Papers

Unlike the two-qubit entangled and CHSH-nonlocal sets, the steerable and Bell-nonlocal ones have no known general closed-form criterion. For any such operational ability whose failing states form a convex set closed under local unitaries, and for a Bell mixture with arbitrary noise, the $X$ part of the noise gives an upper bound on the definitive threshold, the Bell weight above which the mixture attains the ability. That bound is the tightest that the seven of the fifteen Pauli expectation values fixing the $X$ part can support. The same theorem shows that a state has the ability whenever its $X$ part does, so partial tomography of a state can certify its ability. When noise is of $X$ form, the mixture carries a relative phase between the noise and Bell coherences that cannot be gauged away by local unitaries, and it controls the threshold through interference. We prove a monotonicity law: the threshold is nondecreasing in this phase, whether or not a closed-form criterion for the ability exists.

We investigate the impact of self-interactions on the Rényi and entanglement entropies of a scalar field on $(2+1)$-dimensional spacetimes, whose spatial sections are modeled by fuzzy spaces, specifically the fuzzy sphere and the fuzzy disc. We compute the first-order perturbative correction induced by a $\lambda\phi^4$ interaction using the Green's function approach. In contrast to the free theory, where the entanglement entropy is dominated by degrees of freedom near the entangling boundary and obeys an area law, we find that the interaction correction has an extensive bulk contribution, receiving significant contributions from degrees of freedom throughout the fuzzy space. For the fuzzy sphere, the correction exhibits strong infrared sensitivity associated with the zero mode. We isolate and resolve this zero-mode IR divergence by projecting out the zero mode, thereby obtaining a physically meaningful quantity. In the commutative continuum limit, the interaction correction has the same degree of UV divergence as the free entropy but does not obey a pure area law. Furthermore, we analyze the Moyal plane limit, where the interaction correction exhibits a distinct IR divergence. We discuss the physical origin of these extensive bulk features and examine their possible connection to the celebrated UV/IR mixing phenomenon in noncommutative quantum field theories.

We studied the 2-Temperature induced phase separation (2-TIPS) in a system of soft repulsive sphe rocylinders (SRS), confined on the surface of a sphere. We used two different anchoring conditions for the SRS on the spherical surface- free and tangential. For the free anchoring, increasing either the packing fraction or the rod aspect ratio suppresses phase separation between the active and passive subsystems, and the system corresponds to a dense-dilute phase co-existence. These phenomena can be explained via the trapping effect and are emergent due to the confinement. For the tangential anchoring, the system phase separates from its initial isotropic state into a locally ordered dense region and a disordered dilute region. Our work provides useful insights into phase separation in binary mixtures under spherical confinement.

We construct a nonlocal game that self-tests a maximally entangled qubit strategy among pure full-Schmidt-rank projective strategies, but admits an inequivalent optimum using one nonprojective measurement. This resolves a conjecture of Baptista et al. on imposing full rank and projectivity simultaneously. The construction combines CHSH with an auxiliary game $G$ that forces deterministic answers under these assumptions and admits a trine POVM optimum without them. We classify the optimal correlations of $G$ as a line segment parametrized by the tracial states of $\mathbb{C}\oplus M_2(\mathbb{C})$. Projectivity on the state support removes the matrix summand, whereas projective dilations with nonzero nonabort probability have a nontracial local state whose zero left ideal is not two-sided. Finally, a family in local dimension six shows that the full-rank PVM self-test is not robust.

Blood-brain barrier (BBB) permeability is a critical determinant in the development of central nervous system therapeutics because it directly influences the ability of drug candidates to reach their target sites within the brain. In this study, an explainable machine learning framework was developed to predict BBB permeability using molecular descriptors generated from the MoleculeNet BBBP dataset with the RDKit cheminformatics toolkit. Fifteen physicochemical descriptors extracted from 2,039 compounds were used to train four supervised machine learning algorithms, including Logistic Regression, Support Vector Machine (SVM), Random Forest, and Extreme Gradient Boosting (XGBoost). Hyperparameter optimization was performed using GridSearchCV, while model interpretability was investigated using SHapley Additive exPlanations (SHAP). Among the evaluated models, the optimized XGBoost classifier achieved the best predictive performance, with an accuracy of 88.97%, a precision of 88.92%, a recall of 97.76%, an F1-score of 93.13%, and a ROC-AUC of 0.9282. Stratified five-fold cross-validation further demonstrated the robustness of the proposed model, yielding a mean ROC-AUC of 0.8982 +/- 0.0130. Feature importance and SHAP analyses consistently identified TPSA, HBD, and LogP as the most influential molecular descriptors governing BBB permeability prediction. Overall, the proposed framework provides an accurate, interpretable, and computationally efficient approach for BBB permeability prediction and may serve as a valuable tool for the early-stage screening of CNS drug candidates.

