This paper has a threefold aim. On the one hand, we provide a complete description of Laguerre-Hahn forms of class zero. This fills a gap in the literature: more precisely, up to an affine change of variables, there are ten families, including two new ones analogous to the Bessel classical family. On the other hand, we establish the structure relations for all these families, correcting those that have previously been reported in the literature. At last, as an application, using an algorithm previously obtained, with the aid of symbolic computations, we derive four new structure relations and a new fourth-order differential equation for one of the new families analogous to Bessel.

Modern high-rate experiments require rare physics signatures to be identified in real time from continuous streams of reconstructed events under stringent data-throughput and storage constraints. We present a convolutional-neural-network-based trigger concept for selecting events associated with quark-gluon plasma (QGP) formation. Events are encoded as compact multidimensional histograms of reconstructed particle content, including particle species, momentum magnitude, and angular information. The method is first evaluated within the Parton-Hadron-String Dynamics (PHSD) framework, where microscopic QGP-related labels are available. As an independent validation, the same event representation and network architecture are applied to Ultra-relativistic Quantum Molecular Dynamics (UrQMD) simulations, providing a distinct description of the collision dynamics. Cross-checks between PHSD and UrQMD are used to assess the stability of the learned response against generator-dependent effects and to quantify model-transfer robustness. For realistic deployment, a lightweight C++ inference package, ANN4FLES, is employed at the physics-analysis stage after tracking and topology reconstruction. For Au+Au collisions at 30 AGeV, the classification accuracy decreases from 95.1% on generator-level PHSD events to 83.7% after full reconstruction, while retaining practical separation power for online event selection. SHAP-based interpretability analysis is used to identify the dominant particle-species contributions to the network decision.

Cooperative multi-agent systems require robust mechanisms for credit assignment under uncertainty. Here we introduce a variational framework, termed the Game-Theoretic Free Energy Principle (GT-FEP), that models coalition formation through a Gibbs distribution over interacting agents. Within this framework, we derive a precision-dependent formulation of cooperative credit assignment and show that an agent's Shapley value exhibits a non-monotonic relationship with sensory precision beta, reflecting a trade-off between noisy inference and overconfident local estimation. Motivated by this observation, we propose Adaptive Precision Control (APC), an online adaptation algorithm that dynamically adjusts observation precision using local estimates of cooperative contribution. We evaluate APC on real-world Swiss roundabout trajectory datasets and on a multi-agent control task derived from the same trajectories. Across both settings, APC adapts to changing noise conditions online and achieves performance comparable to the best fixed precision without prior tuning. Our results connect variational inference, cooperative game theory, and adaptive multi-agent coordination, and suggest that precision adaptation can improve robust cooperation under uncertainty.

For every integer \(n\ge 3\), every \(1\le \ell\le n-2\), and every sufficiently large integer \(m\), we construct harmonic functions \(u_{m,\ell}\) on the unit ball \(B_1(0)\subset\mathbb{R}^n\) such that the frequency is bounded independently of \(m\), every point of the nodal set \(\{u_{m,\ell}=0\}\cap B_{1/2}(0)\) is regular, but the Betti numbers satisfy \begin{align*} b_\ell\bigl(\{u_{m,\ell}=0\}\cap B_{1/2}(0)\bigr)\ge 2m. \end{align*} Thus bounded frequency, even together with regularity of the nodal set, does not imply a uniform topological bound. In particular, these examples give counterexamples to the claimed global Betti-number bound of Lin and Liu.

We investigate the stability of quantum positivity cones under nonlinear operator means. Specifically, we examine how Kubo--Ando means interact with the separable, positive partial transpose (PPT), and Schmidt-number cones. By analyzing the curvature of operator monotone functions at the identity, we give a strict rigidity phenomenon: weighted arithmetic means are the only Kubo--Ando means that preserve the separable cone in all dimensions. We show that the strictly positive curvature of any non-arithmetic mean explicitly forces a violation of the PPT condition, even in the foundational two-qubit setting, and can strictly increase the Schmidt number of the resulting operator. Finally, using the Choi--Jamiołkowski correspondence, we translate these geometric obstructions to the map-theoretic setting, concluding that convex mixing is the uniquely permissible Kubo--Ando operation for preserving entanglement-breaking quantum channels.

