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Positional Encoder Graph Neural Networks (PE-GNNs) are a leading approach for modeling continuous spatial data. However, they often fail to produce calibrated predictive distributions, limiting their effectiveness for uncertainty quantification. We introduce the Positional Encoder Graph Quantile Neural Network (PE-GQNN), a novel method that integrates PE-GNNs, Quantile Neural Networks, and recalibration techniques in a fully nonparametric framework, requiring minimal assumptions about the predictive distributions. We propose a new network architecture that, when combined with a quantile-based loss function, yields accurate and reliable probabilistic models without increasing computational complexity. Our approach provides a flexible, robust framework for conditional density estimation, applicable beyond spatial data contexts. We further introduce a structured method for incorporating a KNN predictor into the model while avoiding data leakage through the GNN layer operation. Experiments on benchmark datasets demonstrate that PE-GQNN significantly outperforms existing state-of-the-art methods in both predictive accuracy and uncertainty quantification., Comment: 17 main text pages, 4 figures

We propose a nonlinear opinion dynamics model for an agent making decisions about a continuous distribution of options in the presence of distributed input. Inspired by perceptual decision-making, we develop the theory for options distributed on the circle, representing, e.g., the set of possible heading directions in planar robotic navigation problems. Interactions among options are encoded through a spatially invariant kernel. We design the kernel to ensure that decision-making is robust, in the sense that only a finite subset of options can be favored over the continuum. We prove the spatial invariance of the model linearization and use this result to prove an opinion-forming bifurcation in the model with zero input. We then use space and time frequency domain analysis of the model linearization to infer the ultra-sensitive input-output behavior of the nonlinear dynamics with input. We illustrate our model's versatility with a robotic navigation example in crowded spaces.

Studying the orbital motion of stars around Sagittarius A* in the Galactic Center provides a unique opportunity to probe the gravitational potential near the supermassive black hole at the heart of our Galaxy. Interferometric data obtained with the GRAVITY instrument at the Very Large Telescope Interferometer (VLTI) since 2016 has allowed us to achieve unprecedented precision in tracking the orbits of these stars. GRAVITY data have been key to detecting the in-plane, prograde Schwarzschild precession of the orbit of the star S2, as predicted by General Relativity. By combining astrometric and spectroscopic data from multiple stars, including S2, S29, S38, and S55 - for which we have data around their time of pericenter passage with GRAVITY - we can now strengthen the significance of this detection to an approximately $10 \sigma$ confidence level. The prograde precession of S2's orbit provides valuable insights into the potential presence of an extended mass distribution surrounding Sagittarius A*, which could consist of a dynamically relaxed stellar cusp comprised of old stars and stellar remnants, along with a possible dark matter spike. Our analysis, based on two plausible density profiles - a power-law and a Plummer profile - constrains the enclosed mass within the orbit of S2 to be consistent with zero, establishing an upper limit of approximately $1200 \, M_\odot$ with a $1 \sigma$ confidence level. This significantly improves our constraints on the mass distribution in the Galactic Center. Our upper limit is very close to the expected value from numerical simulations for a stellar cusp in the Galactic Center, leaving little room for a significant enhancement of dark matter density near Sagittarius A*., Comment: Submitted to A&A on September 17, 2024

We present new VLTI/GRAVITY near-infrared interferometric measurements of the angular size of the innermost hot dust continuum for 14 type 1 AGNs. The angular sizes are resolved on scales of ~0.7 mas and the inferred ring radii range from 0.028 to 1.33 pc, comparable to those reported previously and a factor 10-20 smaller than the mid-infrared sizes in the literature. Combining our new data with previously published values, we compile a sample of 25 AGN with bolometric luminosity ranging from $10^{42}$ to $10^{47} \rm erg~s^{-1}$, with which we study the radius-luminosity (R-L) relation for the hot dust structure. Our interferometric measurements of radius are offset by a factor 2 from the equivalent relation derived through reverberation mapping. Using a simple model to explore the dust structure's geometry, we conclude that this offset can be explained if the 2 um emitting surface has a concave shape. Our data show that the slope of the relation is in line with the canonical $R \propto L^{0.5}$ when using an appropriately non-linear correction for bolometric luminosity. In contrast, using optical luminosity or applying a constant bolometric correction to it results in a significant deviation in the slope, suggesting a potential luminosity dependence on the spectral energy distribution. Over four orders of magnitude in luminosity, the intrinsic scatter around the R-L relation is 0.2 dex, suggesting a tight correlation between innermost hot dust structure size and the AGN luminosity., Comment: 14 pages, 5 figures, 4 tables, accepted for publication in A&A

This is the User Manual of LASPATED library. This library is available on GitHub (at https://github.com/vguigues/LASPATED)) and provides a set of tools to analyze spatiotemporal data. A video tutorial for this library is available on Youtube. It is made of a Python package for time and space discretizations and of two packages (one in Matlab and one in C++) implementing the calibration of the probabilistic models for stochastic spatio-temporal data proposed in the companion paper arXiv:2203.16371v2., Comment: 25 pages, 6 figures

The International Muon Collider Collaboration (IMCC) [1] was established in 2020 following the recommendations of the European Strategy for Particle Physics (ESPP) and the implementation of the European Strategy for Particle Physics-Accelerator R&D Roadmap by the Laboratory Directors Group [2], hereinafter referred to as the the European LDG roadmap. The Muon Collider Study (MuC) covers the accelerator complex, detectors and physics for a future muon collider. In 2023, European Commission support was obtained for a design study of a muon collider (MuCol) [3]. This project started on 1st March 2023, with work-packages aligned with the overall muon collider studies. In preparation of and during the 2021-22 U.S. Snowmass process, the muon collider project parameters, technical studies and physics performance studies were performed and presented in great detail. Recently, the P5 panel [4] in the U.S. recommended a muon collider R&D, proposed to join the IMCC and envisages that the U.S. should prepare to host a muon collider, calling this their "muon shot". In the past, the U.S. Muon Accelerator Programme (MAP) [5] has been instrumental in studies of concepts and technologies for a muon collider., Comment: This document summarises the International Muon Collider Collaboration (IMCC) progress and status of the Muon Collider R&D programme

In this work, the Ginzburg-Landau theory is represented on a symplectic manifold with a phase space content. The order parameter is defined by a quasi-probability amplitude, which gives rise to a quasi-probability distribution function, i.e., a Wigner-type function. The starting point is the thermal group representation of Euclidean symmetries and gauge symmetry. Well-known basic results on the behavior of a superconductor are re-derived, providing the consistency of representation. The critical superconducting current density is determined and its usual behavior is inferred. The negativety factor associated with the quasi-distribution function is analyzed, providing information about the non-classicality nature of the superconductor state in the region closest to the edge of the superconducting material., Comment: 9 pages, 1 figures

