AI for Science

Adaptive Hamiltonian learning is central to calibrating and characterizing quantum devices. In an adaptive controller, choosing the next experiment is itself a computation. Bayesian design rules are recomputed after every posterior update, and that step can take seconds. Across hundreds of shots, those seconds become a significant wall-clock cost for adaptivity. We introduce SymQNet, an amortized reinforcement-learning approach for low-latency adaptive Hamiltonian learning. SymQNet learns a posterior-conditioned acquisition policy offline, then uses a fast policy forward pass online while retaining Bayesian posterior feedback. On transverse-field Ising benchmarks, SymQNet substantially reduces acquisition latency relative to bounded Fisher-information search and bounded two-step Bayesian active learning by disagreement (BALD). At five qubits, it reduces acquisition-only decision latency by $47.1\times$ and $72.6\times$ relative to these online baselines; at twelve qubits, full simulated steps take $1.02$ s for SymQNet versus $13.27$ s for bounded two-step BALD. Overall, we show that learned acquisition can make adaptive Hamiltonian learning practical for repeated low-latency workloads.

Quantum circuit routing is a key step in compiling programs for noisy intermediate-scale quantum processors. Routes that appear efficient by standard overhead metrics can still lose fidelity when they pass through poorly calibrated couplers. We study a calibration-aware graph reinforcement-learning router that uses same-day IBM Heron r2 calibration data to choose hardware-edge SWAPs. We train the policy with proximal policy optimization and evaluate it with exact simulated fidelity across nine Munich Quantum Toolkit (MQT) Bench circuits and three calibration snapshots. Across these evaluations, pooled mean exact fidelity is $0.727$, compared with $0.440$ for SABRE-best20 and $0.481$ for target-aware SABRE. We observed that fidelity gains came with higher routed two-qubit counts and were concentrated in 5 qubit and 8 qubit circuit families; under the fixed tree action graph, all 10 qubit families favored SABRE-best20. Overall, our results show that calibration-aware learned routing can improve fidelity beyond gate-count-driven compilation.

We develop a data-driven framework for estimating optimal linear response of nonlinear dynamical systems. Our approach is based on kernel-smoothed approximations of the transfer/Koopman operators of the system, built from possibly high-dimensional observations along trajectories. Combining these operator approximations with the theory developed in [Antown et al. (2018), J. Stat. Phys., 170(6), 1051-1087], we formulate a computationally tractable optimization problem for the optimal infinitesimal perturbation realising any desired manipulation of the spectrum. We also introduce a notion of optimal-response vector fields for visualising, and physically interpreting, the system's response to the optimal perturbation under arbitrary observations. Our focus is on finding perturbations that optimally increase the frequency or optimally suppress the decay of correlations of almost-cycles or almost-invariant sets associated with the eigenvalues of the kernel-smoothed transfer operator. We illustrate our approach with applications to low-dimensional periodic and chaotic systems, as well as a high-dimensional example involving the El Nino Southern Oscillation in a comprehensive Earth system model. In these examples our approach discovers nontrivial optimal perturbations of the system, which are post hoc natural and consistent with the desired dynamical objectives.

Determining the neutrino mass ordering remains a central open problem in particle physics. While next-generation long-baseline experiments are expected to resolve this question, current data provide limited sensitivity because the spectral differences between normal and inverted ordering are subtle and entangled with parameter degeneracies. We investigate a machine-learning strategy for mass-ordering determination using a feed-forward neural-network classifier trained on synthetic long-baseline datasets generated with three-flavour oscillation probabilities, matter effects, and statistical fluctuations. We evaluate the classifier against standard $χ^2$ and $\log\mathcal{L}$ approaches using common discrimination metrics, including receiver-operating-characteristic curves, to quantify sensitivity and to illustrate how operating points can be selected to prioritise purity or efficiency. We find that the neural network achieves performance comparable to conventional fits for the scenarios studied, providing a flexible, independent cross-check of established analyses. The framework can be extended to incorporate systematic uncertainties and to explore joint inference of oscillation parameters, and it may also serve as a pedagogical tool for introducing machine-learning methods in neutrino physics.

