We derive integrable deformations of the 2d Breitenlohner-Maison (BM) sigma model that describes the stationary, axisymmetric sector of 4d general relativity, as well as higher-rank generalisations thereof, using the framework of 4d Chern-Simons theory. In particular, we consider deformations of the boundary conditions and action of the 4d Cole-Weck model, which lead to deformations of the BM model associated with solutions to the homogeneous and inhomogeneous classical Yang-Baxter equations respectively.

Paul Erdos posed the following question: Is there a prime number $p>5$ such that the residues of $2!$, $3!$,\ldots, $(p-1)!$ modulo $p$ all are distinct. In this short note, we give the negative answer on this question in an elementary way.

We study the drag force acting on a heavy quark in a holographic plasma with rotational anisotropy and finite density. The bulk dual is the CCLP black hole of five-dimensional minimal gauged supergravity, characterised by two independent rotation parameters and electric charge. In the neutral Kerr--AdS limit, we use the principal Killing string to obtain an exact drag force for arbitrary rotation parameters. The resulting force is purely tangential but generically anisotropic, reducing to the viscous form only in the equal-spin sector. We then analyse stationary strings in the charged CCLP background perturbatively in the slow-rotation regime. A regularity analysis of the Lorentzian worldsheet fixes the angular integration constants that would otherwise remain ambiguous, yielding a finite renormalised transverse drag force with a smooth Kerr--AdS limit. We also show that, in the equal-spin sector, worldsheet regularity selects a unique co-rotating equilibrium quark and compute its renormalised free-energy shift.

Binary neutron-star mergers offer crucial insights into the matter properties of neutron stars. We present the possible imprints in the gravitational wave signal from the nature of phase transition from such events. Our study employs a one-parameter family of equation of states built using a polytropic approach with a control parameter $Δp$ surveying the features of hadron-quark phase transition, from Maxwell construction to the Gibbs construction. It allows us to explore the extent of mixed phases and analyse their direct impact on merger dynamics. Post-merger gravitational wave emissions reveal the expression of specific signatures in the spectrogram and power spectral density, serving as a distinct signature of equations of state with mixed phases. We found additional peaks in power spectral density that are exclusively generated from the post-merger remnant experiencing a phase transition. Additionally, the nature of phase transition leaves specific imprints on the spectrogram, leading to a two-folded signature from gravitational wave analysis. Furthermore, we establish the first correlation between $Δp$ and the threshold mass for prompt collapse. Our analysis shows that $Δp \lesssim 0.04$ is required if GW170817 formed a long-lived remnant or has experienced a delayed collapse into a black hole.

Finite-amplitude gravity waves at the air-water interface induce net fluid and particle transport, known as Stokes drift. While this mechanism is well understood for steady waves, transport under unsteady, evolving conditions remains poorly characterized. Here, we investigate Lagrangian transport in freely decaying waves using high-resolution two-phase simulations and a perturbative analytical model. Wave decay modifies the classical Lagrangian drift by introducing both first- and second-order corrections in the wave amplitude expansion, and generates a net vertical transport, governed by the balance between inertia and viscosity. These effects alter particle trajectories and enhance anisotropic mixing, with implications for interpreting field observations and modelling surface transport processes.

Gravitational wave astronomy presents a promising opportunity to directly observe scalar-induced gravitational waves originating from the early universe. Experiments, including ground-based interferometers like LIGO and Virgo, and the Pulsar Timing Array, such as FAST and SKA, are poised to significantly enhance sensitivity to these gravitational waves. In this paper, we combined Cosmic Microwave Background and Baryon Acoustic Oscillation datasets with upper or lower limits of the stochastic gravitational wave background provided by FAST or SKA, to constrain scalar-induced gravitational waves. To provide a comprehensive forecast, we consider two scenarios at a frequency: one where FAST or SKA does not detect scalar-induced gravitational waves, thereby setting an upper limit on the fractional energy density; and another where these waves are detected successfully, thus establishing a lower limit. In the $Λ$CDM+$r$ model, the scalar spectral index of the power-law power spectrum is constrained to $n_s=0.9598^{+0.0013}_{-0.0009}$ from the combinations of CMB+BAO+SKA datasets in the upper limit scenario where scalar-induced gravitational waves propagate at the speed of light. The constraint shifts to $n_s = 0.9697\pm{0.0033}$ in the lower limit scenario. Comparing with the constraint from the combinations of CMB+BAO datasets, the scalar spectral index $n_s$ in the upper limit scenario exhibits significant changes, which could serve as an indicator for detecting scalar-induced gravitational waves. In the $Λ$CDM+$α_s$+$r$ model and $Λ$CDM+$α_s$+$β_s$+$r$ model, the running of the scalar spectral index $α_s$ and the running of the running $β_s$ also show notable variations, suggesting potential indicators. The numerical findings clearly demonstrate the impact of the upper and lower limits provided by FAST or SKA.

