Ionic mobility determines the rate performance of several applications, such as batteries, fuel cells, and electrochemical sensors and is exponentially dependent on the migration barrier ($E_m$), a difficult to measure/calculate quantity. Previous approaches to identify materials with high ionic mobility have relied on imprecise descriptors given the lack of generalizable models to predict $E_m$. Here, we present a graph neural network based architecture that leverages principles of transfer learning to efficiently and accurately predict $E_m$ across a diverse set of materials. We use a model pre-trained simultaneously on seven distinct bulk properties (labeled MPT), modify the MPT model to classify different migration pathways in a structure, and fine-tune (FT) on a manually-curated literature-derived dataset of 619 $E_m$ data points calculated with density functional theory. Importantly, our best-performing FT model (labeled MODEL-3) demonstrates substantial improvements in prediction accuracy compared to classical machine learning methods, graph models trained from scratch, and a universal machine learned interatomic potential, with a R$^2$ score of 0.703 and a mean absolute error of 0.261 eV on the test set. Notably, MODEL-3 is able to distinguish different migration pathways within a structure and also demonstrates excellent ability to generalize across intercalant compositions and chemistries. As a classifier, MODEL-3 exhibits 80\% accuracy and 82.8\% precision in identifying materials that are `good' ionic conductors (i.e., structures with $E_m <$0.65~eV). Thus, our work demonstrates the effective use of FT strategies and architectural modifications necessary for making swift and accurate $E_m$ predictions, which will be useful for materials discovery in batteries and for predicting other data-scarce material properties.

Functional MRI is a neuroimaging technique that analyzes the functional activity of the brain by measuring blood-oxygen-level-dependent signals throughout the brain. The derived functional features can be used for investigating brain alterations in neurological and psychiatric disorders. In this work, we employed a hypergraph to model high-order functional relations across brain regions, introducing algebraic connectivity (a(G)) for estimating the hyperedge weights. The hypergraph structure was derived from healthy controls to build a common topology across individuals. The considered cohort for subsequent analyses included subjects covering the Alzheimer's disease (AD) continuum, encompassing both mild cognitive impairment and AD patients. Statistical analysis and three classification tasks: HC vs AD, MCI vs AD, and HC vs MCI, were performed to assess differences across the three groups and the potential of the hyperedge weights as functional features. Furthermore, a mediation analysis was performed to evaluate the reliability of the a(G) values, representing functional information as the mediator between tau-PET levels, a key biomarker of AD, and cognitive scores. The proposed approach identified a larger number of hyperedges statistically different across groups compared to state-of-the-art methods. The a(G) hyperedge weights also demonstrated a higher discriminative power in all three binary classifications. Finally, two hyperedges belonging to salience/ventral attention and somatomotor networks showed a partial mediation effect between the tau biomarker and cognitive decline. These results suggested that a(G) can be an effective approach for extracting the hyperedge weights, including important functional information that resides in the brain areas forming the hyperedges.

We investigate a relativistic cosmological model with background rotation, sourced by a non-perfect fluid with anisotropic stress. A modified version of the CLASS Boltzmann code is employed to perform Monte Carlo Markov Chain analyses against Cosmic Microwave Background (CMB) and late-time datasets. The results show that current CMB data constrain the present-day rotation parameter to be negligible. As a consequence, the derived cosmological parameters remain consistent with the standard $Λ$CDM values. In contrast, late-time probes such as Type Ia supernovae (SNe) and Baryonic Acoustic Oscillations (BAO) allow for a higher level of rotation and yield an increased Hubble constant. However, this comes at the cost of a higher $σ_8$, which remains in tension with DES-Y3 measurement. Combining CMB, SNe and BAO data confirms the preference for non-rotation.