Non-Hermitian systems provide remarkable features actively studied in modern photonics. Non-Hermiticity is often related to the properties of open structures and devices, which involve lossy and gain channels. Here, we reveal that electromagnetic fields themselves can be designed in a non-Hermitian way, proposing an additional degree of freedom in non-Hermitian physics. Within classical electromagnetic wave theory, we show that the non-Hermitian behaviors may stem not only from the dispersive properties of the waves, but also from the peculiarities of the light spatial spectrum and local structure of the fields. For the nondiffracting light beams, we identify exceptional points detaching symmetric and asymmetric non-Hermitian phases related to the shape of the beam's intensity profile, the non-Hermiticity being well recognized only for non-paraxial beams. In the local structure of the electromagnetic fields and Poynting vector, we determine exceptional lines differentiating non-Hermitian phases stemming from the behavior of streamlines. We believe that the concept of non-Hermitian light beams will enrich our knowledge of the light-matter interaction.

The three-dimensional electron gas is a fundamental model in condensed matter physics and quantum chemistry, and the exchange-correlation energy derived from it serves as the starting point of ab initio computations of materials. However, the wave-vector-dependent response, and hence the static local field factor $G(q)$, has remained without accurate ground-state benchmark in the strongly coupled regime for three decades. Using diffusion Monte Carlo, we calculate the static density-density response function and $G(q)$ across the liquid phase and find a pronounced structure in $G(q)$ at intermediate wave vectors, already visible at metallic densities and growing with increasing interaction strength. We identify it as a fingerprint of short-range order by showing that it is required to reproduce the static structure factor. Our parametrization, valid in the entire liquid phase, predicts a low-energy resonant mode inside the particle-hole continuum.

High-fidelity Eulerian–Lagrangian simulations of solid particle erosion in curved pipes require hours of compute per operating point, preventing rapid parameter sweeps and real-time wear assessment. Existing reduced-order models (ROMs) speed up these evaluations, yet they are typically trained on a single, fixed empirical erosion formula (e.g., Oka or Finnie). Changing the material law or target hardness then requires a complete retrain of the surrogate. Here, we present a non-intrusive reduced-order framework that avoids this model-locking by approximating the underlying particle collision kinematics instead of scalar wear rates. Specifically, we project and compress 23 Eulerian boundary cross-moments ($\mathbb{E}[V_p^u \sin^v\alpha_p \cos^w\alpha_p]$) across the pipe surface. Using 372 high-fidelity CFD-DPM cases of $90^\circ$ elbows over three bend ratios ($R/D \in \{1.5, 2.0, 5.0\}$), five Reynolds numbers, five density ratios, and six particle diameters in the inertial regime ($St > 1$), we evaluate a hybrid compression scheme. Linear Proper Orthogonal Decomposition (POD) and Mode-1 tensor unfolding SVD are combined with block-wise Convolutional Autoencoders (CNN-AE) to handle both broad convective transport and localized impact craters. An anisotropic Gaussian Process Regression (GPR) surrogate maps four dimensionless $\Pi$-groups to the compressed latent space, evaluating full 2D wear topographies in roughly $2\,\mathrm{ms}$ ($R^2 > 0.99$ on primary kinematic fields). Because kinematics are decoupled from material damage laws, the resulting surrogate evaluates multiple empirical models post-hoc exactly matching Finnie and closely approximating Oka, McLaury, and Arabnejad without retraining.

Symmetry plays a central role throughout physics, from Fourier analysis on discrete lattices to the classification of elementary particles in the standard model. In finite quantum systems, symmetries are often discrete, such as reflection and rotational symmetries. Here, we present the SIM-GRAPH method (Symmetric Ising Models - Graph Reduction And Projected Hamiltonians), which uses such symmetries to efficiently calculate ground-state observables of interacting quantum systems. By projecting all interactions onto a symmetric subset of the system, the method effectively reduces the number of sites, thus providing an exponential speedup over standard exact diagonalization. Furthermore, we introduce two extensions that broaden the applicability of the method and allow for a controlled trade-off between computational cost and accuracy.

