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This paper deals with explicit upper and lower bounds for principal eigenvalues and the maximum principle associated to generalized Lane-Emden systems (GLE systems, for short). Regarding the bounds, we generalize the upper estimate of Berestycki, Nirenberg and Varadhan [Comm. Pure Appl. Math. (1994), 47-92] for the first eigenvalue of linear scalar problems on general domains to the case of strongly coupled GLE systems with $m \geqslant 2$ equations on smooth domains. The explicit lower estimate we obtain is also used to derive a maximum principle to GLE systems relying in terms of quantitative ingredients. Furthermore, as applications of the previous results, upper and lower estimates for the first eigenvalue of weighted poly-Laplacian eigenvalue problems with $L^p$ weights $(p>n)$ and Navier boundary condition are obtained. Moreover, a strong maximum principle depending on the domain and the weight function for scalar problems involving the poly-Laplacian operator is also established.

Graph generation is fundamental in diverse scientific applications, due to its ability to reveal the underlying distribution of complex data, and eventually generate new, realistic data points. Despite the success of diffusion models in this domain, those face limitations in sampling efficiency and flexibility, stemming from the tight coupling between the training and sampling stages. To address this, we propose DeFoG, a novel framework using discrete flow matching for graph generation. DeFoG employs a flow-based approach that features an efficient linear interpolation noising process and a flexible denoising process based on a continuous-time Markov chain formulation. We leverage an expressive graph transformer and ensure desirable node permutation properties to respect graph symmetry. Crucially, our framework enables a disentangled design of the training and sampling stages, enabling more effective and efficient optimization of model performance. We navigate this design space by introducing several algorithmic improvements that boost the model performance, consistently surpassing existing diffusion models. We also theoretically demonstrate that, for general discrete data, discrete flow models can faithfully replicate the ground truth distribution - a result that naturally extends to graph data and reinforces DeFoG's foundations. Extensive experiments show that DeFoG achieves state-of-the-art results on synthetic and molecular datasets, improving both training and sampling efficiency over diffusion models, and excels in conditional generation on a digital pathology dataset.

Binary asteroid formation is a highly complex process, which has been highlighted with recent observations of satellites with unexpected shapes, such as the oblate Dimorphos by the NASA DART mission and the contact binary Selam by NASA's Lucy mission. There is no clear consensus on which dynamical mechanisms determine the final shape of these objects. In turn, we explore a formation pathway where spin-up and rotational failure of a rubble pile asteroid lead to mass-shedding and a wide circumasteroidal debris disk in which the satellite forms. Using a combination of smooth-particle hydrodynamical and N-body simulations, we study the dynamical evolution in detail. We find that a debris disk containing matter corresponding to a few percent of the primary asteroid mass extending beyond the fluid Roche limit can consistently form both oblate and bilobate satellites via a series of tidal encounters with the primary body and mergers with other gravitational aggregates. Principally, satellites end up prolate (elongated) and on synchronous orbits, accreting mainly in a radial direction while tides from the primary asteroid keep the shape intact. However, close encounters and mergers can break the orbital state, leading to orbital migration and deformation. Satellite-satellite impacts occurring in this regime have lower impact velocities than merger-driven moon formation in e.g. planetary rings, leading to soft impacts between differently sized, non-spherical bodies. The resulting post-merger shape of the satellite is highly dependent on the impact geometry. Only moons having experienced a prior mild or catastrophic tidal disruption during a close encounter with the primary asteroid can become oblate spheroids, which is consistent with the predominantly prolate observed population of binary asteroid satellites., Comment: 37 pages, 24 figures, 3 tables. Accepted for publication in Icarus

Reactive graphs are transition structures whereas edges become active and inactive during its evolution, that were introduced by Dov Gabbay from a mathematical's perspective. This paper presents Marge (https://fm-dcc.github.io/MARGe), a web-based tool to visualise and analyse reactive graphs enriched with labels. Marge animates the operational semantics of reactive graphs and offers different graphical views to provide insights over concrete systems. We motivate the applicability of reactive graphs for adaptive systems and for featured transition systems, using Marge to tighten the gap between the existing theoretical models and their usage to analyse concrete systems., Comment: Companion paper of an article accepted at FACS 2024 with a similar name