Recent experiments on graphene multilayers under displacement field have demonstrated a wide variety of electronically ordered phases, including valley and/or spin polarized phases as well as potentially unconventional superconducting phases. In addition, quantum oscillation measurements in Bernal bilayer graphene and rhombohedral trilayer graphene showed the presence of electronic nematic states. Here, we investigate the emergence of nematic order in these systems, with emphasis on Bernal bilayer graphene, within a self-consistent Hartree--Fock framework, using a realistic band structure with trigonal warping and a dual-gate screened Coulomb interaction. We compute the phase diagram as carrier density and displacement field are varied, and find a sequence of isospin (spin and valley) polarized states consistent with experiment, including partially polarized phases with a large Fermi pockets for isospin-majority carriers and smaller Fermi pockets for isospin-minority carriers. Within these partially isospin polarized states, we identify regions with three $C_3$-symmetric pockets for the minority carriers and regions with only one or two such pockets, implying that the system develops a spontaneous nematic order that breaks $C_3$ symmetry. We find numerically that nematicity emerges near the boundary between fully and partially polarized phases and is controlled by the strength of the screened interaction. We analytically derive a criterion for the nematic order, which agrees with our numerical results.

LLM agents process trusted instructions, retrieved records, and tool observations through a common generative channel. This conflates data flow with authority: an untrusted string can affect a secret-bearing response or an action proposal even when no application policy authorizes that influence. We introduce AgentSecBench as an empirical instantiation of a formal security framework for this problem. The framework defines three games-instruction-integrity, retrieval-confidentiality, and capability-integrity-under a common notion of intent-to-execution noninterference with permitted leakage. It represents an application policy as a projection onto authorized observations and capabilities, distinguishes prompt annotations from enforcing projections, and measures both adversarial advantage and whether a defense closes the relevant model-visible channel before generation. The exact-marker experiments are intentionally one observable instantiation of the games rather than a complete semantic security claim: they test disclosure and forbidden-action distinguishers with unambiguous ground truth. We evaluate six defense classes with Qwen3-0.6B and Qwen3-1.7B on paired adversarial and benign-control executions. The measurements show when risk reduction follows channel closure and when a model-visible adversarial capability remains exploitable. The result is a security-oriented evaluation method: prompt text can describe a boundary, whereas provenance projection, capability restriction, and output validation can enforce one.

As CMOS technology scales down, thermal fluctuations increasingly impact circuit behavior, posing challenges to conventional circuit design. However, the inherent stochasticity introduced by thermal noise is now being explored as a potential resource in the emerging field of probabilistic computing. This work presents a fully CMOS experimental platform that enables direct control over its intrinsic thermal fluctuations. These devices function as programmable multivariate Gaussian samplers, offering a hardware primitive for energy-efficient stochastic computing and serving as an experimental platform for studies in electronic noise and stochastic thermodynamics.

We investigate solar X-ray observations as a probe of axions and axion-like particles. These particles can be produced in the interior of the Sun via the conversion of thermal photons, as well as through processes involving axion-electron and axion-nucleon interactions. The resulting axions can then reconvert into photons in the Sun's atmospheric magnetic field, generating a signal in the X-ray energy range. In this work, we derive new limits on axions using X-ray observations with the Nuclear Spectroscopic Telescope Array (NuSTAR) during the 2020 solar minimum. In the regime where ALP production is dominated by couplings to electrons or nucleons, we obtain bounds on the product of couplings $g_{ae}\cdot g_{aγ}\lesssim 1.1\times10^{-24}\,\rm GeV^{-1}$ and $g_{aN}^{\rm eff}\cdot g_{aγ}\lesssim 2.3\times 10^{-19}\,\rm GeV^{-1}$ at 95% CL, for axion masses $m_a\lesssim10^{-6}\,\rm eV$. These constraints strongly improve current ground-based experimental limits, establishing solar X-ray observations as a powerful and robust method for axion searches.

