Electrical resistivity tomography is a suitable technique for non-invasive monitoring of municipal solid waste landfills, but accurate sensitivity analysis is necessary to evaluate the effectiveness and reliability of geoelectrical investigations and to properly design data acquisition. Commonly, a thin high-resistivity membrane in placed underneath the waste to prevent leachate leakage. In the construction of a numerical framework for sensitivity computation, taking into account the actual dimensions of the electrodes and, in particular, of the membrane, can lead to extremely high computational costs. In this work, we present a novel approach for numerically computing sensitivity effectively by adopting a mixed-dimensional framework, where the membrane is approximated as a 2D object and the electrodes as 1D objects. The code is first validated against analytical expressions for simple 4-electrode arrays and a homogeneous medium. It is then tested in simplified landfill models, where a 2D box-shaped liner separates the landfill body from the surrounding media, and 48 electrodes are used. The results show that electrodes arranged linearly along both sides of the perimeter edges of the box-shaped liner are promising for detecting liner damage, with sensitivity increasing by 2-3 orders of magnitude, even for damage as small as one-sixth of the electrode spacing in diameter. Good results are also obtained when simulating an electrical connection between the landfill and the surrounding media that is not due to liner damage. The next steps involve evaluating the minimum number of configurations needed to achieve suitable sensitivity with a manageable field effort and validating the modeling results with downscaled laboratory tests.

In the present-day scenario, Large Language Models (LLMs) are establishing their presence as powerful instruments permeating various sectors of society. While their utility offers valuable support to individuals, there are multiple concerns over potential misuse. Consequently, some academic endeavors have sought to introduce watermarking techniques, characterized by the inclusion of markers within machine-generated text, to facilitate algorithmic identification. This research project is focused on the development of a novel methodology for the detection of synthetic text, with the overarching goal of ensuring the ethical application of LLMs in AI-driven text generation. The investigation commences with replicating findings from a previous baseline study, thereby underscoring its susceptibility to variations in the underlying generation model. Subsequently, we propose an innovative watermarking approach and subject it to rigorous evaluation, employing paraphrased generated text to asses its robustness. Experimental results highlight the robustness of our proposal compared to the~\cite{aarson} watermarking method.

A conjecture of Berge and Fulkerson (1971) states that every cubic bridgeless graph contains 6 perfect matchings covering each edge precisely twice, which easily implies that every cubic bridgeless graph has three perfect matchings with empty intersection (this weaker statement was conjectured by Fan and Raspaud in 1994). Let $m_t$ be the supremum of all reals $\alpha\le 1$ such that for every cubic bridgeless graph $G$, there exist $t$ perfect matchings of $G$ covering a fraction of at least $\alpha$ of the edges of $G$. It is known that the Berge-Fulkerson conjecture is equivalent to the statement that $m_5=1$, and implies that $m_4=\tfrac{14}{15}$ and $m_3=\tfrac45$. In the first part of this paper, we show that $m_4=\tfrac{14}{15}$ implies $m_3=\tfrac45$, and $m_3=\tfrac45$ implies the Fan-Raspaud conjecture, strengthening a recent result of Tang, Zhang, and Zhu. In the second part of the paper, we prove that for any $2\le t \le 4$ and for any real $\tau$ lying in some appropriate interval, deciding whether a fraction of more than (resp. at least) $\tau$ of the edges of a given cubic bridgeless graph can be covered by $t$ perfect matching is an NP-complete problem. This resolves a conjecture of Tang, Zhang, and Zhu.

Let $G$ be a graph of even order, and consider $K_G$ as the complete graph on the same vertex set as $G$. A perfect matching of $K_G$ is called a pairing of $G$. If for every pairing $M$ of $G$ it is possible to find a perfect matching $N$ of $G$ such that $M \cup N$ is a Hamiltonian cycle of $K_G$, then $G$ is said to have the Pairing-Hamiltonian property, or PH-property, for short. In 2007, Fink [J. Combin. Theory Ser. B, 97] proved that for every $d\geq 2$, the $d$-dimensional hypercube $\mathcal{Q}_d$ has the PH-property, thus proving a conjecture posed by Kreweras in 1996. In this paper we extend Fink's result by proving that given a graph $G$ having the PH-property, the prism graph $\mathcal{P}(G)$ of $G$ has the PH-property as well. Moreover, if $G$ is a connected graph, we show that there exists a positive integer $k_0$ such that the $k^{\textrm{th}}$-prism of a graph $\mathcal{P}^k(G)$ has the PH-property for all $k \ge k_0$.

