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.

We rigorously justify the bilayer shallow-water system as an approximation to the hydrostatic Euler equations in situations where the flow is density-stratified with close-to-piecewise constant density profiles, and close-to-columnar velocity profiles. Our theory accommodates with continuous stratification, so that admissible deviations from bilayer profiles are not pointwise small. This leads us to define refined approximate solutions that are able to describe at first order the flow in the pycnocline. Because the hydrostatic Euler equations are not known to enjoy suitable stability estimates, we rely on thickness-diffusivity contributions proposed by Gent and McWilliams. Our strategy also applies to one-layer and multilayer frameworks.

We review recent mathematical results concerning the analysis of hydrostatic equations in the context of stably stratified fluids. Beginning with the simpler and better understood setting of homogeneous fluids, we emphasize the additional mathematical challenges posed by non-homogeneous framework. We present both positive and negative results, including well-posedness and proof of the hydrostatic limit with a suitable regularization, alongside ill-posedness in the fully inviscid setting and the breakdown of the hydrostatic limit in specific scenarios.

In a layered thermal conductor, the inaccessible interface could be dam- aged by mechanical solicitation, chemical infiltration, aging. In this case, the original thermal properties of the specimen are modified. The defect occurs typically in form of delamination. The present paper deals with nondestructive evaluation of interface ther- mal conductance h from the knowledge of the surface temperature when the specimen is heated in some controlled way. The goal is achieved by expanding h in powers of the thickness of the upper layer. The mathematical analysis of the model produces exact formulas for the first coefficients of h which are tested on simulated and real data. The evaluation of interface flaws comes from reliable approximation of h.

In this work, we investigate how fluid flows impact the aggregation mechanisms of Aβ40 proteins and Aβ16–22 peptides and mechanically perturb their (pre)fibrillar aggregates. We exploit the OPEP coarse-grained model for proteins and the Lattice Boltzmann Molecular Dynamics technique. We show that beyond a critical shear rate, amyloid aggregation speeds up in Couette flow because of the shorter collisions times between aggregates, following a transition from diffusion limited to advection dominated dynamics. We also characterize the mechanical deformation of (pre)fibrillar states due to the fluid flows (Couette and Poiseuille), confirming the capability of (pre)fibrils to form pathological loop-like structures as detected in experiments. Our findings can be of relevance for microfluidic applications and for understanding aggregation in the interstitial brain space.

Langevin and Brownian simulations play a prominent role in computational research, and state of the art integration algorithms provide trajectories with different stability ranges and accuracy in reproducing statistical averages. The practical usability of integrators is an important aspect to allow choosing large time steps while ensuring numerical stability and overall computational efficiency. In this work, different use cases and practical features are selected in order to perform a cumulative comparison of integrators with a focus on evaluating the derived velocity and position autocorrelation functions, a comparison that is often disregarded in the literature. A standard industrial open-source software methodology is suggested to compare systematically the different algorithms.

Nucleation and growth of methane clathrate hydrates is an exceptional playground to study crystallisation of multi-component, host-guest crystallites when one of the species forming the crystal, the guest, has a higher concentration in the solid than in the liquid phase. This adds problems related to the transport of the low concentration species, here methane. A key aspect in the modelling of clathrates is the water model employed in the simulation. In previous articles, we compared an all-atom force model, TIP4P/Ewald, with a coarse grain one, which is highly appreciated for its computational efficiency. Here, we perform a complementary analysis considering three all-atoms water models: TIP4P/Ewald, TIP4P/ice and TIP5P. A key difference between these models is that the former predicts a much lower freezing temperature. Intuitively, one expects that to lower freezing temperatures of water correspond to lower water/methane-methane gas-clathrate coexistence ones, which determines the degree of supercooling and the degree of supersaturation. Hence, in the simulation conditions, 250 K (500 atm, and fixed methane molar fraction), one expects computational samples made of TIP4P-ice and TIP5P, with a similar freezing temperature (T-f similar to 273 K), to be more supersaturated with respect to the case of TIP4P-Ew (T-f similar to 245 K), and crystallisation to be faster. Surprisingly, we find that while the nucleation rate is consistent with this prediction, growth rate with TIP4P-ice and TIP5P is much slower than with TIP4P-Ew. The latter was attributed to the slower reorientation of water molecules in strong supercooled conditions, resulting in a lower growth rate. This suggests that the freezing temperature is not a suitable parameter to evaluate the adequacy of a water model.[GRAPHICS]