Magic-state cultivation suppresses errors by measuring logical Clifford checks and discarding inconsistent outcomes. For an entangled resource, several measurement branches are usable, so their outcomes form a multibit classical record whose corruption can produce a logical-frame error. We show that this measurement record can be protected as a binary linear code. For any third-level Clifford-hierarchy unitary $U\in\mathcal C_3$, every parity of the branch bits can be measured by a commuting Hermitian Clifford check $C(v)=UX(v)U^\dagger$. Choosing which parities to measure therefore defines a binary code $y(a)=aG$. If the valid records have minimum distance $d$, at least $d$ readout-bit flips are required to confuse one valid branch with another, giving $P_{\rm wv}=O(q^d)$. A Plotkin bound limits the length of any binary branch record, and the Clifford schedules attain this limit: at distance four, six logical measurements suffice for $|CS\rangle$ and seven for $|CCZ\rangle$, compared with eight and twelve under independent repetition. Thus restricting the logical schedule to Clifford parities requires no additional measurements. In a native-CZZ-assisted Steane implementation, the $[6,2,4]$ CS schedule is also the unique minimum-cost distance-four solution within the compiled Clifford-check family, reducing the cultivation core by $26.6\%$ in active locations. State-vector simulations without a final ideal code-space projection further show higher acceptance and approximately half the residual error weight on the two Steane blocks. Coding the logical measurement record therefore reduces both measurement redundancy and compiled fault-tolerant overhead.

Magic-state cultivation has largely targeted single-qubit non-Clifford resources. We show that the entangled state $|CS\rangle=CS|++\rangle$ can be cultivated directly rather than synthesized from three $T$-type resources. Two commuting Hermitian Clifford involutions project onto four Pauli-frame branches, so no ideal branch is discarded, while a minimal six-bit $[6,2,4]$ record protects their history. The small-code state cannot itself be certified: late two-fault patterns evade its record, placing the certified boundary after surface-code growth. Under a fixed decoder that sees 136 operational detector bits per patch and withholds 168, exact audits find no accepted closed-boundary logical failure through fault order two, while order-three mechanisms exist. Escaping from the small code directly into a distance-3 patch and growing it to distance 13 in a single round keeps this certificate. Compared with a re-decoded three-$T$ comparator matched to the same binary logical-error target, the direct route uses $2\%$ fewer active locations at $p=5\times10^{-4}$ and $16$–$28\%$ more at $8\times10^{-4}$–$10^{-3}$, without charging the comparator for $T$-state storage. Counted in qubit-ticks under one rule for both routes, it uses $21$–$39\%$ less spacetime. Adding idle-memory noise to both routes under one rule and one optimized schedule raises the direct route's cost more, to $8\%$ and $46\%$ above the comparator at $5\times10^{-4}$ and $10^{-3}$, because that cost is limited by acceptance. The result is architectural: an entangled non-Clifford state can itself be cultivated with a certified output interface.

We establish a minimal nonrelativistic realization of scalarization in a self-gravitating bosonic condensate coupled to a scalar response field. A local effective-mass shift and nonlinear saturation generate a multibranch structure with two distinct transition routes. In the linearly stable regime, a finite perturbation drives a first-order transition with type-I logarithmic scaling near threshold. Beyond the linear onset, small perturbations grow tachyonically, and the response time controls both the growth and the subsequent breathing dynamics. These results identify a common mechanism for scalarization across relativistic compact objects and nonrelativistic condensates, and point toward laboratory analogues in coherent media.

