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2021 Articolo in rivista metadata only access

Immunoinformatics based designing a multi-epitope vaccine against pathogenic Chandipura vesiculovirus

Deb D ; Basak S ; Kar T ; Narsaria U ; Castiglione F ; Paul A ; Pandey A ; Srivastava AP

Chandipura vesiculovirus (CHPV) is a rapidly emerging pathogen responsible for causing acute encephalitis. Due to its widespread occurrence in Asian and African countries, this has become a global threat, and there is an urgent need to design an effective and nonallergenic vaccine against this pathogen. The present study aimed to develop a multi-epitope vaccine using an immunoinformatics approach. The conventional method of vaccine design involves large proteins or whole organism which leads to unnecessary antigenic load with increased chances of allergenic reactions. In addition, the process is also very time-consuming and labor-intensive. These limitations can be overcome by peptide-based vaccines comprising short immunogenic peptide fragments that can elicit highly targeted immune responses, avoiding the chances of allergenic reactions, in a relatively shorter time span. The multi-epitope vaccine constructed using CTL, HTL, and IFN-? epitopes was able to elicit specific immune responses when exposed to the pathogen, in silico. Not only that, molecular docking and molecular dynamics simulation studies confirmed a stable interaction of the vaccine with the immune receptors. Several physicochemical analyses of the designed vaccine candidate confirmed it to be highly immunogenic and nonallergic. The computer-aided analysis performed in this study suggests that the designed multi-epitope vaccine can elicit specific immune responses and can be a potential candidate against CHPV.

simulazione pipeline Immunoinformatics vaccine design
2021 Articolo in rivista open access

Emulating complex simulations by machine learning methods

Background: The aim of the present paper is to construct an emulator of a complex biological system simulator using a machine learning approach. More specifically, the simulator is a patient-specific model that integrates metabolic, nutritional, and lifestyle data to predict the metabolic and inflammatory processes underlying the development of type-2 diabetes in absence of familiarity. Given the very high incidence of type-2 diabetes, the implementation of this predictive model on mobile devices could provide a useful instrument to assess the risk of the disease for aware individuals. The high computational cost of the developed model, being a mixture of agent-based and ordinary differential equations and providing a dynamic multivariate output, makes the simulator executable only on powerful workstations but not on mobile devices. Hence the need to implement an emulator with a reduced computational cost that can be executed on mobile devices to provide real-time self-monitoring. Results: Similarly to our previous work, we propose an emulator based on a machine learning algorithm but here we consider a different approach which turn out to have better performances, indeed in terms of root mean square error we have an improvement of two order magnitude. We tested the proposed emulator on samples containing different number of simulated trajectories, and it turned out that the fitted trajectories are able to predict with high accuracy the entire dynamics of the simulator output variables. We apply the emulator to control the level of inflammation while leveraging on the nutritional input. Conclusion: The proposed emulator can be implemented and executed on mobile health devices to perform quick-and-easy self-monitoring assessments.

Type-2 diabetes Emulation Computational modelling Risk prediction Self-assessment
2021 Articolo in rivista open access

Heterogeneity of prodromal Parkinson symptoms in siblings of Parkinson disease patients

