In the context of inertial confinement fusion (ICF) experiments, spatial and temporal laser beam smoothing techniques are used to control the beams propagation in hohlraum plasmas. Currently, spatial and temporal smoothing are either neglected or not properly taken into account in the inline cross beam energy transfer (CBET) models included in the hydrodynamic codes dedicated to the design of these experiments. In some cases, which we will highlight in this study, this simplification leads to important errors in the power transfer of importance for the implosion symmetry of the capsule, either in the direct or indirect drive ICF configurations. In a recent study [A. Oudin et \textit{al}., Phys. Plasmas \textbf{32}, 042706 (2025)], we demonstrated the necessity of accounting for spatial smoothing when modeling CBET, provided that the beams do not have the same wavelength. This work presents a linear kinetic model compared with Hera paraxial fluid simulations and compared with the Smilei particle-in-cell code, demonstrating the important influence of smoothing by spectral dispersion on CBET. Moreover, we demonstrate the importance of accounting for the plasma velocity profile, the beam modulation bandwidth, and the spectral dispersion to better predict the power exchanged between the beams. Additionally, we reveal a strong sensitivity of this power transfer to the synchronization of the phase modulators.

The thermodynamic critical field $B_{\rm c}$ provides direct access to the superconducting condensation energy, yet its pressure dependence has been studied much less extensively than that of the transition temperature. Here, muon-spin-rotation/relaxation measurements of the thermodynamic critical field $B_{\rm c}$ of elemental Pb under hydrostatic pressure up to $\simeq2.3$ GPa are reported. From the magnetic-field distribution in the intermediate state, $B_{\rm c}(T)$ is determined and $B_{\rm c}(0)$ is extracted at different pressures. In combination with previously reported high-pressure data for $B_{\rm c}$ and $T_{\rm c}$, it is shown that the pressure dependence of $B_{\rm c}(0)$ follows that of the superconducting gap $Δ(0)$ more closely than that of the transition temperature $T_{\rm c}$. At higher pressures, the logarithmic pressure derivatives of $B_{\rm c}(0)$ and $T_{\rm c}$ are found to converge, indicating that the coupling strengths ratio $α=Δ(0)/k_{\rm B}T_{\rm c}$ becomes nearly pressure independent. This behavior is interpreted as thermodynamic evidence for a pressure-driven crossover from strong- to weak-coupling superconductivity in Pb.

Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples, including generalised SKT-type competition models, cross-diffusion terms can be rigorously derived as fast-reaction limits, thereby providing a clear biological interpretation while posing significant analytical challenges. In this work, we investigate the impact of biologically derived cross-diffusion on Turing instability. For a generalised SKT framework, we characterise instability conditions for a broad class of cross-diffusion functions arising from fast-reaction mechanisms. We then propose an alternative fast-reaction formulation leading to a different diffusion structure and show that, in this case, diffusion-driven pattern formation is prevented. We further discuss an example motivated by dietary diversity and starvation dynamics, and analyse how the sign structure of the reaction Jacobian interacts with cross-diffusion in determining the onset of patterns. Our results clarify structural features that promote or inhibit spatial self-organisation in competitive systems.

Optical skyrmions are members of the emerging topological branch of solid-state physics and photonics, allowing for control over topological light textures through light-matter interactions. However, in nanophotonics their practical application has been severely limited by high inherent losses in plasmonic materials, resulting in the lack of tunability between different topological properties. Here, we utilize the strong dispersion of silicon carbide thin films to realize highly confined surface phonon-polariton skyrmion lattices, which we image via near-field microscopy. We experimentally demonstrate topological tuning between bubble- and Néel-type skyrmions, a unique advantage that polar dielectrics offer over most existing approaches. Changing the excitation wavelength by only 10% switches the skyrmion type, revealed by examination of the skyrmion number density contrast. Analysis of domain wall size and steepness in analogy to magnetic materials also confirms this transition. Our results are a starting point to investigate other topological features in phononic systems such as merons, skyrmion bags, and other complex structured light fields. Furthermore, strong light-matter hybridization and nonlinear effects owing to anharmonicity of the phonons may be observed in the future, possibly leading towards the discovery of polaritonic skyrmion-skyrmion interactions and hence applications in topology-based information processing.

