Papers

Hydrogen is known to form stable compounds with a variety of simple molecular solids under high pressure. However, ammonia hydride has not been experimentally observed. Here, through a series of laser-heating diamond anvil cell (LHDAC) experiments, we observed the transparent ionic ammonia transformed into an opaque phase above 150 GPa and 1000 K. Raman spectroscopy reveals a pronounced structural change, accompanied by the emergence of two distinct asymmetric H$_2$ vibrons ($\nu_1$ and $\nu_2$). A new ionic phase produced following thermally induced dissociation and hydrogen reorganization in hot dense ammonia. The combination of experimental results and first-principles calculations identify this phase as the theoretically predicted ionic $P4_12_12$ phase of NH$_7$ , which consists of NH$_4^+$, H$^-$and H$_2$ units. Our results suggest that the formation of ammonia hydrides follows a thermodynamic pathway distinct from those of other H$_2$-containing mixtures, revealing a new ionic transformation pathway driven by hydrogen reorganization in hot dense ammonia.

Recent measurements of cosmic expansion have renewed interest in dark-energy scenarios in which the effective equation of state exhibits phantom-like evolution and may cross $w=-1$. Such behavior, however, does not require a fundamental phantom field: in coupled dark-energy-dark-matter~(CDEDM) models, energy exchange between a canonical scalar field and cold dark matter, happens Lagrangian labels, can reproduce the same effective equation of state evolution as that of phenomenological $w_0w_a$CDM model. We show that this microscopic interaction leaves distinctive, testable signatures in structure growth by forming a two-fluid system in which only cold dark matter feels the scalar-mediated fifth force (and an associated drag term), while baryons remain uncoupled. When combined with neutrino-free streaming, this setup generates a characteristic coupling, neutrino-mass degeneracy, whose leading scaling $\sum m_\nu \propto f_c^2 \alpha^2$ follows analytically from the two-fluid growth equations. Using DESI DR2 BAO, CMB distance information, ACT DR6 lensing, redshift-space distortions, and three supernova compilations, we find that this scaling is recovered for both exponential and inverse-power-law potentials. We further show that the dominant contribution to the growth response arises from the coupling-induced modification of the background evolution, with the fifth force enhancing growth and the drag partially counteracting it. Finally, the interaction induces a running dark-matter mass, changing it at recombination by $4.3\%$–$5.5\%$, so CMB distance calculations must account for the evolving dark-matter density. These correlated growth and recombination effects provide a route to distinguish interaction-driven phantom crossing from purely kinematic dark-energy parametrizations.

Dephasing can drive a quantum Boltzmann sampler into an ordered phase while its programmed probability distribution remains disordered. We trace this transition to an enhanced conditional response: coherence loss changes how each spin responds to its neighbors, and interactions amplify the change. For all-to-all coupling, we establish the stationary transition at finite dephasing. Near criticality, the magnetization distribution depends on the ratio of dephasing strength to the square root of system size, retaining a finite imprint of coherence even as the local coherent correction vanishes. In the strong-dephasing limit on a square lattice, the dynamics generates effective multispin interactions and probability currents, with Ising-like critical statistics. Adjusting the local dissipative update restores the target probability process on arbitrary graphs.

Permutation invariant polynomials (PIPs), together with related polynomial-based invariant descriptors such as fundamental invariants (FIs), are widely used in constructing high-fidelity global potential energy surfaces (PESs) of molecules that contain identical atoms. Although the monomial symmetrization approach (MSA) enables fast evaluation of PIPs through recursive factorization, it leads to deeply nested computational graphs that may require large memory and are inefficient in modern automatic differentiation frameworks. In this work, we introduce JaxPIP, a JAX-based implementation that reformulates PIP/FI evaluation into tensorized linear algebra operations. By replacing recursive factorization with dense matrix operations combined with log-exp transformation and segmented summation, the evaluation becomes regular and GPU-friendly. This allows efficient execution with just-in-time compilation and enables large-scale batch evaluation of energies and forces (as well as higher-order derivatives). The resulting architecture supports ensemble simulations such as quasi-classical trajectory (QCT), path-integral molecular dynamics (PIMD), and diffusion Monte Carlo (DMC) in a fully vectorized manner. As demonstrated in examples, JaxPIP provides a practical route for efficient simulations of molecular systems with scalable GPU execution.