The book is interwoven according to the intrinsic logics of modern most important applications of electrospun nanofibers. It discusses such application-oriented nanofibers as self-healing vascular nanotextured materials, biopolymer nanofibers, soft robots and actuators based on nanofibers, biopolymer nanofiber-based triboelectric nanogenerators, metallized nanofibers, and heaters and sensors based on them. It also includes such topics as the injectable nanofibrous biomaterials, fibrous hemostatic agents and their interaction with blood, as well as electrospun nanofibers for face-mask applications. The book also details polyelectrolytes-based complex nanofibers and their use as actuators. It also covers drug release facilitated by polyelectrolytes-based complex nanofibers. The fundamental aspects of electrospinning of polymer nanofibers discussed in the final part of the book link them to the applications described in the preceding chapters. Such topics as polymer solution preparation and their rheological properties, e.g., viscoelasticity and the related spinnability, the electrical conductivity of polymer solutions, and the cascade of the physical phenomena resulting in formation of nanofibers encompass the experimental aspects. Also, the general quasi-1D equations used for modeling of formation of electrospun polymer nanofibers, and the numerical aspects of their solution are discussed in detail, including such modeling-driven applications as nanofiber alignment by electric focusing fields.

inglese

inglese

Early detection of prediabetes is crucial to preventing its progression to diabetes. Providing individuals with a personalized sense of their risk could improve prevention efforts. While complex mathematical models that simulate metabolic and inflammatory processes offer detailed and patient-specific insights, their computational cost usually makes them impractical for real-time prediction on mobile platforms. This work introduces a long short-term memory (LSTM) surrogate for the MT2D model, that simulates the main metabolic and inflammatory processes undergoing the transition to prediabetes. The model is developed using a dataset of 43 669 simulated subjects, each with lifestyle inputs and biomarker outputs over six months. Using 8 time series inputs, the surrogate predicts the dynamics of 11 key metabolic and inflammatory outputs, closely replicating the behaviour of the MT2D model. After training, the proposed LSTM model reduces computational time from an average of 8.4 hours to 0.1 seconds per simulation, making it suitable for mobile device deployment. The model achieves root mean squared errors on the order of 10-2 on scaled data, and shows promise for prediabetes risk assessment by capturing trends in inflammatory biomarkers. This surrogate model can provide real-time and patient-specific insights into the metabolic health, potentially improving the understanding of prediabetes risk.

Monitoring surface and vegetation conditions is crucial for analyzing the impact of climate change on natural resources, especially in regions susceptible to extreme events like land and forest dryness caused by summer heatwaves. Traditional satellite indices, including NDVI, have limitations in distinguishing between barren soil and distressed vegetation. This study shows the potential of two recently validated indices, the Emissivity Contrast Index (ECI) and the Water Deficit Index (WDI), to assess vegetation stress and woodland degradation. These indices, derived from Infrared Atmospheric Sounding Interferometer (IASI) data, utilize an Optimal Interpolation scheme for upscaling and remapping. The effectiveness of ECI and WDI has been validated through a comparison with Surface Soil Moisture (SSM). The methodology allows for simultaneous assessment of surface hydric stress, identifying regions at risk of drought and forest fires. This approach has been applied to southern Italy during year 2023, an area which has been impacted by strong heatwaves in the last decade. These indices could demonstrate significant effectiveness when estimated using high-resolution sounders, such as the Surface Biology and Geology Observing Terrestrial Thermal Emission Radiometer (SBG OTTER). This would allow for more effective monitoring of small, heterogeneous areas.

Since the Laplace transform plays a central role in the solution of differential equations, it seems natural to extend it in the field of fractional calculus, since many applications of this topic have been proposed, and are becoming more and more important. In this paper we extend the classical Laplace Transform by replacing the usual kernel with a suitable one, both in the classical and Laguerre-type case, obtained by constructing the reciprocal of some exponential-type functions with respect to an appropriate differential operator. Some examples are shown, derived using the computer algebra system Mathematica.

