Chiral phonons are mirror-symmetric vibrations that correspond to twisting and rotational motions of atoms. In chiral biomolecules, they correspond to low-energy terahertz (THz)-range vibrations of the molecular segments involving dozens of atoms whose energies are sensitive to the chirality of the molecules and local atomic geometries. Here we present spectral signatures of chiral phonons in circularly polarized low-frequency Raman and Raman optical activity (ROA) spectra from crystals of several amino acids in different enantiomeric forms. Along with complementary THz circular dichroism (TCD) measurements, our ROA data reveal two sets of bisignate peaks in valine, alanine, tyrosine and proline between 1 and 4.5 THz that are more intense than the ROA peaks in the fingerprint region. Density functional theory (DFT) calculations on L-alanine attribute these modes to twisting and shearing molecular motions. The strong agreement between the ROA and TCD data demonstrates the power of these complementary vibrational spectroscopy techniques to identify chiral phonons in biomolecules, and offers new insights into their vibrational properties and interactions with circularly polarized light.

In this paper, we consider the stationary version of the Mean-Field Games (MFG) models. Inspired by \cite{Albuquerque-Silva2020, Bieganowski-Mederski2021, Lin-Wei05, Mederski-Schino2021}, we develop the minimization method on the Pohozaev manifold introduced in \cite{Soave20JDE, Soave20JFA} for the existence theory of the stationary version of the Mean-Field Games (MFG) models with $2$-homogeneous hamiltonians and mixed interactions. As applications, we prove the existence and multiplicity of radial solutions of the Mean-Field Games (MFG) models with general $p$-homogeneous hamiltonians and mixed interactions under more general conditions, some of which are even new for $2$-homogeneous hamiltonians. We hope that our techniques and ideas introduced in this paper would be helpful in understanding the optimal value of the total mass in the existence theory of radial solutions to the Mean-Field Games (MFG) models with general $p$-homogeneous hamiltonians and mixed interactions, as well as that of other models.

Quantum non-demolition measurements facilitate various quantum technologies, including quantum communication. Notably, their operational structure can be replicated by a classical model--referred to as a noncontextual model--making it crucial to identify which features prevents such models from reproducing the corresponding quantum measurements. In this work, we theoretically demonstrate contextual features inherent in the structure of quantum non-demolition measurements. These features not only reveal the nonclassicality of unambiguous state discrimination, but also extend to sequential unambiguous discrimination and probabilistic quantum cloning, both of which involve post-measurement states. Moreover, our analysis extends to noisy scenarios, highlighting its potential relevance for practical implementations. We believe that our results broaden the scope of observing nonclassicality in quantum systems and ultimately contribute to the advancement of various quantum technologies.

Determining the number of change-points is a first-step and fundamental task in change-point detection problems, as it lays the groundwork for subsequent change-point position estimation. While the existing literature offers various methods for consistently estimating the number of change-points, these methods typically yield a single point estimate without any assurance that it recovers the true number of changes in a specific dataset. Moreover, achieving consistency often hinges on very stringent conditions that can be challenging to verify in practice. To address these issues, we introduce a unified test-inverse procedure to construct a confidence set for the number of change-points. The proposed confidence set provides a set of possible values within which the true number of change-points is guaranteed to lie with a specified level of confidence. We further proved that the confidence set is sufficiently narrow to be powerful and informative by deriving the order of its cardinality. Remarkably, this confidence set can be established under more relaxed conditions than those required by most point estimation techniques. We also advocate multiple-splitting procedures to enhance stability and extend the proposed method to heavy-tailed and dependent settings. As a byproduct, we may also leverage this constructed confidence set to assess the effectiveness of point-estimation algorithms. Through extensive simulation studies, we demonstrate the superior performance of our confidence set approach. Additionally, we apply this method to analyze a bladder tumor microarray dataset. Supplementary Material, including proofs of all theoretical results, computer code, the R package, and extended simulation studies, are available online.

