We develop an analytic approach to evaluating the density $ρ({\cal E},Γ)$ of complex resonance poles with real energies $\mathcal{E}$ and widths $Γ$ in the pure reflection problem from a one-dimensional disordered sample with white-noise random potential. We start with establishing a general link between the density of resonances and the distribution of the reflection coefficient $r=|R(E,L)|^2$, where $R(E,L)$ is the reflection amplitude, at {\it complex} energies $E = {\cal E} +iη$, identifying the parameter $η>0$ with the uniform rate of absorption within the disordered medium. We show that leveraging this link allows for a detailed analysis of the resonance density in the weak disorder limit. In particular, for a (semi)infinite sample, it yields an explicit formula for $ρ({\cal E},Γ)$, describing the crossover from narrow to broad resonances in a unified way. Similarly, our approach yields a limiting formula for $ρ({\cal E},Γ)$ in the opposite case of a short disordered sample, with size much smaller than the localization length. This regime seems to have not been systematically addressed in the literature before, with the corresponding analysis requiring an accurate and rather non-trivial implementation of WKB-like asymptotics in the scattering problem. Finally, we study the resonance statistics numerically for the one-dimensional Anderson tight-binding model and compare the results with our analytic expressions.

We investigate the Lieb--Liniger model of interacting one-dimensional bosons coupled to a localized impurity, modeled by a delta barrier. While the Lieb--Liniger gas is integrable, the impurity breaks integrability and induces a transition towards quantum chaos. We show that the low-energy spectrum exhibits random-matrix statistics, in striking contrast to the Bohigas--Giannoni--Schmit conjecture, where chaotic behavior typically emerges at high energy. For two bosons, the odd-parity sector remains integrable, whereas the even-parity sector displays clear signatures of chaos at low energy and a crossover back to quasi-integrable behavior at higher energies. For three bosons, both parity sectors exhibit spectral statistics close to chaos at low energy. We argue that this unconventional form of few-body quantum chaos originates from diffractive processes induced by the impurity.

We study the Mosco-convergence of Cheeger energies on Gromov-Hausdorff converging spaces satisfying different types of curvature dimension conditions. The case of functions of bounded variation is also considered. Applications to the continuity of Neumann eigenvalues are obtained. Our method, covering possibly infinite dimensional settings, is based on a Lagrangian approach and combines the stability properties of Wasserstein geodesics with the characterization of the nonsmooth calculus in duality with test plans.

The semiparametric accelerated failure time (AFT) model offers a direct and interpretable alternative to the Cox proportional hazards model, yet practical diagnostic tools for this framework remain limited. We introduce afttest, an R package that implements martingale-residual-based goodness-of-fit procedures for semiparametric AFT models. In addition to the recently developed multiplier bootstrap diagnostics, the package introduces a new computationally efficient resampling strategy based on an influence-function linear approximation. Unlike the original approach, which requires repeatedly solving estimating equations for each bootstrap replicate, the proposed method avoids iterative optimization and substantially reduces computation time while preserving asymptotic validity. Both the standard multiplier bootstrap and the accelerated linear approximation are implemented, allowing users to balance finite-sample performance and computational scalability. The package supports rank-based and least-squares estimators, provides omnibus, link function, and functional form tests, and includes graphical tools for visualizing residual processes. An application to the Mayo Clinic primary biliary cirrhosis study illustrates the workflow.

We revisit gradient-based optimization for infinite projected entangled pair states (iPEPS), a tensor network ansatz for simulating many-body quantum systems. This approach is hindered by two major challenges: the high computational cost of evaluating energies and gradients, and an ill-conditioned optimization landscape that slows convergence. To reduce the number of optimization steps, we introduce an efficient preconditioner derived from the leading term of the metric tensor. We benchmark our method against standard optimization techniques on the Heisenberg and Kitaev models, demonstrating substantial improvements in overall computational efficiency. Our approach is broadly applicable across various contraction schemes, unit cell sizes, and Hamiltonians, highlighting the potential of preconditioned optimization to advance tensor network algorithms for strongly correlated systems.

