Necessary and sufficient conditions are presented for a fractional Orlicz-Sobolev space on Rn to be continuously embedded into a space of uniformly continuous functions. The optimal modulus of continuity is exhibited whenever these conditions are fulfilled. These results pertain to the supercritical Sobolev regime and complement earlier sharp embeddings into rearrangement-invariant spaces concerning the subcritical setting. Classical embeddings for fractional Sobolev spaces into Hölder spaces are recovered as special instances. Proofs require novel strategies, since customary methods fail to produce optimal conclusions.

The reciprocal energy and enstrophy transfers between normal fluid and superfluid components dictate the overall dynamics of superfluid 4He including the generation, evolution and coupling of coherent structures, the distribution of energy among lengthscales, and the decay of turbulence. To better understand the essential ingredients of this interaction, we employ a numerical two-way model which self-consistently accounts for the back-reaction of the superfluid vortex lines onto the normal fluid. Here we focus on a prototypical laminar (non-turbulent) vortex configuration which is simple enough to clearly relate the geometry of the vortex line to energy injection and dissipation to/from the normal fluid: a Kelvin wave excitation on two vortex anti-vortex pairs evolving in (a) an initially quiescent normal fluid, and (b) an imposed counterflow. In (a), the superfluid injects energy and vorticity in the normal fluid. In (b), the superfluid gains energy from the normal fluid via the Donnelly-Glaberson instability.

In this paper, we study the influence of the boundary conditions of the velocity fields in superfluid helium counterflow experiments. To make progress, we perform numerical simulations where we allow a slip velocity of the viscous component at the walls, and observe how this impacts on velocity fields and density profiles of distribution of quantized vortices. We conclude that the presence of a slip velocity at the walls generates a more homogeneous vortex distribution throughout the channel.

The REDRAW project investigates the exploitation of the federated learning computing paradigm to improve the technologies adopted for the monitoring, diagnosis and treatment management of specific health conditions, developing approaches more respectful of the constraints of privacy, confidentiality and cybersecurity, which are still largely absent from the market. REDRAW proposes the study and fine-tuning of dynamic cloud-edge deployment techniques, which exploits Federated Learning (FL) models, in three real-world contexts, to improve the technological features of existing solutions, while respecting the strategic and non-functional constraints that characterize the Italian and European scenarios .

Multiple sclerosis (MS) is a demyelinating neurological disorder with a highly heterogeneous clinical presentation and course of progression. Disease-modifying therapies are the only available treatment, as there is no known cure for the disease. Careful selection of suitable therapies is necessary, as they can be accompanied by serious risks and adverse effects such as infection. Magnetic resonance imaging (MRI) plays a central role in the diagnosis and management of MS, though MRI lesions have displayed only moderate associations with MS clinical outcomes, known as the clinico-radiological paradox. With the advent of machine learning (ML) in healthcare, the predictive power of MRI can be improved by leveraging both traditional and advanced ML algorithms capable of analyzing increasingly complex patterns within neuroimaging data. The purpose of this review was to examine the application of MRI-based ML for prediction of MS disease progression. Studies were divided into five main categories: predicting the conversion of clinically isolated syndrome to MS, cognitive outcome, EDSS-related disability, motor disability and disease activity. The performance of ML models is discussed along with highlighting the influential MRI-derived biomarkers. Overall, MRI-based ML presents a promising avenue for MS prognosis. However, integration of imaging biomarkers with other multimodal patient data shows great potential for advancing personalized healthcare approaches in MS.

Medical digital twins are computational models of human biology relevant to a given medical condition, which are tailored to an individual patient, thereby predicting the course of disease and individualized treatments, an important goal of personalized medicine. The immune system, which has a central role in many diseases, is highly heterogeneous between individuals, and thus poses a major challenge for this technology. In February 2023, an international group of experts convened for two days to discuss these challenges related to immune digital twins. The group consisted of clinicians, immunologists, biologists, and mathematical modelers, representative of the interdisciplinary nature of medical digital twin development. A video recording of the entire event is available. This paper presents a synopsis of the discussions, brief descriptions of ongoing digital twin projects at different stages of progress. It also proposes a 5-year action plan for further developing this technology. The main recommendations are to identify and pursue a small number of promising use cases, to develop stimulation-specific assays of immune function in a clinical setting, and to develop a database of existing computational immune models, as well as advanced modeling technology and infrastructure.