This paper aims to extend the understanding of the mechanism of photo-electrical detection of magnetic resonance (PDMR) in nitrogen-vacancy (NV) centres. This technique is particularly important for development of solid-state quantum computing platforms. In particular, we report on the new insight in the photocurrent (PC) generation and charge cycling in the single NV centre, which is related to PDMR contrast reaching 50\% and above. We develop a technique to locate PC related features. We find that electrons generated at the NV centre are stored in interface trap levels and establish that the interface states serve as an amplifier that can be driven by introducing a second laser into our confocal setup. We show that controlling these interface states allows one to significantly enhance the PDMR contrast. We develop a model that consistently explains observed amplification effects even without the application of a bias voltage.

Metaphors enable designers to communicate their ideal user experience for platforms. Yet, we often do not know if these design metaphors match users' actual experiences. In this work, we compare design and user metaphors across three different platforms: ChatGPT, Twitter, and YouTube. We build on prior methods to elicit 554 user metaphors, as well as ratings on how well each metaphor describes users' experiences. We then identify 21 design metaphors by analyzing each platform's historical web presence since their launch date. We find that design metaphors often do not match the metaphors that users use to describe their experiences. Even when design and user metaphors do match, the metaphors do not always resonate universally. Through these findings, we highlight how comparing design and user metaphors can help to evaluate and refine metaphors for user experience.

Diffusion exchange spectroscopy (DEXSY) is a method to probe exchange between domains of varying confinement. Analyses of DEXSY signals typically assume Gaussian diffusion within distinct compartments and first-order exchange kinetics between them. Other situations can yield DEXSY signal contrast with respect to mixing time, however, leading to potentially erroneous interpretation. Here, we demonstrate that a one-dimensional compartment with reflecting boundaries and without relaxation can by itself produce such contrast in certain experimental regimes. The origin of this contrast is the diffusive mixing of spin isochromats initially near versus far from either boundary, as the former can be relatively coherent in an effect known as edge enhancement or signal localization. We consider DEXSY signals in the case of extended field gradients and identical encodings. Signals were generated via a numerical approach that solves the Bloch-Torrey equation in discrete space and time using matrix operators. We find that in the localization regime, an apparent first-order rate constant of exchange, $k$, can be extracted from DEXSY signals even in this minimal system. The measured $k$ is approximately proportional to $D/L^2$, where $D$ is the diffusivity and $L$ is the domain size. Typically, $k \approx π^2 D/L^2$. We attribute this localization-driven exchange to the relaxation of spatial magnetization modes with mixing time, noting that $π^2 D/L^2$ is the first non-zero eigenvalue of the Laplacian basis. These results demonstrate that DEXSY and related methods such as filter exchange spectroscopy (FEXSY) may not be specific to genuine barrier permeation.

We study a family of periodically weighted Aztec diamond dimer models near their turning points. We establish that, asymptotically, as $N\rightarrow\infty$, their fluctuations there, scaled by $\sqrt{N}$, are described by a marked GUE-corners process. This limiting point process is constructed by assigning a Bernoulli mark independently to each particle in a realization of the GUE-corners process. The Bernoulli parameters associated with the random marks reflect the periodicity of the model in the limit. To prove this result we use a double-contour integral representation of the inverse Kasteleyn matrix on a higher-genus Riemann surface, which is well-suited for asymptotic analysis.

This paper investigates one-step backward reachability for uncertain max-plus linear systems with additive disturbances. Given a target set, the problem is to compute the set of states from which there exists an admissible control input such that, for all admissible disturbances, the successor state remains in the target set. This problem is closely related to safety analysis and is challenging due to the high computational complexity of existing approaches. To address this issue, we develop a computational framework based on tropical polyhedra. We assume that the target set, the control set, and the disturbance set are all represented as tropical polyhedra, and study the structural properties of the associated backward operators. In particular, we show that these operators preserve the tropical-polyhedral structure, which enables the constructive computation of reachable sets within the same framework. The proposed approach provides an effective geometric and algebraic tool for reachability analysis of uncertain max-plus linear systems. Illustrative examples are included to demonstrate the proposed method.

