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.

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

It is known that executing a perfect shifted QR step via the implicit QR algorithm may not result in a deflation of the perfect shift. Typically, several steps are required before deflation actually takes place. This deficiency can be remedied by determining the similarity transformation via the associated eigenvector. Similar techniques have been deduced for the QZ algorithm and for the rational QZ algorithm. In this paper we present a similar approach for executing a perfect shifted QZ step on a general rank structured pencil instead of a specific rank structured one, e.g., a Hessenberg--Hessenberg pencil. For this, we rely on the rank structures present in the transformed matrices. A theoretical framework is presented for dealing with general rank structured \rev{pencils} and deflating subspaces. We present the corresponding algorithm allowing} to deflate simultaneously a block of eigenvalues rather than a single one. We define the level-rho poles and show that these poles are maintained executing the deflating algorithm. Numerical experiments illustrate the robustness of the presented approach showing the importance of using the improved scaled residual approach.

In this paper, we develop new methods to join machine learning techniques and macroscopic differential models, aimed at estimate and forecast vehicular traffic. This is done to complement respective advantages of data-driven and model-driven approaches. We consider here a dataset with flux and velocity data of vehicles moving on a highway, collected by fixed sensors and classified by lane and by class of vehicle. By means of a machine learning model based on an LSTM recursive neural network, we extrapolate two important pieces of information: (1) if congestion is appearing under the sensor, and (2) the total amount of vehicles which is going to pass under the sensor in the next future (30 min). These pieces of information are then used to improve the accuracy of an LWR-based first-order multi-class model describing the dynamics of traffic flow between sensors. The first piece of information is used to invert the (concave) fundamental diagram, thus recovering the density of vehicles from the flux data, and then inject directly the density datum in the model. This allows one to better approximate the dynamics between sensors, especially if an accident/bottleneck happens in a not monitored stretch of the road. The second piece of information is used instead as boundary conditions for the equations underlying the traffic model, to better predict the total amount of vehicles on the road at any future time. Some examples motivated by real scenarios will be discussed. Real data are provided by the Italian motorway company Autovie Venete S.p.A.

The ongoing reproducibility crisis in psychology and cognitive neuroscience has sparked increasing calls to re-evaluate and reshape scientific culture and practices. Heeding those calls, we have recently launched the EEGManyPipelines project as a means to assess the robustness of EEG research in naturalistic conditions and experiment with an alternative model of conducting scientific research. One hundred sixty-eight analyst teams, encompassing 396 individual researchers from 37 countries, independently analyzed the same unpublished, representative EEG data set to test the same set of predefined hypotheses and then provided their analysis pipelines and reported outcomes. Here, we lay out how large-scale scientific projects can be set up in a grassroots, community-driven manner without a central organizing laboratory. We explain our recruitment strategy, our guidance for analysts, the eventual outputs of this project, and how it might have a lasting impact on the field.

Two different direct methods are proposed to solve Cauchy singular integral equations on the real line. The aforementioned methods differ in order to be able to prove their convergence which depends on the smoothness of the known term function in the integral equation.

The dynamics of stabilised concentrated emulsions presents a rich phenomenology including chaotic emulsification, non-Newtonian rheology and ageing dynamics at rest. Macroscopic rheology results from the complex droplet microdynamics and, in turn, droplet dynamics is influenced by macroscopic flows via the competing action of hydrodynamic and interfacial stresses, giving rise to a complex tangle of elastoplastic effects, diffusion, breakups and coalescence events. This tight multiscale coupling, together with the daunting challenge of experimentally investigating droplets under flow, has hindered the understanding of concentrated emulsions dynamics. We present results from three-dimensional numerical simulations of emulsions that resolve the shape and dynamics of individual droplets, along with the macroscopic flows. We investigate droplet dispersion statistics, measuring probability density functions (p.d.f.s) of droplet displacements and velocities, changing the concentration, in the stirred and ageing regimes. We provide the first measurements, in concentrated emulsions, of the relative droplet–droplet separations p.d.f. and of the droplet acceleration p.d.f., which becomes strongly non-Gaussian as the volume fraction is increased above the jamming point. Cooperative effects, arising when droplets are in contact, are argued to be responsible of the anomalous superdiffusive behaviour of the mean square displacement and of the pair separation at long times, in both the stirred and in the ageing regimes. This superdiffusive behaviour is reflected in a non-Gaussian pair separation p.d.f., whose analytical form is investigated, in the ageing regime, by means of theoretical arguments. This work paves the way to developing a connection between Lagrangian dynamics and rheology in concentrated emulsions.

The paper deals with the numerical solution of Cauchy Singular Integral Equations based on some non standard polynomial quasi-projection of de la Vallée Poussin type. Such kind of approximation presents several advantages over classical Lagrange interpolation such as the uniform boundedness of the Lebesgue constants, the near-best order of uniform convergence to any continuous function, and a strong reduction of Gibbs phenomenon. These features will be inherited by the proposed numerical method which is stable and convergent, and provides a near-best polynomial approximation of the sought solution by solving a well conditioned linear system. The numerical tests confirm the theoretical error estimates and, in case of functions subject to Gibbs phenomenon, they show a better local approximation compared with analogous Lagrange projection methods.

We consider here a cell-centered finite difference approximation of the Richards equation in three dimensions, averaging for interface values the hydraulic conductivity, a highly nonlinear function, by arithmetic, upstream and harmonic means. The nonlinearities in the equation can lead to changes in soil conductivity over several orders of magnitude and discretizations with respect to space variables often produce stiff systems of differential equations. A fully implicit time discretization is provided by backward Euler one-step formula; the resulting nonlinear algebraic system is solved by an inexact Newton Armijo-Goldstein algorithm, requiring the solution of a sequence of linear systems involving Jacobian matrices. We prove some new results concerning the distribution of the Jacobians eigenvalues and the explicit expression of their entries. Moreover, we explore some connections between the saturation of the soil and the ill conditioning of the Jacobians. The information on eigenvalues justifies the effectiveness of some preconditioner approaches which are widely used in the solution of Richards equation. We also propose a new software framework to experiment with scalable and robust preconditioners suitable for efficient parallel simulations at very large scales. Performance results on a literature test case show that our framework is very promising in the advance toward realistic simulations at extreme scale.

In this manuscript we propose a numerical method for non-linear integro-differential systems arising in age-of-infection models in a heterogeneously mixed population. The discrete scheme is based on direct quadrature methods and provides an unconditionally positive and bounded solution. Furthermore, we prove the existence of the numerical final size of the epidemic and show that it tends to its continuous equivalent as the discretization steplength vanishes.