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The classification of all fourth-order anisotropic tensor classes for classical linear elasticity is well known. In this article, we review the related problem of explicitly computing the dimension and the expressions of the elements belonging to these classes, and we extend this computation to fourth-order elasticity tensors acting on non-symmetric matrices. These tensors naturally appear in generalized continuum models. Based on tensor symmetrization, we provide the most general forms of these tensors for orthotropic, transversely isotropic, cubic, and isotropic materials. We present a self-contained discussion and provide detailed calculations for simple examples.

Training supervised deep neural networks that perform defect detection and segmentation requires large-scale fully-annotated datasets, which can be hard or even impossible to obtain in industrial environments. Generative AI offers opportunities to enlarge small industrial datasets artificially, thus enabling the usage of state-of-the-art supervised approaches in the industry. Unfortunately, also good generative models need a lot of data to train, while industrial datasets are often tiny. Here, we propose a new approach for reusing general-purpose pre-trained generative models on industrial data, ultimately allowing the generation of self-labelled defective images. First, we let the model learn the new concept, entailing the novel data distribution. Then, we force it to learn to condition the generative process, producing industrial images that satisfy well-defined topological characteristics and show defects with a given geometry and location. To highlight the advantage of our approach, we use the synthetic dataset to optimise a crack segmentor for a real industrial use case. When the available data is small, we observe considerable performance increase under several metrics, showing the method's potential in production environments.

We study the completion of approximately low rank matrices with entries missing not at random (MNAR). In the context of typical large-dimensional statistical settings, we establish a framework for the performance analysis of the nuclear norm minimization ($\ell_1^*$) algorithm. Our framework produces \emph{exact} estimates of the worst-case residual root mean squared error and the associated phase transitions (PT), with both exhibiting remarkably simple characterizations. Our results enable to {\it precisely} quantify the impact of key system parameters, including data heterogeneity, size of the missing block, and deviation from ideal low rankness, on the accuracy of $\ell_1^*$-based matrix completion. To validate our theoretical worst-case RMSE estimates, we conduct numerical simulations, demonstrating close agreement with their numerical counterparts., Comment: 3 figures. arXiv admin note: text overlap with arXiv:2301.00793

We present the analysis of two recently proposed noise reduction techniques, Hutch++ and XTrace, both based on inexact deflation. These methods were proven to have a better asymptotic convergence to the solution than the classical Girard-Hutchinson stochastic method. We applied these methods to the computation of the trace of the inverse of the Dirac operator with $O(a)$ improved Wilson fermions on the QCD ensemble generated by the RC$^{\star}$ collaboration with $m_{\pi}\approx 400$ MeV and $V = 64\times 32^3$. Unfortunately, we see no noise reduction with a moderate number of sources, and we attempt an explanation of why this is the case. This study was part of the effort to evaluate isospin-breaking effects using the RM123 with C$^{\star}$ boundary conditions in an unquenched set-up., Comment: 7 pages, 4 figures, RC* collaboration, Contribution to the 40th International Symposium on Lattice Field Theory, 31st July-4th August 2023, Fermilab, USA

A challenge that data analysts face is building a data analysis that is useful for a given consumer. Previously, we defined a set of principles for describing data analyses that can be used to create a data analysis and to characterize the variation between analyses. Here, we introduce a concept that we call the alignment of a data analysis between the data analyst and a consumer. We define a successfully aligned data analysis as the matching of principles between the analyst and the consumer for whom the analysis is developed. In this paper, we propose a statistical model for evaluating the alignment of a data analysis and describe some of its properties. We argue that this framework provides a language for characterizing alignment and can be used as a guide for practicing data scientists and students in data science courses for how to build better data analyses.