The dynamics of non-equilibrium closed quantum systems and their route to thermalization are of fundamental interest to several fields, from cosmology to particle physics. However, a comprehensive description of non-equilibrium phenomena still presents a significant challenge. In this work, we report the observation of distinct stages during the relaxation of the decaying turbulence in trapped Bose-Einstein condensates. Our findings show a direct particle cascade from low to high momenta, a consequence of the energy injection in the system, exhibiting a characteristic universal scaling. This stage is followed by an inverse particle cascade responsible for repopulating the previously depleted condensate. Both cascades can be explained through self-similar solutions provided by wave turbulence theory. These findings provide important insights into the relaxation stages of out-of-equilibrium quantum many-body systems.

Strongly interacting systems appear in several areas of physics and are characterized by attractive interactions that can almost, or just barely, loosely bind two particles. Although this definition is made at the two-body level, this gives rise to fascinating effects in larger systems, including the so-called Efimov physics. In this context, the zero-range theory aims to describe low-energy properties based only on the scattering length. However, for a broad range of physical applications, the finite range of the interactions plays an important role. In this work, I discuss some aspects of finite-range effects in strongly interacting systems. I present the zero-range and shapeless universalities in two-body systems with applications in atomic and nuclear physics. I derived an analytical expression for the $s$-wave bound-state spectrum of the modified P\"oschl-Teller potential for two particles in three dimensions, which is compared with the approximations to illustrate their usefulness. Concerning three identical bosons, I presented a trimer energy scaling function that explicitly includes the effective range. The implications for larger systems are briefly discussed., Comment: 22 pages, 5 figures

Graph diffusion models have emerged as state-of-the-art techniques in graph generation, yet integrating domain knowledge into these models remains challenging. Domain knowledge is particularly important in real-world scenarios, where invalid generated graphs hinder deployment in practical applications. Unconstrained and conditioned graph generative models fail to guarantee such domain-specific structural properties. We present ConStruct, a novel framework that allows for hard-constraining graph diffusion models to incorporate specific properties, such as planarity or acyclicity. Our approach ensures that the sampled graphs remain within the domain of graphs that verify the specified property throughout the entire trajectory in both the forward and reverse processes. This is achieved by introducing a specific edge-absorbing noise model and a new projector operator. ConStruct demonstrates versatility across several structural and edge-deletion invariant constraints and achieves state-of-the-art performance for both synthetic benchmarks and attributed real-world datasets. For example, by leveraging planarity in digital pathology graph datasets, the proposed method outperforms existing baselines and enhances generated data validity by up to 71.1 percentage points.

Quantum Machine Learning investigates the possibility of quantum computers enhancing Machine Learning algorithms. Anomaly segmentation is a fundamental task in various domains to identify irregularities at sample level and can be addressed with both supervised and unsupervised methods. Autoencoders are commonly used in unsupervised tasks, where models are trained to reconstruct normal instances efficiently, allowing anomaly identification through high reconstruction errors. While quantum autoencoders have been proposed in the literature, their application to anomaly segmentation tasks remains unexplored. In this paper, we introduce a patch-based quantum autoencoder (QPB-AE) for image anomaly segmentation, with a number of parameters scaling logarithmically with patch size. QPB-AE reconstructs the quantum state of the embedded input patches, computing an anomaly map directly from measurement through a SWAP test without reconstructing the input image. We evaluate its performance across multiple datasets and parameter configurations and compare it against a classical counterpart.

With the advances in the optimization of magnetic field equilibria, stellarators have become a serious alternative to the tokamak, bringing this concept to the forefront of the pursuit of fusion energy. In order to be successful in experimentally demonstrating the viability of optimized stellarators, we must overcome any potential hurdles in the construction of its electromagnetic coils. Finding cost-effective ways of increasing the number of operating optimized stellarators could be key in cementing this magnetic confinement concept as a contender for a reactor. In this work, an alternative to modular coils, permanent magnets, are studied and are shown to enable the possibility of converting a tokamak into a stellarator. This is then applied to the case of ISTTOK tokamak, where an engineering design study is conducted., Comment: 34 pages, 24 figures

