Daily Papers

Different theories of dark matter predict different populations and morphologies of galactic subhaloes below about 10^8M_{odot}. The planned angular resolution and optical stability of the Habitable Worlds Observatory (HWO) should enable it to detect subtle subhalo perturbations in strongly lensed galaxy images. We simulate 2000-second exposures with its High Resolution Imager (HRI) under the fiducial Exploratory Analytic Case 1 (EAC1) design, assuming known source structure and omitting lens-galaxy light. Pre-selecting the top 50 of 965 lenses (5.2%) using only arc signal-to-noise and relative gradient power lowers the median mass threshold for 10% aperture coverage roughly tenfold relative to the full ensemble. The top 12 (1.2%) reach a median of 6.6times10^7M_{odot} for the same coverage. At their most sensitive positions, the top 50 and top 12 reach median thresholds of 3times10^7M_{odot} and 1.5times10^7M_{odot}, respectively. Non-linear fits support the Fisher forecasts at the tested masses and positions. For these 12 lenses, increasing the physical wavefront error from 35 to 65 nm RMS raises the median thresholds by only 0.1 dex when the point spread function (PSF) is modelled correctly. Deliberately mismodelling the 35-nm reference PSF removes detectable positions, although false detections remain rare. Under our illustrative retention criteria, loss of sensitive area sets a median tolerated wavefront mismatch of 5 nm RMS (range 2--10 nm). Selective HWO follow-up of lenses discovered by Euclid or Roman could therefore transform our understanding of the nature of dark matter, provided that the PSF is characterized accurately enough to preserve this sensitivity.

The abundance and properties of low-mass dark matter subhalos can be inferred by measuring the density and velocity structure of stellar streams, testing physical models of dark matter. Which streams make the most promising dark matter detectors, and which subhalos would they encounter? We use the semi-analytic model galacticus to simulate the Milky Way's dark subhalos, including tidal stripping under the influence of the galactic disk. Deriving stream initial conditions that best match present-day observations, we forecast subhalo encounters for 24 globular cluster streams around the Milky Way. Over their lifetimes, the 10 most perturbed streams are predicted to each experience approx 2-12 significant subhalo encounters with velocity kicks v_kick > 0.1 km s^{-1}. Jet, AAU, GD-1, and Palomar 5 lead the list, with Jet encountering twice the subhalos of any other stream. The subhalos that encounter streams have been tidally stripped to 1-20% of their peak mass and are twice as compact as previous works have assumed. A spectroscopic survey of streams with sub-km s^{-1} precision could reveal the influence of dark subhalos below the threshold of galaxy formation. Predicting the abundance and scatter of low-mass subhalos that reach the inner galaxy remains a dominant uncertainty in connecting stellar streams to models of dark matter.

The inner region of a subhalo's density distribution is particularly sensitive to dark matter microphysics, with alternative dark matter models leading to both cored and steeply-rising inner density profiles. This work investigates how the lensing signature and detectability of dark matter subhalos in mock HST-, Euclid-, and JWST-like strong lensing observations depends on the subhalo's radial density profile, especially with regards to the inner power-law slope, beta. We demonstrate that the minimum-mass subhalo detectable along the Einstein ring of a system is strongly dependent on beta. In particular, we show that subhalos with beta sim 2.2 can be detected down to masses over an order-of-magnitude lower than their Navarro-Frenk-White (NFW) counterparts with beta sim 1. Importantly, we find that the detectability of subhalos with steep inner profiles is minimally affected by increasing the complexity of the main lens galaxy's mass model. This is a unique characteristic of these subhalos, as those with NFW or shallower profiles become essentially undetectable when multipole perturbations are added to the lens model. The results of this work highlight how the underlying dark matter physics can significantly impact the expected number of subhalo detections from strong gravitational lensing observations. This is important for testing Cold Dark Matter against alternatives, such as Self-Interacting Dark Matter, which predict the existence of subhalos with diverse inner density profiles.

We develop a linear perturbative formalism to compute the response of an inhomogeneous stellar disk embedded in a non-responsive dark matter halo to perturbations like bars, spiral arms and satellite galaxy encounters. Without self-gravity to reinforce it, the response of a Fourier mode phase mixes away due to an intrinsic spread in the vertical (Omega_z), radial (Omega_r) and azimuthal (Omega_phi) frequencies, giving rise to local phase-space spirals. Collisional diffusion due to scattering of stars by structures like giant molecular clouds causes super-exponential damping of the phase-spiral amplitude. The z-v_z phase-spiral is 1-armed (2-armed) for vertically anti-symmetric (symmetric) bending (breathing) modes. Only transient perturbations with timescales (tau_{P}) comparable to the vertical oscillation period (tau_z sim 1/Omega_z) trigger z-v_z phase-spirals. Each (n,l,m) mode of the response to impulsive (tau_{P}<tau=1/(nOmega_z+lOmega_r+mOmega_phi)) perturbations is power law (sim tau_{P}/tau) suppressed, but that to adiabatic (tau_{P}>tau) perturbations is exponentially weak (sim left[-left(tau_{mathrm{P}/tauright)^alpharight]}) except resonant (tauto infty) modes. Slower (tau_{P}>tau_z) perturbations, e.g., distant encounters with satellite galaxies, induce stronger bending modes. If the Gaia phase-spiral was triggered by a satellite, Sagittarius is the leading contender as it dominates the Solar neighborhood response of the Milky Way disk to satellite encounters. However, survival against collisional damping necessitates that the impact occurred within sim 0.6-0.7 Gyr ago. We discuss how the detailed galactic potential dictates the phase-spiral shape: phase mixing occurs slower and phase-spirals are less wound in the outer disk and in presence of an ambient halo.

We explore the lowest mass limit that can be placed on the halo mass function in CDM using 28 strong gravitational lenses. For this purpose, we study an extreme model in which the halo mass function and mass-concentration relation follow CDM, with a sharp cutoff at some mass scale, m_{low}. Lensing provides a unique window into this quantity as it does not depend on the presence of baryons in dark matter halos and also allows the detection of low mass halos at cosmological distances, both in the lens galaxies and along the line-of-sight. Our model incorporates the effects of tidal stripping of subhalos, leading to the presence of many subhalos below a given model cutoff scale. We place an upper limit on the low-mass cutoff of the halo mass function of m_{low}<10^{8.3} M_odot at 10:1 odds using a prior for the normalization of the subhalo mass function from the semi-analytic model {\tt galacticus} and m_{low}<10^{8.2} M_odot at 10:1 odds using a prior from N-body simulations. These limits are comparable to, or stronger than, existing constraints based on Milky Way satellite galaxies. Based on these results, we forecast more than an order of magnitude improvement with a sample of 200 quadruply imaged quasar lenses. This number represents a small subset of the thousands that are anticipated to be discovered by Rubin, Euclid, and Roman. Furthermore, with this larger sample of lenses we expect to directly constrain the normalization of the subhalo mass function, thereby eliminating a major source of uncertainty in our current measurements.

Gravitational lensing is an invaluable probe of the nature of dark matter, and the structures it forms. Lensed gravitational waves in particular allow for unparalleled sensitivity to small scale structures within the lenses, due to the precise time resolution in combination with the continuous monitoring of the entire sky. In this work, we show two distinct ways of using strongly lensed gravitational waves to identify the presence of dark matter subhalos: {i)} through higher order caustics generating high relative magnification (mu_r > 2), short time delay image pairs that break the caustic universality relations of single dark matter halos, which occur for sim 1-10 percent of strongly lensed events in our cold dark matter models, and ii) through the presence of more than three highly magnified images, which occur for sim 0.01-1 percent of the same simulated events. We find that these results are highly sensitive to the concentrations of subhalos in our simulations, and more mildly to their number densities. The presence of low-mass subhalos increases the probability of observing wave-optics lensing in lensed gravitational waves, which is studied by solving the diffraction integral with the stationary phase approximation, as well as numerically. We also report distinct quantitative and qualitative differences in the distributions of relative magnifications and time delays for subhalo populations with increased number densities or concentrations. With the upcoming detection of strongly lensed events by ground- and space- based detectors, comparisons against these simulated distributions will provide insight into the nature of dark matter.

We prove that all excited states -sin(nx), ngeq2, of the De Gregorio equation on the torus are nonlinearly unstable in the sense of Hadamard. More precisely, perturbations arbitrarily small in H^2 leave a fixed H^1 neighborhood of the state. For every ngeq2, the linearized operator has a real eigenvalue λ_nin(0.56,0.6). To prove this, we transform the eigenvalue problem into a Fuchsian equation on the complex disk and obtain a matching condition for the eigenvalue. This condition is verified rigorously using interval arithmetic. The nonlinear instability follows from a bootstrap argument in the spirit of Guo, Hallstrom, and Spirn.

Due to wave interference, an ultralight light dark matter halo has stochastic, granular substructures which can scatter stars, leading to the heating of stellar distributions. Studies of this phenomenon have placed lower bounds on the ultralight dark matter mass. In this paper we investigate a number of relevant systematic effects, including: (1) the heating by the central soliton, (2) the self-gravity of the stars, (3) the suppression of heating in a tidally stripped halo, and (4) the tidal field suppression of heating when the stellar cluster is much smaller than the de Broglie wavelength. The first three effects are quantified by studying the dynamics of stellar particles in Schrodinger-Poisson simulations of ultralight dark matter halos, while the last effect is studied using analytic approximations.

This paper deals with the formation and evolution of Mars' moons, Phobos and Deimos, assuming the dislocation of a larger progenitor as the origin of these moons. The study by Hyodo et al. (2022) argue that under somewhat simplistic modeling, the post-dislocation orbits of Phobos and Deimos inevitably collide within 10,000 years, leading to their mutual annihilation. These findings are based on N-body simulations, accounting for Mars' J_2 and J_4 gravitational perturbations and mutual perturbations between the moons. In this paper, we challenge these findings by extending their work. We incorporate important perturbations such as solar perturbations, Mars' axial precession and nutation, and its deformation along three axes. We also extend some of the hypotheses made by Hyodo et al. (2022) concerning the initial distribution of Phobos and Deimos after the dislocation. Our analysis reveals that including these additional perturbations as well as the possibility of having more than two fragments after the dislocation does not alter the ultimate fate of Phobos and Deimos. The moons still converge towards collision within comparable timescales, supporting Hyodo et al. (2022) conclusions that the dislocation hypothesis under the dynamical scenario developed by Bagheri et al. (2021) has, in the best conditions, about 10\% chance of surviving after the first 100,000 years following their formation.

Ultralight dark matter is an interesting dark matter candidate describing the lightest end of the mass parameter space. This model produces an oscillating granular pattern in halo densities. These fluctuations have the potential to produce a time-varying density along the line of sight creating a small lensing signal for any stars observed through a dark matter halo which oscillates on the de Broglie timescale. In this work, we study this stochastic lensing signal taking into account the impact of density granules as well as the central soliton. We calculate the amplitude and temporal properties of this signal and estimate how stellar observations may be used to constrain the ultralight dark matter mass and abundance.

Weather Jiu-Jitsu is a control paradigm for extreme climatological events, inspired by chaos theory. As a proposition, small, precise, targeted, and cost-inexpensive perturbations can redirect trajectories of a large dynamical system. This strategy has been demonstrated analytically in the Lorenz-63 system, where a naturally chaotic trajectory switching between two attractors can be confined to a single attractor, indefinitely, via arbitrarily small perturbations. This paper examines the feasibility of Microsoft's Aurora -- a 1.3 billion parameter global atmospheric model -- as a test bed for this strategy. This paper explores three questions: (1) Is Aurora a reliable enough simulation environment to serve as a meaningful testbed? (2) Are the perturbations required to redirect its trajectories small enough to be physically plausible? (3) Does Aurora's learned latent space (the parametric estimators on climatological attributes) yield any apparent, structured, and/or perhaps interpretable features that can convey a geo/atmospheric response to initial conditions? We find evidence consistent with all three: Aurora's modeled trajectories respond to perturbations beyond measurement drift, the perturbation magnitudes required are small relative to the model's own forecast uncertainty, and its latent representations exhibit directional structure that responds to Jiu-Jitsu-type interventions, even though that structure does not separate extreme from normal states outright. These results should be read as feasibility diagnostics rather than a demonstration of control: we do not implement or test an actual steering intervention on Aurora, and several of our findings, particularly around the model's latent-space geometry, are exploratory.

This project focuses on a method to extract a frequency comb in mechanical means, for general interest and numerous practical applications in MEMS. The method of execution is the implementation of a beam that is exhibiting non-linear dynamics that is perturbed and analyzed for its transverse vibrations. The perturbation is an external harmonic driver with a chosen small amplitude and frequency (which is slightly detuned from the beam eigenfrequency), that when engaged with the unperturbed beam oscillations, causes it reach a state of "injection pulling" - an effect that occurs when one harmonic oscillator is coupled with a second one and causes it to oscillate in a frequency near its own. This causes the beam to reach SNIC bifurcation, rendering a frequency comb as desired. Theoretical analysis showed that the problem can be modelled using a non-linear equation of the beam, that translates to a form of the non-linear Duffing equation. While a solution to the dynamics function of the beam is hard to obtain in practice due to mathematical difficulties, a slow evolution model is suggested that is composed of functions of a amplitude and phase. Using several additional mathematical assumptions, the amplitude is seen to be related to the phase, while the phase equation solution is seen to be of the form of Adler's equation. These assumptions ultimately reduce the entire behaviour of the beam to a relatively simple solution to the Adler equation, which has a known analytical solution. Computerized numerical simulations are run on it to check the results and compare them to the theory and desired outcome. The results agreed with the theory and produce the expected frequency comb, showing the assumptions to be valid in extracting the comb.

Cosmological first-order phase transitions can generate curvature perturbations through inhomogeneous quantum tunneling, as studied previously on superhorizon scales. In this work, we for the first time conduct three-dimensional lattice simulations that incorporate scalar metric perturbations and radiation perturbations, covering a range from bubble wall scales to super-horizon scales. We obtain the precise scalar perturbation power spectrum and the probability density function of energy density perturbations. Furthermore, we simulate the gravitational-wave energy spectra generated by each source during the first-order phase transition, including the scalar field itself, scalar metric perturbations, and the energy density and velocity perturbations of radiation. For gravitational waves, the contribution from other sources can exceed 1/3 of that from the scalar field at superhorizon scales. Additionally, we compare the effects of different values of the transition strength and rate on the results. This paper provides more accurate numerical results for research aimed at detecting or constraining first-order phase transitions via gravitational waves and curvature perturbations.

Many previous studies have imposed stringent constraints on the particle mass of fuzzy dark matter (FDM) by analyzing observations of Galactic satellite galaxies, which show no significant evidence of the heating effect predicted by FDM. However, these analyses have generally neglected the tidal influence of the Milky Way, which can substantially suppress the FDM-induced heating in satellites. This oversight arises from computational challenges of accurately capturing the tidal effects in FDM simulations. In this study, we present a novel simulation framework that, for the first time, enables the simulation of an FDM-stellar system within an observationally motivated gravitational potential of the Milky Way. This framework incorporates the diverse Galactic components, including the gravitational influence of the Large Magellanic Cloud. Using the Fornax dwarf galaxy as a case study, we demonstrate that tidal effects significantly alleviate the tension between observational data and the predicted heating effect for an FDM particle mass of m_asim 10^{-22} eV.

Let P_h be a semiclassical pseudodifferential operator on a closed Riemannian manifold (M,g), with principal symbol p. We consider perturbations P_h+h^αQ, with 0<αle 1, where Q is a semiclassical pseudodifferential operator whose symbol oscillates at scale h^β, with 2β<α. Assuming that the classical dynamics of the unperturbed system on a regular energy surface p^{-1}(E) is hyperbolic, we prove a Gutzwiller trace formula for the perturbed operator that holds up to times of order |log h|. This formula relates the distribution of energy levels of the quantum system near the energy E to the periodic orbits of its classical counterpart. The perturbation h^αQ affects only the phases appearing in the trace formula.

