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.

Raccolta, analisi e monitoraggio dei dati economico-finanziari relativi ai progetti comunitari e nazionali con il fine di creare un metodo standardizzato di analisi e monitoraggio dei flussi delle entrate/uscite presso l’Istituto per le Applicazioni del Calcolo “Mauro Picone” e relative sedi secondarie” ha l’obiettivo di analizzare l’andamento dei finanziamenti nazionali ed europei nell’ultimo decennio di attività dell’IAC-CNR (dal 2013 al 2023) con il fine di ottimizzare la gestione della cassa, dare un migliore servizio di pianificazione e controllo, e generare un sistema di misurazione della performance finanziaria dell’Istituto per le Applicazioni del Calcolo “Mauro Picone” e relative sedi secondarie.

Background and objective: Glucagon-like peptide 1 (GLP-1) is classically identified as an incretin hormone, secreted in response to nutrient ingestion and able to enhance glucose-stimulated insulin secretion. However, other stimuli, such as physical exercise, may enhance GLP-1 plasma levels, and this exercise-induced GLP-1 secretion is mediated by interleukin-6 (IL-6), a cytokine secreted by contracting skeletal muscle. The aim of the study is to propose a mathematical model of IL-6-induced GLP-1 secretion and kinetics in response to physical exercise of moderate intensity. Methods: The model includes the GLP-1 subsystem (with two pools: gut and plasma) and the IL-6 subsystem (again with two pools: skeletal muscle and plasma); it provides a parameter of possible clinical relevance representing the sensitivity of GLP-1 to IL-6 (k0). The model was validated on mean IL-6 and GLP-1 data derived from the scientific literature and on a total of 100 virtual subjects. Results: Model validation provided mean residuals between 0.0051 and 0.5493 pg⋅mL-1 for IL-6 (in view of concentration values ranging from 0.8405 to 3.9718 pg⋅mL-1) and between 0.0133 and 4.1540 pmol⋅L-1 for GLP-1 (in view of concentration values ranging from 0.9387 to 17.9714 pmol⋅L-1); a positive significant linear correlation (r = 0.85, p<0.001) was found between k0 and the ratio between areas under GLP-1 and IL-6 curve, over the virtual subjects. Conclusions: The model accurately captures IL-6-induced GLP-1 kinetics in response to physical exercise.

Calcolo stimatore Lasso per processi di Hawkes

We consider periodic piecewise affine functions, defined on the real line, with two given slopes, one positive and one negative, and prescribed length scale of the intervals where the slope is negative. We prove that, in such a class, the minimizers of s-fractional Gagliardo seminorm densities, with 0<1/2, are in fact periodic with the minimal possible period determined by the prescribed slopes and length scale. Then, we determine the asymptotic behavior of the energy density as the ratio between the length of the two intervals, where the slope is constant, vanishes. Our results, for s=1/2, have relevant applications to the van der Merwe theory of misfit dislocations at semicoherent straight interfaces. We consider two elastic materials having different elastic coefficients and casting parallel lattices having different spacing. As a byproduct of our analysis, we prove the periodicity of optimal dislocation configurations and we provide the sharp asymptotic energy density in the semicoherent limit as the ratio between the two lattice spacings tends to one.

We present a variational theory for lattice defects of rotational and translational type. We focus on finite systems of planar wedge disclinations, disclination dipoles, and edge dislocations, which we model as the solutions to minimum problems for isotropic elastic energies under the constraint of kinematic incompatibility. Operating under the assumption of planar linearized kinematics, we formulate the mechanical equilibrium problem in terms of the Airy stress function, for which we introduce a rigorous analytical formulation in the context of incompatible elasticity. Our main result entails the analysis of the energetic equivalence of systems of disclination dipoles and edge dislocations in the asymptotics of their singular limit regimes. By adopting the regularization approach via core radius, we show that, as the core radius vanishes, the asymptotic energy expansion for disclination dipoles coincides with the energy of finite systems of edge dislocations. This proves that Eshelby’s kinematic characterization of an edge dislocation in terms of a disclination dipole is exact also from the energetic standpoint.

We propose nonlinear semi-discrete and discrete models for the elastic energy induced by a finite system of edge dislocations in two dimensions. Within the dilute regime, we analyze the asymptotic behavior of the nonlinear elastic energy, as the core-radius (in the semi-discrete model) and the lattice spacing (in the purely discrete one) vanish. Our analysis passes through a linearization procedure within the rigorous framework of Γ-convergence.

The conformational and dynamical properties of active ring polymers are studied by numerical simulations. The two-dimensionally confined polymer is modeled as a closed bead-spring chain, driven by tangential forces, put in contact with a heat bath described by the Brownian multiparticle collision dynamics. Both phantom polymers and chains comprising excluded volume interactions are considered for different bending rigidities. The size and shape are found to be dependent on persistence length, driving force, and bead mutual exclusion. The lack of excluded volume interactions is responsible for a shrinkage of active rings when increasing driving force in the flexible limit, while the presence induces a moderate swelling of chains. The internal dynamics of flexible phantom active rings shows activity-enhanced diffusive behavior at large activity values while, in the case of self-avoiding active chains, it is characterized by active ballistic motion not depending on stiffness. The long-time dynamics of active rings is marked by rotational motion whose period scales as the inverse of the applied tangential force, irrespective of persistence length and beads' self-exclusion.

