Principal coordinates analysis (PCoA) is a standard exploratory tool for microbiome beta-diversity studies, but its axes are defined by pairwise dissimilarities and therefore do not directly identify the taxa driving an ordination. We propose Bayesian sparse principal coordinates analysis (BSPCoA), a post hoc framework that approximates the leading principal coordinates by a sparse linear surrogate in the observed taxa. A delta-tolerance diagnostic quantifies the discrepancy between the classical ordination and its best linear surrogate, clarifying when taxon-level interpretation is well supported. We place three-parameter beta normal global-local priors on the surrogate coefficients to induce row sparsity, obtain posterior uncertainty, and select influential taxa. The method reduces to sparse principal component analysis under Euclidean distance, while remaining applicable to ecologically meaningful dissimilarities such as Bray--Curtis and Hellinger distances. We conduct simulation studies to demonstrate that BSPCoA provides an approximately linear representation of the dominant ordination geometry while enhancing interpretability in sparse microbiome settings. In the Hadza gut microbiome data, the method produces an ordination close to that of classical PCoA while highlighting a parsimonious set of taxa associated with seasonal variation.

An interpretable, physics-consistent turbulence model correction framework, termed FISR-Equation Learner (EQL), is proposed by embedding equation learning directly into a Partial Differential Equations (PDE)-constrained field inversion process based on the adjoint method. Unlike conventional two-stage approaches, the correction model is optimized end-to-end in parameter space using an EQL architecture, enabling the direct identification of compact analytical expressions while maintaining consistency with the governing equations. The method is applied to the shear-stress-transport (SST) model and trained on two canonical separated flows, the curved backward-facing step and the NASA hump. The resulting explicit expression significantly reduces separation bubble overprediction and improves reattachment prediction, achieving performance comparable to neural-network-based end-to-end methods while retaining full interpretability. Generalization is demonstrated on unseen configurations, including periodic hills, a surface-mounted cube, and the high-lift NLR7301 airfoil. The model improves separated-flow predictions and stall characteristics without degrading attached boundary-layer performance. Overall, FISR-EQL provides a practical pathway toward optimal yet transparent data-driven turbulence model correction.

This study presents an efficient and accurate discrete adjoint gas-kinetic scheme (GKS) for sensitivity analysis and aerodynamic shape optimization in continuum flow regimes. Developed using the backward mode of algorithmic differentiation (AD), the adjoint solver is rigorously verified against a duality-preserving linearized GKS solver generated via forward-mode AD. The robustness and practical effectiveness of the solver are evaluated through three benchmark cases: the inverse design of turbine blades, lift-to-drag ratio enhancement, and shock-strength reduction for a NACA 0012 airfoil. To capture realistic flow physics, fully turbulent optimizations are conducted using the one-equation Spalart--Allmaras (SA) model. Numerical results demonstrate excellent agreement between the discrete adjoint and linearized solvers, exhibiting matching sensitivity convergence behaviors, identical asymptotic residual decay rates, and negligible discrepancies in final sensitivity predictions. Furthermore, the optimization studies confirm that targeted design objectives are consistently achieved within a limited number of design cycles, highlighting the solver's computational efficiency, accuracy, and suitability for complex aerodynamic geometries.

Chitosan is a highly versatile and sustainable polymer with a broad range of potential biological and materials engineering applications. Despite its versatility, the native brittleness of chitosan limits its broader utilization. This limitation can be addressed by blending chitosan with small-molecule additives to modulate its thermomechanical properties. We employ molecular dynamics (MD) simulations to investigate the mechanism underlying antiplasticization followed by plasticization at increasing water content. Decomposition of the elastic moduli reveals a competition between weakened polymer-polymer interactions and enhanced polymer-water interactions, with their relative strengths governing the resulting properties. We introduce a simple model incorporating dynamically accessible free volume regions as a key driver of polymer mobility, effectively capturing the (anti-)plasticization of elastic properties. We show that accessibility of free volume regions is enabled by connectivity of additive-accessible volume regions. This study provides new insights into the molecular interactions that dictate the properties of chitosan-water mixtures and may inform the rational design of chitosan-based materials and other hydrated biopolymers.

