A key goal of the eLTER EnRich project is to create a comprehensive framework for the future implementation of the eLTER Research Infrastructure (RI). This framework is fundamentally based on adopting a Systems Engineering Approach to design and implement the delivery of the RI's services. The project follows an Agile development methodology, where a so-called skeleton infrastructure is first implemented providing an essential core set of services and cyberinfrastructure components covering the minimum requirements of important stakeholders. At the same time, the project will explore how to prioritise the enrichment of this skeleton RI with more advanced features as plans crystallise during the process. This approach will support decision-making by evaluating various opportunities and pathways for connecting stakeholder needs, user requirements, technical solutions, and the distribution of services among hosting organisations. An initial step in developing an operational framework involves streamlining the knowledge base generated in the eLTER PPP and eLTER PLUS projects, which covers numerous aspects essential for the RI's construction, including stakeholder mappings, feedback from the eLTER community, and an initial outline of a potential service portfolio. Additionally, some conceptual data workflows related to Standard Observations and high-level data products enrich the legacy of these projects. Building on this foundation, the objective of the present document is to focus on services identified and selected as priority (core) services by the Interim Council, the RI’s decision-making body, and to outline the necessary workflows required for their delivery. By employing the Systems Engineering Approach, we map the workflows needed to provide these key services in standardised, actionable, machine-readable formats to inform the overall System Engineering setup and implementation planning. This mapping process includes detailed documentation of the steps, roles, and responsibilities required to support specific end-to-end workflows. Users' requirements thereby define the necessary RI functions and information flows, which are evaluated to derive appropriate solutions. These solutions then guide the implementation planning for integrating other infrastructure capabilities and determine the final distribution of service-hosting organisations. This document combines information associated with different views of a selection of services identified as ‘core’ services. That includes the stakeholders’ perspective and the main business roles necessary for the implementation of the service provision, also linking the service workflows to the main components and functionalities of the eLTER Cyberinfrastructure (CI). We aimed to provide sufficient detail to support effective collaboration with the Cyberinfrastructure team while allowing for enough flexibility to account for changes in services and infrastructure structure motivated by different service hosting solutions.

This deliverable presents a detailed overview of advanced modelling and mapping methodologies developed to evaluate, upscale, and project the responses of wetlands to climate change and restoration activities. It primarily addresses the methods and frameworks intended to enhance the understanding and management of wetland ecological conditions, associated trends, and the land-use pressures influencing them. Methods and tools have been developed to carry assessments that integrate data-driven approaches with process-based modelling components, allowing accurate simulations of wetland ecosystem dynamics under diverse environmental pressures. These applications employ mapping products developed at the site level, drawing from existing methodologies established in the SWOS and EOMORES projects, which emphasize land-use and land-cover change, surface water dynamics, and water quality parameters. These mapping products directly inform enhancements to the LUPLES method and are further scaled up for broader regional applications. Moreover, existing models designed for estimating GHG sequestration resulting from restoration actions have been refined into control models with the dual objective of optimizing restoration costs while maximizing both GHG mitigation effectiveness and biodiversity conservation. Additionally, this report incorporates an integrated modelling framework specifically designed to evaluate and quantify the greenhouse gas mitigation potential of wetlands, as well as the adaptability of relevant ecosystems under various scenarios of climate and land-use change, incorporating the effects of restoration interventions. The relationship among land use, pressure levels, ecological status, conservation-alteration-restoration statuses, carbon storage capacities, and GHG emissions has been addressed. The selection of appropriate decision-making tools incorporates recent conceptual advancements regarding the valuation of nature, specifically comparing the ecosystem services framework (WG MAES) with the Nature’s Contributions to People perspective developed by IPBES.

