In 1930, Ramsey proved that every large graph contains either a large clique or a large edgeless graph as an induced subgraph. It is well known that every large connected graph contains a long path, a large clique, or a large star as an induced subgraph. Recently Allred, Ding, and Oporowski presented the unavoidable large induced subgraphs for large and infinite $2$-connected graphs. The $2$-edge-connected (sometimes called bridgeless) graphs form an important class between connected graphs and $2$-connected graphs. In this paper we describe the unavoidable large induced subgraphs for large and infinite $2$-edge-connected graphs. Ubiquitous structures in $2$-edge-connected graphs that we call `chains of pinched super-clean ladders' play an important role in these descriptions. As consequences we obtain results on unavoidable large subgraphs, topological minors, minors, induced topological minors, induced minors, and Eulerian subgraphs in large and infinite $2$-edge-connected graphs. When appropriate we extend our results to multigraphs.

We examine the English translation of Albert Einstein's groundbreaking 1925 paper on Bose-Einstein condensation. We guide readers to execute the calculations Einstein outlined for the specific heat above the condensation temperature, correct some numerical errors, and compare his formula with a different one published in the American Journal of Physics in 2004. The history of the acceptance of Einstein's theory will be summarized.

Social simulation is essential for understanding collective human behavior by modeling how individual interactions give rise to large-scale social dynamics. Recent advances in large language models (LLMs) have enabled multi-agent frameworks with human-like reasoning and communication capabilities. However, existing LLM-based simulations treat social networks as fixed communication scaffolds, failing to leverage the structural signals that shape behavioral convergence and heterogeneous influence in real-world systems, which often leads to inefficient and unrealistic dynamics. To address this challenge, we propose TopoSim, a unified topology-aware social simulation framework that explicitly integrates structural reasoning into agent interactions along two complementary dimensions. First, TopoSim aligns agents with similar structural roles and interaction contexts into shared backbone units, enabling coordinated updates that reduce redundant computation while preserving emergent social dynamics. Second, TopoSim models social influence as a structure-induced signal, introducing heterogeneous interaction patterns grounded in network topology rather than uniform influence assumptions. Extensive experiments across three social simulation frameworks and diverse datasets demonstrate that TopoSim achieves comparable or improved simulation fidelity while reducing token consumption by 50 - 90%. Moreover, our approach more accurately reproduces key structural phenomena observed in real-world social systems and exhibits strong generalization and scalability.

We present TNRKit, an open-source Julia package for Tensor Network Renormalization (TNR) of two- and three-dimensional classical statistical models and Euclidean lattice field theories. Built on top of TensorKit, it provides a symmetry-aware framework for constructing tensor-network representations of partition functions and coarse-graining them using methods such as TRG, HOTRG, and LoopTNR. Beyond thermodynamic quantities, the package enables the extraction of universal conformal data -- including scaling dimensions and the central charge -- directly from fixed-point tensors. TNRKit is designed with both usability and extensibility in mind, offering a practical platform for applying, benchmarking, and developing modern tensor renormalization algorithms. This paper also serves as a self-contained introduction to the TNR framework.

In this note, we investigate the paratrophic determinants attached to the multiplicative semigroup $\mathbb{Z}/N\mathbb{Z}$. We show that, via discrete Fourier, cosine, and sine transforms, these determinants factor into products of group determinants indexed by $d|N$. This yields explicit formulas for several determinant families, including determinants involving periodic Bernoulli functions and powers of the tangent function. As an application, we also prove a corrected version of a conjecture of Sun Zhi-Wei.

We report the first results on ultracold neutron production from a new spallation-driven superfluid $^4$He (He-II) source at TRIUMF, which is being prepared for a new, precise measurement of the neutron electric dipole moment. A total of $(9.3 \pm 0.8)\times 10^{5}$ ultracold neutrons were observed at a proton beam current of \SI{37}{\uA}, when the target was irradiated for a period of \SI{60}{\s}. The results are in fair agreement with expectations based on a detailed simulation of neutron transport and ultracold neutron source cryogenics. There is some indication that the new source might not be as limited by the conduction of heat through the He-II as originally expected. The results indicate that the source is likely to make its ultimate production goals, once the liquid deuterium cold moderator system is completed, with the expectation that $5.7\times 10^7$~UCNs would be detected in the same experiment with full liquid levels. This would, for example, correspond to delivery of $1.4\times 10^6$~UCNs delivered to each of two nEDM measurement cells, and a statistical uncertainty of $1\times 10^{-27}~e$cm on the neutron EDM in 280 days of running.