Recent advances in data-driven evolutionary algorithms (EAs) have demonstrated the potential of leveraging historical data to improve optimization accuracy and adaptability. Despite these advancements, existing methods remain reliant on handcrafted process-level operators. In contrast, Evolutionary Generative Optimization (EvoGO) is a fully data-driven framework designed from the objective level, enabling autonomous learning of the entire search process. EvoGO streamlines the evolutionary optimization process into three stages: data preparation, model training, and population generation. The data preparation stage constructs a pairwise dataset to enrich training diversity without incurring additional evaluation costs. During model training, a tailored generative model learns to transform inferior solutions into superior ones. In the population generation stage, EvoGO replaces traditional reproduction operators with a scalable and parallelizable generative mechanism. Extensive experiments on numerical benchmarks, classical control problems, and high-dimensional robotic tasks demonstrate that EvoGO consistently converges within merely 10 generations and substantially outperforms a wide spectrum of optimization approaches, including traditional EAs, Bayesian optimization, and reinforcement learning based methods. Code is available at: https://github.com/EMI-Group/evogo

The existence of electromagnetic radiation - radio-waves, microwaves, light, x-rays and so on - is one of the most important physical phenomena, and our ability to manipulate them is one of the most significant technological achievement of humankind. Underlying this ability is our understanding of how radiation is produced: whenever an electric charge is accelerated, it radiates. Or, at least, this is how it has been hitherto universally thought. Here we prove that quantum mechanically electric charges can be accelerated without radiating. The physical setup leading to this behavior is relatively simple (once one knows what to do) but its reasons are deep: it relies on the fact that quantum mechanically particles can be accelerated even when no forces act on them, via the Aharonov-Bohm effect. As we argue, the effect presented here is just them tip of an iceberg - it implies the need to reconsider the basic understanding of radiation. Finally, it seems clear that the effect goes far beyond electromagnetism and applies to any kind of radiation.

Uranium monocarbide (UC) is an advanced ceramic fuel candidate due to its superior uranium density and thermal conductivity compared to traditional fuels. To accurately model UC at reactor operating conditions, we developed a machine learning interatomic potential (MLIP) using an active learning procedure to generate a comprehensive training dataset capturing diverse atomic configurations. The resulting MLIP predicts structural, elastic, thermophysical properties, defect formation energies, and diffusion behaviors, aligning well with experimental and theoretical benchmarks. This work significantly advances computational methods to explore UC, enabling efficient large-scale and long-time molecular dynamics simulations essential for reactor fuel qualification.

We study the universal properties of the Lanczos algorithm applied to finite-size many-body quantum systems. Focusing on autocorrelation functions of local operators and on their infinite-time behaviour at finite size, we conjecture that in the large $n$ limit, the ratios between consecutive Lanczos coefficients should have specific scalings with the size of the lattice that we make precise and that depend on the hydrodynamic tail of the autocorrelation function. The scaling associated with strong or approximate zero-modes is also discussed. We support our conjecture with a numerical study of different models.

We establish a Ross-Witt Nyström correspondence for weak geodesic lines in the (completed) space of Kähler metrics. We construct a wide range of weak geodesic lines on arbitrary projective Kähler manifolds that are not generated by holomorphic vector fields, in the process disproving a folklore conjecture popularized by Berndtsson. Remarkably, some of these weak geodesic lines turn out to be smooth. In the case of Riemann surfaces, our results can be significantly sharpened. Finally, we investigate the validity of Euclid's fifth postulate for the space of Kähler metrics.

We revisit the theoretical modeling and simulation of a Gaussian stochastic gravitational wave background (SGWB) signal in a pulsar timing array (PTA). We show that the correlation between Fourier components of pulsar timing residuals can be expressed using transfer functions; that are indicative of characteristic temporal correlations in a SGWB signal observed in a finite time window. These transfer functions, when convolved with the SGWB power spectrum and spatial correlation (Hellings \& Downs curve), describe the variances and correlations of the pulsar timing residuals' Fourier coefficients. The convolutions are the exact frequency- and Fourier-domain representations of the time-domain covariance function. We derive explicit forms for the transfer functions for unpolarized and circularly polarized SGWB signals. We validate our results by comparing Gaussian theoretical expectation values with standard simulations based on point sources and our own covariance-matrix-based approach. The unified frequency- and Fourier-domain formalism provides a robust foundation for future PTA precision analyses and highlights the importance of temporal correlations in interpreting GW signals.