In this report, we advance the description of the RESTORE4Cs Integrative Assessment Framework (IAF) for evaluating the greenhouse gas (GHG) abatement potential and resilience of wetlands and their surrounding social-ecological systems, with a primary focus on coastal wetlands. A preliminary version of the IAF was presented in Deliverable D3.1 Integrative assessment framework of the GHG abatement potential and resilience of wetlands, first version (Marangi, C. et al 2025), which outlined the rationale behind the framework and summarized the approach used to design the project’s architectural structure. The present report takes this work a step further by incorporating the concept of vulnerability into the overall analytical framework and by examining more operational aspects, including the resources and capabilities required for the effective implementation of the IAF. In addition, we provide an overview of the methodological choices adopted within the project to generate the information base upon which the assessment is developed. The report summarizes the criteria, indicators, models, and tools identified and applied across the project to demonstrate how the various components of the IAF are instantiated within the case studies. This includes the scenario-building process developed under the Shared Socioeconomic Pathways (SSPs) framework, which integrates narratives and modelling approaches to project GHG emissions from wetlands as complex social-ecological systems. Finally, the report discusses the value chain generated through the implementation of the IAF, emphasizing how each step of the framework’s application contributes to maximizing the usability and reusability of outputs, thereby enhancing the overall return on investment in the assessment process.

We give analytic description for the completion of C?0 (R+) in Dirichletspace D1,p(R+, ?) := {u : R+ -> R : u is locally absolutely continuous on R+ and ||u? ||_Lp(R+,?) < ?}, for given continuouspositive weight ? defined on R+, where 1 < p < ?. The conditions are described in terms of the modified variants of the Bpconditions due to Kufner and Opic from 1984, which in our approach are focusing on integrability of ?^-p/(p-1) near zero or near infinity. Moreover, we propose applications of our results to: obtaining newvariants of Hardy inequality, interpretation of boundary value problems in ODE's defined on the halpfline with solutions in D1,p(R+, ?),new results from complex interpolation theory dealing with interpolation spaces between weighted Dirichlet spaces, and to derivationof new Morrey type embedding theorems for our Dirichlet space.

Planning petrol station replenishment is an important logistics activity for all the major oil companies. The studied Multi-Depot Periodic Petrol Station Replenishment problem derives from a real case in which the company must replenish a set of petrol stations from a set of depots, during a weekly planning horizon. The company must ensure refuelling according to available visiting patterns, which can be different from customer to customer. A visiting pattern predefines how many times (days) the replenishment occurs during a week and in which visiting days a certain amount of fuel must be delivered. To fulfill the weekly demand of each petrol station, one of the available replenishment plans must be selected among a given set of visiting patterns. The aim is to minimize the total distance travelled by the fleet of tank trucks during the entire planning horizon. A matheuristic approach is proposed, based on the cluster-first route-second paradigm, to solve it. The proposed approach is thoroughly tested on a set of realistic random instances. Finally, a weekly large real instance is considered with 194 petrol stations and two depots.

Magnetoencephalography (MEG) is a valuable non-invasive neurophysiology technique for investigation of brain function and dysfunction. In this chapter, we will discuss the main characteristics of MEG signals, and the great potential it offers for scientific interrogation in psychology, cognitive neuroscience, neurology, and neuropsychiatry. Starting from the physical properties of MEG recordings, the chapter will highlight the main advantages of utilizing MEG in neuroscience (that is a combination of very high temporal resolution and good spatial resolution) and will summarize the current status of MEG in research and clinical settings. To make this topic more relatable to widely available electroencephalography (EEG), we will present several comparisons of MEG with EEG. The objective of the present chapter is to provide a broad overview of the principle concepts and strengths of MEG, aimed at newcomers to the field.

