Papers

We investigate linear matter-density perturbations in full quadratic gravity. Working in the longitudinal gauge and adopting the sub-horizon and quasi-static approximations, we obtain an algebraic expression for the effective gravitational coupling in the theory and the equation for evolution of matter density perturbations. We identify the positive-real poles of this coupling and map their dependence on the quadratic couplings. In the formal infrared continuation, the reduced coupling recovers its general-relativistic value, whereas at large physical wavenumber it is suppressed when both quadratic couplings are nonzero; the single-coupling limits reproduce distinct behaviors. Numerical integrations of the growing mode are performed up to the first pole and show that pole-free regions of the reduced system can support regular matter-growth solutions, while poles obstruct a continuous late-time evolution. Our results show that quadratic gravity cannot generally reproduce the standard cosmological evolution of perturbations and in the regions where it can, it closely matches the behavior of $f(R)$ theories.

Wetting transitions on textured substrates play a central role in the design of functional surfaces, but resolving their transition mechanisms requires efficient exploration of complex energy landscapes. In particular, saddle points are essential for revealing the connectivity among metastable states and transition pathways. In this work, we develop a diffuse-domain accelerated saddle dynamics (DD-ASD) framework for mass-constrained wetting transitions on complex textured substrates. The diffuse-domain formulation embeds complex solid geometries into a Cartesian grid, avoiding body-fitted mesh construction in repeated saddle-point searches. An orthogonal projection is applied consistently to the phase-field state and unstable-direction dynamics, preserving the prescribed droplet mass at the discrete level. Momentum acceleration is incorporated into the saddle dynamics to improve the efficiency of high-index saddle searches. Under the stated local spectral and exact-eigenspace assumptions, we establish a local convergence rate of $1-\mathcal{O}(1/\sqrt{\kappa})$ on the effective mass-conserving subspace. Numerical experiments demonstrate the effectiveness of the proposed method in resolving wetting solution landscapes, transition pathways, and energy barriers on textured substrates. We further extend the framework to fully three-dimensional wetting-landscape computations.

Based on a two-parameter perturbative framework, we derive perturbative formulae for the radii of massive particle spheres and massive shadow radii, where an extremal black hole is employed as the perturbative background. Adopting extremal black holes as the perturbative background enables energy-dependent scans to probe stronger gravitational regimes. Using these formulae, we perform perturbative analyses of the massive shadows for several non-standard black holes, and obtain the expansion expressions near the photon sphere of the extremal black hole. It is found that, although the dependence on the energy parameter $\epsilon$ is the same across models, the coefficients associated with the deviation parameter $\delta$ differ significantly, which can serve to distinguish among different black hole models. Furthermore, we construct a two-point Padé approximant in the form of a continued fraction which achieves a globally accurate approximation for the massive shadow radius of the black hole over the entire parameter range. Numerical tests show that the relative errors based on this approximant are small enough to provide a reliable foundation for model-independent reconstruction of metric parameters.

In nuclear many-body physics, energy density functional (EDF) theory is one of the most powerful approaches for describing finite nuclei and nuclear matter. However, its predictive capability depends on calibrating model parameters to experimental and observational data. In this work, we investigate an alternative approach: Constraining the parameters with the continuous density profiles of finite nuclei obtained from ab initio calculations. We apply Bayesian analysis to infer the parameters of Skyrme EDF from the density profiles and binding energies of 16O, 40Ca, and 48Ca. We show that the data effectively constrain the parameters associated with the properties of uniform nuclear matter, whereas those governing non-uniform nuclear matter remain partially constrained and require additional input. Furthermore, using the inferred parameter distributions, we successfully predict the density profiles and binding energy of 208Pb, which is excluded from the training data. This demonstrates the predictive capability of the framework. In conclusion, these results establish Bayesian analysis of density profiles as a promising route for incorporating accurate ab initio results of light nuclei into EDF development and strengthening the connection between both approaches.