We establish uncertainty principles on compact Riemannian manifolds without boundary by combining restriction estimates for orthonormal systems with spectral projection bounds for Laplace-Beltrami and Schrödinger operators. Our results relate the size of the support of spectrally localized functions to the cardinality of the underlying spectral cluster and to Fourier-ratio type quantities. We obtain analogues for Schrödinger operators with singular potentials belonging to Kato and scaling-critical classes. As an application, we prove uniqueness results for recovery from incomplete spectral data on compact manifolds. Under curvature assumptions, including nonpositive and negative sectional curvatures, we also prove logarithmically improved uncertainty principles associated with shrinking spectral windows.

Let $\mathbb{F}_q$ denote the finite field of order $q$. For $q$ odd, we investigate the planarity over $\mathbb{F}_{q^3}$ of the family $$ f_{E,A,B,C,D}(X) := EX^2+ AX^{q+1}+ BX^{q^2+1}+CX^{2q} +DX^{2q^2}\in \mathbb{F}_{q}[X]. $$ Using results from the theory of q-polynomials, we establish conditions under which these polynomials are planar functions. In particular, we provide characterizations for the planarity property and present new families of planar trinomials, quadrinomials, and pentanomials.

We present a GPU implementation of the finite-temperature Lanczos method (FTLM) for Heisenberg spin Hamiltonians that targets workstation hardware rather than distributed-memory clusters. The Hamiltonian action is evaluated matrix-free in a row-wise gather formulation. We introduce and compare two state-to-index strategies: a compressed lookup table (CLT), which reduces lookup memory by a factor of 16 relative to a full table while retaining a fixed, branch-light access pattern, and a GPU-adapted combinatorial-ranking scheme that removes the lookup table altogether. Numerical tests against FP64 CPU references show that FP32 GPU arithmetic changes heat capacities and magnetic susceptibilities by amounts several orders of magnitude below the stochastic uncertainty of the FTLM trace estimator at typical sample sizes. Benchmarks show speedups of up to about one order of magnitude over optimized multicore CPU calculations and enable Hilbert-space sectors of dimension ~10^8 on a single workstation GPU. The MATLAB/CUDA implementation, including example input files and benchmark scripts, is openly available at https://github.com/ghasdeke/ftlm-gpu (archived at DOI: 10.5281/zenodo.20378647) under the Apache-2.0 license.

Composite optimization problems, where a smooth loss is combined with a nonsmooth regularizer, are common in machine learning and inverse problems. In this work, we study a proximal extension of NAG-GS, a semi-implicit accelerated method obtained from a Gauss-Seidel discretization of an inertial dynamics. The proposed method, called Prox-NAG-GS, keeps the coupled structure of NAG-GS for the smooth part and replaces the second update by a proximal step. It therefore applies to objectives of the form $F=f+r$, where $f$ is smooth and $r$ is convex and proximable. We derive deterministic convergence guarantees for this method. The analysis has to account for a specific feature of the scheme. Prox-NAG-GS keeps two coupled sequences: an $x$-sequence, on which the gradient of the smooth term is evaluated, and a $v$-sequence, produced by the proximal update. The gradient is evaluated at $x_{k+1}$, whereas the proximal step returns $v_{k+1}$, which creates a mismatch absent from the standard proximal-gradient analysis. Under the sufficient condition that the proximal quadratic parameter is at least as large as the smoothness constant of $f$, we control this mismatch through an augmented Lyapunov function involving both sequences. This gives a linear convergence result in the strongly convex composite case. In the convex case, the same Lyapunov structure yields an $O(1/k)$ rate for the best iterate and for the averaged iterate. We test the method on deterministic Elastic Net and Group Lasso problems, and on stochastic sparse softmax-regression benchmarks. In the deterministic tests, Prox-NAG-GS reaches the same solutions as the baselines with substantially fewer iterations; for Group Lasso this also gives the best wall-clock time. In the stochastic tests, Prox-NAG-GS compares favorably with Prox-SGD in terms of data-fit reduction and gives similar test accuracies.

