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The correspondence between commutative rings of ordinary differential operators and algebraic curves has been extensively and deeply studied since the seminal works of Burchnall-Chaundy in 1923. This paper is an overview of recent developments to make this correspondence computationally effective, by means of differential algebra and symbolic computation. The centralizer of an ordinary differential operator $L$ is a maximal commutative ring, the affine ring of a spectral curve $\Gamma$. The defining ideal of $\Gamma$ is described, assuming that a finite set of generators of the centralizer is known. In addition, the factorization problem of $L-\lambda$ over a new coefficient field, defined by the coefficient field of $L$ and $\Gamma$, allows the computation of spectral sheaves on $\Gamma$. The ultimate goal is to develop Picard-Vessiot theory for spectral problems $L(y)=\lambda y$, for a generic $\lambda$.

Transformers, a cornerstone of deep-learning architectures for sequential data, have achieved state-of-the-art results in tasks like Natural Language Processing (NLP). Models such as BERT and GPT-3 exemplify their success and have driven the rise of large language models (LLMs). However, a critical challenge persists: safeguarding the privacy of data used in LLM training. Privacy-preserving techniques like Federated Learning (FL) offer potential solutions, but practical limitations hinder their effectiveness for Transformer training. Two primary issues are (I) the risk of sensitive information leakage due to aggregation methods like FedAvg or FedSGD, and (II) the high communication overhead caused by the large size of Transformer models. This paper introduces a novel FL method that reduces communication overhead while maintaining competitive utility. Our approach avoids sharing full model weights by simulating a global model locally. We apply k-means clustering to each Transformer layer, compute centroids locally, and transmit only these centroids to the server instead of full weights or gradients. To enhance security, we leverage Intel SGX for secure transmission of centroids. Evaluated on a translation task, our method achieves utility comparable to state-of-the-art baselines while significantly reducing communication costs. This provides a more efficient and privacy-preserving FL solution for Transformer models.

Power system operators need new, efficient operational tools to use the flexibility of distributed resources and deal with the challenges of highly uncertain and variable power systems. Transmission system operators can consider the available flexibility in distribution systems (DSs) without breaching the DS constraints through flexibility areas. However, there is an absence of open-source packages for flexibility area estimation. This paper introduces TensorConvolutionPlus, a user-friendly Python-based package for flexibility area estimation. The main features of TensorConvolutionPlus include estimating flexibility areas using the TensorConvolution+ algorithm, the power flow-based algorithm, an exhaustive PF-based algorithm, and an optimal power flow-based algorithm. Additional features include adapting flexibility area estimations from different operating conditions and including flexibility service providers offering discrete setpoints of flexibility. The TensorConvolutionPlus package facilitates a broader adaptation of flexibility estimation algorithms by system operators and power system researchers., Comment: 9 pages, 10 figures

BabyIAXO is the intermediate stage of the International Axion Observatory (IAXO) to be hosted at DESY. Its primary goal is the detection of solar axions following the axion helioscope technique. Axions are converted into photons in a large magnet that is pointing to the sun. The resulting X-rays are focused by appropriate X-ray optics and detected by sensitive low-background detectors placed at the focal spot. The aim of this article is to provide an accurate quantitative description of the different components (such as the magnet, optics, and X-ray detectors) involved in the detection of axions. Our efforts have focused on developing robust and integrated software tools to model these helioscope components, enabling future assessments of modifications or upgrades to any part of the IAXO axion helioscope and evaluating the potential impact on the experiment's sensitivity. In this manuscript, we demonstrate the application of these tools by presenting a precise signal calculation and response analysis of BabyIAXO's sensitivity to the axion-photon coupling. Though focusing on the Primakoff solar flux component, our virtual helioscope model can be used to test different production mechanisms, allowing for direct comparisons within a unified framework., Comment: 36 pages, 18 figures, 4 tables, Submitted to JHEP

