Our study focuses on the strong tidal disruption of a cold helium white dwarf passing a black hole. We model the white dwarf as a Bose-Fermi droplet and use quantum hydrodynamic equations to simulate the binary system's evolution. As the white dwarf passes through periastron, it loses a significant amount of mass. This mass falls onto the black hole and forms an accretion disc. Quantized vortices appear in the accretion disc, manifesting as strong electromagnetic radiation signals that exhibit characteristic flickering patterns changing on a timescale of a few seconds. Meanwhile, the white dwarf moves away from the black hole. As the white dwarf moves through space, vortices run along its surface. This elongates its geometry, causing it to rotate and emit gravitational waves.

We introduce a geometrically constrained hidden-variable framework that generates a family of correlations parametrized by a boundary function, within which the quantum singlet correlation appears as a particular member. Exact expressions for the correlation function are derived. Several structural results are established, including admissibility conditions, symmetry properties, a universal stationary point of the associated CHSH function, and an exact relation between the CHSH value at $\nu=\pi/4$ and a geometric contrast measure defined on the underlying hidden-variable distributions. Rather than treating the quantum singlet correlation as an isolated target to be reproduced, the present framework places it within a broader geometric structure of correlations. These results suggest the existence of a nontrivial geometric structure underlying the family of correlations and motivate the search for a principle capable of selecting the quantum singlet solution from within that family.

We investigate energy supratransmission in a boundary-driven two-dimensional nonlinear Schrödinger equation with a central hole. Harmonic forcing with azimuthal modulation generates standing-wave states whose existence and stability depend on the driving amplitude, the inner radius, and the imposed azimuthal charge. Bifurcation analysis shows that small inner radii produce strongly confined states with higher destabilization thresholds, whereas larger radii yield broader profiles and smoother transitions between stable and unstable branches. The cubic--quintic and saturable models exhibit similar qualitative behaviour but differ quantitatively in their critical amplitudes and parameter dependence. A variational approximation captures the dependence of the critical drive on the azimuthal charge and nonlinear parameters, and clarifies how the nonlinear response shapes the stationary states near the turning point. Time-dependent simulations show that supratransmission occurs through the emission of localized pulses, with nonzero azimuthal charge triggering symmetry breaking and producing two-dimensional localized excitations (pearls). Isosurface plots provide a complementary view of the resulting radial and angular excursions. These results establish a quantitative framework for supratransmission in two-dimensional geometries and are relevant to driven nonlinear systems in optics, Bose--Einstein condensates, and structured media.

The orbital angular momentum of light is an intriguing property for developing light driven applications. It emerged as an independent degree of freedom by which to manipulate light and, consequently, the interaction of light with matter. Several methods exist for the generation of light carrying orbital angular momentum, mostly employing transmitting or reflecting optical components, which radially modulate the phase profile of the light. As one of such components, transmissive q-plates established themselves as standard elements due to their usability over a broad wavelength range. Here, we present our approach to build a highly reflective q-plate based on a plasmonic metasurface capable of converting orbital angular momentum from the nanostructure to ultrashort laser pulses without temporal broadening. We highlight its working principle over a wide range of wavelengths for reflection under normal and gracing incidence.

Kagome FeGe hosts a $2\times2\times2$ charge-density wave (CDW) that strongly interplays with antiferromagnetic order. Here, we report $^{57}$Fe nuclear resonant scattering measurement to study FeGe across its long-range CDW and incommensurate magnetic transitions. Upon entering the CDW state, hardening of acoustic phonons and optical phonons around 22~meV, 27~meV, and 31~meV are observed in the Fe partial phonon density of states, which can be qualitatively captured by first-principle calculations. Upon entering the incommensurate magnetic phase, neither the phonon density of states nor the hyperfine interaction parameters change significantly, although a subtle feature associated with the incommensurate magnetic order or slow fluctuations is detected in the time-domain Mössbauer spectra. These findings show that the CDW in kagome FeGe significantly modifies its lattice dynamics and magnetism, evidencing an intertwined nature of the spin, charge, and lattice degrees of freedom.

