Innovative approach: it is one of the first real scientific contacts between the mathematical community and the experts in cultural heritage Effective multidisciplinary interaction: the results of concrete collaboration projects between research groups dealing with the degradation of the historical and artistic heritage are presented Development potential: the possibility of finding suitable mathematical models to provide an effective and non-invasive predictive analysis tool can be a fundamental task in the cultural heritage conservation field

(1) Background: A better understanding of COVID-19 dynamics in terms of interactions among individuals would be of paramount importance to increase the effectiveness of containment measures. Despite this, the research lacks spatiotemporal statistical and mathematical analysis based on large datasets. We describe a novel methodology to extract useful spatiotemporal information from COVID-19 pandemic data. (2) Methods: We perform specific analyses based on mathematical and statistical tools, like mathematical morphology, hierarchical clustering, parametric data modeling and non-parametric statistics. These analyses are here applied to the large dataset consisting of about 19,000 COVID-19 patients in the Veneto region (Italy) during the entire Italian national lockdown. (3) Results: We estimate the COVID-19 cumulative incidence spatial distribution, significantly reducing image noise. We identify four clusters of connected provinces based on the temporal evolution of the incidence. Surprisingly, while one cluster consists of three neighboring provinces, another one contains two provinces more than 210 km apart by highway. The survival function of the local spatial incidence values is modeled here by a tapered Pareto model, also used in other applied fields like seismology and economy in connection to networks. Model's parameters could be relevant to describe quantitatively the epidemic. (4) Conclusion: The proposed methodology can be applied to a general situation, potentially helping to adopt strategic decisions such as the restriction of mobility and gatherings.

For the finite weighted Hilbert transform we consider two different product integration rules, the VP rule and the L-rule, based on the same nodes and obtained by approximating the density function with filtered de la Vallée Poussin and classical Lagrange interpolation polynomials, respectively. The L-rule is well known and widely studied. The VP rule is here introduced and we will prove the convergence in suitable weighted uniform spaces. Hence we will examine the performance of both the product rules, showing that in case of density functions that have some pathologies (peaks, cusps, etc.) localized in isolated points, VP rules inherit the good properties of the filtered de la Vallée Poussin type approximation, providing better performances than L-rules.

Aggregating transcriptomics data across hospitals can increase sensitivity and robustness of differential expression analyses, yielding deeper clinical insights. As data exchange is often restricted by privacy legislation, meta-analyses are frequently employed to pool local results. However, the accuracy might drop if class labels are inhomogeneously distributed among cohorts. Flimma (https://exbio.wzw.tum.de/flimma/) addresses this issue by implementing the state-of-the-art workflow limma voom in a federated manner, i.e., patient data never leaves its source site. Flimma results are identical to those generated by limma voom on aggregated datasets even in imbalanced scenarios where meta-analysis approaches fail.

FORUM (Far-infrared Outgoing Radiation Understanding and Monitoring) will flight as the 9th ESA's Earth Explorer mission, and an End-to-End Simulator (E2ES) has been developed as a support tool for the mission selection process and the subsequent development phases. The current status of the FORUM E2ES project is presented, together with the characterization of the capabilities of a full physics retrieval code applied to FORUM data. We show how the instrument characteristics and5the observed scene conditions impact on the spectrum measured by the instrument, accounting for the main sources of error related to the entire acquisition process, and the consequences on the retrieval algorithm. Both homogeneous and heterogeneous case studies are simulated in clear and cloudy conditions, validating the E2ES against two independent codes: KLIMA (clear sky) and SACR (cloudy sky). The performed tests show that the performance of the retrieval algorithm is compliant with the project requirements both in clear and cloudy conditions. The far infrared (FIR) part of the FORUM spectrum is shown to be10sensitive to surface emissivity, in dry atmospheric conditions, and to cirrus clouds, resulting in improved performance of the retrieval algorithm in these conditions. The retrieval errors increase with increasing the scene heterogeneity, both in terms of surface characteristics and in terms of fractional cloud cover of the scene.