In this work we present a pedagogically motivated analysis of spin-correlation calculations in a quantum system composed of two spin-$1/2$ particles. Rather than aiming at new physical results, our purpose is to clarify and bring attention to different strategies for evaluating expectation values of the form $\langle ψ| S^{(1)}_{\hat{\boldsymbol{u}}} S^{(2)}_{\hat{\boldsymbol{v}}} | ψ\rangle$, which play an important role in discussions of entanglement and Bell-type correlations. We compare three complementary approaches. The first follows a direct algebraic evaluation in the product basis, closely related to standard textbook methods. The second uses a matrix representation of bipartite states, in which the tensor-product structure is expressed in terms of $2\times2$ complex matrices. This representation keeps the calculation close to the familiar Pauli-matrix algebra and makes the independent action of operators on each subsystem more transparent. The third explores a symmetry-based argument, highlighting both its usefulness and its limitations when applied beyond the singlet state. We show explicitly that the singlet state is rotationally invariant, which explains why the symmetry argument successfully reproduces its correlation function, while a naive extension fails for triplet states. The discussion illustrates how entanglement, tensor-product structure, and rotational symmetry interplay in spin correlations.

Nuclear quantum effects and non-Born--Oppenheimer effects play a vital role in many chemical and biological processes, motivating the incorporation of such effects into dynamical simulations. In real-time nuclear--electronic orbital time-dependent density functional theory (RT-NEO-TDDFT), the electronic and nuclear densities are propagated numerically in time according to the time-dependent Schrödinger equation. In this framework, specified protons are treated quantum mechanically on the same level as the electrons. The classical nuclei can be propagated on the instantaneous NEO vibronic surface using Ehrenfest dynamics. A traveling proton basis (TPB) can be used to describe the dynamics of moving protons in conjunction with Gaussian-type protonic and electronic basis sets for each quantum proton. Herein, we present a constrained TPB (c-TPB) approach that ensures each protonic basis function center coincides with the corresponding proton position expectation value during the dynamics. This approach produces accurate nuclear--electronic quantum dynamics and rigorously conserves energy. We demonstrate the accuracy and stability of this approach for computing molecular vibrational frequencies as well as simulating excited-state intramolecular proton transfer and double proton transfer in the o-hydroxybenzaldehyde and [2,2$'$-bipyridyl]-3,3$'$-diol molecules. These applications show that the c-TPB method provides accurate dynamics, conserves energy, and is computationally efficient.

We introduce a simplicial and categorical formulation of Aharonov-Bohm (AB) type arbitrage in filtered market systems. Given a filtration modeled as a contravariant functor $F : \mathcal T^{op} \to \mathbf{Prob},$ we consider the associated conditional expectation transport functor $\mathcal E \circ F : \mathcal T^{op} \to \mathbf{Ban},$ and the canonical distortion $dF(i) := (\mathcal E \circ F)(i)(1),$ which measures the failure of constant functions to be preserved under non-measure-preserving transitions. Motivated by the multiplicative transport structure of $dF$, we introduce a simplicial distortion operator defined recursively on the nerve $N_\bullet(\mathcal T)$ of the time category. This construction describes recursively accumulated transported distortions along composable chains of morphisms and leads naturally to a notion of holonomy along loops. We interpret non-trivial holonomy as a global inconsistency invisible at the level of individual transitions, analogous to the Aharonov-Bohm effect in physics. This yields a notion of AB arbitrage, in which arbitrage opportunities arise from global loop effects rather than local price discrepancies. We further introduce simplicial admissibility conditions ensuring that recursively accumulated distortions remain integrable, and show how non-trivial holonomy can be translated into predictable self-financing trading strategies through executable loop dynamics. This establishes a connection between categorical holonomy structures and economically realizable arbitrage. The framework developed here suggests a global and homological perspective on arbitrage theory, in which market inconsistencies are encoded by recursively accumulated simplicial distortions and their holonomy along loops in the underlying time category.

The realization of Hawking radiation in optical analogs has historically focused on kinematic observables, such as the effective temperature determined by the horizon's surface gravity. A complete thermodynamic description, however, necessitates a rigorous definition of entropy and irreversibility, which has remained elusive in Hamiltonian optical systems. In this work, we bridge this gap by introducing an operational entropy for solitonic event horizons, derived from the spectral partitioning of the optical field into coherent solitonic and incoherent radiative subsystems. The emission of resonant radiation, driven by the breaking of soliton integrability under higher-order dispersion, is the fundamental mechanism for entropy production. Numerical simulations of the generalized nonlinear Schrödinger equation (GNLSE) demonstrate that, in a coarse-grained sense, this process obeys a generalized second law (GSL), $ΔS_{\mathrm{tot}} \ge 0$, robustly across a wide range of soliton orders and dispersion strengths. These results show that event horizons in dispersive field theories behave as consistent nonequilibrium thermodynamic systems, and that the relevant entropy is accessible from laboratory spectral measurements.