Peptide- and protein-based therapeutics are becoming a promising treatment regimen for myriad diseases. Toxicity of proteins is the primary hurdle for protein-based therapies. Thus, there is an urgent need for accurate in silico methods for determining toxic proteins to filter the pool of potential candidates. At the same time, it is imperative to precisely identify non-toxic proteins to expand the possibilities for protein-based biologics. To address this challenge, we proposed an ensemble framework, called VISH-Pred, comprising models built by fine-tuning ESM2 transformer models on a large, experimentally validated, curated dataset of protein and peptide toxicities. The primary steps in the VISH-Pred framework are to efficiently estimate protein toxicities taking just the protein sequence as input, employing an under sampling technique to handle the humongous class-imbalance in the data and learning representations from fine-tuned ESM2 protein language models which are then fed to machine learning techniques such as Lightgbm and XGBoost. The VISH-Pred framework is able to correctly identify both peptides/proteins with potential toxicity and non-toxic proteins, achieving a Matthews correlation coefficient of 0.737, 0.716 and 0.322 and F1-score of 0.759, 0.696 and 0.713 on three non-redundant blind tests, respectively, outperforming other methods by over on these quality metrics. Moreover, VISH-Pred achieved the best accuracy and area under receiver operating curve scores on these independent test sets, highlighting the robustness and generalization capability of the framework. By making VISH-Pred available as an easy-to-use web server, we expect it to serve as a valuable asset for future endeavors aimed at discerning the toxicity of peptides and enabling efficient protein-based therapeutics.

The field of precision radiation therapy has seen remarkable advancements in both experimental and computational methods. Recent literature has introduced various approaches such as Spatially Fractionated Radiation Therapy (SFRT). This unconventional treatment, demanding high-precision radiotherapy, has shown promising clinical outcomes. A comprehensive computational scheme for SFRT, extrapolated from a case report, is proposed. This framework exhibits exceptional flexibility, accommodating diverse initial conditions (shape, inhomogeneity, etc.) and enabling specific choices for sub-volume selection with administrated higher radiation doses. The approach integrates the standard linear quadratic model and, significantly, considers the activation of the immune system due to radiotherapy. This activation enhances the immune response in comparison to the untreated case. We delve into the distinct roles of the native immune system, immune activation by radiation, and post-radiotherapy immunotherapy, discussing their implications for either complete recovery or disease regrowth.

Antimicrobial resistance prediction is a pivotal ongoing research activity that is currently being explored across various levels. In this context, we present the application of two prediction methods that model the antimicrobial resistance of Neisseria gonorrhoeae on the national level as an outcome of socio-economic processes. The methods use two different implementations of the principal component analysis combined with classification algorithms. Using these two methods, we generated forecasts concerning antimicrobial resistance of Neisseria gonorrhoeae, using publicly available databases encompassing over 200 countries from 1998 to 2021. Both approaches exhibit similar mean absolute averages and correlations when comparing available measurements with predictions. Steps of statistical analysis and applications are discussed, including population-weighted central tendencies, geographical correlations, time trends and error reduction possibilities.

A fundamental challenge for personalized medicine is to capture enough of the complexity of an individual patient to determine an optimal way to keep them healthy or restore their health. This will require personalized computational models of sufficient resolution and with enough mechanistic information to provide actionable information to the clinician. Such personalized models are increasingly referred to as medical digital twins. Digital twin technology for health applications is still in its infancy, and extensive research and development is required. This article focuses on several projects in different stages of development that can lead to specific—and practical–medical digital twins or digital twin modeling platforms. It emerged from a two-day forum on problems related to medical digital twins, particularly those involving an immune system component. Open access video recordings of the forum discussions are available.