The aim of this paper is to study lattice properties of the sharp partial order for complex matrices having index at most 1. We investigate the down-set of a fixed matrix $B$ under this partial order via isomorphisms with two different partially ordered sets of projectors. These are, respectively, the set of projectors that commute with a certain (nonsingular) block of a Hartwig-Spindelb\"ock decomposition of $B$ and the set of projectors that commute with the Jordan canonical form of that block. Using these isomorphisms, we study the lattice structure of the down-sets and we give properties of them. Necessary and sufficient conditions under which the down-set of B is a lattice were found, in which case we describe its elements completely. We also show that every down-set of $B$ has a distinguished Boolean subalgebra and we give a description of its elements. We characterize the matrices that are above a given matrix in terms of its Jordan canonical form. Mitra (1987) showed that the set of all $n \times n$ complex matrices having index at most 1 with $n\geq 4$ is not a lower semilattice. We extend this result to $n=3$ and prove that it is a lower semilattice with $n=2$. We also answer negatively a conjecture given by Mitra, Bhimasankaram and Malik (2010). As a last application, we characterize solutions of some matrix equations via the established isomorphisms., Comment: 19 pages, 4 figures

We characterize the overdensity (spike) of fermionic dark matter (DM) particles around a supermassive black hole (SMBH) within a general relativistic analysis. The initial DM halo distribution is obtained by solving the equilibrium equations of a self-gravitating system of massive fermions at a finite temperature, according to the Ruffini-Arg\"uelles-Rueda (RAR) model. The final fermionic DM spike is calculated around a Schwarzschild SMBH. We explore two possible interpretations for the origin and evolution of the SMBH seed. One corresponds to the traditional scenario proposed by Gondolo & Silk (1999), where a small BH mass of baryonic origin sits at the halo's center and grows adiabatically. The other one, from DM origin, where the dense and degenerate fermion core predicted by the RAR model grows adiabatically by capturing baryons until its gravitational collapse, providing a heavy SMBH seed, whose specific value depends on the fermion mass. We study different initial fermionic DM profiles that the theory allows. We show that overall dilute (i.e., Boltzmannian) fermionic DM develops the well-known spike with density profile $\rho \sim r^{-3/2}$. Instead, for semi-degenerate fermions with a dense and compact core surrounded by a diluted halo, we find novel spike profiles that depend on the particle mass and nature. In the more general case, fermionic spikes do not develop a simple power-law profile. Furthermore, the SMBH does not always imply an enhancement of the surrounding DM density; it might also deplete it. Thus, the self-consistent inclusion of the DM candidate nature and mass in determining the structure and distribution of DM in galaxies, including the DM spikes around SMBHs, is essential for the specification of DM astrophysical probes such as BH mergers, gravitational waves, or stellar orbits.

The strong gravitational potential of neutron stars (NSs) makes them ideal astrophysical objects for testing extreme gravity phenomena. We explore the potential of NS X-ray pulsed lightcurve observations to probe deviations from general relativity (GR) within the scalar-tensor theory (STT) of gravity framework. We compute the flux from a single, circular, finite-size hot spot, accounting for light bending, Shapiro time delay, and Doppler effect. We focus on the high-compactness regime, i.e., close to the critical GR value GM/(Rc^2) = 0.284, over which multiple images of the spot appear and impact crucially the lightcurve. Our investigation is motivated by the increased sensitivity of the pulse to the scalar charge of the spacetime in such high compactness regimes, making these systems exceptionally suitable for scrutinizing deviations from GR, notably phenomena such as spontaneous scalarization, as predicted by STT. We find significant differences in NS observables, e.g., the flux of a single spot can differ up to 80% with respect to GR. Additionally, reasonable choices for the STT parameters that satisfy astrophysical constraints lead to changes in the NS radius relative to GR of up to approximately 10%. Consequently, scalar parameters might be better constrained when uncertainties in NS radii decrease, where this could occur with the advent of next-generation gravitational wave detectors, such as the Einstein Telescope and LISA, as well as future electromagnetic missions like eXTP and ATHENA. Thus, our findings suggest that accurate X-ray data of the NS surface emission, jointly with refined theoretical models, could constrain STTs., Comment: 20 pages, 9 figures. Accepted for publication in EPJC

Long and short gamma-ray bursts (GRBs) are thought to arise from different and unrelated astrophysical progenitors. The association of long GRBs with supernovae (SNe) and the difference in the distributions of galactocentric offsets of long and short GRBs within their host galaxies have often been considered strong evidence of their unrelated origins. Long GRBs have been thought to result from the collapse of single massive stars, while short GRBs come from mergers of compact object binaries. Our present study challenges this conventional view. We demonstrate that the observational properties, such as the association with SNe and the different galactic offsets, are naturally explained within the framework of the binary-driven hypernova model, suggesting an evolutionary connection between long and short GRBs., Comment: Accepted for publication in Phys. Rev. D

