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We study spectral properties of the quantum Korteweg-de Vries hierarchy defined by Buryak and Rossi. We prove that eigenvalues to first order in the dispersion parameter are given by shifted symmetric functions. The proof is based on the boson-fermion correspondence and an analysis of quartic expressions in fermions. As an application, we obtain a new closed evaluation of certain double Hodge integrals on the moduli spaces of curves. Finally, we provide an explicit formula for the eigenvectors to first order in the dispersion parameter. In particular, we show that its Schur expansion is supported on partitions for which the Hamming distance is minimal., Comment: 23 pages

Detecting protoplanets during their formation stage is an important but elusive goal of modern astronomy. Kinematic detections via the spiral wakes in the gaseous disc are a promising avenue to achieve this goal. We aim to test the applicability to observations in the low and intermediate planet mass regimes of a commonly used semi-analytical model for planet induced spiral waves. In contrast with previous works which proposed to use the semi-analytical model to interpret observations, in this study we analyse for the first time both the structure of the velocity and density perturbations. We run a set of FARGO3D hydrodynamic simulations and compare them with the output of the semi-analytic model in the code wakeflow, which is obtained by solving Burgers' equation using the simulations as an initial condition. We find that the velocity field derived from the analytic theory is discontinuous at the interface between the linear and nonlinear regions. After 0.2 r$_p$ from the planet, the behaviour of the velocity field closely follows that of the density perturbations. In the low mass limit, the analytical model is in qualitative agreement with the simulations, although it underestimates the azimuthal width and the amplitude of the perturbations, predicting a stronger decay but a slower azimuthal advance of the shock fronts. In the intermediate regime, the discrepancy increases, resulting in a different pitch angle between the spirals of the simulations and the analytic model. The implementation of a fitting procedure based on the minimisation of intensity residuals is bound to fail due to the deviation in pitch angle between the analytic model and the simulations. In order to apply this model to observations, it needs to be revisited accounting also for higher planet masses., Comment: 10 pages, 7 figures. Accepted for publication in A&A May 27, 2024

Current methods to characterize embedded planets in protoplanetary disc observations are severely limited either in their ability to fully account for the observed complex physics or in their computational and time costs. To address this shortcoming, we developed DBNets: a deep learning tool, based on convolutional neural networks, that analyses substructures observed in the dust continuum emission of protoplanetary discs to quickly infer the mass of allegedly embedded planets. We focussed on developing a method to reliably quantify not only the planet mass, but also the associated uncertainty introduced by our modelling and adopted techniques. Our tests gave promising results achieving an 87% reduction of the log Mp mean squared error with respect to an analytical formula fitted on the same data (DBNets metrics: lmse 0.016, r2-score 97%). With the goal of providing the final user of DBNets with all the tools needed to interpret their measurements and decide on their significance, we extensively tested our tool on out-of-distribution data. We found that DBNets can identify inputs strongly outside its training scope returning an uncertainty above a specific threshold and we thus provided a rejection criterion that helps determine the significance of the results obtained. Additionally, we outlined some limitations of our tool: it can be reliably applied only on discs observed with inclinations below approximately 60{\deg}, in the optically thin regime, with a resolution 8 times better than the gap radial location and with a signal-to-noise ratio higher than approximately ten. Finally, we applied DBNets to 33 actual observations of protoplanetary discs measuring the mass of 48 proposed planets and comparing our results with the available literature. We confirmed that most of the observed gaps imply planets in the sub-Jupiter regime. DBNets is publicly available at dbnets.fisica.unimi.it.