We present the first direct measurement of the Z=6 shell gap in the neutron-rich 20O nucleus. The one-proton removal transfer reaction 2H(20O,3He)19N has been studied using the ACTAR TPC setup at GANIL. The use of ACTAR TPC enabled the measurement of low-cross section proton-removal reactions while preserving resolution. Eight p-hole states with l=1 were identified in 19N accounting for total strengths of 86% and 72% of the 0p3/2 and 0p1/2 single-particle orbitals, respectively. The energies and spectroscopic factors of the measured states allowed to determine the proton spin-orbit splitting 0p3/2 - 0p1/2 in 20O. The Z=6 shell gap has been established to be 5.30(14) MeV. These findings indicate a reduction of the Z=6 shell gap while adding neutrons to the sd-valence orbitals, consistent with the effects of the tensor force predicted by state-of-the-art shell model interaction SFO-tls while at variance with the emergence of a large Z=6 gap observed in other studies.

We perform a theoretical study of a continuous superradiant laser supporting its experimental realization at FEMTO-ST using two sequentially-emitting ensembles of ${}^{171}\mathrm{Yb}$ atoms coupled to the same Fabry-Perot cavity. Using an open quantum system approach, we identify for the simplest case the parameter space where the laser reaches tens of picowatts of power with a sub-millihertz linewidth. Studying the impact of inhomogeneous frequency broadening and variations in atom-cavity coupling on the superradiant emission, we find the laser properties robust with respect to such perturbations, also thanks to the occurrence of synchronization of the atomic dipoles. We then consider a two-site configuration, in which atoms in each site are equally coupled to the cavity and have equal detunings, with different values for the two ensembles. We find for balanced and imbalanced atom numbers that synchronization leads in a certain parameter space to a single narrow spectral line whose central frequency follows the weighted average frequency. This result indicates that sequential loading can enable continuous superradiant emission for metrological applications, provided that the relative frequencies of the two ensembles are controlled to the level required by the target stability.

Cloud users aim to minimize cost while maximizing performance by selecting the most suitable instance types for their workloads. To reduce expenses, spot instances have been widely adopted due to their steep discounts compared to on-demand pricing. However, their use introduces reliability risks due to potential interruptions, and existing research has primarily focused on mitigating this trade-off from a cost or availability perspective alone. Despite the diversity in hardware capabilities among instance types, current provisioning systems tend to ignore performance variation, selecting nodes solely based on minimum resource requirements. In this paper, we present KubePACS, a Kubernetes-native spot instance provisioning system that constructs node pools optimized for both cost and performance while guaranteeing high availability. KubePACS formulates the node selection process as a multi-objective optimization problem, incorporating real-time data such as spot prices, performance benchmarks, and availability scores, including the multi-node Spot Placement Score (SPS). It solves this problem efficiently using an Integer Linear Programming (ILP) approach guided by the Golden Section Search (GSS) algorithm to find the optimal configuration. By integrating with the Karpenter node autoscaler, KubePACS jointly optimizes instance-type selection and node scaling decisions within a standard provisioning workflow. KubePACS also adopts a novel heuristic to support workload-specific preferences by scaling performance metrics for specialized instances. Through extensive evaluation across synthetic and real-world workloads, KubePACS demonstrates on average 55.09% and up to 81.06% higher performance per dollar over state-of-the-art solutions such as Karpenter, SpotVerse, and SpotKube, which only reference the spot instance prices and limited availability data.