H. Fujimoto showed that for a complete minimal surface in $\mathbb{R}^m$, if the Gauss map is non-degenerate, then it omits at most $\frac{m(m + 1)}{2}$ hyperplanes in the complex projective space $\mathbb{P}^{m - 1}$ in general position, and that the number $\frac{m(m + 1)}{2}$ is best possible for all odd integers $m \geq 3$ and for even integers with $4 \leq m \leq 16$. In this paper, we prove that the number $\frac{m(m + 1)}{2}$ is also best possible for all even integers $m \geq 4$, as conjectured by Fujimoto. The main tool is a special planar network $(Γ_0, ω)$ in the theory of positive matrices.

In recent years, increasing aerospace safety requirements have intensified the demand for reliable structural damage detection. This work presents an Operational Modal Analysis approach for accurate modal parameter estimation, with an application to space structure monitoring. The proposed System Identification (SI) method innovatively combines the Natural Excitation Technique (NExT) with the Fast and Relaxed Vector Fitting (FRVF) algorithm, which uses an iterative least-squares optimisation. A preliminary validation is first carried out on a numerical beam model, comparing results with analytical solutions and the established Natural Excitation Technique with Eigensystem Realisation Algorithm (NExT-ERA) and Stochastic Subspace Identification with Canonical Variate Analysis (SSI) methods. Then, operational validation is performed on real acceleration data from the Space Acceleration Measurement Systems aboard the International Space Station. Identified vibration modes from NExT-FRVF and NExT-ERA show comparable results after signal processing, with mode consistency assessed by repeated occurrence and physical interpretation, while SSI fails to identify most. The output-only algorithm proves to be highly reliable, outperforming benchmark methods under noisy conditions on a numerical system and offering reliable identifications on the experimental data.

This paper proposes a systematic framework to assess the small-signal stability of power systems with high shares of grid-following inverter-based resources (IBRs) under varying controller parameters and operating conditions. Stability manifolds are introduced to identify controller-parameter regions that ensure stability across multiple scenarios. Full-network linearization and eigenvalue analysis are combined with adaptive sampling based on probabilistic support vector machine classification to approximate stability boundaries efficiently, while surrogate optimization identifies feasible initial controller settings meeting bandwidth and phase-margin constraints. The approach is validated on a modified Cigré European HV network benchmark with 50 operating scenarios and increasing inverter penetration. Results show that stability sensitivity grows with inverter share, interactions among IBRs reshape admissible parameter regions, and simplified equivalent-network models may overlook critical system-level limitations. The framework supports stability-oriented controller design and interconnection studies in converter-dominated systems.

Length-biased distributions arise naturally in environmental, reliability, and economic studies where the sampling mechanism favors larger observational units. In this paper, we propose a quantile regression model based on the length-biased Birnbaum--Saunders (QLBS) distribution. The model is constructed through a reparameterization of the length-biased Birnbaum--Saunders distribution in terms of its quantile function, thereby allowing direct interpretation of covariate effects on conditional quantiles of the response variable. We derive the log-likelihood function and the corresponding score equations, and obtain maximum likelihood estimators via numerical optimization. Asymptotic and bootstrap confidence intervals are considered. Two types of residuals are proposed for model assessment, namely the generalized Cox--Snell and randomized quantile residuals. An elaborate Monte Carlo simulation study is carried out to evaluate the performance of the maximum likelihood estimators for several sample sizes and quantile levels. The proposed methodology is illustrated with a real meteorological data set from Brazil.