Measurement incompatibility underpins randomness generation in nonlocal phenomena. However, at its root, a more fundamental quantum feature is noncommuting (or coherent) measurements. This raises a central question: How can we operationally characterize the quantum advantage of coherent measurements within nonlocal correlations? We answer this by demonstrating that coherent measurements can leverage semi-device-independent (SDI) steering, enabling local randomness generation from any set of coherent measurements. Specifically, we establish that a measurement assemblage can be used to demonstrate SDI steering if and only if it is coherent, providing a complete operational characterization. To quantify this resource, we formulate a nonconvex resource theory for SDI steering and propose an operational monotone for the two-setting scenario by mapping noncommuting measurements to SDI steering. Our framework enables a practical quantum random number generator based on SDI steering that eliminates the need to certify entanglement and tolerates arbitrarily low detection efficiency. That is, we demonstrate that genuine randomness can be generated via coherent measurements beyond standard steerable states and even beyond entangled states under realistic experimental conditions. These results extend the scope of quantum resources for generating nonlocal correlations beyond measurement incompatibility, revealing the operational power of coherent measurements.

Speech-to-Speech (S2S) models have shown promising dialogue capabilities, but their ability to handle paralinguistic cues - such as emotion, tone, and speaker attributes - and to respond appropriately in both content and style remains under-explored. Progress is further hindered by the scarcity of high-quality and expressive demonstrations. To address this, we introduce a new reinforcement learning (RL) framework for paralinguistic-aware S2S, ParaS2S, which evaluates and optimizes both response content and speaking style directly at the waveform level. We first construct ParaS2SBench, a benchmark that evaluates the naturalness of input-output pairs in terms of content and speaking style using expressive and challenging queries. For the automatic judge, we propose a PolyTone training strategy and a multi-stage framework, preventing the style hallucination of end-to-end audio LLM judging. Our judge correlates well with human preferences and is scalable, enabling the model to interact and learn from unlabeled speech via RL. Experiments show that existing S2S models fail to respond appropriately to paralinguistic attributes, performing no better than pipeline-based baselines. Our RL approach (ParaS2SAlign) achieves a 10% relative improvement in the appropriateness of response content and speaking style on ParaS2SBench over supervised fine-tuning (SFT), surpassing all prior models while requiring substantially fewer paired demonstrations than pure SFT. Our findings highlight the need for a scalable and accurate automatic evaluator for speech-to-speech interaction.

We analyze powder-averaged inelastic neutron scattering and magnetization data for the distorted honeycomb compound Cu$_5$SbO$_6$ using a first-order dimer expansion calculation and quantum Monte Carlo simulations. We show that, in contrast to the previously proposed honeycomb lattice model, Cu$_5$SbO$_6$ accommodates interacting dimerized spin chains with alternating ferromagnetic-antiferromagnetic couplings along the chain. Moreover, unlike the typical couplings observed in other Cu$^{2+}$-based distorted honeycomb magnets, the spin chains in Cu$_5$SbO$_6$ primarily couple through an antiferromagnetic coupling that arises between the honeycomb layers, rather than the expected interchain coupling in the layers. This finding reveals a different magnetic coupling scheme for Cu$_5$SbO$_6$. In addition, utilizing x-ray spectroscopy and transmission electron microscopy, we also refine the crystal structure and stacking-fault model of the compound.

We study the fundamental problem of fairly allocating a multiset $\mathcal{M}$ of $t$ types of indivisible items among $d$ groups of agents, where all agents within a group have identical additive valuations. Gorantla et al. [GMV23] showed that for every such instance, there exists a finite number $μ$ such that, if each item type appears at least $μ$ times, an envy-free allocation exists. Their proof is non-constructive and only provides explicit upper bounds on $μ$ for the cases of two groups ($d=2$) or two item types ($t=2$). In this work, we resolve one of the main open questions posed by Gorantla et al. [GMV23] by deriving explicit upper bounds on $μ$ that hold for arbitrary numbers of groups and item types. We introduce a significantly simpler, yet powerful technique that not only yields constructive guarantees for indivisible goods but also extends naturally to chores and continuous domains, leading to new results in related fair division settings such as cake cutting.

