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In the Standard Model\,(SM) of particle physics, photon-torsion mixing is extended to include the Einstein-Cartan portal to dark-photon-axion-torsion mixing beyond the Standard Model\,(BSM), mediated by torsion. The Barbero-Immirzi(BI) parameter, of the order of $10^{-31}$, is more stringent than those obtained by Aliberti and Lambiase using matter-antimatter asymmetry. This paper presents the coupling of the SM with dark matter\,(DM) axions, both mediated by torsion. We discuss tordions, the quanta of torsion, and the damping of propagating torsion. It is shown that with both kinds of vectorial torsion masses, equations from Einstein-Cartan-Holst gravity can be derived, which reduce to axionic photon equations where torsion appears only through its mass spectrum. Photon-axion conversions and axion mixing are found to depend on the BI parameter. This study demonstrates that when the spin-0 torsion mass is finite and Proca electrodynamics is not ghost-free, dark axion masses align with spin-0 torsion masses via axion-driven torsion and photon-torsion mixing. Our results provide innovative insights into Proca gravity models and the role of torsion in photon-axion conversion and dark matter dynamics, thereby offering a solid foundation for future research and new theoretical frameworks in quantum gravity., Comment: 9 Pages, Submitted to Euro.Phys.J.C

A method for measuring the electrical connectivity between parts of a rectangular superconductor was developed for weak links making an arbitrary angle with the long side of the sample. The method is based on magneto-optical observation of characteristic lines where the critical current makes discontinuous deviations in the flow direction to adapt to the non-uniform condition created by the presence of the weak link. Assuming the Bean critical state model in the full penetration regime for a sample submitted to a perpendicular magnetic field, the complete flow pattern of screening currents is reconstructed, from which the transparency of the weak link, i.e., the ratio between its critical current and that of the pristine sample, $\tau = \frac{J_i}{J_c}$, is then related to the angle $\theta$ formed by two characteristic discontinuity lines which, in turn, are intimately associated to the presence of the weak link. The streamline distribution is compared with magneto-optical observations of the flux penetration in Nb superconducting films, where a weak link was created using focused ion beam milling. The present work generalizes previous analyses in which the weak link was perpendicular to the long sides of the rectangular sample. Equations and measurements demonstrate that the relationship between the transparency and the angle $\theta$ is not affected by the tilting of the weak link. Noticeably, in order to attain optimum connectivity, the weak link critical current can be less than that of the pristine sample, namely, $\tau _{max}=\sin \Phi$, where $\Phi$ is the tilt angle of the weak link. This expression generalizes the previous result of $\tau _{max}=1$ for $\Phi=$ 90$^\circ$.

Mouse and human brains have different functions that depend on their neuronal networks. In this study, we analyzed nanometer-scale three-dimensional structures of brain tissues of the mouse medial prefrontal cortex and compared them with structures of the human anterior cingulate cortex. The obtained results indicated that mouse neuronal somata are smaller and neurites are thinner than those of human neurons. These structural features allow mouse neurons to be integrated in the limited space of the brain, though thin neurites should suppress distal connections according to cable theory. We implemented this mouse-mimetic constraint in convolutional layers of a generative adversarial network (GAN) and a denoising diffusion implicit model (DDIM), which were then subjected to image generation tasks using photo datasets of cat faces, cheese, human faces, and birds. The mouse-mimetic GAN outperformed a standard GAN in the image generation task using the cat faces and cheese photo datasets, but underperformed for human faces and birds. The mouse-mimetic DDIM gave similar results, suggesting that the nature of the datasets affected the results. Analyses of the four datasets indicated differences in their image entropy, which should influence the number of parameters required for image generation. The preferences of the mouse-mimetic AIs coincided with the impressions commonly associated with mice. The relationship between the neuronal network and brain function should be investigated by implementing other biological findings in artificial neural networks., Comment: 41 pages, 4 figures

