On the half line, we introduce a new sequence of near-best uniform approximation polynomials, easily computable by the values of the approximated function at a truncated number of Laguerre zeros. Such approximation polynomials come from a discretization of filtered Fourier–Laguerre partial sums, which are filtered using a de la Vallée Poussin (VP) filter. They have the peculiarity of depending on two parameters: a truncation parameter that determines how many of the n Laguerre zeros are considered, and a localization parameter, which determines the range of action of the VP filter we will apply. As n→∞, under simple assumptions on such parameters and the Laguerre exponents of the involved weights, we prove that the new VP filtered approximation polynomials have uniformly bounded Lebesgue constants and uniformly convergence at a near–best approximation rate, for any locally continuous function on the semiaxis. The numerical experiments have validated the theoretical results. In particular, they show a better performance of the proposed VP filtered approximation versus the truncated Lagrange interpolation at the same nodes, especially for functions a.e. very smooth with isolated singularities. In such cases, we see a more localized approximation and a satisfactory reduction of the Gibbs phenomenon.

Intraguild predation, representing a true combination of predation and competition between two species that rely on a common resource, is of foremost importance in many natural communities. We investigate a spatial model of three species interaction, characterized by a Holling type II functional response and linear cross-diffusion. For this model we report necessary and sufficient conditions ensuring the insurgence of Turing instability for the coexistence equilibrium; we also obtain conditions characterizing the different patterns by multiple scale analysis. Numerical experiments confirm the occurrence of different scenarios of Turing instability, also including Turing–Hopf patterns.

Modified Patankar schemes are linearly implicit time integration methods designed to be unconditionally positive and conservative. In the present work we extend the Patankar-type approach to linear multistep methods and prove that the resulting discretizations retain, with no restrictions on the step size, the positivity of the solution and the linear invariant of the continuous-time system. Moreover, we provide results on arbitrarily high order of convergence and we introduce an embedding technique for the Patankar weights denominators to achieve it.

Droplet microfluidics has emerged as highly relevant technology in diverse fields such as nanomaterials synthesis, photonics, drug delivery, regenerative medicine, food science, cosmetics, and agriculture. While significant progress has been made in understanding the fundamental mechanisms underlying droplet generation in microchannels and in fabricating devices to produce droplets with varied functionality and high throughput, challenges persist along two important directions. On one side, the generalization of numerical results obtained by computational fluid dynamics would be important to deepen the comprehension of complex physical phenomena in droplet microfluidics, as well as the capability of predicting the device behavior. Conversely, truly three-dimensional architectures would enhance microfluidic platforms in terms of tailoring and enhancing droplet and flow properties. Recent advancements in artificial intelligence (AI) and additive manufacturing (AM) promise unequaled opportunities for simulating fluid behavior, precisely tracking individual droplets, and exploring innovative device designs. This review provides a comprehensive overview of recent progress in applying AI and AM to droplet microfluidics. The basic physical properties of multiphase flows and mechanisms for droplet production are discussed, and the current fabrication methods of related devices are introduced, together with their applications. Delving into the use of AI and AM technologies in droplet microfluidics, topics covered include AI-assisted simulations of droplet behavior, real-time tracking of droplets within microfluidic systems, and AM-fabrication of three-dimensional systems. The synergistic combination of AI and AM is expected to deepen the understanding of complex fluid dynamics and active matter behavior, expediting the transition toward fully digital microfluidic systems.

We establish the existence of quasi-periodic traveling wave solutions forthe β-plane equation on T2 with a large quasi-periodic traveling wave external force.These solutions exhibit large sizes, which depend on the frequency of oscillations of theexternal force. Due to the presence of small divisors, the proof relies on a nonlinear Nash-Moser scheme tailored to construct nonlinear waves of large size. To our knowledge,this is the first instance of constructing quasi-periodic solutions for a quasilinear PDEin dimensions greater than one, with a 1-smoothing dispersion relation that is highlydegenerate - indicating an infinite-dimensional kernel for the linear principal operator.This degeneracy challenge is overcome by preserving the traveling-wave structure, theconservation of momentum and by implementing normal form methods for the linearizedsystem with sublinear dispersion relation in higher space dimension.