Compound-refractive lenses (CRL) are a type of x-ray optics that find widespread applications as focusing and imaging lenses. The choice of material is one of the most defining properties of these lenses. In this work, we present a CRL made out of diamond. It provides an advantageous balance between refractivity and absorption, along with good manufacturability. Compared to Be CRLs, it features a higher optical density and thus enables application at higher photon energies without relying on large lens stacks or very small radii of curvature, which are challenging to manufacture. A diamond CRL is characterized for use as an objective for Dark-field X-ray Microscopy (DFXM) at the ID03 beamline of the European Synchrotron Radiation Facility (ESRF) and compared to Al and Be CRLs at 17 keV, 33 keV and 37 keV. Increasing the photon energy in DFXM from 17 keV to 37 keV opens up the possibility to investigate new sample systems, that were previously opaque to low energy x-ray radiation. The capability of the diamond CRL at 33 keV is illustrated through DFXM measurements on two 0.5 mm-thick iron-based samples, which cannot be probed at 17 keV.

We study Krylov construction in periodically driven conformal field theories and their lattice realisations via critical fermions. Two types of driving are considered: a square-wave drive and a continuous sinusoidal drive. Using the Arnoldi construction, we examine Arnoldi coefficients and return amplitudes in periodically driven conformal field theories in the heating and non-heating phases. In the heating phase, the Arnoldi coefficients approach unity exponentially; in contrast, in the non-heating phase, they exhibit oscillatory behaviour. For the lattice realisations, we further analyse the Krylov complexity of the correlation matrix, quasi energy level statistics, and the graph structure induced by the Floquet operator. Although the two drives exhibit similar Krylov growth on the CFT side, their lattice realisations exhibit markedly different spectral and graph signatures, indicating distinct mechanisms governing the transition between the heating and non-heating phases.

Future wireless systems are expected to employ extremely large-scale multiple-input multiple-output (XL-MIMO) arrays at high carrier frequencies, where near-field propagation makes the channel depend jointly on angle and distance. The resulting short coherence intervals make channel state information acquisition challenging, motivating blind channel estimation and data detection (B-CE-DD). In this paper, we propose a two-stage B-CE-DD framework for uplink near-field XL-MIMO systems. First, we formulate the problem as the recovery of user-specific rank-one channel-data products from a superimposed received signal using a polar-domain sparse channel model and a low-dimensional data subspace model. Building on this formulation, we develop an on-grid blind orthogonal matching pursuit (B-OMP) algorithm that exploits polar-domain sparsity to iteratively identify the dominant angle-distance components and estimate the corresponding channel-data products, followed by an off-grid refinement stage based on block-coordinate descent (BCD) that optimizes the angle and distance parameters in the continuous polar domain. Numerical results show that the proposed B-CE-DD framework combining B-OMP and BCD significantly improves the symbol error rate compared with a pilot-based baseline employing zero-forcing beamforming, particularly at low signal-to-noise ratio and when the number of data symbols is small relative to the length of the coherence interval.

In networks with intermittent connectivity, such as mobile, aerial, and space systems, maintaining information freshness is complicated by time-varying arrivals, service disruptions, and interactions among traffic classes with different priorities. To capture these effects, we study a multi-priority single-server queue with time-varying arrivals and service rates under intermittent connectivity. Our main result shows that an appropriately selected collection of state-conditioned first moments closes exactly, leading to a finite-dimensional linear time-periodic Ordinary Differential Equation (ODE) system for the mean Age of Information (AoI) and mean Peak Age of Information (PAoI) of each priority class. For periodic arrival and service rates, we define a one-period state map by propagating the ODE over a single period, and use the periodicity condition to formulate the periodic steady state as a fixed point of this map. We then propose a fixed-point iteration algorithm and prove its convergence to the unique periodic steady state (PSS). Numerical results reveal that high-priority traffic can strongly reshape the service process seen by lower-priority classes.