Surface plasmon polaritons have received much attention over the last decades in fields such as photonics or nanotechnology due to their inherent high sensitivity to metal surface variations (e.g., presence of adsorbates or changes in the roughness). Because of this important property, it is expected that they will find promising major applications in widely cross-disciplinary areas ranging from material science to medicine. Motivated by this ever-growing interest, here we introduce a novel theoretical framework suitable to design new types of structured paraxial surface plasmon beams and to control their propagation along the interface between a dielectric and a lossy metal. This is possible by virtue of a convenient Hermite-Gaussian mode expansion, which constitutes a complete basis set upon which new types of structured paraxial plasmon beams can be generated. The beams obtained from this method present a rather peculiar feature, as they exhibit local intensity maxima at different propagation distances. This way of creating tightly confined structured light allows us control where to place the beam energy. This, thus, opens up worth exploring pathways to manipulate light propagation along metal surfaces at the nanoscale. As a proof-of-concept, we provide numerical evidence of the feasibility of the method by considering the analysis of the propagation of Airy-based surface plasmon polaritons along an air-silver interface., Comment: 20 pages, 3 figures (plus 6 pages with supplemental information)

The exceptionally low mass of $0.77_{-0.17}^{+0.2} M_{\odot}$ for the central compact object (CCO) XMMU J173203.3 -- 344518 (XMMU J1732) in the supernova remnant (SNR) HESS J1731 -- 347 challenges standard neutron star (NS) formation models. The nearby post-AGB star IRAS 17287 -- 3443 ($\approx 0.6 M_\odot$), also within the SNR, enriches the scenario. To address this puzzle, we advance the possibility that the gravitational collapse of a rotating pre-SN iron core ($\approx 1.2 M_\odot$) could result in a low-mass NS. We show that angular momentum conservation during the collapse of an iron core rotating at $\approx 45\%$ of the Keplerian limit results in a mass loss of $\approx 0.3 M_\odot$, producing a stable newborn NS of $\approx 0.9 M_\odot$. Considering the possible spin-down, this indicates that the NS is now slowly rotating, thus fulfilling the observed mass-radius relation. Additionally, the NS's surface temperature ($\approx 2 \times 10^6$ K) aligns with canonical thermal evolution for its $\approx 4.5$ kyr age. We propose the pre -- SN star, likely an ultra-stripped core of $\approx 4.2 M_\odot$, formed a tidally locked binary with IRAS 17287 -- 3443, having a 1.43-day orbital period. The supernova led to a $\approx 3 M_\odot$ mass loss, imparting a kick velocity $\lesssim 670$ km s$^{-1}$, which disrupted the binary. This scenario explains the observed 0.3 pc offset between XMMU J1732 and IRAS 17287 -- 3443 and supports the possibility of CCOs forming in binaries, with rotation playing a key role in core-collapse, and the CCO XMMU J1732 being the lightest NS ever observed., Comment: Accepted for publication in ApJ, comments are welcome!

The template design problem (TDP) is a hard combinatorial problem with a high number of symmetries which makes solving it more complicated. A number of techniques have been proposed in the literature to optimise its resolution, ranging from complete methods to stochastic ones. However, although metaheuristics are considered efficient methods that can find enough-quality solutions at a reasonable computational cost, these techniques have not proven to be truly efficient enough to deal with this problem. This paper explores and analyses a wide range of metaheuristics to tackle the problem with the aim of assessing their suitability for finding template designs. We tackle the problem using a wide set of metaheuristics whose implementation is guided by a number of issues such as problem formulation, solution encoding, the symmetrical nature of the problem, and distinct forms of hybridisation. For the TDP, we also propose a slot-based alternative problem formulation (distinct to other slot-based proposals), which represents another option other than the classical variation-based formulation of the problem. An empirical analysis, assessing the performance of all the metaheuristics (i.e., basic, integrative and collaborative algorithms working on different search spaces and with/without symmetry breaking) shows that some of our proposals can be considered the state-of-the-art when they are applied to specific problem instances., Comment: 30 pages, 4 figures