Previous experimental reports of long-range interactions in ionic liquids (ILs) stand in contradiction with theoretical predictions and numerical simulations. To provide insights into the literature discrepancies regarding the experimental ranges of electrostatic screening, claimed with orders of magnitude larger, the interactions between pairs of mica and borosilicate surfaces confining ILs are investigated by two complementary advanced Surface Force Apparatuses. Regardless of differences in confinement geometries (crossed-cylinders, sphere-flat), radii of curvature (cm-mm), and measurement techniques (stepwise vs continuous approach), two ever present force regimes are evidenced. At small surface separations, oscillatory forces reflect IL structuration and layering, while outside this gap, the interaction is monotonic repulsive. In both regimes the spatial extent and force magnitude depend critically on motion conditions, as demonstrated by achieving velocities as low as 9 pm/s with equilibration times up to 90 s. At large separations, fast surface displacements generate long-range interactions (over tens of ion size) creating the illusion of anomalous underscreening, whereas increasingly slow ones shrink both magnitude and range of the repulsion with decay-lengths converging ultimately to a screening length consistent with Poisson-Boltzmann theory with finite ion sizes. The transition from apparent long-range to short-range screening unfolds over nearly two orders of magnitude in time, revealing slow relaxation dynamics reminiscent of aging phenomena. These findings definitely resolve a decade-old controversy on force measurements and reveal rich out-of-equilibrium dynamics. The hydrodynamic contribution to the net force is admittedly crucial to be reduced especially when relaxations span decades in time, but approaching thermodynamic equilibrium during measurements proves essential.

Quantum anomalies arise when symmetries of a classical theory cannot be preserved upon quantization, leading to unconventional topological responses. A prominent example is the parity anomaly of a single two-dimensional Dirac fermion, which enforces a half-quantized Hall response. Anomaly inflow mechanism allows this effect to be observed at the surfaces of three-dimensional topological insulators, however, its realization in a genuinely two-dimensional system has remained elusive. Here we report the observation of a parity-anomalous Hall response at the critical point of a quantum Hall topological phase transition in a synthetic two-dimensional system of ultracold dysprosium atoms. By coupling a continuous spatial dimension to a finite synthetic dimension encoded in atomic spin states, we engineer tunable Chern bands with C = 0 and 1. At the transition, the bulk gap closes at a single Dirac point, where we observe a robust half-quantized Hall drift despite strong non-adiabatic excitations. We show that this response originates from the global structure of the band topology, is protected by an emergent parity symmetry at criticality, and disappears when parity is explicitly broken. Our work establishes synthetic quantum systems as a powerful platform to probe quantum anomalies and their interplay with topology and non-equilibrium dynamics.

We consider a diffuse-interface model for two-phase incompressible viscous flows with a soluble surfactant in a bounded porous medium. This hydrodynamic system consists of a Darcy--Forchheimer equation for the seepage velocity $\boldsymbol{u}$ coupled with two Cahn--Hilliard equations involving Flory--Huggins type singular potentials, one for the phase-field variable $ϕ$, the difference in volume fractions of the two fluids, and the other for the surfactant concentration $ψ$. We study the initial boundary value problem in two or three dimensions, with impermeability boundary conditions for $\boldsymbol{u}$ and homogeneous Neumann boundary conditions for $(ϕ, ψ)$ and their associated chemical potentials. First, we establish the existence of global weak solutions via an implicit-explicit time-discretization scheme based on the energy dissipation law. Furthermore, applying the seminal results of the first and third authors (arXiv:2510.17296), we prove that every weak solution satisfying an energy inequality converges to a single equilibrium as time tends to infinity. In sharp contrast with the available literature on similar models, in this case weak solutions are enough to guarantee the uniqueness of asymptotic limits, without the necessity of any further eventual regularization.