We present a physics-based neural network framework for the discovery of constitutive models in fully coupled thermomechanics. In contrast to classical formulations based on the Helmholtz energy, we adopt the internal energy and a dissipation potential as primary constitutive functions, expressed in terms of deformation and entropy. This choice avoids the need to enforce mixed convexity--concavity conditions and facilitates a consistent incorporation of thermodynamic principles. In this contribution, we focus on materials without preferred directions or internal variables. While the formulation is posed in terms of entropy, the temperature is treated as the independent observable, and the entropy is inferred internally through the constitutive relation, enabling thermodynamically consistent modeling without requiring entropy data. Thermodynamic admissibility of the networks is guaranteed by construction. The internal energy and dissipation potential are represented by input convex neural networks, ensuring convexity and compliance with the second law. Objectivity, material symmetry, and normalization are embedded directly into the architecture through invariant-based representations and zero-anchored formulations. We demonstrate the performance of the proposed framework on synthetic and experimental datasets, including purely thermal problems and fully coupled thermomechanical responses of soft tissues and filled rubbers. The results show that the learned models accurately capture the underlying constitutive behavior. All code, data, and trained models are made publicly available via https://doi.org/10.5281/zenodo.19248596.

This work presents the application of parametric Operator Inference (OpInf) -- a nonintrusive reduced-order modeling (ROM) technique that learns a low-dimensional representation of a high-fidelity model -- to the numerical model of the purging process in semiconductor manufacturing. Leveraging the data-driven nature of the OpInf framework, we aim to forecast the flow field within a plasma-enhanced chemical vapor deposition (PECVD) chamber using computational fluid dynamics (CFD) simulation data. Our model simplifies the system by excluding plasma dynamics and chemical reactions, while still capturing the key features of the purging flow behavior. The parametric OpInf framework learns nine ROMs based on varying argon mass flow rates at the inlet and different outlet pressures. It then interpolates these ROMs to predict the system's behavior for 25 parameter combinations, including 16 scenarios that are not seen in training. The parametric OpInf ROMs, trained on 36\% of the data and tested on 64\%, demonstrate accuracy across the entire parameter domain, with a maximum error of 9.32\%. Furthermore, the ROM achieves an approximate 142-fold speedup in online computations compared to the full-order model CFD simulation. These OpInf ROMs may be used for fast and accurate predictions of the purging flow in the PECVD chamber, which could facilitate effective particle contamination control in semiconductor manufacturing.

We prove, within the probabilistic framework of Khinchin families, that the generating function $P_k$ of partitions into $k$-th powers is strongly Gaussian in the sense of Báez-Duarte, and even further that it is a Hayman function. Thus the Hardy--Ramanujan asymptotic formula for the number $p_k(n)$ of partitions of $n$ into $k$-th powers which reads \[ p_k(n) \sim \frac{α_k}{n^{(3k+1)/(2k+2)}} \exp\!\Big(β_k\, n^{1/(k+1)}\Big), \qquad n\to\infty, \] where $α_k$ and~$β_k$ are explicit constants depending only on $k$, follows directly from Hayman's asymptotic formula for strongly Gaussian power series. The proof of strong Gaussianity of $P_k$ combines a Gaussianity criterion for Khinchin families with certain bounds of Tenenbaum, Wu and Li on the generating function; the asymptotic formula is recovered by computing asymptotic approximations of the mean and variance of the associated family. Analogous results are presented for the generating function $Q_k$ of partitions into distinct $k$-th powers.