The evolution of neutron stars (NSs) embedded within massive stellar envelopes is a critical phase in binary stellar evolution, potentially leading to the formation of Thorne-Żytkow Objects (TŻOs) or catastrophic collapse. We present the first fully coupled general relativistic hydrodynamics (GRHD) simulations of hypercritical accretion onto NSs that simultaneously incorporate grey two-moment (M1) neutrino transport and an $α$-chain nuclear reaction network. By investigating four distinct progenitor evolutionary stages, we resolve the complex interplay between intense neutrino cooling, multidimensional fluid dynamics, and nuclear feedback. Our results show that while vigorous convection is triggered in the post-shock region, the global energy budget is primarily governed by neutrino cooling, which effectively balances the accretion power. Crucially, even though our M1 transport scheme captures neutrino absorption and localized heating, the efficient cooling sink and high ram pressure of the infalling envelope prevent the formation of any core-collapse supernova-like explosion. We find that all nucleosynthetically processed material ($T > 5$~GK) remains strictly gravitationally bound, challenging the assumption that these systems contribute significantly to galactic nucleosynthetic yields via convective dredge-up. The lack of sustained outflows and the persistent hypercritical accretion rates suggest that embedded NSs will rapidly exceed the Tolman-Oppenheimer-Volkoff mass limit on timescales of minutes to hours. We conclude that these systems are not stable TŻOs, but are rather transient precursors to catastrophic black hole formation and potential central engines for high-energy transients.

We calculate the two-loop quarkonium Hamiltonian in the annihilation channel within the framework of potential-NRQCD effective field theory. The result agrees with the previous calculation of the corresponding four-quark operator in NRQCD for SU(N) color gauge group. We further obtain an expression with a more general color structure applicable to other gauge groups. Combined with the recently calculated two-loop Hamiltonian in the non-annihilation channel, this completes the full two-loop quarkonium Hamiltonian.

We present a uniform framework for constructing $3$-designs from $\mathrm{GL}_2(\mathbb F_q)$-invariant subspaces of $\mathbb F_q[X,Y]_k$, the space of homogeneous polynomials of degree $k$. Given such a subspace $W$, we associate a $\mathrm{PGL}_2(\mathbb F_q)$-invariant family of $k$-subsets of $\mathbb P^1(\mathbb F_q)$. Whenever this family is nonempty, it forms a $3\text{-}(q+1,k,λ)$ design. Via the Cayley transform, the construction is reformulated on the unit circle $U_{q+1}\subseteq \mathbb F_{q^2}^{\times}$, where the block conditions become explicit linear relations among elementary symmetric polynomials. This reformulation unifies several previously disparate constructions and simplifies a number of delicate ad hoc computations. When $k\le q$, the evaluation map on $\mathbb P^1(\mathbb F_q)$ identifies $W$ with a subcode $C_W$ of the projective Reed--Solomon code. We show that the associated block family is nonempty if and only if $d(C_W)=q+1-k$. Under this condition, the supports of minimum-weight codewords in $C_W$, as well as the supports of suitable fixed-weight codewords in the dual code $C_W^\perp$, yield further $3$-designs. Applying this framework to the Lucas subspaces, which form a distinguished family of invariant subspaces, we obtain explicit block descriptions, classify the cases in which the defining conditions reduce to a single equation, and establish several emptiness and nonemptiness results. In particular, for $q=p^e$ and $k=p^m+1$, we show that the associated block family is nonempty if and only if $m\mid e$, in which case it yields the Steiner system $S(3,p^m+1,q+1)$. Finally, in the ternary case $p=3$ and $k=7$, we use the weight distribution of the ternary Melas code to determine the design parameters left undetermined by Xu et al.

Let us denote elements of the symmetric group $S_n$ using square brackets for the one-line notation. Cycles will be represented using parentheses, following the standard cycle notation. Under this convention, the full reversal of the identity element $()$ is the element $s = [n\ n-1 \dots 1]$. In the present work, we obtain a lower bound on the decomposition complexity of elements $s(1n \dots 2)^{i}$ into the generators $(12), (12 \dots n), (1n \dots 2)$, where $i$ ranges over the set $\{1,2,\dots,n\}$. As a consequence, we derive the lower bound $n(n-1)/2$ for the diameter of Cayley graph of the group $S_n$ generated by $(12), (12 \dots n), (1n \dots 2)$.