Beam squint, the frequency-dependent shift of the main beam, poses a major challenge for wideband antenna arrays. This paper focuses on the beam squint effects in super wideband (SW) systems, where high mutual coupling (MC) effects are present. These high MC effects complicate beamforming (BF) by creating frequency-dependent phase relationships that invalidate conventional approaches. To accurately model MC effects, this paper uses a circuit-theoretic framework for tightly coupled SW uniform linear arrays (ULAs). We derive closed-form expressions for the average received signal-to-noise ratio (SNR) with BF in conventional half-wavelength spaced, weakly coupled arrays and validate them. Extending our analysis to tightly coupled SW arrays, we demonstrate that, in contrast to conventional weakly coupled arrays, the effective true time delays exhibit a nonlinear dependence on frequency due to coupling-induced phase shifts. A comparative analysis reveals that strong MC in SW arrays significantly reduces squint in phase-controlled BF, extending the usable bandwidth considerably.

Binary systems are ubiquitous in the Universe and often host circumbinary discs that are misaligned with the binary orbital plane. Such misalignments can affect disc evolution and binary accretion variability. We here present 3D hydrodynamical simulations of circumbinary discs with initial tilts $i_0$ from $0^\circ$ to $180^\circ$, around eccentric binaries with secondary-to-primary mass ratios of $0.11-0.67$. We find that both the initial tilt and mass ratio can affect the long-term accretion variability in our simulations. Discs evolving towards polar and coplanar retrograde generally favour accretion onto the primary star, while discs evolving towards coplanar prograde generally favour accretion onto the secondary. We find preferential accretion ratio $η=\langle\dot{M_2}\rangle/\langle\dot{M_\mathrm{b}}\rangle$ to be a non-monotonic function of the mass ratio. For discs close to coplanar prograde alignment, $η$ increases with decreasing mass ratio, whereas for discs with $30^\circ \le i_0 \le 135^\circ$, $η$ decreases for smaller mass ratios. Polar discs show the lowest mass loss rates, slightly lower than those of coplanar prograde discs, while retrograde discs lose mass faster than their prograde counterparts. Discs that undergo strong warping or breaking experience rapid mass loss. Our findings provide insights into observed circumbinary discs and have implications for circumbinary planet formation.

Mg-IV-N\textsubscript{2} compounds with IV=Si, Ge, Sn are ultra-wide band gap semiconductors with various potential electronic and optoelectronic applications. They share the \textit{Pna}2\textsubscript{1} space group crystal structure. Here we present Density Function Perturbation Theory (DFPT) calculations of the vibrational modes of these materials. We focus on the vibrational modes at the zone center to establish the relation between vibrational modes and their corresponding point-group symmetries, which determine the Raman and infrared spectra but also report the full Brillouin zone phonon dispersions and density of states. We also determine the piezoelectric tensor and the elastic compliance tensor.

We study the navigation of a self-propelled inertial particle in two-dimensional Rayleigh--Bénard convection at Prandtl number $Pr = 0.71$ and cell aspect ratio $Γ= 4$ for Rayleigh numbers $Ra$ ranging from $10^{7}$ to $10^{11}$. A reinforcement-learning (RL) controller selects the propulsive acceleration, subject to an upper bound $\mathcal{A}_{\max}$, to achieve a prescribed horizontal displacement. We find that the success rate increases abruptly with $\mathcal{A}_{\max}$ at moderate $Ra$, whereas at higher $Ra$ the transition becomes more gradual and shifts to larger $\mathcal{A}_{\max}$. Moreover, although the completion time increases with $Ra$, the propulsion energy required for successful traversal decreases. Proper orthogonal decomposition (POD) reveals that these performance differences arise from reorganisation of the carrier flow. At moderate $Ra$, the dominant large-scale circulation partitions the domain through robust transport barriers, requiring a finite thrust surplus to cross them; at higher $Ra$, energy is distributed across many modes, the barriers fragment, and transient plume-assisted pathways emerge. Compared with a constant-heading baseline, the learned policy aligns with local currents and consumes significantly less energy. Lagrangian coherent structure (LCS) analysis further shows that the RL agent inherently learns to cross repelling barriers and surf along attracting pathways. Finally, by mapping these behaviours onto the local Eulerian flow topology using Voronoi tessellation and the $Q$-criterion, we distil an interpretable, physics-based heuristic strategy that achieves robust navigability. These results connect turbulent-flow organisation with autonomous navigation under bounded actuation.

