Online financial scams represent a long-standing and serious threat for which people seek help. We present a study to understand people's in situ motivations for engaging with scams and the help needs they express before, during, and after encountering a scam. We identify the main emotions scammers exploited (e.g., fear, hope) and characterize how they did so. We examine factors -- such as financial insecurity and legal precarity -- which elevate people's risk of engaging with specific scams and experiencing harm. We indicate when people sought help and describe their help-seeking needs and emotions at different stages of the scam. We discuss how these needs could be met through the design of contextually-specific prevention, diagnostic, mitigation, and recovery interventions.

The use of Generative AI (GenAI) for creative content generation has gained popularity in recent years. GenAI allows creators to generate contents that are increasingly becoming indistinguishable to the human--generated counter--part at a much lower cost. While GenAI reshapes the competitive landscape of the contents market, the original creators were typically not compensated for their works that were used in the GenAI training. On the other hands, the wide--spread adoption of GenAI threatens to replace the human--generated shares of contents on content platforms, contaminating training data source for future GenAI models. In this paper, we argue that an unregulated usage of GenAI can also be harmful to the platform by causing a contents distribution distortion which can lower the consumers' engagement and the platform's profit. We show that a simple economically--driven creator compensation scheme, can incentivize more creation of high--value human--generated contents, without the need for an AI--detector. This reduces the data pollution for future GenAI training, while improves the consumer engagement and the platform's profit.

Steady-state visual evoked potential (SSVEP) is widely used in brain-computer interfaces (BCIs) due to its reliability. With the integration of augmented reality (AR), AR-SSVEP enables more intuitive interaction by embedding visual stimuli into real-world environments. However, unlike conventional computer screen-based SSVEP (CS-SSVEP) systems with stable visual conditions, AR-SSVEP performance is influenced by real-world scene factors, such as luminance and color, which degrade stimulus perception and weaken SSVEP elicitation. Nevertheless, existing studies primarily focus on offline analyses of SSVEP-related factors in indoor settings, while online adaptive optimization for outdoor AR-SSVEP remains limited. Therefore, a scenario-aware spatial layout optimization (SASLO) system for AR-SSVEP is proposed, which jointly considers scene luminance and inter-stimulus distance (ISD) for adaptive stimulus layout optimization. Scene luminance is estimated using an RGB-CIE based method, and the extracted context is incorporated into a linear contextual bandit (LCB) model to recommend optimized spatial layouts. Two pilot single-factor experiments are conducted to characterize the effects of luminance and ISD on SSVEP performance and to construct reliable rewards for model training. An outdoor online experiment with ten subjects further validates the proposed joint optimization method, achieving an average accuracy of 0.89 and an information transfer rate of 35.74 bits/min with a 3 s input window, and consistently outperforming two baseline methods. Overall, the proposed SASLO system is shown to improve the robustness of AR-SSVEP in real-world outdoor environments.

Artificial intelligence is increasingly used in hiring, raising concerns about how applicants perceive these systems. While prior work on algorithmic fairness has emphasized technical bias mitigation, little is known about how avatar identity cues influence applicants' justice attributions in an interview context. We conducted a crowdsourcing study with 215 participants who completed an interview with photorealistic AI avatars varied in phenotypic traits (race and sex), followed by a standardized rejection. Using self-reports, sentiment analysis, and eye tracking, we measured perceptions of trust, fairness, and bias. Results show that racial mismatch heightened perceptions of ethnic bias, while partial match (sharing only one identity) reduced fairness judgments compared to both full and no match. This work extends the Computers-Are-Social-Actors paradigm by demonstrating that avatar appearances shape justicerelated evaluations of AI. We contribute to HCI by revealing how identity cues influence fairness attributions and offer actionable insights for designing equitable AI interview systems.

Responsiveness in large language model (LLM) applications is widely assumed to be critical, yet the impact of latency on user behavior and perception of output quality has not been systematically explored. We report a controlled experiment varying time-to-first-token latency (2, 9, 20 seconds) across two taxonomy-driven knowledge task types (Creation and Advice). Log analyses reveal that user interaction behaviors were robust to latency, yet varied by task type: Creation tasks elicited more frequent prompting than Advice tasks. In contrast, participants who experienced 2-second latencies rated the LLM's outputs less thoughtful and useful than those who experienced 9- or 20-second latencies. Participants attributed delays to AI deliberation, though long waits occasionally shifted this interpretation toward frustration or concerns about reliability. Overall, this work demonstrates that latency is not simply a cost to reduce but a tunable design variable with ethical implications. We offer design strategies for enhancing human-LLM interaction.