Motivated by the peculiar features of the trans-Neptunian object (TNO) Máni and the discovery of ring systems around Centaurs and trans-Neptunian bodies, we investigate the stability of particles around a small irregular body hosting a deep equatorial crater. This study is the third contribution in a sequence devoted to the dynamics around non-spherically symmetric bodies. Using Máni as a reference model, whose crater depth exceeds 10% of its radius, we map the system stability through complementary methods: Poincaré surfaces of section (PSS), survival maps, and the finite-time Lyapunov exponent (FTLE). In the nominal case, the 1!:!1, 2!:!1, 3!:!1, and 4!:!1 spin-orbit resonances (SORs) are consistently identified by all techniques. The prominent 3!:!1 SOR exhibits a bifurcated structure at high eccentricities, matching structural transitions observed at lower Jacobi constant values in the PSSs. Increasing the rotation rate (λ) and crater mass ratio (μ) enlarges resonance widths and promotes overlap, making the 2!:!1 and 4!:!1 SORs progressively dominant. Lower rotation rates allow stable trajectories to persist at higher eccentricities, whereas the 1!:!1 SOR is highly sensitive to stronger perturbations and disappears in the most extreme cases. In contrast to mass-anomaly models, which can clear the region interior to the 2!:!1 SOR, the crater configuration considered here preserves stable regions in this vicinity, suggesting alternative scenarios for the formation and maintenance of debris structures around irregular minor bodies.

We study the pseudospectrum of the Kerr black hole for gravitational perturbations with spin weight s=2, the case of greatest interest in gravitational-wave astronomy. In the hyperboloidal framework with two-dimensional Chebyshev collocation, we formulate the quasinormal mode problem as a non-self-adjoint eigenvalue problem. For sneq0 the fields Ψ^{(s)} and Ψ^{(-s)} are independent, so the conserved current method yields no single-field energy norm. We overcome this with the Teukolsky--Starobinsky identities, which relate Ψ^{(-2)} to a fourth-order operator on Ψ^{(2)} and yield an H^2 energy norm after symmetrization. With the H^1 norm known for s=0, this suggests the pattern H^{|s|}, verified for s=0 and s=2. All results use an ω-independent two-field hierarchy. We find that the pseudospectrum tightens by 1.1 to 3.5 decades at each step of L^2to H^1to H^2, yet stays large in every norm. The s=+2 and s=-2 operators are isospectral but not isopseudospectral: at twelve of fourteen probes the ψ_0 resolvent exceeds the ψ_4 one by 0.19 to 0.82 decades in the H^2 norm, while at the two probes furthest along the QNM line the ordering reverses by 0.18 to 0.19 decades. The gravitational pseudospectrum exceeds the scalar one by 0.5 to 5.2 decades in the window minimum and by 5.9 decades in L^2 at ωM=0.47-0.17,i, while along the damping direction the s=2 resolvent is non-monotonic and the s=0 resolvent smooth. QNM spectral instability is therefore a universal feature of Kerr, and is stronger for gravitational perturbations.

We study how a radially oscillating thin shell outside a black hole (BH) affects gravitational wave ringdown and derive matching conditions for polar and axial perturbations from the linearized Israel junction conditions on the moving worldtube. Periodic shell motion produces Floquet sidebands in the scattered wave. For a distant shell, the motion has little effect on the prompt ringdown and only weakly modifies the late time echoes. When the shell is closer to the BH, a replica of a long lived shell mode enters the incident frequency band, increasing the late time echo amplitude by roughly two orders of magnitude. We also identify an exceptional point where two polar modes coalesce and find the contribution of its second order pole in the late time waveform.

We develop a novel systematic method for constructing exact, static, and asymptotically flat black-hole solutions in shift-symmetric and Z_2-symmetric beyond Horndeski theories. In contrast to previous studies, our approach does not rely on the restrictive reciprocal condition g_{tt}g_{rr}=-1, allowing for more general geometries characterized by two independent metric functions. The resulting solution space contains two qualitatively distinct types of hair originating from different branches of the theory. One branch is characterized by khronometric hair, while the other by genuine scalar hair. In both, the scalar profile defines a nontrivial preferred foliation, but the shift-symmetry Noether current and the associated propagating degree of freedom are trivial for the former and nonvanishing for the latter. Focusing mainly on the second branch, we derive several distinct families of exact black-hole solutions. In general, these solutions are singular and exhibit primary scalar hair associated with an independent scalar charge. Nevertheless, we demonstrate that they can be regularized to yield regular black-hole or solitonic configurations, for which the scalar hair becomes secondary. We further investigate the stability properties of these solutions under linear perturbations by analyzing the axial sector and the monopole (ell=0) mode of the even-parity sector. For representative solutions with scalar hair, the perturbative analysis provides evidence for linear stability under the modes considered.

Vacuum Kerr perturbations in general relativity have identical even- and odd-parity quasinormal frequencies. We establish this parity isospectrality for linear gravitoelectromagnetic perturbations of subextremal Kerr--Newman--de Sitter black holes, without a slow-rotation or small-charge expansion. We reconstruct the radiative metric and gauge-potential perturbations directly from gauge-invariant master variables in radiation gauge, without an intermediate complex potential.

In this paper we study quasinormal modes and absorption cross sections for the (1+3)-dimensional Bardeen black hole surrounded by perfect fluid dark matter. Studies of the massless scalar field is already done in Sun:2023slzl. Hence, in this paper we will focus on the massive scalar field perturbations and massless Dirac field perturbations. To compute the quasinormal modes we use the semi-analytical 3rd-order WKB method, which has been shown to be one of the best approaches when the effective potential is adequate and when n < ell and n < lambda. We have also utilized the P\"oschl-Teller method to compare the valus obtained using the WKB approach. We have computed quasinormal frequencies by varying various parameters of the theory such as the mass of the scalar field mu, dark matter parameter alpha and the magnetic charge g. We have summarized our solutions in tables and figures for clarity. As for the absorption cross section, we used third order WKB approach to compute reflection, transmission coefficients and partial absorption cross sections. Graphs are presented to demonstrate the behavior of the above quantities when the dark matter parameter and mass of the massive scalar field are varied.

We show that perturbations of massless fields in the Kerr black hole background enjoy a hidden SL(2,R)U(1) ("Love") symmetry in the properly defined near zone approximation. Love symmetry mixes IR and UV modes. Still, this approximate symmetry allows us to derive exact results about static tidal responses. Generators of the Love symmetry are globally well defined and have a smooth Schwarzschild limit. Generic regular solutions of the near zone Teukolsky equation form infinite-dimensional SL(2,R) representations. In some special cases (ell parameter is an integer), these are highest weight representations. This is the situation that corresponds to vanishing Love numbers. In particular, static perturbations of four-dimensional Schwarzschild black holes belong to finite-dimensional representations. Other known facts about static Love numbers also acquire an elegant explanation in terms of the SL(2,R) representation theory.

We search for dark matter (DM) annihilating subhalos of the Milky Way halo among the Fermi Large Area Telescope (LAT) unassociated sources. We construct, for the first time, a statistical model of the unassociated sources at latitudes above 10 degrees. The latter is built as a combination of both DM annihilation subhalos as well as Galactic and extragalactic astrophysical components. The astrophysical components are constructed based on distributions of associated sources, while the distribution of DM subhalos is derived from Monte Carlo simulations. In this model we take into account the differences in the distributions of associated and unassociated sources including both covariate and prior probability shifts (both being forms of ``dataset shifts''). Previous searches of DM subhalos were based on classify-and-count strategies, while the approach adopted in this work is based on quantification learning, which allows one to determine a well-defined statistical interpretation of the contribution of a population of DM subhalos to the unassociated Fermi-LAT sources. In the bb annihilation channel and for a range of DM masses from 10 GeV to 1 TeV, we don't find a significant contribution from DM subhalos and derive a statistical 95% confidence upper limit on the DM annihilation cross section in this channel. While the derived limits are consistent with previous classify-and-count approaches, our generative statistical model opens new avenues for population studies of Fermi-LAT sources and, more generally, for searches of anomalies on top of backgrounds in presence of statistical and systematic uncertainties.

In arXiv:2008.04330 it was shown that supertranslation and SL(2,mathbb C) current algebra symmetries, corresponding to leading and subleading soft graviton theorems, are enough to determine the tree level MHV graviton scattering amplitudes. In this note we clarify the role of subsubleading soft graviton theorem in this context.

In this paper, we study multidimensional perturbations of radially symmetric rarefactive flows for the compressible Euler equations. No assumptions on the smallness of the background are imposed. We derive lower bounds on both the classical lifespan and stability timespan of the perturbed solution. These lower bounds are demonstrated to tend to infinity as the size of the perturbation approaches zero. Furthermore, owing to the rarefactive nature of the background, the resulting estimate is shown to be substantially longer than the corresponding estimate for a general classical background with bounded first derivatives.

We study spontaneous scalarization of static, spherically symmetric black holes in scalar--Gauss--Bonnet gravity with a Ricci coupling F=1 βϕ^{2}/4+γβ^{2}ϕ^{4}+O(ϕ^{6}) that nonlinearly completes the quadratic one. For arbitrary couplings and potential, we derive the near-horizon regularity condition and horizon curvature invariants in closed form; scalarized branches terminate where this condition degenerates, at finite horizon curvature. A weakly nonlinear expansion fixes the bifurcation direction exactly: for a massless scalar, its governing coefficient is quadratic in β, changes sign at β=1.1156, and depends linearly on a quartic self-interaction. At equal horizon values of the scalar, completions differ in mass, to leading order, in proportion to γ. A radial-perturbation master equation for arbitrary couplings confirms the exchange of stability at the bifurcation and turning points. Consequently, the domain of radially stable black holes shrinks as γ increases over the range studied; it is smaller for the exponential completion than for the quadratic truncation.

This paper extends the creep tide theory to exoplanetary systems with significant obliquities. The extended theory allows us to obtain the stellar and planetary hydrodynamic equilibrium tides and the evolution of the rotational state of the bodies. The dynamic ellipsoidal figure of equilibrium of the body is calculated taking into account that its reaction to external forces is delayed by its viscosity. The derived equations are used to determine the motion of the tidal bulge of the planetary companion CoRoT-3b (a brown dwarf) and its host star. We show how the tides deform the figure of the companion and how its tidal bulge moves close to the substellar meridian from one hemisphere to another. The stellar lag is mostly positive and is braking the star's rotation.

We study a one dimensional nonlinear Klein-Gordon equation with a potential, a localized quadratic nonlinearity, and a non-localized quartic nonlinearity. We assume that the linearized operator has a single discrete eigenvalue below the continuous spectrum, corresponding to an ''internal mode''. This eigenvalue generates localized, time-periodic solutions for the linear equation. Assuming the natural Fermi Golden Rule, we give a global description of the dynamics of the amplitude of the internal mode through the radiation damping mechanism, and prove scattering for the radiation. Our approach is based on the distorted Fourier transform and a collection of refined dispersive decay and smoothing estimates. The corresponding cubic problem is closely related to the question of global-in-space dispersive asymptotics for perturbations of kink solutions in the classical ϕ^4 model, which remains a challenging open question. From the perspective of nonlinear estimates, a quartic (non-localized) interaction is essentially sharp for our analysis, and closing the estimates with such a low degree nonlinear term requires a careful and delicate treatment. As a direct application of our analysis, we prove a result on the asymptotic stability of kinks for classes of scalar field models that can be seen as perturbations of the ϕ^4 model.

Static spherically symmetric asymptotically flat configurations in General Relativity with a minimally coupled scalar field typically possess naked singularities. We study a linear stability of these configurations against radial (monopole) perturbations in case of power-law scalar field potentials. We employ a new shooting method that extracts the eigenvalues corresponding to the exponentially growing modes of the perturbation. The problem is reduced to one second order ``master'' equation in a divergent form with a regularized effective potential. We confirm our previous results showing that instability modes exist for sufficiently small scalar charges of the initial static configurations.

We demonstrate that an axion field can develop perturbations peaked at an intermediate wavenumber through its inflationary dynamics. We compute the resultant spectrum of gravitational waves (GWs) and primordial black holes (PBHs) generated through the curvaton mechanism. The GW spectrum exhibits a triangular shape, with UV and IR slopes determined by the axion's inflationary evolution and treatable as free parameters. In computing the PBH abundance, we properly account for the nonlinear relation between curvature and density perturbations and the primordial non-Gaussianity generated by the curvaton. The PBHs can account for all of dark matter, accompanied by blue-tilted isocurvature perturbations at small scales. The IR slope of the GW spectrum is anti-correlated with the magnitude of the dark matter isocurvature perturbations, offering a multi-messenger test of the model.

We consider Proca field perturbations in a five-dimensional Schwarzschild-anti-de Sitter (Schwarzschild-AdS_{5}) black hole geometry. Using the vector spherical harmonic (VSH) method, we show that the Proca field decomposes into scalar-type and vector-type components according to their tensorial behavior on the three-sphere. Two degrees of freedom of the field are described by scalar-type components, which are coupled due to the mass term, while the remaining two degrees of freedom are described by a vector-type component, which decouples completely. Motivated by the Frolov-Krtouš-Kubizňák-Santos (FKKS) ansatz in the limit of zero spin, we use a field transformation to decouple the scalar-type components at the expense of introducing a complex separation parameter β. This parameter can be determined analytically, and its values correspond to two distinct polarizations of the scalar-type sector: "electromagnetic" and "non-electromagnetic", denoted by β_{+} and β_{-}, respectively. In the scalar-type sector, the radial differential equation for each polarization is a Fuchsian differential equation with five singularities, whereas in the vector-type sector, the radial equation has four singularities. By means of the isomonodromy method, we reformulate the boundary value problem in terms of the initial conditions of the Painlevé VI τ function and, using a series expansion of the τ function, we compute the scalar-type and vector-type quasinormal modes (QNMs) in the small horizon limit. Our results are in overall very good agreement with those obtained via the numerical integration method. This shows that the isomonodromy method is a reliable method to compute quasinormal modes in the small horizon limit with high accuracy.

Traveling wavetrains in generalized two-species predator-prey models and two-component reaction-diffusion equations are considered. The stability of the fixed points of the traveling wave ODEs (in the usual "spatial" variable) is considered. For general functional forms of the nonlinear prey birthrate/prey deathrate or reaction terms, a Hopf bifurcation is shown to occur at two different critical values of the traveling wave speed. The post-bifurcation dynamics is investigated for five different functional forms of the nonlinearities. In cases where the bifurcation is supercritical, the post-bifurcation behaviour yields stable periodic orbits of the traveling-wave ODEs in the spatial variable. These correspond to stable periodic wavetrains of the full PDEs. Subcritical Hopf bifurcations yield more complex post-bifurcation dynamics in the PDE wavetrains. In special cases where the subcritical bifurcation marks the end of the regime of stability, the post-bifurcation behavior in the spatial ODEs is chaotic, corresponding to wavetrains of the original PDEs which are spatially coherent, but have chaotic temporal dynamics. All the models are integrated numerically to investigate the post-bifurcation dynamics and chaotic regimes are characterized by computing power spectra, autocorrelation functions, and fractal dimensions.

