The physics in flat bands has emerged as an essential field in condensed matter physics where a plethora of phenomena can be unveiled, such as anomalous transport properties, superconductivity dominated by quantum geometry or exotic topological phases. Our goal here is to show that even in magnetic systems, the presence of flat bands can give rise to unexpected features. More precisely, we address the impact of an Aharonov-Bohm (AB) flux on the exchange couplings in magnetic diamond chains. The most remarkable result is the significant amplification of magnetic couplings at short distances induced by the AB flux, leading to a considerable increase in the thermal conductivity of the magnons. We have also shown that the flux-dependent decaying length of the couplings is connected to the quantum metric of the flat bands. Our results could be of interest for the control of magnetic properties in spintronic devices and relevant for the heat transport by magnons at the nanoscale in quantum technologies.

We investigate the gravitational wave (GW) signals emitted by planetary-mass primordial black holes (PBHs) passing nearby or traversing neutron stars (NSs). While previous studies mainly focused on the detailed waveforms of the signals, we estimate the rate of PBH-NS gravitational-wave events originating from the Galactic center and compute the probability of detecting a signal over 10 years of LIGO-Virgo-KAGRA observations. We examine in detail the case of PBHs bound to NSs, focusing on eccentric orbits that give rise to repeated GW bursts emitted in correlated series, each burst corresponding to a periastron passage. Despite the enhancement from the large number of bursts produced by a single PBH-NS pair, the total number of signals produced in this way remains subdominant to those due to random unbound encounters of PBHs with NSs. We also find that both types of signals have a very small probability $P\lesssim 10^{-8}$ to be detected in a 10 year period.

We study the free energy and dynamics of a closed elastic filament (a one-dimensional curve in two dimensions) coupled to a scalar concentration field representing, for example, an absorbed species. The density variable has a tendency to phase-separate whereas the local spontaneous curvature is concentration-dependent. We address analytically and by simulation both the free energy landscape and the dynamics (the latter comprising a coupled Willmore flow and Cahn--Hilliard gradient flow on the full differential geometry of a closed filament), addressing issues that previous work typically sidestepped by restricting to the Monge gauge. Specifically we find that the closure constraint for a deformable filament qualitatively changes the free energy landscape compared with either a rigid closed filament or an open elastic one, admitting metastable and stable states with more than one domain of each type. By numerical global free energy minimization we explore equilibrium morphologies across a wide range of model parameters. For selected parameter values we present fully dynamical results, tracking the time evolution of the various contributions to the free energy and confirming the emergence of both metastable and equilibrium multi-domain morphologies.

Four-volumes ($V_4=$ spatial-3-volume$\times$lifetime) are calculated within the model of three-fluid dynamics (3FD) and compared with those of the the JET AA Microscopic Transport Model (JAM). The calculations are performed for central Au+Au collisions at energies $\sqrt{s_{NN}}=$ 3 -- 19.6 GeV. These $V_4$ indicate optimal collision-energy ranges for realizing macroscopic high baryon-density matter. It is found that the 3FD four-volumes noticeably exceed those in the JAM, which indicates a stronger baryon stopping in the 3FD model as compared to that JAM. It is argued that this difference in the baryon stopping correlates with stiffness of the EoS implemented in these models. Contrary to JAM, the four-volume, where a baryon density ($n_B$) exceeds three times the normal nuclear density ($n_0$), does not exhibit a maximum as a function of $\sqrt{s_{NN}}$. It decreases monotonically with increasing $\sqrt{s_{NN}}$, remaining at a fairly macroscopic level (i.e. $V_4\geq 5.5^4$ fm$^4$/c). For higher baryon densities, $V_4$ exhibits maxima in its dependence on $\sqrt{s_{NN}}$. The optimal energy range for densities $n_B/n_0>$ 4 is located at $\sqrt{s_{NN}}=$ 3.2 -- 8 GeV. Even for $n_B/n_0>$ 6, the four-volume remains quite macroscopic ($V_4\geq 4^4$ fm$^4$/c) at $\sqrt{s_{NN}}=$ 4.5 -- 9 GeV contrary to the JAM.