The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) measured the middle-infrared limb emission spectrum of the atmosphere from 2002 to 2012 on board ENVISAT, a polar-orbiting satellite. Recently, the European Space Agency (ESA) completed the final reprocessing of MIPAS measurements, using version 8 of the level 1 and level 2 processors, which include more accurate models, processing strategies, and auxiliary data. The list of retrieved gases has been extended, and it now includes a number of new species with weak emission features in the MIPAS spectral range. The new retrieved trace species include carbonyl chloride (COCl2), also called phosgene. Due to its toxicity, its use has been reduced over the years; however, it is still used by chemical industries for several applications. Besides its direct injection in the troposphere, stratospheric phosgene is mainly produced from the photolysis of CCl4, a molecule present in the atmosphere because of human activity. Since phosgene has a long stratospheric lifetime, it must be carefully monitored as it is involved in the ozone destruction cycles, especially over the winter polar regions.In this paper we exploit the ESA MIPAS version 8 data in order to discuss the phosgene distribution, variability, and trends in the middle and lower stratosphere and in the upper troposphere. The zonal averages show that phosgene volume mixing ratio is larger in the stratosphere, with a peak of 40 pptv (parts per trillion by volume) between 50 and 30 hPa at equatorial latitudes, while at middle and polar latitudes it varies from 10 to 25 pptv. A moderate seasonal variability is observed in polar regions, mostly between 80 and 50 hPa. The comparison of MIPAS-ENVISAT COCl2 v8 profiles with the ones retrieved from MIPAS balloon and ACE-FTS (Atmospheric Chemistry Experiment - Fourier Transform Spectrometer) measurements highlights a negative bias of about 2 pptv, mainly in polar and mid-latitude regions. Part of this bias is attributed to the fact that the ESA level 2 v8 processor uses an updated spectroscopic database. For the trend computation, a fixed pressure grid is used to interpolate the phosgene profiles, and, for each pressure level, VMR (volume mixing ratio) monthly averages are computed in pre-defined 10? wide latitude bins. Then, for each latitudinal bin and pressure level, a regression model has been fitted to the resulting time series in order to derive the atmospheric trends. We find that the phosgene trends are different in the two hemispheres. The analysis shows that the stratosphere of the Northern Hemisphere is characterized by a negative trend of about -7 pptv per decade, while in the Southern Hemisphere phosgene mixing ratios increase with a rate of the order of +4 pptv per decade. This behavior resembles the stratospheric trend of CCl4, which is the main stratospheric source of COCl2. In the upper troposphere a positive trend is found in both hemispheres.

Motivated by the recent outbreak of coronavirus (COVID-19), we propose a stochastic model of epidemic temporal growth and mitigation based on a time-modulated Hawkes process. The model is sufficiently rich to incorporate specific characteristics of the novel coronavirus, to capture the impact of undetected, asymptomatic and super-diffusive individuals, and especially to take into account time-varying counter-measures and detection efforts. Yet, it is simple enough to allow scalable and efficient computation of the temporal evolution of the epidemic, and exploration of what-if scenarios. Compared to traditional compartmental models, our approach allows a more faithful description of virus specific features, such as distributions for the time spent in stages, which is crucial when the time-scale of control (e.g., mobility restrictions) is comparable to the lifetime of a single infection. We apply the model to the first and second wave of COVID-19 in Italy, shedding light onto several effects related to mobility restrictions introduced by the government, and to the effectiveness of contact tracing and mass testing performed by the national health service.

Two-dimensional dissipative and isotropic kinetic models, like the ones used in neutron transport theory, are considered. Especially, steady-states are expressed for constant opacity and damping, allowing to derive a scattering S-matrix and corresponding "truly 2D well-balanced" numerical schemes. A first scheme is obtained by directly implementing truncated Fourier-Bessel series, whereas another proceeds by applying an exponential modulation to a former, conservative, one. Consistency with the asymptotic damped parabolic approximation is checked for both algorithms. A striking property of some of these schemes is that they can be proved to be both 2D well-balanced and asymptotic-preserving in the parabolic limit, even when setting up IMEX time-integrators: see Corollaries 3.4 and A.1. These findings are further confirmed by means of practical benchmarks carried out on coarse Cartesian computational grids.

The phase separation of a two-dimensional active binary mixture is studied under the action of an applied shear through numerical simulations. It is highlighted how the strength of the external flow modifies the initial shape of growing domains. The activity is responsible for the formation of isolated droplets which affect both the coarsening dynamics and the morphology of the system. The characteristic dimensions of domains along the flow and the shear direction are modulated in time by oscillations whose amplitudes are reduced when the activity increases. This induces a broadening of the distribution functions of domain lengths with respect to the passive case due to the presence of dispersed droplets of different sizes.

