Wide-field and high-cadence sky surveys are the first step in the chain of discovery and characterisation of astrophysical transients such as supernovae, kilonovae, and tidal disruption events, each linked to the varied demise of stellar systems. The Gravitational-wave Optical Transient Observer (GOTO) is a telescope array of thirty-two 40 cm unit telescopes split over two almost antipodal sites. It performs a regular time-domain sky-survey in the optical to ~20 mag in addition to immediate scheduling of follow-up observations at the locations of external multi-wavelength and -messenger triggers. To facilitate the timely recovery of optical counterparts to these triggers, as well as the presence of serendipitous discoveries of astrophysical transients in the regular sky-survey, a low-latency data pipeline and workflow was developed. The implementation of this workflow is described herein and the quality of GOTO data delivered by it assessed, alongside its performance for prompt transient recovery. Utilising difference image analysis to identify candidate discoveries, the process is typically complete ~7 minutes after shutter close on the telescope. We further describe later processing of these candidates -- both automated and human-in-the-loop -- including reporting to the wider community and the triggering of more detailed observations, with a focus on immediate, intra-night characterisation. The workflow is meeting the needs of GOTO to promptly discover, report and characterise infant transients. Nevertheless, areas for further development and improvements are also highlighted.

We discuss the problem of projecting a point onto an arbitrary hyperbolicity cone from both theoretical and numerical perspectives. While hyperbolicity cones are furnished with a generalization of the notion of eigenvalues, obtaining closed form expressions for the projection operator as in the case of semidefinite matrices is an elusive endeavour. To address that we propose a Frank-Wolfe method to handle this task and, more generally, strongly convex optimization over closed convex cones. One of our innovations is that the Frank-Wolfe method is actually applied to the dual problem and, by doing so, subproblems can be solved in closed-form using minimum eigenvalue functions and conjugate vectors. To test the validity of our proposed approach, we present numerical experiments where we check the performance of alternative approaches including interior point methods and an earlier accelerated gradient method proposed by Renegar. We also show numerical examples where the hyperbolic polynomial has millions of monomials. Finally, we also discuss the problem of projecting onto p-cones which, although not hyperbolicity cones in general, are still amenable to our techniques.

For many health conditions, there are highly efficacious treatment and prevention products. Maximizing their impact requires strategies that improve the reach of health screening in order to establish who could benefit. For example, HIV prevention strategies aim to expand risk screening and to improve uptake of pre-exposure prophylaxis (PrEP) among those experiencing risk. Often, these strategies induce changes at the group-level (e.g., health clinics or communities) and are evaluated through cluster randomized trials. This scenario creates a complex, multilevel-mediation-missing data problem for the following reasons. First, the strategy is delivered at the cluster-level, while health screening and outcomes are at the individual-level. Second, the strategy improves health outcomes directly and indirectly through improved health screening. Third, everyone has an underlying status, which is only observed among those screened. To formally define the total effect in such settings, we use Counterfactual Strata Effects: causal estimands where the outcome is only relevant for a group whose membership is subject to missingness and/ or impacted by the exposure of interest. To identify and estimate the corresponding statistical estimand, we propose a novel extension of Two-Stage targeted minimum loss-based estimation (TMLE). Simulations demonstrate the practical performance of our approach as well as the limitations of existing approaches.

Upconversion of low-energy photons to higher-energy photons provides an opportunity to surpass traditional limitations in fields such as 3D printing, photovoltaics, and photocatalysis. Triplet--triplet annihilation upconversion (TTA-UC) is particularly appealing for such applications as it can efficiently upconvert low-intensity, incoherent light. However, previously demonstrated thin-film TTA systems are simultaneously constrained by modest efficiencies and limited reach into the near infrared (NIR). Here, we design a single-layer thin-film bulk heterojunction that integrates PbS quantum dots (QDs) as tunable NIR absorbers within an organic semiconductor matrix of TES-ADT, achieving large anti-Stokes shifts up to 500 nm and high internal quantum efficiencies across the NIR-I and NIR-II windows (800-1200 nm). Through the incorporation of 5-tetracene carboxylic acid ligands on the PbS QD surface, the yield of sensitized triplets was boosted, as confirmed by transient absorption and time-resolved photoluminescence measurements. The resulting films demonstrated a 15-fold improvement in UC efficiency. Furthermore, we demonstrate visible imaging of incoherent 1200 nm light via thin-film TTA-UC at incident intensities at the imaging mask as low as 20 mWcm$^2$, marking a significant advance toward practical implementation of solid-state NIR-to-visible upconversion.