We study diffeomorphisms of Banach spaces satisfying generalized hyperbolicity: the stable and unstable subspaces are invariant only up to inclusion, need not depend continuously on the point, and expansivity may fail. On closed manifolds, this condition is equivalent to Axiom~A with strong transversality. We introduce a continuous-selection method that converts uniform orbitwise estimates into bounded continuous solutions of cohomological equations for generalized-hyperbolic cocycles. For diffeomorphisms in the uniform global \(C^1\) category, this yields continuous semiconjugacies in both directions under sufficiently small bounded Lipschitz perturbations, and topological stability in the sense of Walters. For the infinite product of one-dimensional Morse-Smale systems on \(\ell^p(\mathbb Z)\), \(1\leq p\leq\infty\), we construct compatible forward and reverse cohomological solution operators and prove structural stability, including for perturbations that couple coordinates, although the product is not expansive. For \(p=\infty\) this gives a structurally stable diffeomorphism with uncountably many hyperbolic fixed points, in contrast with the finitely many basic sets of Axiom~A diffeomorphisms. The cocycle analysis yields Lipschitz shadowing for the induced operator on bounded continuous vector fields.

A dark-matter core and a soft nuclear equation of state can produce similar mass--radius signatures, motivating a complementary probe through the f-mode spectrum. We compute quadrupolar f-mode frequencies and gravitational-wave damping times in full general relativity for cold, nonrotating neutron stars admixed with self-interacting bosonic dark matter (DM). Our two-fluid survey spans 21 nuclear equations of state covering nucleonic, hyperonic, Δ-admixed, and combined hyperon--Δ compositions at F_{rm DM}=1--20%. The main sequences use λ=π and boson masses of 500 and 100,MeV for the core and halo studies, respectively. Independent normal-matter (NM) and DM displacements couple through the metric, yielding NM-led and DM-led f-mode branches whose radiative damping is determined by outgoing-wave boundary conditions. At 1.4,M_odot, the core DM-led damping time decreases from order 10^3,s at F_{rm DM}=1% to order 1,s at 20%, approximately following an empirical F_{rm DM}^{-2} dependence, while NM-led damping times remain within 0.12--0.33,s. Halo DM-led damping instead increases with dark fraction: at the same stellar mass and F_{rm DM}=20%, dark radii approach 88,km, frequencies fall to 0.14,kHz, and damping times reach approximately 450,s. Selected high-mass core sequences exhibit strong DM-led damping-time upturns not reproduced by the leading mass-quadrupole diagnostic. Representative core calculations show greater DM-led sensitivity to the bosonic self-coupling and retain both branches at ell=3. Under the adopted nonrotating, circular-binary prescriptions, no evaluated configuration satisfies all geometric and perturbative conditions for a controlled linear tidal resonance.

We derive the gravitational radiation generated by a localised matter source in de Sitter spacetime at octupolar order in the multipolar expansion, working in generalised harmonic gauge in the future Poincaré patch. The scalar, vector, and tensor perturbation equations are solved explicitly, taking into account the cosmological tail. This constitutes the first extension of the de Sitter multipolar expansion beyond quadrupolar order. A key technical ingredient is a universal multipole moment differentiation identity, which unifies the relations between multipole moments into a single recursive formula and enables a controlled extension to higher multipoles. Using the symmetric trace-free tensor formalism of Blanchet, Damour, and Iyer, we further develop a systematic translation of the radiative solution into a spherical harmonic basis, and apply it to both the quadrupolar and octupolar metric perturbations. This representation renders the angular structure of the radiation manifest, simplifies the verification of the linearised field equations, and facilitates direct comparison with Bondi-gauge and other perturbative treatments of de Sitter spacetime.

Calculating the action and the interaction Hamiltonian at higher orders in cosmological perturbation theory is a cumbersome task. We employ the formalism of EFT of inflation in models of single field ultra slow-roll inflation and obtain a non-perturbative result for the Hamiltonian in terms of the Goldstone field pi. To complete the dictionary, a non-linear relation between the curvature perturbations and pi is presented. Equipped with these non-linear results, we calculate the higher order loop corrections in USR models which are employed for PBHs formation. It is shown that the loop corrections on long CMB scales increase rapidly with the number of loop L and the setup will go out of perturbative control at the four-loop level.

We first prove a rigidity result for uniformly rotating vortex patch solutions to Euler equations in bounded simply-connected planar domains. Namely, if a bounded simply-connected domain with real-analytic boundary contains a nontrivial vortex patch that remains strictly inside the domain while undergoing a uniform rigid rotation, then the ambient domain must be a disc centered at the rotation center. The proof combines the rotating-frame formulation with harmonic unique continuation and the generalized Schwarz's reflection principle across analytic boundary arcs. These tools imply that, unless the outer domain is rotationally invariant, the velocity must vanish in an open region surrounding the patch, contradicting the nonzero circulation generated by the patch. In the same spirit, we show that only circular domains possess a circular point vortex orbit. As a second result, we construct quasi-periodic vortex patch solutions to the Euler equations in domains that are small perturbations of the unit disc D. The amplitudes of the solutions are linked to the size of the domain deformation, allowing the classical Rankine vortices bcdotD, bin(0,1), to be regarded as equilibrium states. Our analysis is perturbative with respect to the construction developed in the undeformed case, and the resulting quasi-periodic solutions exist for most values of the inner radius b. This provides the first construction of quasi-periodic vortex patch solutions to the Euler equations in non-radial domains. Moreover, combined with the rigidity result established above, this shows that, in the periodic case, these solutions cannot arise from a purely rigid rotation.

Baryonic effects created by feedback processes associated with galaxy formation are an important, poorly constrained systematic effect for models of large-scale structure as probed by weak gravitational lensing. Upcoming surveys require fast methods to predict and marginalize over the potential impact of baryons on the total matter power spectrum. Here we use the FLAMINGO cosmological hydrodynamical simulations to test a recent proposal to approximate the matter power spectrum as the sum of the linear matter power spectrum and a constant multiple, A_{rm mod}, of the difference between the linear and non-linear gravity-only power spectra. We show that replacing this constant multiple with a one-parameter family of sigmoid functions of the wavenumber k allows to us match the predictions of simulations with different feedback strengths for z leq 1, k < 3~hrm Mpc^{-1}, and the different cosmological models in the FLAMINGO suite. The baryonic response predicted by FLAMINGO models that use jet-like AGN feedback instead of the fiducial thermally-driven AGN feedback can also be reproduced, but at the cost of increasing the number of parameters in the sigmoid function from one to three. The assumption that A_{rm mod} depends only on k breaks down for decaying dark matter models, highlighting the need for more advanced baryon response models when studying cosmological models that deviate strongly from LambdaCDM.

Modern cosmological surveys are delivering datasets characterized by unprecedented quality and statistical completeness; this trend is expected to continue into the future as new ground- and space-based surveys come online. In order to maximally extract cosmological information from these observations, matching theoretical predictions are needed. At low redshifts, the surveys probe the nonlinear regime of structure formation where cosmological simulations are the primary means of obtaining the required information. The computational cost of sufficiently resolved large-volume simulations makes it prohibitive to run very large ensembles. Nevertheless, precision emulators built on a tractable number of high-quality simulations can be used to build very fast prediction schemes to enable a variety of cosmological inference studies. We have recently introduced the Mira-Titan Universe simulation suite designed to construct emulators for a range of cosmological probes. The suite covers the standard six cosmological parameters {omega_m,omega_b, sigma_8, h, n_s, w_0} and, in addition, includes massive neutrinos and a dynamical dark energy equation of state, {omega_{nu}, w_a}. In this paper we present the final emulator for the matter power spectrum based on 111 cosmological simulations, each covering a (2.1Gpc)^3 volume and evolving 3200^3 particles. An additional set of 1776 lower-resolution simulations and TimeRG perturbation theory results for the power spectrum are used to cover scales straddling the linear to mildly nonlinear regimes. The emulator provides predictions at the two to three percent level of accuracy over a wide range of cosmological parameters and is publicly released as part of this paper.

We address effects of spin-orbit coupling (SOC), phenomenologically added to a two-component Bose-Einstein condensate composed of particles moving by Levy flights, in one- and two-dimensional (1D and 2D) settings. The corresponding system of coupled Gross-Pitaevskii equations includes fractional kinetic-energy operators, characterized by the Levy index, \alpha < 2 (the normal kinetic energy corresponds to \alpha = 2). The SOC terms, with strength \lambda, produce strong effects in the 2D case: they create families of stable solitons of the semi-vortex (SV) and mixed-mode (MM) types in the interval of 1 < \alpha < 2, where the supercritical collapse does not admit the existence of stable solitons in the absence of the SOC. At \lambda --> 0, amplitudes of these solitons vanish as (\lambda)^{1/(\alpha - 1)}.

The problem of attribution is concerned with identifying the parts of an input that are responsible for a model's output. An important family of attribution methods is based on measuring the effect of perturbations applied to the input. In this paper, we discuss some of the shortcomings of existing approaches to perturbation analysis and address them by introducing the concept of extremal perturbations, which are theoretically grounded and interpretable. We also introduce a number of technical innovations to compute extremal perturbations, including a new area constraint and a parametric family of smooth perturbations, which allow us to remove all tunable hyper-parameters from the optimization problem. We analyze the effect of perturbations as a function of their area, demonstrating excellent sensitivity to the spatial properties of the deep neural network under stimulation. We also extend perturbation analysis to the intermediate layers of a network. This application allows us to identify the salient channels necessary for classification, which, when visualized using feature inversion, can be used to elucidate model behavior. Lastly, we introduce TorchRay, an interpretability library built on PyTorch.

The antenna-elements that make up a radio interferometer form a spatial filter that samples components of the Fourier transform of a target radio astronomical source brightness. Along the signal path, there are multiplicative and additive perturbation effects that alter the signal and that should be corrected. The process of mitigating these perturbation effects is called calibration. In this work, we develop a new and fast Maximum Likelihood based estimator of these perturbation effects using the Exponential Map and Lie groups. To evaluate its performance, we compare it to the Cramér-Rao Lower Bound and, to test the estimation time, we compare it with the Expectation Maximization algorithm, another fast Maximum Likelihood estimator. Finally, we apply our estimator to a real observation of the protoplanetary disk AS 209 made with the Submillimeter Array. We found that our proposed estimator meets the Cramér-Rao Lower Bound and it was approximately 40 times faster than the Expectation Maximization algorithm.

The second part of Hilbert's 16th problem is one of the most fundamental open problems in the qualitative theory of ordinary differential equations and dynamical systems. A central unresolved question is whether the Hilbert number H(d) is finite for arbitrary polynomial degree d. (A very recent manuscript from OpenAI asserts the finiteness of H(d); see the remark at the end of this paper.) In the absence of a general upper bound theory, most existing work constructs explicit perturbed polynomial systems to obtain improved lower bounds for H(d), while rigorous upper bound estimates remain largely unavailable. This paper focuses on improving the quantitative lower bound for polynomial systems through a systematic Hierarchical Melnikov Realization framework. We construct perturbed dynamics based on an anisotropic Chebyshev Hamiltonian, where hierarchically selected perturbation coefficients generate simple zeros of the first-order Melnikov function simultaneously across multiple disjoint period annuli. Two distinct 3-adic filtrations supply the necessary logarithmic correction factors, and a Borel--Gauss analysis establishes the required local rank condition under sufficiently strong anisotropy. As the main result of this work, we prove that H(d)=Ωbigl(d^2ln^2 dbigr), which improves the previously known lower bound by a factor of ln d. The full construction of limit cycles and the resulting dynamical bounds are formally certified using Lean 4 formal verification.

Weak perturbations of equal size can produce terminal Wasserstein errors of different orders. For Gaussian-smoothed infinitely divisible laws, we differentiate distribution functions with respect to variance-weighted Lévy characteristics, including distributional directions generated by moving atoms. We obtain first- and second-order expansions uniform over Lipschitz tests. Gaussian analyticity identifies the signed second coefficient of the Wasserstein-1 distance when the first response is nonzero. When it vanishes, a finite second displacement moment yields a quadratic response, strictly positive for nonzero displacement dispersion. For local balanced remeshing, the error is comparable to the grid-alignment variance, giving sharp quadratic grid rates for compactly supported densities and nonaligned atomic sequences. We derive metric speed and length along admissible non-atomic curves and a response-based linear program with a certified oracle gap and consistent quadrature. We also establish the sharp vanishing-smoothing transition and a multivariate second-order expansion. The Supplement treats state-dependent responses and further stability estimates.

As part of a PhD thesis entitled `Scalar perturbations in warm inflation and during reheating' we present a software for computing warm inflation observables. In particular, our Mathematica implementation computes the power spectrum, spectral tilt, and tensor-to-scalar ratio for a given momentum scale. Compared with other implementations, we start in a Bunch-Davies state deep inside the horizon, ideally at a time when thermal noise is exponentially suppressed. We integrate gauge-invariant equations for three curvature perturbations across horizon exit. We continue deep enough outside of horizon so that all curvature perturbations agree. Results are illustrated for Standard Model embedded warm inflation, and we also provide notebooks for several other popular potentials and friction coefficients. The theoretical foundations for the code can be found in the main part of the thesis or in earlier papers [1,2]. Specifically, part II derives gauge-invariant, model-agnostic evolution equations, as well as the noise autocorrelator interpolating between quantum and classical domains. Part III presents the general ideas behind the numerical implementation, while part IV presents selected results. The code is described, line-by-line, in Appendix A. The published PhD thesis is available at https://doi.org/10.48620/101166 while the notebooks can be downloaded from https://github.com/alicarogeljblackhole/Warm-Inflation.

The binding energies of the five bound rotational levels J=0-4 in the highest vibrational level v=14 in the X^1Sigma_g^+ ground electronic state of H_2 were measured in a three-step ultraviolet-laser experiment. Two-photon UV-photolysis of H_2S produced population in these high-lying bound states, that were subsequently interrogated at high precision via Doppler-free spectroscopy of the F^1Sigma_g^+ - X^1Sigma_g^+ system. A third UV-laser was used for detection through auto-ionizing resonances. The experimentally determined binding energies were found to be in excellent agreement with calculations based on non-adiabatic perturbation theory, also including relativistic and quantum electrodynamical contributions. The s-wave scattering length of the H + H system is derived from the binding energy of the last bound J=0 level via a direct semi-empirical approach, yielding a value of a_s = 0.2724(5) a_0, in good agreement with a result from a previously followed theoretical approach. The subtle effect of the malpha^4 relativity contribution to a_s was found to be significant. In a similar manner a value for the p-wave scattering volume is determined via the J=1 binding energy yielding a_p = -134.0000(6) a_0^3. The binding energy of the last bound state in H_2, the (v=14, J=4) level, is determined at 0.023(4) cm^{-1}, in good agreement with calculation. The effect of the hyperfine substructure caused by the two hydrogen atoms at large internuclear separation, giving rise to three distinct dissociation limits, is discussed.

We calculate first-order corrections to the energy, radial period, and circumferential turning radii of equatorial periodic orbits around rapidly rotating black holes in dynamical Chern--Simons (dCS) gravity. Using an analytic fit to the metric correction, we match each orbit to a Kerr reference at fixed dimensionless spin, dimensionless specific angular momentum, and rational periodicity. The period correction combines a direct contribution at fixed energy with compensation from the energy adjustment that preserves periodicity. Their competition produces sign changes across orbital families and reference paths. In a two-parameter scan, negative period corrections are dominated by energy compensation for sampled prograde orbits and by the direct contribution for sampled retrograde orbits. We locate C_T=0 boundaries, where the coefficient of the first-order fractional period correction vanishes. Circumferential shifts can differ in sign from coordinate shifts. Numerical kludge waveforms at leading quadrupole order and their discrete spectra connect these corrections to phase accumulation and harmonic frequency shifts. At fixed dimensionless orbital parameters and physical mass of the small body, this phase contribution can be reproduced to first order by rescaling the Kerr mass. For the C_T=0 orbit examined here, this contribution is suppressed at equal black hole masses, while corrections to the waveform and spectral amplitudes remain nonzero.