Baldelli Luca ; Schade Sebastian ; Jesús Silvia ; Schreglmann Sebastian R ; Sambati Luisa ; GómezGarre Pilar ; Halsband Claire ; CalandraBuonaura Giovanna ; AdarmesGómez Astrid Daniela ; SixelDöring Friederike ; Zenesini Corrado ; Pirazzini Chiara ; Garagnani Paolo ; Bacalini Maria Giulia ; Bhatia Kailash P ; Cortelli Pietro ; Mollenhauer Brit ; Franceschi Claudio ; Houlden Henry ; Liò Pietro ; Luchinat Claudio ; Delledonne Massimo ; Mills Kevin ; Pedersen Nancy L ; Azevedo Tiago ; BartolettiStella Anna ; BonillaToribio Marta ; BuizaRueda Dolores ; Capellari Sabina ; CarriònClaro Mario ; Clayton Robert ; Dal Molin Alessandra ; Dimitri Giovanna Maria ; Doykov Ivan ; Giuliani Cristina ; Hägg Sara ; Hällqvist Jenny ; Heywood Wendy ; Huertas Ismael ; Jylhävä Juulia ; LabradorEspinosa Miguel A ; Licari Cristina ; Macias Daniel ; Magrinelli Francesca ; Rodríguez Juan Francisco Martín ; Maturo Maria Giovanna ; Mengozzi Giacomo ; Meoni Gaia ; Milazzo Maddalena ; Nardini Christine ; Pedersen Nancy L ; PeriñánTocino Maria Teresa ; Ravaioli Francesco ; Sala Claudia ; Spasov Simeon ; TejeraParrado Cristina ; Tenori Leonardo ; Paola Turano ; Williams Dylan ; Xumerle Luciano ; Zago Elisa ; Broli Marcella ; BuizaRueda Dolores ; De Massis Patrizia ; EscuelaMartin Rocio ; Fabbri Giovanni ; Gabellini Anna ; Guaraldi Pietro ; Houlden Henry ; Macrì Stefania ; Nassetti Stefania Alessandra ; Scaglione Cesa Lorella Maria ; Valzania Franco ; Rosaria Cilea ; Mignani Francesco ; Ortega Rosario Vigo ; Boninsegna Claudia ; De Luca Silvia ; Mir Pablo ; Trenkwalder Claudia ; Provini Federica

A prodromal phase of Parkinson's disease (PD) may precede motor manifestations by decades. PD patients' siblings are at higher risk for PD, but the prevalence and distribution of prodromal symptoms are unknown. The study objectives were (1) to assess motor and non-motor features estimating prodromal PD probability in PD siblings recruited within the European PROPAG-AGEING project; (2) to compare motor and non-motor symptoms to the well-established DeNoPa cohort. 340 PD siblings from three sites (Bologna, Seville, Kassel/Goettingen) underwent clinical and neurological evaluations of PD markers. The German part of the cohort was compared with German de novo PD patients (dnPDs) and healthy controls (CTRs) from DeNoPa. Fifteen (4.4%) siblings presented with subtle signs of motor impairment, with MDS-UPDRS-III scores not clinically different from CTRs. Symptoms of orthostatic hypotension were present in 47 siblings (13.8%), no different to CTRs (p = 0.072). No differences were found for olfaction and overall cognition; German-siblings performed worse than CTRs in visuospatial-executive and language tasks. 3/147 siblings had video-polysomnography-confirmed REM sleep behavior disorder (RBD), none was positive on the RBD Screening Questionnaire. 173/300 siblings had <1% probability of having prodromal PD; 100 between 1 and 10%, 26 siblings between 10 and 80%, one fulfilled the criteria for prodromal PD. According to the current analysis, we cannot confirm the increased risk of PD siblings for prodromal PD. Siblings showed a heterogeneous distribution of prodromal PD markers and probability. Additional parameters, including strong disease markers, should be investigated to verify if these results depend on validity and sensitivity of prodromal PD criteria, or if siblings' risk is not elevated.

Parkinson Disease
2021 Contributo in Atti di convegno restricted access

Attention Based Subgraph Classification for Link Prediction by Network Re-weighting

Lai Darong ; Liu Zheyi ; Huang Junyao ; Chong Zhihong ; Wu Weiwei ; Nardini Christine

