For a homogeneous incompressible 2D fluid confined within a bounded Lipschitz simply connected domain, homo- geneous Neumann pressure boundary conditions are equivalent to a constant boundary vorticity. We investigate the rigidity of such conditions.

A general class of hybrid models has been introduced recently, gathering the advantages of multiscale descriptions. Concerning biological applications, the particular coupled structure fits to collective cell migrations and pattern formation phenomena due to intercellular and chemotactic stimuli. In this context, cells are modeled as discrete entities and their dynamics are given by ODEs, while the chemical signal influencing the motion is considered as a continuous signal which solves a diffusive equation. From the analytical point of view, this class of models has been recently proved to have a mean-field limit in the Wasserstein distance towards a system given by the coupling of a Vlasov-type equation with the chemoattractant equation. Moreover, a pressureless nonlocal Euler-type system has been derived for these models, rigorously equivalent to the Vlasov one for monokinetic initial data. For applications, the monokinetic assumption is quite strong and far from a real experimental setting. The aim of this paper is to introduce a numerical approach to the hybrid coupled structure at the different scales, investigating the case of general initial data. Several scenarios will be presented, aiming at exploring the role of the different terms on the overall dynamics. Finally, the pressureless nonlocal Euler-type system is generalized by means of an additional pressure term.

One of the most crucial and lethal characteristics of solid tumors is represented by the increased ability of cancer cells to migrate and invade other organs during the so-called metastatic spread. This is allowed thanks to the production of matrix metalloproteinases (MMPs), enzymes capable of degrading a type of collagen abundant in the basal membrane separating the epithelial tissue from the connective one. In this work, we employ a synergistic experimental and mathematical modelling approach to explore the invasion process of tumor cells. A mathematical model composed of reaction-diffusion equations describing the evolution of the tumor cells density on a gelatin substrate, MMPs enzymes concentration and the degradation of the gelatin is proposed. This is completed with a calibration strategy. We perform a sensitivity analysis and explore a parameter estimation technique both on synthetic and experimental data in order to find the optimal parameters that describe the in vitro experiments. A comparison between numerical and experimental solutions ends the work.

The shape of liquid droplets in air plays an important role in the aerodynamic behavior and combustion dynamics of miniaturized propulsion systems such as microsatellites and small drones. Their precise manipulation can yield optimal efficiency in such systems. It is desired to have a minimal representation of droplet shapes using as few parameters as possible to automate shape manipulation using self-learning algorithms, such as reinforcement learning. In this paper, we use a neural compression algorithm to represent, with only two parameters, elliptical and bullet-shaped droplets initially represented with 200 points (400 real numbers) at the droplet boundary. The mapping of many to two points is achieved in two stages. Initially, a Fourier series is formulated to approximate the contour of the droplet. Subsequently, the coefficients of this Fourier series are condensed to lower dimensions utilizing a neural network with a bottleneck architecture. Finally, 5000 synthetically generated droplet shapes were used to train the neural network. With a two-real-number representation, the recovered droplet shapes had excellent overlap with the original ones, with a mean square error of ∼10−3 . Hence, this method compresses the droplet contour to merely two numerical parameters via a fully reversible process, a crucial feature for rendering learning algorithms computationally tractable.

We introduce a two-step, fully reversible process designed to project the outer shape of a generic droplet onto a lower-dimensional space. The initial step involves representing the droplet's shape as a Fourier series. Subsequently, the Fourier coefficients are reduced to lower-dimensional vectors by using autoencoder models. The exploitation of the domain knowledge of the droplet shapes allows us to map generic droplet shapes to just two-dimensional (2D) space in contrast to previous direct methods involving autoencoders that could map it on minimum eight-dimensional (8D) space. This six-dimensional (6D) reduction in the dimensionality of the droplet's description opens new possibilities for applications, such as automated droplet generation via reinforcement learning, the analysis of droplet shape evolution dynamics, and the prediction of droplet breakup. Our findings underscore the benefits of incorporating domain knowledge into autoencoder models, highlighting the potential for increased accuracy in various other scientific disciplines.