Quantum error correction is essential for the development of any scalable quantum computer. In this work we introduce a generalization of a quantum interleaving method for combating clusters of errors in toric quantum error-correcting codes. We present new $n$-dimensional toric quantum codes, where $n\geq 5$, which are featured by lattice codes and apply the proposed quantum interleaving method to such new $n$-dimensional toric quantum codes. Through the application of this method to these novel $n$-dimensional toric quantum codes we derive new $n$-dimensional quantum burst-error-correcting codes. Consequently, $n$-dimensional toric quantum codes and burst-error-correcting quantum codes are provided offering both a good code rate and a significant coding gain when it comes to toric quantum codes. Another important consequence from the presented $n$-dimensional toric quantum codes is that if the Golomb and Welch conjecture in \cite{perfcodes} regarding the Lee sphere in $n$ dimensions for the respective close packings holds true, then it follows that these $n$-dimensional toric quantum codes are the only possible ones to be obtained from lattice codes. Moreover, such a methodology can be applied for burst error correction in cases involving localized errors, quantum data storage and quantum channels with memory., Comment: This manuscript is the proposed generalization of the work New Three and Four-Dimensional Toric and Burst-Error-Correcting Quantum Codes

The magnetic textures generated by a perpendicularly applied magnetic field at the ferromagnetic layer of $Co/Al_{2}O_{3}/Nb$ thin film heterostructures are investigated using magneto-optical imaging and micromagnetic simulations. It is observed that the stray field caused by flux avalanches in the superconducting layer prints out a non-trivial in-plane texture in the cobalt layer, which remains stable up to temperatures much above the Nb critical temperature. These textures mimic quite closely the dendritic thermomagnetic flux avalanches that penetrate the Nb layer from its edges. For low cobalt thickness, the filamentary magnetic textures occur in pairs with opposite polarity. The previous in-plane magnetization determines the relative location of the magnetic filaments with respect to the avalanche position. Micromagnetic simulations solving the Landau-Lifshitz-Gilbert equation confirm the interpretation given for the experimental findings., Comment: 13 paginas, 5 figuras, supplementary material

We extend previous works on the multiplicity of solutions to the Allen-Cahn system on closed Riemannian manifolds by considering an arbitrary number of phases. Specifically, we show that on parallelizable manifolds, the number of solutions is bounded from below by topological invariants of the underlying manifold, provided the temperature parameter and volume constraint are sufficiently small. The Allen-Cahn system naturally arises in phase separation models, where solutions represent the distribution of distinct phases in a multi-component mixture. As the temperature parameter approaches zero, the system's energy approximates the multi-isoperimetric profile, leading to solutions concentrating in regions resembling isoperimetric clusters. For two or three phases, these results rely on classifying isoperimetric clusters. However, this classification remains incomplete for a larger number of phases. To address this technical issue, we employ a "volume-fixing variations" approach, enabling us to establish our results for any number of phases and small volume constraints. This offers deeper insights into phase separation phenomena on manifolds with arbitrary geometry.

A minor change in the Barcelos-Wotzasek (BW) symplectic algorithm for constrained systems is proposed. The change addresses some criticism that formalism has received, placing it on the same footing as Dirac's algorithm., Comment: A final version article is available at Brazilian Journal of Physics

We consider models for spatiotemporal Poisson processes with some missing location data. We discuss four models that make provision for missing location data, and their estimation. The corresponding code is available on GitHub as an extension of LASPATED at https://github.com/vguigues/LASPATED/Missing_Data. We tested our models using the process of emergency call arrivals to an emergency medical service where the emergency reports often omit the location of the emergency. We show the difference made by using models that make provision for missing location data.

