The paper is concerned with a generalization of Floater–Hormann (briefly FH) rational interpolation recently introduced by the authors. Compared with the original FH interpolants, the generalized ones depend on an additional integer parameter γ>1, that, in the limit case γ=1 returns the classical FH definition. Here we focus on the general case of an arbitrary distribution of nodes and, for any γ>1, we estimate the sup norm of the error in terms of the maximum (h) and minimum (h∗) distance between two consecutive nodes. In the special case of equidistant (h=h∗) or quasi–equidistant (h≈h∗) nodes, the new estimate improves previous results requiring some theoretical restrictions on γ which are not needed as shown by the numerical tests carried out to validate the theory.

Quasiparticles are low-energy excitations with important roles in condensed matter physics. An intriguing example is provided by Majorana quasiparticles, which are equivalent to their antiparticles. Despite being implicated in neutrino oscillations and topological superconductivity, their experimental realizations remain very rare. Here, we propose a purely classical realization of Majorana fermions in terms of three-dimensional disclination lines in active nematics. The underlying reason is the well-known equivalence, in 3D, between a + 1 / 2 local defect profile and a - 1 / 2 profile, which acts as its antiparticle. The mapping also requires proving that defect profiles transform as spinors, and activity is needed to overcome the elastic cost associated with these excitations, so they spontaneously appear in steady state. We combine topological considerations and numerics to show that active nematics under confinement spontaneously create in their interior topologically charged disclination lines and loops, akin to Majorana quasiparticles with finite momentum. Within a long channel, the phenomenology we observe resembles that of the Kitaev chain, as Majorana-like states appear near the boundaries, while a delocalized topological excitation arises in the form of a chiral disclination line. The analogy between 3D nematic defects and topological quasiparticles further suggests that active turbulence can be viewed as a topological phase, where defects percolate to form delocalized topological quasiparticles similar to those observed in the channel. We propose that three-dimensional active disclinations can be used to probe the physics of Majorana spinors at much larger scale than that for which they were originally introduced, potentially facilitating their experimental study.

High-resolution water vapor fields retrieved over Iberia during the passage of storm Barbara (October 19–20, 2020) by Sentinel-1 and assimilated by the Weanther Research & Forecasting Model (WRF) reveal a substantial positive impact on water vapor forecasting. Due to the path followed by the storm across Iberia, from its southwestern to the northeastern corners, and the geometry of Sentinel-1 data acquisition, it is possible to show, for the first time, the potential added value of precipitable water vapor (PWV) obtained by the Interferometric Synthetic-Aperture Radar (InSAR) technique, as a data source for both the forecast and validation of meteorological forecasts of synoptic-scale storms. Results indicate that data assimilated in the InSARfootprint positively impact the downstream forecasts up to the northeastern boundary, about 850km and 12 hours away, with improved skill scores of the water vapor distribution and improved forecasts of rain.

This article presents a study of the relationship among decorrelation phase in synthetic aperture radar (SAR) interferogram, soil moisture, and water content in vegetation with the aim of mitigating the contribution of decorrelation phase in SAR interferometry estimates of terrain displacements. A methodology for the mitigation of the phase bias based on the temporal variation of the vegetation water content is presented. Decorrelation phases are computed using time series of Sentinel-1 images and compared with in situ measurements of soil moisture. It is shown that soil moisture can partially explain the observed values of decorrelation phases pointing out the role of vegetation water content. A new model is proposed to compute the contribution of vegetation to the decorrelation phase based on the normalized difference water index (NDWI) index. The methodology is applied to all short temporal baseline interferograms obtained from the time series of Sentinel-1 SAR images, using the NDWI maps generated from Sentinel-2 multispectral images. The cumulative displacement is computed by integrating the short temporal baseline interferograms, corrected for the land cover and soil moisture changes. It is shown that the proposed methodology can reduce the variance of estimated cumulative displacement in areas covered by vegetation.

Accuracy of radar interferometry is often hindered by the atmospheric phase screen (APS). To address this limitation, the geostatistical approach known as Kriging has been employed to predict APS from sparse observations for compensation purposes. In this article, we propose an enhanced Kriging approach to achieve more accurate APS predictions in ground-based (GB) radar interferometry applications. Specifically, the Kriging system is augmented with a time-series measure through correlation analysis, effectively leveraging spatiotemporal information for APS prediction. The validity of the introduced Kriging method in the APS compensation framework was tested with Ku-band GB radar datasets collected over two different mountainous sites. A comparison of this method with simple Kriging reveals a noticeable improvement in APS prediction accuracy and temporal phase stability.