Networks of interfaces in materials and living systems evolve through motion and rearrangement of interfaces and junctions. Local equilibrium at a junction requires interfacial force balance. We show that in three dimensions the classical Herring condition for triple lines is necessary but insufficient: four triple lines meeting at a quadruple node may each satisfy Herring equilibrium, while the four conditions remain mutually incompatible. Such a frustrated node has no admissible local equilibrium geometry. In the semi-isotropic limit, the six interfacial energies must form the edge lengths of a non-degenerate tetrahedron, with constructibility determined by the Cayley-Menger determinant. This hidden compatibility constraint arises from three-dimensional geometry and applies broadly to foams, polycrystals, tissues and other interfacial networks.

Atmospheric observations are sparse, heterogeneous, and unevenly distributed, whereas many generative atmospheric models learn distributions over regularly gridded multivariate states. Once pretrained, diffusion models can supply atmospheric priors that can be combined with observation-derived likelihood factors in a Bayesian formulation. However, these observation sources differ substantially in geometry and sampling density, complicating the consistent use of their observations within a common inference framework. Here, we formulate this reconstruction problem as generative atmospheric super-resolution and introduce composable observation interfaces for conditioning a single pretrained 13-variable atmospheric diffusion model. The interfaces convert sparse radiosonde (R), clustered aircraft (A), and dense irregular surface-station (S) observations into source-specific likelihood factors that specify where observations constrain the gridded state, how residuals are counted under uneven sampling, and how strongly each source guides posterior sampling. We developed the aircraft and surface observation interfaces using 2019 observations and evaluated the selected interfaces throughout 2020 without further tuning. Compared with reconstructions conditioned only on radiosonde observations, the composed R+A+S interface reduces RMSE evaluated against ERA5 by $9.24\%$ across all 13 state variables over the CONUS domain. The aircraft and surface factors provide complementary improvements in upper-air and surface variables. The R+A+S combination also lowers the Continuous Ranked Probability Score (CRPS), while evaluations at held-out aircraft and surface-station observations show reduced prediction errors. Together, these results demonstrate a modular route for conditioning a pretrained atmospheric generative prior on heterogeneous in situ observations without retraining the underlying model.

We present a framework that maps harmonic vibrational systems onto effective multi-orbital tight-binding Hamiltonians, establishing a direct correspondence between phononic degrees of freedom and graph-based lattice models. Within this mapping, the Cartesian displacement components of each mass become internal orbitals, while elastic interactions generate effective onsite energies and hopping amplitudes determined by the geometry of the system. This representation enables the application of numerical and conceptual tools originally developed for electronic transport to the study of phononic systems. The method is first applied to a monoatomic chain containing an angular bend. For this benchmark system, analytical expressions for the polarization-resolved transmission and reflection probabilities are derived and compared against calculations performed using a recursive scattering-matrix method within the mapped tight-binding representation. Excellent agreement is obtained, validating the mapping and demonstrating its ability to describe geometry-induced mode conversion and the influence of evanescent states. We then investigate zigzag chains, where alternating bond orientations generate effective dimerized Hamiltonians reminiscent of the Su–Schrieffer–Heeger (SSH) model. Although the uniform zigzag chain develops a spectral gap, no localized edge states are observed. We show that modified boundary parameters generated by the phononic mapping suppress the edge-state formation expected from the ideal SSH picture. Introducing a geometric domain wall restores localized domain-wall states inside the gap, which give rise to resonant transmission channels across an otherwise insulating frequency window. The resonance energies remain robust against system-size variations and the corresponding transmission approaches unity.

Observations of collective signatures within jets of particles have been recently reported by measurements at the Large Hadron Collider at CERN laboratory, providing insights on the minimum conditions required for forming a Quark Gluon Plasma state. A quantitative comparison with data measurements on intrajet azimuthal anisotropies and predictions from PYTHIA event generator soft QCD model parameter tunes: Monash, CP5, and QCD-scheme CR is presented. Energetic jets with transverse momentum over 550 GeV from proton-proton collisions at 13 TeV are reconstructed. Results from predictions using the standard E-scheme (ES) and jet axis choice are compared with those from the Winner-Take-All (WTA) frame. Significant differences are present between predictions from WTA and ES frames at the lowest and highest intrajet charged particles multiplicities ($N_{\mathrm{ch}}$), with the QCD-scheme CR tune showing the smallest variation between frames. Predictions for $v_2$ at the highest $N_{\mathrm{ch}}$ are consistent with the data measurements at a 2.3$\sigma$ uncertainty level. These results set new guidance towards the search for intrajet collective effects and understanding of nonperturbative QCD dynamics originated from a single parton.