Nonadiabatic dynamics through a conical intersection requires both static and dynamic correlation and, at every geometry, an excited-state gradient and interstate nonadiabatic coupling (NACME). Analytic multireference derivatives at this level have been confined to datacenter-scale hardware. We report device-resident \mbox{DMRG-QD-NEVPT2} with analytic gradients and NACMEs within the $8$\,GB of a consumer GPU: a density-matrix-renormalization-group (DMRG) active-space reference supplies the static correlation, and quasi-degenerate SC-NEVPT2 dresses it through a multi-state effective Hamiltonian that remains valid through a conical intersection, where single-state perturbation theory develops a vanishing denominator and fails. Every gradient and NACME is one reverse-mode transpose of a single contraction graph: the DMRG sweep enters as a gauge-free differentiable node, and all two-electron work is AO-direct through Cholesky factors. The DMRG reference is exact within the active space ($\sim\!10^{-15}$\,Ha). The corrected adiabats close smoothly to a real $S_0/S_1$ conical intersection with a non-vanishing, $1/\Delta E$-divergent NACME—where linear-response TDDFT returns zero identically—and the dressing restores the differential dynamic correlation that ionic $\pi\pi^*$ states require. DMRG-NEVPT2 and quasi-degenerate NEVPT2 are each established; what is new is the combined stack—multi-state and through a conical intersection, with analytic gradients and couplings—realized device-resident on commodity hardware.

The Mpemba effect is an anomalous phenomenon in which the time to thermalize does not depend monotonically on the distance from equilibrium, allowing systems with an initially larger temperature difference to thermalize before those with a smaller one. The rarity of the effect makes it hard to find parameters that produce it, complicating the design of experiments and the development of applications. Here, we find necessary and sufficient conditions for the Markovian Mpemba effect in three-level systems and explain its underlying physical mechanisms. Based on our understanding of the three-level case, we develop an efficient algorithm to determine the parameters for the effect in $N$-level systems. This protocol could open the door for the realization of Mpemba experiments and related applications in large systems.

High Performance Computing-Quantum Computing (HPCQC) platforms expose multiple Quantum Processing Units (QPUs) that may differ in size, topology, native gates, and noise characteristics. For current noisy devices, errors compound along the compiled circuits quickly, and minimizing them, that is, maximizing the circuits' execution fidelity, is essential for reliable results. Fidelity depends on the compilation to a specific target device: the same high-level circuit may produce different executables and, therefore, different expected fidelities across QPUs. We present a low-overhead fidelity-aware scheduling framework for multi-QPU systems based on a Graph Neural Network (GNN) that estimates, before compilation, the expected fidelity of each circuit on each available QPU. Then, a tunable scheduler uses these estimates to control the trade-off between execution fidelity and parallelism. Results show that this framework allows for approximating an exhaustive fidelity-based assignment, saving computational resources compared to a brute-force approach that compiles each circuit on every device.

Stochastic switching between gene expression states, coupled with production and degradation dynamics, governs the accumulation of mRNA and proteins in cells. The concentrations of these accumulated entities dictate the phenotypic distribution of genetically identical cells. The underlying accumulation dynamics are well-captured by a two-state promoter switching model, with statistical and thermodynamic properties quantified via the Fano factor and entropy production rates. However, how these measures correlate with concentration distributions and their shifts under varying kinetic parameters remains largely unexplored. To this end, we use chemical master equations to study a generalized model of mRNA accumulation dynamics in the presence of stochastic switching between two activity states and state-dependent production and degradation rates. We derive exact expressions for the steady-state probability distribution and analytically compute the mean concentration, Fano factor, and entropy production rate (EPR). Simplifying these expressions, we identify contributions arising from stochastic switching rates and relaxation dynamics toward equilibrium in each activity state. Next, using our theoretical results, we characterize the variation in the Fano factor and EPR as a function of mean expression during modality changes of the distributions mediated by the variation of switching rates. We also identify the conditions in kinetic parameters that achieve the highest Fano factor and entropy production rates. Our findings establish a generalized framework for examining stochastic accumulation dynamics, clarifying how kinetic parameters dictate molecular distributions, noise, and dissipation. These insights extend readily to broader contexts coupling stochastic switching with accumulation, including protein burst dynamics, phenotype-switching-mediated drug intake, and queuing theory.