We present a systematic construction of non-Hermitian tight-binding lattices whose Bloch spectra are $n$th roots of those of Hermitian parent two-dimensional (2D) lattices, namely graphene and the Lieb lattice. The $n$-roots of these models are constructed from connecting loop modules of unidirectional couplings whose geometrical arrangements match that of the corresponding parent system. Their energy spectrum is shown to consist of $n$ rotated and equivalent branches in the complex energy plane, each matching the real spectrum of the parent model when raised to the $n$th power, together with extra zero-energy flat bands (FBs) accounted for by the generalized index theorem. We show how the low-energy Dirac cones of the parent models translate, for an appropriate choice of phase configuration for the couplings of the $n$-root lattices, as what we call an "exceptional horn" appearing at each branch, with the central Dirac point (DP) converted into zero-energy exceptional points (EPs) of order $n$ or higher at high-symmetry momenta. These exceptional horns reflect the behavior of low-lying excitations that scale with momentum as $E\sim\vert \mathbf{q}\vert^{\frac{1}{n}}$, with $n\geq 3$, as opposed to the linear massless modes that characterize a Dirac cone. Moreover, we derive analytic expressions for the associated Landau levels (LLs), whose energies scale with magnetic flux as $E\simϕ^{\frac{1}{2n}}$. For the case of the $n$-root Lieb lattice, the zeroth LL is shown to be exceptional. These results are analytically derived for both $n$-root models and numerically demonstrated for certain values of $n$. Finally, we propose a realistic photonic implementation based on coupled ring resonators with a split configuration of optical gain and loss.

We develop a systematic framework for the model reduction of multivariate geometric Brownian motions (GBMs), a fundamental class of stochastic processes with broad applications in mathematical finance, population biology, and statistical physics. Our approach leverages the interplay between the method of invariant manifolds and adiabatic elimination to derive closed-form reduced equations for the deterministic drift. An extended formulation of the fluctuation-dissipation theorem is subsequently employed to characterize the stochastic component of the reduced description. As a concrete application, we apply our reduction scheme to a GBM arising from a two-state quantum system, showing that the reduced dynamics accurately capture the localization properties of the original model while significantly simplifying the analysis.

This paper presents an adaptive observer design for semilinear hyperbolic rolling contact ODE-PDE systems with uncertain friction characteristics parameterized by a matrix of unknown coefficients appearing in the nonlinear (and possibly non-smooth) PDE source terms. Under appropriate assumptions of forward completeness and boundary sensing, an adaptive observer is synthesized to simultaneously estimate the lumped and distributed states, as well as the uncertain friction parameters, using only boundary measurements. The observer combines a finite-dimensional parameter estimator with an infinite-dimensional description of the state error dynamics, and achieves exponential convergence under persistent excitation. The effectiveness of the proposed design is demonstrated in simulation by considering a relevant example borrowed from road vehicle dynamics.

The component-wise dimensionally reduced real Schur flows (RSFs) associated to the classical compressible Euler equation [J.-Z. Zhu, J. Math. Phys. \textbf{62}, 083101 (2021)] is reformulated alternatively in terms of mode-truncation, with the untruncated Fourier modes preserving the original interaction structure and thus other important derivatives. A number of results are set up for the mathematical physics of component-wise dimensionally reduced flows (CWDRFs, including those with further dimensional reductions of RSFs); and, it is particularly shown that previous proofs of the helicity invariance in barotropic ideal flows were overkilling in the sense of using the unnecessary condition of local mass conservation, while our new ``sharper'' proof without invoking the latter carries over to our CWDRFs and the inviscid Burgers equation, verified using recent results [S.~G.~Chefranov \& A.~S.~Chefranov, Phys. Scr. \textbf{94}, 054001 (2019)] for the latter case in the infinite domain.

We consider a nonlinear Klein-Gordon equation in the nonrelativistic limit regime with initial data in the form of a modulated highly oscillatory exponential. In this regime of a small scaling parameter $\varepsilon\ll 1$, the solution exhibits rapid oscillations in both time and space. The solution is approximated, up to $\mathcal{O}(\varepsilon)$, by a superposition of two polarized solutions, which are wave packets that move with opposite group velocities proportional to $\varepsilon^{-1}$. The equations for polarized solutions are formulated in co-moving coordinates and are then discretized by an explicit and an implicit exponentially weighted finite difference method. While the explicit weighted leapfrog method needs to satisfy a CFL-type stability condition, the implicit weighted Crank-Nicolson method is unconditionally stable. Both methods achieve second-order accuracy with time steps and mesh sizes that are not restricted in magnitude by $\varepsilon$. For the approximation of polarized solutions, the methods are uniformly convergent in the range from arbitrarily small to moderately bounded $\varepsilon$. Numerical experiments illustrate the theoretical results.