We present a systematic theoretical study of the Raman scattering effect for a two-level atomic system in near proximity of an ultrathin dielectric film with an embedded parallel array of periodically aligned single-wall semiconducting carbon nanotubes. More generally, our model provides a unified description of the quantum near-field medium-assisted enhancement effects for in-plane anisotropic metasurfaces, of which ultrathin periodically aligned carbon nanotube films are the representative example. Particular attention is given to incoming photon parameters of the external light radiation such as polarization and incidence plane orientation relative to the main anisotropy axis (nanotube alignment axis). By explicitly deriving the Raman scattering cross-section, we establish that for the two-level atomic system in the near-field zone of the carbon nanotube metasurface the effect can be enhanced by a factor of up to 10^4, not only for p-polarized but for s-polarized light as well.

Classically, Markov numbers are recovered as perfect matching numbers of domino snake graphs. We extend this correspondence to matrix semigroups by introducing weighted universal generalised snake graphs, or wug-snake graphs for short. These are weighted bipartite graphs whose perfect matching sequences encode linear recurrences. We associate to each wug-snake graph a continuant matrix and prove that its determinant equals the weighted perfect matching number. We use this construction to define polymino wug-tiles for matrices and show that their determinants compute Markov-Davenport forms. Consequently, algebraic and geometric Markov numbers of matrices, and of matrix semigroups, can be expressed through perfect matchings. We develop the corresponding Frobenius maps for semigroups and study examples recovering classical Markov numbers, weighted PLLS-sequences, and higher-dimensional lattice realisations.

In this article, we argue that AI slop in software is creating a tragedy of the commons. Individual productivity gains from AI-generated content externalize costs onto reviewer capacity, codebase integrity, public knowledge resources, collaborative trust, and the talent pipeline. AI slop is cheap to generate and expensive to review, and the review layer is already thin. Commons problems are not solved by individual restraint. We outline concrete next steps for tool developers, team leads, and educators, grounded in Ostrom's design principles for enduring commons institutions.

We propose \emph{ClawXiv}, a workflow and archive architecture for mixed human--AI research. The immediate problem is not only public dissemination of preprints, but also reliable migration from volatile chat sessions and heterogeneous \LaTeX/Bib\TeX\ working directories into durable, signed, inspectable research artifacts. ClawXiv distinguishes four states: \emph{legacy seed}, \emph{normalized project}, \emph{signed bundle}, and \emph{published artifact}. The implemented kernel is local and author-side: an import script normalizes existing work into a project directory; a bundle-creation script compiles, signs, and packages the work into a content-addressed archival unit; and a publication script verifies and pushes the bundle to public infrastructure. Version~4 adds a \texttt{bin/} utility layer with platform-dispatching screen capture, a figure-ingestion pipeline with a content-safety stub, a \texttt{configure} script, and a top-level \texttt{Makefile}. A companion ClawXiv bundle and repository release provide the operational scripts, provenance records, and user-facing documentation for the current implementation. Code is available at \texttt{github.com/kornai/clawxiv}.

Conversational agents have the potential to support intergroup relations when psychological or linguistic barriers prevent direct interaction. Based on intergroup contact theory, we propose GroupEnvoy, a text-based conversational agent that represents outgroup perspectives during ingroup discussions. Its dialogue is grounded in data from a prior outgroup-only discussion. To evaluate this approach and derive design principles, we conducted a mixed-methods, between-subjects study with university students, in which host-country students formed the ingroup and international students formed the outgroup. Ingroup students performed a collaborative task while engaging with outgroup perspectives, either by interacting with GroupEnvoy (AI-mediated contact) or by reading a static document (passive exposure). Quantitatively, AI-mediated contact demonstrated a directional reduction in intergroup anxiety and an improvement in perspective-taking. Qualitatively, AI-mediated contact enhanced outcome expectancies and directed empathy toward the outgroup's evaluations of the ingroup, whereas passive exposure fostered future contact intentions and elicited empathy toward the outgroup's lived experiences. These findings present AI-mediated contact as a promising paradigm for improving intergroup relations.

