We present Visplot, a free, open-source, web-based tool for hardware-aware visibility analysis and heuristic scheduling of both sidereal and non-sidereal astronomical observations. Visplot computes visibility windows as finite unions of disjoint intervals by intersecting user-defined constraints. This framework natively incorporates celestial parameters (airmass, moon distance, twilight), mechanical telescope boundaries (altitude and hour-angle limits), and custom temporal restrictions defined in UTC or Local Sidereal Time, allowing for a high degree of scheduling flexibility. The scheduling engine combines deterministic pre-allocation for mandatory targets with a multi-objective heuristic optimization of the remaining target pool, balancing scientific priority, target urgency, altitude, and telescope slew overhead. Originally developed to address an operational need for flexible and lightweight scheduling support at the Nordic Optical Telescope (NOT) in La Palma, Visplot has been in continuous use since 2016. Its nearly decade-long operational history, together with routine use by astronomers at multiple observatories worldwide, demonstrates its practical value in real-world observational workflows. Its client-side, zero-installation architecture facilitates real-time schedule refinement, making it particularly suited for time-domain triggers (e.g., GRB/GW alerts) and geographically distributed remote observing. A user survey indicates that the tool significantly reduces the cognitive overhead of nightly planning while ensuring that generated schedules remain strictly within the mechanical and operational limits of the telescope hardware. Visplot provides a robust, lightweight alternative to monolithic scheduling suites, supporting the practical needs of modern PI-led observatories.

Non-Hermitian band descriptions capture how loss, gain, and environmental coupling reshape quantum matter, yet most experimental tests rely on wave-based or dynamical probes. Here we establish a new equilibrium route to exceptional physics in Dirac materials: in the weakly non-Hermitian regime, the thermodynamic density of states and the quantum capacitance exhibit a universal equilibrium approach to the exceptional point. In our minimal non-reciprocal graphene model, the hopping imbalance reduces the Dirac velocity as $v_F=v\sqrt{1-β^2}$, implying that the low-energy density of states, the thermodynamic density of states, and the quantum capacitance all scale as $(1-β^2)^{-1}$ as $|β|\to 1^-$. Consequently, at charge neutrality the quantum capacitance remains linear in temperature but with a diverging prefactor, while the inverse response softens linearly on approaching the exceptional point. In a magnetic field, this manifests as a collapse of the Landau-level spacing and a corresponding crowding of thermally active levels. Complementarily, the biorthogonal Bloch states exhibit a Petermann factor $K=(1-β^2)^{-1}$, which isolates the irreducibly non-Hermitian effect of eigenvector non-orthogonality. These results identify quantum capacitance as an experimentally accessible bulk equilibrium probe of effective non-Hermiticity in Dirac materials.

We construct upper bounds on entanglement entropies of many-body quantum states that have fixed energy expectation values with respect to geometrically local Hamiltonians. Our focus is on entanglement entropies of subsystems that make up approximately half of the full system. The upper bound on the von Neumann entanglement entropy is half the sum of the thermal entropies of two fictitious systems at the same temperature as one another, with an additional area-law contribution in some systems. The effective temperature is chosen such that the sum of the thermal energies of the two fictitious systems matches the constraint on the energy of the state in the original problem; at subextensive energies, this temperature decreases with increasing system size. Our upper bounds on Rényi entanglement entropies take an analogous form. As a first application we show that ground-state Schmidt ranks in frustration-free (FF) systems are upper bounded by the ground-state degeneracies of Hamiltonians acting on subsystems. Ground-state von Neumann and Rényi entanglement entropies therefore follow an area law when the zero-temperature thermal entropies of subsystems scale with surface areas, rather than with subsystem volumes. This result holds independently of the spectral gap. For physical models of quantum matter, which have well-defined specific heat capacities (and are not necessarily FF), our bounds provide a way to convert this thermodynamic data into constraints on pure-state entanglement at both subextensive and extensive energies. We also show that our upper bounds on half-system entanglement entropies are optimal, up to subleading corrections, in wide varieties of systems. Our results relate physical thermodynamic properties to the structure of many-body Hilbert space at low energies.