Two different frameworks are developed to model the wave field generated by a transducer and propagating through one or more interfaces, and a Quasi-Monte Carlo (QMC) integration scheme is used to numerically evaluate their results. The first method is based on the Rayleigh-Sommerfeld Integral (RSI), further developing a formulation in the literature and improving its capabilities, while the second relies on a high-frequency approximation, using a ray tracing principle. The advantages and limitations of each model are then compared via in-depth investigations on several use cases, culminating in an efficiency and scope assessment. It was found that the RSI-based model performs well if a large number of field points is needed, such as when modelling a full image of the field. Conversely, for a large number of interfaces, such as when modelling the field through a thin-layered material, the most efficient model was the ray tracing formulation, since it was unnecessary to propagate the field between all the interfaces first. This was especially noticeable for applications requiring only the evaluation of the field at a few points on the other side of multiple interfaces.

We consider the six dimensional energy-critical semilinear heat equation with self-similarly decaying initial data. Our main result shows the existence of sign-changing solutions that exhibit infinite-time blow-up and nonnegative solutions that decay strictly more slowly than the self-similar rate. Moreover, the blow-up and decay rates are not uniquely determined by the decay rate of the initial data, but exhibit a certain flexibility depending on the construction. The proof is based on gluing suitably rescaled bubbles to forward self-similar solutions.

Hadamard matrix-based aperture encoding is a method for producing synthetic aperture datasets with high Signal-to-Noise Ratios. Recently, the pulse inversion capabilities of bias-sensitive Top-Orthogonal to Bottom Electrode (TOBE) arrays have driven the development of multiple Hadamard-based sequences. These sequences produce high-quality static images but are sensitive to motion. This work introduces Recursive Aperture Decoded Imaging (READI) and Estimated Motion-Compensated Compounding (EMC2), which look to reduce this sensitivity. READI is a novel decoding and beamforming technique for Hadamard aperture-encoded sequences that produces multiple low-resolution images from subsets of the full sequence. These READI images are less affected by motion and sum to form the complete high-resolution image. EMC2 describes the process of comparing these low-resolution images to estimate the underlying motion, then warping them to align before compounding. This produces a high-resolution image that is resiliant to motion. READI with EMC2 applied to the TOBE-based Fast Orthogonal Row-Column Electronic Scanning (FORCES) sequence. It is shown to fully restore images corrupted by probe motion and to recover tissue speckle and boundaries in images of a beating heart phantom. READI low-resolution images by themselves are demonstrated to be a marked improvement over a sparse Hadamard scheme with the same transmit count, and are able to recover blood speckle at a flow rate of 42 cm/s.

Trees can accelerate queries that search or aggregate values over large collections. They achieve this by storing metadata that enables quick pruning (or inclusion) of subtrees when predicates on that metadata can prove that none (or all) of the data in a subtree affect the query result. Existing systems implement this pruning logic manually for each query predicate and data structure. We generalize and mechanize this class of optimization. Our method derives conditions for when subtrees can be pruned (or included wholesale), expressed in terms of the metadata available at each node. We efficiently generate these conditions using symbolic interval analysis, extended with new rules to handle geometric predicates (e.g., intersection, containment). Additionally, our compiler fuses compound queries (e.g., reductions on filters) into a single tree traversal. These techniques enable the automatic derivation of generalized single-index and dual-index tree joins that support a wide class of join predicates beyond standard equality and range predicates. The generated traversals match the behavior of expert-written code that implements query-specific traversals, and can asymptotically outperform the linear scans and nested-loop joins that existing systems fall back to when hand-written cases do not apply.

Safety alignment in large language models relies on behavioral training that can be overridden when sufficiently strong in-context patterns compete with learned refusal behaviors. We introduce Involuntary In-Context Learning (IICL), an attack class that uses abstract operator framing with few-shot examples to force pattern completion that overrides safety training. Through 3479 probes across 10 OpenAI models, we identify the attack's effective components through a seven-experiment ablation study. Key findings: (1)~semantic operator naming achieves 100% bypass rate (50/50, $p < 0.001$); (2)~the attack requires abstract framing, since identical examples in direct question-and-answer format yield 0%; (3)~example ordering matters strongly (interleaved: 76%, harmful-first: 6%); (4)~temperature has no meaningful effect (46-56% across 0.0--1.0). On the HarmBench benchmark, IICL achieves 24.0% bypass $[18.6%, 30.4%]$ against GPT-5.4 with detailed 619-word responses, compared to 0.0% for direct queries.