The balanced incomplete block design (BIBD) problem is a difficult combinatorial problem with a large number of symmetries, which add complexity to its resolution. In this paper, we propose a dual (integer) problem representation that serves as an alternative to the classical binary formulation of the problem. We attack this problem incrementally: firstly, we propose basic algorithms (i.e. local search techniques and genetic algorithms) intended to work separately on the two different search spaces (i.e. binary and integer); secondly, we propose two hybrid schemes: an integrative approach (i.e. a memetic algorithm) and a collaborative model in which the previous methods work in parallel, occasionally exchanging information. Three distinct two-dimensional structures are proposed as communication topology among the algorithms involved in the collaborative model, as well as a number of migration and acceptance criteria for sending and receiving data. An empirical analysis comparing a large number of instances of our schemes (with algorithms possibly working on different search spaces and with/without symmetry breaking methods) shows that some of these algorithms can be considered the state of the art of the metaheuristic methods applied to finding BIBDs. Moreover, our cooperative proposal is a general scheme from which distinct algorithmic variants can be instantiated to handle symmetrical optimisation problems. For this reason, we have also analysed its key parameters, thereby providing general guidelines for the design of efficient/robust cooperative algorithms devised from our proposal., Comment: 16 pages, 7 figures

We study the problem of stock replenishment and transshipment in the retail industry. We develop a model that can accommodate different policies, including centralized redistribution (replenishment) and decentralized redistribution (lateral transshipments), allowing for direct comparisons between them. We present a numeric analysis in which the benchmark instances stem from the collaboration with a high-end clothing retail company. The underlying model, as usually in the field, is a large-scale mixed-integer linear programming problem. We develop a specific algorithmic procedure to solve this MILP problem and compare its performance with the direct solution via state-of-the-art solvers.

The task of spatial clustering of transcriptomics data is of paramount importance. It enables the classification of tissue samples into diverse subpopulations of cells, which, in turn, facilitates the analysis of the biological functions of clusters, tissue reconstruction, and cell-cell interactions. Many approaches leverage gene expressions, spatial locations, and histological images to detect spatial domains; however, Graph Neural Networks (GNNs) as state of the art models suffer from a limitation in the assumption of pairwise connections between nodes. In the case of domain detection in spatial transcriptomics, some cells are found to be not directly related. Still, they are grouped as the same domain, which shows the incapability of GNNs for capturing implicit connections among the cells. While graph edges connect only two nodes, hyperedges connect an arbitrary number of nodes along their edges, which lets Hypergraph Neural Networks (HGNNs) capture and utilize richer and more complex structural information than traditional GNNs. We use autoencoders to address the limitation of not having the actual labels, which are well-suited for unsupervised learning. Our model has demonstrated exceptional performance, achieving the highest iLISI score of 1.843 compared to other methods. This score indicates the greatest diversity of cell types identified by our method. Furthermore, our model outperforms other methods in downstream clustering, achieving the highest ARI values of 0.51 and Leiden score of 0.60.

Free-stream preservation is an essential property for numerical solvers on curvilinear grids. Key to this property is that the metric terms of the curvilinear mapping satisfy discrete metric identities, i.e., have zero divergence. Divergence-free metric terms are furthermore essential for entropy stability on curvilinear grids. We present a new way to compute the metric terms for discontinuous Galerkin spectral element methods (DGSEMs) that guarantees they are divergence-free. Our proposed mimetic approach uses projections that fit within the de Rham Cohomology.

Rigid (Uniform) rotation is usually assumed when investigating the properties of mature neutron stars (NSs). Although it simplifies their description, it is an assumption because we cannot observe the NS's innermost parts. Here, we analyze the structure of NSs in the simple case of ''almost rigidity,'' where the innermost and outermost parts rotate with different angular velocities. This is motivated by the possibility of NSs having superfluid interiors, phase transitions, and angular momentum transfer during accretion processes. We show that, in general relativity, the relative difference in angular velocity between different parts of an NS induces a change in the moment of inertia compared to that of rigid rotation. The relative change depends nonlinearly on where the angular velocity jump occurs inside the NS. For the same observed angular velocity in both configurations, if the jump location is close to the star's surface-which is possible in central compact objects (CCOs) and accreting stars-the relative change in the moment of inertia is close to that of the angular velocity (which is expected due to total angular momentum aspects). If the jump occurs deep within the NS, for instance, due to phase transitions or superfluidity, smaller relative changes in the moment of inertia are observed; we found that if it is at a radial distance smaller than approximately $40\%$ of the star's radius, the relative changes are negligible. Additionally, we outline the relevance of systematic uncertainties that nonrigidity could have on some NS observables, such as radius, ellipticity, and the rotational energy budget of pulsars, which could explain the X-ray luminosity of some sources. Finally, we also show that non-rigidity weakens the universal $I$-Love-$Q$ relations., Comment: 12 pages, 5 figures. Accepted for publication in PRD