Given a Nori motivic local system over a smooth, connected complex algebraic variety, we define its exceptional locus as a way to measure the variation in the motivic complexity of its stalks. The definition is given explicitly in terms of motivic Galois groups and Artin motives. Our main result is a motivic analogue of the Cattani--Deligne--Kaplan Theorem, asserting that the exceptional locus is a countable union of closed algebraic subvarieties. Moreover, we show that the maximal such subvarieties are defined over any algebraically closed subfield over which the ambient variety and the motivic local system admit models, and that they are stable under Galois conjugation when these models descend to a further subfield. This strengthens and extends previous results by André in the pure case. We obtain a similar geometric description for the splitting locus of the motivic weight filtration. In the case of 1-motivic local systems, the above properties pass to the underlying variations of mixed Hodge structure via André's fullness theorem.

Autonomous agents operating in uncertain environments must balance fast responses with goal-directed planning. Classical MF RL often converges slowly and may induce unsafe exploration, whereas MB methods are computationally expensive and sensitive to model mismatch. This paper presents a human-inspired hybrid RL architecture integrating Pavlovian, Instrumental MF, and Instrumental MB components. Inspired by Pavlovian and Instrumental learning from neuroscience, the framework considers contextual radio cues, here intended as georeferenced environmental features acting as CS, to shape intrinsic value signals and bias decision-making. Learning is further modulated by internal motivational drives through a dedicated motivational signal. A Bayesian arbitration mechanism adaptively blends MF and MB estimates based on predicted reliability. Simulation results show that the hybrid approach accelerates learning, improves operational safety, and reduces navigation in high-uncertainty regions compared to standard RL baselines. Pavlovian conditioning promotes safer exploration and faster convergence, while arbitration enables a smooth transition from exploration to efficient, plan-driven exploitation. Overall, the results highlight the benefits of biologically inspired modularity for robust and adaptive autonomous systems under uncertainty.

Mass loss from massive stars located in the part of the Hertzsprung-Russell diagram (HRD) where we find luminous blue variables (LBVs) is profoundly important for stellar evolution yet poorly understood. We use time-dependent radiation-hydrodynamic (RHD) simulations to examine the atmosphere and wind properties of such massive stars, computing 2D and 1D RHD models of the coupled envelopes, atmospheres, and wind outflows, tuned to this region in the HRD. Our unified simulations start deep in the stellar envelope (well below T ~ 200 kK) and include the outflowing wind, accounting for line-driving, radiative enthalpy, and photon tiring. Mass-loss rates, wind speeds, and the radiative luminosity at the photosphere are emergent properties in the simulations. A grid of models is created by slightly increasing the stellar energy at the lower boundary. This results in a natural transition from very turbulent atmospheres with line-driven winds to effectively stationary super-Eddington massive outflows. Our sub-Eddington models are essentially blue hypergiant stars with very variable surfaces, effective mass-loss rates $\dot{M} \sim 2 - 5 \times 10^{-5}$ $M_{\odot}$/year, and wind speeds $v_{\infty} \sim 200 - 300$ km/s, resembling quiescent LBVs like P Cygni. The super-Eddington models have optically thick wind envelopes and extremely inflated yellow surfaces (Teff ~ 5000 K), $\dot{M} \sim 0.1 - 1$ $M_{\odot}$/year, and $v_{\infty} \sim 400 - 500$ km/s, resembling a massive star during a great eruption like eta Carinae's. Our models naturally reproduce the overall characteristic stellar and wind parameters inferred for massive stars in their quiescent LBV and yellow giant eruptive phases. It remains an open question whether the energy increase needed to trigger a giant eruption can be obtained solely by the internal evolution of the star itself or if it requires an external energy source.