Observations of luminous quasars at $z\gtrsim7$ reveal supermassive black holes (SMBHs) with inferred masses $M_{\rm BH}\sim10^9 \, M_\odot$ formed within the first $\sim700$~Myr of cosmic history. Standard growth channels \textrm{ -- } Eddington-limited gas accretion and hierarchical mergers \textrm{ -- } face severe timescale restrictions. We consider a super-Eddington accretion mechanism aided by the Bondi accretion of a minimal model of self-interacting dark matter (SIDM). We demonstrate that in a {\it critical regime} with a near-relativistic sound speed, the Bondi accretion yields an accretion rate that depends only on the mass $m$ of SIDM, thus it is universal to the ambient environment. This critical accretion mechanism for $m\gtrsim 10^{-2}\; {\rm eV}$ can grow seeds as small as $10\,M_\odot$ primordial black holes (PBH) in the early Universe into $10^9$ \textrm{--} $10^{10}\,M_\odot$ SMBHs by $z\sim7$ without fine-tuned environments. Therefore, given a mass distribution of PBHs and a value of $m$, the mass function of primary black holes at late time can be fully determined with masses ranging from stellar to SMBHs. This connects the microscopic physics of dark matter to astrophysical observations of black holes.

Integrating two-dimensional semiconductors such as MoS$_2$ with dielectric materials remains a central challenge for their use in future logic technologies. While seed layers are typically introduced to promote dielectric nucleation and adhesion, we show that they also critically govern charge-transfer doping and, in turn, transistor performance. Back-gated monolayer MoS$_2$ transistors passivated on their top-surface with a Ta-seed/HfO$_x$ dielectric stack were fabricated and characterized electrically and physically using Raman, photoluminescence, and X-ray photoelectron spectroscopies. Threshold voltage and on-current varied strongly with Ta-seed thickness and deposition conditions, and these changes correlated with signatures observed across all spectroscopic probes. The results reveal that the seed layer both introduces disorder into the MoS$_2$ channel and modifies the interfacial charge environment controlling charge transfer between HfO$_x$ and MoS$_2$. Optical spectroscopy shows that on-current tracks seed-induced disorder, whereas X-ray photoelectron spectroscopy indicates that threshold voltage correlates with shifts in the local electrostatic environment associated with interfacial charge transfer. Better performance was obtained with ultrathin 0.2 nm Ta seed layers deposited under oxygen-poor conditions, which limit deposition-induced damage while facilitating charge transfer. These findings identify seed-layer engineering as a key strategy for controlling disorder and interfacial doping in MoS$_2$ devices and establish multimodal spectroscopy as a practical during-fabrication approach for process development and monitoring.

Algorithmic predictions are increasingly used to inform the allocation of scarce resources. The promise of these methods is that, through machine learning, they can better identify the people who would benefit most from interventions. Recently, however, several works have called this assumption into question by demonstrating the existence of settings where simple, unit-level allocation strategies can meet or even exceed the performance of those based on individual-level targeting. Separately, other works have objected to individual-level targeting on privacy grounds, leading to an unusual situation where a single solution, unit-level targeting, is recommended for reasons of both privacy and utility. Motivated by the desire to fully understand the interplay of privacy and targeting levels, we initiate the study of aid allocation systems that satisfy differential privacy, synthesizing existing works on private optimization with the economic models of aid allocation used in the non-private literature. To this end, we investigate private variants of both individual and unit-level allocation strategies in both stochastic and distribution-free settings under a range of constraints on data availability. Through this analysis, we provide clean, interpretable bounds characterizing the tradeoffs between privacy, efficiency, and targeting precision in allocation.

Active transmissive metasurfaces are central building blocks for future compact, cascadable optical systems, enabling the stacking of multiple functional layers for advanced dynamic beam shaping, photonic neural networks, depth sensing, and holography. We present a transmissive electro-optic metasurface based on silicon-on-lithium-niobate, where an array of silicon waveguides with periodic perturbations, individually controlled at the 100 pm scale, supports well-defined high-Q (>2000) guided-mode resonances (GMRs). We incorporate interdigitated push-pull electrodes between subwavelength-spaced GMR elements to locally tune the refractive index in the lithium niobate substrate, thereby shifting the GMR resonance and enabling opposite phase and amplitude modulation between neighboring radiative elements. In a geometrically symmetric metasurface, this effect introduces electro-optic beam splitting via diffraction, with diffraction efficiencies as high as 3%. By introducing controlled passive resonance detuning via 100 pm scale perturbation shifts, we realize a Vernier-type enhancement mechanism through geometrical symmetry breaking, thereby increasing the efficiency of amplitude modulation six-fold , and achieving modulation depths of 40% at $\pm$30 V. This work demonstrates the potential of active and passive resonance control enabled by high-Q GMR structures for efficient electro-optic modulation or multifunctional sensing.