The holographic Green's function becomes ambiguous, taking the indeterminate form `$0/0$', at an infinite set of special frequencies and momenta known as ``pole-skipping points''. In this work, we propose that these pole-skipping points can be used to reconstruct both the interior and exterior geometry of a static, planar-symmetric black hole in the bulk. The entire reconstruction procedure is fully analytical and only involves solving a system of linear equations. We demonstrate its effectiveness across various backgrounds, including the BTZ black hole, its $T\bar{T}$-deformed counterparts, as well as geometries with Lifshitz scaling and hyperscaling-violation. Within this framework, other geometric quantities, such as the vacuum Einstein equations, can also be reinterpreted directly in terms of pole-skipping data. Moreover, our approach reveals a hidden algebraic structure governing the pole-skipping points of Klein-Gordon equations of the form $(\nabla^{2} + V(r))ϕ(r) = 0$: only a subset of these points is independent, while the remainder is constrained by an equal number of homogeneous polynomial identities in the pole-skipping momenta. These identities are universal, as confirmed by their validity across a broad class of bulk geometries with varying dimensionality, boundary asymptotics, and perturbation modes.

Scatterings whose cross sections increase as the cosmic temperature decreases, known as temperature - enhanced scatterings, can have a significant impact on the thermal effective potential of scalar fields responsible for driving cosmological first-order phase transitions. We show that such effects naturally manifest as finite-temperature self-energy corrections to the scalar mass term, leading to an additional contribution of the form \(c\,T^{p}ϕ^{2}\) in the effective potential. In this work, we systematically investigate how these loop-induced, temperature-dependent corrections affect key phase transition parameters, including the nucleation temperature, latent heat release, and inverse duration parameter. These modifications influence both the strength and duration of the phase transition, which in turn determine the properties of the resulting stochastic gravitational-wave (GW) background. Employing semi-analytic computational methods, we evaluate the GW spectra generated under these conditions and compare our predictions with the projected sensitivities of forthcoming detectors such as LISA, DECIGO, and BBO. Our analysis demonstrates that finite-temperature scattering effects of this kind can substantially strengthen first-order transitions and produce GW signals that lie within the reach of future observational facilities. The results establish a concrete thermal-field-theoretic origin for temperature-dependent modifications of the scalar potential and emphasize their importance in shaping early-Universe cosmological signatures.

In this paper, we reinvestigate the Starobinsky inflation model and its reheating features in light of the recent ACT results. To make the Starobinsky model consistent with the ACT data at the $68\%$ confidence level, the number of e-folds must increase while the reheating temperature decreases. We find that the Starobinsky model requires a spectator field to achieve efficient preheating. The preheating stage and the reheating temperature must be significantly adjusted to accommodate the lower temperature. In this paper, the favored non-minimal coupling of the produced particles is approximately $10$ or slightly lower. We also present viable parameter sets that fit the preferred reheating mechanism in this model. For certain parameter choices, the daughter fields could potentially be detected in future collider experiments such as the LHC or the ILC. Furthermore, our proposed mechanism can reproduce the lower reheating temperature, but it fails when the temperature falls below $1$ GeV.