Obesity is a global health challenge. According to the World Health Organization (WHO), between 1990 and 2022, adult obesity more than doubled. Weight management interventions (WMIs) support individuals in achieving and maintaining a healthy weight through dietary guidance, physical activity promotion and behavioural counselling. However, traditional WMIs often have limited accessibility. Digital WMIs or DWMIs are delivered via websites or smartphone applications and provide scalable and cost-effective alternatives. However, user needs for digital services and their prevalence in the existing commercial solutions remain underexplored. Hence, our study systematically identified 26 commercial DWMIs to identify their features, services, and data collection practices. Additionally, we performed a user needs analysis by recruiting 207 individuals involved in a real-life WMI. Our findings indicated that DWMIs integrated self-monitoring, goal setting, and behaviour change strategies, yet lack social support, virtual reality applications and adaptive personalisation. WMI clients prefer smartphone Apps and fitness trackers for tracking weight management progress and have varying levels of comfort in using digital resources. The presented results serve as recommendations for future directions in the design and implementation of services for DWMIs.

Financial management has been revolutionized by mobile banking, but increasing usefulness and satisfaction requires a better user experience. This study aims to provide an improved customer experience by offering user-friendly interfaces, and real-time notifications by user-centric design of mobile banking application UI. A survey was carried out on the target audience in which 81% of respondents to a study of 103 people said they regularly used mobile banking apps, while 77% said they had problems with the ones they were using at the time. Furthermore, 44.7% of respondents expressed unhappiness with the current solutions by depending on third-party apps like e-Sewa and Khalti for everyday transactions. Language obstacles, lengthy loading times, unclear terminology, and navigational challenges were among the problems found. With 84% asking for a budgeting function and 46% complaining about biometric authentication, users indicated a need for more individualized interfaces, improved customer service, and increased security. The study included Think Aloud testing, heat maps, and remote usability testing to determine user preferences and pain spots to solve these. Feedback from a wider audience was obtained informally through guerrilla usability testing. The results highlight how important it is for mobile banking apps to guarantee security, increase functionality, simplify navigation, and improve visual design. App grouping and layout can be further enhanced by utilizing Gestalt psychology concepts like closeness and symmetry. The goal of these user-centered insights is to promote greater happiness and adoption of mobile banking.

Behavioral changes in daily life activities at home can be digital markers of cognitive decline. However, such changes are difficult to assess through sporadic clinical visits and remain challenging to interpret from continuous in-home sensing data. Extensive work has been done in the ubiquitous computing area on recognizing activities in smart homes, but only limited efforts have focused on analysing the evolution of patterns of activities, hence identifying behavior changes. In particular, understanding how daily habits and routines evolve and reorganize (e.g., simplification, fragmentation) is still an open challenge for clinical monitoring and decision support. In this paper, we present X-BCD, an explainable, unsupervised framework for detecting and characterizing changes in activity routines from multimodal smart home sensor data, combining change point detection and cluster evolution tracking. To support clinical interpretation, detected changes in routines are transformed into natural-language explanations grounded in interpretable features. Our preliminary evaluation on longitudinal data from real MCI patients shows that X-BCD produces interpretable descriptions of behavioral change, as supported by cohort-level comparisons, expert assessment, and parameter sensitivity analysis.

This letter studies pilot design for orthogonal frequency-division multiplexing-based time-division duplex (TDD) systems under a sliding-window latest-slot recovery framework that jointly exploits delay-Doppler sparsity across recent slots. Under contiguous-subband and fairness constraints, this viewpoint naturally leads to a geometry-aware time-frequency joint pilot assignment. We show that effective patterns should balance grid coverage and redundant-collinearity suppression, with an additional symmetry-avoidance refinement when complete collinearity elimination is infeasible. Based on these principles, we formulate a mixed-integer construction method compatible with practical TDD allocation. Numerical results show that minimum-coverage-radius and collinearity-control (MCC) pattern improves both surrogate geometry metrics and latest-slot recovery performance.