Target of NASA's DART mission, the system of Didymos and Dimorphos will once again be visited by a space mission -- ESA's Hera mission, scheduled to be launch in 2024. Hera will arrive in the system approximately 4 years after the DART impact, a long period compared to Dimorphos' orbital period (about 12 hours). It is therefore imperative to understand the dynamics of material in this environment on a long timescale. Here, we explore the long-term dynamics of the binary system (65038) Didymos, in the context of the perturbed, planar, circular and restricted 3-body problem. We design an analytical description for a symmetrical top-shaped object, the shape assumed for the Didymos, while the Dimorphos is considered an ellipsoid. In the absence of external effects, we identify seven stable equatorial regions where particles persist for more than a decade. However, in the presence of the solar radiation effect, the lifetime of small particles (

Dimorphos' oblate shape challenges formation models. Landslides on Didymos, induced by YORP effect, probably created a debris ring from which Dimorphos would have formed. Nonetheless, ring-derived satellites typically form with a prolate lemon shape. In light of the newest Dimorphos shape model, we revisit our previous work, Madeira et al. (2023a), and conducted new 1D simulations with material deposition in an extended region from 1.0 to 1.5 Didymos radii. An instantaneous landslide leads to a fast formation of a prolate Dimorphos directly from the ring. Now, if Didymos progressively deposits mass, Dimorphos grows through low-velocity impacts with large impactor-to-target mass ratio (pyramidal regime growth). Even during rapid, day-scale depositions, Dimorphos experiences one of these impacts, while for slower depositions, the satellite formation is primarily via pyramidal impacts. This process might reshape the satellite into an oblate shape (Leleu et al., 2018) or even in a contact-binary shape, a scenario worthy of investigation that should be studied in the future with more suitable tools. Our conclusions can be applied to Dinkinesh's satellite, recently discovered by NASA's Lucy mission., Comment: Note accepted for publication in Icarus journal

Graph-based representation approaches have been proven to be successful in the analysis of biomedical data, due to their capability of capturing intricate dependencies between biological entities, such as the spatial organization of different cell types in a tumor tissue. However, to further enhance our understanding of the underlying governing biological mechanisms, it is important to accurately capture the actual distributions of such complex data. Graph-based deep generative models are specifically tailored to accomplish that. In this work, we leverage state-of-the-art graph-based diffusion models to generate biologically meaningful cell-graphs. In particular, we show that the adopted graph diffusion model is able to accurately learn the distribution of cells in terms of their tertiary lymphoid structures (TLS) content, a well-established biomarker for evaluating the cancer progression in oncology research. Additionally, we further illustrate the utility of the learned generative models for data augmentation in a TLS classification task. To the best of our knowledge, this is the first work that leverages the power of graph diffusion models in generating meaningful biological cell structures.

We are concerned with the existence of solution of the problem $ -\Delta ^H_pu+|u|^{p-2}u=\lambda|u|^{q-2}u+ |u|^{p^*-2}u\quad \mbox{in}\quad\Omega,$ $u>0\quad \mbox{in}\quad\Omega,$ $a(\nabla u)\cdot \nu =0\quad \mbox{on}\quad\partial \Omega,$ where $\Delta ^H_pu=\mbox{div\,}(a(\nabla u))$, with $a(\xi)=H^{p-1}(\xi)\nabla H(\xi),\, \xi \in \mathbb{R}^N,$ $N\geqslant3,$ is the anisotropic $p$-Laplacian with $10$ is a parameter, and $p < q

Recent progress in out-of-equilibrium closed quantum systems has significantly advanced the understanding of mechanisms behind their evolution towards thermalization. Notably, the concept of non-thermal fixed points (NTFPs) - responsible for the emergence of spatio-temporal universal scaling in far-from-equilibrium systems - has played a crucial role in both theoretical and experimental investigations. In this work, we introduce a differential equation that has the universal scaling associated with NTFPs as a solution. The advantage of working with a differential equation, rather than only with its solution, is that we can extract several insightful properties not necessarily present in the solution alone. How the differential equation is derived allows physical interpretation of the universal exponents in terms of the time dependence of the amplitude of the distributions and their momentum scaling. Employing two limiting cases of the equation, we determined the universal exponents related to the scaling using the distributions near just two momentum values. We established a solid agreement with previous investigations by validating this approach with three distinct physical systems. This consistency highlights the universal nature of scaling due to NTFPs and emphasizes the predictive capabilities of the proposed differential equation. Moreover, under specific conditions, the equation predicts a power-law related to the ratio of the two universal exponents, leading to implications concerning particle and energy transport. This suggests that the observed power-laws in far-from-equilibrium turbulent fluids could be related to the universal scaling due to NTFPs, potentially offering new insights into the study of turbulence., Comment: 8 pages, 6 figures