Introduction Practicing physical activity (PA) on a regular basis is an important support for people with type 1 diabetes (T1D). However, exercise may induce in them hypoglycaemic events during or after it. One major consequence of this is that, to limit this risk, many people with T1D tend to avoid performing PA. The availability of modern continuous glucose-monitoring (CGM) devices is potentially a great asset for reducing the chances of hypoglycaemia (HP) due to PA. Several algorithms have already been proposed to predict HP in subjects with T1D. However, not many of them are specifically focused on HP induced by exercise. Among those, many involve a large number of covariates making the applicability more difficult, and none uses CGM values available during the training session. Objectives We study the problem of predicting hypoglycaemia events in subjects with T1D during PA. The final aim is to produce algorithms enabling a person with T1D to perform a planned PA session without experiencing HP. Method One of the two algorithms we developed uses the CGM data in an initial part of a PA session. A parametric model is fitted to the data and then used to predict a possible HP during the remaining part of the session. Our second algorithm uses the CGM value at the start of a session. It also relies on statistical information about the average rate of decrease of the aforementioned model, as derived from a previously measured CGM data during PA. Then, the algorithm estimates the probability of HP during the planned PA session. Both algorithms have a very simple structure and therefore are of wide applicability. Results The application of the two algorithms to a very large dataset shows their very good ability to predict HP during PA in people with T1D.

Wetlands are essential for global biogeochemical cycles and ecosystem services, with the dynamics of soil organic carbon (SOC) serving as the critical regulatory mechanism for these processes. However, accurately modeling carbon dynamics in wetlands presents challenges due to their complexity. Traditional approaches often fail to capture spatial variations, long-range transport, and periodical flooding dynamics, leading to uncertainties in carbon flux predictions. To tackle these challenges, we introduce a novel extension of the fractional RothC model, integrating temporal fractional-order derivatives into spatial dimensions. This enhancement allows for the creation of a more adaptive tool for analyzing SOC dynamics. Our differential model incorporates Richardson–Richard's equation for moisture fluxes, a diffusion–advection–reaction equation for fractional-order dynamics of SOC compounds, and a temperature transport equation. We examine the influence of diffusive movement and sediment moisture content on model solutions, as well as the impact of including advection terms. Finally, we validated the model on a restored wetland scenario at the Ebro Delta site, aiming to evaluate the effectiveness of flooding strategies in enhancing carbon sequestration and ecosystem resilience.

The driving mechanisms at the base of the clearance of biological wastes in the brain interstitial space (ISS) are still poorly understood and an actively debated subject. A complete comprehension of the processes that lead to the aggregation of amyloid proteins in such environment, hallmark of the onset and progression of Alzheimer’s disease, is of crucial relevance. Here we employ combined computational fluid dynamics and molecular dynamics techniques to uncover the role of fluid flow and proteins transport in the brain ISS. Our work identifies diffusion as the principal mechanism for amyloid-β proteins clearance, whereas fluid advection may lead transport for larger molecular bodies, like amyloid-β aggregates or extracellular vesicles. We also clearly quantify the impact of large nascent prefibrils on the fluid flowing and shearing. Finally, we show that, even in the irregular brain interstitial space (ISS), hydrodynamic interactions enhance amyloid-β aggregation at all stages of the aggregation pathway. Our results are key to understand the role of fluid flow and solvent-solute interplay on therapeutics like antibodies acting in the brain ISS.