Synthetic aperture radar (SAR) enables versatile, all-time, all-weather remote sensing. Coupled with automatic target recognition (ATR) leveraging machine learning (ML), SAR is empowering a wide range of Earth observation and surveillance applications. However, the surge of attacks based on adversarial perturbations against the ML algorithms underpinning SAR ATR is prompting the need for systematic research into adversarial perturbation mechanisms. Research in this area began in the digital (image) domain and evolved into the physical (signal) domain, resulting in physical adversarial attacks (PAAs) that strategically exploit corner reflectors as attack vectors to evade ML-based ATR. Existing PAAs assume that the attacker knows the SAR platform's aspect angles, restricting their applicability to idealized scenarios. We propose the SAR Aspect-Angles-Invariant Physical Adversarial Attack (SAAIPAA), a framework that determines the optimal positions and orientations of any given set of reflectors, regardless of their number or size, even when the attacker lacks knowledge of the SAR platform's aspect angles. This is enabled by rigorous physics-based modeling of the reflected signal and the SAR imaging process. To facilitate mapping between image and scene coordinates, we additionally propose a method for generating bounding boxes in densely sampled azimuthal SAR images, allowing the target object to serve as a spatial reference. The resultant physical evasion attacks are efficiently realizable and optimal over the considered range of aspect angles between a SAR platform and a target, achieving state-of-the-art fooling rates (80% for DenseNet-121 and ResNet50) in the white-box setting for a four-reflector configuration. When aspect angles are known to the attacker, an average fooling rate of is 99.2% attainable. In black-box settings, SAAIPAA transfers well between some models.

Supernova remnants (SNRs) have been considered as the primary contributors to cosmic rays (CRs) in our Galaxy. However, the maximum energy of particles that can be accelerated by shocks of SNRs is uncertain, and SNRs' contribution to CRs around PeV energies is unclear. In this study, we present observations of high-energy $γ$-ray emission from the SNR IC 443 using the Large High Altitude Air Shower Observatory (LHAASO). The morphological analysis reveals a pointlike source whose location and spectrum are consistent with those of the Fermi-LAT-detected compact source with $π^0$-decay signature, and a more extended source that is associated with a newly discovered Fermi source. The spectrum of the point source can be described by a power-law function with an index of $\sim3.0$, extending beyond $\sim 30$ TeV without apparent cutoff. Assuming a hadronic origin of the $γ$-ray emission, the $95\%$ lower limit of accelerated protons reaches about 300 TeV. The extended source might be associated with IC 443, SNR G189.6+3.3 or the putative pulsar wind nebula CXOU J061705.3+222127, and can be explained by either a hadronic or a leptonic model with particles reaching hundreds of TeV. These LHAASO results provide compelling evidence that sub-PeV CRs can be accelerated efficiently by shocks of SNRs.

Al$_x$Ga$_{1-x}$N alloys are essential for high-performance optoelectronic and power devices, yet the role of composition on defect energetics remains underexplored, largely due to the limitations of first-principles methods in modeling disordered alloys. To address this, we employ a machine learning interatomic potential (MLIP) to investigate the structural and defect-related physical properties in Al$_x$Ga$_{1-x}$N. The MLIP is first validated by reproducing the equation of state, lattice constants, and elastic constants of the binary endpoints, GaN and AlN, as well as known defect formation and migration energies from density functional theory and empirical potentials. We then apply the MLIP to evaluate elastic constants of AlGaN alloys, which reveals a non-linear relation with alloying effect. Our results reveal that nitrogen Frenkel pair formation energies and the migration barriers for nitrogen point defects are highly sensitive to the local chemical environment and migration path. In contrast, Ga and Al vacancy migration energies remain relatively insensitive to alloy composition, whereas their interstitial migration energies exhibit stronger compositional dependence. These results provide quantitative insight into how alloying influences defect energetics in AlGaN, informing defect engineering strategies for improved material performance.

