In this paper, we use the Z-control approach to get further insight on the role of awareness in the management of epidemics that, just like Covid-19, display a high rate of overexposure because of the large number of asymptomatic people. We focus on a SEIR model including a overexposure mechanism and consider awareness as a time-dependent variable whose dynamics is not assigned a priori. Exploiting the potential of awareness to produce social distancing and self-isolation among susceptibles, we use it as an indirect control on the class of infective individuals and apply the Z-control approach to detect what trend must awareness display over time in order to eradicate the disease. To this aim, we generalize the Z-control procedure to appropriately treat an uncontrolled model with more than two governing equations. Analytical and numerical investigations on the resulting Z-controlled system show its capability in controlling some representative dynamics within both the backward and the forward scenarios. The awareness variable is qualitatively compared to Google Trends data on Covid-19 that are discussed in the perspective of the Z-control approach, inferring qualitative indications in view of the disease control. The cases of Italy and New Zealand in the first phase of the pandemic are analyzed in detail. The theoretical framework of the Z-control approach can hence offer the chance to reflect on the use of Google Trends as a possible indicator of good management of the epidemic.

Trends of soil organic carbon (SOC) are significant indicators for land and soil degradation. Decrease in SOC compromises the efforts to achieve by 2030, a land degradation neutral world, as required by Target 15.3 of the Seventeen Sustainable Development Goals (SDGs) adopted by United Nations in September 2015. Differential models, as the Rothamsted Carbon model (RothC) [1], can be useful tools to predict SOC changes, taking into account the interactions among climate, soil and land use management. In this talk, we illustrate some results on the application of a novel nonstandard discretization [2] of the continuous RothC model [3] for assessing the SOC indicator in Alta Murgia National Park, a protected area in Apulia region in the south of Italy. A procedure for determining the initial plant input necessary to run the model is described. Moreover, in order to detect the factors that determine the size and direction of SOC changes, a local sensitivity analysis based on the so-called direct method is performed. This work received fundings from the REFIN project N.0C46E06B (Regione Puglia, Italy) and from the European Union's Horizon 2020 research and innovation programme under grant agreement No 871128 (H2020-eLTER-PLUS project).

We apply the Z-control approach to a SEIR model including a overexposure mechanism and consider awareness as a time-dependent variable whose dynamics is not assigned a priori. Exploiting the potential of awareness to produce social distancing and self-isolation among susceptibles, we use it as an indirect control on the class of infective individuals and apply the Z-control approach to detect what trend awareness must display over time in order to eradicate the disease. To this aim, we generalize the Z-control procedure to appropriately treat an uncontrolled model with more than two governing equations. Analytical and numerical investigations on the resulting Z-controlled system show its capability in controlling some representative dynamics within both the backward and the forward scenarios. The awareness variable is qualitatively compared to Google Trends data on Covid-19 and qualitative indications are inferred in view of the disease control.

A novel model is here introduced for theSOC change indexdefinedas the normalized difference between the actual Soil Organic Carbon and thevalue assumed at an initial reference year. It is tailored on the RothC carbonmodel dynamics and assumes as baseline the value of the SOC equilibriumunder constant environmental conditions. A sensitivity analysis is performedto evaluate the response of the model to changes of temperature, Net PrimaryProduction (NPP), and land use soil class (forest, grassland, arable). A non-standard monthly time-stepping procedure has been proposed to approximatethe SOC change index in the Alta Murgia National Park, a protected areain the Italian Apulia region, selected as test site. In the case of arable class,the SOC change index exhibits a negative trend which can be inverted by asuitable organic fertilization program here proposed.

The diffusive behaviour of simple random-walk proposals of many Markov Chain Monte Carlo (MCMC) algorithms results in slow exploration of the state space making inefficient the convergence to a target distribution. Hamiltonian/Hybrid Monte Carlo (HMC), by introducing fictious momentum variables, adopts Hamiltonian dynamics, rather than a probability distribution, to propose future states in the Markov chain. Splitting schemes are numerical integrators for Hamiltonian problems that may advantageously replace the St ̈ormer-Verlet method within HMC methodology. In this paper a family of stable methods for univariate and multivariate Gaussian distributions, taken as guide-problems for more realistic situations, is proposed. Differently from similar methods proposed in the recent literature, the considered schemes are featured by null expectation of the random variable representing the energy error. The effectiveness of the novel procedures is shown for bivariate and multivariate test cases taken from the literature.