Modern quantum algorithms are increasingly formulated as coherent procedures for implementing polynomial transformations of operators and singular values. This perspective provides a powerful and unifying language for quantum algorithm design, connecting a wide range of distinct problems through five closely related key tools: block-encoding, qubitization, QSP, QSVT and GQSP. Block-encoding embeds non-unitary matrices into larger unitaries; qubitization converts block-encodings into structured operators; QSP, QSVT and GQSP enable polynomial transformations with near-optimal query complexity. Together, these techniques form a general toolkit for transforming matrix functions into implementable quantum circuits. This paper develops these techniques from first principles as a unified framework for constructing quantum algorithms. We apply this framework to representative applications to highlight design principles and demonstrate how distinct algorithms can be constructed from a unified sequence of operator transformations. A central contribution is a systematic decision workflow for selecting the appropriate approach according to the operator structure and the desired transformation polynomial. This perspective clarifies when direct GQSP or through qubitization, or Laurent expansion, or QSVT is most appropriate. We organize algorithmic design into an end-to-end pipeline: identifying the target matrix function, constructing an appropriate block-encoding, determining the relevant spectral domain, designing a polynomial or Laurent-polynomial approximation, synthesizing the phase factors, and translating the transformation into an executable quantum circuit. By applying this unified framework to example applications, we showcase a practical methodology for reasoning, designing, and implementing quantum algorithms based on polynomial transformations.

In this work, we model the long-term impact of recurrent stellar flares on the atmospheres of metal-rich gaseous exoplanets. Using synthetic flare spectra from a fiducial flare model integrated with a photochemical kinetics code, we track the changes in atmospheric composition with time. We further analyze the spectral variability by feeding these abundance profiles into a radiative transfer code at various time steps. Our simulations showed variability and persistent changes in key atmospheric species, such as CH4, CO2, and SO2, when compared to their quiescent state. Extreme flare events cause rapid depletion of molecules in the upper atmosphere and a temporary disappearance of spectral features, especially the SO2 feature at 7-8 microns, which shifted by about 75 ppm. Many species did not fully return to their quiescent state after flares, resulting in lasting changes in abundance, especially for SO2 and CO2, key species when inferring the atmospheric metallicty. We also explored the cumulative effects of recurrent flares, showing that species like H2O and CH4 followed a decreasing abundance trend, with half-lives of around 28 to 31 years. These results indicate that flare activity plays a significant role in shaping both the short- and long-term atmospheric composition and spectral features of giant gaseous exoplanets orbiting M-dwarf stars, underscoring the need to account for stellar activity when characterising such atmospheres. Our findings also highlight that the atmosphere of the modelled planet is not static, suggesting that a probabilistic approach to atmospheric abundances may be more appropriate than static retrievals, particularly for gaseous planets orbiting active stars.

A co-located integration quantum electrical standard is essential to reduce reliance on distributed traceability in high-accuracy metrology, especially for portable and on-site use. Metrologically, realizing any two of voltage, resistance, and current is sufficient, as the third follows from Ohm's law. The combination of Josephson voltage and quantum Hall resistance offers better uncertainty, but conflicts with the tesla-level field for quantum Hall and near-zero field for Josephson operation. Here we report a compact unified platform enabling co-realization of quantum voltage and resistance in a single cryostat near 4 K, with quantum current derived via Ohm's law. A hierarchical magnetic shielding with staged attenuation and spatial confinement allows 6 T and below 50 nT to coexist within 270 mm axial separation with negligible cross-coupling. In integrated operation, the Josephson and quantum Hall subsystems agree with expected quantized values within relative standard uncertainties of 2.6E-9 and 1.4E-8, respectively. Linking them via an improved cryogenic current comparator realizes a 50 {\mu}A quantum current with relative uncertainty of 6.6E-8. These results demonstrate that three basic electrical units can be synchronously realized with superior metrological consistency on a single integrated platform, offering a viable transition from distributed calibration chains toward compact-integrated quantum-based realization.

Pentafluorophenyl triflate has been explored as a highly absorbing neutral photoacid generator (PAG) candidate for next generation chemically amplified resists used in extreme ultraviolet (EUV) lithography. Although increased fluorination enhances EUV absorption, this study demonstrates that such an approach does not necessarily improve photoacid generation efficiency. Using photoelectron-photoion coincidence (PEPICO) spectroscopy at the 92 eV photon energy of the EUV scanners in combination with quantum chemical calculations, the dissociative photoionization of pentafluorophenyl triflate was systematically investigated. The photoionization mass spectrum reveals extensive fragmentation, with the parent ion contributing only 3.1 % of the total signal and CF$_3^+$ representing the dominant product ion. Computed appearance energies align well with experimental trends and support a sequential fragmentation pathway involving loss of SO$_2$, CF$_3$, and CO. Crucially, none of the major dissociation channels yield precursors capable of forming triflic acid, the strong photoacid required for efficient deprotection reactions in chemically amplified resists. Combined with previous dissociative electron attachment studies indicating similarly unfavorable fragmentation, the results demonstrate that despite its high EUV absorption cross section, pentafluorophenyl triflate is unsuitable as a PAG for EUV lithography. The findings highlight the importance of understanding fundamental photoionization and electron interaction mechanisms to guide the rational design of next generation high performance EUV photoresists.