We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this recovery problem and improves upon current approaches by an order of magnitude. It relies on generalized normal forms and stabilizers of group actions via matrix-tensor congruence. We apply randomized transformation techniques that avoid the task of solving nonlinear polynomial systems associated to degenerate paths, and accompany our methods with an efficient implementation in the computer algebra system OSCAR.

The GMTKN55 data set is a collection of standard benchmarks used in molecular quantum chemistry that spans small- and large-molecule thermochemistry, reaction barriers, and non-covalent interactions. Herein, we identify a flaw in the weighted mean absolute deviation (WTMAD) definitions commonly used to quantify performance of various electronic-structure methods for the GMTKN55 set, which under-weight some of its component benchmarks by orders of magnitude. A new WTMAD-4 metric is proposed, based on typical errors observed for a set of ten minimally empirical dispersion-corrected density-functional approximations (DFAs), ensuring fair treatment across all benchmarks. The performance of 115 DFAs is then reassessed using WTMAD-4 and we highlight a literature example where a DFA parametrised by minimising WTMAD-2 underperforms for benchmarks marginalised by that metric.

Amorphous solids exhibit structural short-range order despite lacking long-range crystalline order, with this structural descriptor found to be important for determining mechanical properties. Nanobeam electron diffraction offers a potential route for experimental characterization of structural short-range order, yet efforts to date have been primarily qualitative in nature. In this work, machine learning approaches based on transfer learning are used to enable quantitative analysis of nanobeam electron diffraction data from amorphous solids. A ResNet-18 model is trained on simulated diffraction patterns taken from different locations within simulated metallic glasses and amorphous grain boundary complexions in the Cu-Zr alloy system that were created with hybrid molecular dynamics and Monte Carlo simulations. The disorder parameter is found to be a superior target structural descriptor compared to traditional Voronoi indices for this task. The model achieves a low validation mean absolute error across diffraction patterns corresponding to different interaction volumes, demonstrating excellent performance and potential transferability. Testing was performed using other simulated nanobeam electron diffraction data as well as experimental nanobeam electron diffraction patterns, showing that the model can reliably capture spatial variations in local structural state. As a whole, this framework is able to overcome the challenges in the quantitative experimental characterization of structural short-range order, enabling improved characterization of amorphous solids and the exploration of structure-property relationships.

Exploring novel magnetoelectric coupling mechanisms to achieve control of ferroelectric polarization and magnetism is highly significant for both fundamental science and electronic device applications. Although extensive studies have been conducted on electrical switching of magnetism in multiferroic materials, simultaneous ultrafast laser switching of ferroelectric polarization and altermagnetism remains unexplored. In this letter, we propose that the ultrafast laser can be used to switch ferroelectric polarization and altermagnetism concurrently in charge-order-induced altermagnetic ferroelectrics. Building on this idea, we further demonstrate that such dual switching can be realized in charge-order-induced altermagnetic ferroelectric LiV$_2$F$_6$ by symmetry analysis and time-dependent density functional theory (TDDFT) calculation. Given that LiV$_2$F$_6$ has already been experimentally synthesized, our work not only provides an ideal material platform for experimentally realizing simultaneous switching of ferroelectric polarization and altermagnetism but also holds potential application value in future ultrafast spintronic devices.

High-quality InAs quantum wells grown on InP are a promising platform for topological quantum information processing due to their large g-factor, strong Rashba spin-orbit interaction, and their compatibility with in-situ-deposited superconductors. In this work, we investigate InAs/InGaAs quantum wells grown on InP (001) wafers, focusing on how the layer structure and strain influence the electronic properties and surface morphology. By combining quantum transport measurements with atomic force microscopy, we show that the layer design predominantly affects the mobility anisotropy, which aligns well with the surface morphology. Surface characterization further reveals the mechanism of quantum well collapse when the layer thickness exceeds the strain limit. In addition, transport measurements demonstrate that quantum confinement has a clear impact on band nonparabolicity.