We construct a nonrecursive set \(A\le_T\emptyset'\) and a uniformly computable family of sets \(C_0,C_1,\dots\), all bounded finite-one equivalent to \(A\), such that the corresponding \(1\)-degrees form a copy of the dense linear order \((\mathbb Q,\le)\). Motivated by a recent preprint of Richter, Stephan, and Zhang, which shows that bounded finite-one degrees can be as rigid as a discrete \(ω\)-chain and asks whether there are bounded finite-one degrees consisting exactly of a dense linearly ordered set of \(1\)-degrees, we introduce a block-density profile method for controlling one-one reducibility inside a single bounded finite-one degree. As further applications, in the same bounded finite-one degree we obtain an infinite antichain of \(1\)-degrees and, more generally, an embedded copy of every countable partial order. A single bounded finite-one degree can already exhibit dense, incomparable, and universal order-theoretic behaviour. Our main technical tool is a profile theorem based on computable block-density codings. The witness set constructed here is not \(m\)-rigid, so the phenomena obtained in this paper arise from a mechanism different from earlier \(m\)-rigidity-based constructions. Although our results do not settle the exact realization problem posed by Richter, Stephan, and Zhang, we show that density itself is not the obstruction: a single bounded finite-one degree may already contain a copy of \((\mathbb Q,\le)\), an infinite antichain, and embeddings of all countable partial orders.

Given a semigroup $G$ and a bounded function $f: G \to \mathbb{C}$, a topological Furstenberg system of $f$ is a topological dynamical system $\mathbb{X}=(X, (T_g)_{g \in G})$ that encodes the dynamical behaviour of $f$. We show that $\mathbb{X}$ is unique up to topological isomorphism, thus providing a topological analogue of the measurable case established by Bergelson and Ferré Moragues for amenable semigroups. We also provide necessary and sufficient conditions for subsets of a group to have isomorphic Furstenberg systems. In addition, we study sets with minimal Furstenberg systems and identify them as a special subclass of dynamically syndetic sets. Moreover, we use this notion to obtain a new characterization of sets of topological recurrence.

Totally similar physical process in tidal disruption events (TDEs) basically indicates that there should be potential parameter to distinguish variability properties of TDEs from the other transient events having different physical processes. Here, we try to report such a parameter, the timescale ratio $R_{2/1,rd}$ of rise timescale $t_{1/2,r}$ (from half-max to maximum) to decline timescale $t_{1/2,d}$ (from maximum to half-max), especially based on the 34 optical TDEs with reported $t_{1/2,r}$ and $t_{1/2,d}$. Among the 34 optical TDEs, AT2020wey is an outlier with $R_{2/1,rd}\sim2.7$ which is 4.5 times larger than the mean value 0.6 of the other optical TDEs. However, after considering similar but more flexible model functions, the re-determined $R_{2/1,rd}$ is $\sim$0.9 in AT2020wey, totally similar as the values of the other optical TDEs. Therefore, the parameter $R_{1/2,rd}\sim0.6$ could be a potential classification parameter for optical TDEs. Furthermore, $R_{1/2,rd}$ have been checked in the unique optical transients of AT2019avd, PS1-10adi, SDSS J0946+3512 and J2334+1457. We can find that the second flare with $R_{1/2,rd}\sim11$ in AT2019avd should be very different from the other optical TDEs, but PS1-10adi, SDSS J0946+3512, J2334+1457 and the first flare in AT2019avd should be similar as the other optical TDEs. In the near future, properties of $R_{1/2,rd}$ through large sample of optical transients could provide further clues to support whether $R_{1/2,rd}$ could be a better classification parameter to distinguish TDEs and the other transient events.

This paper investigates how the integration of large language models influences gameplay, playability, and player experience in game development. We report a collaborative autoethnographic study of two game projects in which LLMs were embedded as architectural components. Reflective narratives and development artifacts were analyzed using gameplay, playability, and player experience as guiding constructs. The findings suggest that LLM integration increases variability and personalization while introducing challenges related to correctness, difficulty calibration, and structural coherence across these concepts. The study provides preliminary empirical insight into how generative AI integration reshapes established game constructs and introduces new architectural and quality considerations within game engineering practice.