We analyze the extraction of the rotational energy of a Kerr black hole (BH) endowed with a test charge and surrounded by an external test magnetic field and ionized low-density matter. For a magnetic field parallel to the BH spin, electrons move outward (inward) and protons inward (outward) in a region around the BH poles (equator). For zero charge, the polar region comprises spherical polar angles $-60^\circ\lesssim \theta \lesssim 60^\circ$ and the equatorial region $60^\circ\lesssim \theta \lesssim 120^\circ$. The polar region shrinks for positive charge, and the equatorial region enlarges. For an isotropic particle density, we argue the BH could experience a cyclic behavior: starting from a zero charge, it accretes more polar protons than equatorial electrons, gaining net positive charge, energy, and angular momentum. Then, the shrinking(enlarging) of the polar(equatorial) region makes it accrete more equatorial electrons than polar protons, gaining net negative charge, energy, and angular momentum. In this phase, the BH rotational energy is extracted. The extraction process continues until the new enlargement of the polar region reverses the situation, and the cycle repeats. We show that this electrodynamical process produces a relatively limited increase of the BH irreducible mass compared to gravitational mechanisms like the Penrose process, hence being a more efficient and promising mechanism for extracting the BH rotational energy., Comment: Accepted for publication in EPJC

The aim of this note is to prove that, given two superreflexive Banach spaces $X$ and $Y$, then $X\widehat{\otimes}_\pi Y$ is superreflexive if and only if either $X$ or $Y$ is finite-dimensional. In a similar way, we prove that $X\widehat{\otimes}_\varepsilon Y$ is superreflexive if and only if either $X$ or $Y$ is finite-dimensional.

Ultrarelativistic heavy-ion collisions produce a state of hot, dense, strongly interacting QCD matter known as quark-gluon plasma (QGP). On an event-by-event basis, the volume of the QGP in ultra-central collisions is mostly constant, while its total entropy can vary significantly, leading to variations in the temperature of the system. Exploiting this unique feature of ultra-central collisions allows us to interpret the correlation between the mean transverse momentum $(\langle p_{\mathrm{T}} \rangle)$ of produced charged hadrons and the number of charged hadrons as a measure of the the speed of sound, $c_{s}$. The speed of sound, $c_{s}$, which relates to the speed at which compression waves travel in a medium (in this case the QGP), is determined by fitting the relative increase of $\langle p_{\mathrm{T}} \rangle$ with respect to the relative change of the average charged-particle density $(\langle \mathrm{d}N_{\mathrm{ch}}/ \mathrm{d}\eta \rangle)$ measured at midrapidity. This study reports the $\langle p_{\mathrm{T}} \rangle$ of charged particles in ultra-central Pb-Pb collisions at a center-of-mass energy of 5.02 TeV per nucleon pair, using the ALICE detector. Different centrality estimators based on charged-particle multiplicity or the transverse energy of the event are employed to select ultra-central collisions. By ensuring a pseudorapidity gap between the region used to define the centrality and the region used for measurement, the influence of biases and their potential effects on the rise of the mean transverse momentum are tested. The measured $c_{s}^{2}$ is found to strongly depend on the type of the centrality estimator, ranging from $0.113 \pm 0.003 \, \mathrm{(stat)} \pm 0.007 \, \mathrm{(syst)}$ to $0.438 \pm 0.001 \, \mathrm{(stat)} \pm 0.019 \, \mathrm{(syst)}$ in natural units.

We prove that the norm of $X\widehat{\otimes}_\pi Y$ is SSD if either $X=\ell_p(I)$ for $p>2$ and $Y$ is a finite-dimensional Banach space such that the modulus of convexity is of power type $q

Hypergraphs tackle the limitations of traditional graphs by introducing {\em hyperedges}. While graph edges connect only two nodes, hyperedges connect an arbitrary number of nodes along their edges. Also, the underlying message-passing mechanisms in Hypergraph Neural Networks (HGNNs) are in the form of vertex-hyperedge-vertex, which let HGNNs capture and utilize richer and more complex structural information than traditional Graph Neural Networks (GNNs). More recently, the idea of overlapping subgraphs has emerged. These subgraphs can capture more information about subgroups of vertices without limiting one vertex belonging to just one group, allowing vertices to belong to multiple groups or subgraphs. In addition, one of the most important problems in graph clustering is to find densest overlapping subgraphs (DOS). In this paper, we propose a solution to the DOS problem via Agglomerative Greedy Enumeration (DOSAGE) algorithm as a novel approach to enhance the process of generating the densest overlapping subgraphs and, hence, a robust construction of the hypergraphs. Experiments on standard benchmarks show that the DOSAGE algorithm significantly outperforms the HGNNs and six other methods on the node classification task.