Natural load-bearing and transport networks are not assembled in a single step; they emerge through a temporally ordered process of growth, branching, reinforcement, and loop formation. Inspired by this developmental logic, this work introduces a morphogenetic graph-generation framework for mechanical lattices in which a discrete dot matrix provides potential nodes and the final architecture is created by sequential cross-layer and intra-layer growth. The same rule is visualized in two dimensions as a leaf-vein-like developmental sequence and implemented in three dimensions on a 3x3x3 nodal matrix containing 27 candidate nodes. A dataset of distinct three-dimensional lattices was evaluated by beam-based finite element analysis and represented directly as graphs. A graph convolutional neural network (GCNN) with three graph-convolution layers and dual global pooling learns the topology-property mapping and predicts effective compressive stiffness. Coupling the GCNN surrogate with rapid structural sampling enables inverse design: for a target stiffness of 1000 MPa, the selected design was predicted at 1042.43 MPa and validated by finite element analysis at 1027.49 MPa. Beyond straight members, the framework has also been extended to parameterized horseshoe-shaped curved beams made of nonlinear materials, enabling topology-geometry design toward prescribed deformation shapes. Our work provides a paradigm for augmenting the database of mechanical metamaterials, and the resulting perspective links biological morphogenesis, graph learning, and nonlinear shape programming in a unified generative design framework for architected materials.

We obtain a large number of exact hyperbolic, trigonometric, and periodic solutions in terms of Jacobi elliptic functions as well as algebraic solutions with a power law tail of the integrable local Fokas-Lennels equation and integrable nonlocal Fokas-Lennels equation. Further, we consider a one-parameter family of generalized Fokas-Lenells equations and obtain a few of their exact solutions.

Quantum error-correcting decoders provide both corrections and confidence estimates for the logical-error risk of individual measurement records. Such confidence can guide postselection, but it depends on the accuracy of the decoder noise model. When the physical device drifts away from that model, confidence measures such as the logical gap can become miscalibrated. We show that this mismatch can itself provide useful information. On IBM quantum hardware, syndrome statistics drift across consecutive acquisition windows, and the resulting detector histories differ substantially from those predicted by the stationary detector error model used for decoding. We observe a similar hardware-model mismatch in independent Google surface-code memory data. We exploit this effect by assigning additional rejection weight to detector histories that are unlikely under the assumed model. For minimum-weight perfect matching (MWPM), the minimum weight $W$ provides an inexpensive proxy for syndrome surprisal. On held-out IBM repetition-code memories, likelihood-aware postselection reduces the retained logical-error probability (LEP) by $10.6\%$ at $d=7$ and $28.8\%$ at $d=9$, both at $15\%$ rejection. On Google ten-round $d=5$ XZZX surface-code memory data, it reduces retained LEP by $75.4\%$ at $90\%$ rejection. Applied to Google's magic-state cultivation experiment with the Tesseract decoder, it reduces tomography infidelity by $34.7\%$ with $30\%$ additional grafting-stage rejection, or increases accepted yield by $30.4\%$ at a target fidelity of $97.0\%$. Burst-noise simulations show that the advantage persists as code distance and syndrome-extraction volume increase. The method reuses quantities already produced during logical-gap decoding and requires only an additional fitting step.

A multispecies, collisionless plasma is modeled by the relativistic Vlasov-Maxwell system. Assuming the plasma is globally neutral, we show that solutions can be constructed with arbitrarily fast, polynomial rates of decay, depending upon the cancellation properties of the limiting spatial averages, as well as the masses and charges of the particles. In doing so, we establish a countably infinite number of asymptotic profiles for the charge and current density, electric and magnetic fields, and their derivatives, each of which is necessarily realized by a sufficiently smooth solution. Our approach relies upon a refined field representation that features self-similar behavior away from the boundary of the light cone. In each case we establish a linear scattering result in $L^\infty$ for every particle distribution function, namely we show that they converge as $t \to \infty$ along the transported spatial characteristics at increasingly faster rates. In the case that charge cancellation does not occur, our methods can be further extended to demonstrate polyhomogeneous expansions with logarithmic corrections.