Chariklo has two narrow and dense rings, C1R and C2R, located at 391 km and 405 km, respectively. In the light of new stellar occultation data, we study the stability around Chariklo. We also analyse three confinement mechanisms, to prevent the spreading of the rings, based on shepherd satellites in resonance with the edges of the rings. This study is made through a set of numerical simulations and the Poincar\'e surface of section technique. From the numerical simulation results we verify that, from the current parameters referring to the shape of Chariklo, the inner edge of the stable region is much closer to Chariklo than the rings. The Poincar\'e surface of sections allow us to identify the first kind periodic and quasi-periodic orbits, and also the resonant islands corresponding to the 1:2, 2:5, and 1:3 resonances. We construct a map of a versus e space which gives the location and width of the stable region and the 1:2, 2:5, and 1:3 resonances. We found that the first kind periodic orbits family can be responsible for a stable region whose location and size meet that of C1R, for specific values of the ring particles' eccentricities. However, C2R is located in an unstable region if the width of the ring is assumed to be about 120 m. After analysing different systems we propose that the best confinement mechanism is composed of three satellites, two of them shepherding the inner edge of C1R and the outer edge of C2R, while the third satellite would be trapped in the 1:3 resonance., Comment: Accepted for publication in Astronomy & Astrophysics

Often in Software Engineering, a modeling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such formalism: states evolve through two accessibility relations capturing weighted evidence of a transition or its absence, respectively. Their weights come from a specific residuated lattice. A category of these systems, and the corresponding algebra, is defined as providing a formal setting to model different application scenarios. One of them, dealing with the effect of quantum decoherence in quantum programs, is used for illustration purposes., Comment: In Proceedings LSFA 2022, arXiv:2303.12680

Scattering processes are a fundamental way of experimentally probing distributions and properties of systems in several areas of physics. Considering two-body scattering at low energies, when the de Broglie wavelength is larger than the range of the potential, partial waves with high angular momentum are typically unimportant. The dominant contribution comes from $l=0$ partial waves, commonly known as $s$-wave scattering. This situation is very relevant in atomic physics, e.g. cold atomic gases, and nuclear physics, e.g. nuclear structure and matter. This manuscript is intended as a pedagogical introduction to the topic while covering a numerical approach to compute the desired quantities. We introduce low-energy scattering with particular attention to the concepts of scattering length and effective range. These two quantities appear in the effective-range approximation, which universally describes low-energy processes. We outline a numerical procedure for calculating the scattering length and effective range of spherically symmetric two-body potentials. As examples, we apply the method to the spherical well, modified P\"oschl-Teller, Gaussian, and Lennard-Jones potentials. We hope to provide the tools so students can implement similar calculations and extend them to other potentials., Comment: 19+5 pages, 10+1 figures

This paper presents our methodology to simulate the behavior of the DeLend Platform. Such simulations are important to verify if the system is able to connect the different sets of agents linked to the platform in a functional manner. They also provide inputs to guide the choices of operational parameters, such as the platform spread, and strategies by DeLend, since they estimate how the key variables of interest respond to different policies. We discuss the methodology and provide examples meant to clarify the approach and to how we intend to use the tool in practice -- they should not be interpreted as representative of real life scenarios.

