In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. We incorporate structural and attribute similarities between the vertices in an augmented graph by creating additional vertices and edges as proposed in [1, 2]. The augmented graph is then embedded in a Euclidean space associated to its Laplacian and we cluster vertices via a modified K-means algorithm, using a new vector-valued distance in the embedding space. Main novelty of our method, which can be classified as an early fusion method, i.e., a method in which additional information on vertices are fused to the structure information before applying clustering, is the interpretation of attributes as new realizations of graph vertices, which can be dealt with as coordinate vectors in a related Euclidean space. This allows us to extend a scalable generalized spectral clustering procedure which substitutes graph Laplacian eigenvectors with some vectors, named algebraically smooth vectors, obtained by a linear-time complexity Algebraic MultiGrid (AMG) method. We discuss the performance of our proposed clustering method by comparison with recent literature approaches and public available results. Extensive experiments on different types of synthetic datasets and real-world attributed graphs show that our new algorithm, embedding attributes information in the clustering, outperforms structure-only-based methods, when the attributed network has an ambiguous structure. Furthermore, our new method largely outperforms the method which originally proposed the graph augmentation, showing that our embedding strategy and vector-valued distance are very effective in taking advantages from the augmented-graph representation.

Assessing the validity of a psychometric test is fundamental to ensure a reliable interpretation of its outcomes. Few attempts have been made recently to complement classical approaches (e.g., factor models) with a novel technique based on network analysis. The objective of the current study is to carry out a network-based validation of the Eating Disorder Inventory 3 (EDI-3), a questionnaire designed for the assessment of eating disorders. Exploiting a reliable, open source sample of 1206 patients diagnosed with an eating disorder, we set up a robust validation process encompassing detection and handling of redundant EDI-3 items, estimation of the cross-sample psychometric network, resampling bootstrap procedure and computation of the median network of the replica samples. We then employed a community detection algorithm to identify the topological clusters, evaluated their coherence with the EDI-3 subscales and replicated the full validation analysis on the subpopulations corresponding to patients diagnosed with either anorexia nervosa or bulimia nervosa. Results of the network-based analysis, and particularly the topological community structures, provided support for almost all the composite scores of the EDI-3 and for 2 single subscales: Bulimia and Maturity Fear. A moderate instability of some dimensions led to the identification of a few multidimensional items that should be better located in the intersection of multiple psychological scales. We also found that, besides symptoms typically attributed to eating disorders, such as drive for thinness, also non-specific symptoms like low self-esteem and interoceptive deficits play a central role in both the cross-sample and the diagnosis-specific networks. Our work adds insights into the complex and multidimensional structure of EDI-3 by providing support to its network-based validity on both mixed and diagnosis-specific samples. Moreover, we replicated previous results that reinforce the transdiagnostic theory of eating disorders.

Motivation: Gene-disease associations are fundamental for understanding disease etiology and developing effective interventions and treatments. Identifying genes not yet associated with a disease due to a lack of studies is a challenging task in which prioritization based on prior knowledge is an important element. The computational search for new candidate disease genes may be eased by positive-unlabeled learning, the machine learning setting in which only a subset of instances are labeled as positive while the rest of the data set is unlabeled. In this work, we propose a set of effective network-based features to be used in a novel Markov diffusion-based multi-class labeling strategy for putative disease gene discovery. Results: The performances of the new labeling algorithm and the effectiveness of the proposed features have been tested on ten different disease data sets using three machine learning algorithms. The new features have been compared against classical topological and functional/ontological features and a set of network- and biological-derived features already used in gene discovery tasks. The predictive power of the integrated methodology in searching for new disease genes has been found to be competitive against state-of-the-art algorithms.Availability and implementation: The source code of NIAPU can be accessed at https://github. com/AndMastro/NIAPU. The source data used in this study are available online on the respective websites.

