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We study Hamiltonicity in the union of an $n$-vertex graph $H$ with high minimum degree and a binomial random graph on the same vertex set. In particular, we consider the case when $H$ has minimum degree close to $n/2$. We determine the perturbed threshold for Hamiltonicity in this setting. To be precise, let $\eta:= n/2-\delta(H)$. For $\eta=\omega(1)$, we show that it suffices to add $\Theta(\eta)$ random edges to $H$ to a.a.s. obtain a Hamiltonian graph; for $\eta=\Theta(1)$, we show that $\omega(1)$ edges suffice. In fact, when $\eta=o(n)$ and $\eta=\omega(1)$, we show that $(8+o(1))\eta$ random edges suffice, which is best possible up to the error term. This determines the sharp perturbed threshold for Hamiltonicity in this range of degrees. We also obtain analogous results for perfect matchings, showing that, in this range of degrees, the sharp perturbed thresholds for Hamiltonicity and for perfect matchings differ by a factor of $2$.

We study the possibility that four $\Xi$ resonances $(\Xi(1620)$, $\Xi(1690)$, $\Xi(1820)$, $\Xi(1950))$ could correspond to pentaquark states, in the form of meson-baryon bound systems. We also explore the possible existence of doubly strange pentaquarks with hidden charm $(P_{css})$ and find two candidates structured in a similar form, at energies of $4493~{\rm MeV}$ and $4630~{\rm MeV}$. The meson-baryon interaction is built from t-channel meson exchange processes which are evaluated using effective Lagrangians. Moreover we analyse the $\Xi_b\to\Xi~J/\psi~\phi$ decay process, which permits exploring the existence of the heavy double strange pentaquark, as well as other exotic hadrons, in the three different two-body invariant mass spectra of the emitted particles. In the $J/\psi\phi$ mass spectrum, we analyse the nature of the $X(4140)$ and $X(4160)$ resonances. In the $J/\psi\Xi$ invariant mass spectrum, we study the signal produced by the doubly strange pentaquark, where we conclude that it has a good chance to be detected in this reaction if its mass is around $4580-4680~{\rm MeV}$. Finally, in the $\phi\Xi$ spectrum we study the likelihood to detect the $\Xi(2500)$ state., Comment: 23 pages, 30 figures

In this paper, we focus on estimating the causal effect of an intervention over time on a dynamical system. To that end, we formally define causal interventions and their effects over time on discrete-time stochastic processes (DSPs). Then, we show under which conditions the equilibrium states of a DSP, both before and after a causal intervention, can be captured by a structural causal model (SCM). With such an equivalence at hand, we provide an explicit mapping from vector autoregressive models (VARs), broadly applied in econometrics, to linear, but potentially cyclic and/or affected by unmeasured confounders, SCMs. The resulting causal VAR framework allows us to perform causal inference over time from observational time series data. Our experiments on synthetic and real-world datasets show that the proposed framework achieves strong performance in terms of observational forecasting while enabling accurate estimation of the causal effect of interventions on dynamical systems. We demonstrate, through a case study, the potential practical questions that can be addressed using the proposed causal VAR framework.

We introduce Pixtral-12B, a 12--billion-parameter multimodal language model. Pixtral-12B is trained to understand both natural images and documents, achieving leading performance on various multimodal benchmarks, surpassing a number of larger models. Unlike many open-source models, Pixtral is also a cutting-edge text model for its size, and does not compromise on natural language performance to excel in multimodal tasks. Pixtral uses a new vision encoder trained from scratch, which allows it to ingest images at their natural resolution and aspect ratio. This gives users flexibility on the number of tokens used to process an image. Pixtral is also able to process any number of images in its long context window of 128K tokens. Pixtral 12B substanially outperforms other open models of similar sizes (Llama-3.2 11B \& Qwen-2-VL 7B). It also outperforms much larger open models like Llama-3.2 90B while being 7x smaller. We further contribute an open-source benchmark, MM-MT-Bench, for evaluating vision-language models in practical scenarios, and provide detailed analysis and code for standardized evaluation protocols for multimodal LLMs. Pixtral-12B is released under Apache 2.0 license.

Building on recent advances of the embedded cluster approach combined with multiconfigurational theory, this work investigates the electronic states in thorium-doped CaF2 crystals. Th:CaF2 is currently establishing as a promising material for solid-state nuclear clocks, which utilize the laser-accessible isomeric state in thorium-229. By comparing simulated absorption spectra of a library of defect configurations with experimental data, we demonstrate the impact of fluorine vacancies and calcium vacancies on the Th:CaF2 electronic structure. Our results indicate that fluorine-deficient sites can introduce local electronic states within the band gap, resonant with the isomer energy, potentially contributing to non-radiative decay or quenching of the Th-229 isomer. We also explore the potential of electron-nuclear bridge mechanisms to enhance nuclear excitation or de-excitation, offering a pathway for more efficient control over the nuclear clock. This study provides key insights for optimizing the crystal environment for nuclear metrology applications and opens new avenues for further experimental and theoretical exploration of thorium-doped ionic crystals.

