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This paper explores the nuanced landscape of generative AI (genAI), particularly focusing on neural network-based models like Large Language Models (LLMs). While genAI garners both optimistic enthusiasm and sceptical criticism, this work seeks to provide a balanced examination of its capabilities, limitations, and the profound impact it may have on societal functions and personal interactions. The first section demystifies language-based genAI through detailed discussions on how LLMs learn, their computational needs, distinguishing features from supporting technologies, and the inherent limitations in their accuracy and reliability. Real-world examples illustrate the practical applications and implications of these technologies. The latter part of the paper adopts a systems perspective, evaluating how the integration of LLMs with existing technologies can enhance productivity and address emerging concerns. It highlights the need for significant investment to understand the implications of recent advancements, advocating for a well-informed dialogue to ethically and responsibly integrate genAI into diverse sectors. The paper concludes with prospective developments and recommendations, emphasizing a forward-looking approach to harnessing genAI`s potential while mitigating its risks.

Solar irradiance variations across various timescales, from minutes to centuries, represents a potential natural driver of past regional and global climate cold phases. To accurately assess the Sun's effect on climate, particularly during periods of exceptionally low solar activity known as grand minima, an accurate reconstruction of solar forcing is essential. While direct measurements of Total Solar Irradiance (TSI) only began in the late 1970s with the advent of space radiometers, indirect evidence from various historical proxies suggests that the Sun's magnetic activity has undergone possible significant fluctuations over much longer timescales. Employing diverse and independent methods for TSI reconstruction is essential to gaining a comprehensive understanding of this issue. This study employs a semi-empirical model to reconstruct TSI over the past millennium. Our approach uses an estimated open solar magnetic field ($F_{o}$), derived from cosmogenic isotope data, as a proxy for solar activity. We reconstruct the cyclic variations of TSI, due to the solar surface magnetic features, by correlating $F_{o}$ with the parameter of active region functional form. Instead, we obtain the long-term TSI trend by applying the Empirical Mode Decomposition (EMD) algorithm to the reconstructed $F_{o}$ to filter out the 11-year and 22-year solar variability. We prepare a reconstructed TSI record, spanning 971 to 2020 CE. The estimated departure from modern TSI values occurred during the Sp\"{o}rer Minimum (around 1400 CE), with a decrease of approximately 2.3 $W m^{-2}$. A slightly smaller decline of 2.2 $W m^{-2}$ is reported during the Maunder Minimum, between 1645 and 1715 CE.

Let $\mathscr{C}_{+}(a,b)$ be the submonoid of the bicyclic monoid which is studied in \cite{Makanjuola-Umar=1997}. We describe monoid endomorphisms of the semigroup $\mathscr{C}_{+}(a,b)$ which are generated by the family of all congruences of the bicyclic monoid and all injective monoid endomorphisms of $\mathscr{C}_{+}(a,b)$., Comment: 10 pages

The solar activity, which is driven by a variable magnetic field, exhibits changes along several time scales, the 11-year being the most known. In addition to the SunSpot Number, the Ca II K index and the Mg II index are indices widely employed among those proposed to quantify the solar activity, also because of their ability to trace the solar UV emission. In this work, we compare the Ca II K 0.1nm emission index to the Mg II index over the time interval 1978-2017, which covers almost four solar cycles. We show that they are strongly correlated across each solar cycle (r$\geq$0.94), providing the corresponding linear regression fit parameters. The Hilbert-Huang Transform is then used to decompose such indices into their intrinsic mode of oscillation. By studying how their components are correlated over the different time scales, it is found that the maximum correlation is observed at the 11-year scale, while the correlation is less strong going to smaller time scales.

The Mal'tsev product of two varieties of the same similarity type is not in general a variety, because it can fail to be closed under homomorphic images. In the previous paper we provided a new sufficient condition for such a product to be a variety. In this paper we extend that result by weakening the assumptions regarding the two varieties. We also explore the various special cases of our new result and provide a number of examples of its application.