Galaxies frequently interact with nearby systems, a process that can significantly alter their morphology and star formation activity. However, spectroscopic studies of their faint and diffuse remnants require very long exposure times and often exceed the limited field of view of integral field units (IFUs). On the other hand, broad-band imaging can have a much wider field of view, but lacks the spectral resolution to identify key spectral features, restricting accurate constraints on stellar population properties. With its 54 narrow-band filters in the optical and wide coverage (planned 8000 square degrees), J-PAS fills this gap. In this case study, we examine PGC 3087775, a massive galaxy at z = 0.046179 (~ 201 Mpc) in the later stages of a major merger in the J-PAS early data release. Photometry was validated with MaNGA IFU data (for the central part). Stellar population properties was derived using both J-PAS and SDSS photometry. SDSS indicates a metal-rich population with an extended star formation history (SFH) and elevated star formation rates. J-PAS instead points to a less metal-rich population with moderate extinction and a more rapid SFH, consistent with a quenched stellar population. The average Dn(4000) index of the tidal features is 1.24, suggesting that it was a non-dry merger and a fourfold improvement in the precision of stellar mass and Dn (4000) was found with J-PAS. We also assessed two heuristic methods for estimating the mass-to-light ratio from SDSS filters and found that they overestimate the stellar mass in this galaxy by 0.5 dex and 0.4 dex relative to SED fitting results from J-PAS and SDSS, respectively. Future work will extend this analysis to a larger sample of merging galaxies and evolution of the stellar populations of such structures across the nearby Universe to unprecedented detail. This project is fully reproducible, through Maneage (commit 0f0d7e2).

We investigate s-wave kaon condensation in dense matter and neutron stars within the updated Chiral Mean Field model with an improved meson description (mCMF), which incorporates dynamically generated in-medium meson masses arising from explicit chiral symmetry breaking and vector-meson self-interactions. In contrast to conventional relativistic mean-field descriptions with constant meson masses, the mCMF framework introduces a self-consistent feedback between the meson sector and the dense-matter equations of motion. The kaon dispersion relation is derived from the nonlinear SU(3) Lagrangian, including the Weinberg-Tomozawa interaction and additional baryon-pseudoscalar couplings, and the onset of condensation is determined under conditions of charge neutrality and $β$ equilibrium. Our calculations include the full baryon octet together with electrons and muons at zero temperature. We analyze the impact of hyperons, muons, and kaon condensation on the equation of state, on neutron-star mass--radius relations, and neutron-star thermal evolution, and examine the sensitivity of the onset density and stellar properties to variations in the nucleon--kaon scattering length and to different model vector parameters and vector self-interactions. We find that $K^{-}$ condensation sets in between $n \sim (2-8)\, n_0$ (in units of nuclear saturation density) and leads to a moderate to strong softening (in one case, a slight stiffening of the equation of state), depending on the interplay of kaons and hyperons, while remaining compatible with current $2\,M_\odot$ and small-radius neutron-star observational constraints and producing distinguishable behavior in the neutron-star cooling. This work provides an improved and thermodynamically consistent framework for studying exotic degrees of freedom in neutron-star matter.

Recently, a class of spin chains known as ``free fermions in disguise'' (FFD) has been discovered, which possess hidden free-fermion spectra even though they are not solvable via the standard Jordan-Wigner transformation. In this work, we extend this FFD framework to open quantum systems governed by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. We establish a general class of exactly solvable open quantum systems within the FFD framework: if the Liouvillian frustration graph is claw-free and has a simplicial clique, the Liouvillian possesses a hidden free-fermion spectrum. In particular, the (even-hole, claw)-free condition automatically guarantees this, enabling exact computation of the Liouvillian gap and an infinite-temperature autocorrelation function. Our results provide the first realization of the FFD mechanism in open quantum systems.