Sprinting is a determinant ability, especially in team sports. The kinematics of the sprint have been studied in the past using different methods specially developed considering human biomechanics and, among those methods, markerless systems stand out as very cost-effective. On the other hand, we have now multiple general methods for pixel and body tracking based on recent machine learning breakthroughs with excellent performance in body tracking, but these excellent trackers do not generally consider realistic human biomechanics. This investigation first adapts two of these general trackers (MoveNet and CoTracker) for realistic biomechanical analysis and then evaluate them in comparison to manual tracking (with key points manually marked using the software Kinovea). Our best resulting markerless body tracker particularly adapted for sprint biomechanics is termed VideoRun2D. The experimental development and assessment of VideoRun2D is reported on forty sprints recorded with a video camera from 5 different subjects, focusing our analysis in 3 key angles in sprint biomechanics: inclination of the trunk, flex extension of the hip and the knee. The CoTracker method showed huge differences compared to the manual labeling approach. However, the angle curves were correctly estimated by the MoveNet method, finding errors between 3.2{\deg} and 5.5{\deg}. In conclusion, our proposed VideoRun2D based on MoveNet core seems to be a helpful tool for evaluating sprint kinematics in some scenarios. On the other hand, the observed precision of this first version of VideoRun2D as a markerless sprint analysis system may not be yet enough for highly demanding applications. Future research lines towards that purpose are also discussed at the end: better tracking post-processing and user- and time-dependent adaptation., Comment: Preprint of the paper presented to the Workshop on IAPR International Conference on Pattern Recognition (ICPR) 2024

The binary-driven hypernova (BdHN) model proposes long gamma-ray bursts (GRBs) originate in binaries composed of a carbon-oxygen (CO) star and a neutron star (NS) companion. The CO core collapse generates a newborn NS and a supernova that triggers the GRB by accreting onto the NSs, rapidly transferring mass and angular momentum to them. This article aims to determine the conditions under which a black hole (BH) forms from NS collapse induced by the accretion and the impact on the GRB observational properties and taxonomy. We perform three-dimensional, smoothed-particle-hydrodynamics simulations of BdHNe using up-to-date NS nuclear equations of state (EOS), with and without hyperons, and calculate the structure evolution in full general relativity. We assess the binary parameters leading either NS in the binary to the critical mass for gravitational collapse into a BH and its occurrence time, $t_{\rm col}$. We include a non-zero angular momentum of the NSs and find that $t_{\rm col}$ ranges from a few tens of seconds to hours for decreasing NS initial angular momentum values. BdHNe I are the most compact (about five minutes orbital period), promptly form a BH and release $\gtrsim 10^{52}$ erg. They form NS-BH binaries with tens of kyr merger timescale by gravitational-wave emission. BdHNe II and III do not form BHs, release $\sim 10^{50}$-$10^{52}$ erg and $\lesssim 10^{50}$ erg. They form NS-NS binaries with a range of merger timescales larger than for NS-BH binaries. In some compact BdHNe II, either NS can become supramassive, i.e., above the critical mass of a non-rotating NS. Magnetic braking by a $10^{13}$ G field can delay BH formation, leading to BH-BH or NS-BH of tens of kyr merger timescale., Comment: Version accepted for publication in The Astrophysical Journal