Mixed halide perovskites are highly versatile semiconductors with applications in photovoltaics, light-emitting diodes, and photodetectors. Understanding their thermodynamic phase behavior is central to guiding compositional design and improving device stability. Here, we train machine-learned interatomic potentials (MLIPs) on density functional theory reference data for CsxRb1-xPbBr3yI3-3y, CsxRb1-xPbBr3yCl3-3y, and CsxRb1-xPbCl3yI3-3y halide perovskites, enabling large-scale hybrid Monte Carlo-molecular dynamics simulations that sample both configurational and vibrational degrees of freedom. All three binary halide systems exhibit a miscibility gap, the extent of which correlates with halide ion size mismatch. The gaps in Br-Cl and Br-I close at low temperatures, while the Cl-I gap extends above room temperature. At temperatures above the miscibility gap (200 K to 500 K), all systems show a tendency toward layered halide ordering, with halide species preferentially occupying apical or equatorial octahedral sites. In CsPbBr3yI3-3y, this ordering occurs in a device-relevant temperature regime and is linked to the structural phase transitions, shifting transition temperatures by up to 100 K relative to randomly mixed structures. We attribute the strongly non-linear composition dependence of the orthorhombic-tetragonal phase boundary observed experimentally (a linear decrease followed by a plateau) to halide ordering. Introducing Rb on the A-site weakens halide ordering and eliminates the non-linear behavior, while narrowing the miscibility gap in both the Br-I and Br-Cl systems. These results establish halide ordering as a key determinant of structural phase stability in mixed-halide perovskites.

The millihertz gravitational-wave sky will be dominated by $\sim10^{8}$ double white dwarfs while $\sim10^{4}$ be resolvable in the Milky Way, whose three-dimensional spatial distribution traces the Galaxy's structural parameters. We present Galena, a hierarchical Bayesian pipeline that recovers these parameters from a double white dwarf catalogue through an inhomogeneous Poisson-process likelihood. Each source's $3\times3$ Galactic position covariance is computed from the waveform Fisher information matrix and propagated analytically through a $3\times5$ Jacobian; the resulting measurement-error convolution is factored into a pre-computed sparse weight matrix, rendering the nested-sampling inference tractable. Applied to GBSIEVER-reported LISA Data Challenge sources ($N=2151$ after quality cuts), Galena recovers the disk scale length $R_d=2175^{+51}_{-52}$~pc and scale height $z_d=282^{+7}_{-7}$~pc, consistent with a canonical thin disk, together with the bulge fraction $A=0.187^{+0.011}_{-0.012}$ and bulge scale radius $R_b=773^{+26}_{-25}$~pc; the bulge fraction, now recovered much closer to the literature value of $0.25$ than in our earlier exact-position fit, is measured at $\sim6\%$ statistical precision. An independent particle-swarm optimisation of the same likelihood reproduces these values to within a fraction of a percent, supporting the attribution of the improvement to the Fisher-matrix error propagation rather than to the sampler. The search-stage astrophysical prior improves per-source distance estimates but leaves the hierarchical inference essentially unchanged.