The total solar irradiance (TSI) varies on timescales of minute to centuries. On short timescales it varies due to the superposition of intensity fluctuations produced by turbulent convection and acoustic oscillations. On longer scale times, it changes due to photospheric magnetic activity, mainly because of the facular brightenings and dimmings caused by sunspots. While modern TSI variations have been monitored from space since 1970s, TSI variations over much longer periods can only be estimated using either historical observations of magnetic features, possibly supported by flux transport models, or from the measurements of the cosmogenic isotope (e.g., \textsuperscript{14}C or \textsuperscript{10}Be) concentrations in tree rings and ice cores. The reconstruction of the TSI in the last few centuries, particularly in the 17th/18th centuries during the Maunder minimum, is of primary importance for studying climatic effects. To separate the temporal components of the irradiance variations, specifically the magnetic cycle from secular variability, we decomposed the signals associated with historical observations of magnetic features and the solar modulation potential $\Phi$ by applying an Empirical Mode Decomposition algorithm. Thus, the reconstruction is empirical and does not require any feature contrast or field transport model. The assessed difference between the mean value during the Maunder minimum and the present value is $\simeq2.5 Wm^{-2}$. Moreover it shows, in the first half of the last century, a growth of $\simeq 1.5 W m^{-2}$ which stops around the middle of the century to remain constant for the next 50 years, apart from the modulation due to the solar cycle.

The Earth's magnetosphere extension is controlled by the solar activity level via solar wind properties. Understanding such a relation in the Solar System is important for predicting also the condition of exoplanetary magnetospheres near Sun-like stars. We use measurements of a chromospheric proxy, the Ca II K index, and solar wind OMNI parameters to connect the solar activity variations, on the decennial time scales, to the solar wind properties. The data span over the time interval 1965-2021, which almost entirely covers the last 5 solar cycles. Using both cross-correlation and mutual information analysis, a 3.2-year lag of the solar wind speed with respect to the Ca II K index is found. Analogously, a 3.6-year lag is found once considering the dynamic pressure. A correlation between the solar wind dynamic pressure and the solar UV emission is found and used to derive the Earth's magnetopause standoff distance. Moreover, the advantage of using a chromospheric proxy, such as the Ca II K index, opens the possibility to extend the relation found for the Sun to Sun-like stars, by linking stellar variability to stellar wind properties. The model is applied to a sample of Sun-like stars as a case study, where we assume the presence of an Earth-like exoplanet at 1 AU. Finally, we compare our results with previous estimates of the magnetosphere extension for the same set of Sun-like stars., Comment: 11 pages, 6 figures

Solar variability occurs over a broad range of spatial and temporal scales, from the Sun's brightening over its lifetime to the fluctuations commonly associated with magnetic activity over minutes to years. The latter activity includes most prominently the 11-year sunspot solar cycle and its modulations. Space weather events, in the form of solar flares, solar energetic particles, coronal mass ejections, and geomagnetic storms, have long been known to approximately follow the solar cycle occurring more frequently at solar maximum than solar minimum. These events can significantly impact our advanced technologies and critical infrastructures, making the prediction for the strength of future solar cycles particularly important. Several methods have been proposed to predict the strength of the next solar cycle, cycle 25, with results that are generally not always consistent. Most of these methods are based on the international sunspot number time series, or other indicators of solar activity. We present here a new approach that uses more than 100 years of measured fractional areas of the visible solar disk covered by sunspots and plages and an empirical relationship for each of these two indices of solar activity in even-odd cycles. We anticipate that cycle 25 will peak in 2024 and will last for about 12 years, slightly longer than cycle 24. We also found that, in terms of sunspot and plage areas coverage, the amplitude of cycle 25 will be substantially similar or slightly higher than cycle 24., Comment: 7 pages, 6 figures. Accepted on ApJL

Modeling of planets' climate and habitability requires as fundamental input the UV emission of the hosting star. \citet{lovric2017} employed SORCE/SOLSTICE solar observations to introduce a UV color index which is a descriptor of the UV radiation that modulates the photochemistry of planets atmospheres. After correcting the SOLSTICE data for residual instrumental effects that produced asymmetric signals during different phases of the cycles analyzed, the authors found that the UV color index is linearly correlated with the Mg II index.In this paper we employ an irradiance reconstruction technique to synthetize the UV color and Mg II index with the purpose of investigating whether the correction applied by \citet{lovric2017} to SORCE/SOLSTICE data might have compensated for solar variations, and to investigate the physical mechanisms that produce such a strong correlation between the UV color index and the solar activity. Reconstructed indices reproduce very well the observations and present the same strong linear dependence. Moreover our reconstruction, which extends back to 1989, shows that the UV color - Mg II index relation can be described by the same linear relation for almost three cycles, thus ruling out an overcompensation of SORCE/SOLTICE data in the analysis of \citet{lovric2017}. We suggest that the strong correlation between the indices results from the fact that most of the Far- and Middle- UV radiation originates in the chromosphere, where atmosphere models of quiet and magnetic features present similar temperature and density gradients., Comment: Accepted in ApJ