In Part~I of this tutorial, we showed that introducing angular dispersion (AD) into a collimated optical pulse allows for tuning the wave packet group velocity in free space. In principle, the group velocity can take on arbitrary values, whether superluminal, subluminal, or even negative. However, any significant deviation of the group velocity from $c$ (the speed of light in vacuum) necessitates propagation at large angles with respect to the optical axis in the non-paraxial regime. In Part~II of this tutorial, we describe the recent discovery of a new form of AD we refer to as `non-differentiable AD', which circumvents the limits imposed by conventional (differentiable) AD. Non-differentiable AD does not refer to an AD profile that is discontinuous, contains a kink, or features a singularity. Rather, a non-differentiable AD profile is continuous, smooth, and is differentiable everywhere except for one wavelength at which the derivative is not defined. We show that salutary features follow from this non-differentiability with respect to tuning the group velocity of a pulsed beam in free space; namely, significant deviations in the group velocity away from $c$ are achievable in the paraxial regime while remaining free of group-velocity dispersion and all higher-order dispersive effects. This tutorial presents an outline of these recent results for tuning the group velocity of a wave packet via non-differentiable AD, connecting them with the corresponding results associated with conventional AD – as outlined in Part~I. Moreover, we show that non-differentiable AD undergirds the unique characteristics of propagation-invariant space-time wave packets, thus unifying a large swathe of results in a single conceptual framework.

Various theoretical mass models have consistently achieved impressive accuracy in reproducing experimental masses. However, their predictions in unmeasured neutron-rich regions exhibit noticeable model dependence. In this study, we systematically investigate the differences in model predictions by comparing the liquid-drop mass terms of two representative models. Using two widely used models, Weizsacker-Skyrme-type (WS4) and Duflo-Zuker-type (DZ10), as representative examples, we find that the differences in an isotope chain gradually become more remarkable with increasing neutron number, not only for total binding energies but also for individual mass terms. The most noticeable difference appears in the volume-symmetry energy. By leveraging the term-by-term differences between the liquid-drop energy components of WS4 and DZ10, we introduce a machine learning gating network that adaptively combines the two models to improve predictive accuracy. This conditional hybrid model achieves a lower root-mean-square deviation (rmsd) than either model alone, reducing the overall rmsd from 0.284 MeV (WS4) and 0.560 MeV (DZ10) to 0.232 MeV. In the future, this term-by-term comparison strategy can be extended to models based on density-functional theories.

A plane-wave optical pulse travels in free space at a group velocity $c$ (the speed of light in vacuum) measured along its propagation axis. It is sometimes thought that spatially structuring the field in free space reduces the group velocity below $c$ because – intuitively – the oblique wave vectors undergirding the wave packet increase the average group delay. Here we show that spatiotemporally structuring a pulsed optical beam (or wave packet) can yield – in principle – arbitrary group velocities in free space in contradistinction to this commonly held intuition. We devote our attention here to pulses endowed with angular dispersion (AD) where the propagation angle is wavelength dependent. This class of wave packets is particularly pertinent because their group velocity is constant over the transverse field profile and along the propagation axis, thereby yielding an unambiguous group delay. However, significant deviation of the AD-induced group velocity in free space from~$c$ inevitably requires a large numerical aperture that lies deep in the non-paraxial regime, and such wave packets experience AD-induced group-velocity dispersion. The formulation presented here captures a broad range of results, connecting them in a single framework. In Part~II of this tutorial, we describe recently identified `non-differentiable AD' (associated with propagation-invariant space-time wave packets) that helps circumvent the limits associated with conventional (differentiable) AD as outlined here.