We consider 4-dimensional asymptotically flat vacuum spacetimes near future null infinity endowed with the most general allowable Carroll geometry. We show that the near-boundary radial expansion (to a certain order) can be organised in terms of connections that can be obtained by gauging the conformal Carroll algebra. The only non-vanishing curvatures in this gauging procedure are those that are associated with the special conformal generators and we will refer to these as the $K$-curvatures. The vanishing of these $K$-curvatures defines an asymptotic vacuum spacetime and we use this to construct a boundary (i.e. Carroll) covariant expression for the vacuum (soft) shear in terms of two boundary Carroll scalar fields. The $K$-curvatures transform in a hierarchical fashion into one another under Carroll boosts. This leads to a classification of 4 types of spacetimes: vacuum, strongly and weakly non-radiative, and radiative spacetimes. It is shown that the $K$-curvatures correspond to 5 of the 10 Weyl tensor components at leading order in their $1/r$ expansion. We furthermore observe that one of the $K$-curvatures is equal to the recently found Carroll boost anomaly. Finally, we show that the Bondi loss equations for the boundary energy-momentum-news complex can be cast into a form involving another energy-momentum tensor with vanishing energy flux that is traceless and whose non-conservation is entirely captured by the $K$-curvatures. The BMS currents can be obtained by contracting this latter energy-momentum tensor with a Carroll conformal Killing vector.

Despite being one of the most fundamental properties governing wave propagation, the wave-speed distribution is rarely known accurately in reflection imaging. Its estimation relies on analyzing wave distortions undergone by the incident and reflected waves; however, their contribution is difficult to disentangle from the medium reflectivity, particularly in complex media dominated by speckle. Mismatches between assumed and actual wave speeds result in aberrations that degrade the quality of reflectivity images. Yet these aberrations carry information about the underlying wave-speed heterogeneities. Here, we show that an angular distortion matrix, built upon matrix imaging, can unscramble this information to map the wave speed and correct aberrations across the entire field of view. At each point, this matrix isolates the distortions accumulated by the incident and reflected waves along well-defined propagation directions. It reveals strong angular correlations that can be exploited through time-reversal analysis to estimate local phase aberrations, providing observables for wave-speed tomography. The resulting map improves the propagation model used for matrix imaging, after which the process is iterated to refine the wave speed until residual aberrations become negligible. Using ultrasound as proof of concept, we validate the approach in a tissue-mimicking phantom and illustrate its clinical potential in vivo for breast and liver imaging. Sound-speed maps show contrast consistent with a malignant breast lesion and expected values in a healthy liver, while aberration correction sharpens reflectivity images routinely interpreted by clinicians. Beyond ultrasound, the approach extends naturally to any wave modality in which reflection-matrix imaging can be implemented.

The cosmic web, consisting of an intricate network of voids, walls, filaments, and nodes, encodes key information about structure formation and the cosmological parameters that govern it. In the era of high-precision cosmology, large ensembles of numerical simulations are required to analyse next-generation galaxy surveys, motivating the use of generative models to circumvent their high computational cost. While they have shown promise in emulating high-fidelity cosmic web simulations, their ability to capture distinct cosmic web environments remains largely unexplored. For this study, we trained a diffusion model on the Quijote N-body simulation suite to investigate the semantic information learnt by its self-attention maps. Using statistical estimators such as the Dice coefficient and cross-power spectra, we quantified the correspondence between attention maps and cosmic web environments defined by the T-Web classifier. We find that attention maps of varying spatial resolutions across different layers capture overdense and underdense structures in distinct ways, exhibiting strong positive correlations and anti-correlations with both the overall matter distribution and individual cosmic web environments. Moreover, the diffusion model predominantly encodes cosmological information at intermediate-to-large spatial scales, indicating that attention maps primarily capture globally coherent structures. Our results show that, beyond accurately reproducing two-point statistics, diffusion models learn a multi-scale representation of the cosmic web through self-attention, including non-Gaussian information.

Let $q$ be an odd prime power. We use complements of unions of subsets of $\mathbb F_{q^2}$ as locator sets and establish a sufficient condition under which a generalized Reed–Solomon (GRS) code is Hermitian self-orthogonal. Using cosets of multiplicative subgroups and sets with prescribed trace or norm values, we construct five families of Hermitian self-orthogonal GRS codes over $\mathbb F_{q^2}$. The Hermitian construction then yields five corresponding families of $q$-ary quantum maximum-distance-separable (MDS) codes. Under suitable parameter conditions, these quantum codes have minimum distances greater than $q/2+1$. By comparing codes of the same length, we give conditions under which our codes have strictly larger minimum distances than those obtainable from several previously known constructions based on trace maps, linear transformations, and cosets of multiplicative subgroups, either directly or via the propagation rule. We further show that such improvements occur for infinitely many values of $q$.

