience in ways that deliver audience-oriented interpretations through text-oriented means. This analysis shows how Mark’s ritual narrations are conducive to evoking the audience’s experience of baptism, familiar to audience members as described in the undisputed Pauline epistles, the only descriptions of the rite that clearly antedate the composition of Mark. Publicly reading these narrated rituals creates an audience experience that neither requires the performance of the ritual in the context of the reading event nor an “acting out” of the ritual depicted in the narrative to create a participatory, communal experience of the text.

Adam Ryszard Prokop

Die Görres-Schule zu Leipzig war ein Zeichen der Zeit des frühen XX. Jahrhunderts in der katholischen Landschaft Deutschlands. An der Breite der Angebote, wie auch Anzahl von Zuhörern durfte man sie zu den größten Erscheinungsformen der katholischen Erwachsenenbildung ihrer Zeit zählen. Es ist bemerkenswert, weil Leipzig sich schon damals inmitten des Diasporagebietes befand, zu dem neugegründeten (1921), finanziell und strukturell eher bescheidenen Bistum Meißen gehörend. Im Jahre 1935 übernahm der spätere Bischof Otto Spülbeck die Leitung dieses Werkes. Die vorliegende Abhandlung versucht dieses herausragende  Phänomen aufgrund des im Diözesanarchiv des Bistums Dresden-Meißens erhaltenen Bestandes darzustellen. Die Archivalien erlauben einen tieferen Einblick in die Vorgänge erst ab dem Jahr 1941. Die Ausführungen über die Aktivitätsformen und ihre immer stärkere Beeinflussung durch den Krieg wurden um den Kontext der Erwachsenenseelsorge in der Diözese und kurze Schilderung der Leiterpersönlichkeit ergänzt.

The Tien Mai

In this study, we address the problem of high-dimensional binary classification. Our proposed solution involves employing an aggregation technique founded on exponential weights and empirical hinge loss. Through the employment of a suitable sparsity-inducing prior distribution, we demonstrate that our method yields favorable theoretical results on prediction error. The efficiency of our procedure is achieved through the utilization of Langevin Monte Carlo, a gradient-based sampling approach. To illustrate the effectiveness of our approach, we conduct comparisons with the logistic Lasso on simulated data and a real dataset. Our method frequently demonstrates superior performance compared to the logistic Lasso.

Johann Cook

A relatively recent development in Septuagint studies is a focus on the alleged influence of Platonism on the Bible(s) (Hebrew Bible/Old Testament and the Septuagint). This article argues that Hellenism did in fact have an impact on Judaism. There are basically two groups of views on this issue. The first is that of the so-called minimalists, who make practically no allowance for freedom by the translators, and the second is that of the so-called maximalists, who believe that translators are relatively independent authors and interpreters. As far as the relationship between Judaism and Platonism is concerned, some scholars think Greek thought, specifically in the form of Platonism, had a determinative influence on Judaism, but others are not convinced. This article opts for a middle of the road point of view. It accepts that Hellenism had a definite impact on Judaism but it was not as extensive as stated by some. Contribution: This research fits into the scope of HTS Teologiese Studies/Theological Studies because it has made a study of the alleged impact of Platonism on Judaism. It finds that this impact is based on speculation, especially, by two authors: Evangelia Dafni and Russell Gmirkin.

The LIGO Scientific Collaboration, the Virgo Collaboration, the KAGRA Collaboration et al.

We search for gravitational-wave transients associated with fast radio bursts (FRBs) detected by the Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst Project (CHIME/FRB), during the first part of the third observing run of Advanced LIGO and Advanced Virgo (1 April 2019 15:00 UTC-1 Oct 2019 15:00 UTC). Triggers from 22 FRBs were analyzed with a search that targets compact binary coalescences with at least one neutron star component. A targeted search for generic gravitational-wave transients was conducted on 40 FRBs. We find no significant evidence for a gravitational-wave association in either search. Given the large uncertainties in the distances of the FRBs inferred from the dispersion measures in our sample, however, this does not conclusively exclude any progenitor models that include emission of a gravitational wave of the types searched for from any of these FRB events. We report $90\%$ confidence lower bounds on the distance to each FRB for a range of gravitational-wave progenitor models. By combining the inferred maximum distance information for each FRB with the sensitivity of the gravitational-wave searches, we set upper limits on the energy emitted through gravitational waves for a range of emission scenarios. We find values of order $10^{51}$-$10^{57}$ erg for a range of different emission models with central gravitational wave frequencies in the range 70-3560 Hz. Finally, we also found no significant coincident detection of gravitational waves with the repeater, FRB 20200120E, which is the closest known extragalactic FRB.