This paper studies the cluster-assignment layer of a cluster-first-route-second decomposition for the capacitated pickup-and-delivery problem with time windows (CPDPTW), instead of a direct route-ordering quadratic unconstrained binary optimization (QUBO). Sample-based subspace diagonalization (SQD) degenerates to best-of-shots for any diagonal optimization Hamiltonian, so a useful transfer to routing requires non-diagonal relaxation. Quantum random access optimization (QRAO) provides this non-diagonality by encoding binary variables through non-commuting quantum random access code (QRAC) observables. CPDPTW-derived conflict graphs expose a routing-specific obstruction because dense objectives and penalty-encoded constraints destroy QRAO compression. We keep the Hamiltonian sparse by encoding only the sparsified objective and enforcing one-hot, capacity, and cluster time-budget feasibility by repair after rounding. We make no quantum-advantage claim. Under strong repair the classical pass alone reaches near-optimal cost at the tested sizes. The result is a regime map linking sparsification, achieved compression, linear-combination-of-unitaries (LCU) 1-norm, heavy-hex two-qubit depth, sampling drift, and final routing quality on Qiskit Aer, calibrated FakeTorino, and IBM Heron ibm_quebec. Across a 108-row ideal-calibrated-hardware evaluation grid spanning four to twelve pickup-delivery request pairs, the hardware slice has mean gap 0.0016 and mean device-vs-ideal total variation distance (TVD) 0.279; a decoder ablation at sizes six through twelve isolates the non-diagonal signal.

We study T-odd effects through two-photon exchange in semi-inclusive deeply inelastic scattering in the kinematic region where the produced hadron has a low transverse momentum. The absorptive part of lepton-quark scattering amplitude is calculated. Transverse momentum dependent factorization is performed with the absorptive part. Although the absorptive part is divergent, the physical results, i.e., the obtained differential cross-section, is finite. Including the T-odd effects, the differential cross section receives new contributions which have different angular dependence than that obtained with one-photon exchange. Certain asymmetries can be introduced to detect the T-odd effects. Our results here are not only relevant to detecting new effect beyond the one-photon approximation in the process but also relevant to searching for new physics at lepton-proton colliders.

The microscopic origin of the low-field $1/9$ magnetization plateau in spin-$1/2$ kagome antiferromagnets remains unresolved. Here, we show that chemical pressure reshapes the hierarchy of fractional magnetization plateaus in the titanium-based kagome family $\mathrm{Cs_8AB_3Ti_{12}F_{48}}$ ($A=\mathrm{Rb},\mathrm{Li}$; $B=\mathrm{K},\mathrm{Na}$). High-field magnetization measurements up to 60 T reveal a robust $1/9$ plateau-like phase in the expanded $\mathrm{Cs_8RbK_3Ti_{12}F_{48}}$ and $\mathrm{Cs_8LiK_3Ti_{12}F_{48}}$ compounds, despite the absence of the conventionally more robust $1/3$ plateau. In contrast, compressed $\mathrm{Cs_8LiNa_3Ti_{12}F_{48}}$ exhibits neither the $1/9$ plateau-like phase nor a quantum-disordered ground state. Specific-heat measurements and first-principles calculations show that lattice expansion preserves a frustrated, fully connected kagome exchange network and gapless quantum-disordered ground states, whereas compression reorganizes the exchange network into weakly coupled quasi-one-dimensional subsystems and induces successive magnetic transitions. These results demonstrate that the $1/9$ and $1/3$ plateaus need not share a common microscopic origin and suggest that the $1/9$ plateau may represent a more universal feature of frustrated spin-$1/2$ kagome magnetism.

Kilojoule-class short-pulse (< 10 ps) lasers are excellent tools for generating relativistic ion beams, but achieving high laser-to-ion conversion efficiency remains an open challenge. Recent experiments show a significant increase in conversion efficiency when leveraging targets with an average plasma density approaching the relativistic-critical limit. We present an analytical model that explains this increase by extending the theory of target-normal sheath acceleration (TNSA) to include laser penetration of relativistic-critical density targets, enabling energy transfer to the ion front by heating the expanding electron sheath. This physical process increases the sheath field strength and significantly improves ion cutoff energy and laser-to-ion conversion efficiency relative to classical TNSA. The model predicts a maximum ion conversion efficiency of 37% by optimizing laser transmission and target areal density. Key scalings of the model agree with particle-in-cell (PIC) simulations and published experimental data. A series of 2D and 3D simulations of hydrocarbon plasmas confirm the robustness of the acceleration process, demonstrating a path for maximizing ion yields using relativistic-critical targets.

