We study Einstein deformations of negative Kähler Einstein metrics. We relate the second order Einstein deformation theory of negative Kähler-Einstein metrics to the complex geometry of the underlying Kähler manifold. After suitable gauge normalisation we show that the Taylor expansion to order two of an Einstein deformation tangent to $h_1$ in the infinitesimal deformation space is fully determined by $h_1^2$ and the divergence of the Kodaira-Spencer bracket $[h_1,h_1]^c$. This substantially refines and extends recent results of Nagy-Semmelmann which state that Einstein deformations for negative Kähler-Einstein metrics are unobstructed to second order.

Identification of nonorthogonal quantum states without error is crucial for various applications in quantum information technology, as well as the foundations of quantum physics. Theoretical studies have proposed measurements that maximize the success probability of unambiguously discriminating quantum states. However, these methods are not always experimentally feasible, which has led most demonstrations to focus on equiprobable symmetric states. Here, we establish a projective measurement scheme that optimally discriminates multiple asymmetric qudit states. We experimentally demonstrate this optimal projective measurement using a photonic orbital angular momentum state, where asymmetric qudit states are encoded in the Laguerre-Gaussian modes of a heralded single-photon state. Our results have broad applications in high-dimensional quantum state-based quantum information processing, including quantum key distribution and quantum sensing.

Enterprises increasingly rely on cloud-based applications to process highly sensitive data artifacts. Although cloud adoption improves agility and scalability, it also introduces new security challenges such as expanded attack surfaces, a wider radius of attack from credential compromise, and challenges maintaining strict access controls across users, services, and workflows. These challenges are especially acute for applications that handle privileged data and execute security-critical analysis, where traditional trust boundaries and ad hoc safeguards are insufficient. This paper presents Lockbox; a Zero Trust architecture designed for secure processing of sensitive cloud workloads under strict enterprise security and governance requirements. Lockbox applies explicit trust verification, strong isolation, least-privilege access, and policy-driven enforcement throughout the entire application lifecycle, from user authentication and document ingestion to analysis execution and result storage. The system incorporates modern cloud security primitives including; role-based access control, centralized key management, encryption in transit and at rest, and controlled integration with cloud-based data processing services, ensuring that sensitive artifacts remain protected and accessible only to authorized users. We discuss the usage of Lockbox in processing highly sensitive cybersecurity reports and demonstrate how this architecture enables organizations to safely adopt advanced capabilities, including AI-assisted processing, without weakening their security posture.

We use Lomonosov-2 supercomputing facility for the generation of extensive air shower events with Cherenkov light which is a rather time consuming procedure. At primary energies slightly below 100 PeV a substantial part of events are killed before reaching their end while exceeding the queue time limit. The fact compelled us to develop a multithread version of the code. We report here the main features of our development as well as some evidence of its efficiency.

We study sums of independent random variables that take values $0$, $1/2$, or $1$. We show that the probability mass function of the sum splits into two interleaved parts: one supported on the integers and the other supported on the half-integers. Each part, when normalized, is a Poisson binomial distribution and hence log-concave with one or two modes. We also prove that each of the two conditional means (conditioning on being an integer or a half-integer) lies within $1/2$ of the unconditional mean. As a consequence, any two modes of the two conditional distributions are within $5/2$ of each other.

Optimization of the SPHERE-3 detector configuration, designed to study the mass composition of primary cosmic rays in the energy range 1--1000 PeV by registering Cherenkov light reflected from the snow surface, requires simulation of a large number of extensive air shower events. A software suite with a multi-step computational pipeline is presented: shower generation in CORSIKA, decoding and cloning of events (C++/OpenMP), ray-tracing of optical photons through the detector model (Geant4 MT), and approximation of images by a lateral distribution function (Python/multiprocessing, iminuit). The key property of the problem is its natural atomicity: each event is processed independently at all stages, which provides linear scaling under parallel computation. Thread safety is achieved by architectural means -- shared data are read-only, mutable state is isolated per-worker -- without the use of locks on hot paths.

The Gaia Space Satellite has transformed the field of Galactic Dynamics by collecting 6D phase space information for hundreds of millions of stars. In 2018, it enabled the discovery of the Gaia Phase Spiral (Antoja et al., 2018), a clear signal in the vertical motion of the stars that reveals how far from equilibrium the Galactic disk is. Seven years after the discovery of this structure, a workshop dedicated to the Phase Spiral took place at the Lorentz Center. Workshop participants summarized the current state of knowledge about the Phase Spiral and identified open questions and key areas to continue progressing in understanding the origin of the Phase Spiral and the physics governing the response of the disk to perturbations. Here, we aim to summarize the content and discussions of this workshop, share the resources that have been produced at this workshop with the broader community, and invite interested individuals to join on the projects that started.