The Critical Node Detection Problem (CNDP) consists in finding the set of nodes, defined critical, whose removal maximally degrades the graph. In this work we focus on finding the set of critical nodes whose removal minimizes the pairwise connectivity of a direct graph (digraph). Such problem has been proved to be NP-hard, thus we need efficient heuristics to detect critical nodes in real-world applications. We aim at understanding which is the best heuristic we can apply to identify critical nodes in practice, i.e., taking into account time constrains and real-world networks. We present an in-depth analysis of several heuristics we ran on both real-world and on synthetic graphs. We define and evaluate two different strategies for each heuristic: standard and iterative. Our main findings show that an algorithm recently proposed to solve the CNDP and that can be used as heuristic for the general case provides the best results in real-world graphs, and it is also the fastest. However, there are few exceptions that are thoroughly analyzed and discussed. We show that among the heuristics we analyzed, few of them cannot be applied to very large graphs, when the iterative strategy is used, due to their time complexity. Finally, we suggest possible directions to further improve the heuristic providing the best results.

A reaction-diffusion model, known as the Sel'kov-Schnakenberg model, is considered. The nonlinear stability of the constant steady state is studied by using a special Liapunov functional and a maximum principle for regular solutions.

In this paper we consider a non-standard discretization to a Volterra integro-dierentialsystem which includes a number of age-of-infection models in the literature. The aim is to provide ageneral framework to analyze the proposed scheme for the numerical solution of a class of problemswhose continuous dynamic is well known in the literature and allow a deeper analysis in cases wherethe theory lacks

Epidemic models structured by the age of infection can be formulated in terms of a system of renewal equations and represent a very general mathematical framework for the analysis of infectious diseases ([1, 2]). Here, we propose a formulation of renawal equations that takes into account of the behavioral response of individuals to infection. We use the so called "information index", which is a distributed delay that summarizes the information available on current and past disease trend, and extend some results regarding compartmental behavioral models [3, 4, 5]. For the numerical solution of the equations we propose a non-standard approach [6] based on a non local discretization of the integral term characterizing the mathematical equations. We discuss classical problems related to the behaviour of this scheme and we prove the positivity invariance and the unconditional preservation of the stability nature of equilibria, with respect to the discretization parameter. These properties, together with the fact that the method can be put into an explicit form, actually make it a computationally attractive tool and, at the same time, a stand-alone discrete model describing the evolution of an epidemic. This is a joint work with Bruno Buonomo and Claudia Panico from University of Naples "Federico II", and Antonia Vecchio from IAC-CNR, Naples.

We propose a numerical method for a general integro-differential system of equations which includes a number of age-of-infection epidemic models in the literature [1, 2]. The numerical solution is obtained by a non-standard discretization of the nonlinear terms in the system, and agrees with the analytical solution in many important qualitative aspects. Both the behaviour at finite time and the asymptotic properties of the solution are preserved for any value of the discretization parameter. These properties, together with the fact that the method is linearly implicit, actually make it a computationally attractive tool and, at the same time, a stand-alone discrete model describing the evolution of an epidemic [3, 4]. References [1] F. Brauer. Age of infection in epidemiology models, Electronic Journal of Differential Equations, 2005. [2] D. Breda, O. Diekmann, W. F. de Graaf, A. Pugliese and R. Vermiglio, On the formulation of epidemic models (an appraisal of Kermack and McKendrick), J. of Biological Dynamics, 6:sup2, 103-117, 2012. [3] E. Messina, M. Pezzella and A. Vecchio, A non-standard numerical scheme for an age-of-infection epidemic model, J. Comput. Dyn., 9 (2), 239-252, 2022. [4] E. Messina, C. Panico and A. Vecchio, Global stability properties of nonstandard discretization for renewal epidemic models, in preparation.