Since 2019, GRAVITY has provided direct observations of giant planets and brown dwarfs at separations of down to 95 mas from the host star. Some of these observations have provided the first direct confirmation of companions previously detected by indirect techniques (astrometry and radial velocities). We want to improve the observing strategy and data reduction in order to lower the inner working angle of GRAVITY in dual-field on-axis mode. We also want to determine the current limitations of the instrument when observing faint companions with separations in the 30-150 mas range. To improve the inner working angle, we propose a fiber off-pointing strategy during the observations to maximize the ratio of companion-light-to-star-light coupling in the science fiber. We also tested a lower-order model for speckles to decouple the companion light from the star light. We then evaluated the detection limits of GRAVITY using planet injection and retrieval in representative archival data. We compare our results to theoretical expectations. We validate our observing and data-reduction strategy with on-sky observations; first in the context of brown dwarf follow-up on the auxiliary telescopes with HD 984 B, and second with the first confirmation of a substellar candidate around the star Gaia DR3 2728129004119806464. With synthetic companion injection, we demonstrate that the instrument can detect companions down to a contrast of $8\times 10^{-4}$ ($\Delta \mathrm{K}= 7.7$ mag) at a separation of 35 mas, and a contrast of $3\times 10^{-5}$ ($\Delta \mathrm{K}= 11$ mag) at 100 mas from a bright primary (K<6.5), for 30 min exposure time. With its inner working angle and astrometric precision, GRAVITY has a unique reach in direct observation parameter space. This study demonstrates the promising synergies between GRAVITY and Gaia for the confirmation and characterization of substellar companions., Comment: 16 pages, 14 figures. Submitted to A&A

We derive a quantitative version of the hydrodynamic limit for an interacting particle system inspired by integrate-and-fire neuron models. More precisely, we show that the $L^2$-speed of convergence of the empirical density of states in a generalized contact process defined over a $d$-dimensional torus of size $n$ is of the optimal order $\mathcal O(n^{d/2})$. In addition, we show that the typical fluctuations around the aforementioned hydrodynamic limit are Gaussian, and governed by a inhomogeneous stochastic linear equation.

Electronic Design Automation (EDA) tools are software applications used by engineers in the design, development, simulation, and verification of electronic systems and integrated circuits. These tools typically process specifications written in a Hardware Description Language (HDL), such as Verilog, SystemVerilog or VHDL. Thus, effective testing of these tools requires benchmark suites written in these languages. However, while there exist some open benchmark suites for these languages, they tend to consist of only a handful of specifications. This paper, in contrast, presents ChiBench, a comprehensive suite comprising 50 thousand Verilog programs. These programs were sourced from GitHub repositories and curated using Verible's syntactic analyzer and Jasper(TM)'s HDL semantic analyzer. Since its inception, ChiBench has already revealed bugs in public tools like Verible's obfuscator and parser. In addition to explaining some of these case studies, this paper demonstrates how ChiBench can be used to evaluate the asymptotic complexity and code coverage of typical electronic design automation tools., Comment: 5 pages, 6 figures, 12 references

Recent work in automated program repair (APR) proposes the use of reasoning and patch validation feedback to reduce the semantic gap between the LLMs and the code under analysis. The idea has been shown to perform well for general APR, but its effectiveness in other particular contexts remains underexplored. In this work, we assess the impact of reasoning and patch validation feedback to LLMs in the context of vulnerability repair, an important and challenging task in security. To support the evaluation, we present VRpilot, an LLM-based vulnerability repair technique based on reasoning and patch validation feedback. VRpilot (1) uses a chain-of-thought prompt to reason about a vulnerability prior to generating patch candidates and (2) iteratively refines prompts according to the output of external tools (e.g., compiler, code sanitizers, test suite, etc.) on previously-generated patches. To evaluate performance, we compare VRpilot against the state-of-the-art vulnerability repair techniques for C and Java using public datasets from the literature. Our results show that VRpilot generates, on average, 14% and 7.6% more correct patches than the baseline techniques on C and Java, respectively. We show, through an ablation study, that reasoning and patch validation feedback are critical. We report several lessons from this study and potential directions for advancing LLM-empowered vulnerability repair, Comment: Code, data and artifacts are available: http://tinyurl.com/vrpilot-artifacts

Carbon-based nanostructures have unparalleled electronic properties. At the same time, using an allotrope of carbon as the contacts can yield better device control and reproducibility. In this work, we simulate a single-electron transistor composed of a segment of a graphene nanoribbon coupled to carbon nanotubes electrodes. Using the non-equilibrium Green's function formalism we atomistically describe the electronic transport properties of the system including electron-electron interactions. Using this methodology we are able to recover experimentally observed phenomena, such as the Coulomb blockade, as well as the corresponding Coulomb diamonds. Furthermore, we are able to separate the different contributions to transport and show that incoherent effects due to the interaction play a crucial role in the transport properties depending on the region of the stability diagram being considered.

In this contribution, we present a novel approach for solving the obstacle problem for (linear) conservation laws. Usually, given a conservation law with an initial datum, the solution is uniquely determined. How to incorporate obstacles, i.e., inequality constraints on the solution so that the resulting solution is still "physically reasonable" and obeys the obstacle, is unclear. The proposed approach involves scaling down the velocity of the conservation law when the solution approaches the obstacle. We demonstrate that this leads to a reasonable solution and show that, when scaling down is performed in a discontinuous fashion, we still obtain a suitable velocity - and the solution satisfying a discontinuous conservation law. We illustrate the developed solution concept using numerical approximations., Comment: 36 pages, 10 figures

Recent advances in deep learning have promoted the advent of many computational systems capable of performing intelligent actions that, until then, were restricted to the human intellect. In the particular case of human languages, these advances allowed the introduction of applications like ChatGPT that are capable of generating coherent text without being explicitly programmed to do so. Instead, these models use large volumes of textual data to learn meaningful representations of human languages. Associated with these advances, concerns about copyright and data privacy infringements caused by these applications have emerged. Despite these concerns, the pace at which new natural language processing applications continued to be developed largely outperformed the introduction of new regulations. Today, communication barriers between legal experts and computer scientists motivate many unintentional legal infringements during the development of such applications. In this paper, a multidisciplinary team intends to bridge this communication gap and promote more compliant Portuguese NLP research by presenting a series of everyday NLP use cases, while highlighting the Portuguese legislation that may arise during its development., Comment: LEGAL2024 Legal and Ethical Issues in Human Language Technologies, LREC 2024