We present high-resolution (0.94" $\approx$ 55 pc) ALMA CO(2-1) and 13CO(2-1) observations of the highly inclined (i~87.5 deg) galaxy NGC 4565 covering out to galactocentric radius Rgal > $\pm$ 17 kpc. The combination of sensitivity and resolution enables the detection of CO emission well into the HI-dominated outer disk while isolating individual molecular clouds across the full extent of the galaxy. Although often described as an edge-on Milky Way analog, the molecular gas profile of NGC 4565 has a central gap which is more similar to M31. The 13CO/12CO ratio remains consistent at 0.086 $\pm$ 0.009 from Rgal = 5-13 kpc. Based on fits to position-velocity slices, the molecular disk remains thin, with a FWHM scale height of 79.1 $\pm$ 1.6 pc measured from the vertical intensity profile with little evidence for vertical flaring. Molecular clouds in NGC 4565 show sizes, linewidths, and surface densities consistent with those found in similar environments in PHANGS-ALMA galaxies and in M31. We identify a prominent star-forming complex on the ring-an overdensity of molecular gas we term the East Ring Pileup. This feature hosts a compact, multiwavelength-bright region, which we call the Jewel. Effects of galaxy inclination on molecular cloud radius, velocity dispersion, surface density, and virial parameter appear as second-order effects that are strongest in velocity dispersion. At this resolution, GMCs are preferentially aligned with the disk of the galaxy and horizontally elongated by a factor of~2.

We present a closed formula for the computation of static post-Newtonian corrections to the two-body gravitational dynamics at any odd order, assuming the lower-order results are known. The formula is derived within a correlation function framework and exploits the $\mathbb{Z}_2$ symmetry of the static sector, leading to a novel theoretical interpretation of the factorization theorem. As an application, we compute the gravitational interaction of two compact coalescing objects at the seventh post-Newtonian order in the static limit, which receives contributions from seven-loop graphs at order $\mathcal{O}(G_N^8 v^0)$, and find complete agreement with the results obtained using the diagrammatic approach of the factorization theorem.

We present an extraction of unpolarized quark transverse-momentum-dependent parton distribution functions (TMD PDFs) from Drell-Yan data within a Bayesian inference framework, incorporating artificial intelligence at multiple stages of the analysis. Our analysis is performed at ${\rm N^3LO}$ in perturbative QCD combined with ${\rm N^4LL}$ resummation accuracy. We first employ an AI-driven iterative procedure to explore and rank candidate functional forms for the nonperturbative contributions to TMD PDFs at the initial scale, as well as for the Collins-Soper evolution kernel, using $χ^2$ fits and physics constraints. To enable efficient Bayesian inference, we construct a surrogate model for TMD cross sections by training a machine-learning emulator over the parameter space, replacing computationally expensive repeated evaluations and allowing scalable sampling with an affine-invariant Markov Chain Monte Carlo (MCMC) ensemble. Using this framework, we perform a global analysis of Drell-Yan data from fixed-target, RHIC, and LHC experiments and extract TMD PDFs with quantified uncertainties. We compare the results with those obtained using the replica method and highlight differences in the resulting uncertainty estimates.

Black hole shadow images are primarily determined by the properties of photon spheres and can exhibit degeneracies across different spherically symmetric spacetime geometries. We show that time delay observables associated with higher-order images of transient sources provide a robust probe to break such degeneracies in spacetimes admitting multiple photon spheres. Adopting a model-independent, parametrized, static, spherically symmetric framework that captures the generic features of double-peaked effective potentials, we investigate photon geodesics and quantify them in terms of angular deflection, travel time, and the order of the image. We identify distinctive signatures of trajectories probing the region between the unstable photon spheres. In particular, we find that these trajectories are characterized by the nontrivial temporal behavior, including a minimum travel time, a minimum angular deflection, and a characteristic triplet structure of higher-order images with a specific arrival sequence. We further show that the influence of the depth of the potential well, between the two photon spheres, on the observed time delays provides a direct handle on otherwise inaccessible regions of the spacetime. Our results highlight that time-domain lensing observables encode information beyond static shadow images and offer a promising avenue for probing the structure of compact objects and the strong-field regime of gravity.