Characterizing quantum processes is essential for hardware benchmarking, error diagnosis, and algorithm verification. While recent work [PRX QUANTUM \textbf{4}, 040337 (2023)] extended classical shadows from quantum state to quantum process, enabling efficient single-channel $\mathcal{E}$ property prediction, its applicability to composite processes $f(\mathcal{E}_1, \mathcal{E}_2,\cdots, \mathcal{E}_k)$ remains unexplored. We introduce shadow engineering, a framework encoding the classical shadows of processes into sparse transfer matrices to predict $f(\mathcal{E}_1, \mathcal{E}_2,\cdots, \mathcal{E}_k)$ properties with proven polynomial sample complexity, matching single-channel efficiency while exponentially lower than quantum process tomography. Crucially, this approach repurposes existing $\mathcal{E}_m$-shadow data without physical execution of $f(\mathcal{E}_1, \mathcal{E}_2,\cdots, \mathcal{E}_k)$, enabling flexible quantum process characterization with minimal hardware overhead. We demonstrate the framework's effectiveness and practicality on a superconducting quantum processor for typical applications such as error mitigation and Hamiltonian dynamical simulation. This framework unlocks new capabilities for predicting complex quantum behaviors without physical re-execution, with immediate applications in near-term device calibration and quantum simulation.

Mode visibilities can be estimated from observed power spectra or from theory by making assumptions about the damping processes occurring in the star. However, a quantitative comparison between the two approaches was so far not feasible due to observational biases. The biases arise from the fact that in observations, the power spectrum is divided into frequency segments in which modes of a certain spherical degree are expected to dominate. In this work, we used synthetic power spectra to calculate the visibility as it has been done in observations and compare it with published observed visibilities to quantify the influence of the biases. We find that, taking the biases into account, the observed spatial response of the dipole modes is 1.47, which is closer to the theoretical value than previous estimates. In particular, we predict that the normalized dipole mode visibility of late red-giant branch (RGB) stars might be overestimated by up to 20% in published observations. For stars with depressed dipole modes, we find that the normalized dipole mode visibilities estimated in observational studies might be overestimated by 20% throughout their entire evolution on the RGB. The quadrupole mode visibility, on the other hand, appears to be largely unaffected by the biases, expect on the late RGB. In addition, we investigated the evolution of the visibility and detectability of the mixed mode signature while testing different prescriptions for the energy loss caused by a strong internal magnetic field in the stellar core. We argue that taking into account the inner turning point of the g-mode cavity could allow a portion of the mode energy to be preserved when interacting with a strong magnetic field. We further show that such partial dissipation allows the mixed mode signature to be both present or absent in the observable power spectra, which is consistent with observations.

The central prerequisite of any fault-tolerant quantum architecture is a quantum memory: a block of encoded physical qubits whose logical state is actively preserved against noise across many rounds of error correction. In neutral-atom Rydberg arrays, realizing such a memory is obstructed not by the entangling gates themselves, which are already fast and high-fidelity, but by the auxiliary operations that a conventional error-correction cycle requires: mid-circuit fluorescence measurement, inter-zone atom transport, and locally focused single-qubit addressing. Each of these introduces latency, atom loss, or optical crosstalk that exceeds the cost of the underlying gates by orders of magnitude. These costs accumulate cycle after cycle, progressively degrading the very logical information the code is meant to protect. Here we propose a protocol that stabilizes a toric-code quantum memory without moving, measuring or local addressing atoms. The key is to use a three-species Rydberg atom array for the complete stabilizer cycle, including syndrome extraction, coherent correction, and ancilla reset, under global, species-selective laser pulses. Numerical simulation of a $4 \times 4$ rotated toric code shows a longer qubit lifetime when the physical error rate is below a pseudo-threshold $p^\star \approx 0.034$. The scheme offers a concrete, hardware-efficient route to topological quantum memory in neutral-atom platforms.

