Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.

The Dirichlet-Ferguson measure is a random probability measure that has seen widespread use in Bayesian nonparametrics. Our main results can be seen as a first step towards the development of a stochastic analysis of the Dirichlet-Ferguson measure. We define a gradient that acts on functionals of the measure and derive its adjoint. The corresponding integration by parts formula is used to prove a covariance representation formula for square integrable functionals of the Dirichlet-Ferguson measure and to provide a quantitative central limit theorem for the first chaos. Our findings are illustrated by a variety of examples.

In this paper we study non-linear implicit Volterra discrete equations of convolutiontype and give sufficient conditions for their solutions to converge to a finite limit. Theseresults apply to the stability analysis of linear methods for implicit Volterra integralequations. An application is given to the numerical study of the final size of an epidemicmodelled by renewal equations

Digital transformation is a process that companies start with different purposes. Once an enterprise embarks on a digital transformation process it translates all its business processes (or, at least, part of them) into a digital replica. Such a digital replica, the so-called digital twin, can be described by Mathematical Science tools allowing cost reduction on industrial processes, faster time-to-market of new products and, in general, an increase of competitive advantage for the company. Digital twin is a descriptive or predictive model of a given industrial process or product that is a valuable tool for business management, both in planning--because it can give different scenario analysis--and in managing the daily operations; moreover, it permits optimization of product and process operations. We present widespread applied mathematics tools that can help this modeling process, along with some successful cases.

Motivation: Binary (or Boolean) matrices provide a common effective data representation adopted in several domains of computational biology, especially for investigating cancer and other human diseases. For instance, they are used to summarize genetic aberrations--copy number alterations or mutations--observed in cancer patientcohorts, effectively highlighting combinatorial relations among them. One of these is the tendency for two or more genes not to be co-mutated in the same sample or patient, i.e. a mutual-exclusivity trend. Exploiting this principle has allowed identifying new cancer driver protein-interaction networks and has been proposed to design effectivecombinatorial anti-cancer therapies rationally. Several tools exist to identify and statistically assess mutualexclusive cancer-driver genomic events. However, these tools need to be equipped with robust/efficient methods to sort rows and columns of a binary matrix to visually highlight possible mutual-exclusivity trends.Results: Here, we formalize the mutual-exclusivity-sorting problem and present MutExMatSorting: an R package implementing a computationally efficient algorithm able to sort rows and columns of a binary matrix to highlight mutual-exclusivity patterns. Particularly, our algorithm minimizes the extent of collective vertical overlap between consecutive non-zero entries across rows while maximizing the number of adjacent non-zero entries in the same row. Here, we demonstrate that existing tools for mutual-exclusivity analysis are suboptimal according to these criteria and are outperformed by MutExMatSorting.

During embryonic development, naive pluripotent epiblast cells transit to a formative state. Theformative epiblast cells form a polarised epithelium, exhibit distinct transcriptional and epigeneticprofiles and acquire competence to differentiate into all somatic and germline lineages. However,we have limited understanding of how the transition to a formative state is molecularly controlled.Here we used murine ESC models to show that ESRRB is both required and sufficient to activateformative genes. Genetic inactivation of Esrrb leads to illegitimate expression of mesendodermand extraembryonic markers, impaired formative expression and failure to self-organise in 3D.Functionally, this results in impaired ability to generate Formative Stem cells and primordialgerm cells in the absence of Esrrb. Computational modelling and genomic analyses revealed thatESRRB occupies key formative genes in naive cells and throughout the formative state. In sodoing, ESRRB kickstarts the formative transition, leading to timely and unbiased capacity formulti-lineage differentiation.

The mammalian nervous system is made up of an extraordinary array of diverse cells that form intricate functional connections. The programs underlying cell lineage specification, identity and function of the neuronal subtypes are managed by regulatory proteins and RNAs, which coordinate the succession of steps in a stereotyped temporal order. In the central nervous system (CNS), motor neurons (MNs) are responsible for controlling essential functions such as movement, breathing, and swallowing by integrating signal transmission from the cortex, brainstem, and spinal cord (SC) towards peripheral muscles. A prime role in guiding the progression of progenitor cells towards the MN fate has been largely attributed to protein factors. More recently, the relevance of a class of regulatory RNAs abundantly expressed in the CNS - the long noncoding RNAs (lncRNAs) - has emerged overwhelmingly. LncRNA-driven gene expression control is key to regulating any step of MN differentiation and function, and its derangement profoundly impacts neuronal pathophysiology. Here, we uncover a novel function for the neuronal isoform of HOTAIRM1 (nHOTAIRM1), a lncRNA specifically expressed in the SC. Using a model system that recapitulates spinal MN (spMN) differentiation, we show that nHOTAIRM1 intervenes in the binary cell fate decision between MNs and interneurons, acting as a pro-MN factor. Furthermore, human iPSC-derived spMNs without nHOTAIRM1 display altered neurite outgrowth, with a significant reduction of both branch and junction numbers. Finally, the expression of genes essential for synaptic connectivity and neurotransmission is also profoundly impaired when nHOTAIRM1 is absent in spMNs. Mechanistically, nHOTAIRM1 establishes both direct and indirect interactions with a number of target genes in the cytoplasm, being a novel post-transcriptional regulator of MN biology. Overall, our results indicate that the lncRNA nHOTAIRM1 is essential for the specification of MN identity and the acquisition of proper morphology and synaptic activity of post-mitotic MNs.

