We show that for a certain class of convex functions f, including the exponential functions x↦eλx with λ>0 a real number, and all the powers x↦xβ, x≥0 and β≥2 a real number, with a unique small exception, if (d1,...,dn) ranges over the degree sequences of graphs with n vertices and m edges and m≤n−1, then the maximum of ∑if(di) is uniquely attained by the degree sequence of a quasi-star graph, namely, a graph consisting of a star plus possibly additional isolated vertices. This result significantly extends a similar result in Ismailescu and Stefanica (2002). Dually, we show that for a certain class of concave functions g, including the negative exponential functions x↦1−e−λx with λ>ln(2) a real number, all the powers x↦xα, x≥0 and 0<α≤[Formula presented] for x≥0, if (d1,...,dn) ranges over the degree sequences of graphs with n vertices and m edges, then the minimum of ∑ig(di) is uniquely attained by the degree sequence of a quasi-complete graph, i.e., a graph consisting of a complete graph plus possibly an additional vertex connected to some but not all vertices of the complete graph, plus possibly isolated vertices. This result extends a similar result in the same paper.

Let X be a centered random vector in a finite-dimensional real inner product space E. For a subset C of the ambient vector space V of E and x,y is an element of V, write x <= Cy if y-x is an element of C. If C is a closed convex cone in E, then <= C is a preorder on V, whereas if C is a proper cone in E, then <= C is actually a partial order on V. In this paper, we give sharp Cantelli-type inequalities for generalized tail probabilities such as PrX >= Cb for b is an element of V. These inequalities are obtained by "scalarizing" X >= Cb via cone duality and then by minimizing the classical univariate Cantelli's bound over the scalarized inequalities. Three diverse applications to random matrices, tails of linear images of random vectors, and network homophily are also given.

Releasing capsules are widely employed in biomedical applications as smart carriers of therapeutic agents, including drugs and bioactive compounds. Such delivery vehicles typically consist of a loaded core, enclosed by one or multiple concentric coating strata. In this work, we extended existing mechanistic models to account for such multi-strata structures, including possible concurrent erosion of the capsule itself, and we characterized the release kinetics of the active substance into the surrounding medium. We presented a computational study of drug release from a spherical microcapsule, modeled through a non-linear diffusion equation incorporating radial asymmetric diffusion and space- and time-discontinuous coefficients, as suggested by the experimental data specifically collected for this study. The problem was solved numerically using a finite volume scheme on a grid with adaptive spatial and temporal resolution. Analytical expressions for concentration and cumulative release were derived for all strata, enabling the exploration of parameter sensitivity—such as coating permeability and internal diffusivity—on the overall release profile. The resulting release curves provide mechanistic insight into the transport processes and offer design criteria for achieving controlled release. Model predictions were benchmarked against in vitro experimental data obtained under physiologically relevant conditions, showing good agreement and validating the key features of the model. The proposed model thus serves as a practical tool for predicting the behavior of composite coated particles, supporting performance evaluation and the rational design of next-generation drug delivery systems with reduced experimental effort.

The increasing availability of traffic data from sensor networks has created new opportunities for understanding vehicular dynamics and identifying anomalies. In this study, we employ clustering techniques to analyse traffic flow data with the dual objective of uncovering meaningful traffic patterns and detecting anomalies, including sensor failures and irregular congestion events. We explore multiple clustering approaches, i.e. partitioning and hierarchical methods, combined with various time series representations and similarity measures. Our methodology is applied to real-world data from highway sensors, enabling us to assess the impact of different clustering frameworks on traffic pattern recognition. We also introduce a clustering-driven anomaly detection methodology that identifies deviations from expected traffic behaviour based on distance-based anomaly scores. Results indicate that hierarchical clustering with symbolic representations provides robust segmentation of traffic patterns, while partitioning methods such as k-means and fuzzy c-means yield meaningful results when paired with Dynamic Time Warping. The proposed anomaly detection strategy successfully identifies sensor malfunctions and abnormal traffic conditions with minimal false positives, demonstrating its practical utility for real-time monitoring. Real-world vehicular traffic data are provided by Autostrade Alto Adriatico S.p.A.