TopKAT is the algebraic theory of Kleene algebra with tests (KAT) extended with a top element. Compared to KAT, one pleasant feature of TopKAT is that, in relational models, the top element allows us to express the domain and codomain of a relation. This enables several applications in program logics, such as proving under-approximate specifications or reachability properties of imperative programs. However, while TopKAT inherits many pleasant features of KATs, such as having a decidable equational theory, it is incomplete with respect to relational models. In other words, there are properties that hold true of all relational TopKATs but cannot be proved with the axioms of TopKAT. This issue is potentially worrisome for program-logic applications, in which relational models play a key role. In this paper, we further investigate the completeness properties of TopKAT with respect to relational models. We show that TopKAT is complete with respect to (co)domain comparison of KAT terms, but incomplete when comparing the (co)domain of arbitrary TopKAT terms. Since the encoding of under-approximate specifications in TopKAT hinges on this type of formula, the aforementioned incompleteness results have a limited impact when using TopKAT to reason about such specifications., Comment: A version of this article is accepted at ICALP 2024

Healthcare data contains some of the most sensitive information about an individual, yet sharing this data with healthcare practitioners can significantly enhance patient care and support research efforts. However, current systems for sharing health data between patients and caregivers do not fully address the critical security requirements of privacy, confidentiality, and consent management. Furthermore, compliance with regulatory laws such as GDPR and HIPAA is often deficient, largely because patients typically are asked to provide general consent for healthcare entities to access their data. Recognizing the limitations of existing systems, we present S3PHER, a novel approach to sharing health data that provides patients with control over who accesses their data, what data is accessed, and when. Our system ensures end to end privacy by integrating a Proxy ReEncryption Scheme with a Searchable Encryption Scheme, utilizing Homomorphic Encryption to enable healthcare practitioners to privately search and access patients' documents. The practicality and benefits of S3PHER are further validated through end to end deployment and use case analyses, with tests on real datasets demonstrating promising execution times., Comment: 20 pages, 1 figure, 2 tables in the appendix

The detection of low-mass planets orbiting the nearest stars is a central stake of exoplanetary science, as they can be directly characterized much more easily than their distant counterparts. Here, we present the results of our long-term astrometric observations of the nearest binary M-dwarf Gliese 65 AB (GJ65), located at a distance of only 2.67 pc. We monitored the relative astrometry of the two components from 2016 to 2023 with the VLTI/GRAVITY interferometric instrument. We derived highly accurate orbital parameters for the stellar system, along with the dynamical masses of the two red dwarfs. The GRAVITY measurements exhibit a mean accuracy per epoch of 50-60 microarcseconds in 1.5h of observing time using the 1.8m Auxiliary Telescopes. The residuals of the two-body orbital fit enable us to search for the presence of companions orbiting one of the two stars (S-type orbit) through the reflex motion they imprint on the differential A-B astrometry. We detected a Neptune-mass candidate companion with an orbital period of p = 156 +/- 1 d and a mass of m = 36 +/- 7 Mearth. The best-fit orbit is within the dynamical stability region of the stellar pair. It has a low eccentricity, e = 0.1 - 0.3, and the planetary orbit plane has a moderate-to-high inclination of i > 30{\deg} with respect to the stellar pair, with further observations required to confirm these values. These observations demonstrate the capability of interferometric astrometry to reach microarcsecond accuracy in the narrow-angle regime for planet detection by reflex motion from the ground. This capability offers new perspectives and potential synergies with Gaia in the pursuit of low-mass exoplanets in the solar neighborhood., Comment: Corresponding authors: G.Bourdarot, P.Kervella, O.Pfuhl. Accepted in A&A Letters

We study the probability flux on the central vertex in continuous-time quantum walks on weighted tree graphs. In a weighted graph, each edge has a weight we call hopping. This hopping sets the jump rate of the particle between the vertices connected by the edge. Here, the edges of the central vertex (root) have a hopping parameter $J$ larger than those of the other edges. For star graphs, this hopping gives only how often the walker visits the central vertex over time. However, for weighted spider graphs $S_{n,2}$ and $S_{n,3}$, the probability on the central vertex drops with $J^2$ for walks starting from a state of any superposition of leaf vertices. We map Cayley trees $C_{3,2}$ and $C_{3,3}$ into these spider graphs and observe the same dependency. Our results suggest this is a general feature of such walks on weighted trees and a way of probing decoherence effects in an open quantum system context., Comment: 17 pages, 8 figures, one column

With four companions at separations from 16 to 71 au, HR 8799 is a unique target for direct imaging, presenting an opportunity for the comparative study of exoplanets with a shared formation history. Combining new VLTI/GRAVITY observations obtained within the ExoGRAVITY program with archival data, we perform a systematic atmospheric characterisation of all four planets. We explore different levels of model flexibility to understand the temperature structure, chemistry and clouds of each planet using both petitRADTRANS atmospheric retrievals and fits to self-consistent radiative-convective equilibrium models. Using Bayesian Model Averaging to combine multiple retrievals, we find that the HR 8799 planets are highly enriched in metals, with [M/H] $\gtrsim$1, and have stellar to super-stellar C/O ratios. The C/O ratio increases with increasing separation from $0.55^{+0.12}_{-0.10}$ for d to $0.78^{+0.03}_{-0.04}$ for b, with the exception of the innermost planet which has a C/O ratio of $0.87\pm0.03$. By retrieving a quench pressure and using a disequilibrium chemistry model we derive vertical mixing strengths compatible with predictions for high-metallicity, self-luminous atmospheres. Bayesian evidence comparisons strongly favour the presence of HCN in HR 8799 c and e, as well as CH$_{4}$ in HR 8799 c, with detections at $>5\sigma$ confidence. All of the planets are cloudy, with no evidence for patchiness. The clouds of c, d and e are best fit by silicate clouds lying above a deep iron cloud layer, while the clouds of the cooler HR 8799 b are more likely composed of Na$_{2}$S. With well defined atmospheric properties, future exploration of this system is well positioned to unveil further detail in these planets, extending our understanding of the composition, structure, and formation history of these siblings., Comment: 45 pages, 25 figures, accepted by Astronomy & Astrophysics

Sonatype's 2023 report found that 97% of developers and security leads integrate generative Artificial Intelligence (AI), particularly Large Language Models (LLMs), into their development process. Concerns about the security implications of this trend have been raised. Developers are now weighing the benefits and risks of LLMs against other relied-upon information sources, such as StackOverflow (SO), requiring empirical data to inform their choice. In this work, our goal is to raise software developers awareness of the security implications when selecting code snippets by empirically comparing the vulnerabilities of ChatGPT and StackOverflow. To achieve this, we used an existing Java dataset from SO with security-related questions and answers. Then, we asked ChatGPT the same SO questions, gathering the generated code for comparison. After curating the dataset, we analyzed the number and types of Common Weakness Enumeration (CWE) vulnerabilities of 108 snippets from each platform using CodeQL. ChatGPT-generated code contained 248 vulnerabilities compared to the 302 vulnerabilities found in SO snippets, producing 20% fewer vulnerabilities with a statistically significant difference. Additionally, ChatGPT generated 19 types of CWE, fewer than the 22 found in SO. Our findings suggest developers are under-educated on insecure code propagation from both platforms, as we found 274 unique vulnerabilities and 25 types of CWE. Any code copied and pasted, created by AI or humans, cannot be trusted blindly, requiring good software engineering practices to reduce risk. Future work can help minimize insecure code propagation from any platform., Comment: 8 pages, 2 figures, accepted at Deep Learning Security and Privacy Workshop (DLSP) part of IEEE Symposium on Security and Privacy Workshops (SPW) for 2024