Solid-state phase transformations in molecular crystal hydrates govern stability and functional performance across a range of applications, including pharmaceutical, agrochemical and coordination framework materials. During dehydration, these hydrates can undergo substantial structural reorganisation involving changes in molecular orientation, intermolecular interactions, and lattice symmetry. Despite extensive study, the microscopic crystallographic pathways by which such transformations proceed remain poorly understood. Here, we investigate the dynamics of solid-state dehydration of theophylline monohydrate as a model molecular hydrate using in situ low-dose scanning electron diffraction (SED). Simultaneous observations of changes in morphology and crystallographic phase and orientation mapped across single particles reveal how complete dehydration proceeds via a two-step, reconstructive topotactic solid-state transformation: anisotropic, surface-specific mass loss of material near water channel sides (suggesting the monohydrate adopts a non-centrosymmetric crystal structure) is followed by surface-localised nucleation and growth of anhydrous form II on the parent monohydrate while preserving similar molecular orientations at a common plane. By providing direct, local crystallographic insight into hydrate dehydration, this work demonstrates how surface-controlled mass loss, morphological changes, and lattice orientation jointly govern solid-state transformations in molecular hydrates. More broadly, it establishes low-dose SED as an effective approach for probing dynamic phase transformations in beam-sensitive molecular crystals.

A fundamental concept in linear algebra and its applications to network analysis is the Perron--Frobenius (PF) theorem, which underpins eigenvector-based centrality measures such as eigenvector centrality, PageRank, and hubs and authorities. By invoking the PF theorem, we know for strongly connected networks with positive edge weights that the eigenvector corresponding to the largest eigenvalue of the weight matrix yields a well-defined centrality measure (namely, eigenvector centrality). Traditional formulations of the PF theorem and associated centrality measures assume that networks have real-valued weights. However, many networks in areas such as quantum information, quantum chemistry, electrodynamics, and machine learning have complex-valued edge weights. In this paper, we study generalizations of the PF theorem to complex-valued matrices, establish connections between these generalizations, and propose generalized eigenvector-based centrality measures to analyzing node importances in networks with complex edge weights. We also prove results about the existence of complex-weighted networks that satisfy generalized PF properties and calculate associated centrality measures for several examples, which we draw from application areas such as electron transport, circuit analysis, mathematical chemistry, and communication networks.

The quantum information lost in open evolutions cannot be fully recovered, but partial recovery is possible. The Petz recovery map guarantees almost optimal recovery, notably if the chosen reference state is close to the real one. This map has been widely used in theoretical studies, but has been the object of only a handful of experimental realisations, typically under a single fixed noise model. In this work, we describe and implement the Petz recovery map for a versatile class of qubit channels with tunable decoherence and dissipation. The setup we realize is also the first experimental example of ``tabletop reversibility'': for a good range of choices of the reference state, the Petz recovery map can be implemented with the same devices as the forward dissipative evolution, whose effect it is partially undoing. Our results demonstrate that the Petz recovery map can be resource-efficiently realized without requiring complex ancillary resources, providing a feasible pathway for mitigating information loss in quantum systems.

Human behaviors, particularly non-pharmaceutical interventions (NPIs), are dynamically coupled with epidemic spreading. While prior studies mainly assume a linear interplay, real-world behavioral evolution is driven by nonlinear responses and social influence. Here, we incorporate these multifaceted mechanisms into a co-evolutionary model and analytically derive the critical thresholds. Notably, as the infection rate grows, NPI compliance initially rises but then abruptly drops to zero. This paradoxical decline indicates an emergent social dilemma: at high infection rates, abandoning NPIs is individually optimal but detrimentally triggers an explosive surge in epidemic prevalence. We further show that socially induced overestimation of the infection rate can counterintuitively prompt individuals to abandon NPIs. Moreover, the interplay with social influence induces periodic oscillations, reflecting a tragic cycle of recurrent epidemic waves. Furthermore, we validate the robustness of this NPI-abandonment dilemma in networked population. Our work illustrates rich emergent phenomena in the co-evolution of epidemic and behavior, challenging traditional views on this coupled dynamics.

