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In general, in gauge field theories, physical observables are represented by gauge-invariant composite operators, such as the electromagnetic current. As we recently demonstrated in the context of the $U\left(1\right)$ and $SU\left(2\right)$ Higgs models \cite{Dudal:2019pyg,Dudal:2020uwb,Maas:2020kda}, correlation functions of gauge-invariant operators exhibit very nice properties. Besides the well-known gauge independence, they do not present unphysical cuts, and their K\"{a}ll\'{e}n-Lehmann representations are positive, at least perturbatively. Despite all these interesting features, they are not employed as much as elementary fields, mainly due to the additional complexities involved in their computation and renormalization. In this article, we present a useful trick to compute loop corrections to correlation functions of composite operators. This trick consists of introducing an additional field with no dynamics, coupled to the composite operator of interest. By using this approach, we can employ the traditional algorithms used to compute correlation functions of elementary fields., Comment: 11 pages, 7 figures

In this work, we investigate the renormalization of the gauge-invariant composite operators proposed in \cite{Dudal:2023jsu} to describe the $SU(2)\times U(1)$ Higgs model from a gauge-invariant perspective. To establish the relationship between the counterterms, we use the Algebraic Renormalization approach \cite{Piguet:1995er}. Therefore, we also derive the set of Ward identities of the model after introducing these composite operators. Using these Ward identities, we demonstrate important exact relations between the correlation functions of elementary fields and composite fields., Comment: 57 pages

Models of inelastic (or pseudo-Dirac) dark matter commonly introduce a gauge symmetry spontaneously broken by the introduction of a dark sector version of the Higgs mechanism. We find that this ubiquitous introduction of two extra fields, a vector and complex scalar boson, is indeed unnecessary, with only a mass generating real scalar field being actually required. We consider a simple UV-complete model realizing this minimal setup and study the decays of the excited dark matter state as well as constraints from perturbative unitarity, (in)direct detection and colliders. We find that, in the visible freeze-out scenario ($ \text{DM} \, \text{DM} \leftrightarrow \text{SM} \, \text{SM} $), we still have unconstrained regions of parameter space for dark matter masses $\gtrsim 100$ GeV. Moreover, most of the available regions either present long-lived excited states, which are expected to interfere with the standard cosmological history, or will be probed by future direct detection experiments, such as DARWIN, due to the unavoidable residual elastic interactions. The only regions remaining out of experimental reach present highly fine-tuned parameters., Comment: 7 pages, 3 figures

We show that a two variable Nevanlinna representation for rational Pick functions can be viewed as the Cauchy transform of a simple undirected graph with variables assigned to the vertices. We give relations between representing functions of certain products of such graphs by way of Schur complements applied to adjacency matrices. We also study the connection between the structure of the graph and the regularity of the representing function at a boundary singularity.

The widespread use of machine learning in credit scoring has brought significant advancements in risk assessment and decision-making. However, it has also raised concerns about potential biases, discrimination, and lack of transparency in these automated systems. This tutorial paper performed a non-systematic literature review to guide best practices for developing responsible machine learning models in credit scoring, focusing on fairness, reject inference, and explainability. We discuss definitions, metrics, and techniques for mitigating biases and ensuring equitable outcomes across different groups. Additionally, we address the issue of limited data representativeness by exploring reject inference methods that incorporate information from rejected loan applications. Finally, we emphasize the importance of transparency and explainability in credit models, discussing techniques that provide insights into the decision-making process and enable individuals to understand and potentially improve their creditworthiness. By adopting these best practices, financial institutions can harness the power of machine learning while upholding ethical and responsible lending practices.

We investigate the impact of turbulence on magnetic reconnection through high-resolution 3D MHD simulations, covering Lundquist numbers from $S=10^3$ to $10^6$. Our simulations introduce small-scale perturbations injected into the system until $t=0.1\, t_A$. Even after the initial perturbation ceases, turbulence grows and persists, leading to sustained high reconnection rates of $V_\text{rec}/V_A \sim 0.03-0.08$, which surpass those generated solely by resistive tearing modes (plasmoids) observed in 2D and 3D PIC/MHD simulations by factors of 5 to 6. Our findings reveal that the achieved reconnection rates align with observations in solar phenomena and those reported in 3D MHD global simulations of accretion flows and relativistic jets. Notably, our simulations exhibit a steady-state reconnection rate coinciding with the full development of turbulence, showcasing the robustness and persistence of the reconnection in a turbulent environment. We establish the independence of the reconnection rate from the Lundquist number, consistent with the theory of turbulent reconnection proposed by Lazarian and Vishniac. Our results demonstrate a mild dependence of $V_\text{rec}$ on the plasma-$\beta$ parameter, the ratio between the thermal and magnetic pressure, illustrating a decrease from $0.036$ to $0.028$ as $\beta$ increases from $2$ to $64$ for simulations with $S=10^5$. Finally, we explore the influence of the magnetic Prandtl number ($\text{Pr}_m=\nu/\eta$) on the reconnection rate and find this influence to be negligible during the turbulent regime across the range tested, from $\text{Pr}_m=1$ to $60$. These findings carry significant implications for research into reconnection and particle acceleration within realistic magnetized space and astrophysical environments., Comment: 22 pages, 21 figures