The peculiar velocities of biased tracers of the cosmic density field contain important information about the growth of large scale structure and generate anisotropy in the observed clustering of galaxies. Using N-body data, we show that velocity expansions for halo redshift-space power spectra are converged at the percent-level at perturbative scales for most line-of-sight angles mu when the first three pairwise velocity moments are included, and that the third moment is well-approximated by a counterterm-like contribution. We compute these pairwise-velocity statistics in Fourier space using both Eulerian and Lagrangian one-loop perturbation theory using a cubic bias scheme and a complete set of counterterms and stochastic contributions. We compare the models and show that our models fit both real-space velocity statistics and redshift-space power spectra for both halos and a mock sample of galaxies at sub-percent level on perturbative scales using consistent sets of parameters, making them appealing choices for the upcoming era of spectroscopic, peculiar-velocity and kSZ surveys.

We develop a novel way to probe subgalactic-scale matter distribution with diffractive lensing on gravitational waves. Five-year observations from Einstein Telescope and DECIGO are expected to probe k= 10^5sim 10^8 ,{rm Mpc}^{-1} down to P(k) = 10^{-16} sim 10^{-14} ,{rm Mpc}^3 level. These results can be interpreted in terms of primordial black holes in the range M_{rm PBH} gtrsim 10^{-3}M_odot down to f_{rm PBH} = 10^{-6} level, or QCD axion minihalos in the range m_a = 10^{-3} sim 10^{-12} ,{rm eV}. A key result of the paper is the approximate relation between the scale k and the gravitational wave frequency f, derived in an ensemble of `multi-lensing' events. This relation enables direct measurement of the power spectrum at specific scales, with sensitivities characterized by model-independent kernels delta P(k). Additionally, we delineate the statistical properties of `multi-lensing' based on the `Fresnel number' N_F. When N_F cal O(1), the statistical significance can be approximately calculated by Variance of lensing effects, which is directly related to the power spectrum among other moments of matter distribution.

We investigate the scattering halos resulting from collisions between discrete momentum components in the time-of-flight expansion of interaction-tunable ^6rm Li_2 molecular Bose-Einstein condensates. A key highlight of this study is the observation of the influence of interactions on the collisional scattering process. We measure the production of scattering halos at different interaction levels by varying the number of particles and the scattering length, and quantitatively assess the applicability of perturbation theory. To delve into a general theory of scattering halos, we introduce a scattering factor and obtain a universal relation between it and the halo ratio. Furthermore, we simulate the formation of scattering halos under non-perturbative conditions and analyze the discrepancies between simulation results and experiments through a return pulse experiment. This study enhances our understanding of the physical mechanisms underlying scattering processes in many-body systems and provides new perspectives for further theoretical research.

We reassess the realistic discovery reach of Solar-System experiments for dark energy (DE) and dark matter (DM), making explicit the bridge from cosmology-level linear responses to local, screened residuals. In scalar-tensor frameworks with a universal conformal coupling A(phi) and chameleon/Vainshtein screening, we map cosmological responses {mu(z,k),Sigma(z,k)} inferred by DESI and Euclid to thin-shell or Vainshtein residuals in deep Solar potentials Phi_N. We emphasize a two-branch strategy. In a detection-first branch, a verified local anomaly -- an Einstein equivalence principle (EEP) violation, a Shapiro-delay signal with |gamma-1|simfewtimes 10^{-6}, an AU-scale Yukawa tail, or a ultralight DM (ULDM) line in clocks/atom interferometers in space (AIS) -- triggers a joint refit of cosmology and Solar-System data under a common microphysical parameterization {V(phi),A(phi)}. In a guardrail branch, Solar-System tests enforce constraints (EEP; PPN parameters gamma,beta; and dot G/G) and close unscreened or weakly screened corners indicated by cosmology. We forecast, per conjunction, |gamma-1|lesssim (2-5)times 10^{-6} (Ka-/X-band or optical Shapiro), eta_{EEP}sim (1--10)times 10^{-17} (drag-free AIS), |dot G/G|sim(3-5)times10^{-15},yr^{-1} (sub-mm-class LLR), a uniform ~2x tightening of AU-scale Yukawa/DM-density bounds, and (3-10)times improved ULDM-coupling reach from clocks. For a conformal benchmark, mu_{ lin,0}=0.10 implies chisimeq mu_{lin,0/2} and a Sun thin shell Delta R/Rlesssim (1/3chi)|gamma-1|/2=2.4times 10^{-3} at |gamma-1|=5times 10^{-6}; Vainshtein screening at 1 AU yields |gamma-1|lesssim 10^{-11}, naturally below near-term reach. We recommend a cost-effective guardrail+discovery portfolio with explicit triggers for escalation to dedicated missions.

To study the onset of scalarization, we investigate linear scalar perturbations around Kerr--Newman black holes in the Einstein-Chern-Simons-Maxwell-scalar theory with quadratic Chern--Simons (CS) coupling γ (hatγ=γ/M^2) and Maxwell coupling η. For this purpose, we employ hyperboloidal Rácz--Tóth evolution and a stationary axisymmetric zero-mode computation. The resulting thresholds are compared with the time-domain response at representative points. For hatγ=0, we find two asymmetric threshold branches in η, while for hatγ=η, the two branches have opposite signs and unequal magnitudes. For unequal CS and Maxwell couplings, the two real threshold branches merge as the spin or CS coupling increases.

This paper constitutes Part III of a series investigating the excitation of non-modal perturbations in hypersonic blunt-nose boundary layers. Based on the numerical shock-fitting harmonic linearised Navier-Stokes (SF-HLNS) approach presented in Part I (Zhao & Dong, J. Fluid Mech. 2025, vol. 1013: A44) and the asymptotic analysis developed in Part II (Dong et al., J. Fluid Mech., under review), the present work focuses specifically on the influence of nose bluntness (Reynolds number R) and wall temperature T_w on receptivity efficiency through seven detailed case studies. Analysed via the three-step asymptotic model, the downstream perturbation amplitude is governed by two distinct factors: the stagnation vorticity perturbation, determined through shock-perturbation interaction and the slow-down convection mechanism, and the parabolic evolution of non-modal perturbations driven by the lift-up mechanism. Increasing R strongly amplifies the stagnation vorticity response, with only mild enhancement of the lift-up effect. In contrast, decreasing T_w strengthens the stagnation vorticity perturbation, but slightly weakens the lift-up effect; the net result is an overall intensification of the downstream perturbation amplitude with decreasing T_w. Furthermore, explicit scaling laws for receptivity efficiency with respect to R and T_w are established. This study completes the theoretical foundation for non-modal receptivity in hypersonic blunt boundary layers, and serves as a key step toward a physics-based transition prediction framework.

Numerical relativity (NR) simulations provide the most faithful representation of the gravitational waves (GWs) emitted by binary black hole (BBH) systems during merger. In the context of GW astronomy, tasks such as parameter estimation can require vast numbers of waveform evaluations per second across the entire parameter space. Since performing full NR simulations for each evaluation is not computationally feasible, interpolating methods for existing NR waveforms, known as surrogate models, have been developed with marked success. In this paper, we build on our previous work to introduce methods to train a fast surrogate model based on neural networks in order to generate BBH merger waveforms, including the fundamental (2,2) mode, as well as the (3,3), (2,1), (4,4), (3,2), (4,3) and (5,5) higher-order modes. Applying a pretraining step on approximant data before fine-tuning on NR data allows us to smooth out the parameter space, and making use of the parallelization ability of GPUs to project the NR waveforms in the inclination-phase (ι, ϕ) sphere during training allows the fitting of all the explored modes simultaneously. The developed surrogate model, DANSur\_HM, achieves average mismatches of the order of 10^{-4}, with the worst mismatch at 2.5times10^{-3}, and achieves throughput above 6times10^5 waveforms/second on an NVIDIA V100 GPU. Parameter estimation tests confirm the usefulness of the inclusion of higher modes.

Understanding the galaxy-halo relationship is not only key for elucidating the interplay between baryonic and dark matter, it is essential for creating large mock galaxy catalogues from N-body simulations. High-resolution hydrodynamical simulations are limited to small volumes by their large computational demands, hindering their use for comparisons with wide-field observational surveys. We overcome this limitation by using the First Light and Reionisation Epoch Simulations (FLARES), a suite of high-resolution (M_gas = 1.8 x 10^6 M_Sun) zoom simulations drawn from a large, (3.2 cGpc)^3 box. We use an extremely randomised trees machine learning approach to model the relationship between galaxies and their subhaloes in a wide range of environments. This allows us to build mock catalogues with dynamic ranges that surpass those obtainable through periodic simulations. The low cost of the zoom simulations facilitates multiple runs of the same regions, differing only in the random number seed of the subgrid models; changing this seed introduces a butterfly effect, leading to random differences in the properties of matching galaxies. This randomness cannot be learnt by a deterministic machine learning model, but by sampling the noise and adding it post-facto to our predictions, we are able to recover the distributions of the galaxy properties we predict (stellar mass, star formation rate, metallicity, and size) remarkably well. We also explore the resolution-dependence of our models' performances and find minimal depreciation down to particle resolutions of order M_DM ~ 10^8 M_Sun, enabling the future application of our models to large dark matter-only boxes.

In this work, we consider the generalized Benjamin-Bona-Mahony equation $partial_t u+partial_x u+partial_x( |u|^pu)-partial_t partial_x^{2}u=0, quad(t,x) in R times R, with p>4. This equation has the traveling wave solutions \phi_{c}(x-ct), for any frequency c>1. It has been proved by Souganidis and Strauss Strauss-1990 that, there exists a number c_{0}(p)>1, such that solitary waves \phi_{c}(x-ct) with 1<c<c_{0}(p) is orbitally unstable, while for c>c_{0}(p), \phi_{c}(x-ct) is orbitally stable. The linear exponential instability in the former case was further proved by Pego and Weinstein Pego-1991-eigenvalue. In this paper, we prove the orbital instability in the critical case c=c_{0}(p)$.

We study quantum corrections in the gravitational path integral around nearly 1/16-BPS black holes in asymptotically AdS_5 times S^5 space, dual to heavy states in 4D N=4 super Yang-Mills. The analysis provides a gravitational explanation of why 1/16-BPS black holes exhibit an exact degeneracy at large N and why all such states have the same charges, confirming the belief that the superconformal index precisely counts the entropy of extremal black holes. We show the presence of a gap of order N^{-2} between the 1/16-BPS black holes and the lightest near-BPS black holes within the same charge sector. This is the first example of such a gap for black holes states within the context of AdS_5 holography. We also derive the spectrum of near-BPS states that lie above this gap. Our computation relies on finding the correct version of the N=2 super-Schwarzian theory which captures the breaking of the SU(1, 1|1) symmetry when the black hole has finite temperature and non-zero chemical potential. Finally, we comment on possible stringy and non-perturbative corrections that can affect the black hole spectrum.

We study the impact of higher-order QCD corrections on Higgs production via weak-boson fusion with subsequent decays of the Higgs boson to bottom-quark pairs. We consider realistic fiducial cuts and observe large corrections in a fixed-order calculation. They arise from the interplay of the particular fiducial cuts considered and the radiative corrections to the Higgs decay subprocess. Switching to a parton-shower-matched description of the decay captures a significant portion of the corrections already at the lowest order and improves the perturbative convergence of the calculation.

We study linear perturbations of the Maldacena-Milekhin-Popov (MMP) wormhole in the parity sector that pairs axial metric perturbations with polar gauge perturbations. It contains the axial gravitational mode and the electric field along the magnetic field lines. The lowest Landau level (LLL) of the charged fermions responds through its charge. The gauge components a_τ, a_ρ form a two-dimensional gauge field on the worldsheet of each field line, and the fermions respond with the exact Schwinger current. Lifted over the sphere, it gives the electric field the MMP screening mass m_S^2=αq^2, which is not small and survives in the mouth. In the throat the perturbation tilts the worldsheets, and the Casimir stress tensor acquires mixed components. Force balance then requires a current across the field lines, and charge conservation fixes an accompanying polarisation current, the counterpart of the Hall current of the polar sector. These currents close the Bianchi identities at first order in the fermionic backreaction α. The system reduces to three coupled master equations, given in closed form and matched to the fermion-free mouth. Consistency alone does not select the fermionic constitutive relation, but locality, covariance and the index theorem do. At α=0 the throat reduces to Poschl-Teller problems with masses l(l-1) and (l+1)(l+2) at m_S^2=0. At finite m_S^2 one mode is screened, one tends to the mass l^2+l+2, and one neutral charge-density wave stays exactly massless. The O(α) shifts of the massive normal frequencies are real and negative. The two parity sectors are isospectral only without fermions. The neutral channel sees an attractive region in each mouth, and a numerical solution coupled to the gravitational channel in the exact mouth potential finds no bound state. The sector has no growing mode for lge2 at this order.

The dynamical realisation of the equation of state p +rho =0 is studied. A non-pathological dynamics for the perturbations of such a system mimicking a dynamical cosmological constant (DCC) requires to go beyond the perfect fluid paradigm. It is shown that an anisotropic stress must be always present. The Hamiltonian of the system in isolation resembles the one of a Pais-Uhlenbeck oscillator and linear stability requires that it cannot be positive definite. The dynamics of linear cosmological perturbations in a DCC dominated Universe is studied in detail showing that when DCC is minimally coupled to gravity no dramatic instability is present. In contrast to what happens in a cosmological constant dominated Universe, the non-relativistic matter contrast is no longer constant and exhibits an oscillator behaviour at small scales while it grows weakly at large scales. In the gravitational waves sector, at small scales, the amplitude is still suppressed as the inverse power of the scale factor while it grows logarithmically at large scales. Also the vector modes propagate, though no growing mode is found.

We study the chemical distance of supercritical Bernoulli percolation on Z^d. Recently, Dembin [Dem22] showed that the chemical distance exhibits sublinear variance, a phenomenon now referred to as superconcentration. In this article, we establish an equivalence between this phenomenon and chaotic behavior of geodesics under small perturbations of the configuration, thereby confirming Chatterjee's general principle relating anomalous fluctuations to chaos in the context of Bernoulli percolation. Our methods rely on a dynamical version of the effective radius, refining the notion first proposed in [CN25], in order to measure the co-influence of a given edge whose weight may be infinite. Together with techniques from the theory of lattice animals, this approach allows us to quantify the total co-influence of edges in terms of the overlap between original and perturbed geodesics.

We examine whether the perturbative renormalization group (RG) regime of stochastic turbulence can be continued from small varepsilon to the physical value varepsilon_{phys}=2, corresponding to large-scale forcing. Exploiting the simplifications of the large-d limit, we calculate the correction exponent ω to five-loop order and find a simple structure suggesting a closed analytic form. This form implies that the fixed point stable near varepsilon=0 ceases to be simultaneously real and infrared stable before reaching varepsilon_{phys}=2, pointing to a possible change of infrared regime rather than a controlled perturbative RG extrapolation.

A sample of 60,410 bona fide optical quasars with astrometric proper motions in Gaia EDR3 and spectroscopic redshifts above 0.5 in an oval 8400 square degree area of the sky is constructed. Using orthogonal Zernike functions of polar coordinates, the proper motion fields are fitted in a weighted least-squares adjustment of the entire sample and of six equal bins of sorted redshifts. The overall fit with 37 Zernike functions reveals a statistically significant pattern, which is likely to be of instrumental origin. The main feature of this pattern is a chain of peaks and dips mostly in the R.A. component with an amplitude of 25~muas yr^{-1}. This field is subtracted from each of the six analogous fits for quasars grouped by redshifts covering the range 0.5 through 7.03, with median values 0.72, 1.00, 1.25, 1.52, 1.83, 2.34. The resulting residual patterns are noisier, with formal uncertainties up to 8~muas yr^{-1} in the central part of the area. We detect a single high-confidence Zernike term for R.A. proper motion components of quasars with redshifts around 1.52 representing a general gradient of 30 muas yr^{-1} over 150degr on the sky. We do not find any small- or medium-scale systemic variations of the residual proper motion field as functions of redshift above the 2.5,sigma significance level.