We study the sub-ionospheric VLF transmitter signals recorded by the Austrian Graz station in the year 2020. Those radio signals are known to propagate in the Earth-ionosphere waveguide between the ground and lower ionosphere. The Austrian Graz facility (geographic coordinates: 15.46 degrees E, 47.03 degrees N) can receive such sub-ionospheric transmitter signals, particularly those propagating above earthquake (EQ) regions in the southern part of Europe. We consider in this work the transmitter amplitude variations recorded a few weeks before the occurrence of two EQs in Croatia at a distance less than 200 km from Graz VLF facility. The selected EQs happened on 22 March 2020 and 29 December 2020, with magnitudes of Mw5.4 and Mw6.4, respectively, epicenters localized close to Zagreb (16.02 degrees E, 45.87 degrees N; 16.21 degrees E, 45.42 degrees N), and with focuses of depth smaller than 10 km. In our study we emphasize the anomaly fluctuations before/after the sunrise times, sunset times, and the cross-correlation of transmitter signals. We attempt to evaluate and to estimate the latitudinal and the longitudinal expansions of the ionospheric disturbances related to the seismic preparation areas.

Fully developed turbulence is a universal and scale-invariant chaotic state characterized by an energy cascade from large to small scales at which the cascade is eventually arrested by dissipation1–6. Here we show how to harness these seemingly structureless turbulent cascades to generate patterns. Pattern formation entails a process of wavelength selection, which can usually be traced to the linear instability of a homogeneous state7. By contrast, the mechanism we propose here is fully nonlinear. It is triggered by the non-dissipative arrest of turbulent cascades: energy piles up at an intermediate scale, which is neither the system size nor the smallest scales at which energy is usually dissipated. Using a combination of theory and large-scale simulations, we show that the tunable wavelength of these cascade-induced patterns can be set by a non-dissipative transport coefficient called odd viscosity, ubiquitous in chiral fluids ranging from bioactive to quantum systems8–12. Odd viscosity, which acts as a scale-dependent Coriolis-like force, leads to a two-dimensionalization of the flow at small scales, in contrast with rotating fluids in which a two-dimensionalization occurs at large scales4. Apart from odd viscosity fluids, we discuss how cascade-induced patterns can arise in natural systems, including atmospheric flows13–19, stellar plasma such as the solar wind20–22, or the pulverization and coagulation of objects or droplets in which mass rather than energy cascades23–25.

Small bubbles in fluids rise to the surface due to Archimede’s force. Remarkably, in turbulent flows this process is severely hindered by the presence of vortex filaments, which act as moving potential wells, dynamically trapping light particles and bubbles. Quantifying the statistical weights and roles of vortex filaments in turbulence is, however, still an outstanding experimental and computational challenge due to their small scale, fast chaotic motion, and transient nature. Here we show that, under the influence of a modulated oscillatory forcing, the collective bubble behavior switches from a dynamically localized to a delocalized state. Additionally, we find that by varying the forcing frequency and amplitude, a remarkable resonant phenomenon between light particles and small-scale vortex filaments emerges, likening particle behavior to a forced damped oscillator. We discuss how these externally actuated bubbles can be used as a type of microscopic probe to investigate the space-time statistical properties of the smallest turbulence scales, allowing to quantitatively measure physical characteristics of vortex filaments. We develop a superposition model that is in excellent agreement with the simulation data of the particle dynamics which reveals the fraction of localized/delocalized particles as well as characteristics of the potential landscape induced by vortices in turbulence. Our approach paves the way for innovative ways to accurately measure turbulent properties and to the possibility to control light particles and bubble motions in turbulence with potential applications to oceanography, medical imaging, drug/gene delivery, chemical reactions, wastewater treatment, and industrial mixing.

The potential of a coherent microwave radar for infrastructure health monitoring has been investigated over the past decade. Microwave radar measuring based on interferometry processing is a non-invasive technique that can measure the line-of-sight (LOS) displacements of large infrastructure with sub-millimeter precision and provide the corresponding frequency spectrum. It has the capability to estimate infrastructure vibration simultaneously and remotely with high accuracy and repeatability, which serves the long-term serviceability of bridge structures within the context of the long-term sustainability of civil engineering infrastructure management. In this paper, we present three types of microwave radar systems employed to monitor the displacement of bridges in Japan and Italy. A technique that fuses polarimetric analysis and the interferometry technique for bridge monitoring is proposed. Monitoring results achieved with full polarimetric real aperture radar (RAR), step-frequency continuous-wave (SFCW)-based linear synthetic aperture, and multi-input multi-output (MIMO) array sensors are also presented. The results reveal bridge dynamic responses under different loading conditions, including wind, vehicular traffic, and passing trains, and show that microwave sensor interferometry can be utilized to monitor the dynamics of bridge structures with unprecedented spatial and temporal resolution. This paper demonstrates that microwave sensor interferometry with efficient, cost-effective, and non-destructive properties is a serious contender to employment as a sustainable infrastructure monitoring technology serving the sustainable development agenda.