X-ray Small and Wide Scattering scanning microscopies have been adopted to inspect morphological and structural properties of collagen-based tissues at the atomic and nano scale 1 . Examples will be discussed on specific pathologies: o osteoarthritis of the hip, also named osteoarthrosis of the hip or coxarthrosis, which is a chronic degenerative disorder of the hip joint, causing growing articular pain that can bring the patient to lifestyle limitations until surgical intervention is needed 2 o keratoconus, a pathology affecting cornea, which causes progressive thinning of the stroma and consequently abnormal curvature, inducing irregular astigmatism and myopia, corneal fibrosis, and distortion of vision, due to the modification in the organization of the corneal collagen 3 o abdominal aortic aneurysm, that occurs in the major artery from the hearth that supplies blood to the abdomen, and popliteal aneurysm, that takes place in the legs, behind the knees, characterized by alteration of collagen structure into vessel's wall of the aneurysm tissues, heterogeneous grade of inflammation related to infiltrating cells and extracellular matrix changes, in particular disruption of elastic fibers, fibrosis and calcifications 4 o diabetes mellitus, a metabolic disorder characterized by high blood sugar levels over a prolonged period due to defects in insulin action or secretion, which causes collagen to have a fixed orientation, stiffen the tissue and is likely to disrupt the normal cell interactions.

Spectral emissivity is a key property of the Earth surface of which only very few measurements exist so far in the far-infrared (FIR) spectral region, even though recent work has shown its FIR contribution is important for accurate modelling of global climate. The European Space Agency's 9th Earth Explorer, FORUM (Far-infrared Outgoing Radiation Understanding and Monitoring) will provide the first global spectrally resolved measurements of the Earth's top-of-the-atmosphere (TOA) spectrum in the FIR. In clear-sky conditions with low water vapour content, these measurements will provide a unique opportunity to retrieve spectrally resolved FIR surface emissivity. In preparation for the FORUM mission with an expected launch in 2026, this study takes the first steps towards the development of an operational emissivity retrieval for FORUM by investigating the sensitivity of the emissivity product of a full spectrum optimal estimation retrieval method to different physical and operational parameters. The tool used for the sensitivity tests is the FORUM mission's end-to-end simulator. These tests show that spectral emissivity of most surface types can be retrieved for dry scenes in the 350-600 cm-1 region with an uncertainty ranging from 0.005 to 0.01. In addition, the quality of retrieval is quantified with respect to the precipitable water vapour content of the scene, and the uncertainty caused by the correlation of emissivity with surface temperature is investigated. Two main recommendations are made based on these investigations: (1) As the extent of TOA sensitivity to the surface in the FIR depends on the atmospheric state, the spectral region of the emissivity product should be decided using a so-called information quantifier, calculated from the ratio of the retrieval uncertainty to the a-priori uncertainty. (2) Depending on retrieval input parameters, the correlation of emissivity with surface temperature allows for retrieved emissivities within a small range around the true emissivity. Thus the impact of this correlation on the uncertainty estimates of the product should be quantified in detail during further development of the operational retrieval.

We present mesoscale numerical simulations of Rayleigh-Bénard (RB) convection in a two-dimensional model emulsion. The systems under study are constituted of finite-size droplets, whose concentration is systematically varied from small (Newtonian emulsions) to large values (non-Newtonian emulsions). We focus on the characterisation of the heat transfer properties close to the transition from conductive to convective states, where it is well known that a homogeneous Newtonian system exhibits a steady flow and a time-independent heat flux. In marked contrast, emulsions exhibit non-steady dynamics with fluctuations in the heat flux. In this paper, we aim at the characterisation of such non-steady dynamics via detailed studies on the time-averaged heat flux and its fluctuations. To quantitatively understand the time-averaged heat flux, we propose a side-by-side comparison between the emulsion system and a single-phase (SP) system, whose viscosity is suitably constructed from the shear rheology of the emulsion. We show that such local closure works well only when a suitable degree of coarse-graining (at the droplet scale) is introduced in the local viscosity. To delve deeper into the fluctuations in the heat flux, we furthermore propose a side-by-side comparison between a Newtonian emulsion (i.e., with a small droplet concentration) and a non-Newtonian emulsion (i.e., with a large droplet concentration), at fixed time-averaged heat flux. This comparison elucidates that finite-size droplets and the non-Newtonian rheology cooperate to trigger enhanced heat-flux fluctuations at the droplet scales. These enhanced fluctuations are rooted in the emergence of space correlations among distant droplets, which we highlight via direct measurements of the droplets displacement and the characterisation of the associated correlation function. The observed findings offer insights on heat transfer properties for confined systems possessing finite-size constituents.