Hydrodynamics is based on conservation laws of currents: one starts from the conserved currents of the theory describing the microscopic dynamics, and provides an alternative parameterisation of these currents in terms of hydrodynamic variables (density, pressure, velocity, etc.). This paradigm has recently been extended to incorporate higher-form symmetries. The conservation law of the $p$-form conserved currents can be regarded as the equations of motion of a $BF$ theory that treats the currents as fundamental fields. We argue that the hydrodynamic approximation to a microscopic theory can be regarded as a cospan of differential graded manifolds $X_\mathrm{micro}\to X_{BF}\leftarrow X_\mathrm{hydro}$, where $X_\mathrm{micro}$ and $X_\mathrm{hydro}$ describe the microscopic and hydrodynamic theories, respectively, and $X_{BF}$ describes the $BF$ theory of conserved currents.

LLM-based voice assistants (VAs) increasingly support older adults aging in place, yet how an assistant's agreeableness shapes explanation perception remains underexplored. We conducted a study(N=70) examining how VA agreeableness influences older adults' perceptions of explanations across routine and emergency home scenarios. High-agreeableness assistants were perceived as more trustworthy, empathetic, and likable, but these benefits diminished in emergencies where clarity outweighed warmth. Agreeableness did not affect perceived intelligence, suggesting social tone and competence are separable dimensions. Real-time environmental explanations outperformed history-based ones, and agreeable older adults penalized low-agreeableness assistants more strongly. These findings show the need to move beyond a one-size-fits-all approach to AI explainability, while balancing personality, context, and audience.

We give a counterexample to the following conjecture: the set of isolated periodic points of an automorphism of degree at least two on an affine space is a set of bounded height. As a positive result, we prove that any cohomologically hyperbolic dominant rational self-map on a projective variety admits a non-empty Zariski open subset on which the set of periodic points is height bounded. Concerning preperiodic points, we give an example suggesting that the same statement may fail.

Immediately after the establishment of the New Meiji Government in the 19th century, a system of conscription was adopted. The exemption rule has changed several times. Using individual-level panel data on the academic performance of Keio Gijuku, I found a surge in the family head's student rate between 1884 and 1888, and the rate declined immediately thereafter. After regaining privileges for private school students, family head performance declined, and the difference between head and non-family heads disappeared. This made it evident that conscription increased educational attendance quantitatively, but did not qualitatively improve academic performance.

LLMs have advanced code generation, but their use for generating microservices with explicit dependencies and API contracts remains understudied. We examine whether AI agents can generate functional microservices and how different forms of contextual information influence their performance. We assess 144 generated microservices across 3 agents, 4 projects, 2 prompting strategies, and 2 scenarios. Incremental generation operates within existing systems and is evaluated with unit tests. Clean state generation starts from requirements alone and is evaluated with integration tests. We analyze functional correctness, code quality, and efficiency. Minimal prompts outperformed detailed ones in incremental generation, with 50-76% unit test pass rates. Clean state generation produced higher integration test pass rates (81-98%), indicating strong API contract adherence. Generated code showed lower complexity than human baselines. Generation times varied widely across agents, averaging 6-16 minutes per service. AI agents can produce microservices with maintainable code, yet inconsistent correctness and reliance on human oversight show that fully autonomous microservice generation is not yet achievable.

Doppler broadening presents a major limitation for high-resolution spectroscopy and nonlinear optics in room-temperature atomic vapors. Here, we demonstrate the suppression of Doppler broadening accompanied by pronounced absorption on the upper transition of a three-level ladder system, achieved by dressing the intermediate state with a strong control field. As a concrete realization, we study a hot vapor of $^{87}$Rb where the lower transition is driven by a strong control field resonant with the D2 line at a wavelength of 780 nm, while a weak counter-propagating probe field at the telecom C-band wavelength of 1529 nm ($5P_{(3/2)}\leftrightarrow 4D_{(5/2)}$) interrogates the dressed states. We observe absorption features with a resonant optical depth of approximately 4 and a full width at half maximum of about 17 MHz. Remarkably, this corresponds to an order-of-magnitude reduction relative to the Doppler width, while the optical depth on the upper transition of the ladder scheme exceeds that of the Doppler-broadened lower transition. The measured spectra are in good agreement with theoretical modeling. Combining high optical density with sub-Doppler-width absorption lines typically requires laser-cooled atoms, while our approach profits from the experimental simplicity of a hot-vapor platform.