Forecasting functional time series (FTS) has arguably achieved tremendous success in recent years. Time series of curves, or functional time series, exist in many disciplines. Among the numerous existing contributions for forecasting time series, one-step-ahead functional time series forecasting, that is one-step-ahead prediction of a curve-valued time series, has been studied in several practical studies. Predominantly most traditional functional time series studies use functional (Hilbertian) autoregressive models for one-step-ahead forecast, but their application in real-world data remains a pertinent challenge due to a non-stationary behavior. Opposed to such models, several nonparametric approaches have been proposed in the recent literature for forecasting time series of curves. An analysis of the forecasting performances of such nonparametric approaches, validated empirically with a set of real experiments, is presented in this paper. While a complete understanding of these approaches remains elusive, we hope that our perspectives, discussions, and comparisons serve as a stimulus for new statistical research.

Retrieving LST from infrared spectral observations is challenging because it needs separation from emissivity in surface radiation emission, which is feasible only when the state of the surface-atmosphere system is known. Thanks to its high spectral resolution, the Infrared Atmospheric Sounding Interferometer (IASI) instrument onboard Metop polar-orbiting satellites is the only sensor that can simultaneously retrieve LST, the emissivity spectrum, and atmospheric composition. Still, it cannot penetrate thick cloud layers, making observations blind to surface emissions under cloudy conditions, with surface and atmospheric parameters being flagged as voids. The present paper aims to discuss a downscaling-fusion methodology to retrieve LST missing values on a spatial field retrieved from spatially scattered IASI observations to yield level 3, regularly gridded data, using as proxy data LST from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) flying on Meteosat Second Generation (MSG) platform, a geostationary instrument, and from the Advanced Very High-Resolution Radiometer (AVHRR) onboard Metop polar-orbiting satellites. We address this problem by using machine learning techniques, i.e., Gradient Boosting, Random Forest, Gaussian Process Regression, Neural Network, and Stacked Regression. We applied the methodology over the Po Valley region, a very heterogeneous area that allows addressing the trained models' robustness. Overall, the methods significantly enhanced spatial sampling, keeping errors in terms of Root Mean Square Error (RMSE) and bias (Mean Absolute Error, MAE) very low. Although we demonstrate and assess the results primarily using IASI data, the paper is also intended for applications to the IASI follow-on, that is, IASI Next Generation (IASI-NG), and much more to the Infrared Sounder (IRS), which is planned to fly this year, 2025, on the Meteosat Third Generation platform (MTG).

Literature confirms the crucial influence on glacier and rock glacier flow of non-viscous deformations together with temperature impact. This observation suggests numerical glaciologists ought to reconsider the established mathematical modeling based on the representation of ice as a power-law viscous fluid and the Glen's law. Along this line, we propose the numerical solution of a two-dimensional rock-glacier flow model, based on a constitutive law of second grade of complexity two, as just published for a one-dimensional set-up by two of the authors. With the representation of the composition of the rocky ice as a mixture of ice and rock and sand grains, and the inclusion of the local impact of pressure and of thermal effects, this model has allowed the reproduction of borehole measurement data from alpine glacier internal sliding motion via a similarity solution of the flow governing equations. Here, the adopted numerical procedure uses a second order finite difference scheme and imposes the incompressibility constrain up to computer accuracy via the pressure method, that we have extended from Newtonian computational fluid dynamics. This method solves the governing equations for the flow in primitive variables with the advantage that no pre-/post-processing is required; in addition, it avoids splitted solution of the Poisson equation for pressure which might be source of undesired numerical mass unbalancing. The results of a numerical test on the Murtel-Corvatsch alpine glacier flow, reporting satisfactory matching with published on-field observations, are presented.

Modeling the evolution of the melt front under gravity in the presence of a horizontal thermal gradient is a challenging issue, hitherto tackled exclusively with the concepts and tools of computational continuum thermomechanics, too phenomenologically driven to have satisfactory predictive capabilities. Here, we show that this complex phenomenon is amenable to treatment by the methods and tools of Non-Equilibrium Molecular Dynamics (NEMD). To do so, we addressed all the difficulties caused by the necessity of applying suitable boundary conditions and minimizing surface effects so that the bulk behavior of the system in non-equilibrium conditions can be detected. Sufficient adiabatic separation of the time scales permits us to use macroscopically relatively short-but microscopically long enough-time averages to get the macroscopic bulk behavior of the system accurately. To get an adequate signal-to-noise ratio, we had to use an unphysically large value of the gravity. However, we know from NEMD simulations in transport studies that the phenomena produced are stable over many orders of magnitude. In conclusion, our work proves that molecular simulation can be a good tool to study this family of non-equilibrium phenomena, although further work is needed to achieve quantitative predictive capabilities.