Models of inelastic (or pseudo-Dirac) dark matter commonly assume an accidental symmetry between the left-handed and right-handed mass terms in order to suppress diagonal couplings. We point out that this symmetry is unnecessary, because for Majorana fermions the diagonal couplings are not strongly constrained. Removing the requirement of such an ad-hoc symmetry instead relaxes the relic density constraint due to additional annihilation modes. We consider a simple UV-complete model realising this setup and study constraints from (in)direct detection, beam dump experiments and colliders. We identify two viable mass regions for the dark matter mass, around a few hundred MeV and around a few GeV, respectively. The former region will be fully tested by near-future analyses of NA64 and Belle II data, while the latter turns out to be challenging to explore even with future experiments., Comment: 20 pages, 7 figures, appendices

Large Language Models (LLMs) are increasingly bringing advances to Natural Language Processing. However, low-resource languages, those lacking extensive prominence in datasets for various NLP tasks, or where existing datasets are not as substantial, such as Portuguese, already obtain several benefits from LLMs, but not to the same extent. LLMs trained on multilingual datasets normally struggle to respond to prompts in Portuguese satisfactorily, presenting, for example, code switching in their responses. This work proposes a fine-tuned LLaMA 2-based model for Portuguese prompts named Bode in two versions: 7B and 13B. We evaluate the performance of this model in classification tasks using the zero-shot approach with in-context learning, and compare it with other LLMs. Our main contribution is to bring an LLM with satisfactory results in the Portuguese language, as well as to provide a model that is free for research or commercial purposes., Comment: 10 pages, 3 figures

Axion-like particles (ALPs) emerge in many extensions of the Standard Model as pseudo-Goldstone bosons of a spontaneously broken global symmetry. Understanding their phenomenology in high-energy collisions is crucial for optimizing experimental searches and understanding the exploration potential of future experiments. In this paper, we revise the phenomenology of ALPs with universal couplings to fermions. In particular, we analyze the hierarchy and uncertainty of the various ALP production channels depending on the proton collision energy and the placement of the experiment, and provide improved calculations of the hadronic decay modes., Comment: v3: journal version

Many areas of the world are without basic information on the socioeconomic well-being of the residing population due to limitations in existing data collection methods. Overhead images obtained remotely, such as from satellite or aircraft, can help serve as windows into the state of life on the ground and help "fill in the gaps" where community information is sparse, with estimates at smaller geographic scales requiring higher resolution sensors. Concurrent with improved sensor resolutions, recent advancements in machine learning and computer vision have made it possible to quickly extract features from and detect patterns in image data, in the process correlating these features with other information. In this work, we explore how well two approaches, a supervised convolutional neural network and semi-supervised clustering based on bag-of-visual-words, estimate population density, median household income, and educational attainment of individual neighborhoods from publicly available high-resolution imagery of cities throughout the United States. Results and analyses indicate that features extracted from the imagery can accurately estimate the density (R$^2$ up to 0.81) of neighborhoods, with the supervised approach able to explain about half the variation in a population's income and education. In addition to the presented approaches serving as a basis for further geographic generalization, the novel semi-supervised approach provides a foundation for future work seeking to estimate fine-scale information from aerial imagery without the need for label data., Comment: Updated after acceptance to IEEE J-STARS

We present a set of BRST invariant composite operators in the $SU\left(2\right)\times U\left(1\right)$ Higgs model which exhibit an overlap with the observable scalar and vector particle states of the theory. Some of these operators are non-local in the standard formulation of the Higgs model, however, we show that they can be localized using the Stuckelberg trick, this without changing the physical content. These operators provide thus a BRST invariant resolution of the physical spectrum of the theory, thereby giving the next step in constructing a manifestly BRST invariant formulation of the particle spectrum of the Electroweak and Standard model., Comment: 15 pages