The Swiss system is an increasingly popular competition format as it provides a favourable trade-off between the number of matches and ranking accuracy. However, there is no empirical study on the potential unfairness of Swiss-system chess tournaments if an odd number of rounds is played. To analyse this issue, our paper compares the number of points scored in the tournament between players who played one game more with the white pieces and players who played one game fewer with the white pieces. Using data from 28 highly prestigious competitions, we find that players with an extra white game score significantly more points. In particular, the advantage exceeds the value of a draw in the four Grand Swiss tournaments. A potential solution to this unfairness could be organising Swiss-system chess tournaments with an even number of rounds, and guaranteeing a balanced colour assignment for all players using a recently proposed pairing mechanism.

We study the existence and radial stability of static, spherically symmetric thin shells joining two Schwarzschild--de~Sitter (SdS) spacetimes $(m_\pm,\Lambda_\pm)$. Using the Israel junction formalism, we map the stable equilibria ($V_{\mathrm{eff}}''>0$) of the effective potential. Near the equilibrium radius $R_0$ the shell's surface density $\sigma$ and pressure $p$ obey the linearized barotropic law $p=p_0+c_s^2(\sigma-\sigma_0)$, with sound speed $c_s^2=\lambda c^2$. Since $c_s^2$ is independent of the equilibrium ratio $w_0\equiv p_0/(\sigma_0 c^2)$, tension shells ($w_0<0$) stay radially stable with real $c_s$. Fixing $\Lambda_+$ so that its vacuum energy density equals the critical density (Planck~2018), and taking $m_-$ representative of astrophysical black holes, we systematically map the stable equilibria $(R_0,\sigma_0)$ over $(m_\pm,\Lambda_\pm,\lambda,w_0)$ and find that stable shells with $\sigma_0>0$ and $0<\lambda\le1$ exist only for $m_+/m_->1$, at three scales -- the photon sphere, the SdS static radius, and the cosmological horizon. At $\lambda=1$ the numerical windows, checked against the analytic test-shell bounds, are $(1-\sqrt{13})/6\lesssim w_0\lesssim 1/2$ ($\Lambda_+=\Lambda_-$), $-2/3\lesssim w_0\lesssim 1/2$ ($\Lambda_+>\Lambda_-$), and $0\lesssim w_0$ ($\Lambda_+<\Lambda_-$). Positive-pressure shells ($0\lesssim w_0\lesssim 1/2$) sit near the photon sphere and those with $w_0\gtrsim1/2$ near the static radius scale, while tension shells reach the cosmological horizon scale for $\Lambda_+=\Lambda_-$, only the static radius scale for $\Lambda_+>\Lambda_-$, and are absent for $\Lambda_+<\Lambda_-$. Finally, we compute the dark fluid shell's imprint on the SdS black-hole shadow seen by a static observer at varying radial distance.

We introduce a broad class of families of branching random walks on a countable set $X$, which we refer to as germ-monotone branching random walks (GMBRWs). The processes in each family are parametrized by a positive parameter $\lambda>0$, which controls the overall reproductive speed, and they are monotonically increasing in $\lambda$ with respect to the germ order, a notion that extends classical stochastic domination. This framework encompasses a wide range of models, including classical continuous-time branching random walks, as well as discrete-time counterparts of certain non-Markovian processes such as ageing branching random walks. We define a general notion of critical parameter $\lambda(A)$ associated with each subset $A \subseteq X$, which serves as a threshold separating almost sure extinction in $A$ from positive probability of survival in $A$. This unifies and extends the classical global and local critical parameters $\lambda_w$ and $\lambda_s$, which can be recovered as special cases. We then investigate how modifications of the reproduction laws, either on a finite set or on a more general subset of $X$, affect these critical parameters. Our results extend earlier contributions in the literature.