Finite-temperature properties of strongly correlated quantum matter are central to condensed matter, chemistry, and high-energy physics, yet are often inaccessible to classical methods such as quantum Monte Carlo (QMC). Here, we investigate dissipative thermal state preparation of frustrated spin systems using digital quantum computers. We focus on two paradigmatic models on the kagome lattice: the antiferromagnetic Heisenberg model (AFHM), whose finite-temperature properties are inaccessible to QMC due to a severe sign problem, and the antiferromagnetic Ising model (AFIM), which serves as a sign-problem-free benchmark. Using IBM quantum processors, we prepare approximate thermal states of the AFIM on kagome lattices with up to $79$ spins coupled to $60$ environment qubits. We observe the emergence of a robust steady state with an adjustable effective temperature that persists in circuits with over 1000 layers of two-qubit gates. We further study the scalability of the dissipative protocol through classical statevector simulations of the AFIM and AFHM. On lattices with up to 24 sites, we find that the circuit depth to reach thermal equilibrium is independent of system size and grows at most linearly with inverse temperature. These results establish engineered dissipation as a promising approach to finite-temperature quantum simulation of frustrated matter, and point toward regimes where quantum devices may outperform classical methods.

We investigate gravity-induced entanglement between the output optical fields of two red-detuned pulsed optomechanical systems with their masses coupled by mutual gravitational interaction. For each individual system, the optomechanical interaction realizes a beam-splitter state swap between an incident optical pulse and its mechanical mode. Using two rectangular pulses for each system -- the first to imprint a nonclassical state on the mechanical modes and the second to read the gravitationally generated entanglement back onto the outgoing light -- we show that the amount of entanglement can be amplified by preparing the input in a squeezed or Fock state. However, the threshold for entanglement generation is set by the competition between the gravitational coupling and thermal decoherence, $g_G>2γ_m N_{\rm th}$, and cannot be lowered by any choice of input state. We prove this bound for two-mode Gaussian inputs and show that it continues to hold for Fock-state inputs. We further analyze how imperfect detection modifies the threshold and identify the entanglement-annihilating and entanglement-breaking regimes, which are set by the thermal decoherence accumulated over the interaction time, independent of the gravitational coupling.

We introduce modular inequalities for complements of plane curves, based on a Combinatorial Aomoto complex construction associated with the weak combinatorial type of a curve. We use this as a tool to investigate twisted Alexander polynomials, in particular to study the characteristic polynomial of the Milnor fiber associated to a projective plane curve, i.e. the classical Alexander polynomial. We give criteria for the non-triviality of the resonance in degree $1$, over a positive characteristic field, for curves with quasi fiber--type structure and we compute lower bounds for the multiplicities of some roots of twisted Alexander polynomials for this type of curves. We apply these results to theoretically compute the multiplicities of certain roots of twisted Alexander polynomials for fiber--type curves.

Identifying dense subgraphs known as quasi-cliques is pivotal in numerous graph mining tasks across domains such as social networks, biology, and e-commerce. While prior work has developed efficient algorithms for quasi-clique detection in static graphs, real-world networks are inherently dynamic, where edges appear and disappear continuously. This renders static methods inefficient and ill-suited for real-time analysis. In this paper, we initiate the study of the Dynamic Maximum Quasi-Clique Problem (DMQCP), which aims to maintain and update the largest quasi-clique in a graph under streaming graph updates. We propose DMI, a novel MinHash-based dynamic framework that supports fast, high-quality approximate maintenance of quasi-cliques. DMI leverages two update-efficient hashing schemes, i.e., $l$-buffered $k$-MinHash and Bottom-$k$ MinHash, to maintain candidate quasi-cliques incrementally. To ensure robustness and reduce bias, we further design a batch reconstruction strategy to periodically rebuild the candidate set, guaranteeing both stability and adaptability under frequent updates. Extensive experiments on real-world and synthetic datasets show that DMI achieves up to four orders of magnitude speedup over static baselines, while preserving solution quality. As a side product, we also propose a framework NSF that primarily uses the neighbor-search technique to maintain quasi-clique candidates while edge updating. This work establishes the first efficient algorithmic framework for dynamic quasi-clique extraction, enabling scalable and real-time dense subgraph mining in evolving networks.

