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The structural and electronic properties of the CaMnGe$_2$O$_6$ and SrMnGe$_2$O$_6$ clinopyroxene systems have been investigated by means of perturbed angular correlation (PAC) measurements, performed at ISOLDE, combined with $ab-initio$ electronic structure calculations within the density functional theory (DFT) framework. The partial density of states (PDOS) of the CaMnGe$_2$O$_6$ and SrMnGe$_2$O$_6$ stable compounds has been determined, and it has been observed that the requirement of including an on-site Hubbard-$U$ potential was necessary in order to describe the highly correlated Mn $3d$-states. By considering $U_{eff}$=4 eV, we obtained a band gap width of 1.82 eV and 1.70 eV, for the CaMnGe$_2$O$_6$ and SrMnGe$_2$O$_6$, respectively. Combining electric field gradient (EFG) first principles calculations, using a supercell scheme, with experimental PAC results, we were able to infer that the Cd probe can replace either the $A$ (Ca, Sr) or the Mn sites in the crystalline structures. We also showed that Cd substitution is expected to lead to a reduction in the width of the band gap in these systems, evidencing opportunities for potential band-gap engineering.

Determining which parameters of a non-linear model best describe a set of experimental data is a fundamental problem in science and it has gained much traction lately with the rise of complex large-scale simulators. The likelihood of such models is typically intractable, which is why classical MCMC methods can not be used. Simulation-based inference (SBI) stands out in this context by only requiring a dataset of simulations to train deep generative models capable of approximating the posterior distribution that relates input parameters to a given observation. In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model. The proposed method is built upon recent developments from the flourishing score-based diffusion literature and allows to estimate the tall data posterior distribution, while simply using information from a score network trained for a single context observation. We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost., Comment: 49 pages, 24 figures, 3 tables, 2 algorithms, 12 appendices, in proceedings

Bayesian inference for complex models with an intractable likelihood can be tackled using algorithms performing many calls to computer simulators. These approaches are collectively known as "simulation-based inference" (SBI). Recent SBI methods have made use of neural networks (NN) to provide approximate, yet expressive constructs for the unavailable likelihood function and the posterior distribution. However, the trade-off between accuracy and computational demand leaves much space for improvement. In this work, we propose an alternative that provides both approximations to the likelihood and the posterior distribution, using structured mixtures of probability distributions. Our approach produces accurate posterior inference when compared to state-of-the-art NN-based SBI methods, even for multimodal posteriors, while exhibiting a much smaller computational footprint. We illustrate our results on several benchmark models from the SBI literature and on a biological model of the translation kinetics after mRNA transfection., Comment: 69 pages, 66 figures: new case study added (Biological model of the translation kinetics after mRNA transfection)

This study examines the use of controlled natural languages (CNLs) to specify business intelligence (BI) application requirements. Two varieties of CNLs, CNL-BI and ITLingo ASL (ASL), were employed. A hypothetical BI application, MEDBuddy-BI, was developed for the National Health Service (NHS) to demonstrate how the languages can be used. MEDBuddy-BI leverages patient data, including interactions and appointments, to improve healthcare services. The research outlines the application of CNL-BI and ASL in BI. It details how these languages effectively describe complex data, user interfaces, and various BI application functions. Using the MEDBuddy-BI running example., Comment: 29 pages, 13 figures, 5 tables. New version of the publication to fix a cross reference error to the Appendix section

Many recent works in simulation-based inference (SBI) rely on deep generative models to approximate complex, high-dimensional posterior distributions. However, evaluating whether or not these approximations can be trusted remains a challenge. Most approaches evaluate the posterior estimator only in expectation over the observation space. This limits their interpretability and is not sufficient to identify for which observations the approximation can be trusted or should be improved. Building upon the well-known classifier two-sample test (C2ST), we introduce L-C2ST, a new method that allows for a local evaluation of the posterior estimator at any given observation. It offers theoretically grounded and easy to interpret -- e.g. graphical -- diagnostics, and unlike C2ST, does not require access to samples from the true posterior. In the case of normalizing flow-based posterior estimators, L-C2ST can be specialized to offer better statistical power, while being computationally more efficient. On standard SBI benchmarks, L-C2ST provides comparable results to C2ST and outperforms alternative local approaches such as coverage tests based on highest predictive density (HPD). We further highlight the importance of local evaluation and the benefit of interpretability of L-C2ST on a challenging application from computational neuroscience., Comment: 27 pages, 6 figures, 3 tables, 6 appendices, NeurIPS 2023

Building on the recent trend of new deep generative models known as Normalizing Flows (NF), simulation-based inference (SBI) algorithms can now efficiently accommodate arbitrary complex and high-dimensional data distributions. The development of appropriate validation methods however has fallen behind. Indeed, most of the existing metrics either require access to the true posterior distribution, or fail to provide theoretical guarantees on the consistency of the inferred approximation beyond the one-dimensional setting. This work proposes easy to interpret validation diagnostics for multi-dimensional conditional (posterior) density estimators based on NF. It also offers theoretical guarantees based on results of local consistency. The proposed workflow can be used to check, analyse and guarantee consistent behavior of the estimator. The method is illustrated with a challenging example that involves tightly coupled parameters in the context of computational neuroscience. This work should help the design of better specified models or drive the development of novel SBI-algorithms, hence allowing to build up trust on their ability to address important questions in experimental science., Comment: 7 pages, 2 figures, 1 appendix, published at "Machine Learning and the Physical Sciences" workshop (NeurIPS 2022): https://ml4physicalsciences.github.io/2022/

We show that a collection of generalized Bowen-Franks group, what we call the principal Bowen-Franks $R$-modules, form a complete set of $R$-module invariants for the equivalence relation of profinite conjugacy for similar hyperbolic toral automorphisms. We also show that these principal generalized Bowen-Franks $R$-modules are the principal invariants in a large class of generalized Bowen-Franks $R$-module invariants for similar hyperbolic automorphisms. We further show how the conjugacy invariant of cyclicity, when applied to hyperbolic toral automorphisms, is realized for profinite conjugacy., Comment: 20 pages

Effective characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in diffusion MRI (dMRI). Solving the problem of relating the dMRI signal with cytoarchitectural characteristics calls for the definition of a mathematical model that describes brain tissue via a handful of physiologically-relevant parameters and an algorithm for inverting the model. To address this issue, we propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model. As opposed to other approaches from the literature, our algorithm yields not only an estimation of the parameter vector $\theta$ that best describes a given observed data point $x_0$, but also a full posterior distribution $p(\theta|x_0)$ over the parameter space. This enables a richer description of the model inversion, providing indicators such as credible intervals for the estimated parameters and a complete characterization of the parameter regions where the model may present indeterminacies. We approximate the posterior distribution using deep neural density estimators, known as normalizing flows, and fit them using a set of repeated simulations from the forward model. We validate our approach on simulations using dmipy and then apply the whole pipeline on two publicly available datasets.