We present a spatially resolved, multiphase study of the outflow in the edge-on starburst galaxy ESO~484-036 from the GECKOS survey, combining VLT/MUSE H$α$ and ALMA CO(1$-$0) observations to analyse the atomic ionised and cold molecular gas. Both show extraplanar emission consistent with a conical outflow. Ionised gas is enclosed by molecular gas, which is detected up to 2.5 kpc from the disc. Molecular gas dominates near the disc, except at the nuclear base, while ionised gas extends beyond 3 kpc. The deprojected outflow velocities are $\lesssim400\ \rm km\ s^{-1}$ in both phases and are consistent with ballistic motion, with some gas possibly falling back onto the disc. We find that the mass outflow rates are in the range of $\dot M_{\rm ion}\sim1-5\ \rm M_\odot\ \rm yr^{-1}$ and $\dot M_{\rm mol}\sim13-54\ \rm M_\odot\ \rm yr^{-1}$, giving mass loading factors of $η_{M\rm, ion}\sim 0.1-0.6$ and $η_{M\rm, mol}\sim 1.5-6.2$. These ranges reflect velocity and geometric uncertainties. Despite the short depletion time ($τ_{\rm dep} = 16-48\rm\ Myr$), the outflow may regulate rather than permanently quench the gas reservoir. Energy loading ($η_E\leq0.16$) and momentum loading ($η_p\lesssim1$) support a purely starburst-driven outflow. Comparing ESO~484-036 with a literature sample, we find a systematic 1~dex shift in mass-loading relations when molecular gas is included. This produces a $\sim3.5$~dex discrepancy with cosmological simulations in $η_{M\rm, mol}/η_{M\rm, ion}$, implying that current models strongly underpredict cold gas production and the role of short-range recycling flows in starburst galaxies.

In this paper, we investigate the local boundedness of weak solutions to degenerate parabolic double phase equation of type $$ u_t-\textrm{div}(|Du|^{p-2}Du+a(x,t)|Du|^{q-2}Du)=0\quad \text{in } Ω_T := Ω\times (0,T), $$ where $0\leq a(\cdot)\in L^\infty(Ω_T)$. To this end, we derive the Caccioppoli inequality and a parabolic embedding theorem, which are then utilized in an iteration method.

This paper investigates the approximation of invariant measures for McKean-Vlasov stochastic differential equations (SDEs) using the Euler-Maruyama (EM) scheme under a monotonicity condition. Firstly, the convergence of the numerical solution from the EM scheme to its continuous-time counterpart is established. Secondly, we show that the numerical solution admits a unique invariant measure and derive its convergence rate under the Wasserstein metric. In parallel, it is demonstrated that the associated particle system also possesses these properties.

In this paper, we study the $n$-point function of $t$-core partitions. The main tool is the topological vertex, originally developed to study the topological string theory for toric Calabi--Yau 3-folds. By virtue of the topological vertex, we introduce the $q$-deformed $n$-point function that generalizes both the ordinary $n$-point function of all integer partitions studied by Bloch--Okounkov and $t$-core partition case treated here. As a consequence, we provide a closed formula for the $n$-point function of $t$-core partitions in terms of theta functions, and prove that the corresponding correlation functions are quasimodular forms.

Scattering resonances arise in wave phenomena and play an important role in many applications. While extensive theoretical studies have been conducted, effective numerical computation remains limited, and most existing methods suffer from spurious modes. In this paper, we propose a spurious-mode-free method for computing scattering resonances in transmission problems. The unbounded domain is truncated using a Dirichlet-to-Neumann (DtN) map. The resonances are formulated as eigenvalues of a holomorphic Fredholm operator function, which is discretized by the finite element method. The spectrum indicator method is then used to compute the eigenvalues of the nonlinear matrix eigenvalue problems. We establish optimal order convergence and present extensive examples that demonstrate the effectiveness of the proposed method. The results are consistent with existing theoretical findings in the literature and offer new insights that may inform further theoretical developments.

