The quantum geometric tensor (QGT), whose real and imaginary parts define the quantum metric and Berry curvature, encodes the intrinsic geometry of quantum states. While electronic QGT has recently become experimentally accessible and linked to diverse physical phenomena, its bosonic counterpart remains largely unexplored. Here we show that the dynamical structure factor encodes the momentum-space structure of bosonic wave functions and thereby provides direct access to the full bosonic QGT throughout the Brillouin zone. Applying this framework, we uncover clear geometric signatures in the twofold quadrupole-Weyl phonon of BaPtGe and the nodal-line magnon in Gd, and further generalize the formalism to multiband systems. Our results establish a general route to measuring (non-)Abelian quantum geometry in bosonic systems, a crucial step toward elucidating its impact on condensed matter phenomena.

Superconductivity has been observed for the 2D electron gas (2DEG) at the interface of KTaO3 with other oxides, with a transition temperature about an order of magnitude higher than its 3d cousin SrTiO3. The superconducting transition temperature is strongly dependent on the orientation of the interface. Motivated by this observation, we study pairing due to exchange of the soft transverse optic phonon mode characteristic of quantum paraelectrics and use the resulting theory to comment on the nature of superconductivity of this 2DEG. We find (1) an orientation dependence consistent with experiment along with an anisotropic gap function, but (2) a BCS coupling constant that is smaller than needed and so must be augmented by contributions from other phonons to be consistent with the observed values of Tc.

In this paper, we present a general framework for constructively proving the existence and stability of stationary localized 1D solutions and saddle-node bifurcations in activator--inhibitor systems using computer-assisted proofs. Specifically, we develop the necessary analysis to compute explicit upper bounds required in a Newton--Kantorovich approach. Given an approximate solution $\bar{\mathbf{u}}$, this approach relies on establishing that a well-chosen fixed point map is contracting on a neighborhood $\bar{\mathbf{u}}$. For this matter, we construct an approximate inverse of the linearization around $\bar{\mathbf{u}}$, and establish sufficient conditions under which the contraction is achieved. This provides a framework for which computer-assisted analysis can be applied to verify the existence and local uniqueness of solutions in a vicinity of $\bar{\mathbf{u}}$, and control the linearization around $\bar{\mathbf{u}}$. Furthermore, we extend the method to rigorously establish saddle-node bifurcations of localized solutions for the same type of models, by considering a well--chosen zero--finding problem. This depends on the rigorous control of the spectrum of the linearization around the bifurcation point. Finally, we demonstrate the effectiveness of the framework by proving the existence and stability of multiple steady-state patterns in various activator--inhibitor systems, as well as a saddle--node bifurcation in the Glycolysis model.

In this article, we introduce a novel low-altitude wireless network (LAWN), which is a reconfigurable, three-dimensional (3D) layered architecture. In particular, the LAWN integrates connectivity, sensing, control, and computing across aerial and terrestrial nodes that enable seamless operation in complex, dynamic, and mission-critical environments. Different from the conventional aerial communication systems, LAWN's distinctive feature is its tight integration of functional planes in which multiple functionalities continually reshape themselves to operate safely and efficiently in the low-altitude sky. With the LAWN, we discuss several enabling technologies, such as integrated sensing and communication (ISAC), semantic communication, and fully-actuated control systems. Finally, we identify potential applications and key cross-layer challenges. This article offers a comprehensive roadmap for future research and development in the low-altitude airspace.

This paper investigates the inflationary dynamics of a $β$-exponential potential model within the framework of non-minimally coupled quadratic $(R+R^2)$ gravity. The functional form of the adopted potential provides a well-motivated framework; its physical origin can be interpreted either as the stabilization dynamics of a radion field determining the size of the extra dimension in braneworld cosmology, or as a manifestation of the $q$-exponential function emerging naturally from Tsallis non-extensive thermodynamics. Utilizing the Palatini formalism, we derive an effective Einstein-frame generalized k-inflation theory and analyze its evolution under the constant-roll condition. We perform a comprehensive scan of the parameter space to obtain predictions for the spectral index $n_s$ and the tensor-to-scalar ratio $r$. Our results demonstrate that for specific viable ranges of the model parameters, the inflationary observables are in excellent agreement with the latest observational data from the Atacama Cosmology Telescope (ACT) DR6 and the Planck mission, thereby identifying the physically consistent regions of the parameter space. Furthermore, an evaluation of the primordial non-Gaussianity confirms that the constant-roll dynamics generate a distinct, observationally viable phenomenological signature.