This work investigates symbolic regression (SR) as an interpretable alternative to black-box machine learning for the classification of stars, galaxies, and quasars in the Sloan Digital Sky Survey Data Release 17 (SDSS DR17). We conduct a systematic comparative study of four state-of-the-art SR frameworks: {\tt PySR}, Exhaustive Symbolic Regression ({\tt ESR}) with MDL-based selection, Physical Symbolic Optimization ({\tt PhySO}) using deep reinforcement learning, and Multi-View Symbolic Regression ({\tt MvSR}). By deriving compact analytic functions (complexity $\leq$ 10) on a representative training subset and subsequently evaluating them via an 80,000-sample 5-fold cross-validation threshold optimization phase and a subsequent 10,000-sample unseen hold-out test set, we map spectroscopic redshift ($z$) to continuous classification scores. Our results demonstrate that these low-complexity expressions achieve high predictive reliability, with {\tt MvSR} reaching a cross-validation Cohen's Kappa of 0.8956 (0.8876 on the hold-out set) and {\tt PhySO} achieving exceptional parametric stability ($σ< 0.002$). We note however that the resulting equations returned by Symbolic regression are purely empirical and no physical significance should be ascribed to these equations.

The first part of these notes give an introduction to the theory of Polish group actions on compact Hausdorff spaces, leading up to a proof of the Kechris-Pestov-Todorcevic correspondence and discussions of properties of universal minimal flows. The second part proveides some background on descriptive set theory and culminates with B. Miller's proof of the $\mathcal{G}_0$-dichotomy theorem due to Kechris, Solecki, and Todorcevic.

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 $(m_\pm,Λ_\pm)$. 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 $σ$ and pressure $p$ obey the linearized barotropic law $p=p_0+c_s^2(σ-σ_0)$, with sound speed $c_s^2=λc^2$. Since $c_s^2$ is independent of the equilibrium ratio $w_0\equiv p_0/(σ_0 c^2)$, tension shells ($w_0<0$) stay radially stable with real $c_s$. Fixing $Λ_+$ 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 $(R_0,σ_0)$ over $(m_\pm,Λ_\pm,λ,w_0)$ and find that stable shells with $σ_0>0$ and $0<λ\le1$ exist only for $m_+/m_->1$, at three scales -- the photon sphere, the SdS static radius, and the cosmological horizon. At $λ=1$ the numerical windows, checked against the analytic test-shell bounds, are $(1-\sqrt{13})/6\lesssim w_0\lesssim 1/2$ ($Λ_+=Λ_-$), $-2/3\lesssim w_0\lesssim 1/2$ ($Λ_+>Λ_-$), and $0\lesssim w_0$ ($Λ_+<Λ_-$). 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 $Λ_+=Λ_-$, only the static radius scale for $Λ_+>Λ_-$, and are absent for $Λ_+<Λ_-$. 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 $λ>0$, which controls the overall reproductive speed, and they are monotonically increasing in $λ$ 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 $λ(A)$ 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 $λ_w$ and $λ_s$, 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-α, 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 $α$ in trace norm, thereby allowing for the reuse of samples. We analyze the hypothesis testing problem of distinguishing whether an unknown state $ρ$ is equal to a reference $ρ_0$ or $ε$-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 $α$-gentleness imposes a sample size penalty of $\frac{d}{α^2}$, yielding a total sample complexity of $n = Θ(\frac{d^3}{ε^2 α^2})$. 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 $α$-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 $Γ<GL_{d}(k)$ 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 $3σ$ 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.