Abstract. Electroencephalography (EEG) source imaging aims to reconstruct brainactivity maps from the neuroelectric potential difference measured on the skull. Toobtain the brain activity map, we need to solve an ill-posed and ill-conditionedinverse problem that requires regularization techniques to make the solution viable.When dealing with real-time applications, dimensionality reduction techniques can beused to reduce the computational load required to evaluate the numerical solutionof the EEG inverse problem. To this end, in this paper we use the random dipolesampling method, in which a Monte Carlo technique is used to reduce the numberof neural sources. This is equivalent to reducing the number of the unknownsin the inverse problem and can be seen as a first regularization step. Then, wesolve the reduced EEG inverse problem with two popular inversion methods, theweighted Minimum Norm Estimate (wMNE) and the standardized LOw Resolutionbrain Electromagnetic TomogrAphy (sLORETA). The main result of this paper is theerror estimates of the reconstructed activity map obtained with the randomized versionof wMNE and sLORETA. Numerical experiments on synthetic EEG data demonstratethe effectiveness of the random dipole sampling method.

Understanding brain function from magneto-electroencephalographic (M/EEG) measurements requires advanced mathematical and signal processing tools. Although the analysis of M/EEG data at sensors level sheds light on important brain mechanisms, full exploitation of the information contained in such brain data could be achieved by reconstructing the active neural sources from M/EEG measurements. This involves solving an ill-posed and ill-conditioned inverse problem in which not only the identification of the most suitable inversion method [1, 2] but also the calibration of the regularization parameters is of paramount importance. Once time series representing brain activity are available, a next step is to develop tools to extract meaningful information that characterizes brain activity [3, 4], for example, when the subject under study is affected by diseases that impair brain function. The mini-symposium brings together researchers from various disciplines who have developed methodologies that are being successfully used for the analysis of the M/EEG data, the solution of the underlying inverse problem and in the definition of brain fingerprint. The purpose is not only to present the latest research results in this area but also to create a fruitful environment for the development of new ideas.

Following the methodology of Brasco (Adv Math 394:108029, 2022), we study the long-time behavior for the signed fractional porous medium equation in open bounded sets with smooth boundary. Homogeneous exterior Dirichlet boundary conditions are considered. We prove that if the initial datum has sufficiently small energy, then the solution, once suitably rescaled, converges to a nontrivial constant sign solution of a sublinear fractional Lane-Emden equation. Furthermore, we give a nonlocal sufficient energetic criterion on the initial datum, which is important to identify the exact limit profile, namely the positive solution or the negative one

Image scaling methods allows us to obtain a given image at a different, higher (upscaling) or lower (downscaling), resolution with the aim of preserving as much as possible the original content and the quality of the image. In this paper, we focus on interpolation methods for scaling three-dimensional grayscale images. Within a unified framework, we introduce two different scaling methods, respectively based on the Lagrange and filtered de la Vall\'ee Poussin type interpolation at the 1st kind's Chebyshev zeros. In both cases, using a non-standard sampling model, we take (via tensor product) the associated trivariate polynomial interpolating the input image. It represents a continuous approximate 3D image to resample at the desired resolution. Using discrete linf and l2 norms, we theoretically estimate the error achieved in output, showing how it depends on the error in input and on the smoothness of the specific image we are processing. Finally, taking the special case of medical images as a case study, we experimentally compare the performances of the proposed methods among them and with the classical multivariate cubic and Lanczos interpolation methods.

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PRISMA is a hyperspectral pushbroom sensor, launched by the Italian Space Agency in 2019. PRISMA collects the reflected Earth signal from VNIR to the SWIR with 230 spectral bands with a variable FWHM according to the prism dispersion element. This work intends to develop a procedure suitable to monitor the consistency of photon and thermal noise components across a times series of L1 radiance images collected on different Mediterranean scenarios (i.e. rural and coastal). To improve the retrieval of the useful signal and the random noise on PRISMA images the spatial variability of the scenes has been considered in the new version of the HYperspectral Noise Parameters Estimation (HYNPE) algorithm. The procedure, tested on two PRISMA time series, has assessed quite stable and coherent values for the retrieved noise coefficients, not significantly affected by seasonal radiance variations and scene characteristics

In this paper we study a general class of hybrid mathematical models of collective motions of cells under the influence of chemical stimuli. The models are hybrid in the sense that cells are discrete entities given by ODEs, while the chemoattractant is considered as a continuous signal which solves a diffusive equation. For this model we prove the mean-field limit in the Wasserstein distance to a system given by the coupling of a Vlasov-type equation with the chemoattractant equation. Our approach and results are not based on empirical measures but rather on marginals of a large number of individuals densities, and we show the limit with explicit bounds by proving also existence and uniqueness for the limit system. In the monokinetic case we derive a new pressureless nonlocal Euler-type model with chemotaxis.