Introduction While radiotherapy has long been recognized for its ability to directly ablate cancer cells through necrosis or apoptosis, radiotherapy-induced abscopal effect suggests that its impact extends beyond local tumor destruction thanks to immune response. Cellular proliferation and necrosis have been extensively studied using mathematical models that simulate tumor growth, such as Gompertz law, and the radiation effects, such as the linear-quadratic model. However, the effectiveness of radiotherapy-induced immune responses may vary among patients due to individual differences in radiation sensitivity and other factors.Methods We present a novel macroscopic approach designed to quantitatively analyze the intricate dynamics governing the interactions among the immune system, radiotherapy, and tumor progression. Building upon previous research demonstrating the synergistic effects of radiotherapy and immunotherapy in cancer treatment, we provide a comprehensive mathematical framework for understanding the underlying mechanisms driving these interactions.Results Our method leverages macroscopic observations and mathematical modeling to capture the overarching dynamics of this interplay, offering valuable insights for optimizing cancer treatment strategies. One shows that Gompertz law can describe therapy effects with two effective parameters. This result permits quantitative data analyses, which give useful indications for the disease progression and clinical decisions.Discussion Through validation against diverse data sets from the literature, we demonstrate the reliability and versatility of our approach in predicting the time evolution of the disease and assessing the potential efficacy of radiotherapy-immunotherapy combinations. This further supports the promising potential of the abscopal effect, suggesting that in select cases, depending on tumor size, it may confer full efficacy to radiotherapy.

Leishmania spp. commonly infects phagocytic cells of the immune system, particularly macrophages, employing various immune evasion strategies that enable their survival by altering the intracellular environment. In mammals, these parasites establish persistent infections by modulating gene expression in macrophages, thus interfering with immune signaling and response pathways, ultimately creating a favorable environment for the parasite’s survival and reproduction. In this study, our objective was to use data mining and subsequent filtering techniques to identify the genes that play a crucial role in the infection process of Leishmania spp. We aimed to pinpoint genes that have the potential to influence the progression of Leishmania infection. To achieve this, we exploited prior, curated knowledge from major databases and constructed 16 datasets of human molecular information consisting of coding genes and corresponding proteins. We obtained over 400 proteins, identifying approximately 200 genes. The proteins coded by these genes were subsequently used to build a network of protein–protein interactions, which enabled the identification of key players; we named this set Predicted Genes. Then, we selected approximately 10% of Predicted Genes for biological validation. THP-1 cells, a line of human macrophages, were infected with Leishmania major in vitro for the validation process. We observed that L. major has the capacity to impact crucial genes involved in the immune response, resulting in macrophage inactivation and creating a conducive environment for the survival of Leishmania parasites.

Spatial color algorithms (SCAs) are algorithms grounded in the retinex theory of color sensation that, mimicking the human visual system, perform image enhancement based on the spatial arrangement of the scene. Despite their established role in image enhancement, their potential as dequantizers has never been investigated. Here, we aim to assess the effectiveness of SCAs in addressing the dual objectives of color dequantization and image enhancement at the same time. To this end, we propose the term dequantenhancement. In this paper, through two experiments on a dataset of images, SCAs are evaluated through two distinct pathways: first, quantization followed by filtering to assess both dequantization and enhancement; and second, filtering applied to original images before quantization as further investigation of mainly the dequantization effect. The results are presented both qualitatively, with visual examples, and quantitatively, through metrics including the number of colors, retinal-like subsampling contrast (RSC), and structural similarity index (SSIM).

Precision Viticulture (PV) is becoming an active and interdisciplinary research field since it requires solving interesting research issues to concretely answer the demands of specific use cases. A challenging problem in this context is the development of automatic methods for yield estimation. Computer vision methods can contribute to the accomplishment of this task, especially those that can replicate what winemakers do manually. In this paper, an automatic artificial intelligence method for grape bunch detection from RGB images is presented. A customized Convolutional Neural Network (CNN) is employed for pointwise classification of image pixels and the dependence of classification results on the type of input color channels and grapes color properties are studied. The advantage of using additional perception-based input features, such as luminance and visual contrast, is also evaluated, as well as the dependence of the method on the choice of the training set in terms of the amount of labeled data. The latter point has a significant impact on the practical use of the method on-site, its usability by non-expert users, and its adaptability to individual vineyards. Experimental results show that a properly trained CNN can discriminate and detect grape bunches even under uncontrolled acquisition conditions and with limited computational load, making the proposed method implementable on smart devices and suitable for on-site and real-time applications.