Information processing in neural populations is inherently constrained by metabolic resource limits and noise properties, with dynamics that are not accurately described by existing mathematical models. Recent data, for example, shows that neurons in mouse visual cortex go into a "low power mode" in which they maintain firing rate homeostasis while expending less energy. This adaptation leads to increased neuronal noise and tuning curve flattening in response to metabolic stress. We have developed a theoretical population coding framework that captures this behavior using two novel, surprisingly simple constraints: an approximation of firing rate homeostasis and an energy limit tied to noise levels via biophysical simulation. A key feature of our contribution is an energy budget model directly connecting adenosine triphosphate (ATP) use in cells to a fully explainable mathematical framework that generalizes existing optimal population codes. Specifically, our simulation provides an energy-dependent dispersed Poisson noise model, based on the assumption that the cell will follow an optimal decay path to produce the least-noisy spike rate that is possible at a given cellular energy budget. Each state along this optimal path is associated with properties (resting potential and leak conductance) which can be measured in electrophysiology experiments and have been shown to change under prolonged caloric deprivation. We analytically derive the optimal coding strategy for neurons under varying energy budgets and coding goals, and show how our method uniquely captures how populations of tuning curves adapt while maintaining homeostasis, as has been observed empirically.

Motivated by recent experiments probing the wavefunctions of magic-angle twisted bilayer graphene (tBLG), we perform large-scale first-principles calculations of tBLG with full atomic relaxation across a wide range of twist angles down to $0.99^\circ$. Focusing on the magic angle, we compute wavefunctions of the low energy bands, resolving atomic-scale details and moiré-scale patterns that form triangular, honeycomb, and Kagome lattices. By tuning the interlayer interactions, we illustrate the formation of the flat bands from isolated monolayers and the emergence of the band inversion and fragile topology at a sufficiently large interaction strength. We identify strong indicators of a new phase transition with increasing interlayer interaction strength, achievable with external pressure or a decrease in the twist angle. When this transition occurs, the upper and lower flat bands exchange their wavefunction character and symmetry eigenvalues, which may be correlated with the appearance of superconductivity with electron doping below the magic angle. Our study demonstrates the feasibility of using first-principles wavefunctions to help interpret experimental signatures of topological and correlated phases in tBLG.

We present an exact analytical solution of the Hu-Paz-Zhang master equation in a precise Markovian limit for a system of two harmonically coupled harmonic oscillators interacting with a common thermal bath of harmonic oscillators. The thermal bath is initially considered to be at arbitrary temperatures and characterized by an Ohmic Lorentz-Drude spectral density. In the examined system, couplings between the two harmonic oscillators and the environment ensure a complete decoupling of the center-of-mass and relative degrees of freedom, resulting in undamped dynamics in the relative coordinate. The exact time evolution is used to analyze the system's entanglement dynamics, quantified through logarithmic negativity and quantum mutual information, while ensuring the positivity of the density operator to confirm the physical validity of the results. We demonstrate that, under certain parameter regimes and initial conditions, the asymptotic dynamics can give rise to periodic entanglement-disentanglement behavior. Furthermore, numerical simulations reveal that for negative values of the direct coupling between the oscillators, which are sufficiently close to a critical lower bound beyond which the system becomes unstable, the system can maintain entanglement across a broad temperature range and for arbitrarily long durations.

We study the dynamics of an optomechanical system consisting of a single-mode optical field coupled to a mechanical oscillator, where the nonlinear interaction includes both linear and quadratic terms in the oscillator's position. We present an analytical solution to this quantum-mechanical Hamiltonian problem by employing the formalism of two-phonon coherent states. Quantum estimation theory is applied to the resulting state of the optical field, with a focus on evaluating the quantum Fisher information with respect to the strength of the quadratic coupling. Our estimation scheme employs balanced homodyne photodetection and demonstrates that the corresponding classical Fisher information can reach the quantum Fisher information limit, with the phase of the local coherent oscillator playing a crucial role.

We show how a natural neutrino mass hierarchy with large lepton mixing angles may be achieved in a theory of gauge flavour deconstruction. Hitherto it has been shown that neutrino anarchy may result from such theories, but here we show that this need not necessarily be the case. In particular we consider the minimal tri-hypercharge theory, and show that the decomposition of the family hypercharges into the corresponding $B-L$ gauge groups, together with the charged lepton mass hierarchy, implies the sequential dominance conditions for a neutrino mass hierarchy, where lepton mixing originates from both the neutrino and charged lepton sectors. We present novel and model-independent sequential dominance results applicable to this case, but also useful more generally. We also show how natural quark mass and mixing are included in such a framework.