We report here on studies to determine the accuracy of estimated corrections of Ionospheric Faraday Rotation Measure (IFRM) using observations of the Moon with the Very Large Array (VLA) and MeerKAT telescopes. To estimate the IFRM requires an estimate of the total electron content along the line-of-sight to the observed sources (the so-called Slant Total Electron Content, or STEC). Estimating the STEC requires an estimate of the global 2-D map of Vertical Total Electron Content (VTEC) along with the ray path from the telescope to the source. Traditionally, these global VTEC maps have been utilized along with an assumption that the electrons are in a thin shell at a given altitude to provide an estimate of the IFRM as a function of time. We find that this traditional technique significantly overestimates the IFRM - typically by 0.5 to 1.1 rad/m^2 for the VLA, and -0.3 rad/m^2 for MeerKAT. Alternatively, the software package ALBUS utilizes raw data from nearby Global Navigation Satellite System (GNSS) stations, to generate a local estimate of the IFRM as a function of time. ALBUS provides considerably better estimates of the IFRM - accurate to 0.1 rad/m^2 for both the VLA and MeerKAT, provided the stations utilized have known receiver bias values. A byproduct of our study is the establishment of the intrinsic electric vector position angle (EVPA) of the standard polarized calibrators 3C286 and 3C138 from 500 MHz to 50 GHz, using additional VLA observations of the Moon, Venus, and Mars.

The problem of the existence of nonlocal effects in Quantum Mechanics is discussed. The problem is divided in two: the first ('soft') one is to explain the violation of Bell's inequalities as a statistical magnitude. This can be achieved by a simple model within non-Boolean Locality and Realism. This result shows that quantum non-Locality as a consequence of the statistical violation of Bell's inequalities is inexistent. The second ('hard') problem is to explain the violation as it is calculated from series of detection outcomes. L.Sica has demonstrated that, in order to violate Bell's inequalities, the series recorded at (say) Bob when the setting at station Alice is alfa, can be different from the series that would have been recorded at Bob if that setting had been alfa'instead. Therefore, non-Locality in the series of detection outcomes does exist. It cannot be experimentally verified because of its counterfactual nature, but is observed in computer simulations. An appropriate computer code is based on the simple model mentioned plus a contextual instruction. It explains 'how' (Sica's) non-Locality arises, and solves the hard problem. 'Why' the contextual instruction exists is explained by Hellwig and Kraus' postulate of covariant quantum state collapse. In consequence, (Sica's) non-Locality is not in contradiction with Relativity but, quite the opposite, it is implied by Relativistic covariance.

Measurements of the electron density of populations of extragalactic HII regions in nearby galaxies remain limited, despite the relevance of this quantity for characterizing the porosity of the interstellar medium and the escape of the ionizing radiation. We initiated a project aimed at analyzing the root-mean-square electron density ne_rms, the in-situ density ne and the volume filling factor (phi) of extragalactic HII regions, investigating the dependence of these attributes on nebular and host galaxy properties. We present an image-segmentation methodology for constructing homogeneous HII region catalogues, and apply it to two pilot galaxies: NGC 2403 and NGC 628. We derive ne_rms from their Halpha luminosities and equivalent radii (R_eq), and obtain ne and phi for spectroscopic subsamples. While ne is below 300 cm$^{-3}$, ne_rms is typically one to two orders of magnitude lower, implying that phi is in the range ~$10^{-4}$ to $10^{-1}$. The two galaxies exhibit a similar size-density relation, which breaks for R_eq >~ 50 pc, show at most a weak dependence of ne_rms on galactocentric radius for NGC 2403, and no clear dependence of ne or phi on these parameters. Combining these results with published data, ne_rms presents tentative scaling relations with the median HII region size, the fraction of large regions in the parent galaxy, and the star formation rate surface density. These trends, if confirmed, would provide new constraints for massive cluster formation models and important clues for interpreting dependencies observed at high redshift, underscoring the necessity of consistently extending this analysis to larger samples.