We present a highly optimized thread-safe lattice Boltzmann model in which the non-equilibrium part of the distribution function is locally reconstructed via recursivity of Hermite polynomials. Such a procedure allows the explicit incorporation of non-equilibrium moments of the distribution up to the order supported by the lattice. Thus, the proposed approach increases accuracy and stability at low viscosities without compromising performance and amenability to parallelization with respect to standard lattice Boltzmann models. The high-order thread-safe lattice Boltzmann is tested on two types of turbulent flows, namely, the turbulent channel flow at R e τ = 180 and the axisymmetric turbulent jet at Re = 7000; it delivers results in excellent agreement with reference data [direct numerical simulations (DNS), theory, and experiments] and (a) achieves peak performance [ ∼ 5 × 10 12 floating point operations (FLOP) per second and an arithmetic intensity of ∼ 7 FLOP / byte on a single graphic processing unit] by significantly reducing the memory footprint, (b) retains the algorithmic simplicity of standard lattice Boltzmann computing, and (c) allows to perform stable simulations at vanishingly low viscosities. Our findings open attractive prospects for high-performance simulations of realistic turbulent flows on GPU-based architectures. Such expectations are confirmed by excellent agreement among lattice Boltzmann, experimental, and DNS reference data.

We investigate the consistency and the rate of convergence of the adaptive Lasso estimator for the parameters of linear AR(p) time series with a white noise which is a strictly stationary and ergodic martingale difference. Roughly speaking, we prove that (i) If the white noise has a finite second moment, then the adaptive Lasso estimator is almost sure consistent (ii) If the white noise has a finite fourth moment, then the error estimate converges to zero with the same rate as the regularizing parameters of the adaptive Lasso estimator. Such theoretical findings are applied to estimate the parameters of INAR(p) time series and to estimate the fertility function of Hawkes processes. The results are validated by some numerical simulations, which show that the adaptive Lasso estimator allows for a better balancing between bias and variance with respect to the Conditional Least Square estimator and the classical Lasso estimator.

When collecting several data sets and heterogeneous data types on a given phenomenon of interest, the individual analysis of each data set will provide only a particular view of such phenomenon. Instead, integrating all the data may widen and deepen the results, offering a better view of the entire system. In the context of network integration, we propose the INet algorithm. INet assumes a similar network structure, representing latent variables in different network layers of the same system. Therefore, by combining individual edge weights and topological network structures, INet first constructs a Consensus Network that represents the shared information underneath the different layers to provide a global view of the entities that play a fundamental role in the phenomenon of interest. Then, it derives a Case Specific Network for each layer containing peculiar information of the single data type not present in all the others. We demonstrated good performance with our method through simulated data and detected new insights by analyzing biological and sociological datasets.

The TEXTAROSSA project aims to bridge the technology gaps that exascale computing systems will face in the near future in order to overcome their performance and energy efficiency challenges. This project provides solutions for improved energy efficiency and thermal control, seamless integration of heterogeneous accelerators in HPC multi-node platforms, and new arithmetic methods. Challenges are tacked through a co-design approach to heterogeneous HPC solutions, supported by the integration and extension of HW and SW IPs, programming models, and tools derived from European research.

Source localization from M/EEG data is a fundamental step in many analysis pipelines, including those aiming at clinical applications such as the pre-surgical evaluation in epilepsy. Among the many available source localization algorithms, SESAME (SEquential SemiAnalytic Montecarlo Estimator) is a Bayesian method that distinguishes itself for several good reasons: it is highly accurate in localizing focal sources with comparably little sensitivity to input parameters; it allows the quantification of the uncertainty of the reconstructed source(s); it accepts user-defined a priori high- and low-probability search regions in input; it can localize the generators of neural oscillations in the frequency domain. Both a Python and a MATLAB implementation of SESAME are available as open-source packages under the name of SESAMEEG and are well integrated with the main software packages used by the M/EEG community; moreover, the algorithm is part of the commercial software BESA Research (from version 7.0 onwards). While SESAMEEG is arguably simpler to use than other source modeling methods, it has a much richer output that deserves to be described thoroughly. In this article, after a gentle mathematical introduction to the algorithm, we provide a complete description of the available output and show several use cases on experimental M/EEG data.

Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory dynamics, like spiral waves, relaxation oscillations and spatio-temporal Turing instability. Inspired by the classical “divide and conquer” approach, we propose a piecewise version of DMD (pDMD) to overcome this problem. The main idea is to split the original dataset in N submatrices and then apply the exact (randomized) DMD method in each subset of the obtained partition. We describe the pDMD algorithm in detail and we introduce some error indicators to evaluate its performance when N is increased. Numerical experiments show that very accurate reconstructions are obtained by pDMD for datasets arising from time snapshots of certain reaction-diffusion PDE systems, like the FitzHugh-Nagumo model, a λ-ω system and the DIB morpho-chemical system for battery modeling. Finally, a discussion about the overall computational load and the future prediction features of the new algorithm is also provided.