This study investigates the multi-thermal structure of solar jets by combining extreme ultra-violet (EUV) and Ha observations, addressing whether cool and hot components originate from the same jet, their morphological similarities and differences, and the role of mini-filaments. We analyze 70 jet events simultaneously observed by Atmospheric Imaging Assembly (AIA) and Chinese Ha Solar Explorer (CHASE) from 2023 May 25 to 2026 January 15. The events are classified into four types based on whether or not there are significant differences between the two wavebands in terms of length and width; nonlinear force-free field extrapolations are applied to examine magnetic fields. We find that the cool and hot components correspond to different temperature parts of a unified jet, showing spatiotemporal coincidence and kinematic synchronization. Morphologically, 30% show no significant difference in length/width, 37% differ in one dimension, and 33% differ in both. About 80% involve mini-filament eruptions; jets with filaments more often exhibit morphological differences (filament non-expansion, hot shell thickness, insufficient kinetic energy, or material rarefaction). In contrast, jets without filaments tend to show consistent morphologies; when discrepancies occur, they are mainly linked to small magnetic field curvature, which reduces magnetic tension and leads to less acceleration of cool material. These results highlight the complex interaction between thermal, dynamic, and magnetic factors in shaping jet morphology.

Aligning and maintaining complex optical beam paths is a central challenge across experimental science, because it is a high-dimensional task with strong cross-coupling between controls, often in systems with limited physical access. We present an automated hardware-software framework that resolves this alignment challenge using low-cost, retro-fittable motorized mounts driven by projective-geometry models and a photodiode-fed optimizer. A compact forward model describes the beam path to paraxial order with only the physical mirror angles left free, so it can be rapidly ($\sim$ms) numerically inverted to return the required mirror angles for a desired beam trajectory. A photodiode-fed optimizer then fine-tunes this geometric starting point, and converged mirror settings are tabulated for retrieval in milliseconds and actuation in seconds. We experimentally demonstrate the performance of this approach on a retro-reflected lattice atom-transport system, yielding improvements in both speed and precision over manual alignment. This framework reduces the manual effort required to align complex beam paths, enables programmable optical control in experiments with limited physical access, and enhances the scalability of complex optical architectures.

Hybrid terrestrial-satellite quantum networks combine terrestrial fiber infrastructure with free-space links to enable long-distance entanglement distribution. Entanglement can be routed over different combinations of terrestrial and satellite links, resulting in paths with different entanglement generation rates (EGRs) and fidelities. Existing routing algorithms, however, typically reduce routing to a single-objective problem by optimizing either EGR or fidelity, or by optimizing one while constraining the other, and thus do not explicitly capture the trade-off between the two. In this paper, we present a bi-objective routing framework for hybrid quantum networks that jointly optimizes end-to-end EGR and fidelity. We formulate routing as a Pareto optimization problem and show that it possesses a special mathematical structure: the bottleneck nature of end-to-end EGR and the multiplicative nature of end-to-end fidelity allow the problem to be transformed into a MAXMIN-MINSUM bi-criterion path problem. This transformation enables the exact polynomial-time computation of a minimal complete Pareto set using Martins' bicriterion routing algorithm. Our results demonstrate that hybrid networks expose substantially richer Pareto frontiers than terrestrial-only networks and that the proposed framework outperforms representative single-objective routing policies by allowing applications to select paths based on their EGR and fidelity requirements.

Materials discovery and design campaigns can be formulated as constrained multi-objective Bayesian optimization (CMOBO) problems, within which each experimental decision negotiates between two coupled but competing goals: discovering feasible candidates and refining the underlying Pareto front. Here we recast acquisition-function choice as an adaptive policy-selection problem over a portfolio of conventional and feasibility-focused acquisition functions. This was done using two controllers: UCB-Bandit, a modified UCB multi-armed bandit, and Agentic-Switch, a multi-agent decision system driven by a large language model (LLM). Both were evaluated against fixed-policy baselines in silico across five synthetic benchmark functions and two materials design case studies. The adaptive policies performed competitively in terms of both cumulative feasibility count and feasible hypervolume improvement, while each individual acquisition function performed well for only one metric, suggesting that adaptive policies are better suited for constrained materials science problems.