Electroencephalography (EEG) source imaging aims to reconstruct brain activity maps from the neuroelectric potential difference measured on the skull. To obtain the brain activity map, we need to solve an ill-posed and ill-conditioned inverse problem that requires regularization techniques to make the solution viable. When dealing with real-time applications, dimensionality reduction techniques can be used to reduce the computational load required to evaluate the numerical solution of the EEG inverse problem. To this end, in this paper we use the random dipole sampling method, in which a Monte Carlo technique is used to reduce the number of neural sources. This is equivalent to reducing the number of the unknowns in the inverse problem and can be seen as a first regularization step. Then, we solve the reduced EEG inverse problem with two popular inversion methods, the weighted Minimum Norm Estimate (wMNE) and the standardized LOw Resolution brain Electromagnetic TomogrAphy (sLORETA). The main result of this paper is the error estimates of the reconstructed activity map obtained with the randomized version of wMNE and sLORETA. Numerical experiments on synthetic EEG data demonstrate the effectiveness of the random dipole sampling method.

High beta discharges with dimensionless parameters collisionality (ν*), normalized toroidal Larmor radius (ρ*), and normalized beta (βN) relatively close to the JT-60SA scenarios hybrid and advanced were realized on JET: the JET ρ*=0.04 and bootstrap fraction fBS=0.4 were close to JT60SA values. So the discharges realized on JET are expected having comparable confinement properties as in JT60SA[1]. Since the maximum normalized beta βN_MAX≈ A-1/2 , is slowly dependent on the aspect ratio A, the equilibrium properties at high beta on JET (A=3.1) would not differ in JT60SA(A=2.5). Using the similarity scaling laws [1], JET pulses at BT/Ip (magnetic field/current)=2.4T/1.4MA are ‘similar’, i.e. share confinement and beta behaviour with the JT60SA scenario 5-1 with parameters BT=1.62T, Ip=1.4MA, and auxiliary heating power PAUX_JT60SA >10MW. The JET60SA high beta program can take profit of the high beta JET experiments in particular: i) in the phase of program development at BT=1.6-1.7T at low power to optimize the JT60SA current drive capabilities to get the full current drive , and ii) as a database for the validation of transport models. Strategy of JET experiments was to explore high normalized beta (βN) values, MHD effects at different Ip/BT and find parameters for discharges with mild MHD. Deuterium plasmas were realized in a variant of the hybrid-advanced scenario at toroidal magnetic field BT = 1.7, 2, 2.4 T, plasma current Ip = 1.4 MA, elongation k = 1.6, and high triangularity δ ≈ 0.4, q95=3.5-4.5, and central safety factor q0>1.2 at NBI start, with NBI power PNBI = 16-25 MW, no ICRH. Shots at BT=2.4T were realized in third Deuterium-Tritium (DTE3) campaign. The deuterium dataset is new. Pulses at BT=1.7/Ip=1.4MA are similar to 2014 Hybrid power scan at high δ[2], but there is an extension in the range of NBI power to PNBI=25MW. While pulses at BT=2.4T[3]. are executed at higher q95 with respect to the yr 2014 advanced pulses. Two scans were executed : i) a NBI power scan, affecting βN and ii) a NBI start time scan, affecting the central safety factor q0, which is a key ingredient for MHD stability of the high beta phase. Results of the experiments were: i) Good confinement properties and relatively high βN values; the betaN achievable increases with input power, βN>3.5 for BT/Ip=1.7T/ 1.4MA ; ii) Good control of q0 at start of main heating phase with NBI starting time t0_NBI depending on the toroidal magnetic field value, as investigated in JET hybrid and advanced scenarios; iii) Maximum βN≈ 2.5-2.7 with mild MHD at BT = 2.4 T and q0 > 1 (pulse#103116). Preliminary transport analysis has been done using Bohm-gyroBohm , QuaLiKiz , CDBM codes . The measured ion and electron temperature profiles and neutron fluxes are reproduced by CDBM code at all the magnetic fields. 1.Michele Romanelli and Francesco Paolo Orsitto PPCF 63(2021)125004 2.C Challis et al., Nucl. Fusion 55(2015) 053031 3.J Mailloux et al , 41st EPS Conf. Plasma Physics Berlin 2014 , O4.127. (*) see the author list of ‘Overview of T and D-T results JET with ITER-like wall’ by C Maggi et al. to be published in Nuclear Fusion Special Issue for IAEA FEC23 London 19-21 oct.2023.