The spontaneous breaking of symmetries is a cornerstone of physics, defining the phases of matter from the cosmological scale to the quantum realm. In condensed matter, electronic orders are classified by their behavior under fundamental symmetries like spatial inversion (parity). While even-parity orders, such as conventional superconductivity and charge density waves, are ubiquitous, their odd-parity counterparts--predicted to host exotic phenomena such as gapless quasiparticle excitations and novel collective modes--are comparatively elusive states of quantum matter. Here, using high-resolution scanning tunneling microscopy and angle-resolved photoemission spectroscopy on the kagome metal CsV$_3$Sb$_5$, we report the discovery of an inversion symmetry-breaking $f$-wave charge bond order. We show that this phase, which preserves translation symmetry, is stabilized by the spontaneous opening of a spectral gap at a previously overlooked Dirac point, providing a textbook condensed-matter realization of the Gross-Neveu model for dynamical mass generation and parity breaking. Intriguingly, this $f$-wave order is itself a intervening phase, vanishing abruptly below a temperature of 10\,K and pointing to a subsequent transition into a `hidden' electronic state that is invisible to local STM probes. Our findings establish odd-parity charge order as a novel phase of matter, here, embedded within the intricate hierarchy of correlated electronic orders on the kagome lattice.

For any complete and noncompact manifold $M$ with $\mathrm{Ric}\ge 0$, we define a function $\mathrm{RV}(s)$ that describes the growth of relative volume asymptotically $$\mathrm{RV}(s)=\limsup_{r\to\infty} \dfrac{\mathrm{vol} B_{rs}(p)}{\mathrm{vol} B_r(p)},\quad s\ge 1.$$ Then we study the fundamental groups of such manifolds with slow relative volume growth and sublinear diameter growth. We show that if $\mathrm{RV}(s)\ll s^2$ as $s\to\infty$, then $π_1(M)$ is almost abelian; if $\mathrm{RV}(s)\ll s^{1+δ}$ for some $δ\in (0,1)$ and the Ricci curvature is positive at a point, then $π_1(M)$ is finite. These results generalize our previous work on complete manifolds with $\mathrm{Ric}\ge 0$ and linear (minimal) volume growth.

Oriented cohomology theories provide a general framework to perform intersection-theory-type calculus. The Chow ring, algebraic $K$-theory, and Levine--Morel's algebraic cobordism are all instances of such theories satisfying $\mathbb A^1$-invariance. Topological Hochschild homology, topological cyclic homology, and Hodge cohomology are important examples of theories without $\mathbb A^1$-invariance. In this paper, we prove an additive blowup formula for oriented cohomology theories in the non-$\mathbb A^1$-invariant category of motivic spectra, developed by Annala, Hoyois, and Iwasa. Then, we specialize to $\mathbb A^1$-invariant theories and give presentations of oriented cohomology rings of the blowup of a smooth scheme along a smooth center. We compute explicit examples of such presentations for the cases of del Pezzo surfaces, the blowup of $\mathbb P^3$ along the twisted cubic, and the blowup of $\mathbb P^5$ along the Veronese surface, which can be identified with the moduli space of complete conics. We demonstrate that one can recover solutions to classical enumerative geometry problems, such as Steiner's $3264$ conics, using arbitrary oriented cohomology theories. Finally, we give a presentation of oriented cohomology rings of $\overline M_{0,n}$, which generalizes Keel's presentation of the Chow ring.

The James Webb Space Telescope (JWST) revealed a large population of active galactic nuclei (AGN) with redshifts greater than five. We show that if they emit ultrahigh-energy protons with energies up to $\lesssim 10^{19}$ eV, the cosmogenic neutrino production in the high-redshift CMB field yields a neutrino flux with a bump at around 50~PeV. This flux is consistent with the current estimate of neutrino intensity from the IceCube Neutrino Observatory. We argue that the predicted neutrino intensity naturally arises from the average AGN luminosity and number density observed by JWST, without the need for fine-tuning of relevant parameters. Future neutrino observations that confirm the 50-PeV bump and constrain the small-scale anisotropy will infer ultra-high energy cosmic-ray emissions in the early universe.

