Search

In this study, we utilize the minimal geometric deformation technique of gravitational decoupling to extend the regular Bardeen black hole, leading to the derivation of new black hole solutions within the framework of Rastall theory. By decoupling the field equations associated with an extended matter source into two subsystems, we address the first subsystem using the metric components of the regular Bardeen black hole. The second subsystem, incorporating the effects of the additional source, is solved through a constraint imposed by a linear equation of state. By linearly combining the solutions of these subsystems, we obtain two extended models. We then explore the distinct physical properties of these models for specific values of the Rastall and decoupling parameters. Our investigations encompass effective thermodynamic variables such as density and anisotropic pressure, asymptotic flatness, energy conditions, and thermodynamic properties including Hawking temperature, entropy, and specific heat. The results reveal that both models violate asymptotic flatness of the resulting spacetimes. The violation of energy conditions indicate the presence of exotic matter, for both models. Nonetheless, the energy density, radial pressure, as well as the Hawking temperature exhibit acceptable behavior, while the specific heat and Hessian matrix suggest thermodynamic stability., Comment: 28 pages, 14 figures

Qubit performance is often reported in terms of a variety of single-value metrics, each providing a facet of the underlying noise mechanism limiting performance. However, the value of these metrics may drift over long time-scales, and reporting a single number for qubit performance fails to account for the low-frequency noise processes that give rise to this drift. In this work, we demonstrate how we can use the distribution of these values to validate or invalidate candidate noise models. We focus on the case of randomized benchmarking (RB), where typically a single error rate is reported but this error rate can drift over time when multiple passes of RB are performed. We show that using a statistical test as simple as the Kolmogorov-Smirnov statistic on the distribution of RB error rates can be used to rule out noise models, assuming the experiment is performed over a long enough time interval to capture relevant low frequency noise. With confidence in a noise model, we show how care must be exercised when performing error attribution using the distribution of drifting RB error rate., Comment: 16 pages, 12 figures

We present skwdro, a Python library for training robust machine learning models. The library is based on distributionally robust optimization using optimal transport distances. For ease of use, it features both scikit-learn compatible estimators for popular objectives, as well as a wrapper for PyTorch modules, enabling researchers and practitioners to use it in a wide range of models with minimal code changes. Its implementation relies on an entropic smoothing of the original robust objective in order to ensure maximal model flexibility. The library is available at https://github.com/iutzeler/skwdro, Comment: 6 pages 1 figure

In this paper, we propose a novel data valuation method for a Dataset Retrieval (DR) use case in Ireland's National mapping agency. To the best of our knowledge, data valuation has not yet been applied to Dataset Retrieval. By leveraging metadata and a user's preferences, we estimate the personal value of each dataset to facilitate dataset retrieval and filtering. We then validated the data value-based ranking against the stakeholders' ranking of the datasets. The proposed data valuation method and use case demonstrated that data valuation is promising for dataset retrieval. For instance, the outperforming dataset retrieval based on our approach obtained 0.8207 in terms of NDCG@5 (the truncated Normalized Discounted Cumulative Gain at 5). This study is unique in its exploration of a data valuation-based approach to dataset retrieval and stands out because, unlike most existing methods, our approach is validated using the stakeholders ranking of the datasets., Comment: 5 pages, 1 figure

