This paper presents a new software framework for solving large and sparse linear systems on current hybrid architectures, from small servers to high-end supercomputers, embedding multi-core CPUs and Nvidia GPUs at the node level. The framework has a modular structure and is composed of three main components, which separate basic functionalities for managing distributed sparse matrices and executing some sparse matrix computations involved in iterative Krylov projection methods, eventually exploiting multi-threading and CUDA-based programming models, from the functionalities for setup and application of different types of one-level and multi-level algebraic preconditioners.

In a subsoil bioremediation intervention air or oxygen is injected in the polluted region and then a model for unsaturated porous media it is required, based on the theory of the dynamics of multiphase fluids in porous media. In order to optmize the costs of the intervention it is useful to consider the gas as compressible and this fact introduces nonlinearity in the mathematical model. The physical problem is described by a system of equations and the unknowns are: pollutant; bacteria concentration; oxygen saturation and oxygen pressure. Then, by algebraic manipulations, the model is reduced a to a nonlinear system of partial differential equations describing: oxygen saturation, oxygen density and bacteria concentration. For the proposed model, the results of some simulation experiments performed using COMSOL Multiphysics will be shown.

We present a mathematical model describing the evolution of sea ice and meltwater during summer. The system is described by two coupled partial differential equations for the ice thickness h(x,t) and pond depth w(x,t) fields. The model is similar, in principle, to the one put forward by Luthije et al. (2006), but it features i) a modified melting term, ii) a non-uniform seepage rate of meltwater through the porous ice medium and a minimal coupling with the atmosphere via a surface wind shear term, ?s (Scagliarini et al. 2020). We test, in particular, the sensitivity of the model to variations of parameters controlling fluid- dynamic processes at the pond level, namely the variation of turbulent heat flux with pond depth and the lateral melting of ice enclosing a pond. We observe that different heat flux scalings determine different rates of total surface ablations, while the system is relatively robust in terms of probability distributions of pond surface areas. Finally, we study pond morphology in terms of fractal dimensions, showing that the role of lateral melting is minor, whereas there is evidence of an impact from the initial sea ice topography.

This booklet contains all the abstracts of the results which are going to be presented at the IMACS World Congress taking place in Rome at theEngineering Faculty of University 'La Sapienza', September 11-15, 2023.This is the 21st one in a series of World Conferences whose complete list goes back to 1955 and covered the whole continents. The subsequent World Conferences, usually, take place every three years. Unfortunately, due to the COVID pandemics, IMACS2023, initially scheduled in 2020, had to be postponed also in order to follow the spirit of the IMACS World Conference which prescribes to gather scientists in presence from all over the world. So, in the present occasion, the whole participants are expected to convene in Rome for exchanging their works, ideas and experiences.This Book of Abstracts, reflecting the Congress structure, is organized in sections: Keynote Lectures, General Session, Mini-symposia, Special Sessions and Posters. According to the IMACS philosophy, different aspects of applied mathematics are represented with a special interest towards the numerical methods and solutions.

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) <doi:10.3390/math10213983>.

Background: Major Depressive Disorder (MDD) is a psychiatric illness that is often associated with potentially life -threatening physiological changes and increased risk for suicidal behavior. Electroencephalography (EEG) research suggests an association between depression and specific frequency imbalances in the frontal brain re-gion. Further, while recently developed technology has been proposed to simplify EEG data acquisition, more research is still needed to support its use in patients with MDD.Methods: Using the 14-channel EMOTIV EPOC cap, we recorded resting state EEG from 15 MDD patients with suicidal ideation (SI) vs. 12 healthy controls (HC) to investigate putative power spectral density (PSD) between -group differences at the F3 and F4 electrode sites. Specifically, we explored 1) between-group alpha power asymmetries (AA), 2) between-group differences in delta, theta, alpha and beta power, 3) correlations between PSD data and scores in the Beck's Depression Inventory-II (BDI-II), Beck's Anxiety Inventory (BAI), Reasons for Living Inventory (RFL), and Self-Disgust Questionnaire (SDS).Results: When compared to HC, patients had higher scores on the BAI (p = 0.0018), BDI-II (p = 0.0001) or SDS (p = 0.0142) scale and lower scores in the RFL (p = 0.0006) scale. The PSD analysis revealed no between-group difference or correlation with questionnaire scores for any of the measures considered.Conclusions: The present study could not confirm previous research suggesting frequency-specific anomalies in depressed persons with SI but might suggest that frontal EEG imbalances reflect greater anxiety and negative self -referencing. Future studies should confirm these findings in a larger population sample.

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.

No abstract available

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 &amp; Reid (1988) and that by Mansutti &amp; 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 &amp; 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 &amp; 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.