Background. As digital technologies increasingly shape social domains such as healthcare, public safety, entertainment, and education, software engineering has engaged with ethical and political concerns primarily through the notion of algorithmic fairness. Aim. This study challenges the limits of software engineering approaches to fairness by analyzing how fairness is conceptualized in the human sciences. Methodology. We conducted two secondary studies, exploring 45 articles on algorithmic fairness in software engineering and 25 articles on fairness from the humanities, and compared their findings to assess cross-disciplinary insights for ethical technological development. Results. The analysis shows that software engineering predominantly defines fairness through formal and statistical notions focused on outcome distribution, whereas the humanities emphasize historically situated perspectives grounded in structural inequalities and power relations, with differences also evident in associated social benefits, proposed practices, and identified challenges. Conclusion. Perspectives from the human sciences can meaningfully contribute to software engineering by promoting situated understandings of fairness that move beyond technical approaches and better account for the societal impacts of technologies.

In this paper, we demonstrate an approach to quantum robust control based on the tools of geometric optimal control. The central objects of interest are the sensitivity functions defined as the coefficients in the Taylor expansion of the trajectory with respect to the (unknown, small) parameters which describe the deviation of the actual model from nominal one. In terms of these quantities, we formalize an optimal control problem where one searches for the optimal nominal trajectory which minimizes the size of the sensitivity while taking into account other aspects of the control design such as the energy of the control field. We consider in detail the case of a single qubit with a dephasing Hamiltonian term, and the optimal control problem of obtaining a state transfer by minimizing the weighted sum of the energy of the controlling field and the first order sensitivity. At the limit of a very large weight on the sensitivity, we obtain the optimal control which zeros the sensitivity and minimizes the control field energy. This problem has a rich mathematical structure which enables its solution in terms of elliptic integrals. For this problem, we obtain an explicit solution which is particularly simple and also smooth, avoiding discontinuities which are present in other approaches. We extend the results to the robust control of two quantum bits minimizing cross-talk contamination, as we show that such a problem decouples in two independent one qubit problems.

Two-dimensional (2D) van der Waals (vdW) multiferroics have emerged as a promising platform for next-generation multifunctional devices. Although recent studies have demonstrated that artificial heterostructures can combine dual ferroic orders and exhibit strong magnetoelectric coupling, their performance is sometimes limited by poor interface quality and inadequate long-term stability. By contrast, the realization of intrinsic single-phase materials with coexisting ferromagnetism and ferroelectricity remains a longstanding challenge in the field. Here we report the realization of a single-phase 2D vdW multiferroic system, CuIn0.2V0.8P2S6, which exhibits both ferromagnetism and room-temperature ferroelectricity. The intrinsic ferroelectric nature of CuIn0.2V0.8P2S6 was probed using ferroelectric tunnel junctions, which exhibit a large tunneling electroresistance with an ON/OFF ratio of 107 at 295 K. CuIn0.2V0.8P2S6 develops ferromagnetic ordering with the Curie temperature (TC) of 14.6 K, as evidenced by pronounced magnetic hysteresis and a relatively large remanent magnetization. Notably, the appearance of a magnetodielectric response below TC is consistent with the anticipated interplay between the ferromagnetic and ferroelectric orders. These results highlight a promising route toward single-phase van der Waals multiferroics with coexisting ferroic orders.

Wave-like dark matter described by a high-occupancy self-gravitating bosonic field provides a microscopic setting in which both amplitude and phase are dynamical. We study a one-dimensional Gross--Pitaevskii--Poisson toy model and ask which coarse-grained variable, if any, can be meaningfully compared with the 1+1-dimensional Kardar--Parisi--Zhang (KPZ) fixed point. We show that the relevant field is not the raw microscopic phase but a branch-resolved coarse-grained phase built from the sound sector. Above the Jeans scale and below the microscopic cutoff, self-gravity acts as a weak deformation of local sound dynamics. In this window the exact linear modes admit a local sound form, and a weakly nonlinear projection yields a nonvanishing same-chirality Burgers self-coupling. Under one-branch dominance together with a local Markov closure, the dominant branch reduces conditionally to a KPZ-type equation. We also formulate a dictionary from microscopic initial data to the canonical curved, flat, and stationary KPZ benchmarks. Our results do not establish KPZ universality for self-gravitating bosonic dark matter, but they identify the proper comparison field and the controlled regime in which an exact fixed-point test can be posed.