The measurement of the spin-orbit obliquity, that is, the angle between the orbital axis of a planet and the stellar spin axis, provides crucial insights into how planets form and migrate. Observations of young transiting planets, which have not yet experienced significant tidal alterations, offer a unique opportunity to study their original obliquity configuration. We observed the warm Saturn-sized TOI-837 b (member of the 35 Myr old open cluster IC 2602) in-transit using ESPRESSO at VLT, collecting high-precision radial velocities to measure the Rossiter-McLaughlin effect. We found a sky-projected obliquity of $\lambda = 341.1^{+2.3}_{-2.5}$ deg. Using our knowledge of the stellar rotation period ($3.00 \pm 0.02$ d), we estimated a true obliquity of $\psi = 25.9^{+7.5}_{-6.3}$ deg, which indicates prograde motion and suggests a mildly misaligned orbit. This places TOI-837 b as the first planet younger than 100 Myr with accessible $\psi$ incompatible with an aligned orbit. Together with the primordial circular orbit of TOI-837 b and the presence of a bound stellar companion, this mild misalignment favours the possibility of a primordial obliquity excitation (secular torque on the protoplanetary disc) followed by disc-driven migration, rather than high-eccentricity migration after formation.

A model for predicting the residual stress gradient in a thin film segment is developed on the basis of the theory of dislocation pile-ups. The initial shear stress within the film is relaxed via the formation of a pile-up of screw dislocations against the impenetrable film-substrate interface. Plastic strain is related to the dislocation density, leading to a fundamental equation, which links the residual stress to this density. The distribution of dislocations within the pile-up for an arbitrary, non-uniform residual stress profile is derived analytically by applying the force balance condition. This results in a singular integro-differential equation for the residual stress profile. The equation is solved numerically by a collocation method for various initial stress distributions: constant, linear, parabolic, and exponential functions. The solutions demonstrate that the established residual stress profile strongly depends on the film segment's thickness-to-width ratio and the initial stress distribution. As this ratio increases, stress relaxation becomes more effective away from the film-substrate interface. In all cases, equilibrium requires a pile-up containing dislocations with both positive and negative Burgers vectors. The total number of dislocations and their density distribution vary significantly with the initial stress profile. This model provides a critical step towards more complex models of residual stress formation in constrained material systems, specifically, thin films.

We study spherical T-duality for iterated sphere bundles. We show that for a class of iterated sphere bundles the cohomological data contained in its Gysin sequences can be repackaged into data for a vanishing Massey product. We further show that if these bundles are endowed with an integral cohomology class of transgressive degree one, then they have a T-dual iterated sphere bundle, namely, the one associated to the same Massey product read backwards.

Using a direct scan of 26 energy points near the $J/\psi$ resonance, we perform the first measurement of the relative phase $\phi_{\gamma, 3g}$ between the strong and electromagnetic amplitudes in $J/\psi\to\bar K^0 K^*(892)^0+c.c.$ and $J/\psi\to K^+ K^*(892)^-+c.c.$. Unexpectedly, the phase in the neutral channel is found to be $\sim 150^\circ$, deviating from orthogonality ($90^\circ$) by 4.2$\sigma$ and from a relative real amplitude (0$^\circ$ or 180$^\circ$) by 10.0$\sigma$ or 1.6$\sigma$, respectively. In contrast, the charged channel phase is consistent with $\sim 180^\circ$ within 1$\sigma$, exhibiting model-dependent behavior. The corresponding branching fractions are consistent with the world averages but achieve better than twofold improvement in precision. The ratios between the branching fractions of $J/\psi\to\bar K^0 K^*(892)^0+c.c.$ and $J/\psi\to K^+ K^*(892)^-+c.c.$ are also measured. After subtracting the electromagnetic contribution, the corresponding strong amplitude ratios obey isospin symmetry within $1.8\sigma$. A search for direct $CP$ violation yields asymmetries consistent with zero.