In this paper, we relate $L(1,π,\mathrm{Ad}^\circ)$ to the congruence ideals for cohomological cuspidal automorphic representations $π$ of $\mathrm{GL}_n$ over any number field. We then use this result to deduce relationships between the congruences of automorphic forms and adjoint $L$-functions. For CM and totally real fields, we apply the result to obtain a lower bound on the cardinality of certain Selmer groups in terms of $L(1,π,\mathrm{Ad}^\circ)$.

Quirks are heavy particles connected by a flux tube from a hidden confining force that remain weakly constrained in large regions of their parameter space. This flux tube acts as a string that, at short enough distance, stretches as the quirk pair separates, then pulls the pair back together leading to interesting dynamics. We propose a novel search using the LHCb Vertex Locator (VELO), whose forward geometry and software-based trigger are uniquely suited to detecting the characteristic back-to-back, planar hit patterns produced by quirk pairs with little transverse recoil. Using detailed simulations of the VELO geometry, together with simple geometric selections, we present different sensitivity projections, demonstrating that LHCb can probe parameter regions inaccessible to existing ATLAS and CMS searches and offering a powerful, complementary path toward discovering quirks.

The so-called $I$-Love-$Q$ relations link some normalized versions of the moment of inertia, the Love number, and the quadrupole moment of a star. These relations, in principle, enable the inference of two of the quantities given the third. However, their use has been limited because the normalized versions of the multipole moments rely on the static mass derived from the Tolman-Oppenheimer-Volkoff equation, which is not directly observable. In this work, using perturbation theory, we find that the $I$-Love-$Q$ relations can also be formulated in terms of an alternative set of normalized quantities that do not depend on the static mass, but on the actual (observable) mass.

A physics-constrained Gaussian Process regression framework is developed for predicting shocked material states and their associated uncertainties along the Hugoniot curve using data from a small number of shockwave simulations. The proposed Gaussian process is constrained by the Rankine-Hugoniot jump conditions between the various shocked material states to construct a thermodynamically consistent covariance function. This leads to the formulation of an optimization problem over a small number of interpretable hyperparameters and enables the identification of regime transitions, from a leading elastic wave to trailing plastic and phase transformation waves. Shock Hugoniots are an important measure for understanding material behavior under extreme conditions, including for the development of equations of state and determining material properties such as the Hugoniot Elastic Limit, but they are costly to generate through large-scale molecular dynamics simulations or shock experiments. Under these constraints, the proposed methodology establishes Hugoniot curves from a limited number of molecular dynamics simulations. We consider silicon carbide as a representative material and Molecular Dynamics simulations are performed using a reverse ballistic approach. The framework reproduces the Hugoniot curve with satisfactory accuracy while also quantifying the uncertainty in the predictions using the Gaussian Process posterior. These uncertain Hugoniot predictions can then be used to calibrate equation of state models, estimate material properties, or inform future experimental and/or simulation campaigns.

We provide a new existence result for abstract nonlinear operator systems in normed spaces, by means of topological methods. The solution is located within the product of annular regions and conical shells. The theoretical result possesses a wide range of applicability, which, for concreteness, we illustrate in the context of systems of nonlinear Poisson equations subject to homogeneous Dirichlet boundary conditions. For the latter problem we obtain existence and localization of solutions having all components nontrivial. This is also illustrated with an explicit example in which we also furnish a numerically approximated solution, consistent with the theoretical results. We conclude with an application of our results to a reaction--diffusion Lotka--Volterra system with source terms for competing species.

We present the first assessment of the Ali Cosmic Microwave Background Polarization Telescope's (AliCPT) sensitivity to the reheating epoch after cosmic inflation, based on its ability to detect primordial gravitational waves. We consider three models of inflation, an $α$-attractor T-model, RGI inflation and QCD-driven warm inflation. Assuming a fiducial value of $r=0.01$, we find that AliCPT-1, in its fully loaded focal plane detector configuration and combined with Planck, can provide measurements of the order of magnitude of the reheating temperature with an accuracy around $10\%$. For QCD-driven warm inflation this can be translated into a constraint on the inflaton coupling to gluons, which can be probed independently in axion search experiments. Our results constitute the first demonstration of AliCPT's ability to probe the initial temperature of the hot big bang and the microphysical parameter connecting cosmic inflation and particle physics.