We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in divergence form. We then use them to prove the parabolic strong maximum principle and the parabolic Harnack inequality. We emphasize that our results only rely on the classical theory, and our arguments follow the lines used in the original theory of harmonic functions. We provide two proofs relying on two different formulations of the divergence theorem, one stated for sets with almost C^1 boundary, the other stated for sets with finite perimeter.

We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs. We define an edit distance for Reeb graphs and prove that it is stable and universal, meaning that it provides an upper bound to any other stable distance. In contrast, via a specific construction, we show that the interleaving distance and the functional distortion distance on Reeb graphs are not universal.

We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which - by adding a suitable Chern-Simons term to the particle action - can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U(F) "flavour" symmetry on the worldline particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young Tableau. In particular the occupation numbers of the wavefunction - i.e. the lengths of the columns (rows) of the Young Tableau - are fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We suggest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.

The Italian AGILE space mission, with its Gamma-Ray Imaging Detector (GRID) instrument sensitive in the 30 MeV-50 GeV gamma-ray energy band, has been operating since 2007. Agilepy is an open-source Python package to analyse AGILE/GRID data. The package is built on top of the command-line version of the AGILE Science Tools, developed by the AGILE Team, publicly available and released by ASI/SSDC. The primary purpose of the package is to provide an easy to use high-level interface to analyse AGILE/GRID data by simplifying the configuration of the tasks and ensuring straightforward access to the data. The current features are the generation and display of sky maps and light curves, the access to gamma-ray sources catalogues, the analysis to perform spectral model and position fitting, the wavelet analysis. Agilepy also includes an interface tool providing the time evolution of the AGILE off-axis viewing angle for a chosen sky region. The Flare Advocate team also uses the tool to analyse the data during the daily monitoring of the gamma-ray sky. Agilepy (and its dependencies) can be easily installed using Anaconda.

This paper presents a novel retrieval pipeline for video collections, which aims to retrieve the most significant parts of an edited video for a given query, and represent them with thumbnails which are at the same time semantically meaningful and aesthetically remarkable. Videos are first segmented into coherent and story-telling scenes, then a retrieval algorithm based on deep learning is proposed to retrieve the most significant scenes for a textual query. A ranking strategy based on deep features is finally used to tackle the problem of visualizing the best thumbnail. Qualitative and quantitative experiments are conducted on a collection of edited videos to demonstrate the effectiveness of our approach.

Extragalactic globular clusters (EGCs) are an abundant and powerful tracer of galaxy dynamics and formation, and their own formation and evolution is also a matter of extensive debate. The compact nature of globular clusters means that they are hard to spatially resolve and thus study outside the Local Group. In this work we have examined how well EGCs will be detectable in images from the Euclid telescope, using both simulated pre-launch images and the first early-release observations of the Fornax galaxy cluster. The Euclid Wide Survey will provide high-spatial resolution VIS imaging in the broad IE band as well as near-infrared photometry (YE, JE, and HE). We estimate that the galaxies within 100 Mpc in the footprint of the Euclid survey host around 830 000 EGCs of which about 350 000 are within the survey's detection limits. For about half of these EGCs, three infrared colours will be available as well. For any galaxy within 50Mpc the brighter half of its GC luminosity function will be detectable by the Euclid Wide Survey. The detectability of EGCs is mainly driven by the residual surface brightness of their host galaxy. We find that an automated machine-learning EGC-classification method based on real Euclid data of the Fornax galaxy cluster provides an efficient method to generate high purity and high completeness GC candidate catalogues. We confirm that EGCs are spatially resolved compared to pure point sources in VIS images of Fornax. Our analysis of both simulated and first on-sky data show that Euclid will increase the number of GCs accessible with high-resolution imaging substantially compared to previous surveys, and will permit the study of GCs in the outskirts of their hosts. Euclid is unique in enabling systematic studies of EGCs in a spatially unbiased and homogeneous manner and is primed to improve our understanding of many understudied aspects of GC astrophysics.