Before full fault tolerance, partially error-corrected logical executions may be available but costly. We formulate zero-noise extrapolation as a statistical-design problem in which the physical/logical execution mode is an extrapolation variable. Logical circuits provide low-noise anchors, while physical folded circuits supply a cheaper noise lever arm. In a calibrated $p_L=γp$ model, we derive Richardson variance prefactors, folded-circuit runtime ratios, optimal shot allocation, and bias--variance criteria. We demonstrate that for $γ\lesssim0.1$, the mixed strategy can substantially reduce runtime under the stated resource model.

Rutile RuO$_2$ has recently attracted great interest, as its magnetic ground state remains controversial. Experimental studies have reported either nonmagnetic (NM) or altermagnetic (AM) ground states in different crystalline samples of RuO$_2$, highlighting the need for a reasonable explanation to resolve this contradiction. In this study, density functional theory calculations are performed to reveal the correlation-sensitive and strain-dependent magnetism of bulk RuO$_2$. On one hand, multiple AM phases with different magnitudes of the spin magnetic moment are identified in the Hubbard parameter space for RuO$_2$. On the other hand, when appropriate strains that significantly change the crystal cell volume are applied, the ground state of RuO$_2$ can undergo transitions between the NM state (with no spin splitting) and the magnetic states (with spin splitting in the band structure). These findings not only demonstrate intriguing physics in 4\textit{\textit{d}}-electron-correlated RuO$_2$, but also retain its potential for spintronic applications.

The single orbital, one-dimensional, Hatano-Nelson Hamiltonian provides deep insight into the physics of non-Hermiticity, resulting from asymmetric left/right hopping, and its connections to localization. In the absence of disorder, its single particle eigenvalues $E_α$ lie on an ellipse in the complex plane whose extent in the imaginary direction is controlled by the degree of asymmetry. When randomness is introduced, two sets of real eigenvalues emerge at the extremes of the largest and smallest real part of $E_α$. These real eigenvalues are associated with localized eigenvectors. For spinless fermions, increasing near-neighbor interactions first cause a transition to a charge density wave phase, and ultimately, on finite lattices, a collapse of all eigenvalues to the real axis. In this paper, we explore the presence of real eigenvalues in the interacting, two-particle sector for the spinful case (Hubbard model) in a two-chain (two-band) geometry with a Hermitian interchain hopping. Our key results are to obtain the ``phase" diagrams for the existence of a purely real spectrum, as a function of the interaction strength, degree of non-Hermiticity, and interchain hopping. We study the sensitivity to boundary conditions of the spectral properties of our two-chain model with winding number analysis and explore the relationship between PBC doublon states and OBC skin modes. To address the question of stability in such non-equilibrium systems, we solve the dynamics at low filling according to Lindbladian evolution and find that the non-Hermitian description is able to qualitatively describe such systems.

Convex hulls are useful as tight bounding proxies for a variety of tasks including collision detection, ray intersection, and distance computation. Unfortunately, the complexity of polyhedral convex hulls grows linearly with their input. We consider the problem of conservatively simplifying a convex hull to a specified number of half-spaces while minimizing added volume or surface area. By working in the dual representation, we propose an efficient $O(n \log n)$ greedy optimization. In comparisons, we show that existing methods either exhibit poor efficiency, tightness or safety. We demonstrate the success of our method on a variety of input shapes and downstream application domains.