Heralded entanglement generation between nodes of a future quantum internet is a fundamental operation that unlocks the potential for quantum communication. In this paper, we propose a decentralized synchronization protocol that operates at the classical control-plane of the link layer, to navigate the coordination challenges of generating heralded entanglement across few-qubit quantum network nodes. Additionally, with quantum network simulations using NetSquid, we show that our protocol achieves lower entanglement request latencies than a naive distributed queue approach. We observe a sixfold reduction in average request latency growth as the number of quantum network links increases. The Eventual Synchronization Protocol (ESP) allows nodes to coordinate on heralded entanglement generation in a scalable manner within multi-peer quantum networks. To the best of our knowledge, this is the first decentralized synchronization protocol for managing heralded entanglement requests., Comment: accepted by the 20th International Conference on Network and Service Management (CNSM), 2024

This research explores an introduction to solid-state diffusion, focusing on its importance in materials engineering. It examines vacancy and interstitial diffusion mechanisms, the application of Fick's laws, and their impact on processes such as phase precipitation and recrystallization in metals and alloys. Additionally, it addresses its relevance in grain growth, diffusion welding, and sintering, which are critical processes to improve the properties of materials with engineering applications in various areas such as biomedical, electrical, and chemistry., Comment: 4 pages

Since neutrinos have mass differences, they could decay into one another. But their lifetimes are likely long, even when shortened by new physics, so decay likely impacts neutrinos only during long trips. This makes high-energy astrophysical neutrinos, traveling for up to billions of light-years, sensitive probes of decay. However, their sensitivity must be tempered by reality. We derive from them thorough bounds on the neutrino lifetimes accounting for critical astrophysical unknowns and the nuances of neutrino detection. Using the diffuse neutrino flux, we disfavor lifetimes $\tau \lesssim 20$-450 s $(m/{\rm eV})$, based on present IceCube data, and forecast factor-of-10 improvements by upcoming detectors. Using, for the first time, neutrinos from the active galaxy NGC 1068, extant unknowns preclude placing lifetime bounds today, but upcoming detectors could disfavor $\tau \sim 100$-5000 s $(m/{\rm eV})$., Comment: 20 pages, 6 figures, 2 tables, plus appendices

Graph Neural Networks (GNNs) have achieved state-of-the-art performance in solving graph classification tasks. However, most GNN architectures aggregate information from all nodes and edges in a graph, regardless of their relevance to the task at hand, thus hindering the interpretability of their predictions. In contrast to prior work, in this paper we propose a GNN \emph{training} approach that jointly i) finds the most predictive subgraph by removing edges and/or nodes -- -\emph{without making assumptions about the subgraph structure} -- while ii) optimizing the performance of the graph classification task. To that end, we rely on reinforcement learning to solve the resulting bi-level optimization with a reward function based on conformal predictions to account for the current in-training uncertainty of the classifier. Our empirical results on nine different graph classification datasets show that our method competes in performance with baselines while relying on significantly sparser subgraphs, leading to more interpretable GNN-based predictions.

Ambient awareness refers to the ability of social media users to obtain knowledge about who knows what (i.e., users' expertise) in their network, by simply being exposed to other users' content (e.g, tweets on Twitter). Previous work, based on user surveys, reveals that individuals self-report ambient awareness only for parts of their networks. However, it is unclear whether it is their limited cognitive capacity or the limited exposure to diagnostic tweets (i.e., online content) that prevents people from developing ambient awareness for their complete network. In this work, we focus on in-wall ambient awareness (IWAA) in Twitter and conduct a two-step data-driven analysis, that allows us to explore to which extent IWAA is likely, or even possible. First, we rely on reactions (e.g., likes), as strong evidence of users being aware of experts in Twitter. Unfortunately, such strong evidence can be only measured for active users, which represent the minority in the network. Thus to study the boundaries of IWAA to a larger extent, in the second part of our analysis, we instead focus on the passive exposure to content generated by other users -- which we refer to as in-wall visibility. This analysis shows that (in line with \citet{levordashka2016ambient}) only for a subset of users IWAA is plausible, while for the majority it is unlikely, if even possible, to develop IWAA. We hope that our methodology paves the way for the emergence of data-driven approaches for the study of ambient awareness.

This research aimed to introduce the concept of harmonically m-concave set-valued functions, which is obtained from the combination of two definitions: harmonically m-concave functions and set-valued functions. In this work some properties and characteristics are developed, as well as a Kuhn type theorem and Bernstein-Doetcsh type result for such functions.