Numerous problems in development, regeneration, and disease involve simultaneous evolution of both spatial organization and the internal state of the constituents in addition to local interactions and crowding. This motivates us to study a minimal model for interacting populations evolving in coupled spatial and internal-state coordinates. We focus on a specific transition of particular biological interest: the reorganization of dense collectives from compact or arrested states toward boundary-led peeling and migration. In our formulation, each particle carries a spatial position and a scalar internal state, and interacts through finite-range forces. Mobilities are defined on both spatial and internal-state coordinates with a density dependence, and are asymmetrically cross-coupled. We derive update equations for stochastic dynamics in the overdamped limit and perform numerical simulations. We find that mobility in internal-state coordinates alone provides an independent control axis for large-scale spatial reorganization. In particular, increasing the baseline internal-state diffusivity and tuning its density dependence drives a transition from arrested aggregates to a peeling-like regime with broad spatial excursions, strong outward radial bias, and edge-localized activity, while the baseline positional diffusivity is held fixed. The transition is accompanied by correlated broadening of spatial and internal-state displacements, systematic reorganization of radial density and density-curvature profiles, and a pronounced dependence on system size, consistent with the idea that growing aggregates can cross into a boundary-dominated migratory state. These results establish the utility of our approach and motivate a broader framework aimed at modeling state change, spatial redistribution, and neighborhood structure within a common formalism.

We give a proof of the Morrison-Kawamata cone conjecture for Enriques surfaces independent of their characteristic. It is based on the analysis of certain generically finite morphisms of degree two.

We provide improved space-time tradeoffs for permutation problems over additively idempotent semi-rings. In particular, there is an algorithm for the Traveling Salesperson Problem that solves $N$-vertex instances using space $S$ and time $T$ where $S\cdot T \leq 3.7493^{N}$. This improves a previous work by Koivisto and Parviainen [SODA'10] where $S\cdot T \leq 3.9271^N$, and overcomes a barrier they identified, as their bound was shown to be optimal within their framework. To get our results, we introduce a new parameter of a set system that we call the chain efficiency. This relates the number of maximal chains contained in the set system with the cardinality of the system. We show that set systems of high efficiency imply efficient space-time tradeoffs for permutation problems, and give constructions of set systems with high chain efficiency, disproving a conjecture by Johnson, Leader and Russel [Comb. Probab. Comput.'15].

We investigate hierarchical mergers among subhalos within a $Λ$CDM simulation using the HBT+ subhalo finder. Unlike previous methods, HBT+ tracks subhalo evolution across hierarchy levels, identifying the coalescence of subhalo cores in phase-space as a ''sinking" event. This coalescence marks a distinct stalled phase in orbital decay, providing a physically motivated and natural definition of a resolved merger. Our main findings include: 1) Over 90% of sinking events occur between adjacent subhalo levels, while cross-level pathways arise from tidal stripping, group infall, and numerical constraints. 2) Resolved mergers are predominantly major mergers (mass ratios > 1:10), while the occurrence of minor mergers decreases with the dynamical age of the host halo. 3) Although deep-level subhalos have low mass ratios relative to the host halo, their high mass ratios relative to direct parents significantly boost merger statistics. Consequently, the satellite-satellite merger rate can rival or exceed the central-satellite rate at lower mass thresholds. 4) Satellite-satellite mergers are spatially biased toward the outer regions of the host, suggesting that the central tidal field suppresses their orbital decay. 5) A bidirectional sinking detection recovers 32% more sinking events than the original algorithm, revealing that child-dispersion-driven mergers are dominated by tidal heating at the final stage of sinking, while parent-dispersion-driven and doubly-identified events proceed primarily via orbital decay. Altogether, these results reveal a complex landscape of hierarchical satellite mergers that deviate from the self-similarity of host halo mergers, due to additional physical processes including dynamical friction and the scale-dependent halo growth history.