We present a complete analytic and semi-analytic study of gravitational collapse and primordial black hole (PBH) formation in the quadratic $f(R)$ model $f(R)=R+αR^2$. We first derive the perturbative expansion around General Relativity (GR), working to first order in the small parameter $α$. For a collapsing flat FLRW dust interior we compute the explicit first-order corrections to the scale factor, the stellar radius, and the horizon formation time. { We then use these results to infer the expected trend in the PBH formation threshold $δ_c$, rather than a direct quantitative determination. Within this perturbative framework, the quadratic correction modifies the dust collapse dynamics at first order, while the flat radiation-dominated background does not receive a nontrivial correction at the same order. As result, any modification of PBH formation in the radiation era must arise from nonlinear or non-perturbative effects. The perturbative analysis therefore provides qualitative insight into how curvature corrections influence collapse, particularly in high-curvature regimes.} To access this regime we reformulate the theory in the Einstein frame, where the model becomes GR plus the scalaron field $ϕ$ with the Starobinsky potential. We provide the complete ODE system governing both the cosmological background and the evolution of an overdense closed FLRW patch. This system can be numerically integrated to obtain the critical overdensity $δ_c(k)$ for PBH formation near the end of inflation.

We study equal-time in-in correlators of massless scalar fields in flat space at one loop. Using the time-ordered decomposition of correlators together with a cosmological analogue of the Baikov representation, we systematically construct relatively simple loop integrals and make manifest why, in this setting, loop corrections to correlators are simpler than those of wavefunction coefficients. As benchmark examples, we analyse the bubble and triangle diagrams. The bubble exhibits a UV divergence that can be removed by a local counterterm, while the triangle yields a finite result, which we evaluate explicitly in terms of dilogarithms using an integral transform for the Laplacian Green's function. We classify the kinematic singularities of these diagrams using Landau analysis, identifying novel types of singular behaviour, and validate this analysis against the explicit results. Finally, we derive a factorisation property of one-loop cosmological correlators at singular kinematics, relating them to flat-space loop amplitudes and lower-point tree-level correlators.

We have previously shown that Good-Turing statistics can be applied to molecular dynamics trajectories to estimate the probability of observing completely new (thus far unobserved) biomolecular structures, and showed that the method is stable, dependable and its predictions verifiable. The major problem with that initial algorithm was the requirement for calculating and storing in memory the two-dimensional RMSD matrix of the currently available trajectory. This requirement precluded the application of the method to very long simulations. Here we describe a new variant of the Good-Turing algorithm whose memory requirements scale linearly with the number of structures in the trajectory, making it suitable even for extremely long simulations. We show that the new method gives essentially identical results with the older implementation, and present results obtained from trajectories containing up to 22 million structures. A computer program implementing the new algorithm is available from standard repositories.

This book is a rigorous and conceptually oriented introduction to ring theory. The emphasis is on structural understanding rather than encyclopedic coverage: rings are studied through ideals, homomorphisms, quotients, and universal properties, with systematic attention to factorization and polynomial rings. Core topics include Euclidean domains, principal ideal domains, unique factorization domains, the Chinese Remainder Theorem, and the structure of polynomial rings. The exposition is proof-based and deliberately paced, with review chapters that consolidate core ideas and include selected worked solutions, and with exercises designed to reinforce conceptual insight.

Super-Kamiokande (SK) has observed $^{8}\text{B}$ solar neutrino elastic scattering at recoil electron kinetic energies ($E_{\text{kin}}$) as low as 3.49 MeV to study neutrino flavor conversion within the Sun. At SK-observable energies, these conversions are dominated by the Mikheyev-Smirnov-Wolfenstein (MSW) effect. An upturn in the electron neutrino survival probability in which vacuum neutrino oscillations become dominant is predicted to occur at lower energies, but radioactive background increases exponentially with decreasing energy. New machine learning approaches provide substantial background reduction below 3.49 MeV such that statistical extraction of solar neutrino interactions becomes feasible. This article presents an analysis of the solar neutrino interaction rate at $E_{\text{kin}}$ < 3.49 MeV with the full SK-IV period, using data from a wideband intelligent trigger when available and with a boosted decision tree for event selection. A solar neutrino signal is observed between 2.99 MeV < $E_{\text{kin}}$ < 3.49 MeV with $2.76σ$ significance and a data to unoscillated Monte Carlo ratio of $0.307^{+0.112}_{-0.111}$. These additional low-energy data have a negligible effect on the $1σ$ intervals of the fits to the solar neutrino energy spectrum but have a noticeable effect on the best fit when using the exponential parametrization.