Over the past three decades, generalized parton distributions (GPDs) have emerged as one of the most active and important areas of research in nucleon structure and quantum chromodynamics (QCD). Since the last comprehensive review two decades ago, substantial progress has been made in experimental measurements of hard exclusive processes, such as deeply virtual Compton scattering and near-threshold $J/\psi$ production, as well as in increasingly sophisticated phenomenological analyses of GPDs that enable three-dimensional nucleon tomography. Theoretical advances in perturbative coefficient functions, scale evolutions, and kinematic and power corrections have considerably improved the precision of GPD phenomenology, while new hard exclusive processes for probing GPDs have been explored. More interestingly, lattice QCD can now directly access GPDs at fixed parton momentum fractions $x$ and skewness $\xi$ through large-momentum expansions, in addition to the traditional calculations of their moments, or generalized form factors. Significant progress has also been made in exploring the QCD energy-momentum tensor that encodes fundamental information on the nucleon's mass distribution, complete spin structure, and spatial distributions of momentum current and color-Lorentz forces acting on quarks and gluons.

By constructing Lax operators in the loop algebra of the $\mathbb{Z}_2^2$-graded extension of the Lie superalgebra $\mathfrak{osp}(1|2)$, we derive a $\mathbb{Z}_2^2$-graded extension of the Camassa-Holm equation. The resulting equation is an integrable nonlinear PDE for a system of four $\mathbb{Z}_2^2$-graded commutative functions, each associated with a distinct $\mathbb{Z}_2^2$-degree. We further show that the $\mathbb{Z}_2^2$-Camassa-Holm equation admits a bi-Hamiltonian structure. As a consequence, it possesses infinitely many conserved quantities, including one with non-trivial $\mathbb{Z}_2^2$-degree, which are mutually in involution with respect to the $\mathbb{Z}_2^2$-graded Poisson brackets.

We present an analytical study of the spatial structure of correlations in periodic fermionic systems at the single Slater determinant level, focusing on the cyclic case. Exploiting cyclic symmetry, the transformation from localized orbitals to molecular orbitals is simultaneously a discrete Fourier transform, a Vandermonde matrix on the roots of unity, a complex Hadamard matrix, and the character table of the cyclic group $C_m$. Within this framework, the spatial structure of correlations is fully determined by the occupied irreducible representations (Fourier modes), independently of the specific Hamiltonian generating them. In particular, the fermionic two-point correlator is expressed as a truncated Fourier sum over the occupied orbitals, leading to exact analytical expressions for symmetric occupation patterns of Fourier modes ($\ell$ and $-\ell$ pairs), corresponding in quantum chemistry to aromatic fillings, i.e. fillings satisfying Hückel's $4n + 2$ rule. For the half filling case, we derive exact spatial selection rules. In particular, the two-point correlator vanishes identically for all even distances along the ring. This property propagates to reduced density matrices and implies a complete absence of mutual information between the corresponding orbitals. These results reveal that, despite the global delocalization of molecular orbitals, the correlation structure in cyclic systems is highly non-uniform and governed by symmetry-induced interference. Although formulated in terms of cyclic lattice systems, the present results extend straightforwardly to one-dimensional fermionic chains with periodic conditions, reflecting the underlying translational symmetry of the problem. The framework therefore provides a Hamiltonian-independent and universal reference for understanding correlation patterns in one-dimensional periodic fermionic systems.

To extract complete information about experimental noisy quantum states, as well as correlations among different physical parameters, we develop an efficient machine learning-assisted framework with the normalizing flow based Bayesian parameter estimation (BPE). By embedding a physically interpretable parameter vector, ${s}$, into the quantum state ansatzes, $\rho({s})$, the corresponding parameter distribution $p({s}|D)$ is induced from BPE, based on the available experimental data $D$. The BPE allows us to perform parameter correlation analyses, providing powerful insights about how experimental parameters and related noise sources affect quantum features of the system. As an example, the flexibility of our framework is demonstrated using two different physical ansatzes on the optical cat state experiments, where a noisy single-photon state is added to impure squeezed state. With correlations among the Wigner function negativity, photon-addition fraction, noisy fraction, and pump powers, our framework gives interpretations for complicated experimental mechanisms in generating noisy non-Gaussian states. By leveraging normalizing flow-based neural networks and Bayesian uncertainty estimation, along with physical and experimental constraints incorporated naturally, the valuable information inferred in the posterior learning provides guidelines for experimentalists, as well as theorists, in identifying promising parameters to enhance desirable features.