The ATLAS Collaboration

Inclusive and differential measurements of the top-antitop ($t\bar{t}$) charge asymmetry $A_\text{C}^{t\bar{t}}$ and the leptonic asymmetry $A_\text{C}^{\ell\bar{\ell}}$ are presented in proton-proton collisions at $\sqrt{s} = 13$ TeV recorded by the ATLAS experiment at the CERN Large Hadron Collider. The measurement uses the complete Run 2 dataset, corresponding to an integrated luminosity of 139 fb$^{-1}$, combines data in the single-lepton and dilepton channels, and employs reconstruction techniques adapted to both the resolved and boosted topologies. A Bayesian unfolding procedure is performed to correct for detector resolution and acceptance effects. The combined inclusive $t\bar{t}$ charge asymmetry is measured to be $A_\text{C}^{t\bar{t}} = 0.0068 \pm 0.0015$, which differs from zero by 4.7 standard deviations. Differential measurements are performed as a function of the invariant mass, transverse momentum and longitudinal boost of the $t\bar{t}$ system. Both the inclusive and differential measurements are found to be compatible with the Standard Model predictions, at next-to-next-to-leading order in quantum chromodynamics perturbation theory with next-to-leading-order electroweak corrections. The measurements are interpreted in the framework of the Standard Model effective field theory, placing competitive bounds on several Wilson coefficients.

The ATLAS Collaboration

A measurement of the charge asymmetry in top-quark pair ($t\bar{t}$) production in association with a photon is presented. The measurement is performed in the single-lepton $t\bar{t}$ decay channel using proton-proton collision data collected with the ATLAS detector at the Large Hadron Collider at CERN at a centre-of-mass-energy of 13 TeV during the years 2015-2018, corresponding to an integrated luminosity of 139 fb$^{-1}$. The charge asymmetry is obtained from the distribution of the difference of the absolute rapidities of the top quark and antiquark using a profile likelihood unfolding approach. It is measured to be $A_\text{C}=-0.003 \pm 0.029$ in agreement with the Standard Model expectation.

The Tien Mai

The problem of Bayesian reduced rank regression is considered in this paper. We propose, for the first time, to use Langevin Monte Carlo method in this problem. A spectral scaled Student prior distrbution is used to exploit the underlying low-rank structure of the coefficient matrix. We show that our algorithms are significantly faster than the Gibbs sampler in high-dimensional setting. Simulation results show that our proposed algorithms for Bayesian reduced rank regression are comparable to the state-of-the-art method where the rank is chosen by cross validation.

The Tien Mai

We study the problem of matrix completion in this paper. A spectral scaled Student prior is exploited to favour the underlying low-rank structure of the data matrix. We provide a thorough theoretical investigation for our approach through PAC-Bayesian bounds. More precisely, our PAC-Bayesian approach enjoys a minimax-optimal oracle inequality which guarantees that our method works well under model misspecification and under general sampling distribution. Interestingly, we also provide efficient gradient-based sampling implementations for our approach by using Langevin Monte Carlo. More specifically, we show that our algorithms are significantly faster than Gibbs sampler in this problem. To illustrate the attractive features of our inference strategy, some numerical simulations are conducted and an application to image inpainting is demonstrated.

The Tien Mai

In this paper, we study the low-rank matrix completion problem, a class of machine learning problems, that aims at the prediction of missing entries in a partially observed matrix. Such problems appear in several challenging applications such as collaborative filtering, image processing, and genotype imputation. We compare the Bayesian approaches and a recently introduced de-biased estimator which provides a useful way to build confidence intervals of interest. From a theoretical viewpoint, the de-biased estimator comes with a sharp minimax-optimal rate of estimation error whereas the Bayesian approach reaches this rate with an additional logarithmic factor. Our simulation studies show originally interesting results that the de-biased estimator is just as good as the Bayesian estimators. Moreover, Bayesian approaches are much more stable and can outperform the de-biased estimator in the case of small samples. In addition, we also find that the empirical coverage rate of the confidence intervals obtained by the de-biased estimator for an entry is absolutely lower than of the considered credible interval. These results suggest further theoretical studies on the estimation error and the concentration of Bayesian methods as they are quite limited up to present.