In this work, we obtain an expression for the total observational frequency shift of photons emitted by massive geodesic particles circularly orbiting a black hole in a general spherically symmetric background. Our general relations are presented in terms of the metric components and their derivatives that characterize the black hole parameters. As a concrete example of this general relativistic approach, a special case is studied by applying the formalism to a nonsingular black hole conformally related to the Schwarzchild solution that possesses a length scale parameter $l$ and an integer parameter $N$ in addition to the black hole mass. Besides, we express the nonsingular black hole mass in terms of the observational redshift/blueshift. Finally, we investigate the effects of the free parameters of the conformal gravity theory on the observational frequency shift and compare results with those of the standard Schwarzschild black hole., Comment: 9 pages with 3 captioned figures. Comments are welcome; V2: Published version

Neglecting the effect that decisions have on individuals (and thus, on the underlying data distribution) when designing algorithmic decision-making policies may increase inequalities and unfairness in the long term - even if fairness considerations were taken in the policy design process. In this paper, we propose a novel framework for achieving long-term group fairness in dynamical systems, in which current decisions may affect an individual's features in the next step, and thus, future decisions. Specifically, our framework allows us to identify a time-independent policy that converges, if deployed, to the targeted fair stationary state of the system in the long term, independently of the initial data distribution. We model the system dynamics with a time-homogeneous Markov chain and optimize the policy leveraging the Markov chain convergence theorem to ensure unique convergence. We provide examples of different targeted fair states of the system, encompassing a range of long-term goals for society and policymakers. Furthermore, we show how our approach facilitates the evaluation of different long-term targets by examining their impact on the group-conditional population distribution in the long term and how it evolves until convergence.

The sensitivity of aLIGO detectors is adversely affected by the presence of noise caused by light scattering. Low frequency seismic disturbances can create higher frequency scattering noise adversely impacting the frequency band in which we detect gravitational waves. In this paper, we analyze instances of a type of scattered light noise we call "Fast Scatter" that is produced by motion at frequencies greater than 1 Hz, to locate surfaces in the detector that may be responsible for the noise. We model the phase noise to better understand the relationship between increases in seismic noise near the site and the resulting Fast Scatter observed. We find that mechanical damping of the Arm Cavity Baffles (ACBs) led to a significant reduction of this noise in recent data. For a similar degree of seismic motion in the 1-3 Hz range, the rate of noise transients is reduced by a factor of ~ 50., Comment: 23 pages, 19 figures

In the emerging field of mechanical metamaterials, using periodic lattice structures as a primary ingredient is relatively frequent. However, the choice of aperiodic lattices in these structures presents unique advantages regarding failure, e.g., buckling or fracture, because avoiding repeated patterns prevents global failures, with local failures occurring in turn that can beneficially delay structural collapse. Therefore, it is expedient to develop models for computing efficiently the effective mechanical properties in lattices from different general features while addressing the challenge of presenting topologies (or graphs) of different sizes. In this paper, we develop a deep learning model to predict energetically-equivalent mechanical properties of linear elastic lattices effectively. Considering the lattice as a graph and defining material and geometrical features on such, we show that Graph Neural Networks provide more accurate predictions than a dense, fully connected strategy, thanks to the geometrically induced bias through graph representation, closer to the underlying equilibrium laws from mechanics solved in the direct problem. Leveraging the efficient forward-evaluation of a vast number of lattices using this surrogate enables the inverse problem, i.e., to obtain a structure having prescribed specific behavior, which is ultimately suitable for multiscale structural optimization problems.

The Lie subgroup ${\rm GL}^{+}(2,\mathbb{C})$ of all matrices in the Lie group ${\rm GL}(2,\mathbb{C})$ with positive real determinant is equipped with a left-invariant sub-Lorentzian (anti)metric defined by the natural structure of the 4-dimensional Minkowski space-time on the subspace of Hermitian matrices in its Lie algebra. In base of the corresponding time-anti-optimal control problem, formulated in the paper, and Pontryagin minimum principle for it, using geodesics and shortest arcs of the corresponding left-invariant sub-Riemannian metric on the Lie subgroup ${\rm SL}(2,\mathbb{C})$, the authors found sub-Lorentzian nonspacelike geodesics and longest arcs., Comment: 27 pages

An extensive library of symptom inventories has been developed over time to measure clinical symptoms, but this variety has led to several long standing issues. Most notably, results drawn from different settings and studies are not comparable, which limits reproducibility. Here, we present an artificial intelligence (AI) approach using semantic textual similarity (STS) to link symptoms and scores across previously incongruous symptom inventories. We tested the ability of four pre-trained STS models to screen thousands of symptom description pairs for related content - a challenging task typically requiring expert panels. Models were tasked to predict symptom severity across four different inventories for 6,607 participants drawn from 16 international data sources. The STS approach achieved 74.8% accuracy across five tasks, outperforming other models tested. This work suggests that incorporating contextual, semantic information can assist expert decision-making processes, yielding gains for both general and disease-specific clinical assessment.