Adaptive experiments such as multi-armed bandits offer efficiency gains over traditional randomized experiments but pose two major challenges: invalid inference on the Average Treatment Effect (ATE) due to adaptive sampling and low statistical power for sub-optimal treatments. We address both issues by extending the Mixture Adaptive Design framework (arXiv:2311.05794). First, we propose MADCovar, a covariate-adjusted ATE estimator that is unbiased and preserves anytime-valid inference guarantees while substantially improving ATE precision. Second, we introduce MADMod, which dynamically reallocates samples to underpowered arms, enabling more balanced statistical power across treatments without sacrificing valid inference. Both methods retain MAD's core advantage of constructing asymptotic confidence sequences (CSs) that allow researchers to continuously monitor ATE estimates and stop data collection once a desired precision or significance criterion is met. Empirically, we validate both methods using simulations and real-world data. In simulations, MADCovar reduces CS width by up to 60% relative to MAD. In a large-scale political RCT with 32,000 participants, MADCovar achieves similar precision gains. MADMod improves statistical power and inferential precision across all treatment arms, particularly for suboptimal treatments. Simulations show that MADMod sharply reduces Type II error while preserving the efficiency benefits of adaptive allocation. Together, MADCovar and MADMod make adaptive experiments more practical, reliable, and efficient for applied researchers across many domains. Our proposed methods are implemented through an open-source software package.

We study a generalisation of the one-dimensional Rademacher random walk introduced in Bhattacharya and Volkov (2023) to $\mathbb{Z}^2$ (for $d\ge 3$, the Rademacher random walk is always transient, as follows from Theorem 8.8 in Englander and Volkov (2025)). This walk is defined as the sum of a sequence of independent steps, where each step goes in one of the four possible directions with equal probability, and the size of the $n$th step is $a_n$ where $\{a_n\}$ is a given sequence of positive integers. We establish some general conditions under which the walk is recurrent or transient.

We study a Cahn-Hilliard model for phase separation in composite materials with multiple periodic microstructures. These are modeled by considering a highly oscillating potential. The focus of this paper is in the case where the scales of the microstructures are smaller than that of phase separation. We provide a compactness result and prove that the Γ-limit of the energy is a multiple of the perimeter. In particular, using the recently introduced unfolding operator for multiple scales, we show that the taking the limit of all of the scales together is equivalent to taking one limit at the time, starting from the smaller scale and keeping the larger fixed.

We propose a method to reconstruct the metric and its arbitrary-order derivatives at the horizon for any static, planar-symmetric black hole, using an infinite set of discrete pole-skipping points in momentum space where the boundary Green's function becomes ambiguous. This method is fully analytical and involves solving only linear equations. The near-horizon reconstruction can extend either inside or outside the horizon until reaching the nearest singularity in the complex radial plane. It further enables a reinterpretation of any pure gravitational field equation in pole-skipping data. Moreover, our method reveals that the pole-skipping points are redundant: only a subset is independent, while the rest are fixed by an equal number of homogeneous polynomial constraints. These identities are universal, independent of the details of the bulk geometry, including its dimensionality, asymptotic behavior, or the existence of a holographic duality.