We derive differential equations for multiplicative statistics of the Bessel determinantal point process depending on two parameters. In particular, we prove that such statistics are solutions to an integrable nonlinear partial differential equation describing isospectral deformations of a Sturm-Liouville equation. We also derive identities relating solutions to the integrable partial differential equation and to the Sturm-Liouville equation which imply an analogue for Painlev\'e V of Amir-Corwin-Quastel "integro-differential Painlev\'e II equation". This equation reduces, in a degenerate limit, to the system of coupled Painlev\'e V equations derived by Charlier and Doeraene for the generating function of the Bessel process, and to the Painlev\'e V equation derived by Tracy and Widom for the gap probability of the Bessel process. Finally, we study an initial value problem for the integrable partial differential equation. The approach is based on Its-Izergin-Korepin-Slavnov theory of integrable operators and their associated Riemann-Hilbert problems., Comment: V1: 22 pages. V2: 26 pages, major revision, assumptions on $\sigma$ changed, results unchanged

In this work, we explore how to classify asteroids in co-orbital motion with a given planet using Machine Learning. We consider four different kinds of motion in mean motion resonance with the planet, nominally Tadpole, Horseshoe and Quasi-satellite, building 3 datasets defined as Real (taking the ephemerides of real asteroids from the JPL Horizons system), Ideal and Perturbed (both simulated, obtained by propagating initial conditions considering two different dynamical systems) for training and testing the Machine Learning algorithms in different conditions. The time series of the variable theta (angle related to the resonance) are studied with a data analysis pipeline defined ad hoc for the problem and composed by: data creation and annotation, time series features extraction thanks to the tsfresh package (potentially followed by selection and standardization) and the application of Machine Learning algorithms for Dimensionality Reduction and Classification. Such approach, based on features extracted from the time series, allows to work with a smaller number of data with respect to Deep Learning algorithms, also allowing to define a ranking of the importance of the features. Physical Interpretability of the features is another key point of this approach. In addition, we introduce the SHapley Additive exPlanations for Explainability technique. Different training and test sets are used, in order to understand the power and the limits of our approach. The results show how the algorithms are able to identify and classify correctly the time series, with a high degree of performance.

We express correlators of the Jacobi $\beta$ ensemble in terms of (a special case of) $b$-Hurwitz numbers, a deformation of Hurwitz numbers recently introduced by Chapuy and Dolega. The proof relies on Kadell's generalization of the Selberg integral. The Laguerre limit is also considered. All the relevant $b$-Hurwitz numbers are interpreted (following Bonzom, Chapuy, and Dolega) in terms of colored monotone Hurwitz maps.

We study J\'anossy densities of a randomly thinned Airy kernel determinantal point process. We prove that they can be expressed in terms of solutions to the Stark and cylindrical Korteweg-de Vries equations; these solutions are Darboux tranformations of the simpler ones related to the gap probability of the same thinned Airy point process. Moreover, we prove that the associated wave functions satisfy a variation of Amir-Corwin-Quastel's integro-differential Painlev\'e II equation. Finally, we derive tail asymptotics for the relevant solutions to the cylindrical Korteweg-de Vries equation and show that they decompose asymptotically into a superposition of simpler solutions., Comment: V1: 41 pages, 3 figures. V2: 45 pages, 3 figures; revised introduction, minor corrections. V3: 46 pages, 3 figures; minor corrections

The focus of this work is the current distribution of asteroids in co-orbital motion with Venus, Earth and Jupiter, under a quasi-coplanar configuration and for a medium-term timescale of the order of 900 years. A co-orbital trajectory is a heliocentric orbit trapped in a 1:1 mean-motion resonance with a given planet. As such, to model it this work considers the Restricted Three-Body Problem in the circular-planar case with the help of averaging techniques. The domain of each co-orbital regime, that is, the quasi-satellite motion, the horseshoe motion and the tadpole motion, can be neatly defined by means of an integrable model and a simple bi-dimensional map, that is invariant with respect to the mass parameter of the planet, and turns out to be a remarkable tool to investigate the distribution of the co-orbitals objects of interest. The study is based on the data corresponding to the ephemerides computed by the JPL Horizons system for asteroids with a sufficient low orbital inclination with respect to the Sun-planet orbital plane. These objects are cataloged according to their current dynamics, together with the transitions that occur in the given time frame from a given type of co-orbital motion to another. The results provide a general catalog of co-orbital asteroids in the solar system, the first one to our knowledge, and an efficient mean to study transitions.