The maximum network lifetime is a well known and studied optimization problem. The aim is to appropriately schedule the activation intervals of the individual sensing devices composing a wireless sensor network used for monitoring purposes, in order to keep the network operational for the longest period of time (network lifetime). In this work, we extend this problem by taking into account the issue of charging the sensor batteries. More specifically, it has to be decided how much charge should be provided to each sensor, given the existence of a charging device with limited energy availability. An exact column generation algorithm embedding a genetic algorithm for the subproblem is proposed. Computational results reveal that by appropriately choosing the charge levels, remarkable network lifetime improvements can be obtained, in particular when the available energy is scarce.

In this paper, we show a branch-and-cut approach to solve the minimum spanning tree problem with conflicting edge pairs. This is a NP-hard variant of the classical minimum spanning tree problem, in which there are mutually exclusive edges. We introduce a new set of valid inequalities for the problem, based on the properties of its feasible solutions, and we develop a branch-and-cut algorithm based on them. Computational tests are performed both on benchmark instances coming from the literature and on some newly proposed ones. Results show that our approach outperforms a previous branch-and-cut algorithm proposed for the same problem.

The All-Colors Shortest Path (ACSP) is a recently introduced NP-Hard optimization problem, in which a color is assigned to each vertex of an edge weighted graph, and the aim is to find the shortest path spanning all colors. The solution path can be not simple, that is it is possible to visit multiple times the same vertices if it is a convenient choice. The starting vertex can be constrained (ACSP) or not (ACSP-UE). We propose a reduction heuristic based on the transformation of any ACSP-UE instance into an Equality Generalized Traveling Salesman Problem one. Computational results show the algorithm to outperform the best previously known one.

We present a simple model describing the chemical aggression undergone by calcium carbonate rocks in presence of acid atmosphere. A large literature is available on the deterioration processes of building stones, in particular in connection with problems concerning historical buildings in the field of Cultural Heritage. It is well known that the greatest aggression is caused by SO2 andNO3. In this paper we consider the corrosion caused by sulphur dioxide, which, reacting with calcium carbonate, produces gypsum. The model proposed is obtained by considering both the diffusive and convective effects of propagation and assuming that the porous medium is saturated with a compressible fluid having an assigned polytropic constitutive equation for the pressure

Analisi, modellizzazione e simulazione delle traiettorie dei visitatori nelle aree museali

Motivation Inflammation is part of the complex function that addresses harmful stimuli, and the first phase of wound healing (WH), which guarantees living systems' homeostasis. Deviances from physiology make inflammation turn acute (sepsis, 11M death/y) or chronic (non-communicable diseases, 41M death/y). Therefore, tackling inflammation is a key priority. We recently proposed (Maturo et al., 2020) to revise the conventional inflammatory pathway (innate immune response) to include WH (expanded inflammatory pathway). Methods We manually identified the Reactome pathways that include all reactions and species relevant to WH. Cytoscape was then used to perform the union of the SBML converted pathways, with the largest connected component being retained (732 nodes, 13.944 edges). The same was done for the innate immune response (R-HSA-168249.8) with 487 nodes, 11.744 edges. We then focused on: NF-kB (fundamental hub in all inflammatory reactions), TNF-? (renown target of inflammatory diseases) and RAC1 (key player in mechanotransduction events of WH). Results Preliminary topological results highlight the stability of closeness centrality, i.e. all molecules preserve their efficiency in spreading information. Conversely, betweenness centrality is stable for NF-kB (0.068), confirming NF-kB relevance, while halving its (very low) value in the expanded pathway for TNF-? (from 2.85E-06 to 1.29E-06). This indicates that the ability to bridge different parts of the graphs is less effective if we consider inflammation as an expanded concept, possibly contributing to explain the many side effects of anti-TNF-? therapies. Interestingly, RAC1 presents stable betweenness (from 0.094 to 0.093), comparable to NF-kB, supporting the hypothesis that WH-leveraging therapies could act on a relevant and stable target, so far neglected (Nardini et al., 2016).