We present the results of a thorough investigation of the physical properties of EuAg$_4$Sb$_2$ single crystals using magnetization, heat capacity, and electrical resistivity measurements. High-quality single crystals, which crystallize in a trigonal structure with space group $R\bar{3}m$, were grown using a conventional flux method. Temperature-dependent magnetization measurements along different crystallographic orientations confirm two antiferromagnetic phase transitions around $T_{N1}$ = 10.5 K and $T_{N2}$ = 7.5 K. Isothermal magnetization data exhibit several metamagnetic transitions below these transition temperatures. Antiferromagnetic phase transitions in EuAg$_4$Sb$_2$ are further confirmed by two sharp peaks in the temperature-dependent heat capacity data at $T_{N1}$ and $T_{N2}$, which shift to the lower temperature in the presence of an external magnetic field. Our systematic heat capacity measurements utilizing a long-pulse and single-slope analysis technique allow us to detect a first-order phase transition in EuAg$_4$Sb$_2$ at 7.5 K. The temperature-dependent electrical resistivity data also manifest two features associated with magnetic order. The magnetoresistance exhibits a broad hump due to the field-induced metamagnetic transition. Remarkably, the magnetoresistance keeps increasing without showing any tendency to saturate as the applied magnetic field increases, and it reaches $\sim$20000\% at 1.6 K and 60 T. At high magnetic fields, several magnetic quantum oscillations are observed, indicating a complex Fermi surface. A large negative magnetoresistance of about -55\% is also observed near $T_{N1}$. Moreover, the $H$-$T$ phase diagram constructed using magnetization, heat capacity, and magnetotransport data indicates complex magnetic behavior in EuAg$_4$Sb$_2$., Comment: 10 pages, 6 figures

In this paper, we examine the long-run distribution of stochastic gradient descent (SGD) in general, non-convex problems. Specifically, we seek to understand which regions of the problem's state space are more likely to be visited by SGD, and by how much. Using an approach based on the theory of large deviations and randomly perturbed dynamical systems, we show that the long-run distribution of SGD resembles the Boltzmann-Gibbs distribution of equilibrium thermodynamics with temperature equal to the method's step-size and energy levels determined by the problem's objective and the statistics of the noise. In particular, we show that, in the long run, (a) the problem's critical region is visited exponentially more often than any non-critical region; (b) the iterates of SGD are exponentially concentrated around the problem's minimum energy state (which does not always coincide with the global minimum of the objective); (c) all other connected components of critical points are visited with frequency that is exponentially proportional to their energy level; and, finally (d) any component of local maximizers or saddle points is "dominated" by a component of local minimizers which is visited exponentially more often., Comment: 70 pages, 3 figures; presented in ICML 2024

Many problems in machine learning write as the minimization of a sum of individual loss functions over the training examples. These functions are usually differentiable but, in some cases, their gradients are not Lipschitz continuous, which compromises the use of (proximal) gradient algorithms. Fortunately, changing the geometry and using Bregman divergences can alleviate this issue in several applications, such as for Poisson linear inverse problems.However, the Bregman operation makes the aggregation of several points and gradients more involved, hindering the distribution of computations for such problems. In this paper, we propose an asynchronous variant of the Bregman proximal-gradient method, able to adapt to any centralized computing system. In particular, we prove that the algorithm copes with arbitrarily long delays and we illustrate its behavior on distributed Poisson inverse problems.

Distributionally robust optimization has emerged as an attractive way to train robust machine learning models, capturing data uncertainty and distribution shifts. Recent statistical analyses have proved that robust models built from Wasserstein ambiguity sets have nice generalization guarantees, breaking the curse of dimensionality. However, these results are obtained in specific cases, at the cost of approximations, or under assumptions difficult to verify in practice. In contrast, we establish, in this article, exact generalization guarantees that cover all practical cases, including any transport cost function and any loss function, potentially non-convex and nonsmooth. For instance, our result applies to deep learning, without requiring restrictive assumptions. We achieve this result through a novel proof technique that combines nonsmooth analysis rationale with classical concentration results. Our approach is general enough to extend to the recent versions of Wasserstein/Sinkhorn distributionally robust problems that involve (double) regularizations.