In the recent papers~[18],~[5], respectively, the existence of motions where the perihelions afford periodic oscillations about certain equilibria and the onset of a topological horseshoe have been proved. Such results have been obtained using, as neighbouring integrable system, the so--called two--centre (or {\it Euler}) problem and a suitable canonical setting proposed in~[16],~[17]. Here we review such results., Comment: 27 pages, 3 figures

We study the finite-temperature deformation of the discrete Bessel point process. We show that its largest particle distribution satisfies a reduction of the 2D Toda equation, as well as a discrete version of the integro-differential Painlev\'e II equation of Amir-Corwin-Quastel, and we compute initial conditions for the Poissonization parameter equal to 0. As proved by Betea and Bouttier, in a suitable continuum limit the last particle distribution converges to that of the finite-temperature Airy point process. We show that the reduction of the 2D Toda equation reduces to the Korteweg-de Vries equation, as well as the discrete integro-differential Painlev\'e II equation reduces to its continuous version. Our approach is based on the discrete analogue of Its-Izergin-Korepin-Slavnov theory of integrable operators developed by Borodin and Deift., Comment: 28 pages. V2: minor corrections

Technological tests of Total Ionizing Dose effects are required not only for silicon particle sensors developed in high energy physics experiments, but also for electronic devices and semiconductor elements used in commercial, automotive and space applications. Using x-ray irradiators, these technological tests and studies can be performed not only in facilities explicitly built for this mission, but also in medical or biological research facilities when some minima requirements are satisfied. Generally this irradiation can be performed without interfering with the medical and biological activities of the facility. In this article will be described the minimum instrumentation required for this type of studies and will be given a detailed description of the preparation and realization of a SiPM x-ray irradiation campaign for TID characterization realized in the Italian TIFPA-INFN Trento Center Laboratory in May 2021, using instruments originally realized for medical and biological irradiation., Comment: 4 pages, 1 figure, proceeding of the Proceedings of the African Conference on Fundamental and Applied Physics

In this paper we address, from a purely numerical point of view, the question, raised in [20, 21], and partly considered in [22, 9, 3], whether a certain function, referred to as "Euler Integral", is a quasi-integral along the trajectories of the three-body problem. Differently from our previous investigations, here we focus on the region of the "unperturbed separatrix", which turns to be complicated by a collision singularity. Concretely, we reduce the Hamiltonian to two degrees of freedom and, after fixing some energy level, we discuss in detail the resulting three-dimensional phase space around an elliptic and an hyperbolic periodic orbit. After measuring the strength of variation of the Euler Integral (which are in fact small), we detect the existence of chaos closely to the unperturbed separatrix. The latter result is obtained through a careful use of the machinery of covering relations, developed in [13, 24, 23]., Comment: This paper is supported by the the ERC project 677793 Stable and Chaotic Motions in the Planetary Problem (2016-2022)

Dubrovin has shown that the spectrum of the quantization (with respect to the first Poisson structure) of the dispersionless Korteweg-de Vries (KdV) hierarchy is given by shifted symmetric functions; the latter are related by the Bloch-Okounkov Theorem to quasimodular forms on the full modular group. We extend the relation to quasimodular forms to the full quantum KdV hierarchy (and to the more general quantum Intermediate Long Wave hierarchy). These quantum integrable hierarchies have been defined by Buryak and Rossi in terms of the Double Ramification cycle in the moduli space of curves. The main tool and conceptual contribution of the paper is a general effective criterion for quasimodularity., Comment: 22 pages; V2: minor corrections, Appendix B added