Designing an operational architecture for the Quantum Internet is a challenging task in light of both fundamental limitations imposed by the laws of physics and technological constraints. Here, we propose a method to abstract away most of the quantum-specific elements and formulate a best-effort quantum network architecture based on packet-switching, akin to that of the classical Internet. Such reframing provides an opportunity to exploit the many tools and protocols available and well-understood within the Internet. As an illustration, we tailor and adapt classical congestion control and active queue management protocols to quantum networks, comprising an architecture wherein quantum end- and intermediate nodes effectively regulate demand and resource utilization, respectively. Results show that these classical networking tools can be effectively used to combat quantum memory decoherence and keep end-to-end fidelity around a target value., Comment: 9 pages, 5 figures

Monocular depth estimation is a critical task for autonomous driving and many other computer vision applications. While significant progress has been made in this field, the effects of viewpoint shifts on depth estimation models remain largely underexplored. This paper introduces a novel dataset and evaluation methodology to quantify the impact of different camera positions and orientations on monocular depth estimation performance. We propose a ground truth strategy based on homography estimation and object detection, eliminating the need for expensive lidar sensors. We collect a diverse dataset of road scenes from multiple viewpoints and use it to assess the robustness of a modern depth estimation model to geometric shifts. After assessing the validity of our strategy on a public dataset, we provide valuable insights into the limitations of current models and highlight the importance of considering viewpoint variations in real-world applications., Comment: 17 pages, 5 figures. Accepted at ECCV 2024 2nd Workshop on Vision-Centric Autonomous Driving (VCAD)

The Bi1-xSbx was the first 3D topological insulator found in nature. It presents a complex electronic structure with topological to trivial transition and a semimetallic to semiconductor transition, both achieved by changing the x fraction of Sb. The complex nature of this system may lead to several electronic and topological phases in matter, making it a promising quantum material. Here, we focused on preparing very high-quality thin films samples of Bi1-xSbx with varying fraction of x using the Co-deposition Magnetron Sputtering technique. Our results demonstrate that high-quality samples, with compact and uniform morphology, presenting a preferential direction of growth, can be obtained over SiO2 substrate. Our findings suggest a dependence between the thin films crystalline texture and the composition of the samples, as well as the deposition temperature., Comment: 6 pages and 6 figures

Algebraic lattices are those obtained from modules in the ring of integers of algebraic number fields through the canonical or twisted embeddings. In turn, well-rounded lattices are those with maximal cardinality of linearly independent vectors in its set of minimal vectors. Both classes of lattices have been applied for signal transmission in some channels, such as wiretap channels. Recently, some advances have been made in the search for well-rounded lattices that can be realized as algebraic lattices. Moreover, some works have been published studying algebraic lattices obtained from modules in cyclic number fields of odd prime degree $p$. In this work, we generalize some results of a recent work of Tran et al. and we provide new constructions of well-rounded algebraic lattices from a certain family of modules in the ring of integers of each of these fields when $p$ is ramified in its extension over the field of rational numbers., Comment: 11 pages

Computer Graphics (CG) advancements have allowed the creation of more realistic Virtual Humans (VH) through modern techniques for animating the VH body and face, thereby affecting perception. From traditional methods, including blend shapes, to driven animations using facial and body tracking, these advancements can potentially enhance the perception of comfort and realism in relation to VHs. Previously, Psychology studied facial movements in humans, with some works separating expressions into macro and micro expressions. Also, some previous CG studies have analyzed how macro and micro expressions are perceived, replicating psychology studies in VHs, encompassing studies with realistic and cartoon VHs, and exploring different VH technologies. However, instead of using facial tracking animation methods, these previous studies animated the VHs using blendshapes interpolation. To understand how the facial tracking technique alters the perception of VHs, this paper extends the study to macro and micro expressions, employing two datasets to transfer real facial expressions to VHs and analyze how their expressions are perceived. Our findings suggest that transferring facial expressions from real actors to VHs significantly diminishes the accuracy of emotion perception compared to VH facial animations created by artists.