Neutral atomic hydrogen (HI) reservoirs typically extend far beyond the inner star-forming regions of galaxies, and global HI measurements, which mix these distinct environments, limit our understanding of the gas-star formation cycle. In particular, global HI depletion times combine gas and star formation from different physical scales, contributing to long measured timescales (5-9 Gyr) and large scatter compared to molecular gas. Using 841 gas-rich galaxies from the Widefield ASKAP L-band Legacy All-sky Blind Survey (WALLABY) pilot observations, we investigate how HI depletion time and its scaling relations change when HI and star formation are both confined to the stellar disc (R25, the isophotal radius at 25 mag arcsec-2 in i-band). We find that depletion times within this region are on average 1.4 Gyr shorter than global values, though some remain very long, indicating that a substantial fraction of HI remains inactive for star formation. HI depletion times anti-correlate strongly with stellar surface density, and this trend becomes even tighter within the stellar disc. The Kennicutt-Schmidt relation further reveals an almost constant HI depletion time at fixed stellar surface density, similar to the behaviour seen for molecular gas, suggesting that HI and star formation are regulated by conditions that enable HI-to-H2 conversion, traced by stellar surface density. Beyond the stellar disc, HI depletion times are on average almost 10 Gyr longer than within R25, confirming extremely inefficient star formation in low-density outer regions. These results highlight the critical role of spatial location and local conditions for HI to serve as a fuel for star formation.

Social network simulation aims to model collective opinion dynamics in large populations, but existing LLM-based simulators mainly focus on aggregate dynamics while largely ignoring individual internal states. This limits their ability to capture opinion reversals driven by gradual individual shifts and makes them unreliable in long-horizon simulations. We propose MF-MDP, a social simulation framework that tightly couples macro-level collective dynamics with micro-level individual states. MF-MDP explicitly models per-agent latent opinion states with a state transition mechanism, combining individual Markov Decision Processes at the micro level with a mean-field collective framework at the macro level. This allows individual behaviors to change internal states gradually rather than trigger instant reactions, enabling the simulator to distinguish agents that are close to switching from those that are far from switching, capture opinion reversals, and maintain accuracy over long horizons. Across real-world events, MF-MDP supports stable simulation of long-horizon social processes with up to 40,000 interactions, compared with about 300 in the baseline MF-LLM, while reducing long-horizon KL divergence by 75.3% (1.2490 to 0.3089) and reversal KL by 66.9% (1.6425 to 0.5434), significantly mitigating the drift observed in MF-LLM. Code is available at github.com/AI4SS/MF-MDP.

We present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which $C^{*}$-algebras are responsible for the universal and intrinsic description, whereas von Neumann algebras provide the detailed account obtained after fixing a state compatible with the dynamics. From this standpoint, for bosonic many-body systems the resolvent algebra, rather than the Weyl algebra, is the natural object; in particular, its nuclearity, trivial center, and rich ideal structure faithfully reflect purely quantum-mechanical structures. Macroscopic variables or sector structures associated with phase transitions are captured as the center appearing in the weak closure of the GNS representation. Moreover, the equivalence between representations of operator algebras and functional integrals allows powerful probabilistic methods to be employed. Taking these as guiding principles, we outline research perspectives on concrete objects in constructive quantum field theory and rigorous statistical mechanics.

We determine the normalization of the leading infrared renormalon of the chromomagnetic moment of a heavy quark. Estimates of higher order coefficients of the perturbative series are given. We compute the hyperfine splitting of the $B$ and $D$ mesons for the ground state with hyperasymptotic precision by including the leading terminant, associated with the first infrared renormalon. We fit the experimental data to the operator product expansion theoretical prediction with $\hat μ^2_{G,\rm PV}$ as the free parameter. We obtain $\hat μ^2_{G,\rm PV}=0.507(7)$ GeV$^2$ for the ground state.

Bayesian inference in the physical sciences faces a fundamental challenge: the imperative for high-fidelity physical modeling often clashes with the intrinsic limitations of stochastic sampling algorithms. Complex, high-dimensional parameter spaces expose the universal vulnerability of conventional methods, e.g., Markov Chain Monte Carlo (MCMC), which struggle with the prohibitive costs of likelihood evaluations and the risk of entrapment in local optima. To resolve this impasse, we introduce FluxMC (Flow-guided Unbiased eXploration Monte Carlo), a machine learning-enhanced framework designed to shift the inference paradigm from blind local search to globally guided transport. It integrates Flow Matching with Parallel Tempering MCMC, effectively combining the global foresight of generative AI with the rigorous asymptotic convergence and local robustness of temperature-based sampling. We showcase the efficacy of this framework through the lens of space-based gravitational-wave (GW) astronomy -- a field representing the frontier of challenging parameter inversion. In the analysis of massive black hole binaries using high-fidelity waveforms (IMRPhenomHM), FluxMC achieves robust convergence in under five hours, whereas traditional Parallel Tempering MCMC fails to converge even after hundreds of hours, yielding high Jensen-Shannon divergences (JSD) of $O(10^{-1})$. Our method reduces the distributional error by two to three orders of magnitude. Furthermore, for computationally efficient models (IMRPhenomD), it eliminates systematic biases caused by local-optima entrapment. Ultimately, FluxMC removes the necessity to compromise between model accuracy and analysis speed, establishing a new computational foundation where scientific discovery is limited only by observational data quality, not by algorithmic capacity.