The present paper is dedicated to the study of the discrepancies encountered in electron temperature (Te) measurements carried out with electron cyclotron emission (ECE) and Thomson scattering (TS) diagnostics in the core of the JET tokamak. A large database of discharges has been collected, including high-performance scenarios performed with deuterium only and deuterium-tritium mixtures. Discrepancies have been found between core Te measurements taken with an X-mode ECE interferometer (TECE) and a LIDAR TS system (TLID) for Te > 5 keV. Depending on the plasma scenario, TECE has been found to be systematically higher or lower than TLID. Discrepancies have also been observed between the peaks of the ECE spectrum in the second (X2) and third (X3) harmonic domains, even in high optical thickness conditions. These discrepancies can be interpreted as evidence of the presence of non-Maxwellian features in the electron energy distribution function (EEDF). In order to investigate the relation between the shape of the EEDF and the measured discrepancies, a model for bipolar perturbations of Maxwellian EEDF has been developed. The model allows analytical calculations of ECE absorption and emission coefficients; hence, the comparison of modeled ECE spectra with experimental data. The different experimental results observed for the various JET scenarios have been found to be qualitatively reproducible by adapting the model parameters, suggesting that bipolar distortions of the bulk EEDF could play a role in giving rise to the reported discrepancies between ECE and TS measurements.

In this work, we propose and explore a novel network-constraint survival methodology considering the Weibull accelerated failure time (AFT) model combined with a penalized likelihood approach for variable selection and estimation [2]. Our estimator explicitly incorporates the correlation patterns among predictors using a double penalty that promotes both sparsity and the grouping effect. In or- der to solve the structured sparse regression problems we present an efficient iterative computational algorithm based on proximal gradient descent method [1]. We establish the theoretical consistency of the proposed estimator and moreover, we evaluate its performance both on synthetic and real data examples.

We analyze the bootstrap percolation process on the stochastic block model (SBM), a natural extension of the Erd?s-Rényi random graph that incorporates the community structure observed in many real systems. In the SBM, nodes are partitioned into two subsets, which represent different communities, and pairs of nodes are independently connected with a probability that depends on the communities they belong to. Under mild assumptions on the system parameters, we prove the existence of a sharp phase transition for the final number of active nodes and characterize the sub-critical and the super-critical regimes in terms of the number of initially active nodes, which are selected uniformly at random in each community.

The Dirichlet-Ferguson measure is a cornerstone in nonparametric Bayesian statistics and the study of distributional properties of expectations with respect to such measure is an important line of research. In this paper we provide explicit upper bounds for the d2, the d3 and the convex distance between vectors whose components are means of the Dirichlet-Ferguson measure and a Gaussian random vector.

Electrophysiological source imaging (ESI) aims at reconstructing the precise origin of brain activity from measurements of the electric field on the scalp. Across laboratories/research centers/hospitals, ESI is performed with different methods, partly due to the ill-posedness of the underlying mathematical problem. However, it is difficult to find systematic comparisons involving a wide variety of methods. Further, existing comparisons rarely take into account the variability of the results with respect to the input parameters. Finally, comparisons are typically performed using either synthetic data, or in-vivo data where the ground-truth is only roughly known. We use an in-vivo high-density EEG dataset recorded during intracranial single pulse electrical stimulation, in which the true sources are substantially dipolar and their locations are precisely known. We compare ten different ESI methods, using their implementation in the MNE-Python package: MNE, dSPM, LORETA, sLORETA, eLORETA, LCMV beamformers, irMxNE, Gamma Map, SESAME and dipole fitting. We perform comparisons under multiple choices of input parameters, to assess the accuracy of the best reconstruction, as well as the impact of such parameters on the localization performance. Best reconstructions often fall within 1 cm from the true source, with most accurate methods hitting an average localization error of 1.2 cm and outperforming least accurate ones erring by 2.5 cm. As expected, dipolar and sparsity-promoting methods tend to outperform distributed methods. For several distributed methods, the best regularization parameter turned out to be the one in principle associated with low SNR, despite the high SNR of the available dataset. Depth weighting played no role for two out of the six methods implementing it. Sensitivity to input parameters varied widely between methods. While one would expect high variability being associated with low localization error at the best solution, this is not always the case, with some methods producing highly variable results and high localization error, and other methods producing stable results with low localization error. In particular, recent dipolar and sparsity-promoting methods provide significantly better results than older distributed methods. As we repeated the tests with "conventional" (32 channels) and dense (64, 128, 256 channels) EEG recordings, we observed little impact of the number of channels on localization accuracy; however, for distributed methods denser montages provide smaller spatial dispersion. Overall findings confirm that EEG is a reliable technique for localization of point sources and therefore reinforce the importance that ESI may have in the clinical context, especially when applied to identify the surgical target in potential candidates for epilepsy surgery.