A good edge-labeling (gel for short) of a graph $G$ is a function $\lambda: E(G) \to \mathbb{R}$ such that, for any ordered pair of vertices $(x, y)$ of $G$, there do not exist two distinct increasing paths from $x$ to $y$, where ``increasing'' means that the sequence of labels is non-decreasing. This notion was introduced by Bermond et al. [Theor. Comput. Sci. 2013] motivated by practical applications arising from routing and wavelength assignment problems in optical networks. Prompted by the lack of algorithmic results about the problem of deciding whether an input graph admits a gel, called GEL, we initiate its study from the viewpoint of parameterized complexity. We first introduce the natural version of GEL where one wants to use at most $c$ distinct labels, which we call $c$-GEL, and we prove that it is NP-complete for every $c \geq 2$ on very restricted instances. We then provide several positive results, starting with simple polynomial kernels for GEL and $c$-\GEL parameterized by neighborhood diversity or vertex cover. As one of our main technical contributions, we present an FPT algorithm for GEL parameterized by the size of a modulator to a forest of stars, based on a novel approach via a 2-SAT formulation which we believe to be of independent interest. We also present FPT algorithms based on dynamic programming for $c$-GEL parameterized by treewidth and $c$, and for GEL parameterized by treewidth and the maximum degree. Finally, we answer positively a question of Bermond et al. [Theor. Comput. Sci. 2013] by proving the NP-completeness of a problem strongly related to GEL, namely that of deciding whether an input graph admits a so-called UPP-orientation., Comment: 46 pages, 16 figures

Experiments in Agricultural Sciences often involve the analysis of longitudinal nominal polytomous variables, both in individual and grouped structures. Marginal and mixed-effects models are two common approaches. The distributional assumptions induce specific mean-variance relationships, however, in many instances, the observed variability is greater than assumed by the model. This characterizes overdispersion, whose identification is crucial for choosing an appropriate modeling framework to make inferences reliable. We propose an initial exploration of constructing a longitudinal multinomial dispersion index as a descriptive and diagnostic tool. This index is calculated as the ratio between the observed and assumed variances. The performance of this index was evaluated through a simulation study, employing statistical techniques to assess its initial performance in different scenarios. We identified that as the index approaches one, it is more likely that this corresponds to a high degree of overdispersion. Conversely, values closer to zero indicate a low degree of overdispersion. As a case study, we present an application in animal science, in which the behaviour of pigs (grouped in stalls) is evaluated, considering three response categories., Comment: 22 pages

The widespread application of Artificial Intelligence (AI) techniques has significantly influenced the development of new therapeutic agents. These computational methods can be used to design and predict the properties of generated molecules. Multi-target Drug Discovery (MTDD) is an emerging paradigm for discovering drugs against complex disorders that do not respond well to more traditional target-specific treatments, such as central nervous system, immune system, and cardiovascular diseases. Still, there is yet to be an established benchmark suite for assessing the effectiveness of AI tools for designing multi-target compounds. Standardized benchmarks allow for comparing existing techniques and promote rapid research progress. Hence, this work proposes an evaluation framework for molecule generation techniques in MTDD scenarios, considering brain diseases as a case study. Our methodology involves using large language models to select the appropriate molecular targets, gathering and preprocessing the bioassay datasets, training quantitative structure-activity relationship models to predict target modulation, and assessing other essential drug-likeness properties for implementing the benchmarks. Additionally, this work will assess the performance of four deep generative models and evolutionary algorithms over our benchmark suite. In our findings, both evolutionary algorithms and generative models can achieve competitive results across the proposed benchmarks., Comment: 8 pages, 1 figure, published in 2024 IEEE Congress on Evolutionary Computation (CEC)

Transformer models have achieved state-of-the-art results, with Large Language Models (LLMs), an evolution of first-generation transformers (1stTR), being considered the cutting edge in several NLP tasks. However, the literature has yet to conclusively demonstrate that LLMs consistently outperform 1stTRs across all NLP tasks. This study compares three 1stTRs (BERT, RoBERTa, and BART) with two open LLMs (Llama 2 and Bloom) across 11 sentiment analysis datasets. The results indicate that open LLMs may moderately outperform or match 1stTRs in 8 out of 11 datasets but only when fine-tuned. Given this substantial cost for only moderate gains, the practical applicability of these models in cost-sensitive scenarios is questionable. In this context, a confidence-based strategy that seamlessly integrates 1stTRs with open LLMs based on prediction certainty is proposed. High-confidence documents are classified by the more cost-effective 1stTRs, while uncertain cases are handled by LLMs in zero-shot or few-shot modes, at a much lower cost than fine-tuned versions. Experiments in sentiment analysis demonstrate that our solution not only outperforms 1stTRs, zero-shot, and few-shot LLMs but also competes closely with fine-tuned LLMs at a fraction of the cost., Comment: 13 pages, 3 figures, 8 tables