We present QCommute, a software tool implemented in C++ for symbolic computation of nested commutators between a Hamiltonian and local observables in quantum many-body spin-1/2 systems on one-, two-, and three-dimensional hypercubic lattices. The computation is performed algebraically directly in the thermodynamic limit, and the Hamiltonian parameters are kept symbolic. Importantly, this way the entire parameter space is covered in a single run. The implementation supports extensive parallelization to achieve high computational performance. QCommute enables the investigation of quantum dynamics in strongly correlated regimes that are inaccessible to perturbative approaches, either through direct Taylor expansion in time or via advanced techniques such as the recursion method.

Software testing research has traditionally relied on closed-world assumptions, such as finite state spaces, reproducible executions, and stable test oracles. However, many modern software systems operate under uncertainty, non-determinism, and evolving conditions, challenging these assumptions. This paper uses open-world games as an extreme case to examine the limitations of closed-world testing. Through a set of observations grounded in prior work, we identify recurring characteristics that complicate testing in such systems, including inexhaustible behavior spaces, non-deterministic execution outcomes, elusive behavioral boundaries, and unstable test oracles. Based on these observations, we articulate a vision of software testing beyond closed-world assumptions, in which testing supports the characterization and interpretation of system behavior under uncertainty. We further discuss research directions for automated test generation, evaluation metrics, and empirical study design. Although open-world games serve as the motivating domain, the challenges and directions discussed in this paper extend to a broader class of software systems operating in dynamic and uncertain environments.

We develop a categorical and algebro-geometric treatment of localization for cohomological theories endowed with an open--closed recollement. Starting from a class on a space whose restriction to the open complement vanishes, we show that the natural output of the formalism is, in general, not a distinguished localized class on the closed locus, but rather a torsor of supported refinements; a canonical local term arises only once an additional uniqueness or concentration principle is imposed. We establish excision, a natural pullback map under Cartesian base change, proper pushforward, and compatibility with external products under explicit hypotheses governing the interaction between product constructions and exceptional pullback. We also prove a factorization result showing that any assignment of local terms already compatible with the localization triangle must necessarily take its values in this torsor. When supplemented by Verdier duality and the appropriate orientation data, the resulting localized classes govern local indices and yield global-to-local index formulas. Under purity and concentration, the formalism recovers the familiar Euler-denominator expressions. The later geometric examples should therefore be read as conditional realisations of the same torsorial mechanism, available only once the relevant comparison hypotheses, together with the requisite purity and concentration statements, are in force.

Finite element model updating is a mature discipline for linear structures, yet its extension to nonlinear regimes remains an open challenge. This paper presents a methodology that combines nonlinear model order reduction (NMOR) based on Taylor-series expansion of the equations of motion with the projection-basis adaptation scheme recently proposed by Hollins et al. [2026] for linear model updating. The structural equations of motion, augmented with proportional (Rayleigh) damping and polynomial stiffness nonlinearity, are recast as a first-order autonomous system whose Jacobian possesses complex eigenvectors forming a biorthogonal basis. Taylor operators of second and third order are derived for the nonlinear internal forces and projected onto the reduced eigenvector basis, yielding a low-dimensional nonlinear reduced-order model (ROM). The Cayley transform, generalised from the real orthogonal to the complex unitary group, parametrises the adaptation of the projection basis so that the ROM mode shapes optimally correlate with experimental measurements. The resulting nonlinear model-updating framework is applied to a representative wingbox panel model. Numerical studies demonstrate that the proposed approach captures amplitude-dependent natural frequencies and modal assurance criterion(MAC) values that a purely linear updating scheme cannot reproduce, while recovering the underlying stiffness parameters with improved accuracy.