In this article, we deal with the model selection problem for estimating a Gaussian Graphical Model (GGM) by regression based techniques. In fact, although regression based techniques are well understood and have good theoretical properties, it is still not clear which criterion is more appropriate for model selection. In this work we do a comparative study between CV and BIC, obtaining important conclusions that can be of practical interest in different contexts of data analysis. In this article, we deal with the model selection problem for estimating a Gaussian Graphical Model (GGM) by regression based techniques. In fact, although regression based techniques are well understood and have good theoretical properties, it is still not clear which criterion is more appropriate for model selection. In this work we do a comparative study between CV and BIC, obtaining important conclusions that can be of practical interest in different contexts of data analysis.

In this paper, we propose two models describing the dynamics of heavy and light vehicles on a road network, taking into account the interactions between the two classes. The models are tailored for two-lane highways where heavy vehicles cannot overtake. This means that heavy vehicles cannot saturate the whole road space, while light vehicles can. In these conditions, the creeping phenomenon can appear, i.e., one class of vehicles can proceed even if the other class has reached the maximal density. The first model we propose couples two first-order macroscopic LWR models, while the second model couples a second-order microscopic follow-the-leader model with a first-order macroscopic LWR model. Numerical results show that both models are able to catch some second-order (inertial) phenomena such as stop and go waves. Models are calibrated by means of real data measured by fixed sensors placed along the A4 Italian highway Trieste-Venice and its branches, provided by Autovie Venete S.p.A.

A new immersed boundary approach for high order Weighted Essentially non-Oscillatory (WENO) schemes is proposed. The schemes is based on the main ideas from both the general immersed boundary algorithms and the level-set approach and can be easily applied to both finite difference and finite volume formulation. Although formally only second order accurate, numerical tests prove that the use of higher order approximation for the Eulerian fluxes can be very convenient to capture flow details and to obtain low uncertainty also with very coarse grids.

The observations acquired during the full mission of the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) instrument, aboard the European Space Agency Environmental Satellite (Envisat), have been analysed with version 8.22 of the Optimised Retrieval Model (ORM), originally developed as the scientific prototype of the ESA level-2 processor for MIPAS observations. The results of the analyses have been included into the MI- PAS level-2 version 8 (level2-v8) database containing atmospheric fields of pressure, temperature, and volume mixing ratio (VMR) of MIPAS main targets H2 O, O3 , HNO3 , CH4 , N2 O, and NO2 , along with the minor gases CFC- 11, ClONO2 , N2 O5 , CFC-12, COF2 , CCl4 , CF4 , HCFC-22, C2 H2 , CH3 Cl, COCl2 , C2 H6 , OCS, and HDO. The database covers all the measurements acquired by MIPAS in the nominal measurement mode of the full resolution (FR) part of the mission (from July 2002 to March 2004) and all the observation modes of the optimised resolution (OR) part (from January 2005 to April 2012). The number of species included in the MIPAS level2-v8 dataset makes it of particular importance for the studies of stratospheric chemistry. The database is considered by ESA the final release of the MIPAS level-2 products.The ORM algorithm is operated at the vertical grid coincident to the tangent altitudes of the observations or to a subset of them, spanning (in the nominal mode) the alti- tude range from 6 to 68km in the FR phase and from 6 to 70 km in the OR period. In the latitude domain, FR profiles are spaced by about 4.7o, while the OR profiles are spaced by about 3.7o. For each retrieved species, the auxiliary data and the retrieval choices are described. Each product is characterised in terms of the retrieval error, spatial resolution, and "useful" vertical range in both phases of the MIPAS mission. These depend on the characteristics of the measurements (spectral and vertical resolution of the measurements), the retrieval choices (number of spectral points in- cluded in the analyses, number of altitudes included in the vertical retrieval grid), and the information content of the measurements for each trace species. For temperature, water vapour, ozone, and nitric acid, the number of degrees of freedom is significantly larger in the OR phase than in the FR one, mainly due to the finer vertical measurement grid. In the FR phase, some trace species are characterised by a smaller retrieval error with respect to the OR phase, mainly due to the larger number of spectral points used in the analyses, along with the reduced vertical resolution. The way of handling possible caveats (negative VMR, vertical grid representation) is discussed. The quality of the retrieved profiles is assessed through four criteria, two providing information on the successful convergence of the retrieval iterations, one on the capability of the retrieval to reproduce the measurements, and one on the presence of outliers. An easy way to identify and filter the problematic profiles with the informa- tion contained in the output files is provided. MIPAS level2- v8 data are available to the scientific community through the ESA portal (https://doi.org/10.5270/EN1-c8hgqx4).