Models of soil organic carbon (SOC) frequently overlook the effects of spatial dimensions and microbiological activities. In this paper, we focus on two reaction-diffusion chemotaxis models for SOC dynamics, both supporting chemotaxis-driven instability and exhibiting a variety of spatial patterns as stripes, spots and hexagons when the microbial chemotactic sensitivity is above a critical threshold. We use symplectic techniques to numerically approximate chemotaxis-driven spatial patterns and explore the effectiveness of the piecewise Dynamic Mode Decomposition (pDMD) to reconstruct them. Moreover, we analyse the predictive performance of the pDMD for moderate time horizons. Our findings show that pDMD is effective at precisely recreating and predicting chemotaxis-driven spatial patterns, therefore broadening the range of application of the method to classes of solutions different than Turing patterns. By validating its efficacy across a wider range of models, this research lays the groundwork for applying pDMD to experimental spatiotemporal data, advancing predictions crucial for soil microbial ecology and agricultural sustainability.

Convolutional Neural Networks (CNNs) have become indispensable tools in skin cancer classification, aiding clinical experts to achieve earlier and more accurate diagnoses, improving treatment outcomes, and driving advancements in medical research. Despite their pivotal role, the most popular CNN architecture families exhibit a critical issue related to the distribution and quantity of available data, potentially compromising their performance and generalization abilities. This challenge is commonly overlooked in most skin lesion classification papers, which mainly rely on weighted classification techniques. Directly using appropriately dataset balancing or Transfer Learning (TL) methods, as suggested in recent studies, has the potential to deliver more satisfactory results, providing a more effective approach to addressing this issue. In the effort to tackle this problem, we provide a comprehensive quantitative evaluation aimed at identifying the most critical new emerging computational aspects and the related effective techniques. Specifically, we propose twelve Computational Models (CMs) based on four prominent CNN models with increasing structural complexity. We assess their effectiveness in both pretrained and unpretrained versions, incorporating TL strategies as well. Our experiments focus on the ISIC 2018 image dataset, a benchmark widely recognized for its extensive application in skin cancer research yet challenged by significant class imbalance issues. To mitigate this, we also randomly extracted a balanced image subset from ISIC 2018 for evaluation purposes. The experimental results, regarding four different scenarios, provide valuable insights into the design and utilization of CNNs for skin lesion classification, laying the groundwork for further investigations.

Emulsions are paramount in various interdisciplinary topical areas, yet a satisfactory understanding of their behavior in buoyancy-driven thermal flows has not been established. In the present work, we unravel the dynamical regimes of thermal convection in emulsions by leveraging a large set of mesoscale numerical simulations. Emulsions are prepared with a given volume fraction of the initially dispersed phase, φ, ranging from dilute (low values of φ) to jammed emulsions (high values of φ), resulting in different rheological responses of the emulsion, i.e., from Newtonian to non-Newtonian yield-stress behaviors, respectively. We then characterize the dynamics of the emulsions in the paradigmatic setup of the Rayleigh-Bénard convection, i.e., when confined between two parallel walls at different temperatures under the effect of buoyancy forces, the latter encoded in the dimensionless Rayleigh number Ra. We thoroughly investigated the dynamics of the emulsion in the changing of φ and Ra. For a given φ, at increasing Ra, we observe that the emulsion exhibits convection states, where structural changes may appear (i.e., droplet breakup, coalescence, or phase inversion), which inevitably impact the emulsion rheology. For sufficiently high values of Ra, two states of convection are observed: for low/moderate values of φ (Newtonian emulsions), we observe breakup-dominated dynamics, whereas for high values of φ (non-Newtonian emulsions), we observe phase-inverted states. For both scenarios, the droplet size distribution depends on Ra, and scaling laws for the average droplet size are analyzed and quantified. Our results offer insights into the rich dynamics of emulsions under thermal convection, offering a detailed characterization of the various dynamical regimes to be expected and their relation with structural changes occurring in such complex fluids.