Heterogeneity in efficacy is sometimes observed across baskets in basket trials. In this study, we propose a model-free clustering framework that groups baskets based on transition probabilities derived from the trajectories of treatment response, rather than relying solely on a single efficacy endpoint such as the objective response rate. The number of clusters is not predetermined but is automatically determined in a data-driven manner based on the similarity structure among baskets. After clustering, baskets within the same cluster are analyzed using a hierarchical Bayesian model. This framework aims to improve the estimation precision of efficacy endpoints and enhance statistical power while maintaining the type~I error rate at the nominal level. The performance of the proposed method was evaluated through simulation studies. The results demonstrated that the proposed method can accurately identify cluster structures in heterogeneous settings and, even under such conditions, maintain the type~I error rate at the nominal level while improving statistical power.

Paced finger-tapping tasks are used to probe the error correction mechanism underlying sensorimotor synchronization. Despite their century-long history, fundamental contradictions persist in the literature. One such contradiction arises when comparing the two most common types of period perturbation: step change and phase shift. The stimulus sequence is exactly the same up to and including the (unexpected) perturbed stimulus. Why then would the timing of the next response be different between perturbation types, as observed? We show, both experimentally and theoretically, that responses to both types of perturbation are dynamically incompatible when recorded in separate experiments; that is, they cannot be described by a single underlying dynamical system due to the build-up of different temporal contexts. In contrast, when both types of perturbation are presented randomly within the same experiment, the responses become compatible and can be explained by a single mechanism. We conclude that a single underlying dynamical system can represent the response to all perturbation types, signs, and sizes, which is nevertheless calibrated by temporal context. Our results challenge the established idea of phase and period correction processes that are separately activated for different perturbation types.

We present a unified framework for non-singular bouncing cosmologies in modified gravity, combining $f(R,G,T)$ geometry with quintom scalar dynamics in a flat FLRW universe. While single-field models achieve phantom divide line (PDL) crossing and stable bounces, our $f(R,G,T)$-quintom coupling provides a novel implementation of a \textit{double} PDL crossing of $ω_{\text{eff}}$ during the bounce. We address stability concerns through Hamiltonian analysis, showing that FLRW symmetry constraints suppress Ostrogradsky instabilities by reducing higher-derivative terms to metric invariant. The scalar field equation of motion is explicitly derived, confirming cancellation of pathological modes. Numerical reconstruction of five $f(R,G,T)$ models confirms non-singular bounces with $ρ_{\text{eff}}>0$ and $c_s^2 \geq 0$, alongside parametric control over energy condition violations. Our work extends prior studies by: (1) unifying early-time bounce dynamics with late-time dark energy, (2) demonstrating a novel double-PDL crossing signature compatible with FLRW stability, and (3) establishing explicit ghost-free criteria for higher-derivative terms.

In this work, tunable vanadium dioxide (VO2) metafilms on different substrate materials fabricated via low-oxygen furnace oxidation are demonstrated for self-adaptive daytime solar heating and nighttime radiative cooling. Because of its thermally-driven insulator-to-metal phase transition behavior, the VO2 metafilms work as spectrally-selective solar absorber with a high solar absorptance of 0.86 and a low infrared emissivity of ~0.2 at daytime, while they behave as selective cooler at nighttime to dissipate heat effectively through the atmospheric transparency window with a high emissivity of ~0.76 to cold outer space. From the outdoor vacuum tests, a significant temperature rise up to 169 K upon solar heating and a temperature drop of 17 K at night are experimentally observed from these tunable VO2 metafilms. With the atmosphere temperature fitted in-situ, the accurate heat transfer model shows excellent agreement with the stagnation temperature measurement, and indicates a high heating power of ~400 W/m2 at 80°C sample temperature in the middle of the day, and a cooling power of ~60 W/m2 at 30°C in equilibrium with ambient at night. This work would facilitate the development of self-adaptive coatings with cost-effective and scalable fabrication approaches for all-day energy harvesting.