We investigate the physical properties of high-quality single crystals CeGaGe and PrGaGe using magnetization, heat capacity, and magnetotransport measurements. Gallium-indium binary flux was used to grow these single crystals that crystallize in a body-centered tetragonal structure. Magnetic susceptibility data reveal a magnetic phase transition around 6.0 and 19.4 K in CeGaGe and PrGaGe, respectively, which is further confirmed by heat capacity and electrical resistivity data. A number of additional anomalies have been observed below the ordering temperature in the magnetic susceptibility data, indicating a complex magnetic structure. The magnetic measurements also reveal a strong magnetocrystalline anisotropy in both compounds. Our detailed analysis of the crystalline electric field (CEF) effect as observed in magnetic susceptibility and heat capacity data suggests that the $J$ = 5/2 multiplet of CeGaGe splits into three doublets, while the $J$ = 4 degenerate ground state of PrGaGe splits into five singlets and two doublets. The estimated energy levels from the CEF analysis are consistent with the magnetic entropy., Comment: 10 pages, 5 figures

Wasserstein distributionally robust estimators have emerged as powerful models for prediction and decision-making under uncertainty. These estimators provide attractive generalization guarantees: the robust objective obtained from the training distribution is an exact upper bound on the true risk with high probability. However, existing guarantees either suffer from the curse of dimensionality, are restricted to specific settings, or lead to spurious error terms. In this paper, we show that these generalization guarantees actually hold on general classes of models, do not suffer from the curse of dimensionality, and can even cover distribution shifts at testing. We also prove that these results carry over to the newly-introduced regularized versions of Wasserstein distributionally robust problems., Comment: 49 pages, 2 figures; to be presented at the 37th Annual Conference on Neural Information Processing Systems (NeurIPS 2023)

These are the appendices for the report "Study of Teacher Coaching Based on Classroom Videos: Impacts on Student Achievement and Teachers' Practices. Evaluation Report." This report examined a promising strategy for individualized coaching: professional coaches--rather than district or school staff--providing feedback to teachers based on videos of their instruction. Feedback based on videos gives teachers the opportunity to observe and reflect on their own teaching and allows coaches to show teachers specific moments from their teaching when providing feedback. For this study, 107 elementary schools were randomly divided into three groups: one that received fewer highly structured cycles of focused professional coaching during a single school year (five cycles), one that received more (eight cycles), and one that continued with its usual strategies for supporting teachers. The study compared teachers' experiences and student achievement across the three groups to determine the effectiveness of the two versions of the coaching. This document provides additional details on the coaching provided for the study, the approach to carrying out the study, and the findings presented in the report. The following three appendices are included: (1) The Study's Video-Base Coaching for Teachers; (2) Study Design, Data Collection, and Analytic Methods; and (3) Supplemental Exhibits and Information on Study Findings. [For the full report, see ED619739. For the Study Highlights, see ED619740.]

Helping teachers become more effective in the classroom is a high priority for educators and policymakers. A growing body of evidence suggests that individualized coaching focused on general teaching practices can improve teachers' instruction and student achievement. However, little is known about the benefits of specific approaches to coaching, including who is doing the coaching, how coaches observe teachers' instruction, and how or how often coaches provide feedback to teachers. This study examined one promising strategy for individualized coaching: professional coaches--rather than district or school staff--providing feedback to teachers based on videos of their instruction. Feedback based on videos gives teachers the opportunity to observe and reflect on their own teaching and allows coaches to show teachers specific moments from their teaching when providing feedback. For this study, about 100 elementary schools were randomly divided into three groups: one that received fewer highly structured cycles of focused professional coaching during a single school year (five cycles), one that received more (eight cycles), and one that continued with its usual strategies for supporting teachers. The study compared teachers' experiences and student achievement across the three groups to determine the effectiveness of the two versions of the coaching. Key findings include: (1) Five coaching cycles based on videos of teachers' instruction improved students' achievement, including for novice teachers and those with weaker classroom practices at the start of the study; (2) Eight cycles of coaching was not effective. Eight cycles of the coaching did not affect student achievement, perhaps because teachers had less time during each cycle to work on the practices being addressed; and (3) The study's coaching changed the type of feedback that teachers received. Compared to those who did not receive the study's coaching, teachers who received the coaching were more likely to report receiving feedback that focused on specific teaching practices, included strategies to use in their classrooms, and provided opportunities to observe and reflect on their teaching. [For the Study Highlights, see ED619740. For the appendix, see ED619742.]