Wound healing (WH) is a complex phenomenon recollecting the ability of the body to preserve homeostasis. Its description ranges from the very minute details on the progression of the molecular and cellular events (bench) occurring locally to a wound, to the very general, and almost colloquial description of how injuries recover more or less quickly and smoothly in an individual or a patient (bed).The connection between the two representations of WH is far from clear and rarely discussed from an overarching and theoretical perspective in biological, computational and medical terms that represent three fundamental components of modern PPPM. Importantly, understanding WH and its eliciting/modulating factors (including physical stimuli) as a continuum between molecular (local) and clinical (systemic) events is of particular relevance for advancing in the management of chronic inflammation, a hallmark of non-communicable diseases (NCDs). The ambition of this chapter is to make the necessity for such continuum explicit. This evidence will be supported with the first integrated overview on the scattered basic knowledge existing about WH's neglected eliciting factors: physical stimuli. Further, an exemplar translational process using rheumatoid arthritis (RA), proceeding from experimental data in animal models to a pilot clinical study, will cover from bench to bedside the relevance of WH as a systemic anti-inflammatory phenomenon, and will be discussed in the frame of PPPM for its therapeutic potential.

Image resizing (IR) has a crucial role in remote sensing (RS), since an image's level of detail depends on the spatial resolution of the acquisition sensor; its design limitations; and other factors such as (a) the weather conditions, (b) the lighting, and (c) the distance between the satellite platform and the ground targets. In this paper, we assessed some recent IR methods for RS applications (RSAs) by proposing a useful open framework to study, develop, and compare them. The proposed framework could manage any kind of color image and was instantiated as a Matlab package made freely available on Github. Here, we employed it to perform extensive experiments across multiple public RS image datasets and two new datasets included in the framework to evaluate, qualitatively and quantitatively, the performance of each method in terms of image quality and statistical measures.

Resolution Approximation Methods (RAM) play a crucial role in many real-world applications where preserving the original image quality is essential. Depending on the specific applicative field, the approximation may focus on spatial and/or color (intensity) information [7], [6]. Over the years, several methods have been proposed for color (gray) images, and multiple research directions have been pursued to enhance the performance and robustness of RAM [1],[2], [3], [4] and [5]. This contribution explores some approaches for both spatial and color (intensity) resolution approximation, providing a comprehensive analysis of their benefits, drawbacks, and potential future advancements.

Smart farming is becoming an active and interdisciplinary research field as it requires to solve interesting and challenging research issues to respond concretely to the demands of specific use-cases. One of the most delicate tasks is the automatic yield estimation, as for example in vineyards [1]. Computer vision methods that implement the rules of the human visual system can contribute to task accomplishment as they simulate what winemakers make manually [2]. An automatic artificial-intelligence method for grape bunch detection from RGB images is presented. It properly defines the input of a Convolutional Neural Network whose task is the segmentation of grape bunches [3]. The network input consists of pointwise visual contrast-based measurements that allow us to discriminate and detect grape bunches even in uncontrolled acquisition conditions and with limited computational load. The latter property makesthe proposed method implementable on smart devices and appropriate for onsite and real-time applications.

Switchable and adaptive substrates emerged as valuable tools for controlling wetting and actuation of droplet motion. Here, we report a computational study of the dynamics of an unstable thin liquid film deposited on a switchable substrate, modeled with a space- and time-varying contact angle. For a sufficiently large rate of wettability variation, a topological transition appears. Instead of breaking up into droplets, as expected for a substrate with multiple wetting minima, a metastable rivulet state emerges. A criterion discriminating whether or not rivulets occur is identified in terms of a single dimensionless parameter. Finally, we show and derive theoretically how the film rupture times, droplet shape, and rivulet lifetime depend on the pattern wavelength and speed.

Active turbulence is a paradigmatic and fascinating example of self-organized motion at large scales occurring in active matter. We employ massive hydrodynamic simulations of suspensions of resolved model microswimmers to tackle the phenomenon in semi-diluted conditions at a mesoscopic level. We measure the kinetic energy spectrum and find that it decays as k-3 over a range of interme- diate wavenumbers. The velocity distributions are of L ́evy type, a distinct difference with inertial turbulence. Furthermore, we propose a reduced order dynamical deterministic model for active turbulence, inspired to shell models for classical turbulence, whose numerical and analytical study confirms the spectrum power-law observed in the simulations and reveals hints of a non-Gaussian, intermittent, physics of active turbulence. Direct numerical simulations and modelling also agree in pointing to a phenomenological picture whereby, in the absence of an energy cascade `a la Richardson forbidden by the low Reynolds number regime, it is the coupling between fluid velocity gradients and bacterial orientation that gives rise to a multiscale dynamics.