The relativistic spin-momentum locking has been proven in time-reversal-breaking classes of materials with zero net magnetization in the non-relativistic limit, such as altermagnets and other non-collinear magnets. Using density functional theory calculations, we aim to show relativistic spin-momentum locking in ferromagnets, focusing on a broad class of ferromagnetic materials with magnetic sites connected by rotational symmetry, and compare with fcc Ni. In SrRuO3, the antisymmetric exchange interaction produces a spin canting orthogonal to the easy axis, while in all other cases, spin canting is forbidden. Even when the canted magnetic moment in real space is forbidden, relativistic spin-momentum locking shows sizable contributions in k-space. Using prototypical ferromagnets such as orthorhombic SrRuO3, hexagonal CrTe and CrAs with the NiAs crystal structure, half-Heusler MnPtSb, and fcc Ni, we demonstrate that relativistic spin-momentum locking can generate strong effects in ferromagnets. Subdominant components of centrosymmetric ferro-magnetic materials with magnetic sites connected by rotational symmetry host spin-momentum locking similar to altermagnets, while noncentrosymmetric MnPtSb hosts relativistic p-wave due to the spin-orbit coupling. Fcc Ni shows a more complex behavior with a combination of two spin-momentum locking patterns characteristic of altermagnets. Because ferromagnets typically have larger bandwidths than altermagnets, they provide a promising platform for observing even-wave relativistic spin-momentum locking and associated emergent phenomena. From an application standpoint, relativistic spin-momentum locking governs symmetry-allowed spin Hall currents, spin photocurrents, and other momentum-dependent spin responses in k-space.

An in-principle exact working equation to compute electronic affinity and ionization Fukui functions is derived within the $N$-centered (Nc) ensemble extension of density functional theory (DFT). It circumvents the kernel derivative discontinuity problem of DFT for fractional electron numbers, whose contribution is recovered through weight derivatives of the ensemble density functional potential. Thus, it allows for the design of alternative and effective approximations, such as the weight-dependent scaling of regular functionals or the interpolation between known limits of Nc ensembles

Molecular dynamics simulations are a central computational methodology in materials design for relating atomic composition to mechanical properties. However, simulating materials with atomic-level resolution on a macroscopic scale is infeasible on current classical hardware, even when using the simplest elastic network models (ENMs) that represent molecular vibrations as a network of coupled oscillators. To address this issue, we introduce Quantum Elastic Network Models (QENMs) and utilize the quantum algorithm of Babbush et al. (PRX, 2023), which offers an exponential advantage when simulating systems of coupled oscillators. Here, we extend their algorithm in 2D systems and demonstrate how our method enables the efficient simulation of planar materials. As an example, we apply our algorithm to the task of simulating a 2D graphene sheet. We analyze the complexity for initial-state preparation, Hamiltonian simulation, and measurement of this material, and provide two real-world applications: heat transfer and the out-of-plane rippling effect. We estimate that an atomistic simulation of a graphene sheet on the centimeter scale, classically requiring hundreds of petabytes of memory and prohibitive runtimes, could be encoded and simulated with as few as $\sim 160$ logical qubits.

Federated learning (FL) has emerged as a promising paradigm for managing electric vehicle (EV) battery data in intelligent transportation systems (ITS), enabling privacy-preserving tasks such as anomaly detection and capacity estimation. However, most existing frameworks rely on centralized aggregation schemes, which pose critical limitations in terms of security and trust. To address these challenges, we propose ABC-DFL, an automated Byzantine-resilient clustered decentralized federated learning (C-DFL) framework for connected EVs. The proposed incentive-driven C-DFL system replaces the central server with an open-permissioned blockchain, featuring a new dynamic Quorum Byzantine Fault Tolerance (QBFT) protocol and an oracle-based aggregation layer, to enhance trust, security, and automation. At the core of ABC-DFL lies FLECA (Filtered Layered Enhanced Clustering Aggregation), a robust hierarchical aggregation protocol that mitigates Byzantine attacks by having each EV filter malicious updates using an adaptive threshold based on deviations from its reference model update. Oracle nodes, responsible for inter-group aggregation, employ robust clustering to isolate and aggregate model updates from trustworthy EV groups. Comprehensive experimental evaluations demonstrate that FLECA matches FedProx convergence under benign conditions and significantly outperforms existing defenses with attack impact scores below 0.10 in adaptive adversarial scenarios. Furthermore, several learning experiments with multitask models confirm the effectiveness and fairness of the incentive mechanism. Finally, on-chain and off-chain benchmarks validate the practicality of ABC-DFL.