Design-based inference, also known as randomization-based or finite-population inference, provides a principled framework for trustworthy statistical inference by attributing randomness solely to the design mechanism (e.g., treatment assignment, survey sampling, or missingness), without imposing super-population distributional or modeling assumptions on outcome data. From Fisher's and Neyman's seminal work to the recent resurgence of design-based inference, this perspective has played a central role in causal inference, survey sampling, and missing data analysis. However, a fundamental obstacle has limited its use in many modern applications: existing design-based inference theory typically relies on known propensity scores (i.e., known design probabilities), whereas propensity scores are usually unknown in observational studies, real-world survey settings, and missing data problems. We propose propensity score propagation, a general framework for valid design-based inference with unknown propensity scores. The framework introduces a regeneration-and-union procedure that propagates uncertainty from propensity score estimation into downstream design-based inference without imposing super-population outcome assumptions. It accommodates both parametric and nonparametric propensity score models, integrates seamlessly with existing design-based methods developed under known propensity scores, and applies broadly across design-based inference problems. Theoretical results and simulation studies show that the proposed framework achieves nominal coverage, even when existing approaches exhibit substantial under-coverage.

Protoplanetary disk ice lines shape a multitude of planet formation processes, setting the environmental composition through evolution. Ice line locations depend on molecular sublimation and deposition properties, but in dynamic disks where temperature and density structures change, so do the expected compositions of planets and planetesimals. In turbulent viscous disks with particle drift, thermal evolution, and desorption/adsorption, Price et al. 2021 demonstrated that the CO/H$_2$O ice ratio beyond the CO ice line can become enhanced by $\sim10\times$. We expand on their work by incorporating additional carbon, nitrogen, and oxygen species, more particle sizes, and a broader disk parameter exploration. We find that before $\sim0.5$Myr, volatile ices are enhanced relative to H$_2$O as the outer disk is desiccated by drift, while at later disk times outward advection and volatile deposition further increase relative volatile icy enhancements beyond the evolving critical disk radius. The outcome of these combined relative icy enhancement to H$_2$O mechanisms is solid C/O $\sim$ N/O $\sim1$ beyond the hypervolatile ice lines, much higher than expected in static disks. Hypervolatiles (N$_2$, CO, and CH$_4$) robustly increase to $\sim100\times$ across the explored parameter space, while mid-volatiles (CO$_2$ and NH$_3$) are sensitive to model choices, with enhancements ranging from $\sim2-50\times$. Together these results demonstrate that coupling disk dynamics with simple sublimation and deposition chemistry is fundamental to predicting grain, planetesimal, and planetary compositions, particularly the role of advection in redistributing volatiles across disk radii.

The resource-theoretic approach to quantum thermodynamics typically assumes perfect knowledge of the thermal equilibrium state, an idealization incompatible with finite experimental precision. We develop a framework for equilibrium uncertainty by representing the equilibrium reference as a set of candidate states. Under a generic geometric condition, we prove a no-go theorem that sharply limits athermality ``purification'': converting an uncertain athermal state into a definite target is either trivial or impossible. We then derive exact one-shot entropic characterizations of work extraction and formation for two work-storage models, a clean battery with known equilibrium and a dirty battery with uncertain equilibrium. Both models exhibit strong asymptotic irreversibility even under arbitrarily small uncertainty. An explicit example reveals two distinct extremes: clean batteries display a bound-entanglement-like phenomenon, with positive formation cost but zero extractable work, whereas dirty batteries allow positive work extraction but require infinite formation cost. These phenomena show that equilibrium uncertainty is not a minor perturbation of the standard theory, but a structural ingredient that fundamentally reshapes the limits of quantum thermodynamics.

Understanding corrosion in liquid metal-cooled nuclear systems is essential in order be able to control it. While much literature exists detailing corrosion rates and mechanisms of structural materials in liquid metals, much still remains to be discovered in new regimes of temperature, chemistry, and impurity content. We focus on a less-studied set of conditions, specifically to investigate how liquid lead-bismuth eutectic (LBE) corrodes ferritic/martensitic steels under high-temperature oxidizing conditions. We find that the evolution of corrosion is determined by the formation of protection layer on the surface. The area without effective protection layer experiences oxidation along martensite grain boundaries, transitioning from intergranular attack to broader area corrosion as it progresses. The area a stable, coherent oxide scale will slow the corrosion process and then is oxidized along pre-austenite grain boundaries. Both chromium and oxygen diffusion play vital roles in this process. Most surprisingly, a layer of iron enriched body-centred cubic phase forms on the surface of LBE-corroded T91, contradicting previous studies, which reported only oxide-based surface layers.