Monolayer transition metal dichalcogenides in the T' phase promise to realize the quantum spin Hall (QSH) effect at room temperature, because they exhibit a prominent spin-orbit gap between inverted bands in the bulk. Here we show that the binding energy of electron-hole pairs excited through this gap is larger than the gap itself in MoS2, a paradigmatic material that we investigate from first principles by many-body perturbation theory (MBPT). This paradoxical result hints at the instability of the T' phase against the spontaneous generation of excitons, and indeed we find that it gives rise to a recostructed `excitonic insulator' ground state. Importantly, we show that in this system topological and excitonic order cooperatively enhance the bulk gap by breaking the crystal inversion symmetry, in contrast to the case of bilayers where the frustration between the two orders is relieved by breaking time reversal symmetry. The excitonic topological insulator departs distinctively from the bare topological phase as it lifts the band spin degeneracy, which results in circular dichroism. A moderate biaxial strain applied to the system leads to two additional excitonic phases, different in their topological character but both ferroelectric as an effect of electron-electron interactions.

We construct a spinning particle that reproduces the propagation of the graviton on those curved backgrounds which solve the Einstein equations, with or without cosmological constant, i.e. Einstein manifolds. It is obtained by modifying the N=4 supersymmetric spinning particle by relaxing the gauging of the full SO(4) R-symmetry group to a parabolic subgroup, and selecting suitable Chern-Simons couplings on the worldline. We test it by computing the correct one-loop divergencies of quantum gravity in D=4.

In the near future, our streets will be populated by myriads of autonomous self-driving vehicles to serve our diverse mobility needs. This will raise the need to coordinate their movements in order to properly handle both access to shared resources (e.g., intersections and parking slots) and the execution of mobility tasks (e.g., platooning and ramp merging). In this paper, we firstly introduce the general issues associated to coordination of autonomous vehicles, by identifying and framing the key classes of coordination problems. Following, we overview the different approaches that can be adopted to manage such coordination problems, by classifying them in terms of the degree of autonomy in decision making that is left to autonomous vehicles during coordination. Finally, we overview some further peculiar challenges that research will have to address before autonomously coordinated vehicles can safely hit our streets.

Emulsions are ubiquitous in everyday life and find applications in various industries. Optical tweezers (OTs) have emerged as the preferred method for studying emulsion dynamics. In this review, we first introduce the theory of optical trapping and emulsion stability. We then survey applications in the manipulation of emulsions, stability mechanism, the processes of aggregation and coalescence, and important responsive and switchable behaviors. And we overview the instrumentation framework of various OT setups, and evaluate their complexity and cost with a view towards the democratization of this technology. Following this, we delve into basic experimentation methods, the challenges associated with using OTs in emulsion applications. Additionally, we present a promising research outlook, including studies on stability mechanism of emulsions stabilized by compound or mixed emulsifiers or rigid or soft particles, as well as dynamic processes of responsive or functional emulsions.

Massive sterile neutrinos, also known as heavy neutral leptons, can have a mixing with active neutrinos, $\theta$, as well as a dipole coupling to the photon, $d$. We study the interplay between these two portals, considering the production from meson decays of sterile neutrinos with mass $0.1$ GeV $\lesssim M_N \lesssim 10$ GeV, at beam-dump facilities such as NA62 and SHiP, and at the FASER2 experiment. These sterile neutrinos can be long-lived and decay into a photon in a distant detector, via the dipole operator. We find that all these experiments will be sensitive to values of $d$ which are presently unconstrained. The experimental reach varies strongly with the mass $M_N$ and the mixing $\theta$, and one observes specific correlations with the flavour of active neutrinos. The SHiP experiment will mark a jump in sensitivity, as it will probe dipole couplings as small as $d\sim 10^{-8}$ GeV$^{-1}$, thus testing new physics well above the electroweak scale.

FRB 180916 is a most intriguing source at 150 Mpc distance capable of producing repeating fast radio bursts with a periodic 16.35 day temporal pattern. We report on the X-ray and $\gamma$-ray observations of FRB 180916 obtained by AGILE and Swift. We focused on the recurrent 5-day time intervals of active radio bursting and present results obtained on Feb. 3 - 8; Feb. 25; Mar. 5 - 10; Mar. 22 - 28, 2020 during a multiwavelength campaign involving high-energy and radio observations. We also searched for temporal coincidences at millisecond timescales between all known radio bursts of FRB 180916 and X-ray and MeV events detectable by AGILE. We do not detect any simultaneous event or any extended X-ray and $\gamma$-ray emission on timescales of hours/days/weeks. Our cumulative X-ray (0.3-10 keV) flux upper limit of $5 \times\,10^{-14} \rm \, erg \, cm^{-2} s^{-1}$ (obtained during 5-day active intervals) translates into an isotropic luminosity upper limit of $L_{X,UL} \sim 1.5 \times\, 10^{41} \rm erg \, s^{-1}$. Observations above 100 MeV over a many-year timescale provide an average luminosity upper limit one order of magnitude larger. These results provide the so-far most stringent limits on high-energy emission from FRB 180916 and constrain the dissipation of magnetic energy from a magnetar-like source of radius $R_m$, internal magnetic field $B_m$ and dissipation timescale $\tau_d$ to satisfy the relation $R_{m,6}^3 B_{m,16}^2 \tau_{d,8}^{-1} \lesssim 1$, where$R_{m,6}$is$R_m$ in units of $10^6$ cm, $B_{m,16}$ is $B_m$ in units of $10^{16}$ G, and $\tau_{d,8}$ in units of $10^8$ s.