The present work extends a previous paper where an agent-based and two-dimensional partial differential diffusion model was introduced for describing immune cell dynamics (leukocytes) in cancer-on-chip experiments. In the present work, new features are introduced for the dynamics of leukocytes and for their interactions with tumor cells, improving the adherence of the model to what is observed in laboratory experiments. Each system's solution realization is a family of biased random walk trajectories, affected by the chemotactic gradients and in turn affecting them. A sensitivity analysis with respect to the model parameters is performed in order to assess the effect of their variation on both tumor cells and on leukocyte dynamics.

In recent years an increasing interest is registered in the direction of developing techniques to combine experimental data and mathematical models, in order to produce systems, i.e., in silico models, whose solutions could reproduce and predict experimental outcomes. Indeed, the success of informed models is mainly due to the consistent improvements in computational abilities of the machines and in imaging techniques that allow a wider access to high spatial and temporal resolution data. Here we present an interdisciplinary work in the framework of Organs-on-chip (OoC) technology, and, more precisely, in Canceron-Chip (CoC) technology.

Round Table of MACH2021

In this paper we present a survey about a series of works developed in the last 20 years, with our group, on chemical aggression of stone artifacts. Here we describe the modelling of different phenomena responsible for exterior and internal degradation of porous materials, such as the evolution of gypsum crust in marble stones, the sodium sulphate crystallization inside porous stone (masonry brick), or the effect of injection of consolidants in stones. For sulfation and other surface reactions we adapted our previous models to take into account more possible features, as for instance rugosity of stones and the possible interaction between chemical and mechanical damage, to evaluate the propagation of cracks in stones under stress. For the problem of salt crystallization, a new mathematical model describing the effect of protective products on sodium sulphate crystallization inside bricks has been proposed and tested against experiments. Finally, a mathematical model for evaluating the penetration and the ultimate depth of filtration of a consolidant product (ethyl silicate) on tuff was proposed and calibrated using experimental data. The proposed models were calibrated by tuning model parameters with numerical fitting procedures based on the comparison between simulation results and available experimental data. Since the obtained results were in qualitative and quantitative accordance with data, this confirmed the soundness of implemented procedures and the effectiveness of the proposed methods.

Real scientific contact between mathematical community and experts in cultural heritageResults of concrete collaboration projects are presentedMathematical models can provide an effective and non-invasive analysis tools in this field

The volume contains high quality articles in the framework of multiscale modelling including lab-on-chip framework It includes models of classification and tumour growth in patient-specific framework The present collection covers a large array of topical biomedical applications

Functionally graded materials (FGMs), possessing properties that vary smoothly from one region to another,have been receiving increasing attention in recent years, particularly in the aerospace, automotive andbiomedical sectors. However, they have yet to reach their full potential. In this paper, we explore the potentialof FGMs in the context of drug delivery, where the unique material characteristics offer the potential of finetuningdrug-release for the desired application. Specifically, we develop a mathematical model of drug releasefrom a thin film FGM, based upon a spatially-varying drug diffusivity. We demonstrate that, depending on thefunctional form of the diffusivity (related to the material properties) a wide range of drug release profilesmay be obtained. Interestingly, the shape of these release profiles are not, in general, achievable from ahomogeneous medium with a constant diffusivity.

We describe preliminary results from a multiobjectivegraph matching algorithm, in the coarsening step of anaggregation-based Algebraic MultiGrid (AMG) preconditioner,for solving large and sparse linear systems of equations on highendparallel computers. We have two objectives. First, we wishto improve the convergence behavior of the AMG method whenapplied to highly anisotropic problems. Second, we wish to extendthe parallel package PSCToolkit to exploit multi-threadedparallelism at the node level on multi-core processors. Ourmatching proposal balances the need to simultaneously computehigh weights and large cardinalities by a new formulation ofthe weighted matching problem combining both these objectivesusing a parameter ?. We compute the matching by a parallel2/3 - ?-approximation algorithm for maximum weight matchings.Results with the new matching algorithm show that for a suitablechoice of the parameter ? we compute effective preconditionersin the presence of anisotropy, i.e., smaller solve times, setup times,iterations counts, and operator complexity.