The n-body problem is one of the most important issue in Celestial Mechanics. This article aims to retrace the historical and scientific events that led the Paduan mathematician, Tullio Levi-Civita, to deal with the problem first from a classic and then a relativistic point of view. We describe Levi-Civita's contributions to the theory of relativity focusing on his epistolary exchanges with Einstein, on the problem of secular acceleration and on the proof of Brillouin's cancellation principle. We also point out that the themes treated by Levi-Civita are very topical. Specifically, we analyse how the mathematical formalism used nowadays to test General Relativity can be found in Levi-Civita's texts and evolves over the years up to the current Parametrized version of the Post-Newtonian approximation (PPN) which is used in high precision contexts such as important space missions designed also to test General Relativity and which aim to estimate with very high accuracy the PPN parameters., Comment: 18 pages, 2 figures

Silicon Photo-multipliers (SiPMs) are very sensitive photo-detectors that experienced a big development in the last years in several applications, like LIDAR, astrophysics, medical imaging and high energy physics (HEP) experiments. In HEP experiments, in particular, they are often exposed to significant radiation doses. The main purpose of this manuscript is the characterization of several FBK SiPM technologies when exposed to 74 $MeV$ protons with a total fluence comparable to the one that they would experience in space along circular Low Earth Orbits (LEO), Polar, during a five years mission. In this work, we estimated the expected proton fluences along the selected orbit, by means of the SPENVIS software. Several fluence steps were chosen to consider dense fluence intervals and have a more accurate sight on the whole damage process. We estimated a maximum fluence achieved during the tests of $6.4 \times 10^{11}$ $n_{eq}/cm^2$. Based on such simulations, we irradiated several SiPM technologies. We developed a custom experimental setup, which was used to perform online reverse voltage-current, right after each irradiation step, to minimize the effect of the annealing on the measurement. The results are then displayed, in particular the currents, the noise and the Photon Detection Efficiency. Also a 30-days study on the annealing of the devices was performed. Lastly, the conclusions are drawn on the basis of the Signal-to-Noise Ratio (SNR), taking into account the standard parameters of famous satellites using similar orbits as the ones considered into this work.

We discuss the results of a proton irradiation campaign of a GAGG:Ce (Cerium-doped Gadolinium Aluminium Gallium Garnet) scintillation crystal, carried out in the framework of the HERMES-TP/SP (High Energy Rapid Modular Ensemble of Satellites -- Technological and Scientific Pathfinder) mission. A scintillator sample was irradiated with 70 MeV protons, at levels equivalent to those expected in equatorial and sun-synchronous low-Earth orbits over orbital periods spanning 6 months to 10 years. The data we acquired are used to introduce an original model of GAGG:Ce afterglow emission. Results from this model are applied to the HERMES-TP/SP scenario, aiming at an upper-bound estimate of the detector performance degradation resulting from afterglow emission.

We obtain uniform asymptotics for deformed Airy kernel determinants, which arise in models of finite temperature free fermions and which characterize the narrow wedge solution of the Kardar-Parisi-Zhang equation. The asymptotics for the determinants yield uniform initial data for an associated family of solutions to the Korteweg-de Vries equation, and uniform lower tail asymptotics for the narrow wedge solution of the Kardar-Parisi-Zhang equation., Comment: 43 pages, 3 figures V2: minor revision

A study of initial-state gluon radiation (ISR) in hadron collisions is presented using Drell-Yan (DY) events produced in proton-antiproton collisions by the Tevatron collider at a center-of-mass energy of 1.96 TeV. This paper adopts a novel approach which uses the mean value of the Z/$\gamma^*$ transverse momentum $$ in DY events as a powerful observable to characterize the effect of ISR. In a data sample corresponding to an integrated luminosity of 9.4 fb$^{-1}$ collected with the CDF Run II detector, $$ is measured as a function of the Z/$\gamma^*$ invariant mass. It is found that these two observables have a dependence, $ = -8 + 2.2 \ln m_{DY}^2$ [GeV/c], where $m_{DY}$ is the value of the Z/$\gamma^*$ mass measured in units of GeV/$c^2$. This linear dependence is observed for the first time in this analysis. It may be exploited to model the effect of ISR and constrain its impact in other processes., Comment: 14 pages, 14 figures