Let $\mathbb{K}$ be an algebraically closed field of characteristic zero. An irreducible algebraic variety $X$ over $\mathbb{K}$ of dimension $n$ is called additive if it admits a regular action of the additive group $(\mathbb{K}^n, +)$ with an open orbit, and uniquely additive if this action is unique up to isomorphism. Huang and the second author have previously determined all additive smooth Fano toric threefolds. Here we determine all additive and uniquely additive smooth Fano toric varieties of dimension up to $6$ by computational means, and give a detailed classification for dimension up to $4$. To this effect, we introduce the AdditiveToricVarieties package for Macaulay2, a software system for algebraic geometry and commutative algebra, with methods for working with additive group actions on complete toric varieties. Our work relies on results by Arzhantsev, Dzhunusov and Romaskevich, who relate the existence and uniqueness of such actions to conditions on the Demazure roots of the fans corresponding to the toric varieties. We also prove that every smooth complete toric variety of Picard rank two is additive.

We investigate the role of ultrafast strain on the electronic and optical responses in topological antiferromagnet Mn$_3$Sn thin films using near-infrared femtosecond pump-probe spectroscopy. Coherent acoustic phonons are generated and exhibit remarkably large oscillations in differential transmission exceeding 1% in amplitude. Our quantitative analysis reveals that Mn$_3$Sn possesses an unusually large near-infrared photoelastic coefficient, several times greater than those in conventional materials, indicating a remarkable sensitivity of the electronic states to lattice distortions. This work establishes a quantitative framework for understanding and utilizing strain-induced responses in Mn$_3$Sn, paving a foundation for exploring coupled electron-phonon-magnon dynamics for ultrafast straintronics.

We propose a minimal and predictive framework for asymmetric sterile neutrino dark matter (DM) produced via freeze-in. The standard model (SM) is extended by a gauge-singlet Dirac sterile neutrino carrying a conserved dark charge, a real scalar mediator, and an auxiliary singlet fermion. DM is generated through the out-of-equilibrium decay of the mediator, which simultaneously produces a particle{antiparticle asymmetry in the sterile sector controlled by a CP-violating parameter. We show that the observed relic abundance can be naturally reproduced without thermal equilibration with the SM plasma. The resulting non-thermal momentum distribution is colder than a thermal Fermi{Dirac spectrum, ensuring consistency with structure formation constraints. Combining relic density, Lyman-{\alpha}, Higgs invisible decay, and big bang nucleosynthesis (BBN) bounds, we identify correlated and predictive regions of the parameter space characterized by non-trivial relations among the sterile neutrino mass and the decay parameters. This scenario provides a self-consistent realization of Dirac asymmetric sterile neutrino DM within an asymmetric freeze-in (AFI) framework, offering a constrained and testable alternative to conventional production mechanisms.

We consider a sharp interface formulation for an anisotropic multi-phase Mullins-Sekerka problem with kinetic undercooling. The flow is characterized by a cluster of surfaces evolving such that the total surface energy plus a weighted sum of the volumes of the enclosed phases decreases in time. Upon deriving a suitable variational formulation, we introduce a fully discrete unfitted finite element method. In this approach, the approximations of the moving interfaces are independent of the triangulations used for the equations in the bulk. Our method can be shown to be unconditionally stable. Several numerical examples demonstrate the capabilities of the introduced method. In particular, it is demonstrated that the evolution of multiple ice crystals with junctions can be modeled using the proposed approach.

Cellular signal processing performs reliably despite molecular noise. Mutual information (MI) is widely used to quantify signaling fidelity, capturing how well outputs discriminate input states. However, it fails to capture whether the output preserves the statistical structure of the input, a property crucial in morphogen patterning and dose-dependent signaling. To address this gap, we introduce the 2-Wasserstein (2-WD) distance, which provides a geometric basis for comparing input and output distributions. We define MI as informational fidelity (INF) and the inverse of the 2-WD as geometric fidelity (GMF). Applying this dual-fidelity framework to canonical regulatory motifs under Gaussian channel approximation reveals topology-dependent trade-offs: coherent feed-forward loops can perform well in both dimensions, whereas feedback architectures sacrifice INF to enhance GMF. Experimental analysis of tumor necrosis factor signaling supports the predicted role of feedback regulation. Analysis of RAS-MAPK signaling shows that intracellular signal relay is better described by a balance between INF and GMF than by information transmission alone. Our results demonstrate that reliable signaling need not maximize information alone, but can arise from balancing information transmission with distributional correspondence. Thus, GMF represents a distinct dimension of signaling fidelity and provides a framework for analyzing natural networks and designing task-specific synthetic circuits.