We present a structural analysis of the young massive star cluster Westerlund 1 (Wd 1). With multi-epoch Hubble Space Telescope (HST) observations, we measure the proper motions of 10346 stars and determine their kinematic memberships by fitting a Gaussian mixture model to their proper motions. After correcting for extinction and completeness, we model the stellar density distribution and confirm the presence of an elongation with an eccentricity of 0.71. The eccentricity decreases slightly with increasing mass. We fit the radial profile with the Elson, Fall, and Freeman model, observing a decrease in the core radius with increasing mass, indicative of weak but detectable mass segregation. This finding is further supported by a measured mass segregation ratio of Lambda_rm MSR=1.11pm0.11, only above 1 by 1sigma, and slightly shorter minimum spanning tree length for higher mass bins. The cluster has a 1D velocity dispersion of 3.42 pm 0.10~km,s^{-1}, suggesting it is subvirial. The subvirial state implies either exceptionally high star formation efficiency or inefficient stellar feedback caused by local gas expulsion before stars reach the cluster. The crossing time is 0.30 Myr and the relaxation time is 0.26 Gyr. Given the age of Wd 1 of 10.7 Myr, we expect evident mass segregation for stars more massive than 10~M_odot, which accounts for the minor mass segregation found in the mass range of 1.00x201312.14~M_odot in this work. This suggests the overall mass segregation in Wd 1 is not primordial.

In the BCS theory of superconductivity the amplitude (Higgs) mode is degenerate with the pair-breaking threshold: its frequency coincides with 2Δ, so it is an edge singularity rather than a true collective mode. This is why after a sudden weak perturbation at t=0 its oscillations decay algebraically as 1/t. We show that the retardation effects due to the phonon dynamics in the strong-coupling theory lift this degeneracy. The Higgs mode detaches from the pair-breaking edge 2Δ_g, set by the spectral gap, and becomes a sharp subgap excitation. We determine its frequency from the longitudinal pair susceptibility evaluated directly on the real frequency axis, using the Eilenberger equations for Migdal--Eliashberg theory with the Einstein phonon spectrum. The response of the mass renormalization supplies at least two fifths of the displacement, and possibly all of it: with it switched off, the binding falls below the resolution of the calculation. Its consequences, however, are significant because a percent-level shift transfers about a quarter of the spectral weight of the amplitude channel out of the two-quasiparticle continuum into a discrete energy level. What experiment sees is therefore not the displacement itself but its consequence: amplitude oscillations that persist instead of decaying as 1/t.

Perturbation-based post-hoc image explanation methods are commonly used to explain image prediction models. These methods perturb parts of the input to measure how those parts affect the output. Since the methods only require the input and output, they can be applied to any model, making them a popular choice to explain black-box models. While many different methods exist and have been compared with one another, it remains poorly understood which parameters of the different methods are responsible for their varying performance. This work uses the Randomized Input Sampling for Explanations (RISE) method as a baseline to evaluate many combinations of mask sampling, segmentation techniques, smoothing, attribution calculation, and per-segment or per-pixel attribution, using a proxy metric. The results show that attribution calculation, which is frequently the focus of other works, has little impact on the results. Conversely, segmentation and per-pixel attribution, rarely examined parameters, have a significant impact. The implementation of and data gathered in this work are available online: https://github.com/guspih/post-hoc-image-perturbation and https://bit.ly/smooth-mask-perturbation.

We compute Kerr-Newman quasinormal modes using a recently found exact separation of the gravitoelectric perturbation equations. For each spin-label ς=pm1, a matrix angular ordinary differential equation and a scalar second-order radial ordinary differential equation define a joint spectral problem for the complex frequency ω and separation constant λ. We solve this problem by imposing regularity at the angular poles, ingoing behavior at the event horizon, and outgoing behavior at infinity. We benchmark the numerical code built to solve the separated equations, and the resulting frequencies, against recently published spectral calculations of the coupled system. Comparisons with those results yield absolute differences of order 10^{-10} to 10^{-5}, depending on the BH parameters and overtone number. We also find numerical hints of spin-label isospectrality in both the electromagnetic-led and gravitational-led sectors of fundamental quasinormal modes, even at near-extremal Kerr-Newman configurations. These results provide numerical evidence that the separated equations reproduce Kerr-Newman quasinormal frequencies and offer a practical route to exploring the ringdown of rotating, charged black holes.

A fully differential calculation in perturbative quantum chromodynamics is presented for the production of massive photon pairs at hadron colliders. All next-to-leading order perturbative contributions from quark-antiquark, gluon-(anti)quark, and gluon-gluon subprocesses are included, as well as all-orders resummation of initial-state gluon radiation valid at next-to-next-to-leading logarithmic accuracy. The region of phase space is specified in which the calculation is most reliable. Good agreement is demonstrated with data from the Fermilab Tevatron, and predictions are made for more detailed tests with CDF and DO data. Predictions are shown for distributions of diphoton pairs produced at the energy of the Large Hadron Collider (LHC). Distributions of the diphoton pairs from the decay of a Higgs boson are contrasted with those produced from QCD processes at the LHC, showing that enhanced sensitivity to the signal can be obtained with judicious selection of events.

We prove strong ill-posedness for the two-dimensional incompressible Euler equation in the endpoint velocity space W^{3,1}_σ(mathbb R^2). Given any compactly supported smooth divergence-free background and any δ>0, we construct a single compactly supported divergence-free datum within δ of the background in W^{3,1}. The perturbation can be localized inside any prescribed nonempty open neighborhood of the background support while remaining disjoint from that support. The associated unique global finite-energy solution u satisfies {rm curl} uin C([0,infty);W^{2,1}(mathbb R^2)), but \[ \operatorname*{ess\,sup}_{0<t<T}\|u(t)\|_{W^{3,1}}=\infty \qquadfor every T>0. \] The proof combines localized hyperbolic insertion, the Bonami--Poornima nonmultiplier mechanism, and many-packet dilution. Moment cancellation and positive material separation control the nonlocal Biot--Savart interactions, allowing a nested construction inside one fixed compact region. Without the compact-support requirement on the limiting datum, a complementary far-field argument yields a dense G_δ set of data whose solutions leave W^{3,1} at every positive rational time and on a residual set of times, with unbounded essential supremum on every nonempty open time interval.

In this work, we study the black hole light echoes in terms of the two-photon autocorrelation and explore their connection with the quasinormal modes. It is shown that the above time-domain phenomenon can be analyzed by utilizing the well-known frequency-domain relations between the quasinormal modes and characteristic parameters of null geodesics. We found that the time-domain correlator, obtained by the inverse Fourier transform, naturally acquires the echo feature, which can be attributed to a collective effect of the asymptotic poles through a weighted summation of the squared modulus of the relevant Green's functions. Specifically, the contour integral leads to a summation taking over both the overtone index and angular momentum. Moreover, the dominant contributions to the light echoes are from those in the eikonal limit, consistent with the existing findings using the geometric-optics arguments. For the Schwarzschild black holes, we demonstrate the results numerically by considering a transient spherical light source. Also, for the Kerr spacetimes, we point out a potential difference between the resulting light echoes using the geometric-optics approach and those obtained by the black hole perturbation theory. Possible astrophysical implications of the present study are addressed.

Scalar field theories of modified gravity are strongly constrained by the absence of detectable long range fifth forces in laboratory and Solar System environments. The chameleon mechanism addresses this problem by making the equilibrium value and effective mass of the scalar field dependent on the ambient matter density. In this work, we investigate an effective phenomenological extension of the chameleon framework in which the scalar potential contains an additional quadratic environmental contribution characterized by a density dependent background frequency. This background frequency is distinct from the frequency of scalar perturbations and parametrizes unresolved environmental effects beyond the conventional matter coupling. For an inverse power law scalar potential, we derive the modified equilibrium configuration and identify a frequency dominated regime in which the environmental contribution controls the density dependence of the field. Linear perturbations about the environmental minimum obey a Klein Gordon dispersion relation with a density-dependent effective mass, and the absence of tachyonic instability requires a positive environmental coupling. We further derive analytical consistency conditions associated with frequency dominance, thin shell screening, fifth-force suppression, and the weak field approximation. Numerical illustrations for representative parameter choices demonstrate how the modified density scaling can enhance fifth-force suppression relative to the conventional chameleon case.

We update predictions for observables in the "delicate" D3/anti-D3 inflationary model on the conifold. We use a full CMB likelihood calculation to assess goodness-of-fit, which is necessary because in this model the zeta power spectrum often cannot be modelled as a power-law over observable scales. For the first time we are able to provide accurate forecasts for the amplitude of three-point correlations. In a significant portion of its parameter space the model follows Maldacena's single-field prediction fNL ~ -(5/12)(ns-1) if nt << 1. Therefore |fNL| is usually small when the power spectrum satisfies observational constraints. In a small number of cases the bispectrum is instead dominated by effects from rapid switching between angular minima. The resulting amplitudes are larger, but mostly with unacceptable spectral behaviour. In the most extreme case we obtain |fNLeq| ~ 75 at kt/3 = 0.002/Mpc. It has been suggested that the quasi-single field inflation ("QSFI") mechanism could produce significant 3-point correlations in this model. We do observe rare shifts in amplitude between equilateral and squeezed configurations that could possibly be associated with QSFI effects, but more investigation is needed to establish the full bispectrum shape. There is evidence of "shape" running between equilateral and squeezed configurations that may be inherited from the scale dependence of the spectrum. We explore the dependence of observables on discrete choices such as the truncation point of the potential. Our analysis illustrates the advantages of a standard format for information exchange within the inflationary model-building and testing community.

The large-D membrane paradigm provides a perturbative, non-gravitational description of black hole dynamics. While the local second law of thermodynamics has been established for neutral membranes, the explicit determination of the local entropy production equation within the charged large-D membrane framework remains unsolved. In this paper, we compute the subleading-order correction to the divergence of the membrane velocity for a charged black hole in a flat background. We evaluate the corresponding scalar Einstein-Maxwell constraint equation at the physical event horizon via the non-affine null Raychaudhuri equation, and relate the physical horizon expressions to the auxiliary membrane kinematics, demonstrating that the membrane velocity produces a non-negative divergence at the first non-vanishing order in the membrane worldvolume, which is driven by two quadratic forms: the membrane shear and a novel contribution generated purely by the Maxwell field. Using this result, we construct the membrane entropy current and prove that its divergence is non-negative through this order, thereby establishing the local second law for the charged large-D membrane paradigm.

We present a spacetime that serves as a horizonless mimicker of extremal black holes. Unlike previously studied mimickers of black holes with non-degenerate horizons, whose geometries are of the wormhole type and consist of two asymptotically flat regions connected by a very long throat, the mimicker of an extremal black hole possesses a single asymptotically flat region at one end and an infinitely long throat at the other. In the throat region, the spacetime approaches the direct-product geometry M_{1,1} times S^2, where M_{1,1} is two-dimensional Minkowski spacetime and S^2 is the two-sphere. We investigate scalar-field dynamics and the fate of the Aretakis instability. Although Aretakis-like modes arise in a local analysis of the throat, they do not lead to a physical instability of the mimicker. A scalar perturbation initially localized in the throat gives rise, at late times, to a sequence of signals with a characteristic separation t_{rm delay}sim 1/λ, where λll 1 is a deformation parameter. This timescale is parametrically larger than the echo time t_{rm echo}sim ln(1/λ) characteristic of non-extremal black-hole mimickers. We refer to this sequence as a {\it long-delay signal train}. Geometrically, the periodicity of the long-delay signals is associated with periodic geodesics on S^2. We then extend the construction to extremal Kerr. In this case, the throat region approaches a generalized product geometry involving M_{1,1} and a two-dimensional surface Σ_2. The corresponding signals are expected to form a quasi-periodic signal train, reflecting the quasi-periodic geodesic motion on Σ_2. We also comment on the generalization to wormhole mimickers of non-extremal black holes and on the implications of these results for unitarity in the context of the AdS/CFT correspondence.

We investigate the spectral statistics of random perturbations of semiclassical Schrödinger operators on compact manifolds, near energy levels corresponding to chaotic classical dynamics. The prototypical example is that of an operator h^2Δ+V(x) that is perturbed by a smooth potential h^αV_ω with αin (0,1), and V_ω is a random potential that decorrelates on distances h^β, with 0<β<2α. We show that for a generic perturbation, the spectral fluctuations of the smoothed counting function of eigenvalues obey a universal behavior at a certain mesoscopic scale, which is coherent with the predictions of random matrix theory.

We establish nonlinear stability of three-dimensional Couette flow for the incompressible Navier--Stokes equations on mathbb Ttimesmathbb R^2. Divergence-free perturbations satisfying |u_{rm in}|_{H^2}+|u^perp_{0,rm in}|_{dot B^{-2}_{2,infty}}leq c_*ν generate unique global H^2 solutions that remain close to Couette flow, where u^perp_{0,rm in} denotes the streamwise average of the transverse velocity. This result retains the O(ν) stability threshold despite the absence of a spanwise spectral gap. The nonzero streamwise modes exhibit enhanced dissipation, their wall-normal component satisfies a viscosity-uniform time-integrated inviscid-damping estimate, and the transverse zero mode decays in L^2 at rate (1+νt)^{-1}. The endpoint space dot B^{-2}_{2,infty} controls the transverse low frequencies, accommodates divergence-form nonlinear forcing, and is critical for linear lift-up from the wall-normal zero mode. The proof combines propagation of this endpoint norm, Fourier splitting, and a two-level roll-to-streak representation with an adaptation of the nonzero-mode framework of Wei--Zhang (CPAM, 2021).

We present Hubble Space Telescope (HST) imaging of Pegasus V and Pisces VII, along with a re-analysis of the archival imaging of Pegasus W, and Jansky Very Large Array (VLA) neutral gas (HI) observations of all three. These three ultra-faint dwarfs (UFDs) are all within the Local Group in the approximate direction of M31. The VLA observations place stringent upper limits on their HI content, with all having M_HI < 10^4;M_odot. As the red giant branches of these UFDs are sparsely populated, we determined distances from the HST photometry of horizontal branch (HB) stars in comparison to a fiducial HB population (from M92), with all three falling in the range 0.7-1 Mpc. Using a new Python-based star formation history (SFH) fitting code (based on StarFISH), we derive SFHs of all three UFDs. As found previously, the best fit SFH for Pegasus W includes significant star formation well beyond the end of reionization, while the SFHs calculated for Pegasus V and Pisces VII are consistent with them having quenched shortly after reionization. These findings for the latter two objects indicate that, like those in the vicinity of the Milky Way, lower mass UFDs in the vicinity of M31 likely quenched at early times.