We study the problem of constructing concurrent objects in a setting where $P$ processes run in parallel and interact through a shared memory that is subject to write contention. Our goal is to transform hardware primitives that are subject to write contention into ones that handle contention gracefully. We give contention-resolution algorithms for several basic primitives, and analyze them under a relaxed, roughly-synchronous stochastic scheduler, where processes run at roughly the same rate up to a constant factor with high probability. Specifically, we construct read/write registers and CAS registers that have latency $O(\log P)$ w.h.p. under our scheduler model, using $O(1)$ hardware read/write registers and, in the case of our CAS construction, one hardware CAS register. Our algorithms guarantee performance even when their operations are invoked by an adaptive adversary that is able to see the entire history of operations so far, including their timing and return values. This allows them to be used as building blocks inside larger programs; using this compositionality property, we obtain several other constructions (LL/SC, fetch-and-increment, bounded max registers, and counters). To complement our constructions, we give a trade-off showing that even under a perfectly synchronous schedule and even if each process only executes one operation, any algorithm that implements any of the primitives that we consider, uses space $M$, and has latency at most $L$ with high probability must have expected latency at least $Ω(\log_{ML} P)$.

We demonstrate the existence of bright solitons in a repulsively interacting, harmonically trapped quasi-one-dimensional Bose-Einstein condensate described by the Gross-Pitaevskii equation. Using a neural-network quantum state (NNQS) approach, we parametrize the initial wavefunction and optimize it to find solutions that recur after one trap period, effectively balancing repulsion with trap-induced attraction. Aside from the bright solitonic solution, we also report double bright and dark soliton states. Perturbing the initial state with multiplicative phase and amplitude noise confirms that these periodic orbits are orbitally stable. Our results indicate that NNQS provides a powerful framework for uncovering coherent structures in nonlinear wave systems.

The increasing penetration of inverter-based resources introduces new dynamic challenges to modern power grids, such as sub- and super-synchronous oscillations and other faster dynamics. These dynamics are typically fast in nature and are difficult to accurately model and analyze using standard transient stability (TS) methods, necessitating the need for electromagnetic transient (EMT) analysis. However, EMT simulations are notoriously slow for large-scale grids due to both equation formulations and computational limitations. To overcome this challenge, EMT-TS hybrid simulation is often used, since it offers a balanced trade-off between accuracy and speed, making it feasible to perform EMT analysis on large systems. One open question about EMT-TS hybrid simulation is the accuracy of the EMT-TS boundary or interface. This paper introduces an error index to quantify EMT-TS hybrid interface errors, identifies conditions where the hybrid simulation approach may become inaccurate, and suggests EMT region expansions to improve the simulation accuracy. Additionally, a three-sequence hybrid interface model is proposed to mitigate inaccuracies caused by unbalanced conditions.

We theoretically study the direct and inverse spin Hall effects in a superconductor-normal metal-superconductor junction induced by a spin-orbit interaction that is invariant under spatial inversion. We show that a supercurrent induces a spin Hall effect, leading to a static spin accumulation with opposite polarizations at the two edges, analogous to that in normal conductors. For the inverse effect, we consider a spatially inhomogeneous static magnetic field and show that it induces an anomalous phase shift, which, in the presence of higher harmonics, results in a diode effect. Unlike Rashba systems, the present mechanism does not require broken structural inversion symmetry.