We show that the Baum--Connes assembly map factors canonically through the unitary conjugation groupoid, which serves as a universal mediator among groupoid models that are Morita equivalent to a given transformation groupoid. This establishes a structural link between groupoid-based index theory and the Baum--Connes program at the level of K-theory. Building on our previous development of unitary conjugation groupoids and their associated index theory, we extend the $K_1$ index framework beyond the Type I setting to non-Type I examples, including the irrational rotation algebra and amenable crossed products. Using Morita equivalence, we relate unitary conjugation groupoids to transformation and action groupoids, enabling the transfer of descent-type index constructions to these settings. Our main result shows that, among all groupoid realizations that are Morita equivalent to a transformation groupoid, the factorization through the unitary conjugation groupoid is canonical at the level of K-theory. This identifies the unitary conjugation groupoid as a universal intermediary for the Baum--Connes assembly map. As applications, we recover the classical index pairing with the tracial state for the irrational rotation algebra in the sense of Connes, and we prove that for amenable crossed products the descent construction agrees with the analytic Baum--Connes assembly map under Morita equivalence. These results provide a conceptual interpretation of the assembly map in terms of internal symmetries of crossed product algebras and suggest a unified framework connecting Fredholm-type index data with equivariant K-theory via groupoid methods.

We expand upon our paper (Rice and Yeates, 2021) which introduced `Outflow Fields': alternatives to the widely-used potential field source surface (PFSS) extrapolations of the Sun's coronal magnetic field which take into account the effect of the solar Wind. We showed that our fields have several advantages over PFSS, namely more accurate measurements of the Open Solar Flux (OSF) relative to observations, more realistic streamer shapes and less dependence on the arbitrary source-surface height. In this paper we seek to quantify these improvements. This includes comparison of magnetic field line angles with eclipse photography, an improved solar wind solution model and the introduction of data from a wider range of observations. We use these comparisons to determine the optimum parameters for our model using an evolutionary algorithm, in addition to the creation of synthetic eclipse images. We find that our Outflow Fields can accurately capture the overall topology of the magnetic field, and reduce the well-known discrepancy with in-situ magnetic field measurements by a significant margin relative to PFSS. Specifically, over the period between 2000 and 2022 for a typical source-surface height we find that optimized Outflow fields reduce this discrepancy from around 45% to 24% while also matching the field line topology seen during eclipse photography. Our model is presented for wider use by the community as a new python package "outflowpy".

We give an expression for the determinant of the twisted Laplacian associated with any linear representation of a finite quiver in terms of traces of the holonomy of its cycles. To establish this expression, we prove a general identity for the determinant of a block matrix in terms of traces of products of its blocks. We give two proofs, one purely enumerative and one using generating series. In the special case of a finite graph equipped with a vector bundle and a connection, the twisted Laplacian determinant admits a combinatorial interpretation as a weighted count of tuples of oriented cycle-rooted spanning forests, where the weights involve traces of holonomies along cycles formed by combining the edges of the forests.

The basic and effective reproduction numbers are widely used metrics for characterizing the dynamics of infectious disease epidemics. However, the interpretation of these numbers is based on the assumption of homogeneous mixing and may not hold in real-world populations where the contact patterns deviate from that assumption. In this paper, we present a network-based framework to compare reproduction numbers in populations with and without spatial structure, while other parameters of the disease remain fixed. Using this framework, we show that in homogeneously mixed populations, in the absence of external interventions, the effective reproduction number decreases exponentially as the susceptible population declines. In contrast, in spatially structured populations, the basic reproduction number is smaller, and the effective reproduction number initially decreases faster but eventually converges to unity. We show that the reproduction number is determined by the level of competition between infectious nodes, which is governed by the network structure. Our results suggest that without knowledge of the network structure, reproduction numbers may not be informative for parameterizing the contagiousness of the disease or predicting the behavior of epidemic spreading.

Charge transport in superconducting junctions at finite voltages is governed by Andreev reflections, including multiple Andreev reflections, which are processes that enable multiple charge transfer, a hallmark that shot noise can directly quantify. Since the effective charge extracted from shot noise measurements varies with the transparency of the junction, systematic control of transparency is essential but experimentally challenging. Here, we present shot noise scanning tunneling microscopy measurements enabled by a newly developed amplifier, allowing access to different transparency regimes. We perform shot noise measurements on Pb(111) with tunable transparency at 2.2 K and observe that the shot noise evolves from a single electron tunneling regime to multiple charge transfer regime as transparency increases. Our results are quantitatively consistent with theoretical simulations of Andreev reflections and multiple Andreev reflections for a single-channel system. These results establish junction transparency as the key parameter governing the evolution of charge transport and demonstrate that noise-STM is a powerful platform for investigating microscopic charge transport mechanisms with controlled junction transparency at the atomic scale.