Layered viscoelastic interiors control the frequency dependence of planetary tidal dissipation, but repeated layered Love-number calculations are expensive in long-term orbital and spin integrations. Equivalent homogeneous rheologies provide a cheaper representation of the same response, but their effective parameters do not by themselves identify the interior layers they represent. We develop a local interpretation of such parameters by differentiating the layered-to-homogeneous construction about a fixed-geometry baseline, perturbing only selected layer rigidities and viscosities. We use the pole-residue representation of the degree-two Love number to construct a physical-to-effective transfer matrix. We then use its singular values, resolution matrix, and mode-dominance matrix to determine which physical perturbations are visible in the Love-number response and how they appear in effective-rheology coordinates. Applied to a five-layer lunar model, the full degree-two response is sensitive to seven of eight solid-layer rheological parameters. The single near-null direction is the inner-core rigidity, consistent with shielding by the fluid outer core and with the weak dependence of Love numbers on core elastic structure. Over the LLR frequency interval, fewer physical directions are visible. To first order, the elastic spring, isolated dashpot, and two Voigt elements reproduce the nine-pole response over this interval. Finite perturbations confirm the tangent prediction to within a few percent, with the validity radius limited by a nearly degenerate pair of long-timescale modes.

In a low-energy effective field theory (EFT), scaling logarithmic terms arise from the renormalization of higher-dimensional couplings that absorb divergences generated by loop integrals with lower-order vertices. Consequently, leading logarithms (LLs) are generated entirely by the leading-order Lagrangian, rendering them universal low-energy predictions. Adapting techniques developed for chiral perturbation theory, we analyze the series of LLs in the EFT of general relativity. As a concrete application, we compute LL corrections to the scalar pole mass up to three-loop order and demonstrate that they can be determined recursively to arbitrary loop order. To confirm the physical validity of our results, we carry out the calculation using a general gauge-fixing parameter and explicitly verify its complete cancellation in the physical observable.

We present the first linear polarization measurements from the 2015 long-duration balloon flight of SPIDER, an experiment designed to map the polarization of the cosmic microwave background (CMB) on degree angular scales. Results from these measurements include maps and angular power spectra from observations of 4.8% of the sky at 95 and 150 GHz, along with the results of internal consistency tests on these data. While the polarized CMB anisotropy from primordial density perturbations is the dominant signal in this region of sky, Galactic dust emission is also detected with high significance; Galactic synchrotron emission is found to be negligible in the SPIDER bands. We employ two independent foreground-removal techniques in order to explore the sensitivity of the cosmological result to the assumptions made by each. The primary method uses a dust template derived from Planck data to subtract the Galactic dust signal. A second approach, employing a joint analysis of SPIDER and Planck data in the harmonic domain, assumes a modified-blackbody model for the spectral energy distribution of the dust with no constraint on its spatial morphology. Using a likelihood that jointly samples the template amplitude and r parameter space, we derive 95% upper limits on the primordial tensor-to-scalar ratio from Feldman-Cousins and Bayesian constructions, finding r<0.11 and r<0.19, respectively. Roughly half the uncertainty in r derives from noise associated with the template subtraction. New data at 280 GHz from SPIDER's second flight will complement the Planck polarization maps, providing powerful measurements of the polarized Galactic dust emission.

We confirm for the first time the existence of distinctive halo bias associated with the quadrupolar type of statistical anisotropy (SA) of the linear matter density field using cosmological N-body simulations. We find that the coefficient of the SA-induced bias for cluster-sized halos takes negative values and exhibits a decreasing trend with increasing halo mass. This results in the quadrupole halo power spectra in a statistically anisotropic universe being less amplified compared to the monopole spectra. The anisotropic feature in halo bias that we found presents a promising new tool for testing the hypothesis of a statistically anisotropic universe, with significant implications for the precise verification of anisotropic inflation scenarios and vector dark matter and dark energy models.

We present a comprehensive treatment of relative oscillation theory for finite Jacobi matrices. We show that the difference of the number of eigenvalues of two Jacobi matrices in an interval equals the number of weighted sign-changes of the Wronskian of suitable solutions of the two underlying difference equations. Until now only the case of perturbations of the main diagonal was known. We extend the known results to arbitrary perturbations, allow any (half-)open and closed spectral intervals, simplify the proof, and establish the comparison theorem.

We construct high-accuracy semi-analytic mode functions for scalar cosmological perturbations in mLQC-I within the hybrid approach to study ultraviolet regularity and gravitational particle creation. The evolution comprises an asymptotic pre-de Sitter branch, a pre-inflationary region containing the quantum bounce, and inflation. In the intermediate region, we construct the complete third-order uniform asymptotic solution and introduce adaptive defect correction. The third-order approximation achieves sub-percent complex-mode accuracy for representative higher-wavenumber modes; defect-corrected solutions agree with numerical evolution at the 0.00001% level over the tested low-wavenumber range. Retaining amplitudes and phases provides a controlled basis for future precision calculations of primordial power spectra and non-Gaussian correlations. We compare the de Sitter vacuum selected in the remote contracting branch with a fourth-order adiabatic state imposed at the bounce. Finite-wavenumber matching and the strict ultraviolet limit require different asymptotic treatments: extrapolating the leading connection to infinite wavenumber yields a spurious constant negative-frequency coefficient and an apparent ultraviolet divergence. Instead, the large-wavenumber de Sitter mode agrees with the fourth-order adiabatic expansion through the order required for energy-momentum tensor renormalization, and smooth exact evolution preserves this ultraviolet structure. Finite and intermediate modes can nevertheless undergo nonadiabatic Bogoliubov mixing and particle creation. Finite-mode particle production thus coexists with ultraviolet regularity. The ultraviolet argument also extends to the dressed-metric approach in its corresponding large-wavenumber regime, while quantitative mode functions must be recalculated using its effective mass.

Tobasco et al. [Physics Letters A, 382:382-386, 2018; see https://doi.org/10.1016/j.physleta.2017.12.023] recently suggested that trajectories of ODE systems that optimize the infinite-time average of a certain observable can be localized using sublevel sets of a function that arise when bounding such averages using so-called auxiliary functions. In this paper we demonstrate that this idea is viable and allows for the computation of extremal unstable periodic orbits (UPOs) for polynomial ODE systems. First, we prove that polynomial optimization is guaranteed to produce auxiliary functions that yield near-sharp bounds on time averages, which is required in order to localize the extremal orbit accurately. Second, we show that points inside the relevant sublevel sets can be computed efficiently through direct nonlinear optimization. Such points provide good initial conditions for UPO computations. As a proof of concept, we then combine these methods with a single-shooting Newton-Raphson algorithm to study extremal UPOs for a nine-dimensional model of sinusoidally forced shear flow. We discover three previously unknown families of UPOs, one of which simultaneously minimizes the mean energy dissipation rate and maximizes the mean perturbation energy relative to the laminar state for Reynolds numbers approximately between 81.24 and 125.

Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features (outputs of the penultimate layer) of within-class samples decreases and the mean features of different classes approach a certain tight frame structure. Recent works analyze this behavior via idealized unconstrained features models where all the minimizers exhibit exact collapse. However, with practical networks and datasets, the features typically do not reach exact collapse, e.g., because deep layers cannot arbitrarily modify intermediate features that are far from being collapsed. In this paper, we propose a richer model that can capture this phenomenon by forcing the features to stay in the vicinity of a predefined features matrix (e.g., intermediate features). We explore the model in the small vicinity case via perturbation analysis and establish results that cannot be obtained by the previously studied models. For example, we prove reduction in the within-class variability of the optimized features compared to the predefined input features (via analyzing gradient flow on the "central-path" with minimal assumptions), analyze the minimizers in the near-collapse regime, and provide insights on the effect of regularization hyperparameters on the closeness to collapse. We support our theory with experiments in practical deep learning settings.

In this work, we compute multi-field core and halo properties in wave Dark Matter models. We focus on the case where Dark Matter consists of two light (real) scalars, interacting gravitationally. As in the single-field Ultra Light Dark Matter (ULDM) case, the scalar field behaves as a coherent BEC with a definite ground state (at fixed total mass), often referred to in the literature as a gravitational soliton. We establish an efficient algorithm to find the ground and excited states of such two-field systems. We then use simulations to investigate the gravitational collapse and virialization, starting from different initial conditions, into solitons and surrounding halo. As in the single-field case, a virialized halo forms with a gravitational soliton (ground state) at the center. We find some evidence for an empirical relation between the soliton mass and energy and those of the host halo. We use this to then find a numerical relation between the properties of the two. Finally, we use this to address the issue of alleviating some of the tensions that single-field ULDM has with observational data, in particular, the issue of how a galaxy's core and radius are related. We find that if galaxies of different masses have similar percentages of the two species, then the core-radius scaling tension is not addressed. However, more general possibilities occur if the relative abundance of species in each halo correlates with the total mass of the galaxy. If this is the case, the model predicts several other phenomenological signatures.

The millisecond pulsar PSR J0435+3233, discovered by FAST, exhibits an unusually large apparent spin-down rate, potentially reflecting line-of-sight acceleration from a distant companion. Recent investigations reveal a hierarchical triple consisting of an inner pulsar-helium white dwarf binary with an orbital period of ~8 days, orbited by a G-type subgiant tertiary on an eccentric ~74 yr orbit. The current timing description admits two distinct geometrical solutions. We develop a singly averaged (SA) formulation that averages over the inner orbit while retaining the instantaneous phase of the eccentric outer orbit, thereby capturing the time-dependent quadrupolar perturbations induced by the tertiary. We show how this physical three-body description can be incorporated naturally into pulsar-timing analyses and use it to forward-propagate the two currently viable configurations, Tv1 and Tv2, to forecast when their timing signatures become distinguishable with FAST. The SA evolution predicts that the two configurations will become distinguishable in the coming years, with the effective projected semi-major axis, x_{1,eff}, providing the earliest discriminating observable. We further extend the framework to predict the tertiary's spectroscopic radial-velocity and astrometric evolution, linking FAST timing with LAMOST time-domain spectroscopy and Gaia astrometry. This multi-band framework has the potential to establish PSR J0435+3233 as an exceptionally well-constrained laboratory for three-body dynamics, compact-binary and stellar evolution, and gravitational physics.

We study the response of mono-energetic stellar populations with initially isotropic kinematics to impulsive and adiabatic changes to an underlying dark matter potential. Half-light radii expand and velocity dispersions decrease as enclosed dark matter is removed. The details of this expansion and cooling depend on the time scale on which the underlying potential changes. In the adiabatic regime, the product of half-light radius and average velocity dispersion is conserved. We show that the stellar populations maintain centrally isotropic kinematics throughout their adiabatic evolution, and their densities can be approximated by a family of analytical radial profiles. Metallicity gradients within the galaxy flatten as dark matter is slowly removed. In the case of strong impulsive perturbations, stellar populations develop power-law-like density tails with radially biased kinematics. We show that the distribution of stellar binding energies within the dark matter halo substantially widens after an impulsive perturbation, no matter the sign of the perturbation. This allows initially energetically separated stellar populations to mix, to the extent that previously chemo-dynamically distinct populations may masquerade as a single population with large metallicity and energy spread. Finally, we show that in response to an impulsive perturbation, stellar populations that are deeply embedded in cored dark matter halos undergo a series of damped oscillations before reaching a virialised equilibrium state, driven by inefficient phase mixing in the harmonic potentials of cored halos. This slow return to equilibrium adds substantial systematic uncertainty to dynamical masses estimated from Jeans modeling or the virial theorem.

We investigate scale-dependent modifications to the primordial scalar power spectrum as potential solutions to the Hubble tension. We use the Fisher-bias formalism, recently adapted to examine perturbed recombination solutions to the Hubble tension, and extend its range of validity with an iterative method. We first analyze the Planck cosmic microwave background (CMB) anisotropy data, demonstrating the existence of modifications to the primordial power spectrum capable of fully resolving the tension between Planck and SH0ES. As a proof of concept, we interpret these solutions in terms of small, time-dependent variations in the first slow roll parameter or in the sound speed of curvature perturbations during a stage of primordial inflation. However, these solutions are associated with a low total matter density Ω_m, which makes them inconsistent with baryon acoustic oscillations (BAO) and uncalibrated supernovae (SNIa) data. When incorporating additional BOSS and PantheonPlus data, the solutions that reduce the Hubble tension tend to overfit Planck CMB data to compensate for the worsened fit to BAO and SNIa data, making them less compelling. These findings suggest that modifying the primordial power spectrum alone is unlikely to provide a robust resolution to the tension and highlight how the viability of such data-driven solutions depends on the specific datasets considered, emphasizing the role of future high-precision observations in further constraining possible resolutions to the tension.

In this paper, we study the long time dynamics of small perturbations of static domain walls in weighted Sobolev spaces for the one dimensional Schrödinger map with constant Dzyaloshinskii-Moriya interaction. The perturbation equation contains derivative nonlinearities, and its linearized operator has a threshold resonance. The results are twofold. (i) We prove the asymptotic stability of the domain wall modulo the translation and rotation symmetries. More precisely, the corresponding modulation parameters converge as time tends to infinity, while the radiation decays at the sharp rate t^{-1/2}. (ii) We prove that the radiation exhibits modified scattering, with an explicit logarithmic phase correction generated by the long range cubic interaction. The proof develops geometric reduction to overcome the loss of derivatives and exploits structural cancellations in the nonlinear interactions.

We prove nonlinear stability of the Guderley imploding shock under radial perturbations for the three-dimensional compressible Euler equations in the adiabatic range 1<γleq5{3}. The perturbed solutions develop an asymptotically self-similar implosion in finite time. Our result allows perturbations with small, nonzero constant pressure in the quiescent region ahead of the shock. The proof combines weighted L^infty estimates along characteristics with a computer-assisted proof of stability inequalities for the Guderley profile.

We establish a charge-regular formulation of separated Kerr--Newman perturbations and an explicit map from master solutions to physical radiative fields. We derive regular angular and radial first-order systems and their second-order reductions, with finite-charge deformations of the spin pm1 and pm2 Teukolsky equations. The field and boundary normalizations recover the standard Kerr conventions while accounting for the nonuniform zero-charge limit at infinity. For physical Einstein--Maxwell perturbations with the usual peeling behavior, we obtain explicit outgoing gravitational and electromagnetic amplitudes and energy fluxes at nonzero real frequency. The resulting finite-charge radiation-composition ratios depend only on the regular angular functions, independently of the radial excitation.

In this study of the `Resolving supermAssive Black hole Binaries In galacTic hydrodynamical Simulations' (RABBITS) series, we investigate the orbital evolution of supermassive black holes (SMBHs) during galaxy mergers. We simulate both disc and elliptical galaxy mergers using the KETJU code, which can simultaneously follow galaxy (hydro-)dynamics and small-scale SMBH dynamics with post-Newtonian corrections. With our SMBH binary subgrid model, we show how active galactic nuclei (AGNs) feedback affects galaxy properties and SMBH coalescence. We find that simulations without AGN feedback exhibit excessive star formation, resulting in merger remnants that deviate from observed properties. Kinetic AGN feedback proves more effective than thermal AGN feedback in expelling gas from the centre and quenching star formation. The different central galaxy properties, which are a result of distinct AGN feedback models, lead to varying rates of SMBH orbital decay. In the dynamical friction phase, galaxies with higher star formation and higher SMBH masses possess denser centres, become more resistant to tidal stripping, experience greater dynamical friction, and consequently form SMBH binaries earlier. As AGN feedback reduces gas densities in the centres, dynamical friction by stars dominates over gas. In the SMBH hardening phase, compared to elliptical mergers, disc mergers exhibit higher central densities of newly formed stars, resulting in accelerated SMBH hardening and shorter merger time-scales (i.e. lesssim 500 Myr versus gtrsim 1 Gyr). Our findings highlight the importance of AGN feedback and its numerical implementation in understanding the SMBH coalescing process, a key focus for low-frequency gravitational wave observatories.