Supervised link prediction aims at finding missing links in a network by learning directly from the data suitable criteria for classifying link types into existent or non-existent. Recently, along this line, subgraph-based methods learning a function that maps subgraph patterns to link existence have witnessed great successes. However, these approaches still have drawbacks. First, the construction of the subgraph relies on an arbitrary nodes selection, often ineffective. Second, the inability of such approaches to evaluate adaptively nodes importance reduces flexibility in nodes features aggregation, an important step in subgraph classification. To address these issues, a novel graph-classification based link-prediction model is proposed: Attention and Re-weighting based subgraph Classification for Link prediction (ARCLink). ARCLink first extracts a subgraph around the two nodes whose link should be predicted, by network reweighting, i.e. attributing a weight in the range 0-1 to all links of the original network, and then learns a function to map the subgraph to a continuous vector for classification, thus revealing the nature (non-existence/existence) of the unknown link. For leaning the mapping function, ARCLink generates a vector representation of the extracted subgraph by hierarchically aggregating nodes features according to nodes importance. In contrast to previous studies that either fully ignore or use fixed schemes to compute nodes importance, ARCLink instead learns nodes importance adaptively by employing attention mechanism. Through extensive experiments, ARCLink was validated on a series of real-world networks against state-of-the-art link prediction methods, consistently demonstrating its superior performances.

graph classification graph neural network link prediction
2021 Articolo in rivista open access

Estimage: A webserver hub for the computation of methylation age

Di Lena Pietro ; Sala Claudia ; Nardini Christine

Methylage is an epigenetic marker of biological age that exploits the correlation between the methylation state of specific CG dinucleotides (CpGs) and chronological age (in years), gestational age (in weeks), cellular age (in cell cycles or as telomere length, in kilobases). Using DNA methylation data, methylage is measurable via the so called epigenetic clocks. Importantly, alterations of the correlation between methylage and age (age acceleration or deceleration) have been stably associated with pathological states and occur long before clinical signs of diseases become overt, making epigenetic clocks a potentially disruptive tool in preventive, diagnostic and also in forensic applications. Nevertheless, methylage dependency from CpGs selection, mathematical modelling, tissue specificity and age range, still makes the potential of this biomarker limited. In order to enhance model comparisons, interchange, availability, robustness and standardization, we organized a selected set of clocks within a hub webservice, EstimAge (Estimate of methylation Age, http://estimage.iac.rm.cnr.it), which intuitively and informatively enables quick identification, computation and comparison of available clocks, with the support of standard statistics.

methylation age
2021 Articolo in rivista open access

The evolution of personalized healthcare and the pivotal role of European regions in its implementation

Nardini Christine ; Osmani Venet ; Cormio Paola G ; Frosini Andrea ; Turrini Mauro ; Lionis Christos ; Neumuth Thomas ; Ballensiefen Wolfgang ; Borgonovi Elio ; D'Errico Gianni

Personalized medicine (PM) moves at the same pace of data and technology and calls for important changes in healthcare. New players are participating, providing impulse to PM. We review the conceptual foundations for PM and personalized healthcare and their evolution through scientific publications where a clear definition and the features of the different formulations are identifiable. We then examined PM policy documents of the International Consortium for Personalised Medicine and related initiatives to understand how PM stakeholders have been changing. Regional authorities and stakeholders have joined the race to deliver personalized care and are driving toward what could be termed as the next personalized healthcare. Their role as a key stakeholder in PM is expected to be pivotal.

European Partnership on Personalized Medicine health data healthcare governance local and regional authorities local and regional authorities personalized healthcare personalized medicine
2021 Articolo in rivista open access

Task-oriented attributed network embedding by multi-view features

Lai Darong ; Wang Sheng ; Chong Zhihong ; Wu Weiwei ; Nardini Christine

Network embedding, also known as network representation learning, aims at defining low-dimensional, continuous vector representation of nodes to maximally preserve the network structure. Recent efforts attempt to extend network embedding to attributed networks where nodes are enriched with descriptors, to enhance interpretability. However, most of these efforts seldom consider the additional knowledge relevant to the aim of the downstream network analysis, i.e. task-related information. When they do, they are analysis-specific and thus lack adaptability to alternative tasks. In this article, a unified framework TANE is proposed to learn Task-oriented Attributed Network Embedding that jointly, maximally and consistently preserves multiple types of network information to generate rich nodes representations, robust to a variety of analyses. The framework can flexibly adapt to, and be readily modified for, different network-based tasks in an end-to-end way. The results of extensive experiments on well-known and commonly used datasets demonstrate that the proposed framework TANE can achieve superior performance over state-of-the-art methods in two commonly performed tasks: node classification and link prediction.

