The properties of semiflexible active ring polymers are studied by numerical simulations. The two-dimensionally confined polymer is modeled as a closed bead-spring chain subject to tangential active forces, and the interaction with the fluid is described by the Brownian multiparticle collision dynamics approach. Both phantom polymers and chains with excluded-volume interactions are considered. The size and shape strongly depend on the relative ratio of the persistence length to the ring length as well as on the active force. The long-time dynamics is characterized by a rotational motion whose frequency increases with the active force.

The aim of this work is to propose a fast and reliable algorithm for computingintegrals of the type$$\int_{-\infty}^{\infty} f(x) e^{\scriptstyle -x^2 -\frac{\scriptstyle 1}{\scriptstyle x^2}} dx,$$where $f(x)$ is a sufficiently smooth function, in floating point arithmetic.The algorithm is based on a product integration rule, whose rate of convergencedepends only on the regularity of $f$, since the coefficients of the rule are ``exactly'' computed by means of suitable recurrence relations here derived.We prove stability and convergence in the space of locally continuous functions on $\RR$ equipped with weighted uniform norm.By extensive numerical tests, the accuracy of the proposed product rule is compared with that of the Gauss--Hermite quadrature formula w.r.t. the function $f(x) e^{-\frac{\scriptstyle 1}{\scriptstyle x^2}}$. The numerical results confirm the effectiveness of the method, supporting the proven theoretical estimates.

In this paper, we discuss the convergence of an Algebraic MultiGrid (AMG) method for general symmetric positive-definite matrices. The method relies on an aggregation algorithm, named coarsening based on compatible weighted matching, which exploits the interplay between the principle of compatible relaxation and the maximum product matching in undirected weighted graphs. The results are based on a general convergence analysis theory applied to the class of AMG methods employing unsmoothed aggregation and identifying a quality measure for the coarsening; similar quality measures were originally introduced and applied to other methods as tools to obtain good quality aggregates leading to optimal convergence for M-matrices. The analysis, as well as the coarsening procedure, is purely algebraic and, in our case, allows an a posteriori evaluation of the quality of the aggregation procedure which we apply to analyze the impact of approximate algorithms for matching computation and the definition of graph edge weights. We also explore the connection between the choice of the aggregates and the compatible relaxation convergence, confirming the consistency between theories for designing coarsening procedures in purely algebraic multigrid methods and the effectiveness of the coarsening based on compatible weighted matching. We discuss various completely automatic algorithmic approaches to obtain aggregates for which good convergence properties are achieved on various test cases.

We numerically study the dynamics of quasi-two dimensional cholesteric liquid crystal droplets in the presence of a time-dependent electric field, rotating at constant angular velocity. A surfactant sitting at the droplet interface is also introduced to prevent droplet coalescence. The dynamics is modeled following a hybrid numerical approach, where a standard lattice Boltzmann technique solves the Navier-Stokes equation and a finite difference scheme integrates the evolution equations of liquid crystal and surfactant. Our results show that, once the field is turned on, the liquid crystal rotates coherently triggering a concurrent orbital motion of both droplets around each other, an effect due to the momentum transfer to the surrounding fluid. In addition the topological defects, resulting from the conflict orientation of the liquid crystal within the drops, exhibit a chaotic-like motion in cholesterics with a high pitch, in contrast with a regular one occurring along circular trajectories observed in nematics drops. Such behavior is found to depend on magnitude and frequency of the applied field as well as on the anchoring of the liquid crystal at the droplet interface. These findings are quantitatively evaluated by measuring the angular velocity of fluid and drops for various frequencies of the applied field.

The simulations for the inverse problem of radiative transfer, even if built with a correct Bayesian approach, do not represent the full source of errors present in the experimental data. We point out two categories of errors (atmospheric model errors and non-Gaussian instrumental errors due to the optics and hardware, that are not considered by standard methods. Moreover, we show cases taken from FORUM simulated radiances using an End to End simulator, where se show how the instrument reacts to a non homogeneousneous filed of view.