Using a mathematical model of concrete carbonation that describes the variation in porosity as a consequence of the involved chemical reactions, we both validated and calibrated the related numerical algorithm of degradation. Once calibrated, a simulation algorithm was used as a forecasting tool for predicting the effects on the porosity of concrete exposed to increasing levels of CO2 emissions, as well as to rising temperatures. Taking into account future projections of environmental modifications deriving from climate changes, some scenarios were produced numerically by the mathematical algorithm that showed the effects of different pollution levels and global warming on the porosity of Portland cement in a time window of years. Finally, a theoretical study on the effects of pollution levels on the carbonation constant determining the advancement in the carbonation front was carried out for the analyzed scenarios.

The computation of n-point Gaussian quadrature rules for symmetric weight functions is considered in this paper. It is shown that the nodes and the weights of the Gaussian quadrature rule can be retrieved from the singular value decomposition of a bidiagonal matrix of size n/2. The proposed numerical method allows to compute the nodes with high relative accuracy and a computational complexity of O(n). We also describe an algorithm for computing the weights of a generic Gaussian quadrature rule with high relative accuracy. Numerical examples show the effectiveness of the proposed approach.

Started as a hyped technology a few years ago, IoT is now a reality providing sensing and computing capabilities from SCADA systems to households. At their core, IoT devices connect to the outside world to share sensed or computed data. However, the sensitivity and privacy of shared data has made access management a stringent need also for the IoT. In particular, continuous authentication could solve a few security issues, like session hijacking, via checking device legitimacy for each exchanged message and preventing attackers from pretending their actions came from authenticated devices. To date, device-to-device (D2D) continuous authentication still relies on tokens/certificates or devices' fingerprints such as battery levels or location. The cited solutions, while being not always implementable on resource constrained devices, provide low-entropy and thus sporting a non negligible probability of being guessable during impersonation attacks. In this paper, we overcome the above limitations with LENTO: unpredictable Latency-based continuous authEntication for Network inTensive IoT envirOnments. In addition to a thorough analysis, we also offer experimental validation of our proposal. We have deployed LENTO as an additional authentication module of the well-known NextCloud platform, and we have performed an extensive experimental campaign. Collected results confirm our working hypothesis. Network delays can be exploited as random seeds in continuous authentication protocols as they provide as much entropy as standard approaches. To the best of our knowledge, our approach is the first continuous authentication protocol relying purely on the network characteristics, regardless of the underneath computing base trustworthiness. Given the minimal overhead introduced by our solution, it provides continuous authentication even for those devices that cannot afford to run (defacto) standard protocols. As such, LENTO could be retrofitted, offering enhanced security to a plethora of nowadays unsecured devices.

This work introduces a novel extension of the 0/1 Knapsack Problem in which we consider the existence of so-called forfeit sets. A forfeit set is a subset of items of arbitrary cardinality, such that including a number of its elements that exceeds a predefined allowance threshold implies some penalty costs to be paid in the objective function value. A global upper bound on these allowance violations is also considered. We show that the problem generalizes both the Knapsack Problem with conflicts among item pairs and the Knapsack Problem with forfeit pairs, that have been previously introduced in the literature. We present a polynomial subcase by proving the integrality of its LP relaxation polytope and, we introduce three heuristic approaches, namely a constructive greedy, an algorithm based on the recently introduced Carousel Greedy paradigm and a hybrid Memetic/Carousel Greedy algorithm. Finally, we validate the performances for the proposed algorithms on a set of benchmark instances that consider both random and correlated data.

We present a standalone Matlab software platform complete with visualization for the reconstruction of the neural activity in the brain from MEG or EEG data. The underlying inversion combines hierarchical Bayesian models and Krylov subspace iterative least squares solvers. The Bayesian framework of the underlying inversion algorithm allows to account for anatomical information and possible a priori belief about the focality of the reconstruction. The computational efficiency makes the software suitable for the reconstruction of lengthy time series on standard computing equipment. The algorithm requires minimal user provided input parameters, although the user can express the desired focality and accuracy of the solution. The code has been designed so as to favor the parallelization performed automatically by Matlab, according to the resources of the host computer. We demonstrate the flexibility of the platform by reconstructing activity patterns with supports of different sizes from MEG and EEG data. Moreover, we show that the software reconstructs well activity patches located either in the subcortical brain structures or on the cortex. The inverse solver and visualization modules can be used either individually or in combination. We also provide a version of the inverse solver that can be used within Brainstorm toolbox. All the software is available online by Github, including the Brainstorm plugin, with accompanying documentation and test data.