We study the emergence of superconductivity in the one-band Hubbard model using the spin-rotation-invariant Kotliar-Ruckenstein slave-boson (SB) approach. Motivated by its intrinsically renormalized mean-field ground state, we construct an effective pairing vertex from dynamical fluctuations about the saddle point. Solving the anisotropic, frequency-dependent gap equation on the square lattice, we map the pairing instabilities across doping, interaction, temperature and real-frequency gap structure that qualitatively match experimental cuprate observations. This framework merges strong-correlation SB-type renormalizations with RPA-type pairing transparency, providing a scalable route to modeling multi-orbital superconductivity at strong coupling.

We use cyclic spectroscopy to directly measure the scintillation parameter $C_1$ for the millisecond pulsar B1937+21. This marks the first time this constant has been measured for any pulsar without assuming a pulse broadening function shape prior to deconvolution from the intrinsic pulse profile, removing significant potential biases in scattering delay estimation and letting us consider a wider range of line of sight geometries. At 428 MHz, we find an aggregate weighted mean and standard deviation of $C_1=1.18\pm0.01$, which, along with the presence of scintillation arcs, indicates a thick screen geometry spanning just over 10% of the Earth-pulsar distance. The resulting precision in our weighted average allows us to rule out various thin screen geometries, as well as thick screen geometries comprising more than 30% of the Earth-pulsar distance, with greater than $5σ$ certainty at this observing frequency. We also use our measured $C_1$ values to determine diffraction scales, which we find to be roughly 11$\times10^3$ km between 418$-$438 MHz, suggesting an inner scale on the order of $10^3$ km. Future implementations of our method to other lines of sight through the galaxy may substantially improve efforts to understand structures that contribute to the majority of pulsar emission scattering in the interstellar medium. As flagship instruments like the Green Bank Telescope begin offering the use of cyclic spectroscopy backends, and other instruments begin exploration and commissioning of similar systems, demonstrations like these will be crucial for the widespread adoption of cyclic spectroscopy.

Heavy scalar fields ($m_ϕ\gtrsim10^{-9}$ eV) in scalar-tensor gravity are expected to be hidden from neutron-star observations because their Compton wavelength is sub-stellar. We show that neutron stars can nevertheless scalarize by forming a shell-localized profile, suppressed at their center and exterior but peaked in their interior. This \emph{donutization} reshapes the effective equation of state, making hadronic stars mimic quark-star mass-radius behavior or hybrid-star behavior with split stable branches, and breaks the $I$--$Q$ relation, while remaining hidden from binary pulsar observations.

A parametrically driven classical harmonic oscillator exhibits resonant instability when driven at twice its natural frequency, with the lowest energy configuration remaining unaffected by the drive. In contrast, the ground state of the quantum mechanical counterpart shows a non-trivial response to such a drive due to the spatial delocalization of the wavefunction. The standard realization of PR involves modulating the natural frequency of the oscillator. Here we study a different drive protocol in which the coupling between two such quantum harmonic oscillators is modulated parametrically. We show that the drive frequency can in principle be tuned to selectively excite any desired normal mode, while leaving the other close to its ground state. Only states with even quantum numbers in each normal mode are populated. Within the parametric resonance window the excitations follow a power-law decay with respect to occupation number, in contrast to the exponential decay observed off-resonance. We also briefly discuss how this framework can be extended to a system of N coupled oscillators

We develop a Schwinger--Keldysh effective theory for quantum-interference corrections in a two-dimensional electron system in the hydrodynamic regime. Starting from the clean hydrodynamic fixed point, we introduce a minimal random-friction disorder model that generates a finite momentum-relaxation time within the self-consistent Born approximation. The disorder-averaged theory then allows us to construct a hydrodynamic Cooperon and to compute the associated self-energy corrections to the collective modes. Conservation laws protect the density and momentum sectors, so that the leading quantum-coherence correction is forced into the spin-two stress sector. The associated stress self-energy renormalizes the shear viscosity and modifies both the Gurzhi response and its low-field magnetohydrodynamic signatures.