Thin shells can undergo large shape changes governed by the competition between bending and membrane energies. Here, we identify an instability mechanism in everted toroidal shells, referred to as eversion buckling. After eversion, the axisymmetric configuration may either remain stable or lose stability through symmetry breaking, depending on geometry. A scaling analysis reveals a dimensionless parameter that characterizes the ratio between membrane and bending energies. This parameter defines a critical threshold separating a bistable regime, where the axisymmetric everted state persists, from a monostable regime, where the shell collapses into a non-axisymmetric configuration. The transition is consistent with a pitchfork-type bifurcation, leading to collapse without a preferred in-plane direction. Finite element simulations and experiments validate the proposed scaling and the associated stability boundary across different shell geometries. In the bistable regime, individual everted shells exhibit rapid snap-through accompanied by large volumetric contraction and show limited sensitivity of the critical response to boundary constraints. Building on this mechanism, assemblies of such shells form granular systems with a stable stress plateau and high energy absorption efficiency. These results provide a mechanics-based framework for designing shell-based systems with robust and direction-insensitive energy absorption.

Symmetry-protected ideal flat bands in one-dimensional (1D) Hermitian lattices are populated by compact localized states (CLS) - a special class of localization with wavefunctions confined within a small region. In this work, we discover that the non-Hermitian skin effect (NHSE) can appear in a flat band. Unlike conventional NHSEs for dispersive bands that are protected by nontrivial point-gap topology, the flat band remains a point on the complex-energy plane and is therefore always topologically trivial. We found that, intriguingly, the flat-band skin effect (FBSE) is associated with the non-trivial spectral topology of the dispersive bands enclosing the flat band on the complex-energy plane, so it only emerges within a finite range of non-Hermitian parameters and can counterintuitively disappear at large non-Hermiticity. Moreover, the gaps between the flat and the dispersive bands can close at higher-order exceptional points under both periodic and open boundary conditions. The flat-band wavefunctions are discontinuous in quantum distance across these exceptional points, signifying that the gap-closing is singular. The FBSE was experimentally observed in a non-Hermitian mechanical lattice. Our work reveals flat-band phenomena unique to non-Hermitian systems and highlights new possibilities in quantum geometry and localization control.

We present the baseline design of the electron ring collimation system for the Electron-Ion Collider (EIC) at Brookhaven National Laboratory (BNL). The system addresses beam losses in a high-current electron storage ring with superconducting (SC) final-focus magnets and sensitive detectors, where uncontrolled losses can generate heat loads, radiation, and detector backgrounds and damage. The proposed collimation insertion localizes halo particle losses through reducing interaction region beam losses from beam-gas and Touschek scattering by several orders of magnitude while keeping detector backgrounds and cryostat heat loads within acceptable limits. Multi-turn particle tracking simulations show that the collimators do not significantly impact machine acceptance or beam lifetime, and their positions and apertures can be re-optimized for future lattice configurations. Ongoing work includes incorporating crab cavities and solenoid fields into simulations, refining vacuum conditions, and optimizing collimator geometry and materials. This design establishes a robust baseline for the EIC electron ring collimation system and supports continued lattice optimization for machine operations.

It is shown that the problem of computing the Strahler number of a binary tree given as a term is complete for the circuit complexity class uniform $\mathsf{NC}^1$. For several variants, where the binary tree is given by a pointer structure or in a succinct form by a directed acyclic graph or a tree straight-line program, the complexity of computing the Strahler number is determined as well. We show that the problem of deciding whether a given context-free grammar in Chomsky normal form produces a derivation tree with a Strahler number of at least $k$ is $\mathsf{P}$-complete. If the derivation tree is restricted to be acyclic, the problem becomes $\mathsf{PSPACE}$-complete.

While phonon topology in crystalline solids has been extensively studied, its influence on thermal transport-especially in nanostructures-remains elusive. Here, by combining first-principles-based machine learning potentials with the phonon Boltzmann transport equation and molecular dynamics simulations, we systematically investigate the role of topological surface phonons in the in-plane thermal transport of semiconductor thin films (Si, 4H -SiC, and c-BN). These topological surface phonons, originating from nontrivial acoustic phonon nodal lines, not only serve as key scattering channels for dominant acoustic phonons but also contribute substantially to the overall thermal conductivity. Remarkably, for these thin semiconductor films below 10 nm this contribution can be as large as over 30% of the in-plane thermal conductivity at 300 K, and the largest absolute contribution can reach 82 W/m-K, highlighting their significant role in nanoscale thermal transport in semiconductors. Furthermore, we demonstrate that both temperature and biaxial strain provide effective means to modulate this contribution. Our work establishes a direct link between topological surface phonons and nanoscale thermal transport, offering the first quantitative assessment of their role and paving the way for topology-enabled thermal management in semiconductors.