Understanding how temporal order degrades in quantum systems remains a central issue in nonequilibrium physics. Here we study the melting of discrete time crystals in a periodically driven holographic system, where a distinct (discrete) time semicrystal phase emerges with persistent temporal order in disorder, bridging discrete time crystals and fully disordered regimes. This phase exhibits a periodic skeleton, with discrete subharmonic peaks persisting atop a continuous spectrum. We extract a critical scaling behavior across the discrete time crystal to time semicrystal transition. Furthermore, even dynamical transitions between distinct periodic skeletons can be clearly identified with systematic log-periodic corrections to power-law scaling, revealing discrete scale invariance. These findings in holography significantly enrich the platforms for studying nonequilibrium phases of matter.

On a compact connected Riemann surface $C$ of genus at least $2$, we construct Lagrangian correspondences between moduli spaces of rank-$n$ Higgs bundles (respectively, holomorphic connections) and the Hilbert schemes of points on $T^\ast C$ (respectively, the twisted cotangent bundles of $C$). Central to these constructions are Higgs bundles (respectively, holomorphic connections) which are transversal to line subbundles of the underlying bundles: these naturally induce divisors on $C$ together with auxiliary parameters, namely lifts to divisors on spectral curves for Higgs bundles and residue parameters of apparent singularities for holomorphic connections. We discuss the evidence showing that the Dolbeault geometric Langlands correspondence is generically realized by these Lagrangian correspondences; we expect that the de Rham geometric Langlands correspondence can be realized by their quantization, following Drinfeld's construction of Hecke eigensheaves. We also discuss the relations of our constructions to various topics, including reductions of Kapustin-Witten equations, the conformal limit, separation of variables, and degenerate fields in conformal field theories.

Baroclinic instability is a fundamental mechanism driving atmospheric dynamics. In this work, we revisit Pedlosky's two-layer model for finite amplitude baroclinic waves - a seminal framework for studying the unstable growth of finite perturbations - leveraging modern nonlinear techniques and computational resources. We show that the geophysical state of the baroclinic wave exhibits a rich diversity of dynamical regimes governed by the level of dissipation induced by Ekman boundary layers. In the inviscid limit, we demonstrate that the model is integrable. Upon increasing dissipation, the system undergoes a complex sequence of bifurcations. On one hand, deterministic chaos, identified by means of the Lyapunov exponents, provides a genuine mechanism for destabilization of the wave. On the other hand, in regimes where the wave equilibrates, dependence on the initial condition is crucial, eventually leading to the coexistence of multiple attractors. We study the governing equations of the model and their truncation to a finite-dimensional system of ordinary differential equations, together with the minimal low-order truncated system which is structurally equivalent to the Lorenz model. Its bifurcation diagram allows for elucidating the transition of the wave amplitude from stable equilibration to periodic oscillations - terminating in homoclinic orbits - and, ultimately, deterministic chaos through a period-doubling route. We finally comment on the robustness of these features for higher-dimensional models.

We consider critical site percolation ($p=p_c=1/2$) on the triangular lattice $\mathbf{T}$ in two dimensions. We show that the simple random walk on the clusters of open vertices converges in the scaling limit to a continuous diffusion which lives in the gasket of a conformal loop ensemble with parameter $κ= 6$ $\big(\mathrm{CLE}_6\big)$, the so-called $\mathrm{CLE}_6$ Brownian motion. We also show that the intrinsic (i.e., chemical distance) metric converges in the scaling limit to the geodesic $\mathrm{CLE}_6$ metric. As a consequence, we deduce the existence of the chemical distance exponent, the resistance exponent, and the spectral dimension of the critical percolation clusters. Moreover, we show that the exponents satisfy the Einstein relations.

Intracellular chromophores (e.g., NADH and FAD) play a central role in regulation of cellular metabolism. Though autofluorescence has been extensively used for label-free mapping of chromophores inside a cell, its sensitivity and molecular specificity are constrained by the low quantum yield and the fluorescence spectral overlap. Here, we address these challenges by employing a photothermal approach to measure the optical absorption of chromophores rather than its autofluorescence. By combining near-infrared pump and visible probe beams, our two-photon photothermal (2PPT) microscope exploits localized thermal transients generated through two-photon absorption, enabling detection of chromophore-specific signatures beyond the reach of autofluorescence. We demonstrate sub-micromolar limit of detection for the metabolic coenzymes NADH and FAD of 0.87 uM and 0.99 uM, respectively. Such high sensitivity enables differentiating the influence of different mitochondria shapes on metabolism activity. Importantly, the fluorescence crosstalk-free 2PPT can identify the biomolecular source of contrast from cellular mitochondria in a label-free manner based on spectroscopy. 2PPT microscopy is utilized to study metabolic alterations of mitochondria in cancer under chemotherapy at the single organelle level.