We introduce an intrinsic deformation of the algebra of smooth functions on a compact Riemannian manifold using only the Laplace spectral decomposition. The construction twists the canonical multiplication-projection channels by unimodular phases, producing a well-defined bilinear product on the finite spectral core with values in $L^2(M)$. We give a simple condition for compatibility with complex conjugation and isolate a Sobolev boundedness hypothesis under which the product extends to a Sobolev algebra and admits iteration; in that setting, associativity is equivalent to an explicit identity for the twisted spectral channels. We analyze gauge and coboundary aspects for scalar twists and obtain rigidity statements in the action-free regime. We also compare with classical strict deformation frameworks arising from actions of locally compact abelian groups -- Rieffel's deformation for $\mathbb{R}^d$-actions, Connes-Landi's torus isospectral deformations, and Kasprzak's cocycle deformation via Landstad theory -- showing that, when the relevant abelian group action has a discrete spectral decomposition (in particular, in the compact abelian/periodic case where the algebra decomposes into homogeneous subspaces indexed by characters of the acting group), their deformed products are recovered uniformly as refined instances of our channel twist. Finally, we formulate a grading-based obstruction and classification for graded scalar twists.

We investigate whether Newtonian gravity can generate quantum entanglement between mesoscopic quantum bodies modeled as superposed mass quadrupoles using three complementary approaches: mini-superspace, semiclassical gravity, and stochastic gravity. We systematically analyze gravitationally induced entanglement (GIE) mechanisms and the conditions under which they can arise. Our results support the GIE hypothesis by showing that the mini-superspace framework, which quantizes the parity of the gravitational tidal field, can entangle spatially separate quantum bodies. In contrast, the semiclassical and stochastic gravity models, in which the tidal gravitational field sourced by the quantum bodies remains classical, fail to entangle the final state. These findings clarify recent claims that classical gravity might induce entanglement, and reveal how perturbative treatments can lead to misleading conclusions.

This work presents a novel surface decomposition method for the sensitivity analysis of first-passage dynamic reliability of linear systems subjected to Gaussian random excitations. The method decomposes the sensitivity of first-passage failure probability into a sum of surface integrals over the constrained component limit-state hypersurfaces. The evaluation of these surface integrals can be accomplished, owing to the availability of closed-form linear expressions of both the component limit-state functions and their sensitivities for linear systems. An importance sampling strategy is introduced to further enhance the efficiency for estimating the sum of these surface integrals. The number of function evaluations required for the reliability sensitivity analysis is typically on the order of 10^2 to 10^3. The approach is particularly advantageous when a large number of design parameters are considered, as the results of function evaluations can be reused across different parameters. Three numerical examples are investigated to demonstrate the effectiveness of the proposed method.

We propose and analyze a process that extracts useful work from a single active particle maintained at constant temperature in a harmonic potential by measuring the relative sign of the self-propulsion and the confining force and then adjusting the stiffness of the potential. First, we show analytically that useful work can be extracted by stepwise changes of the stiffness. Then, we use a machine learning procedure to find time-dependent stiffness change protocols. We find that these protocols involve discontinuous initial changes of the stiffness opposite to the expected direction, which resemble initial jumps analytically found by Garcia-Millan et al. [Phys. Rev. Lett. 135, 088301 (2025)] in a different information-based work extraction process. The learned protocols allow to extract significantly larger amounts of useful work. The work extracted exceeds that allowed by the conventional second law for feedback-controlled processes, which can be rationalized by the non-equilibrium character of the system considered.

Given a triangulation of a closed orientable surface, we place single-mode resonators or single-orbital artificial atoms at its vertices, edges and facets, and we devise near-neighbor hopping terms derived from the boundary and Poincaré duality maps of the simplicial complex of the triangulation. Regardless of the surface or its triangulation, these terms always lead to tight-binding Hamiltonians with large and clean topological spectral gaps, carrying non-trivial Chern numbers in the limit of infinite refinement of the triangulation. We confirm this via numerical simulations, and demonstrate how these models enable topological edge modes at the surfaces of real-world objects. Furthermore, we describe a metamaterial whose dynamics reproduces that of the proposed model, thus bringing the topological metamaterials closer to real-world applications.