Standard approaches to quantum statistical inference rely on measurements that induce a collapse of the wave function, effectively consuming the quantum state to extract information. In this work, we investigate the fundamental limits of \emph{locally-gentle} quantum state certification, where the learning algorithm is constrained to perturb the state by at most $\alpha$ in trace norm, thereby allowing for the reuse of samples. We analyze the hypothesis testing problem of distinguishing whether an unknown state $\rho$ is equal to a reference $\rho_0$ or $\epsilon$-far from it. We derive the minimax sample complexity for this problem, quantifying the information-theoretic price of non-destructive measurements. Specifically, by constructing explicit measurement operators, we show that the constraint of $\alpha$-gentleness imposes a sample size penalty of $\frac{d}{\alpha^2}$, yielding a total sample complexity of $n = \Theta(\frac{d^3}{\epsilon^2 \alpha^2})$. Our results clarify the trade-off between information extraction and state disturbance, and highlight deep connections between physical measurement constraints and privacy mechanisms in quantum learning. Crucially, we find that the sample size penalty incurred by enforcing $\alpha$-gentleness scales linearly with the Hilbert-space dimension $d$ rather than the number of parameters $d^2-1$ typical for high-dimensional private estimation.

The origin of recently observed spontaneous chiral symmetry breaking in polar fluids is an unsolved problem, and poses fundamental questions as to how heliconical structures emerge in systems composed of achiral molecules. We report on the softening of bend elasticity close to such phase transition, showing that flexoelectric coupling between the electric polarization and the bend deformation is the responsible mechanism, presumably arising from the bent shape of the constituent highly polar molecules.

We document a sequence of bifurcations and elastic patterns in sheared bent sheets of intermediate aspect ratio. The sheets undergo inversion of curvature through the passage of localized features, often in S-shaped pairs. Nested force-displacement hysteresis loops provide experimental evidence for snaking. Several mechanisms for coarsening and refinement of the patterns are observed, including splitting, merging, and escape through open boundaries. While most forces, including that required for full snap-through, scale with the length of the sheet, the initial drop in force upon pattern nucleation decreases rapidly with length.

The tropical semiring is a semiring of extended real numbers, where the operations of `max' and `+' replace the usual addition and multiplication, respectively. Difference equations obtained from the ultradiscrete limit of discrete dynamical systems are described in terms of the tropical semiring. We propose a tropical linearization approach for the stability analysis of difference equations, including those describing ulradiscrete dynamical systems. We show that the fixed point at the tropical origin is asymptotically stable if the maximum eigenvalue of the tropical Jacobian matrix is negative. On the other hand, it is unstable if the maximum eigenvalue of the tropical Jacobian matrix is positive. Since $0$ is the tropical multiplicative identity, these results are analogous to those in the usual linearization process.

The work functions of 7Li and 6Li metals have been measured as a function of temperature, by using photoionization of pure isolated metal nanoparticles in a beam. These data reveal a marked isotope effect in the temperature variation of these work functions. Furthermore, for both isotopes the curvature of this temperature variation is found to be significantly larger than may be ascribed purely to a change in the electron gas density. These findings enhance the characterization of lithium as a quantum material in which the interplay between electronic and ionic degrees of freedom is nontrivial, and call for a microscopic understanding beyond simple models. Additionally, the slope of the work function curves was observed to vanish in the low temperature limit, as had been predicted on the basis of the Third Law of thermodynamics.