Reliable use of real-world data requires confidence that recorded evidence reflects what actually occurred at the moment of capture. In adversarial or incentive-misaligned cyber-physical settings, device-centric provenance and post-capture verification are insufficient to provide that guarantee. This paper builds on Proof-of-Location (PoL) as a baseline for establishing where and when events take place, and extends it with a witnessing-zone architecture in which multiple independent observers collectively validate physical events. The resulting approach produces auditable evidence artifacts that can support downstream systems in cyber-physical settings, without relying on centralized trust. Through representative scenarios and simulation-based evaluation, this paper shows how such architectures improve sensor data trustworthiness and resilience to fabricated or staged events.

Next generation ISAC networks operating in the mmWave and THz bands must provide physical layer secrecy against potential eavesdroppers (mobile and static) while coordinating distributed hybrid edge nodes under stringent power and QoS constraints. However, these requirements are rarely addressed in a unified manner in existing ISAC physical layer security designs. This paper proposes iBEAMS, a hierarchical Stackelberg--GNE--Bayesian framework for secure and energy efficient ISAC with distributed hybrid nodes. The proposed architecture integrates: (i) a Stackelberg leader at the ISAC base station that jointly optimizes total transmit power, power splitting among confidential data, artificial noise, and sensing, and broadcasts incentive prices to shape follower utilities; (ii) a Generalized Nash Equilibrium Game in which hybrid nodes select transmit powers and transmission versus jamming roles under coupled interference constraints and base-station-imposed leakage penalties; and (iii) a Bayesian cooperative refinement layer that forms geometry-aware jamming coalitions aligned with the posterior distribution of the eavesdropper's Angle of Arrival. Simulations over carrier frequencies from 28 GHz to 3 THz demonstrate hierarchical convergence of both base station and hybrid node decisions with stable cooperative friendly jamming. iBEAMS attains approximately 4.4--4.7 bps/Hz average secrecy rate, achieves about $2\times$ higher Secrecy Energy Efficiency (SEE), and delivers 30--70% higher SEE than a Stackelberg-decision-based baseline, while maintaining zero outage at 28 GHz. Moreover, the posterior-aligned jamming remains sharply directive and resilient under mobile eavesdroppers and increasing adversary density, indicating that iBEAMS can simultaneously act against static and mobile adversaries while coordinating hybrid edge nodes under limited power and QoS constraints.

This paper proposes a specification test for the conventional distributional assumptions of error terms in binary choice models, focusing on its tail properties. Based on extreme value theory, we first establish that the tail index of the unobserved error can be recovered by that of the observed covariates. The null hypothesis of the index being zero essentially covers the widely used probit and logit models. We then construct a simple and powerful statistical test for both cross-sectional and panel data, requiring no model estimation and no parametric assumptions. Monte Carlo simulations demonstrate that our test performs well in size and power, and applications to three empirical examples on firm export and innovation decisions and female labor force participation illustrate its general applicability.

Semileptonic $B_{(s)}$ decays are of great phenomenological interest because they allow to determine e.g. CKM matrix elements or test lepton flavor universality. Taking advantage of already existing lattice data, we demonstrate the analysis steps to extract the four form factors describing exclusive semileptonic $B_s\to D_s^*\ellν_\ell$ decays using the narrow width approximation. Our data are based on RBC/UKQCD's set of 2+1 flavor gauge field ensembles with Shamir domain-wall fermion and Iwasaki gauge field action featuring inverse lattice spacings of $a^{-1}=$1.785, 2.383, and 2.785 GeV as well as pion masses between 268 and 433 MeV. Light, strange and charm quarks are simulated using domain-wall fermions, whereas bottom quarks are generated with the relativistic heavy quark (RHQ) action.