This study presents a control strategy for coordinating multiple unmanned aerial vehicles (UAVs) to monitor unknown flood regions and estimate the extent of inundation. The proposed method adopts a density-driven coverage framework based on Centroidal Voronoi Tessellation (CVT), in which the density function is modeled using a Gaussian Mixture of Density Functions (GMDF). This formulation provides a more accurate characterization of inundated areas compared to conventional axis-aligned Gaussian models. The performance of the two density modeling approaches is systematically evaluated under different UAV fleet sizes (16, 20, and 24), with multiple simulation trials conducted in the ROS/Gazebo environment. The results show that the GMDF-based formulation consistently achieves higher coverage rates, demonstrating its effectiveness in enhancing flood monitoring and improving UAV spatial distribution.

Quantum sensing leverages non-classical resources to enhance precision. In particular, Greenberger-Horne-Zeilinger (GHZ) states can, in principle, attain the Heisenberg limit that surpasses the standard quantum limit. While many studies have examined how open-system noise-typically modeled with Lindblad master equations-degrades GHZ-based metrology, coherent control imperfections during state preparation and readout have received less attention. Here, we analyze the effect of detuning between actual and nominal spin frequencies in a GHZ-state preparation scheme employing a frequency selective pulse. We show that detuning induces coherent, systematic error that prevents GHZ sensing from reaching the Heisenberg limit. To mitigate this effect, we design a composite-pulse protocol that compensates for detuning-induced errors and improves the sensitivity under the effect of coherent error.

We present the second release of the $\texttt{GR-Athena++}$ waveform catalog, comprising four new quasi-circular, non-precessing, spinning binary black hole simulations. These simulations are performed at high resolutions and represent a step toward generating high-fidelity gravitational waveforms that can eventually meet the accuracy requirements of upcoming next-generation detectors, including LISA, Cosmic Explorer, and Einstein Telescope. Gravitational waves are extracted at future null infinity ( $\mathscr{I}^{+}$) using both Cauchy characteristic extraction and finite-radius extraction. For each simulation, we provide strain data across multiple resolutions and analyze waveform accuracy via convergence studies and self-mismatch analyses. The absolute phase and relative amplitude differences reach their largest values near the merger, while the smallest errors are of order $\mathscr{O}(10^{-2})$ and $\mathscr{O}(10^{-3})$, respectively. A self-mismatch analysis of the dominant $(2,2)$ mode yields mismatches between $\mathscr{O}(10^{-5})$ and $\mathscr{O}(10^{-7})$ for a total binary mass of $10^{6}$ $M_{\odot}$ over the frequency range $[0.002, 0.1]$ Hz using LISA noise curve. All waveforms are publicly available via $\texttt{ScholarSphere}$.

We propose a simple and unified framework that simultaneously explains the origins of light Dirac neutrino masses, asymmetric dark matter (ADM), and the baryon asymmetry of the Universe. The model is based on an extended $U(1)_X$ Froggatt-Nielsen--like mechanism, which naturally generates suppressed Yukawa couplings and realizes a Dirac seesaw for neutrino masses. An additional $\mathbb{Z}_4$ symmetry stabilizes the dark sector, where chiral fermions charged under $\mathbb{Z}_4$ serve as ADM candidates. Leptogenesis occurs through the out-of-equilibrium decays of heavy Dirac neutrinos, where the generated asymmetry is shared between the visible and dark sectors due to exact lepton-number conservation. The same suppression mechanism that explains the smallness of neutrino masses also determines the GeV-scale ADM mass. Numerical studies demonstrate that a fully asymmetric DM scenario is realized, consistent with relic abundance, Big Bang nucleosynthesis, and direct detection constraints. This framework provides an experimentally testable connection between neutrino physics, dark matter, and baryogenesis within an anomaly-free setup.