A mode sorter separates a set of M orthogonal spatial modes in a shared input channel into M different output channels. Here we present an analytic derivation and experimental validation of a single plane device for sorting spatial modes from a diverse variety of mode families, including Hermite-Gaussian (HG), Laguerre-Gaussian (LG), Bessel-Gaussian (BG), with almost no cross-talk. This sorting capability is required for a wide range of applications that employ classical or quantum light. We also show that applying this design in order to sort a set of Orbital Angular Momentum (OAM) modes with zero radial index reproduces the well-known Fork grating configuration. Furthermore, by taking the limit of M -> inf, we present an analytical expression for sorting all the modes of a given family. By operating this device in reverse, it can be used to generate arbitrary modes, by illuminating it with a Gaussian beam. The power transmission coefficient for this sorter goes as 1/M and we provide a mathematical proof that this is optimal for any typical arrangement of the detector positions. We further study the sorter sensitivity to wavelength and random phase noise.

Quantum Chromodynamics (QCD) at finite density is most often formulated on the lattice as a grand canonical ensemble. Since lattice QCD has a complex action problem at finite baryo-chemical potential ($μ_B$), its results at finite density are indirect: e.g. in the form of a set of expansion coefficients. In contrast, the canonical formulation offers direct results for integer-valued net-baryon number. In this work we present for the first time results in the canonical formulation with physical quark masses. To this end we use a high statistics finite-volume lattice ($16^3\times8$) data set that we generated at $μ_B=0$ with our 4HEX staggered action. We extend the canonical ensemble to non-integer net-baryon number and connect the results back to the grand canonical ensemble. Unlike reweighing to real $μ_B$, this method can also be used with rooted staggered quarks. For densities where the sign problem can be overcome by brute force computing power, this scheme provides lattice QCD results (e.g. for pressure, baryon density) directly, without relying on any extrapolation in the baryo-chemical potential. In this work we chart the phase diagram by studying bulk thermodynamic observables, which we show to be feasible up to $μ_B\approx500$~MeV.

In this paper, we develop a class of antisymmetrized geminal power configuration interaction (AGP-CI) wave functions that extend the AGP framework by incorporating inter-geminal correlations through a CI expansion. To make these wavefunctions computationally tractable, we evaluate them by rewriting the AGP-CI ansatz as a linear combination of AGPs (LC-AGP), for which overlaps and Hamiltonian matrix elements can be computed with standard AGP machinery. Motivated by border-rank decompositions, we further reorganize this ansatz into a compact linear combination of AGPs depending on a small deformation parameter $τ$, which controls how closely the truncated expansion approximates the full AGP-CI state. Benchmark applications to the Hubbard model and to the small molecules H$_2$O and N$_2$ demonstrate that the proposed wavefunctions achieve consistently high accuracy and outperform the LC-AGP, particularly for systems with more electrons and in strongly correlated regimes.

We derive deterministic equations for the evolution of non-Gaussian fluctuations in relativistic stochastic hydrodynamics. This is achieved by defining the average local Landau frame and corresponding fluctuating hydrodynamic variables. Fully nonlinear stochastic hydrodynamics is expressed in a unified multi-component matrix form. A novel relativistic formalism, also manifestly covariant under SO(3) rotations of the local spatial basis in the average local Landau frame, is introduced. The equations describe correlators of all hydrodynamic variables, including fluctuating velocity (or momentum density) -- a nontrivial problem in relativistic hydrodynamics.

Granular flows are ubiquitous in nature and industrial applications, yet a complete continuum theory remains a long-standing challenge. The leading empirical approach, μ(I) rheology, lacks microscopic foundations and becomes multivalued in dense, slowly sheared flows where nonlocal corrections are required. Exploiting state-of-the-art high-speed X-ray tomography to investigate microscopic dynamics of dense granular flows in a Couette geometry, we establish a new, universal constitutive law spanning quasi-static to inertial regimes based on structural relaxation, resolving the fundamental difficulty in the original μ(I) framework. By further establishing a non-equilibrium statistical framework for granular flows, we demonstrate an intrinsic analogy between driven granular matter and hard-sphere liquids owing to their identical Carnahan-Starling equation of state, naturally explaining our rheological approach and the emergence of glassy behaviors. Our framework unifies granular rheology with the broader physics of disordered systems and provides a complete, microscopically-based theoretical framework for dense granular flow.