We prove the nonlinear asymptotic stability of stably stratified solutions to the Incompressible Porous Media equation (IPM) for initial perturbations in $\dot H^{1-\tau}(\R^2) \cap \dot H^s(\R^2)$ with $s > 3$ and for any $0 < \tau <1$. Such result improves the existing literature, where the asymptotic stability is proved for initial perturbations belonging at least to $H^{20}(\R^2)$. \\ More precisely, the aim of the article is threefold. First, we provide a simplified and improved proof of global-in-time well-posedness of the Boussinesq equations with strongly damped vorticity in $H^{1-\tau}(\R^2) \cap \dot H^s(\R^2)$ with $s > 3$ and $0 < \tau <1$. Next, we prove the strong convergence of the Boussinesq system with damped vorticity towards (IPM) under a suitable scaling. Lastly, the asymptotic stability of stratified solutions to (IPM) follows as a byproduct.\\ A symmetrization of the approximating system and a careful study of the anisotropic properties of the equations via anisotropic Littlewood-Paley decomposition play key roles to obtain uniform energy estimates. Finally, one of the main new and crucial points is the integrable time decay of the vertical velocity $\|u_2(t)\|_{L^\infty (\R^2)}$ for initial data only in $\dot H^{1-\tau}(\R^2) \cap \dot H^s(\R^2)$ with $s >3$.

This article is concerned with the rigorous justification of the hydrostatic limit for continuouslystratified incompressible fluids under the influence of gravity.The main peculiarity of this work with respect to previous studies is that no (regularizing) viscosity contributionis added to the fluid-dynamics equations and only diffusivity effects are included. Motivated byapplications to oceanography, the diffusivity effects included in this work are induced by an advection termwhose specific form was proposed by Gent and McWilliams in the 90's to model effective eddy correlations fornon-eddy-resolving systems.The results of this paper heavily rely on the assumption of stable stratification. We provide the wellposednessof the hydrostatic equations and of the original (non-hydrostatic) equations for stably stratified fluids,as well as their convergence in the limit of vanishing shallow-water parameter. The results are established inhigh but finite Sobolev regularity and keep track of the various parameters at stake.A key ingredient of our analysis is the reformulation of the systems by means of isopycnal coordinates,which allows to provide careful energy estimates that are far from being evident in the original coordinatesystem.

We prove the strong ill-posedness of the two-dimensional Boussinesq system in vorticity form in L8pR2qwithout boundary, building upon the method that Shikh Khalil & Elgindi arXiv:2207.04556v1 developed for scalarequations. We provide examples of initial data with vorticity and density gradient of small L8pR2q size, for which thehorizontal density gradient has a strong L8pR2q-norm inflation in infinitesimal time, while the vorticity and the verticaldensity gradient remain bounded. Furthermore, exploiting the three-dimensional version of Elgindi's decomposition ofthe Biot-Savart law, we apply our method to the three-dimensional axisymmetric Euler equations with swirl and awayfrom the vertical axis, showing that a large class of initial data with vorticity uniformly bounded and small in L8pR2qprovides a solution whose gradient of the swirl has a strong L8pR2q-norm inflation in infinitesimal time. The norminflations are quantified from below by an explicit lower bound which depends on time, the size of the data and is validfor small times

It is known that executing a perfect shifted QR step via the implicit QR algorithm may not result in a deflation of the perfect shift. Typically, several steps are required before deflation actually takes place. This deficiency can be remedied by determining the similarity transformation via the associated eigenvector. Similar techniques have been deduced for the QZ algorithm and for the rational QZ algorithm. In this paper we present a similar approach for executing a perfect shifted QZ step on a general rank structured pencil instead of a specific rank structured one, e.g., a Hessenberg--Hessenberg pencil. For this, we rely on the rank structures present in the transformed matrices. A theoretical framework is presented for dealing with general rank structured \rev{pencils} and deflating subspaces. We present the corresponding algorithm allowing} to deflate simultaneously a block of eigenvalues rather than a single one. We define the level-rho poles and show that these poles are maintained executing the deflating algorithm. Numerical experiments illustrate the robustness of the presented approach showing the importance of using the improved scaled residual approach.