Link prediction Multi-view features Network embedding Network representation learning Node classification
2021 Contributo in Atti di convegno metadata only access

AMG4PSBLAS Linear Algebra Package brings Alya one step closer to Exascale

H Owen ; G Houzeaux ; F Durastante ; S Filippone ; P D'Ambra

In this work, we interfaced to the Alya code the development version of a software framework for efficient and reliable solution of the sparse linear systems for computation of the pressure field at each time step. We developed a software module in Alya's kernel to interface the current development version of the PSBLAS package (Parallel Sparse Basic Linear Algebra Subroutines) and the sibling package AMG4PSBLAS. PSBLAS implements parallel basic linear algebra operations and support routines for sparse matrix management tailored for iterative sparse linear solvers on parallel distributedmemory computers, supporting heterogeneity at the node level. It has gone under extension within the EoCoE-II project with the primary goal to face the exascale challenge. AMG4PSBLAS is a package of Algebraic MultiGrid (AMG) preconditioners built on the top of PSBLAS, which inherits all the flexibility and efficiency features of the PSBLAS infrastructure, and implements up-to-date AMG preconditioners exploiting aggregation of unknowns for the setup of the AMG hierarchy. Many preconditioners employing different aggregation schemes, AMG cycles, and parallel smoothers are available and were tested within the simulation carried out with the Alya code. Results show that the new solvers vastly outperform the original Deflated Conjugate Gradient method available in the Alya kernel in terms of scalability and parallel efficiency and represent a very promising software layer to move the Alya code towards exascale.

CFD HPC Scalable linear solvers
2021 Articolo in rivista open access

Cyber risk quantification: Investigating the role of cyber value at risk

The aim of this paper is to deepen the application of value at risk in the cyber domain, with particular attention to its potential role in security investment valuation. Cyber risk is a fundamental component of the overall risk faced by any organization. In order to plan the size of security investments and to estimate the consequent risk reduction, managers strongly need to quantify it. Accordingly, they can decide about the possibility of sharing residual risk with a third party, such as an insurance company. Recently, cyber risk management techniques are including some risk quantile-based measures that are widely employed in the financial domain. They refer to value at risk that, in the cyber context, takes the name of cyber value at risk (Cy-VaR). In this paper, the main features and challenging issues of Cy-VaR are examined. The possible use of this risk measure in supporting investment decisions in cyber context is discussed, and new risk-based security metrics are proposed. Some simple examples are given to show their potential.

cyber risk management value at risk cyber value at risk security investments
2021 Presentazione / Comunicazione non pubblicata (convegno, evento, webinar...) metadata only access

Cyber risk management: technical and economic factors

The Internet evolution is one of the greatest innovations of the twentieth century and has changed lives of individuals and business organizations. On the other hand, potential attacks on the information systems and eventual crash may cause heavy losses on data, services and business operation. Executives and security professionals are accepting that it is not a matter of if but a matter of when their organization will be hit by a cyber-attack. As a consequence, cyber risk is a fast-growing area of concern. Companies have to include cyber risk in their risk management framework, depicting their risk profile, assessing their risk appetite and looking for corresponding risk transfer solutions. Measures and methods used in financial sector to quantify risk, have been recently applied to cyber world. The aim is to help organizations to improve risk management strategies and to make better decisions about investments in cyber security. On the other hand, they are useful instruments for insurance companies in pricing cyber insurance contracts and setting the minimum capital requirements defined by the regulators. Aim of this contribution, is to offer a review of the recent literature on cyber risk management deepening economic issues and their interplay with technical ones, from both internal (organization) and external (systemic) perspectives.