The non-equilibrium structural and dynamical properties of a flexible polymer pinned to a reflecting wall and subject to oscillatory linear flow are studied by numerical simulations. Polymer is confined in two dimensions and is modeled as a bead-spring chain while the interaction with the fluid is described by the Brownian multiparticle collision dynamics. At low strain the polymer is stretched along the flow direction. When increasing strain, chains are completely elongated and compressed against the wall when the flow is reverted. The conformations are analyzed and compared to the case of stiffer polymers [1]. The dynamics is investigated by looking at the motion of the center of mass which shows a frequency doubling along the shear direction. [1] A. Lamura, R. G. Winkler, and G. Gompper, Wall-Anchored Semiflexible Polymer under Large Amplitude Oscillatory Shear, J. Chem. Phys. 154, 224901 (2021).

After giving some background on neuron physiology, the classical (deterministic) models for the generation of action potentials are briefly introduced and their limitations discussed, so to motivate the need for a stochastic description of the neuronal firing activity. The more relevant stochastic models for single neuron dynamics are reviewed, with particular attention to the phenomenon of spike-frequency adaptation. Then some approaches to the modeling of network dynamics, where populations of excitatory and inhibitory neurons interact, are described. Finally,some recent models applying suitable strategies to reproduce complex neural dynamics emerging from networks of spiking neurons, such as fractional differentiation or other memory effects, are introduced as a perspective for current and future research.

Insieme al teorema dimostrato da Bernoulli nel 1713 e noto oggi come legge dei grandi numeri, il teorema del limite centrale è alla base della statistica inferenziale, che si propone di ricavare informazioni e di trarre conclusioni su una popolazione a partire dall'osservazione di un campione casuale dei suoi elementi.In sintesi, il teorema dice che in ogni situazione in cui i dati da noi osservati sono influenzati da tanti piccoli effetti casuali indipendenti tra loro, la distribuzione risultante sarà approssimativamente una curva gaussiana, detta anche normale. Ciò permette di determinare un valore attendibile per un parametro di interesse, come il valore atteso, con il relativo intervallo di fiducia per la nostra stima; o di valutare la credibilità di un'ipotesi di carattere generale dopo una serie di osservazioni.Le sue applicazione spaziano nei campi più diversi. Per esempio, l'altezza delle donne italiane, la luminosità delle stelle, i valori di colesterolo della popolazione di maschi adulti, le fluttuazioni giornaliere di un indice del mercato azionario, i punteggi registrati in un test preselettivo, fino all'attendibilità dei sondaggi e all'efficacia dei vaccini sulla popolazione.

Mortality shocks, such as pandemics, threaten the consolidated longevity improvements, confirmed in the last decades for the majority of western countries. Indeed, just before the COVID-19 pandemic, mortality was falling for all ages, with a different behavior according to different ages and countries. It is indubitable that the changes in the population longevity induced by shock events, even transitory ones, affecting demographic projections, have financial implications in public spending as well as in pension plans and life insurance. The Short Term Mortality Fluctuations (STMF) data series, providing data of all-cause mortality fluctuations by week within each calendar year for 38 countries worldwide, offers a powerful tool to timely analyze the effects of the mortality shock caused by the COVID-19 pandemic on Italian mortality rates. This dataset, recently made available as a new component of the Human Mortality Database, is described and techniques for the integration of its data with the historical mortality time series are proposed. Then, to forecast mortality rates, the well-known stochastic mortality model proposed by Lee and Carter in 1992 is first considered, to be consistent with the internal processing of the Human Mortality Database, where exposures are estimated by the Lee-Carter model; empirical results are discussed both on the estimation of the model coefficients and on the forecast of the mortality rates. In detail, we show how the integration of the yearly aggregated STMF data in the HMD database allows the Lee-Carter model to capture the complex evolution of the Italian mortality rates, including the higher lethality for males and older people, in the years that follow a large shock event such as the COVID-19 pandemic. Finally, we discuss some key points concerning the improvement of existing models to take into account mortality shocks and evaluate their impact on future mortality dynamics.

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