In this paper, we develop new methods to join machine learning techniques and macroscopic differential models, aimed at estimate and forecast vehicular traffic. This is done to complement respective advantages of data-driven and model-driven approaches. We consider here a dataset with flux and velocity data of vehicles moving on a highway, collected by fixed sensors and classified by lane and by class of vehicle. By means of a machine learning model based on an LSTM recursive neural network, we extrapolate two important pieces of information: (1) if congestion is appearing under the sensor, and (2) the total amount of vehicles which is going to pass under the sensor in the next future (30 min). These pieces of information are then used to improve the accuracy of an LWR-based first-order multi-class model describing the dynamics of traffic flow between sensors. The first piece of information is used to invert the (concave) fundamental diagram, thus recovering the density of vehicles from the flux data, and then inject directly the density datum in the model. This allows one to better approximate the dynamics between sensors, especially if an accident/bottleneck happens in a not monitored stretch of the road. The second piece of information is used instead as boundary conditions for the equations underlying the traffic model, to better predict the total amount of vehicles on the road at any future time. Some examples motivated by real scenarios will be discussed. Real data are provided by the Italian motorway company Autovie Venete S.p.A.

The ongoing reproducibility crisis in psychology and cognitive neuroscience has sparked increasing calls to re-evaluate and reshape scientific culture and practices. Heeding those calls, we have recently launched the EEGManyPipelines project as a means to assess the robustness of EEG research in naturalistic conditions and experiment with an alternative model of conducting scientific research. One hundred sixty-eight analyst teams, encompassing 396 individual researchers from 37 countries, independently analyzed the same unpublished, representative EEG data set to test the same set of predefined hypotheses and then provided their analysis pipelines and reported outcomes. Here, we lay out how large-scale scientific projects can be set up in a grassroots, community-driven manner without a central organizing laboratory. We explain our recruitment strategy, our guidance for analysts, the eventual outputs of this project, and how it might have a lasting impact on the field.

Two different direct methods are proposed to solve Cauchy singular integral equations on the real line. The aforementioned methods differ in order to be able to prove their convergence which depends on the smoothness of the known term function in the integral equation.

The dynamics of stabilised concentrated emulsions presents a rich phenomenology including chaotic emulsification, non-Newtonian rheology and ageing dynamics at rest. Macroscopic rheology results from the complex droplet microdynamics and, in turn, droplet dynamics is influenced by macroscopic flows via the competing action of hydrodynamic and interfacial stresses, giving rise to a complex tangle of elastoplastic effects, diffusion, breakups and coalescence events. This tight multiscale coupling, together with the daunting challenge of experimentally investigating droplets under flow, has hindered the understanding of concentrated emulsions dynamics. We present results from three-dimensional numerical simulations of emulsions that resolve the shape and dynamics of individual droplets, along with the macroscopic flows. We investigate droplet dispersion statistics, measuring probability density functions (p.d.f.s) of droplet displacements and velocities, changing the concentration, in the stirred and ageing regimes. We provide the first measurements, in concentrated emulsions, of the relative droplet–droplet separations p.d.f. and of the droplet acceleration p.d.f., which becomes strongly non-Gaussian as the volume fraction is increased above the jamming point. Cooperative effects, arising when droplets are in contact, are argued to be responsible of the anomalous superdiffusive behaviour of the mean square displacement and of the pair separation at long times, in both the stirred and in the ageing regimes. This superdiffusive behaviour is reflected in a non-Gaussian pair separation p.d.f., whose analytical form is investigated, in the ageing regime, by means of theoretical arguments. This work paves the way to developing a connection between Lagrangian dynamics and rheology in concentrated emulsions.