This paper introduces the mollified-sharp decomposition, a probabilistic regularization of moving shocks in parametric reduced-order models. Each detected shock location is treated as a random variable with a prescribed probability density. Averaging over this artificial distribution replaces the localized pressure change by a smooth transition whose spatial extent is set by the density width, rather than by direct filtering of the pressure field. Each snapshot is decomposed exactly into a regularized mollified field and a local sharp correction that restores the shock. This probabilistic construction and exact additive split define the general method; the detector, kernel, treatment of multiple shocks, alignment coordinates, and regression are implementation choices. In the present realization, a calibrated indicator detects shocks, a compactly supported Wendland kernel mollifies them, and a peak-normalized and, where necessary, partitioned weight derived from each shock-location probability density defines the centroid, principal axes, and scales of its local alignment domain. Separate POD-GPR models represent the mollified field and aligned corrections, with additional regressions for shock presence and alignment. The method is demonstrated on the transonic airfoil pressure data of Catalani et al. (2023) and compared with a standard POD-GPR model constructed from the same data and POD-energy criterion. The mollified-sharp model reduces the mean test-set relative $L^2$ pressure error by 31.2% and the mean test-set surface-pressure-coefficient error by 33.2%, while also improving the predicted shock locations and pressure changes; the trade-off is a median online evaluation time 2.24 times as long. The construction is applicable in principle to other parameter-dependent fields with moving sharp features, such as moving material interfaces in multiphase flows.

Receiver Operating Characteristic (ROC) and Precision-Recall (PR) curves are widely used to assess the discrimination ability of forecasts for binary events, such as threshold exceedances or warnings of extreme events. In weather forecasting, forecasts are provided as spatial fields, yielding location-wise ROC and PR curves that are often aggregated to facilitate comparison. However, the effect of the aggregation strategy on performance assessment remains poorly understood. We investigate how different aggregation strategies for ROC and PR curves affect the assessment of discrimination ability. In particular, we identify conditions under which aggregation strategies satisfy two desirable properties for fair comparison: preservation of dominance between forecasts and preservation of concavity or achievability of the curves. We obtain sufficient conditions and propose two strategies satisfying them. They are compared with existing strategies from the literature, and we analyze their properties and highlight potential pitfalls that may lead to misleading interpretations. Based on these findings, we provide practical guidelines for the interpretation of aggregated ROC and PR curves. The proposed framework is illustrated with AI-based global weather forecasts, showing how different aggregation strategies can yield different rankings of competing forecasts.

Electrical resistivity is a fundamental physical property that provides powerful constraints on subsurface structure, lithology, fluid distribution, and mineralization. We present a continental-scale electrical resistivity model of Australia's shallow crust with quantified uncertainty, extending to depths of up to ~650 m. The model is derived from probabilistic inversion of more than 26.6 million airborne electromagnetic (AEM) soundings acquired along 352,600 line-kilometers from the AusAEM program. We develop a deep learning-based probabilistic inversion framework using invertible neural networks (INNs). To accommodate differences among AEM surveys, we trained 11 networks using a common set of synthetic resistivity models and the same training strategy, enabling consistent integration of inversion results across Australia. The entire inversion was completed in only 4.37 GPU hours, overcoming long-standing computational barriers to continental-scale probabilistic geophysical imaging. The resulting resistivity model exhibits clear spatial patterns that closely align with Australia's major geological provinces, sedimentary basins, aquifer and mineralizing systems. We further define the depth of investigation using posterior resistivity distributions to support uncertainty-informed geological interpretation. The resistivity model together with quantified uncertainty provides new physical constraints on regolith thickness, basin architecture, paleochannel and mineralized systems across Australia, serving as a foundation for interpreting continental-scale electrical structure and its geological, hydrological, and mineral system implications.