The Remeika series superconductor, $(\text{Ca}_x\text{Sr}_{1-x})_3\text{Rh}_4\text{Sn}_{13}$, shows a rare nonmagnetic quantum critical point (QCP) associated with the continuous charge-density wave (CDW) and structural transition under the ``dome'' of superconductivity achieved by tuning composition and applying pressure. Here we use a nonmagnetic point-like disorder induced by 2.5 MeV electron irradiation to suppress the CDW and drive the system to and even beyond the QCP. This conclusion is based on a clear evolution of temperature-dependent resistivity, $ρ\left(T\right)$, from the Fermi liquid to the non-Fermi liquid regime with increasing amount of disorder. Starting on the CDW side, below the suggested QCP concentration of $x_c=0.9$, added disorder resulted in a progressively larger linear term and a reduced quadratic term in $ρ\left(T\right)$. Nearly perfect $T-$linear dependence is observed at the dose at which long-range CDW order is suppressed to $T=$0, consistent with the expectations. We refine the QCP location in this system and place it in the interval between $x=$0.75 and 0.85. Our results strongly support the concept that the disorder can tune the system to the quantum critical regime and even beyond. It follows from the argument by Imry and Ma that any ordered phase is unstable toward quenched disorder. Introduced in a controlled way, this disorder becomes a novel non-thermal tuning parameter likely applicable to a variety of different systems.

Disorder in magnetic systems typically suppresses long-range order, promoting short-range states such as spin glasses and magnetic clusters. This is particularly prominent in high-entropy materials, characterized by the random distributions of local magnetic entities and exchange interactions. However, in rare exceptions, long-range magnetic order can persist in high-entropy systems, while the microscopic characters and underlying mechanisms remain elusive, especially the magnetic behaviors of individual elements. Here, combining neutron diffraction and resonant soft x-ray scattering, we have conducted an element-specific investigation into the magnetic order of a high-entropy honeycomb-lattice van der Waals material (Mn1/4Fe1/4Co1/4Ni1/4)PS3. Despite significant atomic disorder, long-range zigzag antiferromagnetic order is observed below 72 K, with all four transition-metal elements participating in a unified phase transition. However, the spin orientations of various elements are distinct, attributed to the competition between single-ion anisotropies and exchange interactions. Our findings showcase a novel form of long-range magnetic order with disordered spin orientations, which is synergically stabilized by distinct magnetic elements in a high entropy magnet, offering a new paradigm for understanding complex magnetic systems.

Small and Medium Enterprises (SMEs) constitute 99.9% of U.S. businesses and generate 44% of economic activity, yet systematically identifying high-potential SMEs remains an open challenge. We introduce SME-HGT, a Heterogeneous Graph Transformer framework that predicts which SBIR Phase I awardees will advance to Phase II funding using exclusively public data. We construct a heterogeneous graph with 32,268 company nodes, 124 research topic nodes, and 13 government agency nodes connected by approximately 99,000 edges across three semantic relation types. SME-HGT achieves an AUPRC of 0.621 0.003 on a temporally-split test set, outperforming an MLP baseline (0.590 0.002) and R-GCN (0.608 0.013) across five random seeds. At a screening depth of 100 companies, SME-HGT attains 89.6% precision with a 2.14 lift over random selection. Our temporal evaluation protocol prevents information leakage, and our reliance on public data ensures reproducibility. These results demonstrate that relational structure among firms, research topics, and funding agencies provides meaningful signal for SME potential assessment, with implications for policymakers and early-stage investors.

Generating quantum data by learning the underlying quantum distribution poses challenges in both theoretical and practical scenarios, yet it is a critical task for understanding quantum systems. A fundamental question in quantum machine learning (QML) is the universality of approximation: whether a parameterized QML model can approximate any quantum distribution. We address this question by proving a universality theorem for the Many-body Projected Ensemble (MPE) framework, a method for quantum state design that uses a single many-body wave function to prepare random states. This demonstrates that MPE can approximate any distribution of pure states within a 1-Wasserstein distance error. This theorem provides a rigorous guarantee of universal expressivity, addressing key theoretical gaps in QML. For practicality, we propose an Incremental MPE variant with layer-wise training to improve the trainability. Numerical experiments on clustered quantum states and quantum chemistry datasets validate MPE's efficacy in learning complex quantum data distributions.

Atmospheric Methane Removal (AMR) is a third class of climate intervention, along with Carbon Dioxide Removal (CDR) and Solar Radiation Management (SRM). We show that, unlike CDR, the avoided warming by AMR is not durable due to methane's short atmospheric lifetime, although its temperature rebound upon termination is less abrupt than that of SRM. AMR's impact on tropospheric ozone can be further modulated by background pollutant levels.