Financial markets are undergoing an unprecedented transformation. Technological advances have brought major improvements to the operations of financial services. While these advances promote improved accessibility and convenience, traditional finance shortcomings like lack of transparency and moral hazard frictions continue to plague centralized platforms, imposing societal costs. In this paper, we argue how these shortcomings and frictions are being mitigated by the decentralized finance (DeFi) ecosystem. We delve into the workings of smart contracts, the backbone of DeFi transactions, with an emphasis on those underpinning token exchange and lending services. We highlight the pros and cons of the novel form of decentralized governance introduced via the ownership of governance tokens. Despite its potential, the current DeFi infrastructure introduces operational risks to users, which we segment into five primary categories: consensus mechanisms, protocol, oracle, frontrunning, and systemic risks. We conclude by emphasizing the need for future research to focus on the scalability of existing blockchains, the improved design and interoperability of DeFi protocols, and the rigorous auditing of smart contracts., Comment: 2

We study Just-in-time (JIT) liquidity provision in blockchain-based decentralized exchanges. A JIT liquidity provider (LP) monitors pending swap orders in public mempools of blockchains to sandwich orders of their choice with liquidity, depositing right before and withdrawing right after the order. Our game-theoretic model with asymmetrically informed agents reveals that a JIT LP's presence does not always enhance liquidity pool depth, as one might expect. While passive LPs face adverse selection by informed arbitrageurs, a JIT LP's ability to detect pending orders for toxic order flow prior to liquidity provision lets them avoid being adversely selected. JIT LPs thus only provide liquidity to uninformed orders and crowd out passive LPs when order volume is not sufficiently elastic to pool depth, possibly reducing overall market liquidity. We show that using a two-tiered fee structure which transfers a part of a JIT LP's fee revenue to passive LPs or allowing for JIT LPs to compete \`{a} la Cournot are potential solutions to mitigate the negative effects of JIT liquidity.

X-ray free-electron lasers are sources of coherent, high-intensity X-rays with numerous applications in ultra-fast measurements and dynamic structural imaging. Due to the stochastic nature of the self-amplified spontaneous emission process and the difficulty in controlling injection of electrons, output pulses exhibit significant noise and limited temporal coherence. Standard measurement techniques used for characterizing two-coloured X-ray pulses are challenging, as they are either invasive or diagnostically expensive. In this work, we employ machine learning methods such as neural networks and decision trees to predict the central photon energies of pairs of attosecond fundamental and second harmonic pulses using parameters that are easily recorded at the high-repetition rate of a single shot. Using real experimental data, we apply a detailed feature analysis on the input parameters while optimizing the training time of the machine learning methods. Our predictive models are able to make predictions of central photon energy for one of the pulses without measuring the other pulse, thereby leveraging the use of the spectrometer without having to extend its detection window. We anticipate applications in X-ray spectroscopy using XFELs, such as in time-resolved X-ray absorption and photoemission spectroscopy, where improved measurement of input spectra will lead to better experimental outcomes., Comment: 14 pages, 8 figures

Federated learning (FL) has shown promising potential in safeguarding data privacy in healthcare collaborations. While the term "FL" was originally coined by the engineering community, the statistical field has also explored similar privacy-preserving algorithms. Statistical FL algorithms, however, remain considerably less recognized than their engineering counterparts. Our goal was to bridge the gap by presenting the first comprehensive comparison of FL frameworks from both engineering and statistical domains. We evaluated five FL frameworks using both simulated and real-world data. The results indicate that statistical FL algorithms yield less biased point estimates for model coefficients and offer convenient confidence interval estimations. In contrast, engineering-based methods tend to generate more accurate predictions, sometimes surpassing central pooled and statistical FL models. This study underscores the relative strengths and weaknesses of both types of methods, emphasizing the need for increased awareness and their integration in future FL applications.

In this paper, we analyze parity-violating effects in the propagation of gravitational waves (GWs). For this purpose, we adopt a newly proposed parametrized post-Einstenian (PPE) formalism, which encodes modified gravity corrections to the phase and amplitude of GW waveforms. In particular, we focus our study on three well-known examples of parity-violating theories, namely Chern-Simons, Symmetric Teleparallel and Hor\v ava-Lishitz gravity. For each model, we identify the PPE parameters emerging from the inclusion of parity-violating terms in the gravitational Lagrangian. Thus, we use the simulated sensitivities of third-generation GW interferometers, such as the Einstein Telescope and Cosmic Explorer, to obtain numerical bounds on the PPE coefficients and the physical parameters of binary systems. In so doing, we find that deviations from General Relativity cannot be excluded within given confidence limits. Moreover, our results show an improvement of one order of magnitude in the relative accuracy of the GW parameters compared to the values inferred from the LIGO-Virgo-KAGRA network. In this respect, the present work demonstrates the power of next-generation GW detectors to probe fundamental physics with unprecedented precision., Comment: 19 pages, 8 figures. Accepted for publication in Phys. Rev. D