Precise mass constraints are vital for the characterisation of brown dwarfs and exoplanets. Here we present how the combination of data obtained by Gaia and GRAVITY can help enlarge the sample of substellar companions with measured dynamical masses. We show how the Non-Single-Star (NSS) two-body orbit catalogue contained in Gaia DR3 can be used to inform high-angular-resolution follow-up observations with GRAVITY. Applying the method presented in this work to eight Gaia candidate systems, we detect all eight predicted companions, seven of which were previously unknown and five are of a substellar nature. Among the sample is Gaia DR3 2728129004119806464 B, which - detected at an angular separation of (34.01 $\pm$ 0.15) mas from the host - is the closest substellar companion ever imaged. This translates to a semi-major axis of (0.938 $\pm$ 0.023) AU. WT 766 B, detected at a greater angular separation, was confirmed to be on an orbit exhibiting an even smaller semi-major axis of (0.676 $\pm$ 0.008) AU. The GRAVITY data were then used to break the host-companion mass degeneracy inherent to the Gaia NSS orbit solutions as well as to constrain the orbital solutions of the respective target systems. Knowledge of the companion masses enabled us to further characterise them in terms of their ages, effective temperatures, and radii via the application of evolutionary models. The inferred ages exhibit a distinct bias towards values younger than what is to be expected based on the literature. The results serve as an independent validation of the orbital solutions published in the NSS two-body orbit catalogue and show that the combination of astrometric survey missions and high-angular-resolution direct imaging holds great promise for efficiently increasing the sample of directly imaged companions in the future, especially in the light of Gaia's upcoming DR4 and the advent of GRAVITY+., Comment: Accepted for publication in Astronomy and Astrophysics

We report the discovery of three Transiting Exoplanet Survey Satellite Objects of Interest (TOI) with signatures of pulsation, observed in more than one sector. Our main goal is to explore how large is the variety of classical pulsators such as $\delta$ Sct, $\gamma$ Dor, RR Lyrae and Cepheid among TOI pulsators. The analysis reveals two stars with signatures of $\delta$ Sct and one of $\gamma$ Dor, out of a sample of 3901 TOIs with available light curves (LCs). To date, there is a very scarce number of known pulsating stars hosting planets. The present finding also emerges as an exciting laboratory for studying different astrophysical phenomena, including the effects of star-planet interaction on pulsation and timing detection of planetary companions. We have also identified 16 TOI stars with periodicities and LCs morphology compatible with different classical pulsating classes, but for most of them, the dominant frequency signals originate from contaminating sources., Comment: 14 pages, 3 figures, Submitted to ApJS and accepted for publication on January 15, 2024

Dual-field interferometric observations with VLTI/GRAVITY sometimes require the use of a "binary calibrator", a binary star whose individual components remain unresolved by the interferometer, with a separation between 400 and 2000 mas for observations with the Units Telescopes (UTs), or 1200 to 3000 mas for the Auxiliary Telescopes (ATs). The separation vector also needs to be predictable to within 10 mas for proper pointing of the instrument. Up until now, no list of properly vetted calibrators was available for dual-field observations with VLTI/GRAVITY on the UTs. Our objective is to compile such a list, and make it available to the community. We identify a list of candidates from the Washington Double Star (WDS) catalogue, all with appropriate separations and brightness, scattered over the Southern sky. We observe them as part of a dedicated calibration programme, and determine whether these objects are true binaries (excluding higher multiplicities resolved interferometrically but unseen by imaging), and extract measurements of the separation vectors. We combine these new measurements with those available in the WDS to determine updated orbital parameters for all our vetted calibrators. We compile a list of 13 vetted binary calibrators for observations with VLTI/GRAVITY on the UTs, and provide orbital estimates and astrometric predictions for each of them. We show that our list guarantees that there are always at least two binary calibrators at airmass < 2 in the sky over the Paranal observatory, at any point in time. Any Principal Investigator wishing to use the dual-field mode of VLTI/GRAVITY with the UTs can now refer to this list to select an appropriate calibrator. We encourage the use of "whereistheplanet" to predict the astrometry of these calibrators, which seamlessly integrates with "p2Gravity" for VLTI/GRAVITY dual-field observing material preparation., Comment: 16 pages, 6 figures. Submitted to A&A

We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with the region where uniformity breaks. Based on annealed and quenched polynomial decay of correlations, our quenched result adopts annealed Kac-type time-normalization and finds limits to be noise-independent. The technique involves a probabilistic blockapproximation where the quenched hit-counting function up to annealed Kac-normalized time is split into equally sized blocks which are mimicked by an independency of random variables distributed just like each of them. The theory is made operational due to a result that allows certain hitting quantities to be recovered from return quantities. Our application is to a class of random piecewise expanding one-dimensional systems, casting new light on the well-known deterministic dichotomy between periodic and aperiodic points, their usual extremal index formula EI=1-1/JT^p(x_0) , and recovering the PolyaAeppli case for general Bernoulli-driven systems, but distinct behavior otherwise. Future and on-going investigations aim to produce and accommodate examples of bonafide nonuniformly expanding random systems and targets approaching their neutral points., Comment: 52 p

Reasoning about resources used during the execution of programs, such as time, is one of the fundamental questions in computer science. When programming with probabilistic primitives, however, different samples may result in different resource usage, making the cost of a program not a single number but a distribution instead. The expected cost is an important metric used to quantify the efficiency of probabilistic programs. In this work we introduce $\mathbf{cert}$, a call-by-push-value (CBPV) metalanguage extended with primitives for probability, cost and unbounded recursion, and give it denotational semantics for reasoning about the average cost of programs. We justify the validity of the semantics by presenting case-studies ranging from randomized algorithms to stochastic processes and showing how the semantics captures their intended cost.