At the Fermilab Tevatron proton-antiproton ($p\bar{p}$) collider, high-mass electron-neutrino ($e\nu$) pairs are produced predominantly in the process $p \bar{p} \rightarrow W(\rightarrow e\nu) + X$. The asymmetry of the electron and positron yield as a function of their pseudorapidity constrain the slope of the ratio of the $u$- to $d$-quark parton distributions versus the fraction of the proton momentum carried by the quarks. This paper reports on the measurement of the electron-charge asymmetry using the full data set recorded by the Collider Detector at Fermilab in 2001--2011 and corresponding to 9.1~fb$^{-1}$ of integrated luminosity. The measurement significantly improves the precision of the Tevatron constraints on the parton-distribution functions of the proton. Numerical tables of the measurement are provided., Comment: 27 pages, 25 figures. To be published in PRD

The spectral problem for the quantum dispersionless Korteweg-de Vries (KdV) hierarchy, aka the quantum Hopf hierarchy, is solved by Dubrovin. In this article, following Dubrovin, we study Buryak-Rossi's quantum KdV hierarchy. In particular, we prove a symmetry property and a non-degeneracy property for the quantum KdV Hamiltonians. On the basis of this we construct a complete set of common eigenvectors. The analysis underlying this spectral problem implies certain vanishing identities for combinations of characters of the symmetric group. We also comment on the geometry of the spectral curves of the quantum KdV hierarchy and we give a representation of the quantum dispersionless KdV Hamiltonians in terms of multiplication operators in the class algebra of the symmetric group., Comment: 21 pages

We consider the moduli space of vector bundles of rank $n$ and degree $ng$ over a fixed Riemann surface of genus $g\geq 2$. We use the explicit parametrization in terms of the Tyurin data. In the moduli space there is a "non-abelian" Theta divisor, consisting of bundles with $h^1\geq 1$. On the complement of this divisor we construct a non-abelian Cauchy kernel explicitly in terms of the Tyurin data. With the additional datum of a non-special divisor, we can construct a reference flat holomorphic connection which is also dependent holomorphically on the moduli of the bundle. This allows us to identify the bundle of Higgs fields, i.e. the cotangent bundle of the moduli space, with the affine bundle of holomorphic connections and provide a monodromy map into the ${\rm GL}_n$ character variety. We show that the Goldman symplectic structure on the character variety pulls back along this map to the complex canonical symplectic structure on the cotangent bundle and hence also on the space of affine connections. The pull-back of the Liouville one-form to the affine bundle of connections is then shown to be a logarithmic form with poles along the non-abelian theta divisor and residue given by $h^1$., Comment: V2: 29 pages, figure added and more accurate review of literature. V3: 31 pages, minor revision

GAGG:Ce (Cerium-doped Gadolinium Aluminium Gallium Garnet) is a promising new scintillator crystal. A wide array of interesting features, such as high light output, fast decay times, almost non-existent intrinsic background and robustness, make GAGG:Ce an interesting candidate as a component of new space-based gamma-ray detectors. As a consequence of its novelty, literature on GAGG:Ce is still lacking on points crucial to its applicability in space missions. In particular, GAGG:Ce is characterized by unusually high and long-lasting delayed luminescence. This afterglow emission can be stimulated by the interactions between the scintillator and the particles of the near-Earth radiation environment. By contributing to the noise, it will impact the detector performance to some degree. In this manuscript we summarize the results of an irradiation campaign of GAGG:Ce crystals with protons, conducted in the framework of the HERMES-TP/SP (High Energy Rapid Modular Ensemble of Satellites - Technological and Scientific Pathfinder) mission. A GAGG:Ce sample was irradiated with 70 MeV protons, at doses equivalent to those expected in equatorial and sun-synchronous Low-Earth orbits over orbital periods spanning 6 months to 10 years, time lapses representative of satellite lifetimes. We introduce a new model of GAGG:Ce afterglow emission able to fully capture our observations. Results are applied to the HERMES-TP/SP scenario, aiming at an upper-bound estimate of the detector performance degradation due to the afterglow emission expected from the interaction between the scintillator and the near-Earth radiation environment., Comment: 8 pages, 3 figures. Proceedings of SPIE "Astronomical Telescopes and Instrumentation" 2020