The study at the Peggy Guggenheim Collection in Venice highlights critical interactions between indoor air quality, visitor dynamics, and microclimatic conditions, offering insights into preventive conservation of modern artworks. By analyzing pollutants such as ammonia, formaldehyde, and organic acids, alongside visitor density and environmental data, the research identified key patterns and risks. Through three seasonal monitoring campaigns, the concentrations of SO2 (sulphur dioxide), NO (nitric oxide), NO2 (nitrogen dioxide), NOx (nitrogen oxides), HONO (nitrous acid), HNO3 (nitric acid), O3 (ozone), NH3 (ammonia), CH3COOH (acetic acid), HCOOH (formic acid), and HCHO (formaldehyde) were determined using passive samplers, as well as temperature and relative humidity data loggers. In addition, two specific short-term monitoring campaigns focused on NH3 were performed to evaluate the influence of visitor presence on indoor concentrations of the above compounds and environmental parameters. NH3 and HCHO concentrations spiked during high visitor occupancy, with NH3 levels doubling in crowded periods. Short-term NH3 campaigns confirmed a direct correlation between visitor numbers and the above indoor concentrations, likely due to human emissions (e.g., sweat, breath) and off-gassing from materials. The indoor/outdoor ratios indicated that several pollutants originated from indoor sources, with ammonia and acetic acid showing the highest indoor concentrations. By measuring the number of visitors and microclimate parameters (temperature and humidity) every 3 s, we were able to precisely estimate the causality and the temporal shift between these quantities, both at small time scale (a few minute delay between peaks) and at medium time scale (daily average conditions due to the continuous inflow and outflow of visitors).

In this paper we propose a novel macroscopic (fluid dynamics) model for describing pedestrian flow in low and high density regimes. The model is characterized by the fact that the maximal density reachable by the crowd – usually a fixed model parameter – is instead a state variable. To do that, the model couples a conservation law, devised as usual for tracking the evolution of the crowd density, with a Burgers-like PDE with a nonlocal term describing the evolution of the maximal density. The variable maximal density is used here to describe the effects of the psychological/physical pushing forces which are observed in crowds during competitive or emergency situations. Specific attention is also dedicated to the fundamental diagram, i.e., the function which expresses the relationship between crowd density and flux. Although the model needs a well defined fundamental diagram as known input parameter, it is not evident a priori which relationship between density and flux will be actually observed, due to the time-varying maximal density. An a posteriori analysis shows that the observed fundamental diagram has an elongated “tail” in the congested region, thus resulting similar to the concave/concave fundamental diagram with a “double hump” observed in real crowds. The main features of the model are investigated through 1D and 2D numerical simulations. The numerical code for the 1D simulation is freely available on this Gitlab repository.

In this work, we deal with a mathematical model describing the dissolution process of irregularly shaped particles. In particular, we consider a complete dissolution model accounting for surface kinetics, convective diffusion, and relative velocity between fluid and dissolving particles, for three drugs with different solubility and wettability: theophylline, griseofulvin, and nimesulide. The possible subsequent recrystallization process in the bulk fluid is also considered. The governing differential equations are revisited in the context of the level-set method and Hamilton-Jacobi equations, then they are solved numerically. This choice allows us to deal with the simultaneous dissolution of hundreds of different polydisperse particles. We show the results of many computer simulations which investigate the impact of the particle size, shape, area/volume ratio, and the dependence of the interfacial mass transport coefficient on the surface curvature.

In this paper, we derive a kinetic description of swarming particle dynamics in an interacting multi-agent system featuring emerging leaders and followers. Agents are classically characterized by their position and velocity plus a continuous parameter quantifying their degree of leadership. The microscopic processes ruling the change of velocity and degree of leadership are independent, non-conservative and non-local in the physical space, so as to account for long-range interactions. Out of the kinetic description, we obtain then a macroscopic model under a hydrodynamic limit reminiscent of that used to tackle the hydrodynamics of weakly dissipative granular gases, thus relying in particular on a regime of small non-conservative and short-range interactions. Numerical simulations in one- and two-dimensional domains show that the limiting macroscopic model is consistent with the original particle dynamics and furthermore can reproduce classical emerging patterns typically observed in swarms.