Temporal variability in the photometric and spectroscopic properties of protoplanetary disks is common in YSO. However, evidence pointing toward changes in their morphology over short timescales has only been found for a few sources, mainly due to a lack of high cadence observations at mas resolution. We combine GRAVITY multi-epoch observations of HD98922 at mas resolution with PIONIER archival data covering a total time span of 11 years. We interpret the interferometric visibilities and spectral energy distribution with geometrical models and through radiative transfer techniques. We investigated high-spectral-resolution quantities to obtain information on the properties of the HI BrG-line-emitting region. The observations are best fitted by a model of a crescent-like asymmetric dust feature located at 1 au and accounting for 70% of the NIR emission. The feature has an almost constant magnitude and orbits the central star with a possible sub-Keplerian period of 12 months, although a 9 month period is another, albeit less probable, solution. The radiative transfer models show that the emission originates from a small amount of carbon-rich (25%) silicates, or quantum-heated particles located in a low-density region. Among different possible scenarios, we favor hydrodynamical instabilities in the inner disk that can create a large vortex. The high spectral resolution differential phases in the BrG-line show that the hot-gas component is offset from the star and in some cases is located between the star and the crescent feature. The scale of the emission does not favor magnetospheric accretion as a driving mechanism. The scenario of an asymmetric disk wind or a massive accreting substellar or planetary companion is discussed. With this unique observational data set for HD98922, we reveal morphological variability in the innermost 2 au of its disk region., Comment: 45 pages, 20 figures, accepted by and to be published in Astronomy & Astrophysics (A&A)

Undefined behavior in C often causes devastating security vulnerabilities. One practical mitigation is compartmentalization, which allows developers to structure large programs into mutually distrustful compartments with clearly specified privileges and interactions. In this paper we introduce SECOMP, a compiler for compartmentalized C code that comes with machine-checked proofs guaranteeing that the scope of undefined behavior is restricted to the compartments that encounter it and become dynamically compromised. These guarantees are formalized as the preservation of safety properties against adversarial contexts, a secure compilation criterion similar to full abstraction, and this is the first time such a strong criterion is proven for a mainstream programming language. To achieve this we extend the languages of the CompCert verified C compiler with isolated compartments that can only interact via procedure calls and returns, as specified by cross-compartment interfaces. We adapt the passes and optimizations of CompCert as well as their correctness proofs to this compartment-aware setting. We then use compiler correctness as an ingredient in a larger secure compilation proof that involves several proof engineering novelties, needed to scale formally secure compilation up to a C compiler., Comment: CCS'24 camera ready version, extended with appendices and a few more references

Tight relationships exist in the local universe between the central stellar properties of galaxies and the mass of their supermassive black hole. These suggest galaxies and black holes co-evolve, with the main regulation mechanism being energetic feedback from accretion onto the black hole during its quasar phase. A crucial question is how the relationship between black holes and galaxies evolves with time; a key epoch to probe this relationship is at the peaks of star formation and black hole growth 8-12 billion years ago (redshifts 1-3). Here we report a dynamical measurement of the mass of the black hole in a luminous quasar at a redshift of 2, with a look back time of 11 billion years, by spatially resolving the broad line region. We detect a 40 micro-arcsecond (0.31 pc) spatial offset between the red and blue photocenters of the H$\alpha$ line that traces the velocity gradient of a rotating broad line region. The flux and differential phase spectra are well reproduced by a thick, moderately inclined disk of gas clouds within the sphere of influence of a central black hole with a mass of 3.2x10$^{8}$ solar masses. Molecular gas data reveal a dynamical mass for the host galaxy of 6x10$^{11}$ solar masses, which indicates an under-massive black hole accreting at a super-Eddington rate. This suggests a host galaxy that grew faster than the supermassive black hole, indicating a delay between galaxy and black hole formation for some systems., Comment: 5 pages Main text, 8 figures, 2 tables, to be published in Nature, under embargo until 29 January 2024 16:00 (London)

The 2nd generation VLTI instrument GRAVITY is a two-field infrared interferometer operating in the K band between 1.97 and 2.43 $\mu$m with either the four 8 m or the four 1.8 m telescopes of the Very Large Telescope (VLT). Beams collected by the telescopes are corrected with adaptive optics systems and the fringes are stabilized with a fringe-tracking system. A metrology system allows the measurement of internal path lengths in order to achieve high-accuracy astrometry. High sensitivity and high interferometric accuracy are achieved thanks to (i) correction of the turbulent phase, (ii) the use of low-noise detectors, and (iii) the optimization of photometric and coherence throughput. Beam combination and most of the beam transport are performed with single-mode waveguides in vacuum and at low temperature. In this paper, we present the functions and performance achieved with weakly birefringent standard single-mode fiber systems in GRAVITY. Fibered differential delay lines (FDDLs) are used to dynamically compensate for up to 6 mm of delay between the science and reference targets. Fibered polarization rotators allow us to align polarizations in the instrument and make the single-mode beam combiner close to polarization neutral. The single-mode fiber system exhibits very low birefringence (less than 23{\deg}), very low attenuation (3.6-7 dB/km across the K band), and optimized differential dispersion (less than 2.04 $\mu$rad cm2 at zero extension of the FDDLs). As a consequence, the typical fringe contrast losses due to the single-mode fibers are 6% to 10% in the lowest-resolution mode and 5% in the medium- and high-resolution modes of the instrument for a photometric throughput of the fiber chain of the order of 90%. There is no equivalent of this fiber system to route and modally filter beams with delay and polarization control in any other K-band beamcombiner., Comment: 14 pages including 2 appendices, 8 figures in the main text plus 2 figures in the appendices, final version published in A&A

We describe methods, tools, and a software library called LASPATED, available on GitHub (at https://github.com/vguigues/) to fit models using spatio-temporal data and space-time discretization. A video tutorial for this library is available on YouTube. We consider two types of methods to estimate a non-homogeneous Poisson process in space and time. The methods approximate the arrival intensity function of the Poisson process by discretizing space and time, and estimating arrival intensity as a function of subregion and time interval. With such methods, it is typical that the dimension of the estimator is large relative to the amount of data, and therefore the performance of the estimator can be improved by using additional data. The first method uses additional data to add a regularization term to the likelihood function for calibrating the intensity of the Poisson process. The second method uses additional data to estimate arrival intensity as a function of covariates. We describe a Python package to perform various types of space and time discretization. We also describe two packages for the calibration of the models, one in Matlab and one in C++. We demonstrate the advantages of our methods compared to basic maximum likelihood estimation with simulated and real data. The experiments with real data calibrate models of the arrival process of emergencies to be handled by the Rio de Janeiro emergency medical service.