We present a detailed analysis of the universal relationship between grain boundary (GB) free energy and GB self-diffusion coefficient derived by Borisov et al. (1964). This relationship was expressed by a simple equation that was used in many publications to predict GB energies on the basis of experimental diffusion data. Meanwhile, the physical assumptions and approximations underlying the Borisov model are poorly understood. As a result, the Borisov equation was often used outside its intended limits. Here, we re-derive the Borisov equation from ground up, identifying its underlying assumptions, correcting some errors and inconsistencies, and extending the original model to the case of impurity diffusion and diffusion by the interstitialcy and interstitial-dumbbell mechanisms. The meaning of the key assumption of the Borisov model, related to the free energy of the activated complex, is discussed, and ways to test this assumption are proposed.

This work follows from a previous study on the estimation of an initial distribution of telomere length from a senescence times distribution done in [10.1051/m2an/2026022, J. Olay{é}]. In this previous study, we have presented an estimation method based on the fact that our telomere shortening model can be approximated by a transport equation. This method has encouraging results, but fails to provide a good estimation when the variability of the initial telomere length distribution is too small. We improve here this method by approximating our model with an advection-diffusion equation, which allows us to better take into account the randomness of the shortening values. We show that under this approximation, there exists a simple link between the Laplace transform of the initial telomere length distribution and that of the senescence times distribution. Then, by using a numerical method for inverting Laplace transforms called Gaver-Stehfest algorithm, we exploit this link to construct a new estimator.

This study develops two robust, quantile-sliced moment systems, mean and median absolute deviation (MAD and MedAD moments), to serve as foundational tools in parametric modeling, statistical inference, and describing distributional location, scale, skewness, and tail behavior in settings where classical moments and L-moments fail. MAD moments use block-wise absolute deviations around the median and exist whenever the mean is finite, while MedAD moments replace expectations with medians, ensuring existence for all distributions, including heavy-tailed cases with undefined mean or variance. The systems exhibit strong consistency, slice-based robustness, and bounded influence. The results indicate that MAD and L moment ratios are efficient for light to moderate tails, whereas MedAD ratios remain uniquely stable when higher moments do not exist. Applications to Cauchy parameter estimation highlight the practical value of MedAD estimators as simple, fully robust alternatives to likelihood-based approaches. Together, these systems offer a unified, median-anchored framework for reliable distributional inference under heavy tails and contamination.

The proliferation of users, devices, and novel vehicular applications - propelled by advancements in autonomous systems and connected technologies - is precipitating an unprecedented surge in novel services. These emerging services require substantial bandwidth allocation, adherence to stringent Quality of Service (QoS) parameters, and energy-efficient implementations, particularly within highly dynamic vehicular environments. The complexity of these requirements necessitates a fundamental paradigm shift in service orchestration methodologies to facilitate seamless and robust service delivery. This paper addresses this challenge by presenting a novel framework for service orchestration in Unmanned Aerial Vehicles (UAV)-assisted 6G aerial-terrestrial networks. The proposed framework synergistically integrates UAV trajectory planning, Multiple-Access Control (MAC), and service placement to facilitate energy-efficient service coverage while maintaining ultra-low latency communication for vehicular user service requests. We first present a non-linear programming model that formulates the optimization problem. Next, to address the problem, we employ a Hierarchical Deep Reinforcement Learning (HDRL) algorithm that dynamically predicts service requests, user mobility, and channel conditions, addressing the challenges of interference, resource scarcity, and mobility in heterogeneous networks. Simulation results demonstrate that the proposed framework outperforms state-of-the-art solutions in request acceptance, energy efficiency, and latency minimization, showcasing its potential to support the high demands of next-generation vehicular networks.