Phobos is the target of the return sample mission Martian Moons eXploration by JAXA that will analyze in great details the physical and compositional properties of the satellite from orbit, from the surface and in terrestrial laboratories, giving clues about its formation. Some models propose that Phobos and Deimos were formed after a giant impact giving rise to an extended debris disk. Assuming that Phobos formed from a cascade of disruptions and re-accretions of several parent bodies in this disk, and that they are all characterized by a low material cohesion, Hesselbrock & Milton (2017) have showed that a recycling process may happen during the assembling of Phobos, by which Phobos' parents are destroyed into a Roche-interior ring and reaccreted several times. In the current paper we explore in details the recycling model, and pay particular attention to the characteristics of the disk using 1D models of disk/satellite interactions. In agreement with previous studies we confirm that, if Phobos' parents bodies are gravitational aggregates (rubble piles), then the recycling process does occur. However, Phobos should be accompanied today by a Roche-interior ring. Furthermore, the characteristics of the ring are not reconcilable with today`s observations of Mars' environment, which put stringent constraints on the existence of a ring around Mars. The recycling mechanism may or may not have occurred at the Roche limit for an old moon population, depending on their internal cohesion. However, the Phobos we see today cannot be the outcome of such a recycling process., Comment: Accept in The Astronomical Journal

Didymos is a binary near-Earth asteroid. It is the target of the DART and HERA space missions. The primary body, Didymos, rotates close to the spin at which it is expected to shed mass. The secondary body, Dimorphos, is a 140 meters moon that orbits the primary body in about 12 hours. Here we investigate the possible origin of Dimorphos. Using 1D models of ring/satellite interactions, we study the evolution of material lost from Didymos' surface and deposited as a ring at its equator. We find that due to viscous spreading, the ring spreads outside the Didymos' Roche limit forming moonlets. A fraction of the mass will form Dimorphos and a set of objects near the Roche limit, while most of the ring's mass falls back on Didymos. To match the properties of today's Dimorphos, the total mass that must be deposited in the ring is about 25% of Didymos' mass. It is possible that a fraction of the material travelled several times between the ring and the surface of Didymos. The models produce an orbit similar to that observed for a Didymos tidal parameter k2/Q<1e-5. If the ring deposition timescale is long (>100 yr) (so the material flux is small) Dimorphos could be irregularly shaped as it forms from the collision of similar-sized satellitesimals. However, the top-shape of Didymos is expected to be achieved due to a fast spin-up of the asteroid, which would result in a short deposition timescale (

We studied a rotating Bose-Einstein condensate confined in ring trap configurations that can be produced starting with a bubble trap confinement, approximated by a Mexican hat and shifted harmonic oscillator potentials. Using a variational technique and perturbation theory, we determined the vortex configurations in this system by varying the interparticle interaction and the angular velocity of the atomic cloud. We found that the phase diagram of the system has macrovortex structures for small positive values of the interaction parameter, and the charge of the central vortex increases with rotation. Strengthening the atomic interaction makes the macrovortex unstable, and it decays into multiple singly-charged vortices that arrange themselves in a lattice configuration. We also look for experimentally realizable methods to determine the vortex configuration without relying upon absorption imaging since the structures are not always visible in the latter. More specifically, we study how the vortex distribution affects the collective modes of the condensate by solving the Gross-Pitaevskii equation numerically and by analytical predictions using the sum-rule approach for the frequencies of the modes. These results reveal important signatures to characterize the macrovortices and vortex lattice transitions in the experiments., Comment: 20 pages, 15 figures

We study the effects of quasidisorder and Anderson disorder on a two dimensional topological superconductor with an applied external magnetic field. The cases of a $p$-wave superconductor and a noncentrosymmetric superconductor with mixed $p$ and $s$-wave pairings and Rashba spin-orbit coupling are studied. We show that, for a perpendicular magnetic field, the introduction of quasidisorder leads to the appearance of topological phases in new regions, characterised by an integer value of the Chern number. For a parallel magnetic field, we identify regimes with the appearance of new Majorana flat bands and also new unidirectional Majorana edge states, as quasidisorder is introduced. We show that the Majorana flat bands have a quantized Berry phase of $\pi$ and identify it as a topological invariant. Two topological transitions are identified and the values of the critical exponents $z$ and $\nu$ are obtained. The fractal nature of the eigenstates is discussed both for Anderson disorder and Aubry-Andr\'e disorder., Comment: 23 pages, 27 figures. Accepted for publication in The Physical Review B