If a sender in a persuasion game can use a sequence of experiments rather than a single experiment, does this change the sender's value? We show, within a large class of non-Bayesian updating rules, divisibility, introduced in Cripps (2018), exactly characterizes the receiver's updating rules under which the sender is indifferent between static and dynamic persuasion in any environment. Consequently, restricting attention to static persuasion is without loss precisely under divisible updating rules.

Binary interactions during the AGB phase can lead to the formation of chemically peculiar stars with overabundances of s-process elements. Only a few hundreds of these stars have been subject to detailed chemical or dynamical studies. This work aims at compiling a systematic sample of s-process-polluted candidates using GALAH DR4. We also want to compare their properties with those of confirmed s-polluted stars to have stronger evidence of their nature. GALAH DR4 uses neural networks and automatic spectral analysis methods as well as data of a lower spectral resolution than normally used to characterise these objects. Because of this, we built a validation sample, for which we obtained UVES@VLT and HERMES@Mercator high-resolution spectra. We compare our stellar parameters and abundances with those of the survey and use this validation to define the thresholds that a star in GALAH DR4 must pass to be flagged as a good s-process-rich candidate. Based on our comparisons, we define thresholds on [s/Fe], [Y/Fe], [Zr/Fe], [Ba/Fe], and [La/Fe]. We identified 1059 stars in GALAH DR4 that are good candidates to be s-process polluted stars, covering a broad parameter space. They share many similarities with the samples of confirmed s-rich stars, especially their ratios of heavy over light s-elements ([hs/ls]), which strengthen our confidence in the purity of the sample. We find that only 7% of the candidates have measured orbital periods and eccentricities, limiting for now a full comparison with confirmed Ba and related stars. However, their binary fraction is, as expected, higher than the one we found for the full GALAH DR4 catalogue. Our sample of candidates is almost five times larger than the number of currently confirmed polluted stars. This and the fact that it has been homogeneously treated by GALAH open very interesting avenues to confront nucleosynthesis and binary evolution models.

We present a systematic study of static solutions to the source-free SU(2) Yang-Mills equations, in which the gauge potential explicitly depends on spin operators. By employing the \emph{vector potential extraction approach} -- which requires the total angular momentum operator (orbital plus spin) to satisfy the standard angular momentum algebra -- we derive the most general form of the spin vector potential $\vec{A}$. This leads to the static ansatz $\{ \vec{A} = [k_1(\hat{r}\times\vecΓ) + k_2\vecΓ + k_3(\vecΓ\cdot\hat{r})\hat{r}]/r, φ= f_1(r)\,(\vecΓ\cdot\hat{r}) + f_2(r)\}$, parametrized by three constants $\{k_1, k_2, k_3\}$ and two radial functions $\{f_1(r), f_2(r)\}$. After substituting this static ansatz into the Yang-Mills equations we obtain a set of consistency equations. Solving these equations provides a complete classification of the exact static solutions, including both real and complex families. The known simple SU(2) static solution $\{\vec{A}=\tilde{k} (\hat{r}\times\vecΓ)/r, φ=κ/r \}$ is recovered as a special case. Our classification reveals new static configurations that could be valuable for non-perturbative studies and for models where the internal spin couples to non-Abelian gauge fields.

This Perspective is part of a Special Topic that explored the maturity of nonadiabatic molecular dynamics for predicting photochemical processes. In 2023, a prediction challenge was issued to the community of computational photochemists to simulate the photochemistry of cyclobutanone, photoexcited at 200 nm, and the resulting time-resolved MeV-UED signal. The challenge attracted 15 theoretical predictions from more than 70 researchers, employing a wide range of strategies for electronic structure and nonadiabatic molecular dynamics to predict the time-resolved MeV-UED signal before the experiment had been conducted at SLAC (Stanford, USA). The MeV-UED instrument at Shanghai Jiao Tong University was also used to provide a second independent time-resolved MeV-UED signal for the photochemistry of cyclobutanone. This Perspective discusses the various approaches and strategies used by the participants to predict the photochemistry of cyclobutanone. This work also summarizes the strengths and weaknesses of various methods used for photoexcitation, electronic structure, nonadiabatic dynamics, and calculation of observables, as agreed by the participants during a CECAM workshop dedicated to the results of the challenge and organized in Lausanne in April 2025. This Perspective also collects all the predicted time-resolved MeV-UED signals into a single figure, together with the experimental signal. This challenge (i) demonstrated the qualitative predictive power of nonadiabatic molecular dynamics and (ii) underscore the impact of electronic-structure theory on the outcome of the excited-state dynamics and the need for its careful benchmarking. This effort allowed the community to share practical strategies to perform nonadiabatic dynamics (discussed in the present Perspective) and constitutes a 'calibration' exercise for computational photochemistry.