Quantum systems face a fundamental trade-off: they must remain decoupled from the environment to maintain long coherence times, yet they require interactions with the environment to be accessible for measurement. As a prime example, emitter arrays coupled to waveguides facilitate collective modes that, owing to interference, can suppress radiation into the waveguide. While complete destructive interference creates perfectly dark states with infinite lifetimes, their inherent decoupling makes them unmeasurable in standard waveguide quantum electrodynamics. Consequently, current approaches must rely on system non-idealities that permit measurement but limit the coherence times. In this work, we lift this limitation by proposing the use of weakly squeezed light generated in \{chi}(2) nonlinear waveguides for the spectroscopy of completely dark states. We show that the fluorescence spectrum probes transitions between the dressed dark states of the emitter array. This work paves the way towards the measurement and control of dark states, with applications for robust quantum memories, computation, and communication.

In this work, we apply deformed light-cone null reduction method to a complex Maxwell theory in a manifestly gauge-invariant formulation. We show that the local U(1) gauge structure degenerates in the $c\to 0$ limit: the Gauss law constraint reduces from a restriction on initial data to a conservation law, releasing the longitudinal gauge mode as an independent degree of freedom (d.o.f). This raises the physical field count from $2(d-1)$ to $2d$. We prove a no-go theorem: under the single-mode Kaluza-Klein(KK)-like ansatz, no scaling of the field components can simultaneously preserve nontrivial dynamics and a first-class Gauss law, due to an inherent mismatch between velocity-type and constraint-type contributions in the parent action. Rather than representing the Carrollian electrodynamics derived via group contraction, the free complex scalar theory that emerges is merely an artifact of the truncation procedure at $c\to0$.

Quantum integrability in a system is characterized by a large number of conserved charges. However, finding the conserved charges in a generic quantum system is highly challenging. The integrable matrix theory provides a unified framework to obtain the conserved charges in a certain class of systems. We demonstrate this framework in case of a single-particle system on a 1D finite-sized lattice with inhomogeneous nearest neighbor hopping to study the statistical properties of the system across its chaotic--integrable crossover from the perspective of the conserved charges. The eigenspectrum of our random matrix model is studied first. We then estimate the conserved charges and find their properties throughout the chaotic to integrable transition of the system. We calculate the number of conserved charges across this crossover and observe that it is nearly equal to the size of the system at its integrable limit. Our result suggests that the number of conserved charges, estimated using the integrable matrix theory, can be a measure of quantum integrability.

Hybrid manganese halides enable the coexistence of molecular chirality, polar order, and magnetic exchange within a single lattice. Here, we combine first-principles calculations with spin-space-group analysis to investigate the synthesized enantiomeric pair [(R)/(S)-MPA]2[MnCl4(H2O)] (MPA = beta-methylphenethylammonium). We predict that its compensated magnetic state hosts altermagnetic spin splitting in the nonrelativistic limit, and that the coupled chiral, polar, and magnetic degrees of freedom define a symmetry-related manifold. From this manifold, we derive simple sign rules for the electronic and magneto-optical response: reversing both chirality and polarity, or reversing the magnetic domain alone, inverts the spin splitting throughout the Brillouin zone, whereas reversing chirality alone or polarity alone changes the spin-splitting sign only in symmetry-selected regions. With spin-orbit coupling, reversing chirality or magnetic order flips the Kerr rotation angle, while changing the polar variant leaves it unchanged. These results reveal a chemically accessible route to translate molecular handedness into symmetry-controlled spin splitting and magneto-optical readout in hybrid manganese halides. Critically, we show that the sign and momentum pattern of the splitting are governed by the interplay of the chiral, polar, and magnetic degrees of freedom. This interplay opens the possibility to control the spin splitting through a judicious design of the organic cations, by modulating their chirality and polarity.