We present observations from two consecutive TRACERS-2 orbits through the northern low-altitude cusp. During the first crossing, TRACERS-2 observed reversed cusp ion dispersion and sunward convection, consistent with magnetopause reconnection tailward of the cusp during this northward IMF interval. Simultaneous THEMIS-D observations at the equatorial magnetopause show heated magnetosheath plasma captured on closed field lines, with similar particle spectra as in in the low-altitude cusp, indicating that reconnection indeed occurred tailward of the cusp and in both hemispheres. When TRACERS-2 traversed the northern cusp again, 95 minutes later, the IMF was dominated by a negative BX component. Despite the different IMF conditions, TRACERS-2 recorded nearly the same cusp signatures as before, i.e., reversed ion dispersion and sunward convection. The observations indicate that tailward-of-cusp reconnection can occur for both northward and BX-dominated IMF and that these distinct IMF geometries can produce remarkably similar plasma and field signatures in the low-altitude cusp.

The localization of chiral fermionic zero modes in scalar field backgrounds with domain wall structure is a central mechanism in brane-world scenarios. We investigate this mechanism in a system that provides an effective realization of the $(1+1)$-dimensional Jackiw--Rebbi model, using a two-kink scalar background generated by the deformation method applied to the $φ^4$ model. The two-kink profile introduces two physically distinct parameters: an asymmetry parameter $a_2$ controlling the left-right symmetry of the scalar background, and an inter-kink separation parameter $b$ controlling the distance between the constituent domain walls. We establish two independent scaling laws. First, the collective center-of-mass position of the chiral zero modes responds linearly to $a_2$, providing a mechanism for continuously tuning the effective brane position in the extra dimension. Second, the differential spatial separation between the two chiral modes diverges as the two-kink background collapses into a simple kink, following a power law in $(b-1)$ with exponent statistically consistent with $-1$. These two results are physically independent and each admits a precise interpretation in the language of brane-world scenarios. The mechanism is realized concretely in bilayer graphene under an asymmetric two-kink electrostatic potential, providing a tunable platform for probing extra-dimensional localization physics.

We study quantum light-matter interfaces based on bilayer atomic arrays in free space, considering interlayer spacings $a_z$ that may deviate from the Bragg-symmetric condition, $a_z\in \mathrm{integer}\times λ/2$ with $λ$ the light wavelength. Mapping the problem to a one-dimensional model, we show that the interface efficiency is fully determined by simple scattering observables $-$ reflection and transmission $-$ providing a direct, experimentally accessible characterization. This reveals new opportunities for optimizing light-matter coupling by operating beyond the Bragg symmetry. In particular, we identify configurations that suppress diffraction losses via destructive interference, enabling substantially improved interface efficiencies compared to Bragg-constrained designs. In addition, we introduce a new quantum memory scheme based on a collective dark state whose coupling to light is continuously controlled by tuning the interlayer spacing. More broadly, our results establish non-symmetric atomic arrays as a flexible platform for efficient quantum interfaces in free space.

Quantum metrology promises precision beyond classical limits but environmental noise, unless properly controlled, reduces the quantum advantage to at most a constant improvement. A key challenge is therefore to design quantum control strategies that suppress noise while preserving sensitivity to the targeted signal. Here, we suggest to use dressed states generated by static fields to achieve this goal and show that success of this strategy depends on the spectral properties of the environment. For low-temperature noise, we show that Heisenberg scaling can be achieved if and only if the signal generator lies outside the linear span of the system-environment coupling operators. This implies that the proper dressed states may enable Heisenberg scaling even in cases where the well-known Hamiltonian-not-in-Lindblad-span criterion, evaluated without dressing, would forbid it. We illustrate dressed state metrology for the example of NV-center thermometry under magnetic-field fluctuations, with the framework readily applicable to other platforms.