Semi-supervised learning has attracted significant attention due to the proliferation of applications featuring limited labeled data but abundant unlabeled data. In this paper, we examine the statistical inference problem in an assumption-lean framework which involves a high-dimensional regression parameter, defined by minimizing the least squares, within the context of semi-supervised learning. We investigate when and how unlabeled data can enhance the estimation efficiency of a regression parameter functional. First, we demonstrate that a straightforward debiased estimator can only be more efficient than its supervised counterpart if the unknown conditional mean function can be consistently estimated at an appropriate rate. Otherwise, incorporating unlabeled data can actually be counterproductive. To address this vulnerability, we propose a novel estimator guaranteed to be at least as efficient as the supervised baseline, even when the conditional mean function is misspecified. This ensures the dependable use of unlabeled data for statistical inference. Finally, we extend our approach to the general M-estimation framework, and demonstrate the effectiveness of our methodology through comprehensive simulation studies and a real data application.

Inspired by the recent 90th anniversary of the Scottish Book we present some reflections about its impact. First we discuss new areas of mathematics it helped launch. Then we argue that it was actively used in stimulating the interests and results of junior mathematicians and students. Also, we summarize the progress during the decade that has passed since the publication of [55], which contained a review of solved problems from the Scottish Book. We also provide an overview of collections of open problems related in one way or another to the Scottish Book. All formulations of the Scottish Book problems in English are cited here from Mauldin, Richard Daniel (ed.) 2015: The Scottish Book. Mathematics from the Scottish Café. With selected problems from the New Scottish Book. 2nd updated and enlarged edition. Cham: Birkhäuser/Springer

We consider the Dirichlet-Neumann operator for a nearly spherical domain in R^n, and prove sharp analytic and tame estimates in Sobolev class. The novelty of this paper concerns technical improvements, the most important of which are the independence of the analyticity radius on the high norms and the regularity loss of one in the elevation function. These properties are expectable but nontrivial to prove. The result is obtained by introducing local charts and a convenient class of non-isotropic Sobolev spaces of high, possibly fractional tangential regularity and integer, limited regularity in the normal direction.

We review recently proposed Bayesian approaches for clustering high-dimensional data. After identifying the main limitations of available approaches, we introduce an alternative framework based on vertical consensus inference (VCI) to mitigate the curse of dimensionality in high-dimensional Bayesian clustering. VCI builds on the idea of consensus Monte Carlo by dividing the data into multiple shards (smaller subsets of variables), performing posterior inference on each shard, and then combining the shard-level posteriors to obtain a consensus posterior. The key distinction is that VCI splits the data vertically, producing vertical shards that retain the same number of observations but have lower dimensionality. We use an entropic regularized Wasserstein barycenter to define a consensus posterior. The shard-specific barycenter weights are constructed to favor shards that provide meaningful partitions, distinct from a trivial single cluster or all singleton clusters, favoring balanced cluster sizes and precise shard-specific posterior random partitions. We show that VCI can be interpreted as a variational approximation to the posterior under a hierarchical model with a generalized Bayes prior. For relatively low-dimensional problems, experiments suggest that VCI closely approximates inference based on clustering the entire multivariate data. For high-dimensional data and in the presence of many noninformative dimensions, VCI introduces a new framework for model-based and principled inference on random partitions. Although our focus here is on random partitions, VCI can be applied to any dimension-independent parameters and serves as a bridge to emerging areas in statistics such as consensus Monte Carlo, optimal transport, variational inference, and generalized Bayes.

Migrating heterogeneous high-performance computing (HPC) systems to resource-aware scheduling introduces both technical and behavioral challenges, particularly in production environments with established user workflows. This paper presents a case study of transitioning a production academic HPC cluster from node-exclusive to consumable resource scheduling mid-lifecycle, without disrupting active workloads. We describe an operational strategy combining a time-bounded compatibility layer, observability-driven feedback, and targeted user engagement to guide adoption of explicit resource declaration. This approach protected active research workflows throughout the transition, avoiding the disruption that a direct cut-over would have imposed on the user community. Following deployment, median queue wait times fell from 277 minutes to under 3 minutes for CPU workloads and from 81 minutes to 3.4 minutes for GPU workloads. Users who adopted TRES-based submission exhibited strong long-term retention. These results demonstrate that successful scheduling transitions depend not only on system configuration, but on aligning observability, user engagement, and operational design.