Witten recently proposed a background-independent algebraic framework for quantum gravity, wherein an observer endowed with a Hamiltonian defines a diffeomorphism invariant worldline algebra manifested by the modified Hamiltonian constraint. In the semiclassical limit, this construction admits a lift to a von Neumann algebra acting on a Hilbert space defined by geodesic in a fixed background. Motivated by this, we revisit quantization of certain class of deformed CFT Hamiltonian on a cylinder to capture non-perturbative aspects of black holes. We construct a type-I Von-Neuman algebra by imposing conformal boundary conditions on cut-offs near fixed points of Hamiltonian flow, acting on a GNS Hilbert space built from highest-weight representation of `emergent modular Virasoro algebra'. Upon identifying the Hamiltonian with the modular Hamiltonian of a sharp subregion associated to a fixed reference KMS (vacuum) state, the algebra changes to type-III$_{1}$ factor. We also discuss the structure of emergent Hilbert spaces using `open-closed string' duality after incorporating an emergent non-trivial center made out of scalars at fixed points. We further employ this modular quantization of a single holographic CFT to demonstrate how the boundary limit of exact Hartle-Hawking correlator of smooth BTZ background emerge in the strict semiclassical limit in an alternative dual description, while at finite $G_{N}$, the corresponding description is intrinsically non-smooth, featuring both a stretched horizon and a boundary cutoff. The exact correlator has also been precisely reproduced from the vacuum correlators in modular quantization. We further discuss the effect of incorporating gravity by including the center via AdS/CFT on boundary correlators, for which the description of a smooth horizon is replaced by a (stretched) horizon containing explicit microstructures embedded within it.

We quantify an unusual flux-dependent systematic which is periodic in raw counts in flight data from the James Webb Space Telescope's Near Infrared Imager and Slitless Spectrograph (JWST/NIRISS), used extensively for exoplanet imaging and spectroscopy. Originally discovered in the aperture masking interferometry (AMI) mode, it also manifests in the Single Object Slitless Spectroscopy (SOSS) mode with the same dominant period of 1024 in raw analog-to-digital units (ADU). The likely cause of the signal is an analog-to-digital converter (ADC) integral nonlinearity (INL) in which case it will apply to all observations taken with the NIRISS instrument. Fortunately, it is straightforward to correct the data in postprocessing. The periodic INL is shown to be flux-dependent, increasing in amplitude with higher pixel counts on the detector. We derive a model of this periodic INL by fitting a combination of a polynomial and sinusoid multiplied with the residuals of ramp fits to the uncalibrated data and find an amplitude of 125ppm, up to a 2.5-count shift for a pixel with 20,000ADU. We apply this model to correct the well-studied NIRISS SOSS Program ERS1366 dataset of WASP-39b and reduce the data into a transmission spectrum. We find that our corrected transmission spectrum removes the INL systematic from the uncorrected spectrum at the 30ppm level across both orders, and also corrects a 55ppm offset between Order 1 and Order 2. We recommend a larger scale data-driven calibration of the periodic INL and the adoption of the outcome into NIRISS data pipelines.

The mechanism of a pressure-induced quantum critical point in the heavy fermion ferromagnet CeRh$_6$Ge$_4$ has attracted interest, as ferromagnetic quantum criticality in a clean itinerant Ce compound is typically avoided. The localized versus itinerant character of the 4\textit{f} electrons is a key aspect for understanding this behavior. We investigated the electronic structure of the 4\textit{f} shell in CeRh$_6$Ge$_4$ using core-level photoelectron and x-ray absorption spectroscopy, demonstrating the hybridization of Ce 4\textit{f} with the conduction electrons. Linearly polarized x-ray absorption reveals a temperature-dependent linear dichroism consistent with the crystal-electric-field (CEF) sequence as inferred from the static susceptibility. This dichroism cannot be described by an ionic full-multiplet model alone, but is reproduced by including the Kondo effect within a single-impurity Anderson model in the non crossing approximation (SIAM/NCA). The Kondo effect mixes higher lying crystal-field states into a resulting multiorbital ground state with 4\textit{f} occupancy \textit{n}$_f$\,$\sim$\,0.9. Deviations at low temperatures between the measured linear dichroism and calculated dichroism suggest an orbital-dependent Kondo effect. A scenario in which there is a multiorbital ground state and orbital-dependent Kondo hybridization should be a starting point for a model of pressure-induced criticality in CeRh$_6$Ge$_4$.