Historical post-16 data for UK A-Level Physics, Maths and Further Maths are analysed to determine the relative popularity of A-Level exam boards. A curriculum mapping of the exam board specifications is implemented and compared against first year syllabi of undergraduate physics courses at high-ranked UK universities. Gaps in curricula are identified and recommendations are made to both university module designers and A-level exam board curriculum setters, with regards to remedial action and a reconsideration of included content.

Existing aviation emissions inventories lack accurate trajectory data for high-resolution social cost and health impact assessment. This paper develops a 3-D emissions map by reconstructing flight trajectories for US west coast hubs to estimate regional environmental and near-airport health impacts. A physics-informed autoencoder (AE) is applied to ADS-B trajectory records for January 2025 covering US west coast hubs. The encoder combines a Convolutional Neural Network (CNN), a Bi-GRU, and a 3-D CNN with skip connection; the decoder is a Temporal Convolutional Network (TCN). It is benchmarked against a baseline-AE and cubic spline interpolation. Emissions are mapped via EUROCONTROL Base of Aircraft Data (BADA) performance tables and ICAO Engine Emissions Databank (EEDB) emission indices, with altitude corrections via Boeing Fuel Flow Method 2 (BFFM2). Social costs are quantified for all flight phases, with health impacts assessed for Landing and Takeoff cycles within 50 km of each hub. The proposed AE model outperforms both a TCN-AE and cubic spline interpolation across 5% to 50% missing rates. Monetizing the emissions inventory shows NOx produces a small net cooling effect in direct climate forcing, while accounting for 99.7% of monetized air-quality and health cost despite being under 0.4% of CO2 by mass, making it the dominant health-cost driver. To our knowledge, this is among the first studies combining AE-based trajectory reconstruction with separate spatial-temporal feature encoding and altitude-based emissions modeling to produce a regional aviation emissions inventory for air quality, climate impact and population exposure. The resulting emissions map and social cost estimates provide quantitative context for environmental impact assessment and near-airport health policy evaluation for US domestic aviation.

We investigate matter creation in the cosmological framework of unimodular gravity. We keep the energy density $\rho$, pressure $p$, particle number density $n$, and particle number $N=nV$ as the physical thermodynamic variables of the matter sector, and introduce particle creation directly through the balance equation $N^{\mu}{}_{;\mu}=n\Gamma$. Combining this open-system formulation with the unimodular diffusion term $Q$, we derive the exact identity $nT\dot\sigma=-3Hp_c-(\rho+p)\Gamma-\dot Q$, which shows that the creation pressure $p_c$, the creation rate $\Gamma$, and the diffusion term $Q$ are, in general, three independent sources of entropy production per particle. Adopting the standard postulate that particle creation is itself adiabatic, the first two terms cancel identically and the relation reduces to the particular case $nT\dot\sigma=-\dot Q$, so that the entropy per particle is constant only when $Q$ is constant. Thus, even when the creation process associated with $\Gamma$ is adiabatic in the usual Prigogine sense, the full matter evolution in unimodular gravity is non-adiabatic whenever $\dot Q\neq0$. The general identity, however, remains available as a starting point for relaxing this postulate in future work.

Neural networks provide expressive representations for scientific computing. However, even sufficiently expressive networks can suffer training failure in weak-gradient regimes, limiting their practical use in quantum many-body physics and ab initio quantum chemistry. Here we derive an unbiased direct gradient estimator and introduce the adaptive minimum-variance phase (AMVP) estimator for neural-network variational optimization. By improving the signal-to-noise ratio of weak gradients, these methods enable reliable scientific calculations where training previously failed, while substantially reducing computational cost. The framework enables compact networks to outperform larger and fine-tuned default standard-estimator models with over an order of magnitude less GPU time on correlated flux models, and ultimately exceed the density matrix renormalization group (DMRG) accuracy. It further achieves chemical accuracy in N$_2$ bond breaking and, for the first time, in heavy-element I$_2$ with explicit spin-orbit coupling. These results demonstrate that gradient-estimator design expands the capabilities of neural-network variational methods for accurate scientific computing.