We aim to investigate the origin of the HI Br$\gamma$ emission in young stars by using GRAVITY to image the innermost region of circumstellar disks, where important physical processes such as accretion and winds occur. With high spectral and angular resolution, we focus on studying the continuum and the HI Br$\gamma$-emitting area of the Herbig star HD58647. Using VLTI-GRAVITY, we conducted observations of HD58647 with both high spectral and high angular resolution. Thanks to the extensive $uv$ coverage, we were able to obtain detailed images of the circumstellar environment at a sub-au scale, specifically capturing the continuum and the Br$\gamma$-emitting region. Through the analysis of velocity-dispersed images and photocentre shifts, we were able to investigate the kinematics of the HI Br$\gamma$-emitting region. The recovered continuum images show extended emission where the disk major axis is oriented along a position angle of 14\degr. The size of the continuum emission at 5-sigma levels is $\sim$ 1.5 times more extended than the sizes reported from geometrical fitting (3.69 mas $\pm$ 0.02 mas). This result supports the existence of dust particles close to the stellar surface, screened from the stellar radiation by an optically thick gaseous disk. Moreover, for the first time with GRAVITY, the hot gas component of HD58647 traced by the Br$\gamma$ ,has been imaged. This allowed us to constrain the size of the Br$\gamma$-emitting region and study the kinematics of the hot gas; we find its velocity field to be roughly consistent with gas that obeys Keplerian motion. The velocity-dispersed images show that the size of the hot gas emission is from a more compact region than the continuum (2.3 mas $\pm$ 0.2 mas). Finally, the line phases show that the emission is not entirely consistent with Keplerian rotation, hinting at a more complex structure in the hot gaseous disk., Comment: accepted in A&A on 20/11/2023

In this paper, following the studies of Amorim and al. in Partial Differ.Equ. Appl. '23, we consider some new aspects of the motion of the director field of a nematic liquid crystal submitted to a magnetic field and to a laser beam. In particular, we study the existence and partial orbital stability of special standing waves, in the spirit of Cazenave and Lions and Hadj Selem and al. in Milan J. Math. '14 and we present some numerical simulations.

Young, low-mass Brown Dwarfs orbiting early-type stars, with low mass ratios ($q\lesssim0.01$), appear intrinsically rare and present a formation dilemma: could a handful of these objects be the highest mass outcomes of ``planetary" formation channels (bottom up within a protoplanetary disk), or are they more representative of the lowest mass ``failed binaries" (formed via disk fragmentation, or core fragmentation)? Additionally, their orbits can yield model-independent dynamical masses, and when paired with wide wavelength coverage and accurate system age estimates, can constrain evolutionary models in a regime where the models have a wide dispersion depending on initial conditions. We present new interferometric observations of the $16\,\mathrm{Myr}$ substellar companion HD~136164~Ab (HIP~75056~Ab) with VLTI/GRAVITY and an updated orbit fit including proper motion measurements from the Hipparcos-Gaia Catalogue of Accelerations. We estimate a dynamical mass of $35\pm10\,\mathrm{M_J}$ ($q\sim0.02$), making HD~136164~Ab the youngest substellar companion with a dynamical mass estimate. The new mass and newly constrained orbital eccentricity ($e=0.44\pm0.03$) and separation ($22.5\pm1\,\mathrm{au}$) could indicate that the companion formed via the low-mass tail of the Initial Mass Function. Our atmospheric fit to the \texttt{SPHINX} M-dwarf model grid suggests a sub-solar C/O ratio of $0.45$, and $3\times$ solar metallicity, which could indicate formation in the circumstellar disk via disk fragmentation. Either way, the revised mass estimate likely excludes ``bottom-up" formation via core accretion in the circumstellar disk. HD~136164~Ab joins a select group of young substellar objects with dynamical mass estimates; epoch astrometry from future \textit{Gaia} data releases will constrain the dynamical mass of this crucial object further., Comment: Accepted for publication in The Astronomical Journal. 9 figures, 3 tables

We propose a threshold decision-making framework for controlling the physical dynamics of an agent switching between two spatial tasks. Our framework couples a nonlinear opinion dynamics model that represents the evolution of an agent's preference for a particular task with the physical dynamics of the agent. We prove the bifurcation that governs the behavior of the coupled dynamics. We show by means of the bifurcation behavior how the coupled dynamics are adaptive to the physical constraints of the agent. We also show how the bifurcation can be modulated to allow the agent to switch tasks based on thresholds adaptive to environmental conditions. We illustrate the benefits of the approach through a decentralized multi-robot task allocation application for trash collection.

The dark compact object at the centre of the Milky Way is well established to be a supermassive black hole with mass $M_{\bullet} \sim 4.3 \cdot 10^6 \, M_{\odot}$, but the nature of its environment is still under debate. In this work, we used astrometric and spectroscopic measurements of the motion of the star S2, one of the closest stars to the massive black hole, to determine an upper limit on an extended mass composed of a massive vector field around Sagittarius A*. For a vector with effective mass $10^{-19} \, \rm eV \lesssim m_s \lesssim 10^{-18} \, \rm eV$, our Markov Chain Monte Carlo analysis shows no evidence for such a cloud, placing an upper bound $M_{\rm cloud} \lesssim 0.1\% M_{\bullet}$ at $3\sigma$ confidence level. We show that dynamical friction exerted by the medium on S2 motion plays no role in the analysis performed in this and previous works, and can be neglected thus., Comment: 9 pages, 5 figures, accepted to MNRAS

Parallel programs are frequently modeled as dependency or cost graphs, which can be used to detect various bugs, or simply to visualize the parallel structure of the code. However, such graphs reflect just one particular execution and are typically constructed in a post-hoc manner. Graph types, which were introduced recently to mitigate this problem, can be assigned statically to a program by a type system and compactly represent the family of all graphs that could result from the program. Unfortunately, prior work is restricted in its treatment of futures, an increasingly common and especially dynamic form of parallelism. In short, each instance of a future must be statically paired with a vertex name. Previously, this led to the restriction that futures could not be placed in collections or be used to construct data structures. Doing so is not a niche exercise: such structures form the basis of numerous algorithms that use forms of pipelining to achieve performance not attainable without futures. All but the most limited of these examples are out of reach of prior graph type systems. In this paper, we propose a graph type system that allows for almost arbitrary combinations of futures and recursive data types. We do so by indexing datatypes with a type-level vertex structure, a codata structure that supplies unique vertex names to the futures in a data structure. We prove the soundness of the system in a parallel core calculus annotated with vertex structures and associated operations. Although the calculus is annotated, this is merely for convenience in defining the type system. We prove that it is possible to annotate arbitrary recursive types with vertex structures, and show using a prototype inference engine that these annotations can be inferred from OCaml-like source code for several complex parallel algorithms., Comment: 65 pages, 41 figures, submitted to POPL 2024