We report on analysis of the two-color VR CCD observations of the newly discovered variable 2MASS J18024395+4003309=VSX J180243.9+400331 obtained using the 1-m telescope of the Mt. Lemmon Observatory (LOAO) in the field of the intermediate polar V1323 Her. The extended version of this conference talk we published in 2015JASS...32..127A. The variability was reported in 2012OAP....25..150A, and the object was monitored. The two-color observations covered all phase interval. The object is classified as an Algol-type variable with tidally distorted components, and shows an asymmetry of the maxima (the O\'Connell effect). For phenomenological modeling, we used the trigonometric polynomial approximation of statistically optimal degree, and a recent method "NAV" (New Algol Variable) using local specific shapes for the eclipse. Methodological aspects are described, especially for the case of few color observations. Estimates of the physical parameters based on analysis of phenomenological parameters, are presented.

Photometric and spectroscopic observations of GV Leo were performed from 2017 to 2024. The light curves show a flat bottom at the primary eclipse and the conventional O'Connell effect. The echelle spectra reveal that the effective temperature and rotation velocity of the more massive secondary are T_{rm eff,2} = 5220pm120 K and v_2 sin i = 223pm40 km s^{-1}, respectively. Our binary modeling indicates that the program target is a W-subclass contact binary with a mass ratio of q = 5.48, an inclination angle of i = 81^circ.68, a temperature difference of (T_{rm eff,1}-T_{rm eff,2}) = 154 K, and a filling factor of f = 36 \%. The light asymmetries were reasonably modeled by a dark starspot on the secondary's photosphere. Including our 26 minimum epochs, 84 times of minimum light were used to investigate the orbital period of the system. We found that the eclipse times of GV Leo have varied by a sinusoid with a period of 14.9 years and a semi-amplitude of 0.0076 days superimposed on a downward parabola. The periodic modulation is interpreted as a light time effect produced by an unseen outer tertiary with a minimum mass of 0.26 M_odot, while the parabolic component is thought to be a combination of mass transfer (secondary to primary) and angular momentum loss driven by magnetic braking. The circumbinary tertiary would have caused the eclipsing pair of GV Leo to evolve into its current short-period contact state by removing angular momentum from the primordial widish binary.

Outer-learning algorithms use infinitesimal sensitivities to propose finite changes to initialization or training parameters. For hard-ReLU training, the derivative of the finite program and the derivative of its flow limit do not by themselves specify the response at a chosen radius. We characterize the intervening regime in which the perturbation radius is proportional to the GD step. Integer event rounding then survives at leading order: smooth Euler bias shifts each discrete phase, and upstream rounding moves downstream branch boundaries. We derive the crossing indices and a uniform endpoint expansion for finitely many separated transverse events in piecewise-C^2 dynamics, away from recursive phase boundaries. In contractive affine regions, an explicit remainder and complete branch verification certify finite candidate comparisons. Scalar phase frequencies and a coupled feedback ablation test the mechanism; frozen nonlinear-network experiments show radius-dependent prediction accuracy, including incomplete branch matches and failed-word tails. Together with local AD and uniform flow consistency, the result identifies sufficient response regimes: differentiating training is a choice of perturbation resolution as well as a choice of derivative.

The origins of the colors of Trans-Neptunian Objects (TNOs) represent a crucial unresolved question, central to understanding the history of our Solar System. Recent observational surveys have revealed correlations between the eccentricity and inclination of TNOs and their colors. This has rekindled the long-standing debate on whether these colors reflect the conditions of TNO formation or their subsequent collisional evolution. In this study, we address this question with 98.7% certainty, using a model-agnostic, data-driven approach based on causal graphs. First, as a sanity check, we demonstrate how our model can replicate the currently accepted paradigms of TNOs' dynamical history, blindly and without any orbital modeling or physics-based assumptions. In fact, our causal model (with no knowledge of the existence of Neptune) predicts the existence of an unknown perturbing body, i.e., Neptune. We then show how this model predicts, with high certainty, that the color of TNOs is the root cause of their inclination distribution, rather than the other way around. This strongly suggests that the colors of TNOs reflect an underlying dynamical property, most likely their formation location. Moreover, our causal model excludes formation scenarios that invoke substantial color modification by subsequent irradiation. We therefore conclude that the colors of TNOs are predominantly primordial.

We study scalaron quasinormal modes and quasi-bound states of Schwarzschild black holes directly within the Bondi-Sachs formulation of metric f(R) gravity, combining frequency-domain analyses with characteristic time evolution. Starting from the linearised characteristic equations, we obtain the massive scalar master equation and show that the tensor master equation takes the same form as in general relativity. For the analytic models considered here, the linear scalar spectra depend on the f(R) theory only through the dimensionless combination μM. We compute both quasinormal and quasi-bound spectral branches using Leaver's continued-fraction method and compare them with independent literature benchmarks. To complement the frequency domain analysis, we evolve the scalaron perturbation equations using a fourth order convergent characteristic scheme. Applying matrix-pencil stability scans to the resulting waveforms, we independently recover fundamental quasinormal frequencies consistent with the continued-fraction results within the measured extraction-stability scales. Finally, for a selected finite-mass case, we demonstrate the extraction of both oscillation frequencies and damping rates of the fundamental quasinormal mode and quasi-bound state from separate time windows of the same waveform at one extraction radius, without imposing either spectral branch at the finite outer boundary.

We present cosmological parameter results from the final full-mission Planck measurements of the CMB anisotropies. We find good consistency with the standard spatially-flat 6-parameter LambdaCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted "base LambdaCDM" in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Omega_c h^2 = 0.120pm 0.001, baryon density Omega_b h^2 = 0.0224pm 0.0001, scalar spectral index n_s = 0.965pm 0.004, and optical depth tau = 0.054pm 0.007 (in this abstract we quote 68,% confidence regions on measured parameters and 95,% on upper limits). The angular acoustic scale is measured to 0.03,% precision, with 100theta_*=1.0411pm 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-LambdaCDM cosmology, the inferred late-Universe parameters are: Hubble constant H_0 = (67.4pm 0.5)km/s/Mpc; matter density parameter Omega_m = 0.315pm 0.007; and matter fluctuation amplitude sigma_8 = 0.811pm 0.006. We find no compelling evidence for extensions to the base-LambdaCDM model. Combining with BAO we constrain the effective extra relativistic degrees of freedom to be N_{rm eff} = 2.99pm 0.17, and the neutrino mass is tightly constrained to sum m_nu< 0.12eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base -LambdaCDM at over 2,sigma, which pulls some parameters that affect the lensing amplitude away from the base-LambdaCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. (Abridged)

Context. Understanding how the shape of cloud particle size distributions affects the atmospheric properties of sub-stellar atmospheres is a key area to explore, particularly in the JWST era of broad wavelength coverage, where observations are sensitive to particle size distributions. It is therefore important to elucidate how underlying cloud microphysical processes influence the size distribution, in order to better understand how clouds affect observed atmospheric properties. Aims. In this follow-up paper, we aim to extend our sub-stellar atmosphere microphysical cloud formation framework from Paper I to include effects of assuming a polydisperse gamma particle size distribution, requiring a three-moment solution set of equations. Methods. We develop a three-moment framework for sub-stellar mineral cloud particle microphysical nucleation, condensation, evaporation and collisional growth assuming a gamma distribution. As in the previous paper, we demonstrate the effects of polydispersity using a simple one-dimensional Y-dwarf KCl cloud formation scenario, and compare the results with the monodisperse case. Results. Our three-moment scheme provides a generalised framework applicable to any size distribution with a defined moment generation expression. In our test case, we show that the gamma distribution evolves with altitude, initially broad at the cloud base and narrowing at lower pressures. We find that differences between the gamma and monodisperse cloud structures can be significant, depending on the surface gravity of the atmosphere. Conclusions. We present a self-consistent framework for including the effects of polydispersity for sub-stellar microphysical cloud studies using the moment method.

Despite the recent advances in the field of computational Schr\"odinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal solver which plays the role of simple-yet-effective baseline for SB just like, e.g., k-means method in clustering, logistic regression in classification or Sinkhorn algorithm in discrete optimal transport. We address this issue and propose a novel fast and simple SB solver. Our development is a smart combination of two ideas which recently appeared in the field: (a) parameterization of the Schr\"odinger potentials with sum-exp quadratic functions and (b) viewing the log-Schr\"odinger potentials as the energy functions. We show that combined together these ideas yield a lightweight, simulation-free and theoretically justified SB solver with a simple straightforward optimization objective. As a result, it allows solving SB in moderate dimensions in a matter of minutes on CPU without a painful hyperparameter selection. Our light solver resembles the Gaussian mixture model which is widely used for density estimation. Inspired by this similarity, we also prove an important theoretical result showing that our light solver is a universal approximator of SBs. Furthemore, we conduct the analysis of the generalization error of our light solver. The code for our solver can be found at https://github.com/ngushchin/LightSB

The properties of the stellar cluster surrounding Sagittarius A* can be assessed indirectly through the motion of the S-stars. Specifically, the current accuracy to which the prograde precession of the S2 star is measured allows to place significant constraints on the extended mass enclosed by its orbit. We suggest that high velocity destructive collisions (DCs) offer a natural mechanism for depleting the mass inside the S2 orbit, thus allowing to reconcile the measured precession and the existence of a dense stellar cluster. Such a solution is especially necessary when considering that stars are supplied to the inner part of the cluster by both dynamical relaxation and by stars being captured in tight orbits during tidal disruption of binaries. We use analytic arguments and results from simulations to demonstrate that in order to obtain a precession that is consistent with observations, collisional depletion is necessary if the capture rate is greater than a few 10^{-6} yr^{-1}. We also show that fluctuations arising from the finite number of stars cannot serve as an alternative to DCs for generating consistency with the observed S2 precession. We conclude that astrometric observations of the S-stars provide a meaningful indication that the inner part of our galactic center is shaped by collisional depletion, supporting the hypothesis that DCs occur in galactic nuclei at an astrophysically significant rate.

In this paper we use a traveling wave reduction or a so-called spatial approximation to comprehensively investigate the periodic solutions of the complex cubic-quintic Ginzburg-Landau equation. The primary tools used here are Hopf bifurcation theory and perturbation theory. Explicit results are obtained for the post-bifurcation periodic orbits and their stability. Generalized and degenerate Hopf bifurcations are also briefly considered to track the emergence of global structure such as homoclinic orbits.

We determine the quadrupolar logarithmic tidal response of electrically charged Einstein-Euler-Heisenberg black holes from the coupled static odd-parity gravitational and electromagnetic equations. Although the second electromagnetic invariant vanishes on the electric background, its quadratic interaction contributes to the axial fluctuation equations. At first order in the Euler-Heisenberg coupling a, a direct asymptotic recursion gives the canonical running matrix C_{rm can}^{rm EH}=(9aQ^2/10)left(smallmatrix0&-Q-Q&Msmallmatrixright), defined as the coefficients multiplying the canonical source vector in the r^{-2}log(r_0/r) term. The resulting local coefficients retain the full dependence on the subextremal ratio Q{M} at this perturbative order. The two quartic invariants partially cancel in both nonzero channels, while the action-normalized fields make gravitoelectromagnetic reciprocity explicit. The local extremal limit of the running matrix reproduces the corresponding two-invariant effective-field-theory result after convention conversion. Allowing independent quartic couplings further shows that identical electric background geometries can have different axial running matrices and yields algebraic inverse relations within the specified two-operator model. The calculation determines local logarithmic running within minimally coupled quartic electrodynamics; the finite horizon-matched response requires an additional global matching calculation.

We study the pole mass for a heavy quark probe in the Gross--Neveu model, at the first non-trivial order in the 1/N expansion. We show that this mass suffers from a perturbative renormalon ambiguity structurally similar to the one in QCD. The exact large N solution leads however to an explicit expression for the pole mass which can be decoded as a trans-series, and we find that non-perturbative corrections cure the renormalon ambiguity. We also calculate the self-energy of the heavy quark beyond perturbation theory by using the OPE method with condensates, and show that the results are in agreement with the large N solution. The non-perturbative corrections to the pole mass turn out to be determined to a large extent by the condensate corrections to the self-energy. However, there is a class of corrections that has to be reorganized due to on-shell effects and cannot be obtained from the conventional condensate expansion. We discuss possible implications of this toy model for QCD.

We continue our program of investigation of the proper motions of spectrally separated structures in the Herbig-Haro outflows with the aid of Fabry-Perot scanning interferometry. This work mainly focuses on the physical nature of various structures in the jets. The aim of the present study is to measure the proper motions of the previously discovered kinematically separated structures in the working surface of the HH 83 collimated outflow. We used observations from two epochs separated by 15 years, which were performed on the 6m telescope with Fabry-Perot scanning interferometer. We obtained images corresponding to different radial velocities for the two separate epochs, and used them to measure proper motions. In the course of our data analysis, we discovered a counter bow-shock of HH 83 flow with positive radial velocity, which makes this flow a relatively symmetric bipolar system. The second epoch observations confirm that the working surface of the flow is split into two structures with an exceptionally large (250 km\ s^{-1}) difference in radial velocity. The proper motions of these structures are almost equal, which suggests that they are physically connected. The asymmetry of the bow shock and the turning of proper motion vectors suggests a collision between the outflow and a dense cloud. The profile of the Halpha line for the directly invisible infrared source HH 83 IRS, obtained by integration of the data within the reflection nebula, suggests it to be of P Cyg type with a broad absorption component characteristic of the FU Ori like objects. If this object underwent an FU Ori type outburst, which created the HH 83 working surfaces, its eruption took place about 1500 years ago according to the kinematical age of the outflow.

We use deep, mu_{r} lesssim 28,mag,arcsec^{-2}, r-band imaging from the Dark Energy Camera Legacy Survey (DECaLS) to search for past, or ongoing, merger activity in a sample of 282 Low Excitation Radio Galaxies (LERGs) at z<0.07. Our principle aim is to assess the the role of mergers in the evolution of LERGs. Exploiting the imaging depth, we classify tidal remnants around galaxies as both minor and major morphological disturbances for our LERG sample and 1,622 control galaxies matched in redshift, stellar mass, and environment. In groups and in the field, the LERG minor merger fraction is consistent with the control population. In galaxy clusters, 8.8 pm 2.9, % of LERGs show evidence of recent minor mergers in contrast to 23.0pm 2.0, % of controls. This sim 4 sigma deficit of minor mergers in cluster LERGs suggests these events may inhibit this type of nuclear activity for galaxies within the cluster environment. We observe a > 4sigma excess of major mergers in the LERGs with M_{*} lesssim 10^{11},M_{odot}, with 10 pm 1.5, % of these AGN involved in such large-scale interactions compared to 3.2 pm 0.4,% of control galaxies. This excess of major mergers in LERGs decreases with increasing stellar mass, vanishing by M_{*} > 10^{11.3},M_{odot}. These observations show that minor mergers do not fuel LERGs, and are consistent with typical LERGs being powered by accretion of matter from their halo. Where LERGs are associated with major mergers, these objects may evolve into more efficiently accreting active galactic nuclei as the merger progresses and more gas falls on to the central engine.

We present results of the long-term multi-wavelength study of optical, UV and X-ray variability of the nearby changing-look (CL) Seyfert NGC 1566 observed with the Swift Observatory and the MASTER Global Robotic Network from 2007 to 2019. We started spectral observations with South African Astronomical Observatory 1.9-m telescope soon after the brightening was discovered in July 2018 and present here the data for the interval between Aug. 2018 to Sep. 2019. This paper concentrates on the remarkable post-maximum behaviour after July 2018 when all bands decreased with some fluctuations. We observed three significant re-brightenings in the post-maximum period during 17 Nov. 2018 - 10 Jan. 2019, 29 Apr. - 19 Jun. 2019 and 27 Jul.- 6 Aug. 2019. An X-ray flux minimum occurred in Mar. 2019. The UV minimum occurred about 3 months later. It was accompanied by a decrease of the Luv/Lx ratio. New post-maximum spectra covering (31 Nov. 2018 - 23 Sep. 2019) show dramatic changes compared to 2 Aug. 2018, with fading of the broad lines and [Fe X]6374 until Mar. 2019. These lines became somewhat brighter in Aug.-Sep. 2019. Effectively, two CL states were observed for this object: changing to type 1.2 and then returning to the low state as a type 1.8 Sy. We suggest that the changes are due mostly to fluctuations in the energy generation. The estimated Eddington ratios are about 0.055% for minimum in 2014 and 2.8% for maximum in 2018.