APOGEE delivers high-resolution, near-infrared spectroscopy and highly precise radial velocities (RVs), with extensive repeat observations spanning more than a decade. Long-term RV repeatability is nevertheless limited by instrumental zero-point systematics: exposure-to-exposure drift and fiber-dependent offsets that are only partially tracked by lamp-based wavelength calibration, and that can evolve as fibers are serviced or replaced. We infer and remove these zero points directly from the published per-visit RVs using an uber-calibration framework based on shared repeat observations. We solve sequentially for two sets of minimal calibration units: (plate, night) exposure-level offsets and time-dependent (fiber, observing year) offsets. We apply the method independently to APO and LCO DR17 and to APO DR19. After correction, the same-fiber repeatability within two days reaches a limiting precision of ~14 m/s, and the long-baseline single-visit precision improves by a factor of two from 98.2 to 44.7 m/s. We release per-visit, value-added RV catalogs for DR17 (APO+LCO) and DR19 (APO) containing 3,501,727 visits (3,336,141 fully corrected) of 930,519 unique stars, enabling more reliable RV variability, binary, and Galactic-dynamics studies.

Finite-domain normalized spatial measurements combine an incident field, geometric support, local response, and channel weighting. These operations can break an otherwise separable response, so accurate single-axis calibration alone does not establish separability of a multidimensional measurement. We represent normalized readouts as channel-weight expectations under a parameter-dependent effective measure. For fixed reception and channel operators, local sensitivity is the covariance between the channel weight and the source score. This representation distinguishes axis separability, parameter mixing, and local recoverability, and applies at the appropriate detector level to continuous-electrode position-sensitive detectors, Shack–Hartmann and pyramid wavefront sensors, back-focal-plane split detection, and finite pixel arrays. A quadrant photodetector (QPD) provides an analytically tractable case. Starting from the complete two-dimensional power integrals, we identify the spatial-moment origin of its lowest-order cross term. Axis calibration and system symmetry then constrain the inverse map, giving Axis-Anchored Cross-Residual Inversion (ACRI). Numerical tests of this QPD realization support the sensitivity relations and show that the constrained cross correction substantially reduces the off-axis bias retained by single-axis inversion. The results illustrate how the general measurement representation guides inverse construction, with performance bounded by the working domain, calibration state, and preserved symmetries.

We construct an exactly solvable extension of the spin-$1/2$ Kitaev honeycomb model in which conserved $\mathbb{Z}_2$ fluxes determine not only the signs but also the connectivity of nearest-neighbor Majorana hopping. At a tuned loop point, hopping survives only across opposite-flux plaquettes, so every vertex has active degree zero or two and the matter Hamiltonian fragments in each flux sector into independent Majorana rings and isolated zero modes. Exact ring spectra and bond counting then bound the matter energy over all local flux configurations and all four Wilson-loop sectors, and split it exactly into a frustrated triangular-lattice Ising term, whose extensively degenerate ground states are the fully packed loop coverings, and a non-negative Majorana residual. On admissible commensurate tori, the residual selects precisely the three translation-related $2/3$-vison crystals, which saturate the bound, and an exact fermion-parity identity shows that for antiferromagnetic coupling their vacua also survive projection, making them rigorous ground states of the spin model. Within a single crystal, a depth-one local unitary then maps the ground space onto that of a sheared square-lattice toric code, giving fourfold topological degeneracy. The model thus realizes exact nonperturbative gauge-matter feedback: the flux fixes where the Majorana fermions may move, and their zero-point energy selects in return a topologically ordered vison crystal with spontaneously broken translation symmetry.