We express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix ensembles. We also provide effective formulae for generating functions of multipoint correlators of the Jacobi Unitary Ensemble in terms of Wilson polynomials, generalizing the known relations between one point correlators and Wilson polynomials., Comment: 28 pages V3: section 3 revised

The FragmentatiOn Of Target (FOOT) experiment aims to provide precise nuclear cross-section measurements for two different fields: hadrontherapy and radio-protection in space. The main reason is the important role the nuclear fragmentation process plays in both fields, where the health risks caused by radiation are very similar and mainly attributable to the fragmentation process. The FOOT experiment has been developed in such a way that the experimental setup is easily movable and fits the space limitations of the experimental and treatment rooms available in hadrontherapy treatment centers, where most of the data takings are carried out. The Trigger and Data Acquisition system needs to follow the same criteria and it should work in different laboratories and in different conditions. It has been designed to acquire the largest sample size with high accuracy in a controlled and online-monitored environment. The data collected are processed in real-time for quality assessment and are available to the DAQ crew and detector experts during data taking.

We study a family of unbounded solutions to the Korteweg-de Vries equation which can be constructed as log-derivatives of deformed Airy kernel Fredholm determinants, and which are connected to an integro-differential version of the second Painlev\'e equation. The initial data of the Korteweg-de Vries solutions are well-defined for $x>0$, but not for $x<0$, where the solutions behave like $\frac{x}{2t}$ as $t\to 0$, and hence would be well-defined as solutions of the cylindrical Korteweg-de Vries equation. We provide uniform asymptotics in $x$ as $t\to 0$; for $x>0$ they involve an integro-differential analogue of the Painlev\'e V equation. A special case of our results yields improved estimates for the {tails} of the narrow wedge solution to the Kardar-Parisi-Zhang equation., Comment: 44 pages

We highlight the existence of a topological horseshoe arising from a a--priori stable model of the binary asteroid dynamics. The inspection is numerical and uses correctly aligned windows, as described in a recent paper by A. Gierzkiewicz and P. Zgliczy\'nski, combined with a recent analysis of an associated secular problem., Comment: 20 pages, 10 figures

Inspired by recent formul\ae\ of Dubrovin, Yang, and Zagier, we interpret the tau function enumerating stationary Gromov-Witten invariants of $\mathbb{P}^1$ as an isomonodromic tau function associated with a difference equation. As a byproduct we obtain an analogue of the Kontsevich matrix model for this tau function. A connection with the Charlier ensemble is also considered., Comment: v3: new appendix B

We consider the Laguerre partition function, and derive explicit generating functions for connected correlators with arbitrary integer powers of traces in terms of products of Hahn polynomials. It was recently proven that correlators have a topological expansion in terms of weakly or strictly monotone Hurwitz numbers, that can be explicitly computed from our formulae. As a second result we identify the Laguerre partition function with only positive couplings and a special value of the parameter $\alpha=-1/2$ with the modified GUE partition function, which has recently been introduced as a generating function of Hodge integrals. This identification provides a direct and new link between monotone Hurwitz numbers and Hodge integrals., Comment: 41 pages. v5: the value of the normalization constant $C_N$ in Theorem 1.5 has been corrected. No other result in the paper is affected by this change