This work, together with its companion paper, Secco and Samuroff et al. (2021), presents the Dark Energy Survey Year 3 cosmic shear measurements and cosmological constraints based on an analysis of over 100 million source galaxies. With the data spanning 4143 deg^2 on the sky, divided into four redshift bins, we produce the highest significance measurement of cosmic shear to date, with a signal-to-noise of 40. We conduct a blind analysis in the context of the ΛCDM model and find a 3% constraint of the clustering amplitude, S_8equiv σ_8 (Ω_{rm m}/0.3)^{0.5} = 0.759^{+0.025}_{-0.023}. A ΛCDM-Optimized analysis, which safely includes smaller scale information, yields a 2% precision measurement of S_8= 0.772^{+0.018}_{-0.017} that is consistent with the fiducial case. The two low-redshift measurements are statistically consistent with the Planck Cosmic Microwave Background result, however, both recovered S_8 values are lower than the high-redshift prediction by 2.3σ and 2.1σ (p-values of 0.02 and 0.05), respectively. The measurements are shown to be internally consistent across redshift bins, angular scales and correlation functions. The analysis is demonstrated to be robust to calibration systematics, with the S_8 posterior consistent when varying the choice of redshift calibration sample, the modeling of redshift uncertainty and methodology. Similarly, we find that the corrections included to account for the blending of galaxies shifts our best-fit S_8 by 0.5σ without incurring a substantial increase in uncertainty. We examine the limiting factors for the precision of the cosmological constraints and find observational systematics to be subdominant to the modeling of astrophysics. Specifically, we identify the uncertainties in modeling baryonic effects and intrinsic alignments as the limiting systematics.

We use the First Light And Reionisation Epoch Simulations (FLARES) to study the evolution of the rest-frame ultraviolet (UV) and far-infrared (FIR) sizes for a statistical sample of massive (gtrsim10^{9}M_{odot}) high redshift galaxies (z in [5,10]). Galaxies are post-processed using the SKIRT radiative transfer code, to self-consistently obtain the full spectral energy distribution and surface brightness distribution. We create mock observations of the galaxies for the Near Infrared Camera (NIRCam) to study the rest-frame UV 1500 xC5 morphology. We also generate mock rest-frame FIR (50 mum) photometry and mock ALMA (158 mum) (0.01"-0.03" and approx0.3" angular resolution) observations to study the dust-continuum. We find the effect of dust on observed sizes reduces with increasing wavelength from the UV to optical (sim0.6 times the UV at 0.4mum), with no evolution in FIR sizes. Observed sizes vary within 0.4-1.2 times the intrinsic sizes at different signal to noise ratios (SNR = 5-20) across redshifts. The effect of PSF and noise makes bright structures prominent, whereas fainter regions blend with noise, leading to an underestimation (factor of 0.4-0.8) of sizes at SNR=5. At SNR=15-20, the underestimation reduces (factor of 0.6-0.9) at z=5-8 but due to PSF, at z=9-10, bright cores are dominant, resulting in an overestimation (factor of 1.0-1.2). For ALMA, low resolution sizes are effected by noise which acts as extended emission. The size evolution in UV broadly agrees with current observational samples and other simulations. This work is one of the first to analyse the panchromatic sizes of a statistically significant sample of simulated high-redshift galaxies, complementing a growing body of research highlighting the importance of conducting an equivalent comparison between observed galaxies and their simulated counterparts in the early Universe.

A detailed measurement is made of the metallicity distributions, kinematics and dynamics of the thin and thick disks, across a large disk volume (5.0 leq R leq 15.0 kpc and |Z| leq3.0 kpc), by using the LAMOST-APOGEE red clump stars. The metallicity distributions results show that the radial metallicity gradient Delta[Fe/H]/DeltaR of the thin disk weakens with |Z| from -0.06 dex kpc^{-1} at around |Z| < 0.25 kpc to -0.02 dex kpc^{-1} at around |Z| > 2.75 kpc, while the thick disk displays a global weak positive Delta[Fe/H]/DeltaR, generally weaker than 0.01 dex kpc^{-1}. The vertical metallicity gradient Delta[Fe/H]/Delta|Z| weakened steadily from -0.36 dex kpc^{-1} at R sim 5.5 kpc to -0.05 dex kpc^{-1} at around R > 11.5 kpc for the thin disk, while the thick disk presents an almost constant value (nearly -0.06 sim -0.08 dex kpc^{-1}) for all the R bins. These results indicate the contribution of the radial migration to the disk evolution, and the obvious north-south asymmetry in [Fe/H] may be linked to the disk warp and/or the disk perturbation events. The oscillations of the corrected Delta[Fe/H]/Delta|Z| with R are likely because of the resonances with the Galactic Bar. Our detailed measurements of DeltaV_{phi}/Delta[Fe/H] indicate an "inside-out" and "upside-down" star formation scenario for the thick disk. The results of eccentricity distributions and [alpha/Fe]--velocity dispersion relations are likely to suggest that the thick disk stars require an obvious contribution from other heating mechanisms such as merger and accretion, or born in the chaotic mergers of gas-rich systems and/or turbulent interstellar medium.

We revisit the flat-sky approximation for evaluating the angular power spectra of projected random fields by retaining information about the correlations along the line of sight. With broad, overlapping radial window functions, these line-of-sight correlations are suppressed and are ignored in the Limber approximation. However, retaining the correlations is important for narrow window functions or unequal-time spectra but introduces significant computational difficulties due to the highly oscillatory nature of the integrands involved. We deal with the integral over line-of-sight wave-modes in the flat-sky approximation analytically, using the FFTlog expansion of the 3D power spectrum. This results in an efficient computational method, which is a substantial improvement compared to any full-sky approaches. We apply our results to galaxy clustering (with and without redshift-space distortions), CMB lensing and galaxy lensing observables. For clustering, we find excellent agreement with the full-sky results on large (percent-level agreement) and intermediate or small (subpercent agreement) scales, dramatically out-performing the Limber approximation for both wide and narrow window functions, and in equal- and unequal-time cases. In the case of lensing, we show on the full sky that the angular power spectrum of the convergence can be very well approximated by projecting the 3D Laplacian (rather than the correct angular Laplacian) of the gravitational potential, even on large scales. Combining this approximation with our flat-sky techniques provides an efficient and accurate evaluation of the CMB lensing angular power spectrum on all scales.

In this paper, we present GALEX-SDSS-WISE Legacy Catalog (GSWLC), a catalog of physical properties (stellar masses, dust attenuations and star formation rates (SFRs)) of ~700,000 galaxies with SDSS redshifts below 0.3. GSWLC contains galaxies within the GALEX footprint, regardless of a UV detection, covering 90% of SDSS. The physical properties were obtained from UV/optical SED fitting following Bayesian methodology of Salim et al. (2007), with improvements such as blending corrections for low-resolution UV photometry, flexible dust attenuation laws, and emission line corrections. GSWLC includes mid-IR SFRs derived from IR templates based upon 22 micron WISE observations. These estimates are independent of UV/optical SED fitting, in order to separate possible systematics. The paper argues that the comparison of specific SFRs (SSFRs) is more informative and physically motivated than the comparison of SFRs. SSFRs resulting from the UV/optical SED fitting are compared to the mid-IR SSFRs, and to SSFRs from three published catalogs. For "main sequence" galaxies with no AGN contribution all SSFRs are in very good agreement (within 0.1 dex on average). In particular, the widely-used aperture-corrected SFRs from MPA/JHU catalog show no systematic offsets, in contrast to some integral-field spectroscopy results. For galaxies below the main sequence (log SSFR<-11), mid-IR (S)SFRs based on fixed luminosity-SFR conversion are severely biased (up to 2 dex) because the dust is primarily heated by old stars. Furthermore, mid-IR (S)SFRs are overestimated by up to 0.6 dex for galaxies with AGN, presumably due to non-stellar dust heating. UV/optical (S)SFRs are thus preferred to IR-based (S)SFRs for quenched galaxies and those which host AGN.

We study resonance expansions and localised long-time dynamics for three-dimensional semiclassical Dirac operators. For smooth Hermitian matrix-valued perturbations which are analytic outside a compact set, we first obtain exponential cut-off resolvent bounds away from the resonance set and polynomial bounds in thin resonance-free rectangles adjacent to the real axis. Combining these estimates with a local Oc(h^{-3}) upper bound on the number of resonances, a pigeonhole selection of admissible contours, almost-analytic functional calculus, and a Cauchy--Green deformation, we derive resonance expansions for spectrally localised propagators. Positive-energy resonances contribute for large positive times, whereas negative-energy resonances contribute for large negative times. We then specialise to mass-type perturbations mbfβV(x) in a nontrapping energy window. Using the logarithmic resonance-free region established in our earlier work together with a quantitative FBI-transform/escape-function argument, we obtain a polynomial bound for the continued cut-off resolvent and deduce rapid local-energy decay. We subsequently refine this polynomial estimate by a finite-time propagation argument in the undistorted region. Introducing the maximal positive-sheet connection time T_χ associated with the spatial cutoff, we prove a geometric continued-resolvent estimate and, for every fixed M below the resonance-free depth constant, derive the explicit local-energy decay threshold T_N>T_χ+(N+1)/M. The same analysis gives a rigorous microlocal obstruction to a uniform [hlog(1/h)]^{-1} bound for the full distorted resolvent and identifies a finite-flight-time amplification mechanism for the sandwiched continued resolvent at logarithmic depth.

We disprove a conjecture of Davis, Drusvyatskiy, and Jiang (2026) that subdifferential regularity can be removed from the generic guarantee of convergence to local minimizers for stochastic subgradient methods. We construct a globally Lipschitz, coercive, semialgebraic function in two dimensions for which the method converges to a nonminimizing Clarke critical point. For suitable power-law stepsizes, this convergence holds for open sets of initial points and linear tilts of the objective, uniformly over all perturbation sequences within a prescribed bound.

We have updated the PlanetS catalog of transiting planets with precise and robust mass and radius measurements and use this catalog to explore mass-radius (M-R) diagrams. On the one hand, we propose new M-R relationships to separate exoplanets into three populations. On the other hand, we explore the transition in radius and density between super-Earths and sub-Neptunes around M-dwarfs and compare them with those orbiting K- and FG-dwarfs. Using Kernel density estimation method with a re-sampling technique, we estimated the normalized density and radius distributions, revealing connections between observations and theories on composition, internal structure, formation, and evolution of these exoplanets orbiting different spectral types. The 30% increase in the number of well-characterized exoplanets orbiting M-dwarfs compared with previous studies shows us that there is no clear gap in either composition or radius between super-Earths and sub-Neptunes. The "water-worlds" around M-dwarfs cannot correspond to a distinct population, their bulk density and equilibrium temperature can be interpreted by several different internal structures and compositions. The continuity in the fraction of volatiles in these planets suggests a formation scenario involving planetesimal or hybrid pebble-planetesimal accretion. We find that the transition between super-Earths and sub-Neptunes appears to happen at different masses (and radii) depending on the spectral type of the star. The maximum mass of super-Earths seems to be close to 10~M_oplus for all spectral types, but the minimum mass of sub-Neptunes increases with the star's mass. This effect, attributed to planet migration, also contributes to the fading of the radius valley for M-planets compared to FGK-planets. While sub-Neptunes are less common around M-dwarfs, smaller ones exhibit lower density than their equivalents around FGK-dwarfs.

The Simons Observatory (SO), due to start full science operations in early 2025, aims to set tight constraints on inflationary physics by inferring the tensor-to-scalar ratio r from measurements of CMB polarization B-modes. Its nominal design targets a precision σ(r=0) leq 0.003 without delensing. Achieving this goal and further reducing uncertainties requires the mitigation of other sources of large-scale B-modes such as Galactic foregrounds and weak gravitational lensing. We present an analysis pipeline aiming to estimate r by including delensing within a cross-spectral likelihood, and demonstrate it on SO-like simulations. Lensing B-modes are synthesised using internal CMB lensing reconstructions as well as Planck-like CIB maps and LSST-like galaxy density maps. This B-mode template is then introduced into SO's power-spectrum-based foreground-cleaning algorithm by extending the likelihood function to include all auto- and cross-spectra between the lensing template and the SAT B-modes. Within this framework, we demonstrate the equivalence of map-based and cross-spectral delensing and use it to motivate an optimized pixel-weighting scheme for power spectrum estimation. We start by validating our pipeline in the simplistic case of uniform foreground spectral energy distributions (SEDs). In the absence of primordial B-modes, σ(r) decreases by 37% as a result of delensing. Tensor modes at the level of r=0.01 are successfully detected by our pipeline. Even with more realistic foreground models including spatial variations in the dust and synchrotron spectral properties, we obtain unbiased estimates of r by employing the moment-expansion method. In this case, delensing-related improvements range between 27% and 31%. These results constitute the first realistic assessment of the delensing performance at SO's nominal sensitivity level. (Abridged)

Motivated by applications in Diophantine approximation, we develop a new fibering mechanism for non-degenerate manifolds in R^n, showing that they admit local decompositions into families of non-degenerate curves with uniform quantitative non-degeneracy properties. The manifolds are required to be C^N with the essentially optimal bound Ngeq maxlbrace n,l+1rbrace, where the manifold is l non-degenerate. Furthermore, we show that this uniform quantitative local control can be globalised into a qualitative statement, so that almost every point of a non-degenerate manifold lies on a non-degenerate curve contained in the manifold. Our approach is perturbative and shows that the fibering structure arising in the analytic setting is stable under sufficiently small C^N perturbations. The method provides a framework for extending fibering based results in Diophantine approximation from curves to manifolds. Such applications are considered in the paper.

Using solar-cycle long helioseismic measurements of meridional and zonal flows in the near-surface shear layer (NSSL) of the Sun, we study their spatio-temporal variations and connections to active regions. We find that near-surface inflows towards active latitudes are part of a local circulation with an outflow away from them at depths around 0.97 R, which is also the location where the deviations in the radial gradient of rotation change sign. These results, together with opposite-signed changes over latitude and depth in the above quantities observed during the solar minimum period, point to the action of the Coriolis force on large-scale flows as the primary cause of changes in the rotation gradient within the NSSL. We also find that such Coriolis force-mediated changes in near-surface flows towards active latitudes only marginally change the amplitude of zonal flow and hence are not likely to be its driving force. Our measurements typically achieve a high signal-to-noise ratio (>5σ) for near-surface flows but can drop to 3σ near the base (0.95 R) of the NSSL. Close agreements between the depth profiles of changes in rotation gradient and in meridional flows measured from quite different global and local helioseismic techniques, respectively, show that the results are not dependent on the analysis techniques.

One-parameter Darboux deformations are effected for the simple ODE satisfied by the continuous generalizations of the Fibonacci sequence recently discussed by Faraoni and Atieh [Symmetry 13, 200 (2021)], who promoted a formal analogy with the Friedmann equation in the FLRW homogeneous cosmology. The method allows the introduction of deformations of the continuous Fibonacci sequences, hence of Darboux-deformed Fibonacci (non integer) numbers. Considering the same ODE as a parametric oscillator equation, the Ermakov-Lewis invariants for these sequences are also discussed.