Bursting behaviors, driven by environmental variability, can substantially influence ecosystem services and functions and have the potential to cause abrupt population breakouts in host-parasitoid systems. We explore the impact of environment on the host-parasitoid interaction by investigating separately the effect of grazing-dependent habitat variation on the host density and the effect of environmental fluctuations on the average host population growth rate. We hence focus on the discrete host-parasitoid Beddington-Free-Lawton model and show that a more comprehensive mathematical study of the dynamics behind the onset of on-off intermittency in host-parasitoid systems may be achieved by considering a deterministic, chaotic system that represents the dynamics of the environment. To this aim, some of the key model parameters are allowed to vary in time according to an evolution law that can exhibit chaotic behavior. Fixed points and stability properties of the resulting 3D nonlinear discrete dynamical system are investigated and on-off intermittency is found to emerge strictly above the blowout bifurcation threshold. We show, however, that, in some cases, this phenomenon can also emerge in the sub-threshold. We hence introduce the novel concept of long-term reactivity and show that it can be considered as a necessary condition for the onset of on-off intermittency. Investigations in the time-dependent regimes and kurtosis maps are provided to support the above results. Our study also suggests how important it is to carefully monitor environmental variability caused by random fluctuations in natural factors or by anthropogenic disturbances in order to minimize its effects on throphic interactions and protect the potential function of parasitoids as biological control agents.

Ecological systems are subject to environmental variability and fluctuations: understanding the role of such stochastic perturbations in inducing on–off intermittency is the central motivation for this study. This research extends the exploration of parameters leading to the emergence of on–off intermittency within a discrete Beddington-Free-Lawton host-parasitoid model. We introduce random perturbation factors that impact both the grazing intensity and the growth rate of the host population. An intriguing aspect of this study is the numerical evidence of the reactivity of the free-parasitoid fixed point as a route to on–off intermittency. This finding is significant because it sheds light on how stable ecological equilibria can transition into intermittency before progressing toward chaotic behaviour. Moreover, our study explores the host-parasitoid coupling within the Beddington-Free-Lawton model when it is applied to a complex network, a significant framework for modelling ecological interactions. The paper reveals that such network-based interactions induce parasitoid bursts that are not observed in a single population scenario.

Introduction: Connections among neurons form one of the most amazing and effective network in nature. At higher level, also the functional structures of the brain is organized as a network. It is therefore natural to use modern techniques of network analysis to describe the structures of networks in the brain. Many studies have been conducted in this area, showing that the structure of the neuronal network is complex, with a small-world topology, modularity and the presence of hubs. Other studies have been conducted to investigate the dynamical processes occurring in brain networks, analyzing local and large-scale network dynamics. Recently, network diffusion dynamics have been proposed as a model for the progression of brain degenerative diseases and for traumatic brain injuries. Methods: In this paper, the dynamics of network diffusion is re-examined and reaction-diffusion models on networks is introduced in order to better describe the degenerative dynamics in the brain. Results: Numerical simulations of the dynamics of injuries in the brain connectome are presented. Different choices of reaction term and initial condition provide very different phenomenologies, showing how network propagation models are highly flexible. Discussion: The uniqueness of this research lies in the fact that it is the first time that reaction-diffusion dynamics have been applied to the connectome to model the evolution of neurodegenerative diseases or traumatic brain injury. In addition, the generality of these models allows the introduction of non-constant diffusion and different reaction terms with non-constant parameters, allowing a more precise definition of the pathology to be studied.

For a graph G and a positive integer c, let Mc(G) be the size of a subgraph of G induced by a randomly sampled subset of c vertices. Second-order moments of Mc(G) encode part of the structure of G. We use this fact, coupled to classical moment inequalities, to prove graph theoretical results, to give combinatorial identities, to bound the size of the c-densest subgraph from below and the size of the c-sparsest subgraph from above, and to provide bounds for approximate enumeration of trivial subgraphs.

We propose AFTNet, a novel network-constraint survival analysis method based on the Weibull accelerated failure time (AFT) model solved by a penalized likelihood approach for variable selection and estimation. When using the log-linear representation, the inference problem becomes a structured sparse regression problem for which we explicitly incorporate the correlation patterns among predictors using a double penalty that promotes both sparsity and grouping effect. Moreover, we establish the theoretical consistency for the AFTNet estimator and present an efficient iterative computational algorithm based on the proximal gradient descent method. Finally, we evaluate AFTNet performance both on synthetic and real data examples.