The goal of this work is to characterize the polarization effects of the VLTI and GRAVITY. This is needed to calibrate polarimetric observations with GRAVITY for instrumental effects and to understand the systematic error introduced to the astrometry due to birefringence when observing targets with a significant intrinsic polarization. By combining a model of the VLTI light path and its mirrors and dedicated experimental data, we construct a full polarization model of the VLTI UTs and the GRAVITY instrument. We first characterize all telescopes together to construct a UT calibration model for polarized targets. We then expand the model to include the differential birefringence. With this, we can constrain the systematic errors for highly polarized targets. Together with this paper, we publish a standalone Python package to calibrate the instrumental effects on polarimetric observations. This enables the community to use GRAVITY to observe targets in a polarimetric observing mode. We demonstrate the calibration model with the galactic center star IRS 16C. For this source, we can constrain the polarization degree to within 0.4 % and the polarization angle within 5 deg while being consistent with the literature. Furthermore, we show that there is no significant contrast loss, even if the science and fringe-tracker targets have significantly different polarization, and we determine that the phase error in such an observation is smaller than 1 deg, corresponding to an astrometric error of 10 {\mu}as. With this work, we enable the use of the polarimetric mode with GRAVITY/UTs and outline the steps necessary to observe and calibrate polarized targets. We demonstrate that it is possible to measure the intrinsic polarization of astrophysical sources with high precision and that polarization effects do not limit astrometric observations of polarized targets., Comment: Accepted by A&A

Using the formalism of generalized fractional derivatives, a two-dimensional non-relativistic meson system is studied. The mesons are interacting by a Cornell potential. The system is formulated in the domain of the symplectic quantum mechanics by means of the generalized fractional Nikiforov-Uvarov method. The corresponding Wigner function and the energy eigenvalues are then derived. The effect of fractional parameters $\alpha$ and $\beta$ with the ground state solution is analyzed through the Wigner function for the charm-anticharm, bottom-antibottom and $b\overline{c}$ mesons. One of the fundamental achievements of such Cornell model is the determination of heavy quarkonia mass spectra. We have computed these masses and the, Comment: 11 pages, 3 figures

In this article we analyze the behavior of a non-relativistic spinless particle near the event horizon of a Schwarzschild-like black hole. In this way, the Schr\"odinger covariant equation that describes the particle is obtained from the Galilean covariance technique. The Schr\"odinger equation in a Schwarzschild-like spacetime is solved analytically and its solutions are given in terms of the confluent Heun function. As a relevant result, we discovered that the energy levels of the particles are quantized and that the particle does not escape to infinity. We obtain the existing transmission and reflection coefficients for a particle and anti-particle pair at the event horizon. We thus verify that there is no non-relativistic equivalent of Hawking radiation., Comment: 10 pages, no figures

Flaky tests are tests that nondeterministically pass and fail in unchanged code. These tests can be detrimental to developers' productivity. Particularly when tests run in continuous integration environments, the tests may be competing for access to limited computational resources (CPUs, memory etc.), and we hypothesize that resource (in)availability may be a significant factor in the failure rate of flaky tests. We present the first assessment of the impact that computational resources have on flaky tests, including a total of 52 projects written in Java, JavaScript and Python, and 27 different resource configurations. Using a rigorous statistical methodology, we determine which tests are RAFT (Resource-Affected Flaky Tests). We find that 46.5% of the flaky tests in our dataset are RAFT, indicating that a substantial proportion of flaky-test failures can be avoided by adjusting the resources available when running tests. We report RAFTs and configurations to avoid them to developers, and received interest to either fix the RAFTs or to improve the specifications of the projects so that tests would be run only in configurations that are unlikely to encounter RAFT failures. Our results also have implications for researchers attempting to detect flaky tests, e.g., reducing the resources available when running tests is a cost-effective approach to detect more flaky failures., Comment: This work has been submitted to the IEEE for possible publication

We unveil a novel mechanism for quasicondensation of hard-core bosons in the presence of quasiperiodicity-induced multifractal single-particle states. The new critical state, here dubbed fractal quasicondensate, is characterized by natural orbitals with multifractal properties and by an occupancy of the lowest natural orbital, {\lambda}0 ~ L{\gamma}, which grows with system size but with a nonuniversal scaling exponent, {\gamma} < 1/2. In contrast to fractal quasicondensates obtained when the chemical potential lies in a region of multifractal single-particle states, placing the chemical potential in regions of localized or delocalized states yields, respectively, no condensation or the usual 1D quasicondensation with {\gamma} = 1/2. Our findings are established by studying one-dimensional hardcore bosons subjected to various quasiperiodic potentials, including the well-known Aubry-Andre model, employing a mapping to non-interacting fermionics that allows for numerically exact results. We discuss how to test our findings in state-of-the-art ultracold atom experiments., Comment: 8 pages (SM included)

Giant exoplanets have been directly imaged over orders of magnitude of orbital separations, prompting theoretical and observational investigations of their formation pathways. In this paper, we present new VLTI/GRAVITY astrometric data of HIP 65426 b, a cold, giant exoplanet which is a particular challenge for most formation theories at a projected separation of 92 au from its primary. Leveraging GRAVITY's astrometric precision, we present an updated eccentricity posterior that disfavors large eccentricities. The eccentricity posterior is still prior-dependent, and we extensively interpret and discuss the limits of the posterior constraints presented here. We also perform updated spectral comparisons with self-consistent forward-modeled spectra, finding a best fit ExoREM model with solar metallicity and C/O=0.6. An important caveat is that it is difficult to estimate robust errors on these values, which are subject to interpolation errors as well as potentially missing model physics. Taken together, the orbital and atmospheric constraints paint a preliminary picture of formation inconsistent with scattering after disk dispersal. Further work is needed to validate this interpretation. Analysis code used to perform this work is available at https://github.com/sblunt/hip65426., Comment: 28 pages, 14 figures. Revised and resubmitted to AJ

Classical Be stars are fast rotating, near main sequence B-type stars. The rotation and the presence of circumstellar discs profoundly modify the observables of active Be stars. Our goal is to infer stellar and disc parameters, as well as distance and interstellar extinction, using the currently most favoured physical models for these objects. We present BeAtlas, a grid of 61.600 NLTE radiative transfer models for Be stars, calculated with the HDUST code. The grid was coupled with a Monte Carlo Markov chain code to sample the posterior distribution. We test our method on two well-studied Be stars, $\alpha$ Eri and $\beta$ CMi, using photometric, polarimetric and spectroscopic data as input to the code. We recover literature determinations for most of the parameters of the targets, in particular the mass and age of $\alpha$ Eri, the disc parameters of $\beta$ CMi, and their distances and inclinations. The main discrepancy is that we estimate lower rotational rates than previous works. We confirm previously detected signs of disc truncation in $\beta$ CMi and note that its inner disc seems to have a flatter density slope than its outer disc. The correlations between the parameters are complex, further indicating that exploring the entire parameter space simultaneously is a more robust approach, statistically. The combination of BeAtlas and Bayesian-MCMC techniques proves successful, and a powerful new tool for the field: the fundamental parameters of any Be star can now be estimated in a matter of hours or days.