The stochastic gravitational-wave background (SGWB), arising from the incoherent superposition of numerous compact binary coalescences, serves as a powerful probe of both astrophysical populations and fundamental physics. In this work, we investigate the influence of gravitational lensing on the SGWB, focusing on primordial black holes (PBHs) as potential lenses. Assuming PBHs as dark matter candidates with a broad cosmic distribution, we show that their lensing optical depth can be significantly enhanced, producing pronounced effects with relative deviations at the 10^-1 level. By systematically varying the PBH mass (M_PBH) and abundance (f_PBH), we demonstrate that the mass predominantly determines the frequency-dependent diffraction features of the spectrum, while the abundance primarily amplifies the overall lensing-induced deviation. Although the SGWB from binary black holes has not yet been observed, our analytical results provide theoretical insight into the possible imprint of lensing on its spectrum and suggest that future detections could offer a novel avenue to constrain dark matter scenarios.

In this work, we study nonconformally Ricci-flat gravitational instantons in four-dimensional Conformal Gravity, both in vacuum and in the presence of nonlinear conformal matter. First, the one-parameter extension of the Kerr-NUT-AdS metric is analyzed. We obtain their conserved charges by using the Noether-Wald formalism. It turns out that they receive corrections from the linear modes present in Conformal Gravity, which are properly identified. Then, we perform the analytic continuation into the Euclidean section and find the curve in parameter space along which this solution becomes regular and globally (anti)self-dual. Using the Dunajski-Tod theorem, we show that the self-dual metric is not conformally Ricci-flat. Then, the backreaction of nonlinear conformal matter is considered. In particular, we find new gravitational instantons in the presence of conformally coupled scalar fields and ModMax electrodynamics. We compute the partition function and conserved charges, which turn out to be finite by virtue of the conformal invariance of the theory. As a byproduct, we also obtain a generalization of the Riegert metric dressed with nonlinear conformal matter as a particular limit of these instantons. For all cases, we analyze the global properties, the curve in parameter space where the solutions are (anti)-self-dual, and the on-shell Euclidean action, among other features.

Two body tunneling problems are hard to treat analytically due to the incompatibility between tunneling and perturbation theory. The lack of classical solutions of the Euclidean Lagrangian of continuous systems further thwarts semi-classical expansions. To develop an analytic theory which provides insight on interacting two-particle tunneling, we use new results to derive the Bethe-Salpeter equation of a tunneling field theory with Yukawa coupling. We show that in the one plus one dimensional case a closed form solution in the instantaneous positive-energy regime is permitted. We then compute the scattering amplitude by perturbing on interparticle interaction and recover the Lippmann-Schwinger equation to confirm physical consistency and relevancy.

A data-driven framework is proposed for online estimation of quadrotor motor efficiency via residual minimization. The problem is formulated as a constrained nonlinear optimization that minimizes trajectory residuals between measured flight data and predictions generated by a quadrotor dynamics model. A sliding-window strategy enables online estimation, and the optimization is efficiently solved using an iteratively reweighted least squares (IRLS) scheme combined with a primal-dual interior-point method, with inequality constraints enforced through a logarithmic barrier function. Robust z-score weighting is employed to reject outliers, which is particularly effective in motor clipping scenarios where the proposed estimator exhibits smaller spikes than an EKF baseline. Compared to traditional filter-based approaches, the batch-mode formulation allows selective inclusion of data segments via IRLS reweighting and hard-rejection. This structure is well-suited for online estimation and supports applications such as fault detection and isolation (FDI), health monitoring, and predictive maintenance in aerial robotic systems. Simulation results under various degradation scenarios demonstrate the accuracy and robustness of the proposed estimator.

We study the over-damped dynamics of individual one-dimensional elastic filaments subjected to a chiral active force which propels each point of the filament at a fixed angle relative to the tangent vector of the filament at that point. Such a model is a reasonable starting point for describing the behavior of polymers such as microtubules in gliding assay experiments. We derive sixth-order nonlinear coupled partial differential equations for the intrinsic properties of the filament, namely, its curvature and metric, and show that these equations are capable of supporting multiple different stationary solutions in a co-moving frame, i.e.\ that chiral active elastic filaments exhibit dynamic multi-stability in their shapes. A linear stability analysis of these solutions is carried out to determine which solutions are stable and a brief analysis of the time-dependent approach to stationary shape is considered. Finally, simulations are presented which confirm many of our predictions while also revealing additional complexity.