Although tens of thousands of two-dimensional (2D) crystals are now known, the nanotubes they can form are usually constructed for individual materials, using procedures derived for graphene. Here, we develop a general theory of the rolling construction for arbitrary 2D crystals and implement it in \ntbuilder{} (NanoTube Builder), an open-source library with desktop and web interfaces. We express the size of the exact unit cell of a tube through the reduced form of a single rational number built from the lattice metric, which explains why triangular and square lattices always close with small cells, whereas rectangular, centered rectangular, and oblique lattices can require cells larger by many orders of magnitude. The optimal approximate cells are the best rational approximations of a second number, so that a cell small enough for first-principles calculations can be chosen with a controlled departure from periodicity, as in the biphenylene network, where such a cell is eight orders of magnitude smaller than the exact one. The 17 plane groups reduce to seven distinct chirality maps once rolling is taken into account, the rolling sense of layers without a horizontal mirror defines distinct tubes, and bonds formed or broken by curvature are detected pair by pair against the flat layer. The same framework assembles multiwalled tubes whose walls share one axial period, periodic bundles, and strained or twisted structures that remain periodic. Applied to 46,403 distinct 2D systems, it produced a public catalog of 20,334,372 nanotubes, of which 57.1% show no bond change upon rolling. All structures can be exported directly as input for first-principles and molecular dynamics codes.

We define a rank-two extension $\mathcal{H}^{(2)}$ of the spherical $\mathcal{H}$-transform, together with its associated transform $\mathcal{R}^{(2)}$. For sums, both transforms are additive. The transform $\mathcal{R}^{(2)}$ yields a $4\times4$ formula for the average product of two hermitized resolvents, and hence for off-diagonal eigenvector overlaps, recovering the Ginibre, elliptic, and bi-invariant formulas. We also treat correlated pairs of matrices, and obtain overlaps between their eigenvectors or singular vectors.

Universality in nonlinear nonequilibrium systems is typically expressed through scaling laws that render macroscopic behavior insensitive to microscopic details. Whether this universality survives when periodic forcing and nonlocal dissipative memory act simultaneously remains an open question in driven open dynamics. Here, we demonstrate that barrier-crossing processes in periodically driven dissipative systems are governed not merely by modified exponential scaling, but by an explicit two-parameter universal response function. Within a semiclassical instanton framework incorporating Floquet modulation and Ohmic environmental coupling, the tunneling exponent factorizes into a system-dependent static contribution and a universal function of two dimensionless control parameters: normalized driving frequency and dissipation strength. This factorization arises from the combined modification of a single saddle-point trajectory and introduces no additional independent scaling variables. Weak-to-moderate dissipation acts as a smooth dynamical renormalization of the effective action, preserving the saddle-point structure and enabling controlled analytical expansion. In the high-frequency regime, the response exhibits universal dynamical averaging, while an explicit integral representation establishes a continuous adiabatic to Floquet crossover. Direct numerical evaluation of the nonlocal instanton action confirms that the normalized tunneling exponent exhibits a universal dependence on the driving parameters across different model systems. These results identify driven dissipative barrier crossing as a distinct two-parameter universality class within nonlinear nonequilibrium dynamics and provide a predictive functional framework for response phenomena in driven systems with memory.

We investigate the one-dimensional Coulomb problem on the positive half-line for a fourth-order Schrödinger equation generated by a commonly used realization of the Generalized Uncertainty Principle (GUP). The problem is treated directly in position space by a higher-order Bethe–Ansatz construction, with the wave function represented as a polynomial multiplied by an exponential factor. The resulting residue conditions yield an analytic quantization condition and explicit polynomial solutions for the first three bound states. We identify the branch that is continuously connected to the ordinary Coulomb problem and show that its energies, decay constants, polynomial factors, and Bethe–Ansatz roots recover the ordinary half-line Coulomb results in the vanishing-deformation limit. On this Coulomb-connected branch, the deformation produces a lower admissibility bound on the principal quantum number, while arbitrarily high quantum numbers remain admissible. We also discuss the physical interpretation of the deformation strength: for ordinary microscopic systems, the weak-GUP regime is the conservative expectation in Planck-scale motivated models, whereas intermediate and strong regimes are primarily theoretical regimes in the present analysis. Since the differential equation is truncated at first order in the GUP parameter, quantitative predictions outside the weak-deformation regime should be interpreted with care.