The nonlinear filter model is an old and well understood approach to the design of secure stream ciphers. Extensive research over several decades has shown how to attack stream ciphers based on this model and has identified the required security properties of the Boolean function used as the filtering function to resist such attacks. This led to the problem of constructing Boolean functions which provide adequate security \textit{and} at the same time are efficient to implement. Unfortunately, over the last two decades no fully satisfactory solutions to this problem appeared in the literature. The lack of good solutions has effectively led to the nonlinear filter model becoming more or less obsolete. This is a big loss to the cryptographic design toolkit, since the great advantages of the nonlinear filter model are its simplicity, well understood security and the potential to provide low cost solutions for hardware oriented stream ciphers. In this paper, we revive the nonlinear filter model by constructing appropriate Boolean functions which provide required security and are also efficient to implement. We put forward concrete suggestions of stream ciphers which are $κ$-bit secure against known types of attacks for $κ=80$, 128, 160, 192, 224 and 256. For the 80-bit and the 128-bit security levels, the gate count estimates of our proposals compare quite well to the famous ciphers Trivium and Grain-128a respectively, while for the 256-bit security level, we do not know of any other stream cipher design which has such a low gate count.

Numerical approximations of Landau-type operators represent fundamental components of time integration methods for demanding problems such as inhomogeneous Vlasov-Landau-type equations. Substantial computational issues arise from the treatment of the physically most relevant three-dimensional case with Coulomb-type interaction. This work is concerned with the introduction and numerical comparison of novel approaches for the reliable and efficient evaluation of Landau-type collision operators, where the focus is on the treatment of integral operators involving general singular kernels. In the spirit of collocation, common tools are the identification of fundamental integrals, series expansions of the integral kernel and the density function on the main part of the velocity domain, and interpolation as well as quadrature approximation nearby the singularity of the kernel. Focusing on the favourable choice of the Fourier spectral method, their practical implementation uses the reduction to basic integrals, fast Fourier techniques, and summations along certain directions. Moreover, an important observation is that a significant percentage of the overall computational effort can be transferred to precomputations which are independent of the density function. For the purpose of exposition and numerical validation, the cases of constant, regular, and singular integral kernels are distinguished, and the procedure is adapted accordingly to the increasing complexity of the problem.

We consider the Maxwell's equations with perfect electric conductor boundary conditions in three-dimensional unbounded domains which are the union of a bounded resonator and one or several semi-infinite waveguides. We are interested in the existence of electromagnetic trapped modes, i.e. $L^2$ solutions of the problem without source term. These trapped modes are associated to eigenvalues of the Maxwell's operator, that can be either below the essential spectrum or embedded in it. First for homogeneous waveguides, we present different families of geometries for which we can prove the existence of eigenvalues. Then we exhibit certain non homogeneous waveguides with local perturbations of the dielectric constants that support trapped modes. Let us mention that some of the mechanisms we propose are very specific to Maxwell's equations and have no equivalent for the scalar Dirichlet or Neumann Laplacians.

Cosmological emulation of observables such as the Cosmic Microwave Background (CMB) spectra and matter power spectra have become increasingly common in recent years because of the potential for saving computation time in connection with cosmological parameter inference or model comparison. In this paper we present CLiENT (Cosmological Likelihood Emulator using Neural networks with TensorFlow), a new method which circumvents the computation of observables in favour of directly emulating the likelihood function for a data set given a model parameter vector. We find that the method is competitive with observable emulators in terms of the required number of function evaluations, but has the distinct advantage of producing a surrogate likelihood which is completely auto-differentiable. Using less than $2 \times 10^4$ function evaluations CLiENT typically achieves credible intervals within better than $0.1 σ$ of those obtained using the true likelihood and single-point emulator precision better than $Δχ^2 \sim 0.5$ across relevant regions in parameter space.

In this paper, we use a formula obtained by Dubrovin and Yang (2017) to study certain asymptotic behaviors of GUE (Gaussian unitary ensemble) correlators. More precisely, we obtain large genus asymptotics of enumerations of ordinary graphs and ribbon graphs with 1 face.