The investigation of dynamics of the small scale magnetic field on the Sun photosphere is necessary to understand the physical processes occurring in the higher layers of solar atmosphere due to the magnetic coupling between the photosphere and the corona. We present a simulation able to address these phenomena investigating the statistics of magnetic loops reconnections. The simulation is based on N-body model approach and is divided in two computational layers. We simplify the convection problem, interpreting the larger convective scale, mesogranulation, as the result of the collective interaction of convective downflow of granular scale. The N-body advection model is the base to generate a synthetic time series of nanoflares produced by interacting magnetic loops. The reconnection of magnetic field lines is the result of the advection of the magnetic footpoints following the velocity field generated by the interacting downflows. The model gives a quantitative idea of how much energy is expected to be released by the reconfiguration of magnetic loops in the quiet Sun., Comment: 6 pages, 2 figures. To be published in "Journal of Physics: Conference Series" as part of the proceedings of the sixth edition of the Young Researcher Meeting (YRM), 12-14 October 2015, L'Aquila, Italy. http://www.yrmr.it/

Understanding the reasons of the cyclic variation of the total solar irradiance is one of the most challenging targets of modern astrophysics. These studies prove to be essential also for a more climatologic issue, associated to the global warming. Any attempt to determine the solar components of this phenomenon must include the effects of the magnetic field, whose strength and shape in the solar interior are far from being completely known. Modelling the presence and the effects of a magnetic field requires a 2D approach, since the assumption of radial symmetry is too limiting for this topic. We present the structure of a 2D evolution code that was purposely designed for this scope; rotation, magnetic field and turbulence can be taken into account. Some preliminary results are presented and commented., Comment: Accepted for publication on Astrophysics and Space Science

In the second paper of this series we pursue two objectives. First, in order to make the code more sensitive to small effects, we remove many approximations made in Paper I. Second, we include turbulence and rotation in the two-dimensional framework. The stellar equilibrium is described by means of a set of five differential equations, with the introduction of a new dependent variable, namely the perturbation to the radial gravity, that is found when the non-radial effects are considered in the solution of the Poisson equation; following the scheme of the first paper, we write the equations in such a way that the two-dimensional effects can be easily disentangled. The key concept introduced in this series is the equipotential surface. We use the underlying cause-effect relation to develop a recurrence relation to calculate the equipotential surface functions for uniform rotation, differential rotation, rotation-like toroidal magnetic fields and turbulence. We also develop a more precise code to numerically solve the two-dimensional stellar structure and evolution equations based on the equipotential surface calculations. We have shown that with this formulation we can achieve the precision required by observations by appropriately selecting the convergence criterion. Several examples are presented to show that the method works well. Since we are interested in modeling the effects of a dynamo-type field on the detailed envelope structure and global properties of the Sun, the code has been optimized for short timescales phenomena (down to 1 yr). The time dependence of the code has so far been tested exclusively to address such problems., Comment: 56 pages, 8 figures, submitted to ApJS

Pores are one of the various features forming in the photosphere by the emergence of magnetic field onto the solar surface. They lie at the border between tiny magnetic elements and larger sunspots. Light bridges, in such structures, are bright features separating umbral areas in two or more irregular regions. Commonly, light bridges indicate that a the merging of magnetic regions or, conversely, the breakup of the area is underway. We investigate the velocity structure of a solar pore (AR10812) with light bridge, and of the quiet solar photosphere nearby, analyzing high spatial and spectral resolution images. The pore area has been observed with the Interferometric BI-dimensional Spectrometer (IBIS) at the Dunn Solar Telescope, acquiring monochromatic images in the Ca II 854.2 nm line and in the Fe I 709.0 nm line as well as G-band and broad-band images. We also computed the Line of Sight (LoS) velocity field associated to the Fe I and Fe II photospheric lines. The amplitude of the LoS velocity fluctuations, inside the pore, is smaller than that observed in the quiet granulation near the active region. We computed the azimuthal average LoS velocity and derived its radial profile. The whole pore is characterized by a downward velocity -200 m/s and by an annular downflow structure with an average velocity of -350 m/s with respect to the nearby quiet sun. The light bridge inside the pore, when observed in the broad-band channel of IBIS and in the red wing of Ca II 854.2 nm line, shows an elongated dark structure running along its axis, that we explain with a semi-analytical model. In the highest resolution LoS velocity images the light bridge shows a profile consistent with a convective roll: a weak upflow, 50-100m/s, in correspondence of the dark lane, flanked by a downflow, -(200-300) m/s., Comment: 7 pages, 10 figures