In modern generative-AI workloads, matrix-vector/matrix-matrix multiplications (\emph{MatMul}) dominate the compute and energy cost. Achieving dramatic reductions in energy per token therefore requires a novel, specialized hardware that is co-designed across materials, devices, interconnects, circuits, and architectures rather than optimized at any single layer in isolation. In this \emph{Perspectives} article, we argue that \emph{predictive} (first-principles, fitting-parameter-free) device and interconnect simulations can close the loop between nanoscale physics and workload-level metrics, enabling the identification of device/interconnect operating regimes that plausibly support \emph{orders-of-magnitude} improvements in energy efficiency of AI accelerators.

We present a stable finite element method for incompressible nonlinear elasticity based on a four-field mixed formulation involving the displacement, displacement gradient, first Piola--Kirchhoff stress and pressure. Unlike existing four-field mixed formulations, such as the compatible strain mixed finite element method (CSFEM), the proposed approach employs a discontinuous displacement field and requires no stabilisation in either 2D or 3D. A Newton--Raphson linearisation is derived and finite element pairs satisfying the relevant inf-sup conditions are identified. To recover accurate continuous displacement fields, an efficient postprocessing technique is further introduced. We establish the well-posedness of the linearised continuous problem together with a priori error estimates for the discrete formulation. Extensive numerical experiments in both 2D and 3D demonstrate optimal or even super convergence rates and enhanced robustness, particularly in 3D where CSFEM typically requires stabilisation.

We show that the Rényi tripartite information $I_3^{(α)}$ of free fermions exhibits a qualitatively $α$-dependent scaling at small Fermi momentum, in sharp contrast to bipartite entropy where only the prefactor changes. In the rank-1 regime ($z = k_F w \ll 1$), $I_3^{(α)}$ receives contributions from two competing channels -- a fractional-moment channel $\sim z^α$ (active for non-integer $α$) and a polynomial channel $\sim z^m$ from the first nonvanishing inclusion-exclusion moment $σ_m$ -- yielding the scaling exponent $β_m(α) = \min(α, m)$ for $m$-partite information of $m$ adjacent strips. Integer Rényi indices $α= 2, 3, \ldots$ are anomalous: the fractional channel closes and the exponent jumps to $m$ or higher. A direct consequence is a replica obstruction: $I_m^{(n)}/I_m^{(1)} \sim z^{m-1} \to 0$ for all integer $n \geq 2$, so the leading von Neumann signal cannot be reconstructed from integer Rényi data at the level of leading scaling -- a situation with no bipartite analog. Conversely, negativity-based measures ($α= 1/2$) give a $20\times$ enhanced signal compared to von Neumann. We derive the underlying product formula for the coefficient $c(w_A, w_B, w_D)$, prove an $m$-partite generating function for the inclusion-exclusion moments, and verify all results numerically to high precision.

We present a policy-aware, cross-layer methodology for edge-side auditing of service tiering and quota-based throttling in Starlink. Using a multi-week plan-hopping campaign (232.8 h) on a UK residential terminal, we align 1 Hz terminal telemetry with host-side probes to obtain portal-labeled traces spanning priority (pre-quota), post-quota throttling, stay-active operation, and residential service. Using portal status only as ground truth (independent of throughput), we show these policy regimes manifest as distinct signatures in goodput, PoP RTT, and an internal-to-user ratio $R=C_{\mathrm{int}}/T_{\mathrm{user}}$. A lightweight rule on windowed medians separates high-speed from low-rate operation without operator visibility.

Investigating the apparent anomalies in lithium (Li) surface abundance observed in the Sun and young stellar globular clusters holds significant promise for advancing our understanding of the mechanisms influencing Li depletion. This study delves into the intricate interplay between rotational mixing and rotational hydrostatic effects in pre-main-sequence (PMS) and main-sequence (MS) solar-type stars by employing grids of rotating models. We implement a novel approach in which both the magnetic field strength (B) and the mixing-length parameter (alpha-MLT) vary dynamically with stellar parameters. This avoids fixed values and aims to reduce free parameters while capturing key physical variability. Our models reproduce the observed Li abundance of Sun-like stars (A(Li) = 1.12 dex) consistent with the present-day solar value (1.1 +- 0.1 dex) and yield qualitatively consistent rotational spin-down trends across PMS and MS phases. However, at the solar age (4.57 Gyr), the same models over-predict the equatorial rotation rate (v = 4.72 kms-1 vs. 2.0 kms-1) and the mean surface magnetic field (B = 36.9 G vs. 1 G). These discrepancies reflect the omission of additional angular momentum loss mechanisms and possible oversimplifications in magnetic saturation physics. While the adaptive alpha-MLT converges to the solar-calibrated value ([1.76, 1.78]) at the present age, its variability during earlier phases significantly influences Li depletion. We compare predictions with observational data from 64 open clusters. The results demonstrate that incorporating time-dependent B and alpha-MLT improves Li predictions and captures rotational evolution trends, but cannot yet reproduce the present-day solar rotation and magnetic flux without additional physics. We discuss these limitations and outline future work for a more complete model of solar-type stars.