We give a representation of the extension class associated to a holomorphic fibration by curvature, generalizing the work of Atiyah on holomorphic principal bundles in a natural way. As an application, we obtain a nonlinear analogue of the classical result of Weil on characterizing the existence of flat connections on holomorphic vector bundles over compact Riemann surfaces. We further establish a faithful functor from the category of nonlinear flat bundles reductive of Kähler type to the category of nonlinear Higgs bundles over the same base, which is assumed to be a compact complex manifold of Kähler type. Finally, we establish a notion of nonlinear harmonic bundle and prove that the variation of nonabelian Hodge structure is a nonlinear harmonic bundle in the rank one case and in the semisimple case.

Astrophysics has experienced an overwhelming increase in research output, as is evident from the year-over-year increase in the number of research papers submitted to the online repository arXiv. As a result, keeping up with progress happening outside our respective sub-fields can be exhausting. While it is impossible to be informed on every single aspect of every sub-field, this paper aims to be the next best thing. We present a summary of statistics for every paper uploaded onto the Astrophysics arXiv over the past year - 2025. We analyse a host of metrics like the most used keywords, subfields and telescopes, the distribution of journals, the most studied astrophysical objects like GW, GRB, FRB events, exoplanets and much more. We also indexed the authors' affiliations to put into context the global distribution of research and collaboration. Combining this data with the citation information of each paper allows us to understand how influential different papers have been on the progress of the field this year. We also present a first of its kind Astrophysical Spectral Fingerprint showing the distribution of research across the electromagnetic spectrum as well as the distribution of research by redshift. Overall, these statistics highlight the general current state of the field, the hot topics people are working on and the different research communities across the globe and how they function. We hope that this is helpful for both students and professionals alike to adapt their current trajectories to better benefit the field.

It is shown that the reduced C*-algebra of a nontrivial linear group $\Gamma<GL_{d}(k)$ with trivial amenable radical is selfless. Thus selflessness and simplicity coincide for reduced C*-algebras of linear groups. Similar results are obtained for twisted reduced group C*-algebra.

We present a hybrid a-priori/a-posteriori goal oriented error estimator for a combination of dynamic iteration-based solution of ordinary differential equations discretized by finite elements. Our novel error estimator combines estimates from classical dynamic iteration methods, usually used to enable splitting-based distributed simulation, and from the dual weighted residual method to be able to evaluate and balance both, the dynamic iteration error and the discretization error in desired quantities of interest. The obtained error estimators are used to conduct refinements of the computational mesh and as a stopping criterion for the dynamic iteration. In particular, we allow for an adaptive and flexible discretization of the time domain, where variables can be discretized differently to match both goal and solution requirements, e.g. in view of multiple time scales. We endow the scheme with efficient solvers from numerical linear algebra to ensure its applicability to complex problems. Numerical experiments compare the adaptive approach to a uniform refinement.

Hypersonic glide vehicles (HGVs) operate in challenging flight regimes characterized by strong nonlinearities in actuation and stringent physical constraints. These include state-dependent actuator limitations, asymmetric control bounds, and thermal loads that vary with maneuvering conditions. This paper introduces an iterative control allocation method to address these challenges in real time. The proposed algorithm searches for control inputs that achieve the desired moment commands while respecting constraints on input magnitude and rate. For slender HGV configurations, thermal loads and drag generation are strongly correlated-lower drag typically results in reduced surface heating. By embedding drag-sensitive soft constraints, the method improves energy efficiency and implicitly reduces surface temperatures, lowering the vehicle's infrared signature. These features are particularly advantageous for long-range military operations that require low observability. The approach is demonstrated using the DLR's Generic Hypersonic Glide Vehicle 2 (GHGV-2) simulation model. The results confirm the method's effectiveness in maintaining control authority under realistic, constrained flight conditions.