Nel cuore della scuola primaria, luogo privilegiato per la costruzione delle conoscenze di base e per lo sviluppo delle prime competenze trasversali, si colloca il progetto STI2MA, acronimo di Scienza, Tecnica, Ingegno, Italiano, Matematica e Arte. Si tratta di una proposta strutturata di rinnovamento della didattica della matematica in chiave interdisciplinare e sostenibile, nel solco delle Indicazioni Nazionali e dei più recenti orientamenti internazionali in materia di educazione alla cittadinanza globale. L’autrice mette a punto un curricolo integrato che muove dall’idea, tanto Montessoriana quanto di epistemologia scientifica contemporanea, secondo cui la matematica non è solo una disciplina ma un linguaggio per pensare, per interpretare il mondo, per agire con consapevolezza, per riflettere e per scoprire tutte le dimensioni del proprio universo culturale. L’autrice mette a punto un curricolo integrato che muove dall’idea, tanto Montessoriana quanto di epistemologia scientifica contemporanea, secondo cui la matematica non è solo una disciplina ma un linguaggio per pensare, per interpretare il mondo, per agire con consapevolezza, per riflettere e per scoprire tutte le dimensioni del proprio universo culturale.

il presente rapporto mira a esplorare come le nuove modalità di lavoro flessibile, favorite dalla digitalizzazione, possano promuovere un equilibrio virtuoso tra vita professionale e privata, migliorando al contempo le performance e il benessere individuale e organizzativo. Attraverso l'analisi della letteratura e del quadro normativo, si esamina il concetto di work-life balance, delineandone vantaggi e criticità. Si indaga, poi, come il benessere organizzativo si traduca in risultati concreti sia per i lavoratori che per le organizzazioni, creando un circolo virtuoso che lega la salute psico-fisica dei dipendenti a una maggiore produttività, efficienza, efficacia e sostenibilità nel lungo periodo, con un focus sul settore pubblico. Viene dedicata particolare attenzione all'impatto della digitalizzazione come fattore chiave per l'implementazione di politiche di work-life balance, analizzando sia le opportunità offerte dagli strumenti per una maggiore flessibilità sia le criticità legate ai confini sempre più sfumati tra le due sfere di vita. Le conclusioni sintetizzano i principali risultati emersi, offrendo una riflessione sulle sfide e le opportunità che caratterizzano il futuro del lavoro, delineando possibili prospettive future.

Human behavior is a key determinant of epidemic outcomes. During health crises, variations in people's responses to control measures, often driven by different levels of risk perception, lead to variability in epidemic parameters such as infectiousness and susceptibility. We introduce a model within the Susceptible-Infected-Removed (SIR) class that accounts for these heterogeneities. We find that there is a region in the space of parameters just above the epidemic threshold, where trajectories showing an initial decline in the number of Infected can suddenly reverse and give rise to widespread transmission. Such heterogeneity can lead to an underestimation of transmission potential and delayed recognition of epidemic resurgence, thereby severely compromising efforts for a timely response. We examine this phenomenon in the mean-field scenario and then simulate the dynamics on homogeneous and heterogeneous contact networks, confirming that this phenomenology persists beyond mean field. Our model also encompasses cases where the heterogeneity originates from biological or other factors.

Motivation The rapid expansion of single-cell RNA sequencing (scRNA-seq) technologies has increased the need for robust and scalable clustering evaluation methods. To address these challenges, we developed robin2, an optimized version of our R package robin. It introduces enhanced computational efficiency, support for high-dimensional datasets, and harmonious integration with R's base functionalities for robust network analysis.Results robin2 offers improved functionality for clustering stability validation and enables systematic evaluation of community detection algorithms across various resolutions and pipelines. The application to Tabula Muris and PBMC scRNA-seq datasets confirmed its ability to identify biologically meaningful cell subpopulations with high statistical significance. The new version reduces computational time by 9-fold on large-scale datasets using parallel processing.Availability and implementation The robin2 package is freely available on CRAN at https://CRAN.R-project.org/package=robin. Comprehensive documentation and a detailed analysis vignette are available on GitHub at https://drighelli.github.io/scrobinv2/index.html.

