Electrical source imaging (ESI) aims at reconstructing the electrical brain activity from measurements of the electric field on the scalp. Even though the localization of single focal sources should be relatively straightforward, different methods provide diverse solutions due to the different underlying assumptions. Furthermore, their input parameter(s) further affects the solution provided by each method, making localization even more challenging. In addition, validations and comparisons are typically performed either on synthetic data or through post-operative outcomes, in both cases with considerable limitations. We use an in-vivo high-density EEG dataset recorded during intracranial single pulse electrical stimulation, in which the true sources are substantially dipolar and their locations are known. We compare ten different ESI methods under multiple choices of input parameters, to assess the accuracy of the best reconstruction, as well as the impact of the parameters on the localization performance. Best reconstructions often fall within 1 cm from the true source, with more accurate methods outperforming less accurate ones by 1 cm, on average. Expectedly, dipolar methods tend to outperform distributed methods. Sensitivity to input parameters varies widely between methods. Depth weighting played no role for three out of six methods implementing it. In terms of regularization parameters, for several distributed methods SNR=1 unexpectedly turned out to be the best choice among the tested ones. Our data show similar levels of accuracy of ESI techniques when applied to "conventional" (32 channels) and dense (64, 128, 256 channels) EEG recordings. Overall findings reinforce the importance that ESI may have in the clinical context, especially when applied to identify the surgical target in potential candidates for epilepsy surgery.

Defining accurate and flexible models for real-world networks of human beings is instrumental to understand the observed properties of phenomena taking place across those networks and to support computer simulations of dynamic processes of interest for several areas of research - including computational epidemiology, which is recently high on the agenda. In this paper we present a flexible model to generate age-stratified and geo-referenced synthetic social networks on the basis of widely available aggregated demographic data and, possibly, of estimated age-based social mixing patterns. Using the Italian city of Florence as a case study, we characterize our network model under selected configurations and we show its potential as a building block for the simulation of infections' propagation. A fully operational and parametric implementation of our model is released as open-source.

The COVID-19 pandemic triggered a global research effort to define and assess timely and effective containment policies. Understanding the role that specific venues play in the dynamics of epidemic spread is critical to guide the implementation of fine-grained non-pharmaceutical interventions (NPIs). In this paper, we present a new model of context-dependent interactions that integrates information about the surrounding territory and the social fabric. Building on this model, we developed an open-source data-driven simulator of the patterns of fruition of specific gathering places that can be easily configured to project and compare multiple scenarios. We focused on the greatest park of the City of Florence, Italy, to provide experimental evidence that our simulator produces contact graphs with unique, realistic features, and that gaining control of the mechanisms that govern interactions at the local scale allows to unveil and possibly control non-trivial aspects of the epidemic.

The definition of suitable generative models for synthetic yet realistic social networks is a widely studied problem in the literature. By not being tied to any real data, random graph models cannot capture all the subtleties of real networks and are inadequate for many practical contexts--including areas of research, such as computational epidemiology, which are recently high on the agenda. At the same time, the so-called contact networks describe interactions, rather than relationships, and are strongly dependent on the application and on the size and quality of the sample data used to infer them. To fill the gap between these two approaches, we present a data-driven model for urban social networks, implemented and released as open source software. By using just widely available aggregated demographic and social-mixing data, we are able to create, for a territory of interest, an age-stratified and geo-referenced synthetic population whose individuals are connected by "strong ties" of two types: Intra-household (e.g., kinship) or friendship. While household links are entirely data-driven, we propose a parametric probabilistic model for friendship, based on the assumption that distances and age differences play a role, and that not all individuals are equally sociable. The demographic and geographic factors governing the structure of the obtained network under different configurations, are thoroughly studied through extensive simulations focused on three Italian cities of different size.

The challenge of exascale requires rethinking numerical algorithms and mathematical software for efficient exploitation of heterogeneous massively parallel supercomputers. In this talk, we present some activities aimed at developing highly scalable and robust sparse linear solvers for solving scientific and engineering applications with a huge number of degrees of freedom (dof)[1]. We discuss algorithmic advances and implementation aspects in the design of Algebraic MultiGrid (AMG) preconditioners based on aggregation, to be used in conjunction with Krylov-subspace projection methods, suitable to exploit high levels of parallelism of current petascale supercomputers. These activities are carried on within two ongoing European Projects, the Energy-oriented Center of Excellence (EoCoE-II) and the EuroHPC TEXTAROSSA project, having the final aim to provide methods and tools for preparing scientific applications in facing and successfully grasping the near future exascale challenge. Beyond possible advances in base software technology to make available programming environments that tend to hide the details of the hardware, we still need to rethink and redesign numerical methods and applications, especially for irregular computations and memory-bound kernels, like sparse solvers.

Soil Organic Carbon (SOC) is one of the key indicators of land degradation. SOC positively affects soil functions with regard to habitats, biological diversity and soil fertility; therefore, a reduction in the SOC stock of soil results in degradation, and it may also have potential negative effects on soil-derived ecosystem services. Dynamical models, such as the Rothamsted Carbon (RothC) model, may predict the long-term behaviour of soil carbon content and may suggest optimal land use patterns suitable for the achievement of land degradation neutrality as measured in terms of the SOC indicator. In this paper, we compared continuous and discrete versions of the RothC model, especially to achieve long-term solutions. The original discrete formulation of the RothC model was then compared with a novel non-standard integrator that represents an alternative to the exponential Rosenbrock-Euler approach in the literature. Soil Organic Carbon (SOC) is one of the key indicators of land degradation. SOC positively affects soil functions with regard to habitats, biological diversity and soil fertility; therefore, a reduction in the SOC stock of soil results in degradation, and it may also have potential negative effects on soil-derived ecosystem services. Dynamical models, such as the Rothamsted Carbon (RothC) model, may predict the long-term behaviour of soil carbon content and may suggest optimal land use patterns suitable for the achievement of land degradation neutrality as measured in terms of the SOC indicator. In this paper, we compared continuous and discrete versions of the RothC model, especially to achieve long-term solutions. The original discrete formulation of the RothC model was then compared with a novel non-standard integrator that represents an alternative to the exponential Rosenbrock-Euler approach in the literature.

We consider two-dimensional zero-temperature systems of N particles to which we associate an energy of the form E[V](X):=?1?iR2E[V](X)?NE ̄sq[V]+O(N12).Moreover E ̄ [V] is also re-expressed as the minimizer of a four point energy. In particular, this happens if the potential V is such that V(r) = + ? forr< 1 , V(r) = - 1 for r?[1,2], V(r) = 0 if r>2, in which case E ̄ [V] = - 4. To the best of our knowledge, this is the first proof of crystallization to the square lattice for a two-body interaction energy.

We introduce a notion of uniform convergence for local and nonlocal curvatures. Then, we propose an abstract method to prove the convergence of the corresponding geometric flows, within the level set formulation. We apply such a general theory to characterize the limits of s-fractional mean curvature flows as (Formula presented.) and (Formula presented.) In analogy with the s-fractional mean curvature flows, we introduce the notion of s-Riesz curvature flows and characterize its limit as (Formula presented.) Eventually, we discuss the limit behavior as (Formula presented.) of the flow generated by a regularization of the r-Minkowski content.

prefazione special issue

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).