This paper proposes a fully Bayesian framework for node-level outlier detection in graph signals, where measurements are observed on the nodes of an underlying graph. Unlike traditional outlier detection methods, our approach accounts for the relational dependencies induced by the graph, identifying outliers that disrupt the underlying smoothness. We model the observed signal as a combination of a graph-smooth component, captured via an intrinsic Gaussian Markov random field (IGMRF) prior, and a sparse outlier component modeled by a spike-and-slab prior. A key advantage of the proposed method is its ability to provide principled uncertainty quantification by estimating the posterior probability that each node is an outlier, rather than enforcing a deterministic binary decision. To facilitate posterior inference, we develop an efficient Gibbs sampling algorithm. We demonstrate the effectiveness of the proposed method through simulation studies on various graph structures, as well as a real data analysis of PM2.5 levels in California, exploring their relationship with wildfire occurrences.

Multipartite entanglement is an essential quantum resource for various distributed quantum applications. One promising method for preparing multipartite entanglement is to interfere independent photons at linear optical interference setups. While heralding the successful interference and thereby the state generation is often costly, postselecting entangled states provides an achievable alternative in this framework. We introduce a family of interference schemes for postselecting symmetric qudit Dicke states, useful resources in quantum communication and variational quantum computing. We present schemes with and without ancillary photons and show that using ancillary photons can exceed the upper bound on the success probability of schemes without ancillary photons. Our results accommodate a wide range of linear optical schemes, providing multiple viable approaches for postselecting Dicke states.

The quantum random number generation based on laser phase noise, which is featured with high generation rate and ease for photonic integration, has been extensively investigated and demonstrated. Despite these advancements, a theoretical model to achieve optimal performance in terms of maximizing the generation rate or entropy is still incomplete. In this work, a comprehensive physical model for this scheme is introduced to accurately predict the power spectrum and probability distribution of raw data, based on which the entropy source bandwidth and quantum min-entropy can be accordingly calculated and thus the system performance can be quantitatively evaluated. The model is sufficiently validated through both simulation and experiment with significant agreement under various setups. Furthermore, our proposal enables the priori configuration of experimental setups to achieve designed power spectrum and probability distribution of the raw data, thereby maximizing the generation rate or the min-entropy for system performance optimization.

As the number of theoretically predicted materials continues to grow, it becomes increasingly important to assess not only their thermodynamic stability but also their kinetic viability under realistic synthesis conditions. In this study, we investigate the hypothesis that the kinetic persistence of a metastable polymorph is related to the topography of the potential energy landscape separating it from lower energy phases. To accomplish this, we develop a new method for identifying diffusionless transformation pathways between metastable polymorphs and their ground-state counterparts and discuss the energetics of those pathways with respect to the experimental observation of each phase. This algorithm is underpinned by the recently developed Crystal Normal Form, which provides a graph representation of crystal configuration space and supplies the substrate for our pathfinding algorithm. We apply this method to the titanium dioxide system which contains the well-known anatase, rutile, and brookite phases in addition to a number of hypothetical metastable polymorphs.

In low-energy supergravity treatment of type IIB superstring on general D-instanton wormhole profiles in the bulk, we obtain non-vanishing scalar two-point functions in addition to the vanishing $\langle τ^* τ^* \rangle$ that corresponds to the BPS amplitude detected by two D-instantons at their respective boundaries. This is exploited to show that the modes of broken local supersymmetry in the bulk deliver the fermionic (diagonal) modes on the boundaries through the deformation by the form of current-current two point functions propagating on the tree level cylinder geometry. Our treatment is generalizable to multi D-instanton cases and general Euclidean branes.

We examine the gravitational lensing signatures of a Hayward-like regular black hole and its potential observational distinction from a Schwarzschild black hole. In the weak-field limit, the deflection angle includes a small positive correction proportional to $m \ell^2/b^3$, indicating slightly stronger light bending than in Schwarzschild, though the effect remains observationally negligible at large impact parameters. Current galaxy-scale Einstein-ring data, such as from ESO325-G004, cannot yet constrain the regular-core scale $\ell$. In the strong-deflection regime, for Sgr A* and M87*, the asymptotic position $θ_{\infty}$ is identical to Schwarzschild's. Nevertheless, $\ell$ modifies strong-lensing coefficients $\bar a, \bar b$, influencing angular separations s, relative flux ratio $r_\mathrm{mag}$, and time delays $ΔT_{2,1}$. Our predicted values for these observables remain consistent with current data, suggesting that future high-precision measurements of strong-field lensing may distinguish Hayward-like from Schwarzschild black holes.