We use the three-dimensional Monte Carlo radiative transfer code HDUST to model Be stars where the disc is tilted from the equatorial plane of the star. We compute 128 models across 4 spectral types, B0, B2, B5 and B8, tilting the disc by $0^o$, $10^o$, $20^o$, and $40^o$, while varying disc density according to spectral type. We also compute every model for an average and high stellar rotation rate. We first discuss non-tilted disc temperatures and show its non-linear dependence on stellar and disc parameters. We find that tilting the disc minimally affects the density-weighted average disc temperature, but tilting does create a temperature asymmetry in disc cross sections, which is more pronounced for a faster rotation rate. We also investigate the effect tilting has on $V$-band magnitude, polarization, and the H$\alpha$ line. Tilting the disc does affect these observables, but the changes are entirely dependent on the position of the observer relative to the direction of tilt. We find the observables that distinguish tilting from a change in density or geometry are the H$\alpha$ line shape, where it can transition between single-peaked and double-peaked, and the polarization position angle, whose value is dependent on the projected major elongation axis of the disc on the sky. We also present one early and one late-type model with warped discs. We find their temperature structure varies a small amount from the uniformly tilted models, and the different observables correspond to different tilt angles, consistent with their expected volume of origin within the disc., Comment: 20 pages, 23 figures

Tension remains between the observed and modeled properties of substellar objects, but objects in binary orbits, with known dynamical masses can provide a way forward. HD 72946 B is a recently imaged brown dwarf companion to the nearby, solar type star. We achieve $\sim100~\mu\mathrm{as}$ relative astrometry of HD 72946 B in the K-band using VLTI/GRAVITY, unprecedented for a benchmark brown dwarf. We fit an ensemble of measurements of the orbit using orbitize! and derive a strong dynamical mass constraint $\mathrm{M_B}=69.5\pm0.5~\mathrm{M_{Jup}}$ assuming a strong prior on the host star mass $\mathrm{M_A}=0.97\pm0.01~\mathrm{M_\odot}$ from an updated stellar analysis. We fit the spectrum of the companion to a grid of self-consistent BT-Settl-CIFIST model atmospheres, and perform atmospheric retrievals using petitRADTRANS. A dynamical mass prior only marginally influences the sampled distribution on effective temperature, but has a large influence on the surface gravity and radius, as expected. The dynamical mass alone does not strongly influence retrieved pressure-temperature or cloud parameters within our current retrieval setup. Independent of cloud prescription and prior assumptions, we find agreement within $\pm2\,\sigma$ between the C/O ratio of the host ($0.52\pm0.05)$ and brown dwarf ($0.43$ to $0.63$), as expected from a molecular cloud collapse formation scenario, but our retrieved metallicities are implausibly high ($0.6-0.8$) in light of an excellent agreement of the data with the solar abundance model grid. Future work on our retrieval framework will seek to resolve this tension. Additional study of low surface-gravity objects is necessary to assess the influence of a dynamical mass prior on atmospheric analysis., Comment: Accepted for publication in the Astrophysical Journal. 32 pages, 14 figures, 7 tables. v2&3 correct errors in co-author's affiliations, figure rendering, and some grant acknowledgements

We rigorously derive the quadrupole formula within the context of the Einstein-Vlasov system. The main contribution of this work is an estimate of the remainder terms, derived from well-defined assumptions, with explicitly stated error terms that depend on the solution's boundedness and decay properties, and the distance to the source. The assumptions are linked to established properties of global solutions of the Einstein-Vlasov system as in \cite{LT}. Prior derivations of the quadrupole formula have relied on post-Newtonian analysis and lacked comparisons with global solution properties. The importance of the no-incoming-radiation condition is emphasized underscoring the need for solutions satisfying this condition. This work thus addresses the limitations of existing results and provides motivation for further research on global solution properties of the Einstein-Vlasov system., Comment: 92 pages. To appear in Dissertationes Mathematicae

We present a method for finding envy-free prices in a combinatorial auction where the consumers' number $n$ coincides with that of distinct items for sale, each consumer can buy one single item and each item has only one unit available. This is a particular case of the {\it unit-demand envy-free pricing problem}, and was recently revisited by Arbib et al. (2019). These authors proved that using a Fibonacci heap for solving the maximum weight perfect matching and the Bellman-Ford algorithm for getting the envy-free prices, the overall time complexity for solving the problem is $O(n^3)$. We propose a method based on dynamic programming design strategy that seeks the optimal envy-free prices by increasing the consumers' utilities, which has the same cubic complexity time as the aforementioned approach, but whose theoretical and empirical results indicate that our method performs faster than the shortest paths strategy, obtaining an average time reduction in determining optimal envy-free prices of approximately 48\%.

The construction of 3D geological models is an essential task in oil/gas exploration, development and production. However, it is a cumbersome, time-consuming and error-prone task mainly because of the model's geometric and topological complexity. The models construction is usually separated into interpretation and 3D modeling, performed by different highly specialized individuals, which leads to inconsistencies and intensifies the challenges. In addition, the creation of models following geological rules is paramount for properly depicting static and dynamic properties of oil/gas reservoirs. In this work, we propose a sketch-based approach to expedite the creation of valid 3D geological models by mimicking how domain experts interpret geological structures, allowing creating models directly from interpretation sketches. Our sketch-based modeler (Geo-Sketcher) is based on sketches of standard 2D topographic and geological maps, comprised of lines, symbols and annotations. We developed a graph-based representation to enable (1) the automatic computation of the relative ages of rock series and layers, and (2) the embedding of specific geological rules directly in the sketching. We introduce the use of Hermite-Birkhoff Radial Basis Functions to interpolate the geological map constraints, and demonstrate the capabilities of our approach with a variety of results with different levels of complexity., Comment: 21 pages, 30 Figures

A network of coupled dynamical systems is represented by a graph whose vertices represent individual cells and whose edges represent couplings between cells. Motivated by the impact of synchronization results of the Kuramoto networks, we introduce the generalized class of Laplacian networks, governed by mappings whose Jacobian at any point is a symmetric matrix with row entries summing to zero. By recognizing this matrix with a weighted Laplacian of the associated graph, we derive the optimal estimates of its positive, null and negative eigenvalues directly from the graph topology. Furthermore, we provide a characterization of the mappings that define Laplacian networks. Lastly, we discuss stability of equilibria inside synchrony subspaces for two types of Laplacian network on a ring with some extra couplings.

In this paper we rectify two previous results found in the literature. Our work leads to a new upper bound for the largest sum-free subset of $[1,n]$ with lowest value in $\left [\frac{n}{3},\frac{n}{2}\right ]$, and the identification of all patterns that can be used to form sum-free sets of maximum cardinality.