In this paper we establish an higher integrability result for second derivatives of the local solution of elliptic equation div(A(x,Du))=0in?where ? ? R, n>= 2 and A(x, ?) has linear growth with respect to ? variable. Concerning the dependence on the x-variable, we shall assume that, for the map x-> A(x, ?) , there exists a non negative function k(x), such that |DxA(x,?)|?k(x)(1+|?|)for every ?? R and a.e. x? ?. It is well known that there exists a relationship between this condition and the regularity of the solutions of the equation. Our pourpose is to establish an higher integrability result for second derivatives of the local solution, by assuming k(x) in a suitable Zygmund class.

In this paper we establish the boundedness and the higher differentiability of solutions to the {div(A(x,Du))+b(x)|u(x)|u(x)=fin ?u=0on ?? under a Sobolev assumption on the partial map x->A(x,?). The novelty here is that we deal with degenerate elliptic operator A(x,?) with p-growth, p>=2, with respect to the gradient variable, in presence of lower order terms. The interplay between b(x) and f(x), introduced in ([1]), gives a regularizing effect also in the degenerate elliptic setting.

Meditation practices have been claimed to have a positive effect on the regulation of mood and emotions for quite some time by practitioners, and in recent times there has been a sustained effort to provide a more precise description of the influence of meditation on the human brain. Longitudinal studies have reported morphological changes in cortical thickness and volume in selected brain regions due to meditation practice, which is interpreted as an evidence its effectiveness beyond the subjective self reporting. Using magnetoencephalography (MEG) or electroencephalography to quantify the changes in brain activity during meditation practice represents a challenge, as no clear hypothesis about the spatial or temporal pattern of such changes is available to date. In this article we consider MEG data collected during meditation sessions of experienced Buddhist monks practicing focused attention (Samatha) and open monitoring (Vipassana) meditation, contrasted by resting state with eyes closed. The MEG data are first mapped to time series of brain activity averaged over brain regions corresponding to a standard Destrieux brain atlas. Next, by bootstrapping and spectral analysis, the data are mapped to matrices representing random samples of power spectral densities in ?, ?, ?, and ? frequency bands. We use linear discriminant analysis to demonstrate that the samples corresponding to different meditative or resting states contain enough fingerprints of the brain state to allow a separation between different states, and we identify the brain regions that appear to contribute to the separation. Our findings suggest that the cingulate cortex, insular cortex and some of the internal structures, most notably the accumbens, the caudate and the putamen nuclei, the thalamus and the amygdalae stand out as separating regions, which seems to correlate well with earlier findings based on longitudinal studies.

Neural oscillations contribute to speech parsing via cortical tracking of hierarchical linguistic structures, including syllable rate. While the properties of neural entrainment have been largely probed with speech stimuli at either normal or artificially accelerated rates, the important case of natural fast speech has been largely overlooked. Using magnetoencephalography, we found that listening to naturally-produced speech was associated with cortico-acoustic coupling, both at normal (~6 syllables/s) and fast (~9 syllables/s) rates, with a corresponding shift in peak entrainment frequency. Interestingly, time-compressed sentences did not yield such coupling, despite being generated at the same rate as the natural fast sentences. Additionally, neural activity in right motor cortex exhibited stronger tuning to natural fast rather than to artificially accelerated speech, and showed evidence for stronger phase-coupling with left temporo-parietal and motor areas. These findings are highly relevant for our understanding of the role played by auditory and motor cortex oscillations in the perception of naturally produced speech.