We present realistic forecasts for the constraining power of the Nancy Grace Roman Space Telescope on fundamental cosmological parameters, with particular emphasis on the absolute neutrino mass scale, using full-shape analyzes of the galaxy power spectrum. We analyze simulated lightcone mock catalogs of H$α$ emission-line galaxies spanning the redshift range $0.5 < z < 2$ over $2400\ \mathrm{deg}^2$, designed to reproduce the expected properties of the Roman High Latitude Wide Area Spectroscopic Survey. We perform parameter inference on the galaxy power spectrum multipoles using two complementary theoretical frameworks: a model-dependent approach based on the Effective Field Theory of Large-Scale Structure (EFT of LSS) within $Λ$CDM, and a model-independent phenomenological approach that makes no assumptions about the background cosmological model. In the $Λ$CDM analysis, we find $m_ν< 0.380(0.162)\ \mathrm{eV}$ at $95(68)\%$ C.L. using Big Bang Nucleosynthesis (BBN) prior and a broad prior on $n_s$, which tightens to $m_ν< 0.276(0.121)\ \mathrm{eV}$ when Planck priors on $ω_b$, $ω_\mathrm{cdm}$, and $n_s$ are added. Our forecasts show that Roman can additionally constrain $H_0$, $Ω_m$, and $σ_8$ with precisions of $1.3\%$, $4.3\%$, and $2.9\%$ in line with Stage IV galaxy survey measurements and forecasts. In the model-independent analysis, we demonstrate that the phenomenological model can robustly recover unbiased measurements of the angular diameter distance, the Hubble parameter, and the growth of structure across all redshift bins, in the same range of scales as the EFT model, and obtain $m_ν< 0.63(0.36)\ \mathrm{eV}$ at $95(68)\%$ C.L. when Planck priors are included.

This work introduces a simple and efficient linesearch method for composite minimization that accelerates proximal-gradient iterations with fast Newton-type directions. Our algorithm is based on simple operations and only requires the standard proximal-gradient oracle, similar to PANOC and ZeroFPR, provided that the nonsmooth term is convex. Noteworthy improvements include a cheaper backtracking procedure, in the sense that no additional gradients need to be evaluated, and an enlarged range of permitted stepsizes. Global subsequential convergence and local superlinear convergence are established under conventional assumptions by considering a novel merit function which is less expensive to evaluate than alternatives like the forward-backward envelope. Finally, the proposed approach is validated on model predictive control problems with collision avoidance constraints, as well as on the LIBSVM and CUTEst benchmarks.

We present a robust method to empirically infer the timing of the last significant merger in the Milky Way which is tested against fully cosmological models of galaxy formation. We apply it to Milky Way subgiant stars with spectro-photometric ages, finding that the last significant merger (Gaia-Sausage-Enceladus, GSE), occurred $\sim11\,$Gyrs ago. This coincides with the birth of a coeval in-situ group of globular clusters (GCs), which constrains the merger-induced starburst (hereafter {\it Tainá}) to have occurred at $11.2\pm 0.1\,\rm{Gyr}$, the most precise dating of this merger event. The GSE's most metal-rich GCs were also born around this time ($τ=10.9\pm0.1\,\rm{Gyr}$) and likely formed during the merger interaction prior to disruption of the GSE. We argue that $ω$ Centauri is the most likely candidate for the surviving remnant of the GSE, and show that its stellar populations have final ages and metallicities consistent with the GSE GCs together with observational evidence it may have been affected by bar resonances. Furthermore, we argue that the mean metallicity for which stellar orbits transition from halo-like to disc-like kinematics shows an upward inflexion point at $[\rm{Fe/H}]\sim-1.33$, and this sets an upper-limit for the age when the disc was forming. To corroborate this, we identify proto-MW GCs with highly disc-like orbits that formed before the last significant merger (with ages up to $τ=13.0\pm0.5\,\rm{Gyr}$). This places the disc formation time as far back as as $z_{\rm disc\, form}\gtrsim4$.