This paper utilizes video analytics to study pedestrian and vehicle traffic behavior, focusing on analyzing traffic patterns during football gamedays. The University of Florida (UF) hosts six to seven home football games on Saturdays during the college football season, attracting significant pedestrian activity. Through video analytics, this study provides valuable insights into the impact of these events on traffic volumes and safety at intersections. Comparing pedestrian and vehicle activities on gamedays versus non-gamedays reveals differing patterns. For example, pedestrian volume substantially increases during gamedays, which is positively correlated with the probability of the away team winning. This correlation is likely because fans of the home team enjoy watching difficult games. Win probabilities as an early predictor of pedestrian volumes at intersections can be a tool to help traffic professionals anticipate traffic management needs. Pedestrian-to-vehicle (P2V) conflicts notably increase on gamedays, particularly a few hours before games start. Addressing this, a "Barnes Dance" movement phase within the intersection is recommended. Law enforcement presence during high-activity gamedays can help ensure pedestrian compliance and enhance safety. In contrast, we identified that vehicle-to-vehicle (V2V) conflicts generally do not increase on gamedays and may even decrease due to heightened driver caution.

Aedes aegypti is still one of the main concerns when it comes to disease vectors. Among the many ways to deal with it, there are important protocols that make use of egg numbers in ovitraps to calculate indices, such as the LIRAa and the Breteau Index, which can provide information on predictable outbursts and epidemics. Also, there are many research lines that require egg numbers, specially when mass production of mosquitoes is needed. Egg counting is a laborious and error-prone task that can be automated via computer vision-based techniques, specially deep learning-based counting with object detection. In this work, we propose a new dataset comprising field and laboratory eggs, along with test results of three neural networks applied to the task: Faster R-CNN, Side-Aware Boundary Localization and FoveaBox.

In this paper, we examined the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the two-dimensional XY model on the honeycomb lattice. To address its thermodynamical behavior, we conducted standard numerical Monte Carlo simulations with the simulated annealing protocol and entropic simulations based on the Wang-Landau algorithm. The inverse transition temperature ($\beta_{BKT}$) was determined using the second ($\Upsilon$) and fourth-order ($\Upsilon_4$) helicity modulus as the order parameter. We also used the fourth-order Binder cumulant of the magnetization as an additional tool to address the critical properties of the model. Our finite-size scaling analysis suggests $\beta_{BKT} = 1.687(3)$ from $\Upsilon$ and $\beta_{BKT}=1.635(11)$ from $\Upsilon_4$. From the Binder cumulant crossing we found $\beta_{BKT}=1.724(2)$. These values deviate significantly from the expected theoretical value of $\sqrt{2}$. We believe that this discrepancy suggests that the theoretical assumptions regarding the analytical calculation may need to be revisited. Additionally, we calculated the vortex density and the formation energy of the vortex-antivortex pairs, where the obtained vortex formation energy is $2\mu=4.0(5)$. Upon comparison with the square lattice, our results support the notion of instability of the honeycomb lattice to support the spin long-range order and give additional backing to the critical behavior we found.

This paper presents an initial exploration on the use of 2D cellular automata (CA) for generating 3D terrains through a simple yet effective additive approach. By experimenting with multiple CA transition rules, this preliminary investigation yielded aesthetically interesting landscapes, hinting at the technique's potential applicability for real-time terrain generation in games.