The interferometric synthetic aperture radar (InSAR) technique has demonstrated its ability to capture temporal variations in tropospheric water vapor, providing a valuable source of information for numerical weather prediction (NWP) models. Integrating InSAR data into NWP models has the potential to significantly enhance their forecasting capabilities, especially for predicting local extreme weather events. The challenge lies in extracting a single epoch from the InSAR differential observations. In this work, we introduced a method based on the least-squares approach to estimate single epochs using the ERA5 reanalysis data from the European Centre for Medium-Range Weather Forecasts (ECMWFs) as a first guess. By leveraging ERA5 data, distinct atmospheric components can be disentangled without additional assumptions or external measurements. Since ERA5 is globally available at 1-h temporal resolution, the proposed method can be applied in remote areas without in situ data, providing improved high-resolution maps at all times (day/night) and in all weather conditions.

The health monitoring of infrastructure is vital for ensuring the safety and structural integrity of bridges. Recently, ground-based real aperture radar (GB-RAR) systems have been successfully utilized in the dynamic and static monitoring of bridges. In this study, a comprehensive and innovative approach is presented to monitor the vertical deformation of a long-span metallic railway bridge and a reinforced concrete Shinkansen bridge in Japan using a polarimetric GB-RAR system. Distinct from conventional signal processing procedures, the proposed method omits the coherent scatterer selection step. Instead, polarization analysis is employed to evaluate the properties of scatterers and identify those corresponding to bridge sections requiring monitoring, while considering the structural characteristics of the bridge. Simultaneously, the signal-to-noise ratio for monitoring is enhanced by combining co-polarization responses from scatterers. Furthermore, the radar look angle is determined by accounting for the spatial configuration of the survey and the polarization orientation angle. Lastly, vertical deformation is assessed by projecting line of sight deformation in the vertical direction. The findings reveal the dynamic responses of the two bridges under diverse loading conditions, which include the transit of a low-speed train and a high-speed Shinkansen bullet train. The results demonstrate that the polarimetric GB-RAR interferometry technique, coupled with the developed algorithms, can be effectively applied to monitor any type of bridge with unparalleled spatial and temporal resolutions.

This work presents the analysis model of the study data available in the LMS platforms specifically designed to analyze potential critical issues as a functional indicator for the possible achievement of the training objectives and completion of the course. The illustrated system highlights how the use of statistical indicators and predictability can be an effective tool for the early identification of possible critical issues in the field of training results, as well as design and organizational inconsistencies that can weigh on the effectiveness of the training system made available. Our work explains how adopting a data analysis model applied to training environments provides the tutoring system with adequate information on potential critical issues to favor targeted interventions on the participants to prevent risks of training ineffectiveness. At the same time, it analyzes the global quality of the courses made available through a perspective of data exploration that starts from the learning experience and enhances the data already present in the LMS platforms.

The medical discourse, entails the analysis of the modalities, far from unbiased, by which hypotheses and results are laid out in the dissemination of findings in scientific publications, giving different emphases on the background, relevance, robustness, and assumptions that the audience should take for granted. While this concept is extensively studied in socio-anthropology, it remains generally overlooked within the scientific community conducting the research. Yet, analyzing the discourse is crucial for several reasons: to frame policies that take into account an appropriately large screen of medical opportunities, to avoid overseeing promising but less walked paths, to grasp different types of representations of diseases, therapies, patients, and other stakeholders, understanding and being aware of how these very terms are conditioned by time, culture and so on. While socio-anthropologists traditionally use manual curation methods, automated approaches like topic modeling offer a complementary way to explore the vast and ever-growing body of medical literature. In this work, we propose a complementary analysis of the medical discourse regarding the therapies offered for rheumatoid arthritis using topic modeling and large language model-based emotion and sentiment analysis.

Quantum annealers are commercial devices that aim to solve very hard computational problems1, typically those involving spin glasses2,3. Just as in metallurgic annealing, in which a ferrous metal is slowly cooled4, quantum annealers seek good solutions by slowly removing the transverse magnetic field at the lowest possible temperature. Removing the field diminishes the quantum fluctuations but forces the system to traverse the critical point that separates the disordered phase (at large fields) from the spin-glass phase (at small fields). A full understanding of this phase transition is still missing. A debated, crucial question regards the closing of the energy gap separating the ground state from the first excited state. All hopes of achieving an exponential speed-up, compared to classical computers, rest on the assumption that the gap will close algebraically with the number of spins5–9. However, renormalization group calculations predict instead that there is an infinite-randomness fixed point10. Here we solve this debate through extreme-scale numerical simulations, finding that both parties have grasped parts of the truth. Although the closing of the gap at the critical point is indeed super-algebraic, it remains algebraic if one restricts the symmetry of possible excitations. As this symmetry restriction is experimentally achievable (at least nominally), there is still hope for the quantum annealing paradigm11–13.