A nonlinear crime model is generalized by introducing self- and cross-diffusion terms. The effect of diffusion on the stability of non-negative constant steady states is applied. In particular, the cross-diffusion-driven instability, called Turing instability, is analyzed by linear stability analysis, and several Turing patterns driven by the cross-diffusion are studied through numerical investigations. When the Turing–Hopf conditions are satisfied, the type of instability highlighted in the ODE model persists in the PDE system, still showing an oscillatory behavior.

This Special Issue of Applied Numerical Mathematics contains selected and refereed papers presented at the 21st IMACS World Congress which was held during September 11–15, 2023 in Rome, Italy.

We study the process of thermal convection in jammed emulsions with a yield-stress rheology. We find that heat transfer occurs via an intermittent mechanism, whereby intense short-lived convective “heat bursts” are spaced out by long-lasting conductive periods. This behavior is the result of a sequence of fluidization-rigidity transitions, rooted in a nontrivial interplay between emulsion yield-stress rheology and plastic activity, which we characterize via a statistical analysis of the dynamics at the droplet scale. We also show that droplets’ coalescence induced during heat bursts leads to a spatially heterogeneous phase inversion of the emulsion which eventually supports a sustained convective state.

The paper concerns the weighted Hilbert transform of locally continuous functions on the semiaxis. By using a filtered de la Vallée Poussin type approximation polynomial recently introduced by the authors, it is proposed a new “truncated” product quadrature rule (VP- rule). Several error estimates are given for different smoothness degrees of the integrand ensuring the uniform convergence in Zygmund and Sobolev spaces. Moreover, new estimates are proved for the weighted Hilbert transform and for its approximation (L-rule) by means of the truncated Lagrange interpolation at the same Laguerre zeros. The theoretical results are validated by the numerical experiments that show a better performance of the VP-rule versus the L-rule.

We are concerned with the uniform approximation of functions of a generic reproducing kernel Hilbert space (RKHS). In this general context, classical approximations are given by Fourier orthogonal projections (if we know the Fourier coefficients) and their discrete versions (if we know the function values on well-distributed nodes). In case such approximations are not satisfactory, we propose to improve the approximation using the same data but combined with a new kernel function. For the resulting (both continuous and discrete) new approximations, theoretical estimates and concrete examples are given.

In this paper the interpolating rational functions introduced by Floater and Hormann are generalized leading to a whole new family of rational functions depending on γ, an additional positive integer parameter. For γ=1, the original Floater–Hormann interpolants are obtained. When γ>1 we prove that the new rational functions share a lot of the nice properties of the original Floater–Hormann functions. Indeed, for any configuration of nodes in a compact interval, they have no real poles, interpolate the given data, preserve the polynomials up to a certain fixed degree, and have a barycentric-type representation. Moreover, we estimate the associated Lebesgue constants in terms of the minimum (h∗) and maximum (h) distance between two consecutive nodes. It turns out that, in contrast to the original Floater–Hormann interpolants, for all γ>1 we get uniformly bounded Lebesgue constants in the case of equidistant and quasi-equidistant nodes configurations (i.e., when h∼h∗). For such configurations, as the number of nodes tends to infinity, we prove that the new interpolants (γ>1) uniformly converge to the interpolated function f, for any continuous function f and all γ>1. The same is not ensured by the original FH interpolants (γ=1). Moreover, we provide uniform and pointwise estimates of the approximation error for functions having different degrees of smoothness. Numerical experiments illustrate the theoretical results and show a better error profile for less smooth functions compared to the original Floater–Hormann interpolants.