Questo rapporto tecnico illustra la metodologia e gli strumenti utilizzati per il monitoraggio integrato di vari progetti PRIN finanziati dal PNRR nel corso del 2022 e attivi presso l’IAC-CNR. La struttura proposta ha l’obiettivo di tenere sotto controllo la documentazione amministrativa, la rendicontazione delle risorse umane impiegate e la gestione finanziaria, inclusa la proiezione di chiusura e l’analisi degli scostamenti per ciascun progetto. Vengono presentati esempi specifici che evidenziano l’efficacia del metodo applicato e indicazioni utili per garantire una gestione ottimale delle risorse.

In this work an optimized multicomponent lattice Boltzmann (LB) model is deployed to simulate axisymmetric turbulent jets of a fluid evolving in a quiescent, immiscible environment over a wide range of dynamic regimes. The implementation of the multicomponent LB code achieves peak performance on graphic processing units (GPUs) with a significant reduction of the memory footprint, retains the algorithmic simplicity inherent to standard LB computing, and, being based on a high-order extension of the thread-safe LB algorithm, allows us to perform stable simulations at vanishingly low viscosities. The proposed approach opens attractive prospects for high-performance computing simulations of realistic turbulent flows with interfaces on GPU-based architectures.

Cyclic nucleotide-gated (CNG) ion channels are crucial to the intracellular calcium dynamics in neurons and other sensory cells, in several organisms. Mutations in CNG genes are linked to various dysfunctions and diseases. In this work, we propose a theoretical investigation of the structural and functional properties of wild-type TAX-4, a non-selective CNG ion channel, expressed in various sensory neurons of Caenorhabditis elegans, and involved in the permeation of monovalent and multivalent cations. Using a recent cryo-electron microscopy structure of the open state of the channel as the starting conformation, we conduct all-atom molecular dynamics simulations of the full-length channel in a membrane/water/ions system, both in the cGMP-bound and unbound conformations. Several channel structural descriptors are examined and a first-level functional annotation is carried out, on the microsecond time scale. A comparison with the available experimental data on TAX-4 and human homologues allows us to assign the simulated bound and unbound models as the pre-open and closed conformations of TAX-4, respectively. Comparisons between the bound and unbound conformations enable us to suggest key conformational changes underlying the binding-to-gating transition.

We present a mathematical framework to include quantum interfacial interactions, provided by Keldysh nonequilibrium quantum transport formalism, bottom-up coupled to a nanoscale lattice Boltzmann method. As an applicative scenario, we simulate a two-dimensional water flow between two parallel solid plates hosting electrons and phonons in the solid bottom wall. The corresponding tool may prove useful for the computational design of quantum-engineered nanofluidic devices, showing its capability to explore the effects of the interfacial quantum transport phenomena at scales of experimental relevance.

A key step to optimize the tests of semiconductors during the production process is to improve the prediction of the final yield from the defects detected on the wafers during the production process. This study investigates the link between the defects detected by a Scanning Electron Microscope (SEM) and the electrical failure of the final semiconductors, with two main objectives: (a) to identify the best layers to inspect by SEM; (b) to develop a model that predicts electrical failures of the semiconductors from the detected defects. The first objective has been reached by a model based on Odds Ratio that gave a (ranked) list of the layers that best predict the final yield. This allows process engineers to concentrate inspections on a few important layers. For the second objective, a regression/classification model based on Gradient Boosting has been developed. As a by-product, this latter model confirmed the results obtained by Odds Ratio analysis. Both models take account of the high lacunarity of the data and have been validated on two distinct datasets from STMicroelectronics.