Impedance eduction methods are the current standard approach to measure the impedance of acoustic liner under sheared grazing flow. The dedicated facilities for these methods consists on a waveguide with rectangular cross-section, which implies a sheared grazing flow. A current debate in the literature is the effect of this sheared flow in the impedance eduction methods. We assess the impact of the flow profile shape on acoustic propagation in a two-dimensional duct within the typical operating range of impedance eduction facilities. Firstly, a numerical experiment is proposed in which the Pridmore--Brown equation is assumed to represent the true physical behaviour, and is used with both simplified flow profiles commonly used in the literature and a realistic representation of a turbulent boundary layer using a van Driest universal law of the wall model. The data from these numerical experiments are then used with a traditional impedance eduction process, and the resulting variation in obtained impedances are investigated. Secondly, we apply a less-traditional impedance eduction method that incorporates the sheared velocity profile to data obtained from real-world experiments. The results suggest that the Ingard--Myers boundary condition remains a good approximation to a realistic boundary layer profile, such as the universal law of the wall, at least in the two-dimensional case. However, it is also shown that the simplified flow profiles often used in the literature can lead to significant deviations from the results obtained using a realistic velocity distribution.

Single-cell omics technologies have transformed our understanding of cellular diversity by enabling high-resolution profiling of individual cells. However, the unprecedented scale and heterogeneity of these datasets demand robust frameworks for data integration and annotation. The Cell Ontology (CL) has emerged as a pivotal resource for achieving FAIR (Findable, Accessible, Interoperable, and Reusable) data principles by providing standardized, species-agnostic terms for canonical cell types - forming a core component of a wide range of platforms and tools. In this paper, we describe the wide variety of uses of CL in these platforms and tools and detail ongoing work to improve and extend CL content including the addition of transcriptomic types, working closely with major atlasing efforts including the Human Cell Atlas and the Brain Initiative Cell Atlas Network to support their needs. We cover the challenges and future plans for harmonising classical and transcriptomic cell type definitions, integrating markers and using Large Language Models (LLMs) to improve content and efficiency of CL workflows.

Let $Y$ be a compact Gorenstein analytic space with only isolated singularities and trivial dualizing sheaf. A recent paper of Imagi studies the deformation theory of $Y$ in case the singularities of $Y$ are weighted homogeneous and rational and $Y$ is Kähler. In this note, assuming that $H^1(Y;\mathcal{O}_Y) =0$, we generalize Imagi's results to the case where the singularities of $Y$ are Du Bois, with no assumption that they be weighted homogeneous, and where the Kähler assumption is replaced by the hypothesis that there is a resolution of singularities of $Y$ satisfying the $\partial\bar\partial$-lemma. As a consequence, if the singularities of $Y$ are additionally local complete intersections, then the deformations of $Y$ are unobstructed. The log Calabi-Yau and Fano cases are also discussed.

The fidelity of operations on a solid-state quantum processor is fundamentally bounded by environmental decoherence. Characterizing environmental fluctuations is challenging because the acquisition time of nonadaptive experimental protocols limits temporal precision and can average out rapid features of the underlying dynamics. Here, we overcome this temporal-resolution limit by two orders of magnitude using a field-programmable gate-array (FPGA) powered classical controller that adaptively and continuously tracks the relaxation-time fluctuations of two fixed-frequency superconducting transmon qubits, which exhibit average relaxation times of approximately 0.17 ms and occasionally exceed 0.5 ms. We report events in which the relaxation time switches by nearly an order of magnitude over timescales of just tens of milliseconds, rather than minutes or hours as previously reported. Our real-time Bayesian estimation protocol estimates relaxation times within a few milliseconds, close to the decoherence timescale itself. Our statistical analysis further suggests that some of these fast fluctuations arise from two-level systems switching at rates up to 10 Hz, four orders of magnitude faster than earlier reports. These results redefine the timescales relevant for calibration in superconducting quantum processing units, establish a reference for rapid relaxation-rate characterization in device screening, and improve our understanding of fast relaxation dynamics.