Recent results from the Atacama Cosmology Telescope (ACT), indicating a higher and more tightly constrained scalar spectral index, $n_s = 0.9743 \pm 0.0034$, place several inflationary models under tension, with quintessential inflation pushed close to or beyond the $2σ$ boundary in the $r$--$n_s$ plane. In this work, we revisit quintessential inflation within the framework of Einstein--Gauss--Bonnet (EGB) gravity, where a scalar field non-minimally coupled to the Gauss--Bonnet invariant modifies the inflationary dynamics. We consider three representative coupling functions -- exponential, hyperbolic secant, and hyperbolic tangent -- and show that the exponential and sech-type couplings can shift the predicted values of $r$ and $n_s$ into the $1σ$ region allowed by ACT, thereby restoring consistency with observations. In contrast, the tanh-type coupling remains disfavored, underscoring the sensitivity of inflationary observables to the coupling structure. We further investigate the reheating phase using a model-independent parametrization and demonstrate that viable thermal histories can be realized even in the absence of a potential minimum, with reheating temperatures consistent with Big Bang nucleosynthesis bounds. Overall, our analysis shows that EGB corrections provide a viable and robust extension that reconciles quintessential inflation with current precision cosmological data, and we identify the corresponding allowed parameter space.

A provably stable summation-by-parts simultaneous approximation term (SBP-SAT) finite-difference time-domain (FDTD) subgridding method without region split is proposed. By designing projection SBP operators tailored for embedded topological features and deriving the corresponding SAT boundary conditions, this approach guarantees long-time stability through discrete energy analysis. Unlike conventional SBP-SAT FDTD subgridding techniques that rely on aligned or multi-block configurations, the proposed method enables a direct coupling between an internal refined region and a single surrounding coarse-grid domain without introducing auxiliary blocks or causing domain fragmentation. Numerical results validate the efficiency, accuracy, and topological flexibility of the proposed method. Compared with existing multi-block SBP-SAT methods, this method effectively reduces computational complexity by minimizing SAT boundary conditions and improves calculation accuracy near grid interfaces.

Foundation models show strong potential for large-scale, high-dimensional biomedical applications, yet their ability to capture relevant neurobiological characteristics remains underexplored. We systematically evaluate embeddings from two neuroimaging foundation models, BrainLM and SwiFT, across multi-site fMRI datasets using a comprehensive evaluation framework. Our results show that foundation model embeddings encode substantial batch-related variability, often dominating diagnosis-related information across heterogeneous datasets. We further investigate how harmonization, applied to reduce batch effects, influences these embeddings. In addition, we find that BrainLM prefers to capture fine-grained regional activity, whereas SwiFT tends to represent interactions between regions, consistent with their respective model architectures. Our study highlights the importance of accounting for batch effects in foundation models and motivates future work on disentangling biologically meaningful signals from acquisition-related variability.