Artificial-intelligence (AI) agent frameworks have been developed for autonomous scientific simulations, but most current agent frameworks are tailored to a single or a small set of software packages. Herein, FermiLink, a unified and extensible open-source agent framework is introduced for multidomain scientific simulations. Its key design principle is the separation of package knowledge bases from simulation workflows, so that simulation workflows in FermiLink, from figure-level simulations to full-paper-level research on high-performance computing clusters, operate uniformly among supported packages via a four-layer progressive disclosure mechanism. Using OpenAI Codex as the agent provider, the capabilities of FermiLink are demonstrated across approximately 50 scientific software packages spanning nine research domains from physics to engineering. Systematic benchmarks on 132 real-world figure-level reproduction tasks with 44 packages show that FermiLink reproduces 74 (56.1%) of published figures with simulations, among which 30 achieve high-fidelity agreement and 35 reach qualitative agreement with the target figures. A smaller set of human expert-guided reproduction benchmarks with 10 packages further highlights the importance of expert insights for improving the simulation fidelity. Beyond reproduction, a single-blinded study demonstrates that FermiLink can produce research-grade results on unpublished polariton physics problems when provided with sufficiently detailed research objectives and source code, even in the absence of external documentation or tutorials. Overall, FermiLink provides a scalable research infrastructure that may accelerate the path from scientific questions to computational results across diverse domains.

With the development of 6G technologies, traditional uniform linear arrays (ULAs) and uniform planar arrays (UPAs) can hardly meet the demands of three-dimensional (3D) full-space coverage and high angular resolution. Spherical antenna arrays (SAAs), with elements uniformly distributed on a spherical surface, provide an effective solution. This article analyzes the issues of traditional arrays, summarizes the advantages and typical structures of SAAs, discusses their potential application scenarios, and verifies their superiority over UPAs via a case study. Finally, key technical challenges and corresponding research directions of SAAs are identified, providing a reference for their research and application in future wireless communications.

The Tree Evaluation Problem ($\mathsf{TreeEval}$) is a computational problem originally proposed as a candidate to prove a separation between complexity classes $\mathsf{P}$ and $\mathsf{L}$. Recently, this problem has gained significant attention after Cook and Mertz (STOC 2024) showed that $\mathsf{TreeEval}$ can be solved using $O(\log n\log\log n)$ bits of space. Their algorithm, despite getting very close to showing $\mathsf{TreeEval} \in \mathsf{L}$, falls short, and in particular, it does not run in polynomial time. In this work, we present the first polynomial-time, almost logarithmic-space algorithm for $\mathsf{TreeEval}$. For any $\varepsilon>0$, our algorithm solves $\mathsf{TreeEval}$ in time $\mathrm{poly}(n)$ while using $O(\log^{1 +\varepsilon}n)$ space. Furthermore, our algorithm has the additional property that it requires only $O(\log n)$ bits of free space, and the rest can be catalytic space. Our approach is to trade off some (catalytic) space usage for a reduction in time complexity.

Maximally-localized Wannier functions are quantum wavefunctions resembling atomic orbitals that are used to describe electrons in condensed matter. Since their introduction in 1997, these functions have become ubiquitous in ab initio materials simulations, including applications in linear-scaling methods, strongly-correlated electron systems, quantum transport, electron-phonon interactions, and topological materials. Despite their widespread adoption in a vast software ecosystem, Wannier functions have not yet attained their fullest potential in the presence of entangled bands, as their optimization remains challenging and labor-intensive. Here, we introduce a universal meta-optimization method that leverages workflow abstraction and machine learning techniques like differential evolution and Bayesian optimization to generate globally optimized Wannier functions without human intervention. We demonstrate this approach through three applications: (i) autonomous interpolation of entangled band structures with millielectronvolt accuracy starting from coarse Brillouin zone grids, (ii) thousand-fold acceleration of fully ab initio Boltzmann transport calculations via the use of minimal coarse Brillouin zone grids, and (iii) ultra-fast high-throughput calculations of high-precision Wannier functions for large materials libraries. This work brings calculations that previously required supercomputers within the reach of personal computers.