Proximity ferroelectricity is a novel paradigm for inducing ferroelectricity, where a non-ferroelectric polar material, which is unswitchable with an external field below the dielectric breakdown field, becomes a practically switchable ferroelectric in direct contact with a thin switchable ferroelectric layer. Here, we develop a Landau-Ginzburg-Devonshire approach to study the proximity effect of local piezoelectric response and polarization reversal in wurtzite ferroelectric multilayers under a sharp electrically biased tip. Using finite element modeling we analyze the probe-induced nucleation of nanodomains, the features of local polarization hysteresis loops and coercive fields in the Al1-xScxN/AlN bilayers and three-layers. Similar to the wurtzite multilayers sandwiched between two parallel electrodes, the regimes of "proximity switching" (where the multilayers collectively switch) and the regime of "proximity suppression" (where they collectively do not switch) are the only two possible regimes in the probe-electrode geometry. However, the parameters and asymmetry of the local piezo-response and polarization hysteresis loops depend significantly on the sequence of the layers with respect to the probe. The physical mechanism of the proximity ferroelectricity in the local probe geometry is a depolarizing electric field determined by the polarization of the layers and their relative thickness. The field, whose direction is opposite to the polarization vector in the layer(s) with the larger spontaneous polarization (such as AlN), renormalizes the double-well ferroelectric potential to lower the steepness of the switching barrier in the "otherwise unswitchable" polar layers. Tip-based control of domains in otherwise non-ferroelectric layers using proximity ferroelectricity can provide nanoscale control of domain reversal in memory, actuation, sensing and optical applications.

Homogeneous and nearly-isotropic cosmological models are natural extensions of standard Friedmann cosmologies. Constraining their features is crucial, as any detection of their properties would impact our understanding of inflation and the cosmological principle. Since these models evolve as a set of non-interacting scalar, vector, and tensor modes on top of homogeneous and isotropic spacetimes, their imprints on cosmological observables, particularly the CMB, can be obtained using standard line-of-sight methods. This requires (1) that one resorts on Laplacian eigenmodes on spatially curved spaces and (2) that radial functions for these modes are analytically continued to accommodate complex (i.e., supercurvature) wavenumbers. We introduce two line-of-sight integrators implementing the evolution of the CMB anisotropies in these models: \texttt{AniLoS}, a user-friendly and easy to modify \texttt{Python} package, and \texttt{AniCLASS}, an advanced and efficient extension of the Boltzmann solver \texttt{CLASS}. We discuss possible initial conditions that could generate such fluctuations and provide illustrative examples using our codes. This work offers a pathway for leveraging diverse cosmological datasets to constrain superhorizon anisotropies of the late-time universe.

In this note, we use isothermic coordinate systems to explore global properties of space-like surfaces with constant mean curvature in the Lorentz-Minkowski three-space.

We construct motivic power operations on the mod-$p$ motivic cohomology of $\Fb_p$-schemes using a motivic refinement of Nizioł's theorem. The key input is a purity theorem for motivic cohomology established by Levine. Our operations satisfy the expected properties (naturality, Adem relations, and the Cartan formula) for all bidegrees, generalizing previous results of Primozic which were only know along the ``Chow diagonal.'' We offer geometric applications of our construction: 1) an example of non-(quasi-)smoothable algebraic cycle at the characteristic, 2) an answer to the motivic Steenrod problem at the characteristic, 3) a counterexample to the integral version of a crystalline Tate conjecture.

We consider unconventional magnets with and without spin-singlet $s$-wave superconductivity and demonstrate the emergence of spin triplet states due to light drives. In particular, we find that a high-frequency linearly polarized light drive induces a spin-triplet density in $d$-wave altermagnets which does not exist in the static regime and can directly reveal the strength of the altermagnetic field. In this high-frequency regime, we also show that linearly polarized light enables the formation of odd-frequency spin-triplet superconducting correlations possessing $d$-wave and $s$-wave parities, which can be controlled by the light drive and accessed by measuring the spin density. Moreover, for low-frequency linearly and circularly polarized light drives, we obtain that the types of superconducting correlations are broadened due to the presence of Floquet bands, enabling spin-triplet pairs in $d$- and $p$-wave unconventional magnets, which are absent in the undriven phase.