Determining isotopic ratios on the surfaces of extraterrestrial objects can provide insight into their formation conditions and evolution. Recently, remote-sensing detections of the 4.14 {\mu}m HDO absorption band have enabled astronomers to estimate the D/H ratio on several icy objects in the outer solar system. Here, we quantify how ice phase and radiation processing affect the 4.14 {\mu}m absorption band. While the band is visible in H2O-ice samples with a crystalline component, we cannot detect it in amorphous H2O-ice. Furthermore, we find that radiation processing, using 10 keV electrons as a proxy, quickly makes this absorption feature undetectable at a rate consistent with the amorphization of an initially crystalline sample. Interestingly, we also find that recrystallizing the irradiated sample causes this band to reappear nearly to its original band depth. For the Saturnian satellite Mimas, we estimate that the HDO feature will decrease by a factor of two within ~1 x 10^4 yrs at typical depths probed by remote sensing spectroscopy. While we suspect that existing methods could still determine the D/H ratio from a surface composed entirely of crystalline H2O-ice, deriving it for surfaces with a significant amorphous fraction may lead to severe underestimation of the true D/H ratio. However, given the direct correlation between the amorphous fraction of the sample and the HDO band depth, we propose that one could still estimate the D/H ratio of a surface with mixed phases by determining the crystalline fraction of the surface H2O-ice using other absorption features.

The simulation of nonlinear ordinary differential equations on quantum computers is inherently challenging, as quantum gates are linear operators on qubit states. In this paper, we put forth a Koopman-von Neumann (KvN) operator based algorithm for solving nonlinear ordinary differential equations on a quantum computer which overcomes the innate limitations of quantum operations. In this approach, a Liouville probability density is embedded into a wavefunction, the evolution of which is governed by an operator dual to the Koopman operator. The trajectories corresponding to the nonlinear differential equations are reconstructed from the average value of Koopman observables evaluated through quantum measurements. We specifically evaluate the computational limitations of solving nonlinear equations within this Liouville embedding framework. An Ehrenfest-type estimate is derived that relates the reconstruction error to the covariance of the transported density, highlighting the competition between linear stretching and Hessian-induced folding.This leads to a key stability criterion, which depends on the local Ehrenfest-Reynolds number. We discuss the effects of measurement-induced errors including those due to Hadamard-test sampling, amplitude estimation, and bias due to covariance in probabilistic Grover-type inference on the evaluation of trajectories. The limiting bounds on the accuracy of quantum computations are numerically verified for the Lotka-Volterra system and for the quartic oscillator. We observe a rapid growth in computational errors when the Ehrenfest-Reynolds number approaches the predicted threshold. The bounds resulting from our analysis provide key guidelines for selecting the width of the initial Gaussian probability distribution associated with a system of nonlinear ordinary differential equations.

The dissipative transverse-field Ising (TFI) model provides a paradigmatic setting for nonequilibrium quantum many-body physics. We show that a class of boundary-driven TFI models subject to dissipation at only one boundary possesses hidden time-reversal symmetry, which enables an exact construction of their nonequilibrium steady states. The solution admits a matrix-product representation and defines a nonequilibrium partition function from which steady-state observables can be evaluated efficiently. We use the exact solution to characterize the microscopic structure of the steady state through its z-magnetization and two-point correlations. A striking feature is that the local field at the dissipative boundary governs the spatial organization of the steady state throughout the chain. The steady state typically exhibits boundary-localized magnetization profiles and exponentially decaying correlations, whose characteristic length scales are set by the dissipative boundary. In the weak-driving limit, suitably tuned boundary fields can reorganize the NESS into a delocalized single-interface structure, giving rise to long-range correlations that decay linearly with distance.

We construct an off-shell BRST-invariant gauge-fixed formulation of a nonlinear sigma model coupled to a non-Abelian gauge field. Starting from the dynamics of GBs and their consistent couplings to gauge and ghost fields, we construct the corresponding BRST-invariant quantum theory and provide a geometrical interpretation in terms of Killing vectors. A central point of our treatment is that the Lie-bracket closure of the target-space Killing vectors provides the geometric realization of the algebra entering the BRST differential. The physical state space is characterized by the cohomology of the nilpotent BRST charge, providing a consistent separation of physical and non-physical degrees of freedom. We explicitly derive the BRST charge and present the associated symmetry transformations. Finally, we analyze the structure of the physical Hilbert space and discuss the conditions under which BRST symmetry supports unitarity and constrains the quantum effective theory. Quantum statements are conditional on a BRST-preserving measure and regulator, and the four-dimensional model is treated as an effective field theory.