We evaluate the performance of two-way quantum repeater chains with sequential entanglement swapping. Within the analysis we consider memory decoherence, gate imperfections, and imperfect link-level entanglement generation. Our main results include closed-form expressions for the average entanglement fidelity of the generated end-to-end entangled states. We generalize previous findings for the one-shot fidelity analysis and study the case where repeater chains serve end-to-end requests continuously. We provide solutions to the continuous request scenario by combining results from quantum information theory and queuing theory. Finally, we apply the formulas obtained to analyze the impacts of hardware parameters, i.e., coherence times and gate fidelity, and distance on the entanglement fidelity and secret key rate of homogeneous quantum repeater chains., Comment: 10 pages, 5 figures

With the recent popularity of neural networks comes the need for efficient serving of inference workloads. A neural network inference workload can be represented as a computational graph with nodes as operators transforming multidimensional tensors. The tensors can be transposed and/or tiled in a combinatorially large number of ways, some configurations leading to accelerated inference. We propose TGraph, a neural graph architecture that allows screening for fast configurations of the target computational graph, thus representing an artificial intelligence (AI) tensor compiler in contrast to the traditional heuristics-based compilers. The proposed solution improves mean Kendall's $\tau$ across layout collections of TpuGraphs from 29.8% of the reliable baseline to 67.4% of TGraph. We estimate the potential CO$_2$ emission reduction associated with our work to be equivalent to over 50% of the total household emissions in the areas hosting AI-oriented data centers.

Errors are the fundamental barrier to the development of quantum systems. Quantum networks are complex systems formed by the interconnection of multiple components and suffer from error accumulation. Characterizing errors introduced by quantum network components becomes a fundamental task to overcome their depleting effects in quantum communication. Quantum Network Tomography (QNT) addresses end-to-end characterization of link errors in quantum networks. It is a tool for building error-aware applications, network management, and system validation. We provide an overview of QNT and its initial results for characterizing quantum star networks. We apply a previously defined QNT protocol for estimating bit-flip channels to estimate depolarizing channels. We analyze the performance of our estimators numerically by assessing the Quantum Cram\`er-Rao Bound (QCRB) and the Mean Square Error (MSE) in the finite sample regime. Finally, we provide a discussion on current challenges in the field of QNT and elicit exciting research directions for future investigation., Comment: 11 pages, 5 figures, accepted for publication at IEEE Network

We identify an issue in multi-task learnable compression, in which a representation learned for one task does not positively contribute to the rate-distortion performance of a different task as much as expected, given the estimated amount of information available in it. We interpret this issue using the predictive $\mathcal{V}$-information framework. In learnable scalable coding, previous work increased the utilization of side-information for input reconstruction by also rewarding input reconstruction when learning this shared representation. We evaluate the impact of this idea in the context of input reconstruction more rigorously and extended it to other computer vision tasks. We perform experiments using representations trained for object detection on COCO 2017 and depth estimation on the Cityscapes dataset, and use them to assist in image reconstruction and semantic segmentation tasks. The results show considerable improvements in the rate-distortion performance of the assisted tasks. Moreover, using the proposed representations, the performance of the base tasks are also improved. Results suggest that the proposed method induces simpler representations that are more compatible with downstream processes., Comment: Published in ICME Workshops 2024

Traditional methods of model diagnostics may include a plethora of graphical techniques based on residual analysis, as well as formal tests (e.g. Shapiro-Wilk test for normality and Bartlett test for homogeneity of variance). In this paper we derive a new distance metric based on the half-normal plot with a simulation envelope, a graphical model evaluation method, and investigate its properties through simulation studies. The proposed metric can help to assess the fit of a given model, and also act as a model selection criterion by being comparable across models, whether based or not on a true likelihood. More specifically, it quantitatively encompasses the model evaluation principles and removes the subjective bias when closely related models are involved. We validate the technique by means of an extensive simulation study carried out using count data, and illustrate with two case studies in ecology and fisheries research.

We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded Kolmogorov maps and coupling terms are defined by nonlinear functions taking values in $(0,1)$. These couplings describe the proportions of individuals dispersing between regions. We first give a brief survey of similar discrete-time dispersal models. We then derive sufficient conditions for the stability/instability of the extinction equilibrium, for the existence of a positive fixed point and for ensuring uniform strong persistence. Finally we numerically explore a planar version of our model in a source-sink context, to show some of the qualitative behaviour that the model we consider can capture: for example, periodic behaviour and dynamics reminiscent of chaos.