Star evolution models predict the lightest compact objects in the universe to have masses greater than that of the Sun. Nonetheless, alternative scenarios could lead to the formation of sub-solar mass (SSM) compact objects, such as primordial black holes (PBHs). The LIGO-Virgo-KAGRA Collaboration (LVK) has performed a search for gravitational-wave (GW) signals from compact binary coalescences (CBCs) including at least one SSM component during the first part of their fourth observing run (O4a), reporting no statistically significant candidate. This non-detection sets upper limits on the merger rate of such systems, which can be used to constrain PBH formation models and the fraction of dark matter (DM) in PBHs. For PBH binaries forming at late times, the fraction of DM in PBHs is constrained to be <= 1 for masses above 0.9 M_sun in the case of monochromatic mass functions. In the early-formation scenario, this fraction is limited to $\le 7\%$ at 1 $M_\odot$ and $\le 40\%$ at 0.35 $M_\odot$.

Using integral field spectroscopy from SDSS-IV MaNGA, we investigate the radial distributions of star formation rate (SFR) and gas-phase metallicity in spiral galaxies that reside in spiral-elliptical (S+E) pairs. Spirals in S+E pairs show suppressed central star formation and elevated metallicities, whereas spirals in spiral-spiral pairs exhibit centrally enhanced star formation and reduced metallicities. The degree of SFR suppression and metallicity enhancement in S+E pairs depends on the masses of the pair members. Spirals with more massive elliptical companions experience stronger star-formation suppression and larger increases in metallicity, while lower-mass spirals show more pronounced metallicity enhancement. In addition, within S+E systems, galaxies with asymmetric gas velocity fields display enhanced SFR and higher metallicities, whereas those with symmetric velocity fields exhibit clear central suppression. Based on these results, we infer that in S+E pairs, the spiral galaxy experiences suppressed gas accretion once it enters the hot circumgalactic medium of its early-type companion, which leads to the observed decline in star-formation activity. When a close encounter takes place, tidal perturbations can compress the remaining cold gas and trigger enhanced star formation, producing rapid chemical enrichment and the associated increase in metallicity.

In this work, we investigate three typical new physics resonances which couple to the standard model (SM) quarks via direct top-quark flavor-changing interactions. We identify the possible SMEFT operators electroweak scale and analyze their phenomenology.

Grover's algorithm accelerates unstructured database search quadratically compared to classical algorithms. In the NISQ era, distributed quantum computing can decrease circuit depth and reduce noise. In this paper, an algorithm for constructing query operators for subfunctions is proposed. By dividing the target string of the search problem into several substrings and integrating the query operator of each subfunction, a low-depth distributed exact quantum search algorithm is designed. The contributions of this paper are as follows: (1) The proposed distributed algorithm has a lower circuit depth and can mitigate error accumulation compared to distributed quantum search algorithms; (2) The target can be accurately located by the proposed distributed algorithm; (3) Experiments conducted with the quantum software MindQuantum confirm the effectiveness and feasibility of the proposed distributed algorithm. Moreover, the introduction of noise to the circuit during these experiments indicates that the algorithm possesses an inherent capacity for noise resistance.

An observation of a large prominence on the solar limb took place on February 15, 2022, by the Extreme Ultraviolet Imager (EUI) on board Solar Orbiter. We aim to determine the range of physical parameters of this prominence, such as temperature, radial velocity, and altitude, and examine how these parameters affect the formation of the 304~Å line of \ion{He}{2}, especially how collisional excitation and radiative processes contribute to line formation. After constraining these parameters, we generate 200 random models and compute the \ion{He}{2} 304~Å line profile. We present these results using parallel coordinate plots to explore how these parameters affect the results. This allows us to infer the key physical parameters that impact the formation of the \ion{He}{2} 304~Å line. This study demonstrates that column mass and the steepness of the temperature profile are key factors in the formation of the \ion{He}{2} 304~Å line during the solar prominence eruption on February 15, 2022. Radiative processes remain dominant in the formation of the \ion{He}{2} 304~Å line. These insights provide a foundation for future research and comparative studies.