In this paper, we study fluctuations and precise deviations of cumulative INAR time series, both in a non-stationary and in a stationary regime. The theoretical results are based on the recent mod- convergence theory as presented in Féray et al., 2016. We apply our findings to the construction of approximate confidence intervals for model parameters and to quantile calculation in a risk management context.

Machine learning (ML) is increasingly used in cognitive, computational and clinical neuroscience. The reliable and efficient application of ML requires a sound understanding of its subtleties and limitations. Training ML models on datasets with imbalanced classes is a particularly common problem, and it can have severe consequences if not adequately addressed. With the neuroscience ML user in mind, this paper provides a didactic assessment of the class imbalance problem and illustrates its impact through systematic manipulation of data imbalance ratios in (i) simulated data and (ii) brain data recorded with electroencephalography (EEG), magnetoencephalography (MEG) and functional magnetic resonance imaging (fMRI). Our results illustrate how the widely-used Accuracy (Acc) metric, which measures the overall proportion of successful predictions, yields misleadingly high performances, as class imbalance increases. Because Acc weights the per-class ratios of correct predictions proportionally to class size, it largely disregards the performance on the minority class. A binary classification model that learns to systematically vote for the majority class will yield an artificially high decoding accuracy that directly reflects the imbalance between the two classes, rather than any genuine generalizable ability to discriminate between them. We show that other evaluation metrics such as the Area Under the Curve (AUC) of the Receiver Operating Characteristic (ROC), and the less common Balanced Accuracy (BAcc) metric - defined as the arithmetic mean between sensitivity and specificity, provide more reliable performance evaluations for imbalanced data. Our findings also highlight the robustness of Random Forest (RF), and the benefits of using stratified cross-validation and hyperprameter optimization to tackle data imbalance. Critically, for neuroscience ML applications that seek to minimize overall classification error, we recommend the routine use of BAcc, which in the specific case of balanced data is equivalent to using standard Acc, and readily extends to multi-class settings. Importantly, we present a list of recommendations for dealing with imbalanced data, as well as open-source code to allow the neuroscience community to replicate and extend our observations and explore alternative approaches to coping with imbalanced data.

We derive bounds on the Kolmogorov distance between the dis- tribution of a random functional of a {0, 1}-valued random sequence and the normal distribution. Our approach, which relies on the general framework of stochastic analysis for discrete-time normal martingales, extends existing results obtained for independent Bernoulli (or Rademacher) sequences. In particular, we obtain Kolmogorov distance bounds for the sum of normalized random sequences without any independence assumption.

The accurate characterization of cortical functional connectivity from Magnetoencephalography (MEG) data remains a challenging problem due to the subjective nature of the analysis, which requires several decisions at each step of the analysis pipeline, such as the choice of a source estimation algorithm, a connectivity metric and a cortical parcellation, to name but a few. Recent studies have emphasized the importance of selecting the regularization parameter in minimum norm estimates with caution, as variations in its value can result in significant differences in connectivity estimates. In particular, the amount of regularization that is optimal for MEG source estimation can actually be suboptimal for coherence-based MEG connectivity analysis. In this study, we expand upon previous work by examining a broader range of commonly used connectivity metrics, including the imaginary part of coherence, corrected imaginary part of Phase Locking Value, and weighted Phase Lag Index, within a larger and more realistic simulation scenario. Our results show that the best estimate of connectivity is achieved using a regularization parameter that is 1 or 2 orders of magnitude smaller than the one that yields the best source estimation. This remarkable difference may imply that previous work assessing source-space connectivity using minimum-norm may have benefited from using less regularization, as this may have helped reduce false positives. Importantly, we provide the code for MEG data simulation and analysis, offering the research community a valuable open source tool for informed selections of the regularization parameter when using minimum-norm for source space connectivity analyses.