Deepfake speech represents a real and growing threat to systems and society. Many detectors have been created to aid in defense against speech deepfakes. While these detectors implement myriad methodologies, many rely on low-level fragments of the speech generation process. We hypothesize that breath, a higher-level part of speech, is a key component of natural speech and thus improper generation in deepfake speech is a performant discriminator. To evaluate this, we create a breath detector and leverage this against a custom dataset of online news article audio to discriminate between real/deepfake speech. Additionally, we make this custom dataset publicly available to facilitate comparison for future work. Applying our simple breath detector as a deepfake speech discriminator on in-the-wild samples allows for accurate classification (perfect 1.0 AUPRC and 0.0 EER on test data) across 33.6 hours of audio. We compare our model with the state-of-the-art SSL-wav2vec model and show that this complex deep learning model completely fails to classify the same in-the-wild samples (0.72 AUPRC and 0.99 EER)., Comment: Submitted to ACM journal -- Digital Threats: Research and Practice

In this paper, we delve into the influence of torsion axial pseudo vector on dark photons in an axion torsionic background, as investigated previously by Duncan et al[ Nucl Phys B 387:215 (1992)]. Notably, axial torsion, owing to its significantly greater mass compared to axions, gives rise to magnetic helicity in torsionful Chern-Simons (CS) electrodynamics, leading to the damping of magnetic fields. In QCD scale the damping from dark massive photons leads us to obtain a magnetic field of $10^{-8}$ Gauss, which is approximated the order of magnitude of magnetic fields at present universe. This result is obtained by considering that torsion has the value of the 1 MeV at the early universe, and can be improved to the higher value of $10^{-3}$ Gauss when the axial torsion 0-component is given by $10^{8}$ MeV and the mass of dark photon is approximated equal to the axion. The axion plays a crucial role in achieving CS dynamo action arising from axions. This study is useful in deepening our understanding of fundamental physics, from nuclear interactions to the nature of dark matter., Comment: 14 pages, to be submiited

We build on previous work on multirings (\cite{roberto2021quadratic}) that provides generalizations of the available abstract quadratic forms theories (special groups and real semigroups) to the context of multirings (\cite{marshall2006real}, \cite{ribeiro2016functorial}). Here we raise one step in this generalization, introducing the concept of pre-special hyperfields and expand a fundamental tool in quadratic forms theory to the more general multivalued setting: the K-theory. We introduce and develop the K-theory of hyperbolic hyperfields that generalize simultaneously Milnor's K-theory (\cite{milnor1970algebraick}) and Special Groups K-theory, developed by Dickmann-Miraglia (\cite{dickmann2006algebraic}). We develop some properties of this generalized K-theory, that can be seen as a free inductive graded ring, a concept introduced in \cite{dickmann1998quadratic} in order to provide a solution of Marshall's Signature Conjecture., Comment: arXiv admin note: substantial text overlap with arXiv:2307.01674

In this ongoing work, we extend to a class of well-behaved pre-special hyperfields the work of J. Min\'a\v c and Spira (\cite{minac1996witt}) that describes a (pro-2)-group of a field extension that encodes the quadratic form theory of a given field $F$: in \cite{adem1999cohomology} it is shown that its associated cohomology ring contains a copy of the cohomology ring of the field $F$. Our construction, a contravariant functor into the category of "pointed" pro-2-groups, is essentially given by generators and relations of profinite-2-groups. We prove that such profinite groups $\mbox{Gal}(F)$ encode the space of orders of the special group canonically associated to the hyperfield $F$ and provide a criterion to detect when $F$ is formally real or not., Comment: The authors want to express their gratitude to Coordena\c{c}\~ao de Aperfei\c{c}oamento de Pessoal de N\'ivel Superior (Capes-Brazil) by the financial support to develop this work: project Capes Math-Amsud number 88881.694471/2022-01