Reliable geolocation of non-cooperative emitters in environments where Global Navigation Satellite Systems (GNSS) are unavailable or degraded is a key enabler for spectrum regulation, emergency response, autonomous mobility, and Integrated Sensing and Communication (ISAC) services in 5G/6G systems. Doppler-based techniques - from single-receiver Signal Doppler Frequency (SDF) fixes through multi-node Frequency Difference of Arrival (FDOA) and Direct Position Determination (DPD) to derivative-enhanced and learning-assisted hybrids - exploit radial-velocity-induced frequency shifts as a passive, high-resolution localization cue accessible with commodity software-defined radios, millimeter-wave access points, or acoustic sensors. This review consolidates over a decade of research across radio, acoustic, and satellite domains. It introduces a unifying taxonomy that divides the field into five technique families, outlining their evolution, measurement models, and estimator archetypes. It then compares algebraic, Bayesian, convex, and neural inference frameworks under realistic impairments such as oscillator drift, multipath, and asynchronous clocks, highlighting conditions where derivative Doppler metrics tighten the Cramer-Rao bound with minimal hardware cost. Environment-specific deployments are examined, from urban canyons and GNSS-denied tunnels to underwater, radar, UAV-swarm, and multi-orbit satellite scenarios, with prototype accuracies reaching meter scale using low-size, weight, and power payloads. Finally, the survey distils design recommendations for mobile and tactical operations and identifies open research challenges in frequency-reference integrity, multipath-aware modelling, edge-constrained computation, and trajectory-aware sensing.

Particle-in-Cell (PIC) Monte Carlo (MC) simulations are central to plasma physics but face increasing challenges on heterogeneous HPC systems due to excessive data movement, synchronization overheads, and inefficient utilization of multiple accelerators. In this work, we present a portable, multi-GPU hybrid MPI+OpenMP implementation of BIT1 that enables scalable execution on both Nvidia and AMD accelerators through OpenMP target tasks with explicit dependencies to overlap computation and communication across devices. Portability is achieved through persistent device-resident memory, an optimized contiguous one-dimensional data layout, and a transition from unified to pinned host memory to improve large data-transfer efficiency, together with GPU Direct Memory Access (DMA) and runtime interoperability for direct device-pointer access. Standardized and scalable I/O is provided using openPMD and ADIOS2, supporting high-performance file I/O, in-memory data streaming, and in-situ analysis and visualization. Performance results on pre-exascale and exascale systems, including Frontier (OLCF-5) for up to 16,000 GPUs, demonstrate significant improvements in run time, scalability, and resource utilization for large-scale PIC MC simulations.

We extend Schwinger's proper-time formalism to provide a method for computing the one-loop effective action for both spinor and scalar quantum electrodynamics in $d=2n>4$ dimensions. We give the closed form expression for the higher-dimensional Euler-Heisenberg Lagrangian, and extract its weak-field approximation in 6, 8 and 10 dimensions. A subsequent analysis of pair production in $d$ dimensions is also given. In the $d=6$ case, we present a composite conformal primary field of dimension $+6$ which determines the contribution of the electromagnetic field to the Weyl anomaly in curved space.

The oscillation modes of stars play an important role in observations, and on the understanding of stellar stability properties. The role of viscosity in the oscillation modes of compact stars has been so far understood very loosely only, in absence of a well posed framework. We use recent breakthroughs in the formulation of a causal and stable theory of relativistic hydrodynamics, to study oscillation modes of neutron stars. We characterize the axial spectrum of compact stars and uncover new, viscosity-driven families of modes, without a perfect fluid counterpart. Our results show mode avoidance in some of these families, and a spectrum of long-lived modes, whose role in astrophysical, dynamical processes is yet to be understood.

Linear complexions are stable defect states that form along dislocations and recent experiments have demonstrated strengthening effects exceeding classical precipitation hardening predictions, motivating a detailed study of nanoscale strengthening mechanisms. Here, molecular dynamics simulations in Al-Cu and Ni-Al face-centered cubic alloys are used to demonstrate distinct plasticity mechanisms associated with linear complexions. Both nanoparticle array and platelet array complexions exhibit appreciable strengthening. In addition to direct interactions with the particles, stress field modification in nearby regions can restrict dislocation motion as well. Finally, the relative particle-dislocation orientation is found to have a large effect, with the strongest resistance observed when the dislocation stress field aligns with the original complexion nucleation condition. As a whole, these findings provide mechanistic insight into the strengthening observed experimentally and establish design principles for linear complexion-induced strengthening in structural alloys.