We present astrometric measurements for 13 cold brown dwarfs in the solar neighborhood (d < 20pc). By combining archival Spitzer data with our own Hubble Space Telescope (HST) observations, we achieve parallax uncertainties typically around 10%. Using Spitzer and HST photometry we compare our targets with other known late T and Y dwarfs in the Solar neighborhood, confirming that there is large intrinsic scatter in the near- and mid-infrared absolute magnitudes and colors of this population, further highlighting the diversity observed spectroscopically by several James Webb Space Telescope (JWST) programs. This scatter makes photometric distance estimates highly unreliable and, therefore, makes astrometric parallax measurements fundamental for a meaningful characterization of even the nearest cold brown dwarfs.

Extreme weather poses a large risk to critical energy systems (Ekisheva, Rieder, Norris, Lauby, & Dobson 2021; Levin, Botterud, Mann, Kwon, & Zhou 2022). Uncertainty quantification of negative impacts is important for developing resilience, especially during compound extreme weather events involving multiple climate variables. We leverage BMW-GAM (Economou & Garry 2022), a copula workflow that relies on fitting marginal distributions with Bayesian generalized additive models in moving windows -- an embarrassingly parallel task. The Gaussian copula has separable multivariate space-time correlation, allowing for efficient emulation and likelihood fitting with big datasets. Overall, the formulation is interpretable and provides uncertainty quantification through probabilistic simulations of weather variables during extreme events. Our method is illustrated in an analysis of temperature, wind speed, and global horizontal irradiance from Argonne National Laboratory's high-fidelity climate model output ADDA.

Electroweak precision tests, expressed through the oblique parameters $S$, $T$, and $U$, impose stringent constraints on physics beyond the Standard Model. Gauge extensions of the Standard Model based on the $SU(3)_L \times U(1)_N$ symmetry predict a rich scalar and gauge spectrum that contribute to these parameters. Previous studies have shown that 3-3-1 gauge bosons give negligible contributions to the oblique parameters, while the contributions of the scalar sector to these parameters have received comparatively little attention. In particular, for the version of the $SU(3)_L \times U(1)_N$ model with right-handed neutrinos, the impact of the scalar sector on $S$, $T$ , and $U$ has not yet been addressed. In this work, we fill this gap and address sistematically the scalar contributions to the $S$, $T$ and $U$ within this version. As main result, we show that the parameter $T$ put stringent constraints on the masses and energy scales associated to the spectrum of scalars of the model.

A well-established method exists for predicting the detectability of solar-like oscillations and has been widely used to support target selection for space-based photometric missions. The method evaluates the probability of an asteroseismic detection from the expected global signal-to-noise ratio (SNR) of the oscillation signal relative to the broadband background from shot noise and granulation. Stellar parameters are used to estimate the oscillation and granulation signals, while instrumental properties and apparent stellar brightness determine the expected shot noise. We investigate whether there is an optimal choice for the frequency range, $W$, over which the global SNR is calculated. The oscillation power is assumed to follow a Gaussian-like envelope with full width at half maximum $Γ_{\rm env}$ centred on the frequency of maximum oscillation power. It has commonly been assumed that $W \simeq 2Γ_{\rm env}$ when predicting detections. We compute numerical predictions of the global SNR and corresponding detection probabilities for a range of stellar and observational parameters, adopting widths $W=αΓ_{\rm env}$ where $α$ is a multiplicative factor. We also examine the impact of this choice on detection yields across a population of targets using bright solar-like oscillators observed by TESS as a representative sample. We find that the commonly adopted value $α\simeq 2$ is suboptimal and that $α\simeq 1.2$ maximises the detection probability. This choice can also significantly affect predicted detection yields for stellar samples. We therefore recommend adopting $W \simeq 1.2Γ_{\rm env}$ both when computing detection probabilities and when searching for oscillations in real data via tests of excess mode power, as it optimises the probability of robust detections.