The diagnosis and monitoring of eosinophilic esophagitis (EoE), a common pediatric pathology, typically involves invasive procedures such as an upper endoscopy with biopsies, imposing a significant burden on patients and healthcare systems. We aimed to assess miR-21-5p and miR-223-3p levels in pediatric EoE patients and evaluate their as potential non-invasive biomarkers of disease activity and response to treatments. We enrolled 13 children with EoE and 8 controls. Plasma and esophageal mucosa samples from patients were collected at diagnosis and after 8-10 weeks of therapy and compared with control samples. After microRNA(miRNA) extraction, the levels of miR-21-5p and miR-223-3p and their relevant target genes were analyzed. Bioinformatic analysis was used to identify the predicted target genes and pathways that are potentially relevant for disease pathophysiology. Plasma levels of miR-21-5p and miR-223-3p were significantly higher in EoE patients than in the controls, reflecting their levels in esophageal mucosa. The target genes of these miRNAs are involved in key signaling pathways (MAPK, Ras, and FoxO), relevant for EoE pathophysiology. Among these, STAT3 (Signal Transducer and Activator of Transcription 3) and PTEN (Phosphatase and Tensin Homolog), which are significantly downregulated in patient esophageal mucosa, are implicated in eosinophilic gastroenteropathies and autoimmune diseases. Following therapy (proton pump inhibitors and/or fluticasone propionate), plasma and tissue expression of both miRNAs significantly decreased and were no longer different from the controls. These microRNAs may serve as complementary non-invasive EoE markers and reduce the need for endoscopy/biopsies.

Engineering mammalian cells with synthetic circuits drives innovation in next-generation biotherapeutics and industrial biotechnology. However, applications often depend on cellular productivity, which is constrained by finite cellular resources. Here, we harness computational biology to identify drugs that boost productivity without additional genetic modifications. We perform RNA-sequencing on cells expressing an incoherent feed-forward loop (iFFL), a genetic circuit that enhances operational capacity. To find drugs that mimic this effect, we use DECCODE (Drug Enhanced Cell COnversion using Differential Expression), an unbiased method that matches our transcriptional data with thousands of drug-induced profiles. Among the compound candidates, we select Filgotinib, that enhances expression of both transiently and stably expressed genetic payloads across various experimental scenarios and cell lines, including AAV and lentivirus transduction. Our results reveal cell-specific responses, underscoring the context dependency of small-molecule treatments. Altogether, we present a versatile tool for biomedical and industrial applications requiring enhanced productivity from engineered cells.

We give analytic description for the completion of C?0 (R+) in Dirichletspace D1,p(R+, ?) := {u : R+ -> R : u is locally absolutely continuous on R+ and ||u? ||_Lp(R+,?) < ?}, for given continuouspositive weight ? defined on R+, where 1 < p < ?. The conditions are described in terms of the modified variants of the Bpconditions due to Kufner and Opic from 1984, which in our approach are focusing on integrability of ?^-p/(p-1) near zero or near infinity. Moreover, we propose applications of our results to: obtaining newvariants of Hardy inequality, interpretation of boundary value problems in ODE's defined on the halpfline with solutions in D1,p(R+, ?),new results from complex interpolation theory dealing with interpolation spaces between weighted Dirichlet spaces, and to derivationof new Morrey type embedding theorems for our Dirichlet space.

Planning petrol station replenishment is an important logistics activity for all the major oil companies. The studied Multi-Depot Periodic Petrol Station Replenishment problem derives from a real case in which the company must replenish a set of petrol stations from a set of depots, during a weekly planning horizon. The company must ensure refuelling according to available visiting patterns, which can be different from customer to customer. A visiting pattern predefines how many times (days) the replenishment occurs during a week and in which visiting days a certain amount of fuel must be delivered. To fulfill the weekly demand of each petrol station, one of the available replenishment plans must be selected among a given set of visiting patterns. The aim is to minimize the total distance travelled by the fleet of tank trucks during the entire planning horizon. A matheuristic approach is proposed, based on the cluster-first route-second paradigm, to solve it. The proposed approach is thoroughly tested on a set of realistic random instances. Finally, a weekly large real instance is considered with 194 petrol stations and two depots.