Fast radio bursts (FRBs) emit broadband radio emission that may, in rare cases, encode atomic hydrogen (HI) absorption signals as they traverse the interstellar medium of their host galaxies. Though considered in the early FRB literature, the demanding observational prerequisites and the rarity of suitable events have meant that no thorough search for HI absorption in FRB spectra has yet been undertaken. Here, we present an updated systematic analysis assessing the likelihood of modern facilities to detect such absorption features. As a proof of concept, we search for absorption in the spectrum of the bright ASKAP-localised FRB 20211127I, finding a $3\sigma$ opacity upper limit of 0.51. While this test case offers little constraining power, we find that narrow FRBs with fluences exceeding 20/70/150 Jy ms observed with MeerKAT/ASKAP/DSA can probe opacities below 0.1 - a regime in which absorption detections become physically meaningful. We further highlight that stacking thousands of bursts from hyperactive repeaters with FAST offers a very powerful avenue toward detection. Finally, we discuss the broad scientific potential of such detections, including constraints on extragalactic HI spin temperatures, a means to physically probe the environment surrounding the progenitor, and a path towards disentangling host galaxy contributions to dispersion and scattering.

We present efficient and practical protocols to measure the second Rényi entropy, whose exponential is known as the purity. Our approach is based on expressing the purity in terms of transition probabilities generated by an echo-type forward-backward evolution sequence, making it applicable to quantum many-body systems. Notably, our approach does not rely on random-noise averaging, a feature that can be extended to protocols to measure out-of-time-order correlation functions, as we demonstrate. By way of example, we show that our protocols can be practically implemented in superconducting qubit-based platforms, as well as in cavity-QED trapped ultra-cold gases.

Brittle materials subjected to thermal shocks experience strong temperature gradients that in turn give rise to mechanical stresses that can be large enough to induce fracture. This work presents a complete model for phase-field fracture for coupled thermo-mechanical problems, wherein the bulk material properties, the material strength, and the fracture toughness are specified independently. The capabilities of the model are assessed across a wide span of scenarios in thermo-mechanical fracture, from the propagation of large pre-existing cracks to crack nucleation under spatially uniform states of stress. In particular, we revisit the controlled quenching of glass plates, and demonstrate how the model captures experimentally observed crack patterns across a range of thermal loads. Ceramic disks subjected to infrared radiation are also examined, with the model reproducing both straight cracks in notched specimens and branching in intact specimens. Finally, ceramic pellets subjected to rapid power pulses are examined, with the model explaining experimental transitions from intact to fractured pellets and the important role of material strength. The results demonstrate that the complete phase-field model unifies the treatment of distinct fracture scenarios under thermal shock, surpassing classical approaches and enabling more reliable prediction of brittle fracture in extreme environments.

By modelling the upper layers of the Sun in terms of a two-layer setup where a free-surface exists within the computational domain, we numerically study the interaction between the surface gravity, or the fundamental ($f$) mode, and the magnetic fields. Earlier such works were idealized in the sense that the static magnetic fields were imposed below the photosphere, i.e., the free-surface, to detect signatures of sub-surface magnetic fields and flows on the $f$-mode. In this work, we perform three-dimensional (3D) numerical simulations where the interior fluid below the photosphere is stirred helically at small scales, thus facilitating an $\alpha^2$-dynamo. This allows us to investigate how these self-consistently generated large-scale magnetic fields influence the properties of the $f$-mode. We find that when the magnetic fields saturate near the equipartition values with the turbulent kinetic energy of the flow, the $f$-mode is significantly perturbed. Compared to the non-magnetic case, or the kinematic phase of the dynamo when fields are too weak, we note that the frequencies and the strengths of the $f$-mode are enhanced in presence of saturated magnetic fields, with these effects being larger at larger wavenumbers. This qualitatively confirms the earlier findings from observational and numerical works which reported the $f$-mode strengthening due to strong sub-surface magnetic fields.

Lax-Wendroff methods combined with discontinuous Galerkin/flux reconstruction spatial discretization provide a high-order, single-stage, quadrature-free method for solving hyperbolic conservation laws. In this work, we introduce automatic differentiation (AD) for performing the Cauchy-Kowalewski procedure used in the element-local time average flux computation step (the predictor step) of Lax-Wendroff methods. The application of AD is similar for methods of any order and does not need positivity corrections during the predictor step. This contrasts with the approximate Lax-Wendroff procedure, which requires different finite difference formulas for different orders of the method and positivity corrections in the predictor step for fluxes that can only be computed on admissible states. The method is Jacobian-free and problem-independent, allowing direct application to any physical flux function. Numerical experiments demonstrate the order and positivity preservation of the method. Additionally, performance comparisons indicate that the wall-clock time of automatic differentiation is always on par with the approximate Lax-Wendroff method.