Crystal structure determination requires the phases of scattered waves – yet diffraction measures only their intensities. Direct methods exploit phase invariants but become less reliable as diffraction information diminishes. Learned phase prediction has lowered the resolution barrier, yet remains primarily confined to centrosymmetric crystals with binary phases. We introduce PhiGen, a generative reformulation of traditional direct methods that learns origin-independent phase relationships for binary and continuous phasing. Across 210 space groups, including groups absent from training, it recovered high-quality maps for 99.0% of centrosymmetric structures and invariant-consistent phases for 92.8% of non-centrosymmetric structures. From simulated 3 Å zeolite powder data, the network recovered framework maps for 84.2% of held-out structures, versus 1.0% for Superflip. For experimental ZSM-25 and TNU-9, generated phases seeded high-resolution phase extension. These results suggest a route to structure determination from low-resolution, incomplete, and overlapped diffraction data.

Recurrent invariant solutions provide a dynamical framework for interpreting turbulence, but their computation becomes increasingly difficult in spatially extended flows, where close whole-domain recurrences are rare. We study two-dimensional Kolmogorov flow in a [Lx,Ly] = [2pi,12pi] domain with Re = 10 using a distributed reduced-order model composed of a patch-based autoencoder and a neural ordinary differential equation. Near- recurrence candidates are refined by latent multiple shooting, decoded to physical space, screened under the full Navier-Stokes dynamics and supplied to a full-state Newton- Krylov solver. Fourteen candidates converge to relative periodic orbits (RPOs), with periods 3.65 < T <16.45. The catalogue contains both domain-filling states and RPOs with recurrent activity localised to a restricted cross-stream region. The weakly modulated surroundings generally remain finite-amplitude and distinct from the laminar solution. Selected localised RPOs persist under continuation in Reynolds number, and recurrent states can be reconverged after truncating substantial portions of their surroundings. In addition, the model trained at Ly = 12pi generates convergent RPO seeds at Ly = 6pi and 8pi without retraining. These results demonstrate that distributed learned dynamics can provide useful initial conditions for exact coherent states searches in extended domains and reveal recurrent solutions with strongly localised temporal dynamics.

Identifying the minimal set of nodes whose removal breaks a complex network apart, also referred as the network dismantling problem, is a highly non-trivial task with applications in multiple domains. Whereas network dismantling has been extensively studied over the past decade, research has primarily focused on the formulations of the optimization problem for single-layer networks, neglecting that many, if not all, real networks display multiple layers of interdependent interactions. In such networks, the optimization problem is fundamentally different as the effect of removing nodes propagates within and across layers in a way that can not be predicted using a single-layer perspective. Here, we propose a dismantling algorithm named MultiDismantler, which leverages multiplex network representation and deep reinforcement learning to optimally dismantle multi-layer interdependent networks. MultiDismantler is trained on small synthetic multiplex graphs; when applied to large, real and synthetic networks, it displays exceptional dismantling performance, clearly outperforming all existing methods that rely on a single-layer approach to network dismantling. We show that MultiDismantler is effective in guiding strategies for the containment of diseases in social networks characterized by multiple layers of social interactions. Also, we show that MultiDismantler is useful in the design of protocols aimed at delaying the onset of cascading failures in interdependent critical infrastructures.