Magnetoencephalography (MEG) is a valuable non-invasive neurophysiology technique for investigation of brain function and dysfunction. In this chapter, we will discuss the main characteristics of MEG signals, and the great potential it offers for scientific interrogation in psychology, cognitive neuroscience, neurology, and neuropsychiatry. Starting from the physical properties of MEG recordings, the chapter will highlight the main advantages of utilizing MEG in neuroscience (that is a combination of very high temporal resolution and good spatial resolution) and will summarize the current status of MEG in research and clinical settings. To make this topic more relatable to widely available electroencephalography (EEG), we will present several comparisons of MEG with EEG. The objective of the present chapter is to provide a broad overview of the principle concepts and strengths of MEG, aimed at newcomers to the field.

We prove the nonlinear asymptotic stability of stably stratified solutions to the Incompressible Porous Media equation (IPM) for initial perturbations in $\dot H^{1-\tau}(\R^2) \cap \dot H^s(\R^2)$ with $s > 3$ and for any $0 < \tau <1$. Such result improves the existing literature, where the asymptotic stability is proved for initial perturbations belonging at least to $H^{20}(\R^2)$. \\ More precisely, the aim of the article is threefold. First, we provide a simplified and improved proof of global-in-time well-posedness of the Boussinesq equations with strongly damped vorticity in $H^{1-\tau}(\R^2) \cap \dot H^s(\R^2)$ with $s > 3$ and $0 < \tau <1$. Next, we prove the strong convergence of the Boussinesq system with damped vorticity towards (IPM) under a suitable scaling. Lastly, the asymptotic stability of stratified solutions to (IPM) follows as a byproduct.\\ A symmetrization of the approximating system and a careful study of the anisotropic properties of the equations via anisotropic Littlewood-Paley decomposition play key roles to obtain uniform energy estimates. Finally, one of the main new and crucial points is the integrable time decay of the vertical velocity $\|u_2(t)\|_{L^\infty (\R^2)}$ for initial data only in $\dot H^{1-\tau}(\R^2) \cap \dot H^s(\R^2)$ with $s >3$.

This article is concerned with the rigorous justification of the hydrostatic limit for continuouslystratified incompressible fluids under the influence of gravity.The main peculiarity of this work with respect to previous studies is that no (regularizing) viscosity contributionis added to the fluid-dynamics equations and only diffusivity effects are included. Motivated byapplications to oceanography, the diffusivity effects included in this work are induced by an advection termwhose specific form was proposed by Gent and McWilliams in the 90's to model effective eddy correlations fornon-eddy-resolving systems.The results of this paper heavily rely on the assumption of stable stratification. We provide the wellposednessof the hydrostatic equations and of the original (non-hydrostatic) equations for stably stratified fluids,as well as their convergence in the limit of vanishing shallow-water parameter. The results are established inhigh but finite Sobolev regularity and keep track of the various parameters at stake.A key ingredient of our analysis is the reformulation of the systems by means of isopycnal coordinates,which allows to provide careful energy estimates that are far from being evident in the original coordinatesystem.

We prove the strong ill-posedness of the two-dimensional Boussinesq system in vorticity form in L8pR2qwithout boundary, building upon the method that Shikh Khalil & Elgindi arXiv:2207.04556v1 developed for scalarequations. We provide examples of initial data with vorticity and density gradient of small L8pR2q size, for which thehorizontal density gradient has a strong L8pR2q-norm inflation in infinitesimal time, while the vorticity and the verticaldensity gradient remain bounded. Furthermore, exploiting the three-dimensional version of Elgindi's decomposition ofthe Biot-Savart law, we apply our method to the three-dimensional axisymmetric Euler equations with swirl and awayfrom the vertical axis, showing that a large class of initial data with vorticity uniformly bounded and small in L8pR2qprovides a solution whose gradient of the swirl has a strong L8pR2q-norm inflation in infinitesimal time. The norminflations are quantified from below by an explicit lower bound which depends on time, the size of the data and is validfor small times