Manganese(II) mobilised by mining activity poses a persistent water-quality challenge, yet the mechanisms by which low-cost sorbents, such as biochar, sequester Mn(II) remain poorly resolved. This study identifies the specific chemical drivers of Mn(II) sequestration by combining fixed-bed column and batch experiments with atomistic molecular dynamics simulations. Oilseed rape straw biochars, produced at 350\textdegree C, 550\textdegree C, and 700\textdegree C, removed 20-50% of dissolved Mn from acidic influent (pH 4, 5 ppm). High-temperature biochar achieved the greatest removal ($\sim$50%) and rapidly increased effluent pH to 9, triggering alkaline precipitation. Conversely, lower-temperature biochars removed 20-30% of Mn while maintaining a near-neutral pH (7-7.5). Enhanced \ce{K+} release in these systems indicates significant cation exchange and non-precipitative pathways. Molecular simulations confirmed that while neutral surfaces show weak Mn(II) association, deprotonated sites drive strong adsorption through inner-sphere complexation ($\sim$50% removal) and outer-sphere association ($\sim$10%). These results establish a mechanistic framework to distinguish between precipitation-led and surface-complexation-led removal. By providing specific chemical criteria for Mn-targeted sequestration, this work enables the rational design of engineered biochars for sustainable water remediation.

This paper addresses the topic of equidistribution and recurrence for polynomial sequences over function fields. The main focus is to note and correct two small errors in [V. Bergelson and A. Leibman, A Weyl-type equidistribution theorem in finite characteristic, Adv. Math. 289 (2016) 928-950], contextualized within the broader developing literature on number theory and additive combinatorics in function fields. Connected with the resolution of these issues, we also prove new results characterizing intersective polynomials in finite characteristic in terms of various algebraic, combinatorial, and dynamical properties.

Ansatz selection is a key factor in the performance of variational quantum algorithms (VQAs). While much of the state-of-the-art still relies on heuristic choices, an inadequate circuit structure can compromise both the expressive power and the trainability of the resulting model. Recent results have also established theoretical connections between expressibility and the onset of barren plateaus, highlighting the need for systematic criteria for ansatz selection. In this work, the ansatz is treated as a design feature to be optimized rather than a fixed block, and a design space exploration (DSE) is performed over a diverse set of parametrized quantum circuits (PQCs). Three complementary metrics -- expressibility, trainability, and resource cost -- are evaluated and used to analyze the trade-offs that emerge across different PQCs. Beyond identifying Pareto-optimal candidates, this multi-objective perspective helps clarify the interplay between these metrics and contributes quantitative evidence toward understanding the expressibility--trainability tension in variational circuits.

Quantum simulations before fault tolerance suffer from the intrinsic noise present in quantum computers. In this regime, extracting meaningful results greatly benefits from stability against that noise. This stability, defined as an error in observables that is independent of the system's size, is expected in local systems under local noise. In fermionic systems, the encoding of the fermionic degrees of freedom into qubits can introduce non-locality, making stability more delicate. Here, we investigate the stability to noise of fermion-to-qubit mappings. We consider noisy quantum circuits in $D$ dimensions modeled by alternating layers of local unitaries and general, single-qubit Pauli noise. We show that, when using local fermionic encodings, expectation values of quadratic fermionic observables are stable to noise in states with spatially decaying correlations: a power-law decay with exponent $μ>D$ is sufficient for stability. By contrast, we show that this stability cannot be achieved by non-local encodings such as Jordan-Wigner in $2D$, or quasi-local ones such as the Bravyi-Kitaev transform. Our findings formalize the intuition that decaying correlations of the physical systems under study provide protection against noise for local fermionic encodings, and help inform design principles in near-term quantum simulations.