Kagome FeSn exhibits an occupied flat band at its terminated surface, whereas bulk FeSn adopts A-type antiferromagnetic order and does not display the same feature. Here, we combine density functional theory with primitive- and doubled-cell analysis and a double-layer tight-binding model to determine how interlayer electronic coupling and magnetic stacking control flat-band formation in FeSn. We identify an occupied Fe-$d_{z^2}$-derived flat-band manifold in the ferromagnetic state that is consistent with the experimentally observed surface feature. Brillouin-zone folding reveals that its flat branch originates from the $k_z=\frac{\pi}{c}$ sector of the primitive cell, demonstrating that it cannot be understood as an isolated kagome-layer state. Instead, the state depends on coupling between neighboring kagome layers and can be seen as a result of antibonding coupling between nearest neighbor kagome layers. A double-layer tight-binding analysis identifies interlayer Fe-Fe hopping as the dominant microscopic coupling responsible for this behavior, while a contrasting unoccupied flat-band-related manifold is governed primarily by intralayer Fe-Sn hybridization. These results establish interlayer coupling and magnetic stacking as key control parameters for kagome flat bands and highlight how coupling between layers can generate and tune extended correlated-electron states in quantum materials.

Minimal strings offer two ways to study quantum surfaces: through a spectral curve or through a differential equation. We ask how much of the quantum equation can be recovered once the classical curve and its motion with the background are known. Our starting point is the resolvent of a scalar differential operator. We require its one-boundary integral to have poles only at branch points, with the resulting differential regular at infinity. These conditions give a finite reconstruction procedure at each genus. When the branch points are simple and their energy values move, we prove that the quantum corrections are unique whenever the procedure is consistent. A specified string equation provides a solution if its trace primitive satisfies the same analytic conditions. The scalar construction also leads to amplitudes with several boundaries. We introduce the method through pure gravity and Ising, then explore higher-order, dual and nonunitary models. Higher-Airy examples connect the calculation to $r$-spin theory on a degenerate locus that requires a separate treatment of the inverse problem.

What happens to information carried through an evaporating black-hole horizon? We introduce a solvable model of evaporation built from coupled Sachdev-Ye-Kitaev systems, in which an initially two-sided black hole is coupled at a finite time to a larger, colder bath. Evaporation is rapid in this model, so we refer to the process as “blast freezing” of a black hole. In an appropriate large-$N$ and large-$p$ limit, the two-point functions and certain four-point probes can be computed analytically. Using the two-point functions as input to a generalized HKLL reconstruction, we obtain the emergent bulk geometry of the evaporation process. We then track the information carried by an infalling particle using operator size and Renyi-2 mutual information, showing how it is preserved in nonlocal many-body degrees of freedom after the blast-freezing transition.

Detecting quadratic quasi-normal modes in black hole ringdowns would provide evidence for nonlinear gravitational dynamics, while measuring their properties would enable tests of the corresponding predictions of general relativity. Specifically, second-order black hole perturbation theory predicts that their amplitudes scale with the product of the amplitudes of their parent linear modes, with a coupling coefficient that depends on the spin of the remnant black hole. This mode-specific coupling coefficient has not yet been directly measured from gravitational wave data. Here, we use Bayesian inference on the GW250114 ringdown, modeled with the $220$, $221$, and $220\times220$ modes, to infer the amplitude-coupling coefficient of the $220\times220$ mode. The inferred coefficient is consistent with predictions from numerical relativity fits and second-order perturbation theory; no comparison shows a deviation exceeding $1.3 \sigma$. Although the current data cannot distinguish among these spin-dependent predictions, this measurement establishes a basis for more stringent observational tests of nonlinear gravitational dynamics in black-hole ringdowns.

Wide-field surveys now report thousands of transients per month, while spectra are obtained for only a few per cent of them. We present DETECT (DESI–Transient Event Cross-matching Tool), a pipeline that turns each Transient Name Server (TNS) alert into a distance-informed candidate within an hour by placing it in the context of the Dark Energy Spectroscopic Instrument (DESI) archive. DETECT cross-matches every new report against the 22 million spectra of DESI EDR and DR1 through a HEALPix index, associates the transient with a host galaxy by a directional-light-radius rule whose morphology-dependent thresholds are calibrated on 4,474 supernovae with known redshifts (92.5% completeness, 0.4% wrong hosts), and passes ambiguous cases to a reviewer through a web interface. With a validated host redshift it derives the peak absolute magnitude, the projected offset and basic host properties of each event, and ranks it for spectroscopic follow-up. Applied retrospectively to ~1.2x10^5 TNS reports from 2020–2024, DETECT recovers a spectroscopic host for 15% of them, from these we build a Gold Sample of ~5,400 well-sampled light curves whose luminosity distributions by class reproduce those of untargeted surveys. Because the absolute magnitude is known at discovery, intrinsically overluminous events stand out immediately: in the prospective 2025 run this is how the lensed superluminous supernova SN~2025wny was flagged within hours of its report, and how faint, fast-declining kilonova candidates were screened against model grids and archival photometry. DETECT shows how an archival spectroscopic survey can make host redshifts a routine part of transient triage ahead of the Rubin Observatory's LSST.