Cyber risk management Economic issues cyber attacks
2021 Working paper metadata only access

Altered brain criticality in Schizophrenia: New insights from MEG

Golnoush Alamian ; Tarek Lajnef ; Annalisa Pascarella ; JeanMarc Lina ; Laura Knight ; James Walters ; Krish D Singh ; Karim Jerbi

Schizophrenia has a complex etiology and symptomatology that is difficult to untangle. After decades of research, important advancements towards a central biomarker are still lacking. One of the missing pieces is a better understanding of how non-linear neural dynamics are altered in this patient population. In this study, the resting-state neuromagnetic signals of schizophrenia patients and healthy controls were analyzed in the framework of criticality. When biological systems like the brain are in a state of criticality, they are thought to be functioning at maximum efficiency (e.g., optimal communication and storage of information) and with maximum adaptability to incoming information. Here, we assessed the self-similarity and multifractality of resting-state brain signals recorded with magnetoencephalography in patients with schizophrenia patients and in matched controls. Our analysis showed a clear ascending, rostral to caudal gradient of self-similarity values in healthy controls, and an opposite gradient for multifractality (descending values, rostral to caudal). Schizophrenia patients had similar, although attenuated, gradients of self-similarity and multifractality values. Statistical tests showed that patients had higher values of self-similarity than controls in fronto-temporal regions, indicative of more regularity and memory in the signal. In contrast, patients had less multifractality than controls in the parietal and occipital regions, indicative of less diverse singularities and reduced variability in the signal. In addition, supervised machine-learning, based on logistic regression, successfully discriminated the two groups using measures of self-similarity and multifractality as features. Our results provide new insights into the baseline cognitive functioning of schizophrenia patients by identifying key alterations of criticality properties in their resting-state brain data.

Complexity criticality multifractal analysis machine-learning magnetoencephalography resting-state scale-free schizophrenia
2021 Working paper metadata only access

An in-vivo validation of ESI methods with focal sources

Annalisa Pascarella ; Ezequiel Mikulan ; Federica Sciacchitano ; Simone Sarasso ; Annalisa Rubino ; Ivana Sartorie ; Francesco Cardinale ; Flavia Zauli ; Pietro Avanzini ; Lino Nobili ; Andrea Pigorini ; Alberto Sorrentino

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.

ESI EEG inverse methods
2021 Contributo in Atti di convegno restricted access

A Model for Urban Social Networks

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.

Urban social network Graph model Simulator Epidemic
2021 Contributo in Atti di convegno restricted access

Data-driven simulation of contagions in public venues

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.

epidemics contact networks agent-based data-driven
2021 Articolo in rivista open access

Inferring urban social networks from publicly available data

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.

simulator open source data-driven graph model urban social network
2021 Contributo in Atti di convegno metadata only access

Scalable AMG Preconditioners for Computational Science at Extreme Scale

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.

Parallel Scalability Numerical Linear Algebra
2021 Articolo in rivista open access

Non-standard discrete rothc models for soil carbon dynamics

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.

soil organic carbon RothC nonstandard integrators Exponential Rosenbrock-Euler
2021 Articolo in rivista open access

Crystallization to the Square Lattice for a Two-Body Potential

Betermin L ; De Luca L ; Petrache M

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.

crystallization
2021 Articolo in rivista open access

Stability results for nonlocal geometric evolutions and limit cases for fractional mean curvature flows

Cesaroni A ; De Luca L ; Novaga M ; Ponsiglione M

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.

Fractional mean curvature flow; fractional perimeter; level set formulation; local and nonlocal geometric evolutions; Minkowski content; Riesz energy; viscosity solutions
2021 Breve introduzione open access

Variational models in elasticity

De Luca L ; Ponsiglione M

prefazione special issue

variational models in elasticity