We study axial gravitational perturbations of a hairy black hole constructed in the framework of gravitational decoupling and investigate the geometric origin of echo-like late-time signals in this spacetime. We derive the odd-parity master equation and the corresponding effective potential, and we compute the quasinormal-mode spectrum by using frequency-domain and time-domain methods. We show that, in a suitable region of parameter space, the axial potential develops a double-peak structure that supports a trapping cavity and gives rise to echo-like late-time waveforms. Rather than imposing near-horizon reflectivity by hand, the delayed pulses therefore arise dynamically from the geometry of the effective potential. We also clarify that the parameter region exhibiting echoes need not coincide with the region in which the weak energy condition is satisfied everywhere outside the event horizon, and this distinction must be taken into account when interpreting the physical status of the solution. Our results provide a useful framework for probing black-hole hair through gravitational-wave ringdown and for exploring possible observational departures from the standard no-hair paradigm.

(ABRIDGED BUT NOT TOO FAR) Multiplicity is ubiquitous among massive stars and its understanding is constrained by the sample of well-determined orbits. The immediate goal of M3W is to significantly increase the number of massive multiple systems with well-determined orbits and masses. We will address issues such as multiplicity statistics, the mass function in clusters and the field, the properties of binaries with compact companions and gravitational-wave progenitors, the origin and characteristics of runaways and their 3-D motions, the use of apsidal motion as a probe of stellar interiors, and the mass discrepancy between different methods (evolutionary, spectroscopic, and Keplerian). In this first paper, we present the project; describe the data and tools that will be used, including the disentangling UNWIND tool; analyse the very massive twin binary system GLS 11 448; and briefly introduce some of the following papers of the series. We present a new orbit for GLS 11 448, using UNWIND to obtain for the first time disentangled spectra for the full 3820-11 000 $\mathring{A}$ range for an OB spectroscopic binary. We derive the stellar parameters, making new stellar lines available for the study of O stars. The Aa and Ab components of GLS 11 448, both classified as O3.5 II(f*), are the two most massive O stars ever detected according to the evolutionary masses of 70$\pm$10 M$_\odot$ and 76$\pm$11 M$_\odot$ determined in this paper. We also report the first-ever detection of the interstellar He I 10 830 triplet in absorption in an OB-star sightline. As a by-product of the ISM model derived for UNWIND using GLS 11 448 and five other standard stars, we present the most detailed diffuse-interstellar-band (DIB) library ever built, with a total of 631 DIBs in the 4000-17 100 $\mathring{A}$ range, of which 37 are fitted with multiple-Gaussian profiles and 119 had never been identified before.

We present a systematic description of the structure of Bose-Einstein condensation (BEC) in the free Bose gas from the viewpoint of the correspondence between the operator-algebraic formulation based on the resolvent algebra and the functional integral representation. By clarifying the representation-theoretic structure of finite-temperature BEC states and rigorously analyzing the correspondence between their direct integral decomposition and the ergodic decomposition of the associated probability measures, we provide a framework in which general features of phase transitions-such as the emergence of order parameters, the decomposition of states, and clustering properties-are explicitly described using BEC in the free Bose gas as a concrete example. Furthermore, we construct in detail the correspondence between the decomposition of measures in the functional integral approach and that of operator-algebraic representations, thereby establishing the equivalence between the probabilistic and algebraic aspects, and providing a guiding principle for isolating the essential structures by disentangling the additional mathematical complications arising from the treatment of infrared singularities in interacting systems. These results lay a foundation for the rigorous analysis of phase transitions in non-relativistic constructive quantum field theory and quantum statistical mechanics, and serve as a starting point for extensions to interacting models.

Explicit expressions are proven for derivatives of the ratio of a determinant or Pfaffian determinant and a Vandermonde determinant. Such ratios appear for example in general group integrals of Harish-Chandra--Itzykson--Zuber type and in expectation values of products of characteristic polynomials in random matrix theory. In the latter case we start from known results for general non-Hermitian and Hermitian ensembles for expectation values without derivatives, at finite matrix size. They are given in terms of the determinant or Pfaffian of the corresponding kernel, for unitary or orthogonal and symplectic ensembles, respectively. Several equivalent expressions are proven for general ratios of determinants, starting from first order derivatives containing the Borel transform of the corresponding matrix or kernel. Higher order derivatives are expressed as sums over partitions containing determinants of derivatives of these, with coefficients given in terms of combinatorial expressions. Our most general result is valid for mixed higher order derivatives of ratios of determinants in several variables. This generalises previous findings, e.g. for mixed moments in specific ensembles of random matrices, relevant in applications to the Riemann $ζ$-function. Applications of our results to several examples are presented, including the complex Ginibre ensemble and the circular unitary ensemble.