The aim of the work is to propose a methodology for the stimulation of a 3D in vitro skin model to activate wound healing. The presented work is in the frame of the national research project, CronXCov, "Checking the CHRONIC to prevent COVid-19", devoted to understand how physiologic and inflamed skin on chip 3D models evolve upon a range of physical (e.g., electrical, mechanical, optical) stimulations, over time. Thanks to the 3D modelling, using Next Generation Sequencing and the network medicine frame of analysis to process the data, we will systematically characterize the effects of the applied stimuli, offering new insight for the exploitation of wound healing.

Thanks to innovative sample-preparation and sequencing technologies, gene expression in individual cells can now be measured for thousands of cells in a single experiment. Since its introduction, single-cell RNA sequencing (scRNA-seq) approaches have revolutionized the genomics field as they created unprecedented opportunities for resolving cell heterogeneity by exploring gene expression profiles at a single-cell resolution. However, the rapidly evolving field of scRNA-seq invoked the emergence of various analytics approaches aimed to maximize the full potential of this novel strategy. Unlike population-based RNA sequencing approaches, scRNA seq necessitates comprehensive computational tools to address high data complexity and keep up with the emerging single-cell associated challenges. Despite the vast number of analytical methods, a universal standardization is lacking. While this reflects the fields' immaturity, it may also encumber a newcomer to blend in. In this review, we aim to bridge over the abovementioned hurdle and propose four ready-to-use pipelines for scRNA-seq analysis easily accessible by a newcomer, that could fit various biological data types. Here we provide an overview of the currently available single-cell technologies for cell isolation and library preparation and a step by step guide that covers the entire canonical analytic workflow to analyse scRNA-seq data including read mapping, quality controls, gene expression quantification, normalization, feature selection, dimensionality reduction, and cell clustering useful for trajectory inference and differential expression. Such workflow guidelines will escort novices as well as expert users in the analysis of complex scRNA-seq datasets, thus further expanding the research potential of single-cell approaches in basic science, and envisaging its future implementation as best practice in the field.

?1-Antitrypsin (AAT) deficiency is a common genetic disease presenting with lung and liver diseases. AAT deficiency results from pathogenic variants in the SERPINA1 gene encoding AAT and the common mutant Z allele of SERPINA1 encodes for Z ?1-antitrypsin (ATZ), a protein forming hepatotoxic polymers retained in the endoplasmic reticulum of hepatocytes. PiZ mice express the human ATZ and are a valuable model to investigate the human liver disease of AAT deficiency. In this study, we investigated differential expression of microRNAs (miRNAs) between PiZ and control mice and found that miR-34b/c was up-regulated and its levels correlated with intrahepatic ATZ. Furthermore, in PiZ mouse livers, we found that Forkhead Box O3 (FOXO3) driving microRNA-34b/c (miR-34b/c) expression was activated and miR-34b/c expression was dependent upon c-Jun N-terminal kinase (JNK) phosphorylation on Ser. Deletion of miR-34b/c in PiZ mice resulted in early development of liver fibrosis and increased signaling of platelet-derived growth factor (PDGF), a target of miR-34b/c. Activation of FOXO3 and increased miR-34c were confirmed in livers of humans with AAT deficiency. In addition, JNK-activated FOXO3 and miR-34b/c up-regulation were detected in several mouse models of liver fibrosis. This study reveals a pathway involved in liver fibrosis and potentially implicated in both genetic and acquired causes of hepatic fibrosis.

We present a new method for assessing homophily in networks whose vertices have categorical attributes, namely when the vertices of networks come partitioned into classes. We apply this method to Protein- Protein Interaction networks, where vertices correspond to proteins, partitioned according to they func- tional role, and edges represent potential interactions between proteins. Similarly to other classical and well consolidated approaches, our method compares the relative edge density of the subgraphs induced by each class with the corresponding expected relative edge density under a null model. The novelty of our approach consists in prescribing an endogenous null model, namely, the sample space of the null model is built on the input network itself. This allows us to give exact explicit expression for the z-score of the relative edge density of each class as well as other related statistics. The z-scores directly quantify the statistical significance of the observed homophily via ?Ceby?s ?ev inequality. The expression of each z-score is entered by the network structure through basic combinatorial invariant such as the number of subgraphs with two spanning edges. Each z-score is computed in O(n3) worst-case time for a network with n vertices. This leads to an overall effective computational method for assesing homophily. Theoretical results are then exploited to prove that Protein-Protein Interaction networks networks are significantly homophillous.