Here we present a density matrix based KS inversion method formulated entirely within a Gaussian basis representation to optimize a KS potential matrix that reproduces a target electron density. Inverse Kohn-Sham (KS) density functional theory (DFT) aims to determine the effective local KS potential that reproduces a target electron density, and is important both for electronic structure analysis and for the development of orbital based correction methods. In finite Gaussian basis implementations, however, conventional inverse KS-DFT approaches such as the Zhao-Morrison-Parr (ZMP) method often become poorly constrained and inefficient, because the real space penalty potential is projected onto a limited number of Gaussian basis matrix elements, which can strongly coarse-grain its spatial variation. In the present method, the density matrix mismatch is defined in a Lowdin orthogonalized basis, which yields a penalty energy invariant under unitary rotations in that basis. The corresponding penalty potential contribution to the KS Hamiltonian is derived analytically in the original nonorthogonal Gaussian basis. Across a wide range of penalty strengths, the self consistent field (SCF) optimization remains robust and efficient for various open shell systems, while progressively tightening the penalty drives the electron density into accurate agreement with the target. Benchmarks on molecules and condensed phase systems show that the method achieves substantially smaller attainable density deviations than the conventional ZMP method. The method provides a fast and accurate route to KS inversion in finite Gaussian basis sets and may also be useful for future orbital based correction schemes.

For ethylene carbonate on the (100) surface of lithium, we calculate the adsorption energy in two binding motifs as well as the barrier height for a ring-opening decomposition reaction. We validate a scheme for producing results in the thermodynamic limit by correcting results obtained on finite lithium clusters containing only 40-100 atoms, which enables the use of hybrid density functionals, the random-phase approximation, and correlated wavefunction theories such as coupled-cluster theory and auxiliary-field quantum Monte Carlo. We find that the high-level theories agree to within 2-5 kcal/mol and can therefore serve as benchmarks for more affordable methods. Using our reference data, we demonstrate that generalized gradient approximation functionals, such as PBE, are not sufficiently accurate for reaction barrier heights, and we identify $ω$B97X-V as an especially promising functional for the interfacial chemistry of electrolyte solvents at lithium metal anodes.

We propose a new marked two-point correlation function weighted by the global gravitational potential as a probe for testing gravity models. Using the LCDM model based on general relativity (GR) as a reference, we investigate two representative modified gravity (MG) scenarios: f(R) gravity and nDGP. The mark used in this work, the global gravitational potential that is reconstructed from the galaxy distribution via the Poisson equation, is in contrast to the local property based mark (e.g., local galaxy number density or gravitational potential of host halo) used in previous studies. By applying two weighting schemes to quantify environment-dependent clustering, we find that this statistic is able to distinguish MG models from GR, with the signal being enhanced in regions corresponding to particular ranges of gravitational potential. These results indicate that the proposed statistic can serve as a useful complement to conventional clustering probes in future surveys, once observational effects and modeling uncertainties are properly taken into account.

Nonlinear response functions, formulated as multipoint correlation functions or Volterra kernels, encode the dynamical and spectroscopic properties of physical systems and underpin a wide range of nonlinear transport and optical phenomena. However, their evaluation rapidly becomes prohibitive at high orders because of combinatorial (often factorial) scaling or severe numerical errors. Here, we establish a systematic and efficient framework to compute nonlinear response functions directly from real-time dynamics, without explicitly constructing multipoint correlators or relying on numerically unstable finite-difference methods for order-resolved extraction. Our approach is based on the Gateaux derivative with respect to the external field in function space, which yields a closed hierarchy of tangent equations of motion (TEOM). Propagating the TEOM alongside the original dynamics isolates each perturbative order with high accuracy, providing a term-by-term decomposition of physical contributions. The computational cost scales exponentially with response order in the fully general setting and reduces to polynomial complexity when all perturbation directions are identical; both regimes avoid the factorial scaling of explicit multipoint-correlator evaluations. We demonstrate the power of TEOM by computing frequency-resolved fifth-order response functions for a solid-state electron model and by obtaining nonlinear response functions up to the 49th order with controlled accuracy in a classical Duffing oscillator. We further show that our time-evolution formulation allows optical conductivities to be evaluated directly while remaining numerically stable even near zero frequency. TEOM can be incorporated seamlessly into existing real-time evolution methods, yielding a general framework for computing nonlinear response functions in quantum and classical dynamical systems.