We explore an array of quantum emitters as non-equilibrium probes, coupled to a one-dimensional photonic waveguide, aiming to estimate its properties such as wave number which encodes the waveguide frequency and dispersive characteristics. By considering transient dynamics following initial excitation, we show that the quantum Fisher information (QFI) can be significantly enhanced through careful emitter positioning. For two-emitter probes, optimal spacing stabilizes populations and coherences in the single-excitation subspace, suppressing super radiant decay and extending both the magnitude and longevity of QFI. Randomized emitter configurations also reveal that vanishing waveguide-mediated cross decay maximizes both achievable sensitivity and the temporal duration over which information about the parameter remains accessible. Extending to multipartite probes, we demonstrate that the maximum QFI and its temporal integral scale with system size, exceeding the Heisenberg limit for all positioning strategies. Our results highlight the potential of waveguide-coupled emitter arrays as versatile quantum sensors, where collective radiative dynamics can be harnessed to achieve tunable, long-lived, and enhanced precision.

Graphene nanoribbons (GNRs) synthesized on metal substrates experience electronic coupling and screening from the underlying surface, which, although often weak, can modify their observed properties and complicate their transfer to device-compatible substrates. Intercalation of GNRs by self-assembled monolayers (SAMs) offers a possible route to reduce this interaction. Here, we investigate the intercalation of 7-atom-wide armchair graphene nanoribbons (7-AGNRs) on Au(111) using N-heterocyclic carbenes (NHCs). Low-temperature scanning tunneling microscopy and spectroscopy, Raman spectroscopy, and density functional theory calculations reveal that the adsorption geometry of the NHCs strongly influences the intercalation yield for GNRs. Methyl-substituted NHCs form flat-lying dimers that partially intercalate the GNRs, producing locally decoupled segments. In contrast, bulkier isopropyl-substituted NHCs form upright monomers that embed the GNRs within the monolayer, preventing intercalation. The low intercalation yield indicates that lifting the nanoribbon from the Au surface is energetically costly. These results establish molecular adsorption geometry and packing as key parameters controlling intercalation at GNR-metal interfaces, with implications for the rational design of decoupling layers for GNR-based device integration pathways.

The $^{12}$CO/$^{13}$CO ratio was introduced as an indicator for where in the disk a planet has formed. Previously a lower value compared to the host star's was suggested to show that a planet accreted CO ice beyond the disk's CO ice line. In this letter we aim to determine the $^{12}$CO/$^{13}$CO value of the directly imaged planet $\beta$ Pictoris b, and whether we can link it to its formation. Its apparent brightness results in an exceptional S/N of up to ~60 per wavelength point. We present the first science observations with the upgraded GRAVITY+ instrument at a spectral resolution of R ~ 4000, which we analyse with petitRADTRANS. Our retrievals robustly indicate the presence of $^{13}$CO with a $^{12}$CO/$^{13}$CO ratio of 91$^{+24}_{-17}$, consistent with both a solar to ISM-like value. Our $^{12}$CO/$^{13}$CO value corroborates recent interpretations that $^{13}$CO may be a less useful tracer of formation location in the disk than previously thought; nonetheless, we discuss theories with which this value is consistent. As our observations span ~7 hours, this enabled us to search for atmospheric variability in $\beta$ Pictoris b; we report a tentative constraint on the variability amplitude of about 1.4$^{+0.6}_{-0.7}$%.