Magnetoencephalography and electroencephalography (M/EEG) seed-based connectivity analysis typically requires regions of interest (ROI)-based extraction of measures. M/EEG ROI-derived source activity can be treated in different ways. For instance, it is possible to average each ROI's time series prior to calculating connectivity measures. Alternatively one can compute connectivity maps for each element of the ROI, prior to dimensionality reduction to obtain a single map. The impact of these different strategies on connectivity estimation is still unclear. Here, we address this question within a large MEG resting state cohort (N=113) and simulated data. We consider 68 ROIs (Desikan-Kiliany atlas), two measures of connectivity (phase locking value-PLV, and its imaginary counterpart- ciPLV), and three frequency bands (theta 4-8 Hz, alpha 9-12 Hz, beta 15-30 Hz). We consider four extraction methods: (i) mean, or (ii) PCA of the activity within the ROI before computing connectivity, (iii) average, or (iv) maximum connectivity after computing connectivity for each element of the seed. Connectivity outputs from these extraction strategies are then compared with hierarchical clustering, followed by direct contrasts across extraction methods. Finally, the results are validated by using a set of realistic simulations. We show that ROI-based connectivity maps vary remarkably across strategies in both connectivity magnitude and spatial distribution. Dimensionality reduction procedures conducted after computing connectivity are more similar to each-other, while PCA before approach is the most dissimilar to other approaches. Although differences across methods are consistent across frequency bands, they are influenced by the connectivity metric and ROI size. Greater differences were observed for ciPLV than PLV, and in larger ROIs. Realistic simulations confirmed that after aggregation procedures are generally more accurate but have lower specificity (higher rate of false positive connections). Although computationally demanding, after dimensionality reduction strategies should be preferred when higher sensitivity is desired. Given the remarkable differences across aggregation procedures, caution is warranted in comparing results across studies applying different extraction methods.

The aim of this work was to characterize the palette and painting technique used for the realization of three late sixteenth century paintings from "Galleria dell'Accademia Nazionale di San Luca" in Rome attributed to Cavalier d'Arpino (Giuseppe Cesari), namely "Cattura di Cristo" (Inv. 158), "Autoritratto" (Inv. 546) and "Perseo e Andromeda" (Inv. 221). This study presents a diagnostic campaign that was carried out with non-invasive and portable techniques such as Energy Dispersive X-ray Fluorescence (ED-XRF) spectrometry, Fiber Optics Reflectance Spectroscopy (FORS) and Multispectral (MS) Imaging. This work was part of a project founded by Regione Lazio and MUR ("IMAGO - Multispectral Imaging for Art, Gamification and hOlografic reality" project). FORS and ED-XRF analyses allowed the preliminary characterization of the pictorial materials in a reliable non-invasive way. In particular, it was possible to identify most of the pigments used for the production of the paintings attributed to Cavalier d'Arpino. The MS images were acquired between the ultraviolet and the near-infrared regions of the electromagnetic spectrum (UV-Vis-NIR) by using different illumination sources and a cooled CCD camera equipped with interferential filters. It was possible to observe significant differences between the visible and the NIR images with some details of the paintings which resulted transparent in the infrared region. Furthermore, MS images were investigated in-depth by the application of data clustering algorithms to obtain semantic segmentation. This methodology exploits the information reported in MS images to generate a pixel classification based on statistical methods together with image analysis techniques. The result provides both an extrapolation of salient parts of the work as well as a better perception of some details. The combined results of this work allowed to investigate in-depth the production of one of the main painters from Italian mannerism.

The IMAGO project aims to develop an innovative system that utilizes Multispectral Imaging and Augmented Reality (AR) techniques for studying and preserving cultural heritage. By employing machine learning algorithms on multispectral images, the system can detect lost original elements and hidden features in cultural artifacts, offering a unique perspective beyond human vision. Here we show some preliminary results related to the multi spectral analysis conducted on three paintings attributed to Cavalier d'Arpino (Giuseppe Cesari) located at the Galleria dell'Accademia Nazionale di San Luca in Rome. Non-invasive and portable techniques such as Energy Dispersive X-ray Fluorescence (ED-XRF) spectrometry, Fiber Optics Reflectance Spectroscopy (FORS), UV fluorescence imaging, and Multispectral (MS) imaging were employed. Preliminary characterization of the pictorial materials was achieved through FORS and ED-XRF analyses, allowing the identi- fication of pigments used for the creation of the three paintings and highlighting similarities and differences in the palette. MS images, acquired between the ultraviolet and near-infrared regions (NIR), revealed significant differences between visible and NIR images with some details of the paintings transparent in the infrared region. Furthermore, data clustering algorithms were applied to the MS images, enabling semantic segmentation and providing extrapolation of salient parts of the artwork and better per- ception of details. The combined results of this work contribute to the preservation and interpretation of cultural heritage and are of paramount importance for the developing of the IMAGO system

Estimates networks of conditional dependencies (Gaussian graphical models) from multiple classes of data (similar but not exactly, i.e. measurements on different equipment, in different locations or for various sub-types). Package also allows to generate simulation data and evaluate the performance. Implementation of the method described in Angelini, De Canditiis and Plaksienko (2022)