Exciton-polariton condensates combine ultrafast dynamics with strong optical nonlinearities, making them promising for optical neuromorphic computing. Here, we numerically demonstrate image recognition using the transient response of an exciton-polariton condensate. Downscaled MNIST images are encoded as optical pulse sequences, and the resulting condensate dynamics are sampled and processed by a linear classifier. For ten-class classification, condensate features achieve 92.2% accuracy, compared with 91.4% for raw-pixel linear classification. Combining both feature sets increases the accuracy to 93.2%. For the challenging binary classification of digits 7 and 9, the combined model reaches 97.3%, exceeding both the linear (95.5%) and feed-forward neural-network (96.6%) baselines. These results demonstrate that polariton dynamics can extract useful nonlinear features for ultrafast optical information processing.

Self-assembly of hard particles with diverse shapes gives rise to a rich variety of structures through excluded-volume constraints alone. Here we show that even a minimal system of three hard squares confined in a two-dimensional periodic box exhibits nontrivial configurational behavior relevant to structure selection. As the packing fraction increases, radial distribution functions obtained from Markov-chain Monte Carlo and uniform non-overlapping insertion sampling agree at low densities, deviate markedly over an intermediate range, and converge again at higher densities. Pressure measurements provide strong numerical evidence that the discrepancy originates from the separation of the allowed configurational space into two disconnected regions above a characteristic density. We identify the separation density as $\phi_{\rm sep}=3/5$, construct explicit overlap-free transition pathways connecting the two regions immediately below it, and quantify their relative configurational-space volumes. At higher packing fractions, an approximately L-shaped arrangement of the particle centers becomes strongly favored over a staggered one, revealing a structural motif characteristic of tetratic and square-lattice ordering in larger hard-square systems. These results show that excluded-volume geometry can govern both configurational connectivity and local structure selection even in a three-particle system, revealing how signatures of many-particle self-assembly can already emerge in the few-particle limit.

The results of detailed long-slit spectroscopy of the bipolar planetary nebula \ESO\ are presented. The observations were obtained with the facility spectrograph RSS of the SALT telescope. The total measured extent of the nebula reaches $\approx$55$^{\prime\prime}$, and the kinematics along the slit directly confirms its bipolar structure. The inclination of the nebula to the line of sight is estimated as $i\approx 45^{\circ}$, and the kinematic ages of two morphological structures are measured: the expanding ring and the polar outflow in the direction perpendicular to the ring. The age of the former is $\approx$1.5$\times$10$^4$~yr and that of the latter is $\approx$(3–4)$\times$10$^4$~yr, i.e. the polar outflow is 2–3 times older than the central ring. The ratio of these ages does not depend on the adopted distance. The weighted mean heliocentric velocity of \ESO\ is V$_{\rm hel}$=74.7$\pm$1.6~\kms. Chemical abundances are obtained for 19 regions along the major axis of the nebula, over an extent of 40$^{\prime\prime}$, i.e. for different morphological parts of \ESO. The abundances were derived with the T$_{\rm e}$–method, where the electron temperature was calculated directly using the measured faint auroral lines [\ion{O}{iii}]~$\lambda$4363~Å\ and [\ion{N}{ii}]~$\lambda$5755~Å. The abundances of O, N, Ne, S, Ar, Cl and He were determined. Despite a significant stratification, the measured abundances along the slit can be considered nearly constant.

Can propagating gravitational waves serve as operational probes of the quantum nature of gravity? We address this question by developing a unified theoretical framework that combines spacetime geometry, quantum information, and gravitational-wave physics. Starting from the geodesic deviation equation in linearized General Relativity, we derive the effective detector Hamiltonian directly from spacetime geometry and construct the complete quantum dynamics for detector subsystems interacting with both classical and quantized propagating gravitational-wave fields. This unified formulation enables a direct comparison between classical and quantum descriptions of gravitational radiation within the same physical framework. We demonstrate that classical gravitational-wave backgrounds can induce mixedness in the detector state but cannot generate genuine quantum correlations between the detector subsystems. In contrast, quantized gravitational waves coherently mediate gravity-induced entanglement, quantum coherence, quantum memory, and nonclassical correlations, providing clear operational signatures of the quantum nature of propagating gravitational radiation. We further discuss how mesoscopic quantum mechanical oscillators offer a promising route towards experimentally probing these effects. Our results establish a geometric and quantum-information-based framework for exploring quantum gravity through propagating gravitational waves.