Aims: To unveil the influence of galaxy-galaxy interactions on material transport driven by galactic bars towards the central regions of active galactic nuclei (AGN) galaxies and assess the efficiency of the combined mechanisms of interactions and bars in fueling massive black holes, we examine barred active galaxies in paired systems. Methods: Our study targets barred AGN galaxies in pairs with projected separations $r_{p}< 100 \rm \,kpc \,h^{-1}$ and relative radial velocities of $\Delta V< 500 \rm \,km \,s^{-1}$ within $z<0.1$, using Sloan Digital Sky Survey (SDSS) data. To quantify the impact of interactions, we also created a control sample of barred active galaxies without companions, matched in redshift, absolute r-band magnitude, stellar mass, color, and stellar age. We assessed galactic bar structures through two-dimensional image modeling, considering their wide range of shapes and sizes that may affect material transport ability. Results: We found that nuclear activity, measured by $Lum[OIII]$, increases as projected separations between galaxy pair members decrease. Barred AGN galaxies in close pairs ($r_p<$ 25 kpc $h^{-1}$) show significantly higher nuclear activity compared to the control sample. Barred galaxies with close companions exhibit enhanced nuclear activity across all luminosity, stellar mass, and color ranges. Barred AGN with longer bars show more efficient nuclear activity than those with shorter bars, with a pronounced effect in close pair systems. Nuclear activity increases as pair separations decrease. Barred AGNs in close pairs undergoing major interactions show a substantial excess of high $Lum[OIII]$ values, reflecting increased accretion onto central black holes. These findings suggest that nearby galaxy companions enhance gas flows driven by galactic bars, amplifying central nuclear activity and influencing black hole accretion., Comment: 12 pages, 13 figures, accepted for publication in A&A

This study explores the potential of Modern Hopfield Networks (MHN) in improving the ability of computer vision models to handle out-of-distribution data. While current computer vision models can generalize to unseen samples from the same distribution, they are susceptible to minor perturbations such as blurring, which limits their effectiveness in real-world applications. We suggest integrating MHN into the baseline models to enhance their robustness. This integration can be implemented during the test time for any model and combined with any adversarial defense method. Our research shows that the proposed integration consistently improves model performance on the MNIST-C dataset, achieving a state-of-the-art increase of 13.84% in average corruption accuracy, a 57.49% decrease in mean Corruption Error (mCE), and a 60.61% decrease in relative mCE compared to the baseline model. Additionally, we investigate the capability of MHN to converge to the original non-corrupted data. Notably, our method does not require test-time adaptation or augmentation with corruptions, underscoring its practical viability for real-world deployment. (Source code publicly available at: https://github.com/salehsargolzaee/Hopfield-integrated-test)

Energy dissipation in collisionless plasmas is one of the most outstanding open questions in plasma physics. Magnetic reconnection and turbulence are two phenomena that can produce the conditions for energy dissipation. These two phenomena are closely related to each other in a wide range of plasmas. Turbulent fluctuations can emerge in critical regions of reconnection events, and magnetic reconnection can occur as a product of the turbulent cascade. In this study, we perform 2D particle-in-cell simulations of a reconnecting Harris current sheet in the presence of turbulent fluctuations to explore the effect of turbulence on the reconnection process in collisionless non-relativistic pair-plasmas. We find that the presence of a turbulent field can affect the onset and evolution of magnetic reconnection. Moreover, we observe the existence of a scale dependent amplitude of magnetic field fluctuations above which these fluctuations are able to disrupt the growing of magnetic islands. These fluctuations provide thermal energy to the particles within the current sheet and preferential perpendicular thermal energy to the background population.

We obtain new progresses about the diameter two property and the Daugavet property in tensor product spaces. Namely, the main results of the paper are: -If $X^*$ has the WODP, then $X\widehat{\otimes}_\varepsilon Y$ has the DD2P for any Banach space $Y$. -If $X$ has the WODP, then $X\widehat{\otimes}_\pi Y$ has the DD2P for any Banach space $Y$. -If $X^*$ and $Y^*$ have the WODP then $X\widehat{\otimes}_\varepsilon Y$ has the Daugavet property. The above improve many results in the literature and establish progresses on some open questions., Comment: 17 pages

In this paper we analyse when every element of $X\widehat{\otimes}_\pi Y$ attains its projective norm. We prove that this is the case if $X$ is the dual of a subspace of a predual of an $\ell_1(I)$ space and $Y$ is $1$-complemented in its bidual under approximation properties assumptions. This result allows us to provide some new examples where $X$ is a Lipschitz-free space. We also prove that the set of norm-attaining elements is dense in $X\widehat{\otimes}_\pi Y$ if, for instance, $X=L_1(\mu)$ and $Y$ is any Banach space, or if $X$ has the metric $\pi$-property and $Y$ is a dual space with the RNP.