Deep-layered machines, in which each node computes a Boolean function of all nodes below it, underpin deep learning and digital computation. Yet the statistics of their global output function remain poorly understood. We derive the exact finite-depth distribution of the output of a machine with width $k$ and depth $n$. The distribution depends only on the Hamming weight of the output, and as $n$ increases favors functions with low and high Hamming weights. But this bias peaks at a crossover depth proportional to $2^k$ before collapsing onto the constant functions true and false.

Spherically symmetric, general relativistic Bondi accretion is known as the Michel flow. The stationary integral transonic solutions for the Michel flow has been constructed for multi-component accretion described by an equation of state where the adiabatic index varies with the radial distance along which the streamlines are studied, and the corresponding phase portrait spanned by such radial distance and the flow Mach number has been obtained. Borrowing the techniques used in the dynamical systems theory, the nature of the transonic points of the aforementioned flow has been classified. The steady state flow has been perturbed to study the stability of the stationary solutions, and it has been found that such flows are stable under the (linear) radial perturbation. As a consequence of the stability analysis, the corresponding acoustic space time embedded within the accreting matter has been obtained, and the horizon of the metric of such sonic space time has been identified by constructing the causal structure with the help of the Carter-Penrose diagrams. In this way, the accreting black hole systems in the general relativistic set up has been investigated from various different perspectives - from its astrophysical aspects, from the dynamical systems point of view, as well as within the realm of the classical analogue gravity phenomena.

Neural operators provide a powerful framework for learning solution mappings of partial differential equations directly in function space. However, many existing architectures still struggle to represent nonlinear time-dependent systems that involve multi-scale structures, long-range interactions, and stable long-time evolution. In this work, we introduce the Hierarchical Adaptive Multi-scale Neural Operator (HAMNO), a neural-operator architecture that combines local convolutional representations, global spectral operators, and hierarchical encoder-decoder processing. The central component of HAMNO is a data-dependent gating mechanism that adaptively balances local and global information at each spatial location, allowing the model to resolve fine-scale features while preserving long-range dependencies. We further develop a physics-informed extension, PI-HAMNO, based on a multi-objective loss strategy that combines data fitting with strong- and weak-form physics constraints. The strong-form term penalizes the domain-integrated squared PDE residual in physical coordinates, while the weak-form term is constructed by multiplying the governing residual by finite-element test functions and evaluating the resulting element integrals using centroid-based tetrahedral quadrature. The framework is evaluated on non-periodic Allen-Cahn (AC), Cahn-Hilliard (CH), and Swift-Hohenberg (SH) equations defined on cubic domains. Across long-horizon rollout, data-limited training, out-of-distribution initial-condition shifts, and random-seed variations, HAMNO improves predictive accuracy over standard neural-operator baselines, while PI-HAMNO further enhances stability, physical consistency, and data efficiency. The implementation is publicly available at this https URL.

$g$ mode resonances in eccentric binary neutron star systems are potential probes of internal stratification, superfluidity, composition gradients, and the equation of state. Although such weak dynamical tidal signatures are unlikely to be resolved with current detector sensitivities, third generation observations may make them accessible, in which case identifying the weak resonant phase shift would provide information beyond the bulk adiabatic tidal deformability. We build a four class dataset in an eccentric harmonic framework, containing point particle, adiabatic tide, resonant $g$ mode, and pure noise samples, and use Einstein Telescope (ET) and Cosmic Explorer (CE) detector data to test whether this weak resonant phase signature can be identified from noisy time domain strain. The ET, CE, and ET+CE deep learning models reach accuracies of $0.655$, $0.815$, and $0.897$, respectively. On the same simulated samples, the matched filtering method reaches lower accuracies of $0.514$, $0.677$, and $0.689$. This result arises from the fact that the resonant correction manifests as a weak phase morphology difference superimposed on the adiabatic tidal background, whereas matched filtering is sensitive only to the overall similarity. Hence, in the presence of weak phase differences, the neural classifier employed in deep learning is better able to learn these local phase and morphology features from the complete time domain strain segment. The results indicate that joint third generation observations improve the identifiability of weak internal mode phase information.