Low-metallicity massive stars are assumed to be progenitors of certain supernovae, gamma-ray bursts, and gravitational wave emitting mergers. These exotic phenomena contribute to their host galaxies through strong ionizing radiation and mechanical feedback. Here we investigate a certain type of very metal-poor (0.02 Zsun) hot massive single stars that rotate fast and evolve chemically homogeneously. Combining state-of-the-art theories of stellar evolution and stellar atmospheres modelling we predict synthetic spectra of these stars corresponding to different masses and evolutionary phases. The predicted spectra in early evolutionary phases is classified mainly as an early-O type giant or supergiant while in later evolutionary phases most of our model spectra are assigned to the WO-type spectral class. The Hubble Space Telescope's (HST) Ultraviolet Legacy Library of Young Stars as Essential Standards (ULLYSES) program will enable us to compare our predicted spectra with observations of stars of similar nature (e.g., metal-poor stars in Sextant A).

Virtual reality (VR) systems have the potential to be an innovation in the field of e-learning. Starting with fully functional e-classes, VR technologies can be used to build entire e-campuses. The power of VR is that it allows for stronger contact with students than computer-mediated technology. Deceptive behaviour, both verbal and nonverbal, refers to intentional activities designed to deceive others. Students often engage in dishonest practices to make progress. Whether it is cheating on an exam, copying another student's essay, or inflating their GPA, the motivation for cheating is rarely simply a lack of preparation. Even though some may see academic dishonesty as an asset, the reality is that it can have major consequences. This poster demonstrates the findings from a study of students' deceitful behaviour during a test in VR and in real-life situations. For this user study, 22 volunteers were invited to participate, with each experiment involving exactly two participants and the examiner present in the room. Students were invited to take two tests: one in VR and one on a laptop. Their goal was to score as many points as possible by simulating a real-world online exam. Participants were requested to complete questionnaires during and after each experiment, which assisted in collecting additional data for this study. The results indicate that the amount of cheating that happened in VR and on a laptop was exactly the same.

This study investigates the impact of the Degree of Interactivity on User Experience (UX) and social acceptability (SA) in Mobile Augmented Reality (MAR) applications. As AR technologies become more prevalent, understanding how varying levels of interactivity influence both user perception and social dynamics is crucial for their design and adoption. Two commercially available MAR applications, IKEA and Virtlo, which differ significantly in their interactivity levels, were used to conduct a user study. The study examines how body movements required for interaction with AR content affect both UX and SA, shedding light on users' comfort levels and potential social barriers in public settings. The findings suggest a complex relationship between interactivity, perceived usability, and social considerations, emphasizing the need for a balanced design approach. This research provides valuable insights into the development of future AR applications by addressing not only usability but also the broader social implications of AR interactions. By integrating social acceptability into traditional UX evaluations, this study highlights its significance in ensuring the seamless integration of AR technologies into everyday environments.

Virtual Reality (VR) and Augmented Reality (AR) are emerging as transformative tools in education, offering new possibilities for engagement and immersion. This paper explores their potential in language learning within public education, focusing on their ability to enhance traditional schooling methods and address existing educational gaps. The integration of VR and AR in schools, however, is not without challenges, including usability, technical barriers, and the alignment of these technologies with existing curricula. Drawing on two empirical studies, this work investigates the opportunities and challenges of VR- and AR-assisted language learning and proposes strategies for their effective implementation in the public sector. The findings show that VR increases motivation and immersion but has an unclear impact on vocabulary retention, with technical limitations and cognitive overload identified as key challenges. AR enhances contextual learning and accessibility but faces usability constraints and limited personalization. To facilitate effective adoption, this paper recommends improving interface design, reducing cognitive load, increasing adaptability, and ensuring adequate infrastructure and teacher training. Overcoming these barriers will enable a more effective integration of immersive technologies in language education.

In this paper, we consider a left-invariant Riemannian metric $g$ on the Lie group $F^4$. We classify Ricci solitons on $(F^4,g)$ and show that all such solitons are expanding and non-gradient. Moreover, we study the existence of harmonic maps from compact Riemannian manifolds into $(F^4,g)$. Finally, we characterize a class of harmonic vector fields on $(F^4,g)$.