In this paper, we extend the result on the probability of (falsely) connecting two distinct components when learning a GGM (Gaussian Graphical Model) by the joint regression based technique. While the classical method of regression based technique learns the neighbours of each node one at a time through a Lasso penalized regression, its joint modification, considered here, learns the neighbours of each node simultaneously through a group Lasso penalized regression.

Given a random sample drawn from a Multivariate Bernoulli Variable (MBV), we consider the problem of estimating the structure of the undirected graph for which the distribution is pairwise Markov and the parameters' vector of its exponential form. We propose a simple method that provides a closed form estimator of the parameters' vector and through its support also provides an estimate of the undirected graph associated with the MBV distribution. The estimator is proved to be asymptotically consistent but it is feasible only in low-dimensional regimes. Synthetic examples illustrate its performance compared with another method that represents state of the art in literature. Finally, the proposed procedure is used to analyze a data set in the pediatric allergology area showing its practical efficiency.

Nowadays, Predictive Maintenance is a mandatory tool to reduce the cost of production in the semiconductor industry. This paper considers as a case study a critical part of the electrochemical deposition system, namely, the four Pins that hold a wafer inside a chamber. The aim of the study is to replace the schedule of replacement of Pins presently based on fixed timing (Preventive Maintenance) with a Hardware/Software system that monitors the conditions of the Pins and signals possible conditions of failure (Predictive Maintenance). The system is composed of optical sensors endowed with an image processing methodology. The prototype built for this study includes one optical camera that simultaneously takes images of the four Pins on a roughly daily basis. Image processing includes a pre-processing phase where images taken by the camera at different times are coregistered and equalized to reduce variations in time due to movements of the system and to different lighting conditions. Then, some indicators are introduced based on statistical arguments that detect outlier conditions of each Pin. Such indicators are pixel-wise to identify small artifacts. Finally, criteria are indicated to distinguish artifacts due to normal operations in the chamber from issues prone to a failure of the Pin. An application (PINapp) with a user friendly interface has been developed that guides industry experts in monitoring the system and alerting in case of potential issues. The system has been validated on a plant at STMicroelctronics in Catania (Italy). The study allowed for understanding the mechanism that gives rise to the rupture of the Pins and to increase the time of replacement of the Pins by a factor at least 2, thus reducing downtime.

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This contribution outlines current research aimed at developing models for personalized type 2 diabetes mellitus (T2D) prevention in the framework of the European project PRAESIIDIUM (Physics Informed Machine Learn-ing-Based Prediction and Reversion of Impaired Fasting Glucose Management) aimed at building a digital twin for preventing T2D in patients at risk. Specifically, the modelling approaches include both a multiscale, hybrid computational model of the human metaflammatory (metabolic and inflammatory) status, and data-driven models of the risk of developing T2D able to generate personalized recommendations for mitigating the individ-ual risk. The prediction algorithm will draw on a rich set of information for training, derived from prior clinical data, the individual's family history, and prospective clinical trials including clinical variables, wearable sensors, and a tracking mobile app (for diet, physical activity, and lifestyle). The models developed within the project will be the basis for building a platform for healthcare professionals and patients to estimate and monitor the indi-vidual risk of T2D in real time, thus potentially supporting personalized prevention and patient engagement.

During melting under gravity in the presence of a horizontal thermal gradient, buoyancy-driven convection in the liquid phase affects significantly the evolution of the liquid-solid interface. Due to the obvious engineering interest in understanding and controlling melting processes, fluid dynamicists and applied mathematicians have spent many efforts to model and simulate them numerically. Their endeavors concentrated in the twenty-five years period between the publication of the paper by Brent, Voller & Reid (1988) and that by Mansutti & Bucchignani (2011). The former--and most of the following ones--adopted a phase-field model (where the interface is blurred into a smooth transition zone), while the latter was based on a Stefan-like model with sharp interface. With suitably chosen values of many ad-hoc material and numerical parameters, all of the above simulations were able to attain some agreement with their common benchmark, the melt fronts obtained experimentally by Gau & Viskanta (1986) on a sample of gallium enclosed in a parallelepipedal box with one vertical wall heated. This left unresolved several fine issues, such as whether the elastic response of the solid phase plays a role in determining the shape of the liquid-solid interface.Here, for the first time, we tackle this problem at the atomistic level with a molec- ular dynamics approach. The advantage we gain is that a unique microscopic model describes all of the aggregation states of the molecules, and in particular the solid- liquid interface, without any further assumptions. The price we have to pay is that the hydrodynamical quantities of interest, computed out of the microscopic state using the Irwing & Kirkwood (1950) prescriptions, need to be obtained under gravitational acceleration and thermal gradients much larger than those in real experiments.

Recent literature confirms the crucial influence of non-viscous deformations together with temperature impact on glacier and rock glacier flow numerical simulation. Along this line, supported by the successful test on a one-dimensional set-up developed by two of the author, we propose the numerical solution of a two-dimensional rock-glacier flow model based on an ice constitutive law of second grade differential type . The procedure adopted uses a 2nd order finite difference scheme and imposes the incompressibility constrain up to computer precision via the pressure method, ex- tended from newtonian computational fluid dynamics. The governing equations are solved in primitive variables with the advantage to avoid pre-/post-processing; splitted solution of the derived Poisson equation for pressure, source of undesired numerical mass unbalancing, is avoided as well. Numerical results will be shown.The financial support of Piano Nazionale Ricerca Antartide (project PNRA16-0012) is acknowledged.

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.