Collaborative Filtering (CF), the most common approach to build Recommender Systems, became pervasive in our daily lives as consumers of products and services. However, challenges limit the effectiveness of Collaborative Filtering approaches when dealing with recommendation data, mainly due to the diversity and locality of user preferences, structural sparsity of user-item ratings, subjectivity of rating scales, and increasingly high item dimensionality and user bases. To answer some of these challenges, some authors proposed successful approaches combining CF with Biclustering techniques. This work assesses the effectiveness of Biclustering approaches for CF, comparing the impact of algorithmic choices, and identifies principles for superior Biclustering-based CF. As a result, we propose USBFC, a Biclustering-based CF approach that creates user-specific models from strongly coherent and statistically significant rating patterns, corresponding to subspaces of shared preferences across users. Evaluation on real-world data reveals that USBCF achieves competitive predictive accuracy against state-of-the-art CF methods. Moreover, USBFC successfully suppresses the main shortcomings of the previously proposed state-of-the-art biclustering-based CF by increasing coverage, and coclustering-based CF by strengthening subspace homogeneity.

We consider the influence of topological phases, or their vicinity, on the spin density and spin polarization through a chiral chain. We show the quantization of the Berry phase in a one-dimensional polarization helix structure, under the presence of an external magnetic field, and show its influence on the spin density. The polar angle of the momentum space spin density becomes quantized in the regime that the Berry phase is quantized, as a result of the combined effect of the induced spin-orbit coupling and the external transverse magnetic field, while the edge states do not show the polar angle quantization, in contrast with the bulk states. Under appropriate conditions, the model can be generalized to have similarities with a chain with nonhomogeneous Rashba spin- orbit couplings, with zero- or low-energy edge states. Due to the breaking of time-reversal symmetry, we recover the effect of chiral-induced spin polarization and spin transport across the chiral chain, when coupling to external leads. Some consequences of the quantized spin polarization and low-energy states on the spin transport are discussed., Comment: 16 figures

The origin and evolution of Martian moons have been intensively debated in recent years. It is proposed that Phobos and Deimos may originate directly from a splitting of an ancestral moon orbiting at around the Martian synchronous orbit. At this hypothetical splitting, the apocenter of the inner moon (presumed as Phobos) and the pericenter of the outer moon (presumed as Deimos) are reported to coincide, in that, their semi-major axes reside inside and outside the Martian synchronous orbit with non-zero eccentricities, respectively. However, the successive orbital evolution of the two moons is not studied. Here, we perform direct $N$-body orbital integrations of the moons, including the Martian oblateness of the $J_2$ and $J_4$ terms. We show that the two moons, while they precess, likely collide within $\sim 10^4$ years with an impact velocity of $v_{\rm imp} \sim 100-300$ m s$^{-1}$ ($\sim 10-30$ times moons' escape velocity) and with an isotropic impact direction. The impact occurs around the apocenter and the pericenter of the inner and outer moons, respectively, where the timescale of this periodic orbital alignment is regulated by the precession. By performing additional impact simulations, we show that such a high-velocity impact likely results in a disruptive outcome, forming a debris ring at around the Martian synchronous orbit, from which several small moons would accrete. Such an evolutionary path would eventually form a different Martian moons system from the one we see today. Therefore, it seems unlikely that Phobos and Deimos are split directly from a single ancestral moon., Comment: 11 pages, 5 Figures, accepted for publication in Planetary Science Journal (PSJ)

We report on large exciton tuning in WSe$_2$ monolayers via substrate induced non-degenerate doping. We observe a redshift of $\sim$62 meV for the $A$ exciton together with a 1-2 orders of magnitude photoluminescence (PL) quenching when the monolayer WSe$_2$ is brought in contact with highly oriented pyrolytic graphite (HOPG) compared to the dielectric substrates such as hBN and SiO$_2$. As the evidence of doping from HOPG to WSe$_2$, a drastic increase of the trion emission intensity was observed. Using a systematic PL and Kelvin probe force microscopy (KPFM) investigation on WSe$_2$/HOPG, WSe$_2$/hBN, and WSe$_2$/graphene, we conclude that this unique excitonic behavior is induced by electron doping from the substrate. Our results propose a simple yet efficient way for exciton tuning in monolayer WSe$_2$, which plays a central role in the fundamental understanding and further device development., Comment: 14 pages, 10 figures