Lost architectural heritage presents interpretive challenges due to vanished structures and fragmented historical records. Using Hanyuan Hall of the Tang dynasty's Daming Palace as a case study, we conducted a formative investigation with archaeologists, heritage administrators, and visitors to identify key issues in current interpretation practices. We found that these practices often compress complex cultural layers into factual summaries and rely on linear narratives that overlook the continuing reinterpretations following a site's disappearance. In response, we designed Pre/Absence, a virtual reality experience grounded in the presence-absence dialectic to interweave tangible and vanished aspects of heritage within a spatiotemporal narrative. A mixed-method study with 28 participants compared Pre/Absence to a paper-based experience. Both improved users' factual understanding, but the VR experience more strongly enhanced cultural awareness, evoked emotional engagement with loss, and encouraged critical reflection on the evolving social and political meanings of heritage. The findings suggest that VR can move beyond static reconstruction to engage users as co-constructors of cultural meaning, providing a nuanced framework for critical heritage narrative design in human-computer interaction.

In Bayesian analysis, prior elicitation, or the process of facilitating the expression of one's beliefs to inform statistical modeling, is an essential yet challenging step. Analysts often have beliefs about real-world variables and their relationships. However, existing tools require analysts to translate these beliefs and express them indirectly as probability distributions over model parameters. We present PriorWeaver, an interactive visualization system that facilitates prior elicitation through iterative dataset construction and refinement. Analysts visually express their assumptions about individual variables and their relationships. Under the hood, these assumptions create a dataset used to derive statistical priors. Prior predictive checks then help analysts compare the priors to their assumptions. In a lab study with 17 participants new to Bayesian analysis, we compare PriorWeaver to a baseline incorporating existing techniques. Compared to the baseline, PriorWeaver gave participants greater control, clarity, and confidence, leading to priors that were better aligned with their expectations.

We show that the threshold to form a black hole, in an asymptotically flat and radiation-dominated Friedman-Robertson-Walker (FRW) Universe, is not solely (mainly) determined by the behaviour of the compaction function at its extrema, as earlier thought, but also by the Ricci scalar of the spatial geometry at smaller (but super-horizon) scales, which we call ``the core''. We introduce three classes of initial conditions characterised by an open (O), closed (C), or flat (F) FRW core surrounded by a shell with higher three-dimensional curvature. In the C case, the core helps the collapse so that the black hole formation threshold is the lowest among all cases. Type-II black holes might only be generated by Type-O or F (each of those with different thresholds, with O being the highest) or by a Type-C with a negligible Ricci scalar at the centre, which we call an effective F core. Finally, we argue that an F core is typically more probable for a sharp power spectrum, however, it is also more likely related to non-spherical initial conditions. On the other hand, a very broad power spectrum, which might be related to the observed NanoGrav signal, would favour the formation of Type-I black holes with a mass spectrum peaked at the Infra-Red scale.

The abundance and mass function of primordial black holes (PBHs) are often estimated using the Press-Schechter (PS) formalism. In the case of halo formation, the PS formalism suffers from the miscounting of regions collapsing into halos, known as the cloud-in-cloud problem, which is usually corrected by introducing a multiplicative `fudge factor 2'. By analogy, this factor has sometimes been applied to PBH calculations, although its validity has remained unsettled. We reformulate the PS approach for PBHs (forming during radiation-dominated epoch) within the excursion-set framework, where the smoothed density contrast undergoes a stochastic random walk as the smoothing scale varies and collapse is identified with the first threshold crossing. While the halo case is described by a Markovian process, we show that the PBH case is non-Markovian, even when the sharp-k filter Window function is adopted. Decomposing the total collapse probability into two distinct components of the stochastic motion, we numerically confirm that their contributions are exactly equal in the case of halo formation, justifying the fudge factor. For PBHs, however, we demonstrate that this equality no longer holds, and consistent inclusion of both contributions is essential to ensure a positive-definite mass function. Our results clarify the origin of the ambiguity surrounding the fudge factor and establish a robust theoretical foundation for PBH abundance calculations.