We test whether collisions involving Titan can eject enough water-rich material onto sufficiently distant Saturn-bound orbits to form Iapetus, while also accounting for Titan's orbital eccentricity. Three-dimensional impact calculations and post-impact trajectories examine initially Saturn-unbound and bound impactors. In the oblique unbound case with a differentiated impactor roughly a tenth the mass of Titan at a speed of 10 km s\(^{-1}\), outgoing predominantly icy material from a selected population totaling about 3.5 times Iapetus's mass remains Saturn-bound for days after impact. We track an icy sample whose orbital apoapsis extends beyond Iapetus's distance. After impact, Titan's eccentricity increases to near 0.13, while the impactor's rocky core escapes Saturn. In another case, a bound companion one quarter Titan's mass collides at \(45^\circ\) and about 3.7 km s\(^{-1}\), ejecting 0.60 Iapetus masses of ice. The rocky impactor core initially skips past Titan; an orbital continuation reaches return contact after 6.9 yr. This run also retains 0.48 Iapetus masses of ice. Titan's eccentricity evolves due to the initial impact and debris scattering. The merger results in a Titan with an eccentricity of about 0.10. These results establish the collisional production of an icy debris reservoir, with some material on orbits of large semimajor axis; raising Iapetus's periapse would require gas drag or dynamical friction.

Vibrational spectral prediction can become inaccurate when localized stereoelectronic environments perturb intermediate response states and high-risk response units dominate characteristic spectral fingerprints, making prediction across external chemical space difficult. SO(3) Equivariant Neural Kalman Networks (SENK) form a response-state cascade that combines an equivariant transformer backbone for Hessian, dipole-derivative and polarizability-derivative learning, an Equivariant Neural Kalman bridge for state-dependent refinement and reliability sensing, and an NBO-informed electronic-prior pathway coupling consistency regularization with bounded, branch-specific guided spectral calibration. SENK outperforms DetaNet on QM9S and QMe14S while preserving full-spectrum IR and Raman fidelity from small molecules to drug-like systems. SENK remains stable and selectively improves spectrally sensitive features in biomolecular systems with complex stereoelectronic effects. It therefore integrates tensor prediction, reliability diagnosis and physics-informed calibration, supporting transferable vibrational spectroscopy from molecular systems to functional molecular materials.

Bound states in the continuum (BICs) exhibit rich momentum-space dynamics, including merging, annihilation, and reconnection across symmetry directions and bands. Yet these phenomena have largely been explained case by case, without a unified framework to classify or predict them. Here we develop a global symmetry-equivariant theory for the dynamics of nondegenerate and degenerate BICs. We show that BIC dynamics can be classified into $\alpha$-, $\beta$-, and $\gamma$-processes according to root motion, which not only encompass the reported dynamics in $C_{2v}$, $C_{4v}$, and $C_{6v}$ systems but also include previously unrecognized ones. More importantly, we reveal that distinct dynamics are bridged by the criticality of BICs through a merging of merging, in which selected direction–band branches acquire higher-order radiation zeros. Such a theory predicts which branches become critical and how to tune system parameters to realize them. Following this framework, we construct high-order BICs in full-wave calculations, realizing $Q\sim k^{-10}$ nondegenerate criticality and $Q\sim k^{-8}$ single-branch and band-paired degenerate criticalities. Our framework provides a systematic route to understanding, discovering, and selectively controlling BIC dynamics and high-$Q$ states.