We release a set of GPU programs for the study of the Quantum (S=1/2) Spin Glass on a square lattice, with binary couplings. The library contains two main codes: MCQSG (that carries out Monte Carlo simulations using both the Metropolis and the Parallel Tempering algorithms, for the problem formulated in the Trotter-Suzuki approximation), and EDQSG (that obtains the extremal eigenvalues of the Transfer Matrix using the Lanczos algorithm). EDQSG has allowed us to diagonalize transfer matrices with size up to 236×236. From its side, MCQSG running on four NVIDIA A100 cards delivers a sub-picosecond time per spin-update, a performance that is competitive with dedicated hardware. We include as well in our library GPU programs for the analysis of the spin configurations generated by MCQSG. Finally, we provide two auxiliary codes: the first generates the lookup tables employed by the random number generator of MCQSG; the second one simplifies the execution of multiple runs using different input data. Program summary: Program Title: QISG Suite CPC Library link to program files: https://doi.org/10.17632/g97sn2t8z2.1 Licensing provisions: MIT Programming language: CUDA-C Nature of problem: The critical properties of quantum disordered systems are known only in a few, simple, cases whereas there is a growing interest in gaining a better understanding of their behaviour due to the potential application of quantum annealing techniques for solving optimization problems. In this context, we provide a suite of codes, that we have recently developed, to the purpose of studying the 2D Quantum Ising Spin Glass. Solution method: We provide a highly tuned multi-GPU code for the Montecarlo simulation of the 2D QISG based on a combination of Metropolis and Parallel Tempering algorithms. Moreover, we provide a code for the evaluation of the eigenvalues of the transfer matrix of the 2D QISG for size up to L=6. The eigenvalues are computed by using the classic Lanczos algorithm that, however, relies on a custom multi-GPU-CPU matrix-vector product that speeds-up dramatically the execution of the algorithm.

Rejuvenation and memory, long considered the distinguishing features of spin glasses, have recently been proven to result from the growth of multiple length scales. This insight, enabled by simulations on the Janus II supercomputer, has opened the door to a quantitative analysis. We combine numerical simulations with comparable experiments to introduce two coefficients that quantify memory. A third coefficient has been recently presented by Freedberg et al. We show that these coefficients are physically equivalent by studying their temperature and waiting-time dependence.

Weunveil the multifractal behavior of Ising spin glasses in their low-temperature phase. Using the Janus II custom-built supercomputer, the spin-glass correlation function is studied locally. Dramatic fluctuations are found when pairs of sites at the same distance are compared. The scaling of these fluctuations, as the spin-glass coherence length grows with time, is characterized through the computation of the singularity spectrum and its corresponding Legendre transform. A comparatively small number of site pairs controls the average correlation that governs the response to a magnetic field. We explain how this scenario of dramatic fluctuations (at length scales smaller than the coherence length) can be reconciled with the smooth, self-averaging behavior that has long been considered to describe spin-glass dynamics.

Many systems, when initially placed far from equilibrium, exhibit surprising behavior in their attempt to equilibrate. Striking examples are the Mpemba effect and the cooling-heating asymmetry. These anomalous behaviors can be exploited to shorten the time needed to cool down (or heat up) a system. Though, a strategy to design these effects in mesoscopic systems is missing. We bring forward a description that allows us to formulate such strategies, and, along the way, makes natural these paradoxical behaviors. In particular, we study the evolution of macroscopic physical observables of systems freely relaxing under the influence of one or two instantaneous thermal quenches. The two crucial ingredients in our approach are timescale separation and a nonmonotonic temperature evolution of an important state function. We argue that both are generic features near a first-order transition. Our theory is exemplified with the one-dimensional Ising model in a magnetic field using analytic results and numerical experiments.

The new σ-IASI/F2N radiative transfer model is an advancement of the σ-IASI model, introduced in 2002. It enables rapid simulations of Earth-emitted radiance and Jacobians under various sky conditions and geometries, covering the spectral range of 3-100 μm. Successfully utilized in δ-IASI, the advanced Optimal Estimation tool tailored for the IASI MetOp interferometer, its extension to the Far Infrared (FIR) holds significance for the ESA Earth Explorer FORUM mission, necessitating precise cloud radiative effect treatment, crucial in regions with dense clouds and temperature gradients. The model's update, incorporating the "linear-in-T" correction, addresses these challenges, complementing the "linear-in-tau" approach. Demonstrations highlight its effectiveness in simulating cloud complexities, with the integration of the "linear-in-T" and Tang correction for the computation of cloud radiative effects. The results presented will show that the updated σ-IASI/F2N can treat the overall complexity of clouds effectively and completely, at the same time minimizing biases.

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.