The paper deals with a special filtered approximation method, which originates interpolation polynomials at Chebyshev zeros by using de la Vallée Poussin filters. In order to get an optimal approximation in spaces of locally continuous functions equipped with weighted uniform norms, the related Lebesgue constants have to be uniformly bounded. In previous works this has already been proved under different sufficient conditions. Here, we complete the study by stating also the necessary conditions to get it. Several numerical experiments are also given to test the theoretical results and make comparisons to Lagrange interpolation at the same nodes.

In this paper, some recent applications of the so-called Generalized Bernstein polynomials are collected. This polynomial sequence is constructed by means of the samples of a continuous function f on equispaced points of [0; 1] and depends on an additional parameter which can be suitable chosen in order to improve the rate of convergence to the function f, as the smoothness of f increases, overcoming the well-known low degree of approximation achieved by the classical Bernstein polynomials or by the piecewise polynomial approximation. The applications considered here deal with the numerical integration and the simultaneous approximation. Quadrature rules on equidistant nodes of [0; 1] are studied for the numerical computation of ordinary integrals in one or two dimensions, and usefully employed in Nyström methods for solving Fredholm integral equations. Moreover, the simultaneous approximation of the Hilbert transform and its derivative (the Hadamard transform) is illustrated. For all the applications, some numerical details are given in addition to the error estimates, and the proposed approximation methods have been implemented providing numerical tests which confirm the theoretical estimates. Some open problems are also introduced.

The present paper concerns filtered de la Vallée Poussin (VP) interpolation at the Chebyshev nodes of the four kinds. This approximation model is interesting for applications because it combines the advantages of the classical Lagrange polynomial approximation (interpolation and polynomial preserving) with the ones of filtered approximation (uniform boundedness of the Lebesgue constants and reduction of the Gibbs phenomenon). Here we focus on some additional features that are useful in the applications of filtered VP interpolation. In particular, we analyze the simultaneous approximation provided by the derivatives of the VP interpolation polynomials. Moreover, we state the uniform boundedness of VP approximation operators in some Sobolev and Hölder-Zygmund spaces where several integro-differential models are uniquely and stably solvable.

A methodology to generate calibrated maps of soil moisture from C-band synthetic aperture radar (SAR) images processed by SAR interferometry (InSAR) technique is presented. The proposed methodology uses atmospheric phase delay (APD) maps obtained from a time series of Sentinel-1 interferograms, to disentangle the APD and soil moisture contributions to Sentinel-1 interferograms. We show how the high spatial resolution and short temporal baseline of Sentinel-1 image can help to estimate soil moisture using a daisy chain InSAR processing. The estimated soil moisture maps are compared with in situ data collected by five soil moisture sensors installed in an experimental field, characterized by bare soil, located close to Lisbon, Portugal. Results show that after removing the APD effects in SAR interferogram, there is a correction of the bias in the soil moisture estimation and an improvement in the correlation coefficient with the soil moisture measurements, from 0.38 to 0.78. Soil moisture changes were measured during a sequence of rain events in the winter season. A root-mean-square (rms) error less than 0.04 m3/m3 was found over a variety of meteorological conditions.

Starting from recent experimental observations of starlings and jackdaws, we propose a minimal agent-based mathematical model for bird flocks based on a system of second-order delayed stochastic differential equations with discontinuous (both in space and time) right-hand side. The model is specifically designed to reproduce self-organized spontaneous sudden changes of direction, not caused by external stimuli like predator's attacks. The main novelty of the model is that every bird is a potential turn initiator, thus leadership is formed in a group of indistinguishable agents. We investigate some theoretical properties of the model and we show the numerical results. Biological insights are also discussed.