We propose quantum algorithms for complex-valued nonlinear partial differential equations in the strongly nonlinear regime, where the dynamics is governed by vortex cores, phase singularities, and nonlinear vortex interactions. Examples include the complex-valued nonlinear Schrödinger equation, as well as nonlinear heat and wave equations with Ginzburg--Landau-type nonlinearity. In the strongly nonlinear regime, the solutions to these equations are asymptotically governed by, in leading order, linear elliptic equations, coupled with low-dimensional vortex dynamics, where the vortex cores correspond to topological defects in superconductors. Our hybrid quantum-classical algorithms utilize this asymptotic property, in which the vortex dynamic is advanced classically while the boundary-value problem of linear elliptic equation is handled by quantum algorithms. For the two-dimensional nonlinear Schrödinger equation, we also combine quantum BPX preconditioning with Schrödingerization to estimate physically relevant observables in the small-output regime. This yields, already in two dimensions, an {\it exponential} improvement in the dependence on the spatial problem size, while the dependence on the target accuracy remains essentially linear up to polylogarithmic factors. We further show that the same principle extends to dissipative Ginzburg--Landau vortex dynamics and to vortex filaments in three-dimensional superconductivity. Numerical results support the validity of this PDE reduction and the effectiveness of the proposed approach.

Long-term chemical durability of glass, crucial for immobilizing nuclear waste, is governed by glass properties such as composition, surface geometry, as well as external factors like thermodynamic conditions and surrounding medium. Despite decades of research, there are no models that account for these intrinsic and extrinsic factors to predict the dissolution rates of glass compositions. To address this challenge, we evaluate the role of natural language embeddings capturing the synthesis and testing conditions in enhancing the predictability of glass dissolution. Evaluating the approach on hand-curated ~700 datapoints extracted from the literature, we reveal that the machine learning (ML) model including natural language embeddings (NLP-ML) outperforms classical ML model in predicting glass dissolution rate. Furthermore, we developed a generalizable ML model by transforming the compositional features to structural descriptors of glass alongside NLP-derived features, enabling extrapolation capability to glass compositions with completely new elements absent in the training data. Evaluating this model on a completely new dataset of glass compositions 34 chemical components in contrast to the training dataset that had only 28 components, we demonstrate that the model indeed exhibits generalizability to glass compositions that are out-of-distribution. Altogether, this integrated approach offers a pathway towards high-fidelity glass dissolution prediction and accelerate the discovery of novel glass compositions with tailored durability for sustainable nuclear waste management.

The idea of a $\bigvee$-system was introduced by Veselov in the study of rational solutions of the WDVV equations of associativity. These are algebraic/geometric conditions on the set of covectors that appear in rational solutions to the WDVV equations. Here, this idea is generalized to open WDVV equations, which are an additional set of PDEs originating from open Gromow-Witten Theory. We develop -- for rank-one extensions -- algebraic/geometric conditions on the covectors that supplement the $\bigvee$-system to give rational solutions to the open WDVV equations. Examples, and the relation to superpotentials and to Dubrovin almost-duality, are given.

We study physical (near-kernel of constraints) states of 4-d Euclidean loop quantum gravity in Smolin's weak coupling limit on the complete graph $K_5$ using variational Monte Carlo with neural network quantum states. We investigate the Hamilton constraint $\hat{H}$ in the ordering proposed by Thiemann, as well as $\hat{H}^\dagger$ and $\hat{H}+\hat{H}^\dagger$. We find that the variational optimisation selects distinct solution families for $\hat{H}$ and $\hat{H}^\dagger$ across several considered cutoffs on the kinematical degrees of freedom. The solution family of $\hat{H}$ is flat on all minimal loops and has non-vanishing volume expectation values. Its edge-charge marginals delocalise with increasing cutoff, which indicates they are approximations to solutions that are non-normalisable in the kinematical inner product. The solution family for $\hat{H}^\dagger$ is normalisable, shows non-trivial charge correlations, lies in the kernel of volume and is not flat. $\hat{H}+\hat{H}^\dagger$ turns out to be much harder to solve and yields quasi-solutions combining features of both previous families. We characterise all solutions using chromaticity 1- and 2-point functions, minimal loop holonomies, geometric area and volume observables and show that the two families can be interpreted as, on the one hand, a family of states close to the Ashtekar-Lewandowski vacuum and the Dittrich-Geiller vacuum with some numerical noise on the other hand. We also present some results that link solutions of the truncated theory to solutions of the continuum theory.