The paper deals with the numerical solution of Cauchy Singular Integral Equations based on some non standard polynomial quasi-projection of de la Vallée Poussin type. Such kind of approximation presents several advantages over classical Lagrange interpolation such as the uniform boundedness of the Lebesgue constants, the near-best order of uniform convergence to any continuous function, and a strong reduction of Gibbs phenomenon. These features will be inherited by the proposed numerical method which is stable and convergent, and provides a near-best polynomial approximation of the sought solution by solving a well conditioned linear system. The numerical tests confirm the theoretical error estimates and, in case of functions subject to Gibbs phenomenon, they show a better local approximation compared with analogous Lagrange projection methods.

We consider here a cell-centered finite difference approximation of the Richards equation in three dimensions, averaging for interface values the hydraulic conductivity, a highly nonlinear function, by arithmetic, upstream and harmonic means. The nonlinearities in the equation can lead to changes in soil conductivity over several orders of magnitude and discretizations with respect to space variables often produce stiff systems of differential equations. A fully implicit time discretization is provided by backward Euler one-step formula; the resulting nonlinear algebraic system is solved by an inexact Newton Armijo-Goldstein algorithm, requiring the solution of a sequence of linear systems involving Jacobian matrices. We prove some new results concerning the distribution of the Jacobians eigenvalues and the explicit expression of their entries. Moreover, we explore some connections between the saturation of the soil and the ill conditioning of the Jacobians. The information on eigenvalues justifies the effectiveness of some preconditioner approaches which are widely used in the solution of Richards equation. We also propose a new software framework to experiment with scalable and robust preconditioners suitable for efficient parallel simulations at very large scales. Performance results on a literature test case show that our framework is very promising in the advance toward realistic simulations at extreme scale.

In this manuscript we propose a numerical method for non-linear integro-differential systems arising in age-of-infection models in a heterogeneously mixed population. The discrete scheme is based on direct quadrature methods and provides an unconditionally positive and bounded solution. Furthermore, we prove the existence of the numerical final size of the epidemic and show that it tends to its continuous equivalent as the discretization steplength vanishes.

In this paper we consider the computation of the modified moments for the system of Laguerre polynomials on the real semiaxis with the Hermite weight. These moments can be used for the computation of integrals with the Hermite weight on the real semiaxis via product rules. We propose a new computational method based on the construction of the null-space of a rectangular matrix derived from the three-term recurrence relation of the system of orthonormal Laguerre polynomials.It is shown that the proposed algorithm computes the modified moments with high relative accuracy and linear complexity.Numerical examples illustrate the effectiveness of the proposed method.

In this paper we analyze the stability of the problem of performing a rational QZ$step with a shift that is an eigenvalue of a given regular pencil H-lambda K in unreduced Hessenberg-Hessenberg form. In exact arithmetic, the backward rational QZ step moves the eigenvalue to the top of the pencil, while the rest of the pencil is maintained in Hessenberg-Hessenberg form, which then yields a deflation of the given shift. But in finite-precision the rational QZ step gets ``blurred'' and precludes the deflation of the given shift at the top of the pencil. In this paper we show that when we first compute the corresponding eigenvector to sufficient accuracy, then the rational QZ step can be constructed using this eigenvector, so that the exact deflation is also obtained in finite-precision.

: The liquid-vapor phase separation is investigated via lattice Boltzmann simulations in three dimensions. After expressing length and time scales in reduced physical units, we combined data from several large simulations (on 512^{3} nodes) with different values of viscosity, surface tension, and temperature, to obtain a single curve of rescaled length l[over ̂] as a function of rescaled time t[over ̂]. We find evidence of the existence of kinetic and inertial regimes with growth exponents α_{d}=1/2 and α_{i}=2/3 over several time decades, with a crossover from α_{d} to α_{i} at t[over ̂]≃1. This allows us to rule out the existence of a viscous regime with α_{v}=1 in three-dimensional liquid-vapor isothermal phase separation, differently from what happens in binary fluid mixtures. An in-depth analysis of the kinetics of the phase separation process, as well as a characterization of the morphology and the flow properties, are further presented in order to provide clues into the dynamics of the phase-separation process.