Land cover, or the biophysical cover of the earth's surface, plays an essential role in climate and environmental dynamics. Processes involving land cover change, are among the factors that most threaten the ecosystems sustainability and services. The objective of the work is to explore the potential of the PRISMA multi-temporal hyperspectral imagery in generating new EO products to complement/improve the products provided by Copernicus' Land Monitoring Service for the analysis and monitoring of complex and fragile ecosystems such as the coastal Metaponto (Southern Italy) by estimating of the land biological and economic productivity loss and land degradation vulnerability. Preliminary results showed that an improvement in ecosystem mapping is supported by the use of Artificial Neural Networks (ANN), k-Nearest Neighbors (KNN) and Support Vector Machines (SVM) and a hybrid approach to define the vegetation trait, leads to significant improvement in the damage assessment and land degradation assessment

Cyber insurance is a crucial tool for managing risks associated with cyber threats. A challenging task for insurance companies lies in pricing cyber risk. Our study is motivated by the reasonable assumption that firms entering into cyber insurance contracts face diverse cyber threats in terms of types and magnitude. Considering these differences ensures that premiums align with the actual risk exposure of the insured. The study discusses this approach proposing a case study based on the Chronology of Data Breaches provided by the Privacy Rights Clearinghouse.

Background: Osteoarthritis (OA) is a multifactorial, hypertrophic, and degenerative condition involving the whole joint and affecting a high percentage of middle-aged people. It is due to a combination of factors, although the pivotal mechanisms underlying the disease are still obscure. Moreover, current treatments are still poorly effective, and patients experience a painful and degenerative disease course. Methods: We used an integrative approach that led us to extract a consensus signature from a meta-analysis of three different OA cohorts. We performed a network-based drug prioritization to detect the most relevant drugs targeting these genes and validated in vitro the most promising candidates. We also proposed a risk score based on a minimal set of genes to predict the OA clinical stage from RNA-Seq data. Results: We derived a consensus signature of 44 genes that we validated on an independent dataset. Using network analysis, we identified Resveratrol, Tenoxicam, Benzbromarone, Pirinixic Acid, and Mesalazine as putative drugs of interest for therapeutics in OA for anti-inflammatory properties. We also derived a list of seven gene-targets validated with functional RT-qPCR assays, confirming the in silico predictions. Finally, we identified a predictive subset of genes composed of DNER, TNFSF11, THBS3, LOXL3, TSPAN2, DYSF, ASPN and HTRA1 to compute the patient's risk score. We validated this risk score on an independent dataset with a high AUC (0.875) and compared it with the same approach computed using the entire consensus signature (AUC 0.922). Conclusions: The consensus signature highlights crucial mechanisms for disease progression. Moreover, these genes were associated with several candidate drugs that could represent potential innovative therapeutics. Furthermore, the patient's risk scores can be used in clinical settings.

Claude Shannon, eclettico matematico e ingegnere del Novecento, è considerato il padre della teoria dell’informazione, perché offrì una definizione formale, quantitativamente misurabile, di questo concetto, assimilandolo a quello di altre grandezze fisiche che possono essere descritte e calcolate matematicamente. Dimostrò poi fino a che punto l’informazione contenuta in un messaggio possa essere compressa, in modo da aumentare la velocità di trasmissione. Il secondo e fondamentale risultato di Shannon riguarda invece il canale di trasmissione, un qualunque mezzo attraverso il quale il messaggio viaggia e che può degradare parte dei contenuti trasmessi se il tasso di trasmissione supera la capacità del canale. Entrano in gioco quindi grandezze come l’errore, che si può ridurre inserendo nel messaggio strumenti matematici di correzione, e la stessa entropia, concetto sviluppato nella termodinamica ma che può riguardare anche la trasmissione delle informazioni, quale misura dell’incertezza di un risultato (la probabilità che sia quello giusto). Per esempio, in un testo italiano, la «e» è più probabile di una «z» e la stringa «le banche hanno un anno di tempo» è più probabile di «le banche anno un hanno di tempo». La teoria dell’informazione di Shannon è alla base di tutta la comunicazione digitale, che utilizza strumenti matematici per la compressione dei segnali, oggi indispensabile, per la riduzione degli errori di tramissione e per la gestione delle reti.