We present a data-driven inverse construction of the dilaton field in a bottom-up AdS/QCD description of heavy vector quarkonia. Instead of adopting an \emph{ad hoc} analytic ansatz, we use a multilayer perceptron to learn \(\Phi'(z)\) as a smooth function of the holographic coordinate, with \(\Phi(0)=0\) imposed to ensure ultraviolet consistency. The dilaton and its derivatives obtained by automatic differentiation generate the holographic potential \(U(z)\), and the associated Schrödinger-like equation is discretized and diagonalized to extract the low-lying eigenmodes. Masses and decay constants are then evaluated from the eigenvalues and the near-boundary behavior of the bulk-to-boundary modes. Training on PDG data for charmonium and bottomonium yields a non-quadratic dilaton profile that resolves the longstanding difficulty of simultaneously reproducing both the heavy-quarkonium spectrum and the monotonic suppression of leptonic decay constants with radial excitation. The combined fit achieves RMS deviations of \(1.26\%\) (charmonium) and \(3.32\%\) (bottomonium). This work establishes neural-network reconstruction as a flexible tool for holographic modeling and provides a basis for future extensions incorporating additional channels, lattice constraints, or finite-temperature backgrounds.

In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative importance to these attributes. Since saliences are known to change in practice, a central question arises: how robust is a stable matching to such perturbations? We address several fundamental questions in this context. First, we formalize robustness as a radius within which a stable matching remains immune to blocking pairs under any admissible perturbation of salience vectors (which are assumed to be normalized). Given a stable matching and a radius, we present a polynomial-time algorithm to verify whether the matching is stable within the specified radius. We also give a polynomial-time algorithm for computing the maximum robustness radius of a given stable matching. Further, we design an anytime search algorithm that uses certified lower and upper bounds to approximate the most robust stable matching, and we characterize the robustness-cost relationship through efficiently computable bounds that delineate the achievable tradeoff between robustness and cost. Finally, we show that for each stable matching, the set of salience profiles that preserve its stability factors is a product of low-dimensional polytopes within the simplex. This geometric structure precisely characterizes the polyhedral shape of each robustness region; its volume can then be computed efficiently, with approximate methods available as the dimension grows, thereby linking robustness analysis in matching markets with classical tools from convex geometry.

Tantalum pentoxide (Ta2O5) is a polymorphic wide-bandgap semiconductor with outstanding dielectric properties and widespread use in optical and electronic technologies. Its rich structural diversity, arising from multiple polymorphs accessible under different synthesis conditions, has made Ta2O5 a long-standing subject of interest. However, a unified understanding of the thermodynamic stability and phase transitions of its polymorphs across pressure-temperature (P-T) space has remained elusive. Here, using first-principles calculations, we map the thermodynamic landscape of Ta2O5 and establish a comprehensive P-T phase diagram together with a phase-stability hierarchy. We find that Gamma-Ta2O5 and B-Ta2O5 dominate the phase diagram over a broad range of P-T conditions: Gamma-Ta2O5 is stabilized at low pressures, while B-Ta2O5 becomes thermodynamically favored at higher pressures up to ~ 60 GPa, beyond which Y-Ta2O5 emerges as the most stable phase. Crucially, the zero-point energy (ZPE), one aspect of nuclear quantum effects (NQEs), plays a significant role in determining relative phase stability, contributing substantially to the Gibbs free energy and altering phase boundaries. A re-entrant phase transition between Gamma and B-Ta2O5 is predicted near ~ 2 GPa, revealing unexpected complexity in the phase behavior of this oxide. More generally, we identify a characteristic temperature (T_0), at which zero-point and thermal phonon contributions to the free energy become comparable, and show that T_0 is approximately one-third of the Debye temperature. This relationship provides a simple, physically transparent criterion for assessing the importance of NQEs in phase stability, with implications extending beyond Ta2O5 to a broad class of complex oxides.