In the first-quantised worldline approach to quantum field theory, a long-standing problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with $N$ photons, in terms of the "$N$-photon kernel," where off-shell this kernel appears also in "subleading" terms involving only $N-1$ of the $N$ photons. Although the parameter integrals generated by the master formula are equivalent to the usual Feynman diagrams, they are quite different since the use of the inverse symbol map avoids the appearance of long products of Dirac matrices. As a test we use the $N=2$ case for a recalculation of the one-loop fermion self energy, in $D$ dimensions and arbitrary covariant gauge, reproducing the known result. We find that significant simplification can be achieved in this calculation choosing an unusual momentum-dependent gauge parameter.

The widespread adoption of machine learning surrogate models has significantly improved the scale and complexity of systems and processes that can be explored accurately and efficiently using atomistic modeling. However, the inherently data-driven nature of machine learning models introduces uncertainties that must be quantified, understood, and effectively managed to ensure reliable predictions and conclusions. Building upon these premises, in this Perspective, we first overview state-of-the-art uncertainty estimation methods, from Bayesian frameworks to ensembling techniques, and discuss their application in atomistic modeling. We then examine the interplay between model accuracy, uncertainty, training dataset composition, data acquisition strategies, model transferability, and robustness. In doing so, we synthesize insights from the existing literature and highlight areas of ongoing debate.

We report on a systematic search for hard X-ray and gamma-ray emission in coincidence with fast radio bursts (FRBs) observed by the AGILE satellite. We used 13 years of AGILE archival data searching for time coincidences between exposed FRBs and events detectable by the MCAL (0.4-100 MeV) and GRID (50 MeV-30 GeV) detectors at timescales ranging from milliseconds to days/weeks. The current AGILE sky coverage allowed us to extend the search for high-energy emission preceding and following the FRB occurrence. We considered all FRBs sources currently included in catalogues, and identified a sub-sample (15 events) for which a good AGILE exposure either with MCAL or GRID was obtained. In this paper we focus on non-repeating FRBs, compared to a few nearby repeating sources. We did not detect significant MeV or GeV emission from any event. Our hard X-ray upper limits (ULs) in the MeV energy range were obtained for timescales from sub-millisecond to seconds, and in the GeV range from minutes to weeks around event times. We focus on a sub-set of 5 non-repeating and 2 repeating FRB sources whose distances are most likely smaller than that of 180916.J0158+65 (150 Mpc). For these sources, our MeV ULs translate into ULs on the isotropically-emitted energy of about 3x10^46 erg, comparable to that observed in the 2004 giant flare from the Galactic magnetar SGR 1806-20. On average, these nearby FRBs emit radio pulses of energies significantly larger than the recently detected SGR 1935+2154 and are not yet associated with intense MeV flaring.

AGILE is an ASI space mission launched in 2007 to study X-ray and gamma-ray phenomena in the energy range from $\sim20$ keV to $\sim10$ GeV. The AGILE Team developed a real-time analysis pipeline for the fast detection of transient sources, and the follow-up of external science alerts received through networks such as the General Coordinates Network. We developed a new Deep Learning method for detecting and localizing Gamma-Ray Bursts (GRB) in the AGILE/GRID sky maps. We trained the model using sky maps with GRBs simulated in a radius of 20 degrees from the center of the map, which is larger than 99.5 \% of the error region present in the GRBWeb catalog. We also plan to apply this method to search for counterparts of gravitational wave events, which typically have a wider localization error region. The method comprises two Deep Learning models implemented with two Convolutional Neural Networks. The first model detects and filters sky maps containing a GRB, while the second model localizes its position. We trained and tested the models using simulated data. The detection model achieves an accuracy of 95.7 \%, and the localization model has a mean error lower than 0.8 degrees. We configured a Docker container with all the required software for data simulation and deployed it using the Amazon Web Service to calculate the p-value distribution under different conditions. With the p-value distribution, we can calculate the statistical significance of a detection.