Governance theory presupposes a rough cognitive comparability between governors and governed. This paper makes that assumption explicit and testable through a six-dimension evaluation framework covering legitimacy, accountability, corrigibility, non-domination, subsidiarity, and institutional resilience, drawn from political legitimacy theory, principal-agent models, republican theory, and the AI alignment literature. The framework is first demonstrated on existing non-majoritarian institutions, where capability asymmetry is real but bounded, and then applied to a prospective case of bounded superintelligent authority, where the asymmetry is radical. Four of six dimensions show structural failures. Two of the four appear tractable to institutional design (subsidiarity scope limitation and institutional resilience). The other two, the public reason problem under cognitive incomprehensibility and the non-domination problem under permanent capability asymmetry, call for new normative theory rather than better institutional design. The analysis also finds that dimensions which operate as independent checks under bounded asymmetry begin to degrade together under radical asymmetry, because each depends on the same oversight capacity. The assumptions that allowed these checks to remain independent have gone unexamined so far because they have always held.

The steep rise of viscosity as a liquid cools is one of the defining signatures of glass formation, yet the standard descriptions-Vogel-Fulcher-Tammann (VFT) and its divergence-free successors MYEGA and Avramov-Milchev-treat the slowdown as a single fixed curvature fitted across the whole temperature range. This work reports a constraint-modulated alternative built on a different premise: that a cooling liquid resolves its configuration continuously in the present, one state after another under the constraints then in force, rather than reading its viscosity off a globally predetermined free-energy surface. This premise, Continuous Present Actualization (CPA), calls for a rate law whose resolution cost changes as the liquid cools. The resulting model, CPA + Constraint (CPA + C), adds a single bounded constraint-load term C(T) that tracks how configurational access narrows toward structural lock-in. Tested against VFT, MYEGA, and Avramov-Milchev on canonical datasets for ortho-terphenyl, salol, and boron trioxide, CPA + C is favored by AIC and BIC on four of five datasets after full penalization for its two extra parameters, with margins reaching ΔAIC = 140.9 on the largest set (salol, n = 95); on two datasets the baseline kinetic term vanishes, reducing the model to four effective parameters. A smooth sigmoid form of C(T) fits equally well or better, and leave-one-out cross-validation on salol shows CPA + C generalizing to held-out data with mean prediction error three times lower than the next-best model. The single exception is the narrowest-window dataset, where the temperature range is too small for the constraint transition to separate CPA + C from simpler forms.

Clusters of co-rotating vortices on compact fluid domains exhibit a simple collective dynamics, combining coherent global rotation with a slow breathing of the cluster size. In this work, we investigate an analytic model of vortex interactions on a doubly periodic inviscid fluid domain, based on an exact representation in terms of the Schottky-Klein prime function and its $q$-representation. The two-vortex problem reduces to a single complex degree of freedom, from which explicit expressions for the orbital rotation frequency and dipole translation velocity are obtained. Building on this framework, we derive a small-cluster expansion that reveals a decomposition of the dynamics into universal planar interactions, isotropic torus corrections, and geometry-induced anisotropic modes. At leading order, the collective dynamics is encoded in a single complex quadrupole moment: its real part governs corrections to the rotation rate, while its imaginary part controls the slow breathing of the cluster. These predictions are quantitatively confirmed by direct numerical simulations, establishing a reduced description of vortex clusters on the flat torus and compact fluid domains.

We present a quantum optimization framework for the Shipment Selection Problem (SSP) in electric freight logistics, developed jointly by IonQ and Einride. Idle gaps arising from stochastic shipment cancellations reduce fleet utilization and revenue; filling them optimally requires solving a combinatorial assignment problem with quadratic inter-gap dependencies. We formulate the SSP as a Mixed-Integer Quadratic Program, map it to an Ising cost Hamiltonian, and solve it using Iterative-QAOA, a non-variational warm-start extension of the Quantum Approximate Optimization Algorithm (QAOA) with a fixed linear-ramp parameter schedule. An end-to-end hybrid workflow integrates Einride's vehicle routing problem (VRP) solver with IonQ's quantum simulations, enabling evaluation on real, anonymized logistics data spanning up to 130 qubits. We assess solution quality through application-level performance metrics, including Shipments Delivered (SD), Schedule Compatibility Score (SCS), and Total Drive Distance (TDD). When the quantum assignment is passed to the classical solver as a warm start, the resulting hybrid workflow achieves improvements of up to 12% in SD and a reduction of up to 6% in total drive distance per shipment for specific instances, while total operational cost remains effectively unchanged. For the subset of instances within reach of current devices (20-32 qubits), the workflow is additionally executed on IonQ trapped-ion quantum hardware, where the hardware results closely reproduce the noiseless simulations. These results show that Iterative-QAOA can generate compatibility-aware assignments that become operationally valuable when embedded in a hybrid logistics optimization workflow.