SPHEREx is a NASA mission designed to perform an all-sky spectroscopic survey in the 0.75 - 5 $μ$m wavelength range. Its primary science objectives are to investigate: (1) inflationary cosmology, (2) the history of galaxy formation, and (3) the abundance of molecular ices - critical for prebiotic chemistry - found on the surfaces of interstellar dust grains within planet-forming regions. This paper focuses on the third theme, the SPHEREx Ices investigation, for which SPHEREx is conducting a spectroscopic survey of nearly ten million preselected sources throughout the Milky Way and Magellanic Clouds to characterize their ice absorption features. By selecting targets based on infrared color, spatial isolation, and brightness, the Ices Investigation secures high-signal-to-noise spectra across a broad range of astrophysical environments that are relatively free of spectral contamination. Rather than attempting to decompose each spectrum into its individual ice components, the Ices Investigation prioritizes accurate measurements of the integrated optical depths of key molecular ice absorption features. This approach enables statistically powerful correlation studies between ice abundances and environmental parameters - including extinction, temperature, gas composition, radiation field strength, cosmic ray flux, and star formation activity. The data pipeline developed for this purpose incorporates machine learning for continuum estimation, drawing on both SPHEREx and ancillary datasets. Ultimately, the expansive spectral archive produced by SPHEREx, combined with targeted follow-up from facilities like JWST, will transform our understanding of Galactic ice formation, evolution, abundance and their inheritance into planetary systems and prebiotic inventories.

In this paper, we prove the commutativity between the Pansu pullback of a smooth contact map between Carnot groups and the differentials appearing in the spectral complexes. As a direct application, we also present a way of "lifting" a Pansu derivative (viewed as a Lie algebra homomorphism) from Carnot groups to their central extensions.

Generative AI systems produce meaning with a quality indistinguishable from - and occasionally surpassing - human performance, yet the epistemic mechanism through which this occurs remains poorly understood. This paper argues that generative AI instantiates a fundamentally new mode of knowledge production: geometric navigation through high-dimensional manifolds, grounded in indexical rather than symbolic signification. Drawing on the structural properties of high-dimensional spaces, we demonstrate that meaning in generative AI is constituted through positional relation and orientation rather than through symbolic convention. This shift corresponds precisely to what Peirce identified as indexical signification: a mode of meaning in which the sign is constituted by its real causal connection to its object, not by arbitrary assignment. We develop the pedagogical implications of this shift through a geometrized reading of Papert's constructionism, reconceptualizing the generative AI system as a new kind of microworld - high-dimensional, non-visualizable, and indexical - in which knowledge is constructed through navigation rather than symbolic programming. From this analysis, we derive the concept of Navigational Thinking: a mode of knowing characterized by positional, enactive, and bounded engagement with geometrically structured spaces. We argue that Navigational Thinking and Computational Thinking are not alternatives, but two sequential phases of the same cognitive process: while a problem remains indexical, Navigational Thinking is operative; when the problem space stabilizes into symbolizable form, Computational Thinking becomes applicable. Vibe-coding is merely the visible tip of an iceberg - the iceberg being a new cognitive ecology in which these two modes coexist as the necessary phases of problem-solving in the age of generative AI.

In this paper, we provide a combinatorial characterization of those collections of cells whose inner $2$-minor ideals are complete intersections. More precisely, given a collection of cells $\mathcal C$ and its associated inner $2$-minor ideal $I_{\mathcal C}$, we prove that $I_{\mathcal C}$ is a complete intersection if and only if $\mathcal C$ is a chessboard.