A meticulous description of a real network with respect to its heterogeneous physical infrastructure and properties is necessary for network design assessment. Quantifying the costs of making these structures work together effectively, and taking into account any hidden charges they may incur, can lead to improve the quality of service and reduce mandatory maintenance requirements, and mitigate the cost associated with finding a valid solution. For these reasons, we devote our attention to a novel approach to produce a more complete representation of the overall costs on the reload cost net-work. This approach considers both the cost of reloading due to linking structures and their internal charges, which we refer to as the penalized reload cost. We investigate the complexity and approximability of finding an optimal path, walk, tour, and maxi-mum flow problems under penalized reload cost. All these problems turn out to be NP-complete. We prove that, unless P=NP, even if the reload cost matrix is symmetric and satisfies the triangle inequality, the problem of finding a path, tour, and a maxi-mum flow with a minimum penalized reload cost cannot be approximated within any constant alpha < 2 , and finding a walk is not approximable within any factor beta <= 3.

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 non-equilibrium structural and dynamical properties of a flexible polymer tethered 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 immersed in a fluid described by the Brownian multiparticle collision dynamics. At high strain, the polymer is stretched along the flow direction following the applied flow, then recoils at flow inversion before flipping and elongate again. When strain is reduced, it may happen that the chain recoils without flipping when the applied shear changes sign. Conformations are analyzed and compared to stiff polymers revealing more compact patterns at low strains and less stretched configurations at high strain. The dynamics is investigated by looking at the center-of-mass motion which shows a frequency doubling along the direction normal to the external flow. The center-of-mass correlation function is characterized by smaller amplitudes when reducing bending rigidity.

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.

In microfluidic systems, droplets undergo intricate deformations as they traverse flow-focusing junctions, posing a challenging task for accurate measurement, especially during short transit times. This study investigates the physical behavior of droplets within dense emulsions in diverse microchannel geometries, specifically focusing on the impact of varying opening angles within the primary channel and injection rates of fluid components. Employing a sophisticated droplet tracking tool based on deep-learning techniques, we analyze multiple frames from flow-focusing experiments to quantitatively characterize droplet deformation in terms of ratio between maximum width and height and propensity to form liquid with hexagonal spatial arrangement. Our findings reveal the existence of an optimal opening angle where shape deformations are minimal and hexagonal arrangement is maximal. Variations of fluid injection rates are also found to affect size and packing fraction of the emulsion in the exit channel. This paper offers insight into deformations, size, and structure of fluid emulsions relative to microchannel geometry and other flow-related parameters captured through machine learning, with potential implications for the design of microchips utilized in cellular transport and tissue engineering applications.

This work addresses the Knapsack Problem with Forfeit Sets, a recently introduced variant of the 0/1 Knapsack Problem considering subsets of items associated with contrasting choices. Some penalty costs need to be paid whenever the number of items in the solution belonging to a forfeit set exceeds a predefined allowance threshold. We propose an effective metaheuristic to solve the problem, based on the Biased Random-Key Genetic Algorithm paradigm. An appropriately designed decoder function assigns a feasible solution to each chromosome, and improves it using some additional heuristic procedures. We show experimentally that the algorithm outperforms significantly a previously introduced metaheuristic for the problem.

Il rapporto analizza i principi che regolano il Programma HORIZON EUROPE e le modalità di rendicontazione dei costi sostenuti per la realizzazione delle attività progettuali, soffermandosi sulle caratteristiche dello strumento finanziario, sulla tipologia dei costi e sul sistema di controlli attraverso il quale la Commissione Europea vigila sul rispetto delle norme gli obblighi previsti dalla convenzione di sovvenzione.

We analyze the dynamics of the Sun-Earth-Moon system in the context of a particular class of theories of gravity where curvature and matter are nonminimally coupled (NMC). These theories can potentially violate the Equivalence Principle as they give origin to a fifth force and a extra non-Newtonian force that may imply that Earth and Moon fall differently towards the Sun. We show, through a detailed analysis, that consistency with the bound on Weak Equivalence Principle arising from 48 years of Lunar Laser Ranging data, for a range of parameters of the NMC gravity theory, can be achieved via the implementation of a suitable screening mechanism.

In questo report si affrontano gli aspetti tecnici e di sviluppo che hanno portato all’attuale sito web di istituto, all’interno di un approfondimento generale relativo alla comunicazione istituzionale e al posizionamento dell’IAC nel contesto della comunicazione della matematica. Sono, inoltre, discusse le modalità di misurazione delle performance (Analytics) del sito, con una panoramica sulle necessarie attività di miglioramento in termini di Search Engine Optimization (SEO).

The volume collects the long abstracts of the 79 contributions presented during the fourth edition of the “Young Applied Mathematicians Conference” (YAMC, www.yamc.it). Organized in Rome under the sponsorship of the Institute for Applied Mathematics (IAC) of the CNR and the Department of Mathematics at Sapienza, University of Rome, the conference took place from September 16 to 20, 2024, and brought together primarily young researchers (students, PhD candidates, post-docs, etc.) from 37 universities and research centers across 8 countries. This volume is intended to promote the communication of the research presented in the field of applied mathematics, with a primary focus on numerical analysis, artificial intelligence, statistics, and mathematical modeling. Il volume raccoglie i long abstracts dei 79 contributi presentati durante la quarta edizione del convegno "Young Applied Mathematicians Conference" (YAMC, www.yamc.it). Organizzato a Roma sotto il patrocinato dell'Istituto per le Applicazioni del Calcolo (IAC) del CNR e del dipartimento di Matematica di Sapienza, Università di Roma, il convegno si è svolto nelle giornate 16--20 settembre 2024 ed ha riunito principalmente giovani ricercatori (studenti, dottorandi, post-doc, ...) provenienti da 37 fra università e centri di ricerca di 8 nazioni. Il presente volume è indirizzato a favorire la comunicazione delle ricerche presentate nel panorama della matematica applicata, con principale attenzione in analisi numerica, intelligenza artificiale, statistica e modellistica matematica.