Vitamin D has been proven to be a strong stimulator of mechanisms associated with the elimination of pathogens. Because of its recognized effectiveness against viral infections, during SARS-CoV-2 infection, the effects of Vitamin D supplementation have been the object of debate. This study aims to contribute to this debate by the means of a qualitative phenomenological mathematical model in which the role of Vitamin D and its interactions with the innate immune system are explicitly considered. We show that Vitamin D influx and degradation can be considered as possible control parameters for the disease evaluation and recovery. By varying Vitamin D influx, three dynamical scenarios have been found with different modalities of recovery from the disease. Inside each scenario, Vitamin D degradation has been related to different degrees of severity in disease development. Interestingly, the emergence of hysteretic phenomenologies when Vitamin D influx is too low can be related to the onset of Long-COVID syndrome, confirming clinical evidence from recent studies on the topic.

We tackle the problem of coupling a spatiotemporal model for simulating the spread and control of an invasive alien species with data coming from image processing and expert knowledge. In this study, we implement a spatially explicit optimal control model based on a reaction-diffusion equation which includes an Holling II type functional response term for modeling the density control rate. The model takes into account the budget constraint related to the control program and searches for the optimal effort allocation for the minimization of the invasive alien species density. Remote sensing and expert knowledge have been assimilated in the model to estimate the initial species distribution and its habitat suitability, empirically extracted by a land cover map of the study area. The approach has been applied to the plant species Ailanthus altissima (Mill.) Swingle within the Alta Murgia National Park. This area is one of the Natura 2000 sites under the study of the ongoing National Biodiversity Future Center (NBFC) funded by the Italian National Recovery and Resilience Plan (NRRP), and pilot site of the finished H2020 project ECOPOTENTIAL, which aimed at the integration of modeling tools and Earth Observations for a sustainable management of protected areas. Both the initial density map and the land cover map have been generated by using very high resolution satellite images and validated by means of ground truth data provided by the EU Life Alta Murgia project (LIFE12 BIO/IT/000213), a project aimed at the eradication of Ailanthus altissima in the Alta Murgia National Park

A new fractional q-order variation of the RothC model for the dynamics of soil organic carbon is introduced. A computational method based on the discretization of the analytic solution along with the finite-difference technique are suggested and the stability results for the latter are given. The accuracy of the scheme, in terms of the temporal step size h, is confirmed through numerical testing of a constructed analytic solution. The effectiveness of the proposed discrete method is compared with that of the classical discrete RothC model. Results from real-world experiments show that, by adjusting the fractional order q and the multiplier term ?(t,q), a better match between simulated and actual data can be achieved compared to the traditional integer-order model.

To evaluate changes in the Soil Organic Carbon (SOC) index, one of the key indicators of land degradation neutrality, soil carbon modeling is of primary importance. In litera-ture, the analysis has been focused on the stability characterization of soil carbon steady states and in the calculation of the resilience of the stable equilibria. Neither stability nor resilience, however, provide any information about transient dynamics, and models with highly resilient equilibria can exhibit dramatic transient responses to perturbations. To trace how environmental changes affect the transient dynamics of SOC indicator, we use the concept of generalized reactivity (g-reactivity) to models belonging to two main classes: the first-order, linear and semilinear carbon transfer models and fully nonlinear microbe-explicit models. A novel formulation of a general two-dimensional model allows to deal with different functional forms and to perform a systematic analysis of both stabil-ity of soil carbon equilibria and SOC-reactivity. Using temperatures and Net Primary Pro-duction (NPP) data of Alta Murgia National Park, the RothC, MOMOS and the fully implicit dynamical planar system are compared in predicting the impact of increased temperatures in the years 2005-2019 on the asymptotic stability of carbon steady states and in increas-ing the SOC-reactivity.(c) 2023 Elsevier Inc. All rights reserved.