The centralized circumcentered-reflection method (\cCRM) of Behling, Bello-Cruz, Iusem, and Santos~\cite{Behling:2024} is known to converge superlinearly for the feasibility problem $\operatorname{find}\;z\in X\cap Y$ under a $\mathcal{C}^1$ smoothness assumption on the boundaries of $X$ and $Y$. We sharpen this to a quantitative rate: when the boundaries are $\mathcal{C}^2$ near the limit point $\bar z$, \cCRM\ converges Q-quadratically, with an asymptotic constant \( 2\max(κ_X,κ_Y)/ω\) governed by the boundary curvatures $κ_X,κ_Y$ at $\bar z$ and the local error-bound modulus $ω$. The estimate matches Newton-type second-order behavior even though \cCRM\ uses only projections and circumcenters, and numerical experiments on equality-constrained and spectral feasibility problems exhibit the predicted quadratic rate, with \cCRM\ reaching machine precision in a handful of steps where alternating projections and Douglas--Rachford take many. The argument is local and does not require $X\cap Y$ to have nonempty interior in $\re^n$: it suffices that the sets share an affine hull $L=\aff(X)=\aff(Y)$ and meet with nonempty relative interior, which is the natural setting for equality-constrained and spectral feasibility problems, where the classical full-dimensional hypothesis necessarily fails. A $\mathcal{C}^1$ version of the argument recovers and extends the superlinear rate of~\cite{Behling:2024} to this lower-dimensional regime. The case $\aff(X)\neq\aff(Y)$ is identified as open.

In this work, we consider maxima of systems of randomly time-changed Lévy particles. We give a general construction to obtain infinite-dimensional classes $\{Z^α\}$ of stationary max-infinitely divisible (max-id) processes. These classes are indexed by admissible mass functions $α$, which induce state-dependent time changes of the underlying Lévy particles. This gives a generalization of the well-known (Lévy--)Brown--Resnick process $Z^{1}$. In contrast to $α\equiv 1$, the variability of non-constant mass functions $α$ changes the dependence structure of the max-id process and goes beyond the max-stable setting while preserving stationarity. We then explore the extent of the so-called max-domain of attraction (MDA) of a given (Lévy--)Brown--Resnick process $Z^1$, by studying convergence of rescaled maxima of independent copies of $Z^α$ to $Z^1$. Thus, our work combines potential theory for Markov processes and extreme value theory to yield a novel, infinite-dimensional, and interpretable class $\{Z^α\}$ of stationary processes in the MDA of a given (Lévy--)Brown--Resnick process $Z^{1}$. So far, results on the extent of such domains have been scarce in the literature.

Age-Period-Cohort (APC) models are of special importance in Demography and Epidemiology for analyzing panel data according to three different factors: biological (age), technological (period) and cultural (cohort). The main goal of APC modeling is to separate the explanation of both period and cohort effects to the phenomenon. The objective of this paper is to develop a Bayesian Age-Period-Cohort framework that can model a wide range of demographic and epidemiological phenomena and improve upon existing statistical methodologies. The APC framework consists of addressing three main challenges: (1) the identification problem of all APC models, usually managed by imposing constraints on effect groups, (2) considering expert knowledge in the model definition, and (3) efficient solution of computational issues. By allowing full parameter uncertainty, use of robust priors, and an efficient computational implementation, a Bayesian methodology manages these concerns. Bayesian models also produce results that allow intuitive implementation and support theoretical knowledge. Our original methodology consists of the use of (i) a Scaled Beta2 prior distribution for the scale parameters, (ii) imposing different period and cohort constraints and comparing them,(iii) user-friendly implementation that can be easily adapted to the event, and (iv) various model comparison criteria that leads to reasonable interpretation of APC effects. We examine the dramatic collapse of fertility in Puerto Rico, an application that is difficult to model due to the accelerated changes and has interesting demographic implications that challenge the predominance of period effects in lowest-low fertility countries, emphasizing the cohort (cultural) momentum. The scope of the methodology introduced here is wide, including applications to obesity or smoking studies, for example.