Background: Time-to-event data with multiple time scales are observed in many epidemiological and clinical studies. While models that allow for simultaneous consideration of multiple time scales for the hazard of an event have been proposed, their use is still not wide-spread in applied research. One reason for this might be the lack of convenient statistical software to estimate such models. Here we introduce the R-package TwoTimeScales. The package provides tools to estimate models for hazards that vary smoothly over two time scales, including proportional hazards models with such a two-dimensional baseline hazard. Extensions to competing risks models are implemented as well. Methodology is based on two-dimensional smoothing with P-splines. Results: We demonstrate the features of the R-package by analysing a freely available dataset containing post-surgery follow-up data on patients with breast cancer. We present two examples, a proportional hazards regression and a competing risks problem. Besides estimation, we illustrate the plotting utilities of the package. Conclusion: The R-package TwoTimeScales can be easily used to fit flexible hazard models with two time scales, allowing new perspectives in the analysis of time-to-event data with multiple time scales.

Reservoir computing leverages rich, non-linear dynamics to process temporal data. Quantum variants promise enhanced expressivity from high-dimensional Hilbert spaces, yet their practical applicability is hindered by hardware noise and concentration effects that can erase input-output distinguishability at large system sizes. In this work, we present and experimentally demonstrate a Quantum Extreme Learning Machine (QELM) tailored to state-of-the-art superconducting platforms, employing up to 124 qubits and circuits with more than 5,000 two-qubit gates on IBM Quantum computers. We introduce a practical multi-objective hyperparameter tuning strategy that jointly monitors observable variability, capacity, and task performance to identify noise-robust operating points. In addition, we develop a local eigentask analysis that enables computationally efficient feature selection and effective information retrieval. We report evidence of a regime of optimality that is identifiable at small scales and transferable across tasks and larger systems, and we achieve performances competitive with leading classical baselines on representative benchmarks for time-series forecasting and satellite image classification. Together, our results establish a viable and robust framework for large-scale, pre-fault-tolerant quantum machine learning and provide a foundation for extending reservoir-based methods to more expressive architectures and real-world scenarios.

The polarization of gamma rays produced in strong-field quantum electrodynamics (SFQED) is a fundamental and long-standing prediction, the verification of which has remained elusive, limiting both foundational tests and applications. Here, we report the first experimental measurement of gamma-ray polarization generated via all-optical nonlinear Compton scattering. Colliding a laser-wakefield-accelerated electron beam with an intense counter-propagating laser pulse reflected from a plasma mirror, we produce bright gamma rays in the strong-field regime ($a_0 > 1$). For gamma rays with $a_0 \approx 3$, a linear polarization degree of $\sim 50\%$ is measured via the azimuthal asymmetry of photoneutrons from a deuterium target, and independently verified by a Compton polarimeter.The results show excellent agreement with SFQED calculations employing the locally monochromatic approximation, while diverging from predictions based on the locally constant field approximation, highlighting the importance of quantum interference effects in this regime. Our work provides experimental evidence for polarization dynamics in SFQED, supports a key prediction of nonperturbative QED, and paves the way for compact, laser-driven sources of polarized gamma rays.}

This paper provides a solution to the open problen formulated in Glotko and Kuzminov article, as well as examples of non-strict universal epimorphisms and monomorphisms.

Ring Imaging Cherenkov (RICH) detectors are a key component of particle identification systems in many particle, nuclear and astroparticle physics experiments. Their ultimate performance depends not only on detector design and hardware implementation, but also crucially on the quality of pattern recognition and data analysis algorithms used to reconstruct Cherenkov ring images and to perform particle identification. In recent years, significant advances have been made both in traditional reconstruction approaches, such as likelihood-based methods and Hough-transform techniques, and in the application of modern machine learning tools. This contribution reviews the current state of RICH reconstruction algorithms, highlights representative use cases from operating experiments, and discusses emerging trends including global particle identification strategies and generative machine learning approaches for fast simulation and reconstruction.

Bin Packing with $k$ bins is a fundamental optimisation problem in which we are given a set of $n$ integers and a capacity $T$ and the goal is to partition the set into $k$ subsets, each of total sum at most $T$. Bin Packing is NP-hard already for $k=2$ and a textbook dynamic programming algorithm solves it in pseudopolynomial time $\mathcal O(n T^{k-1})$. Jansen, Kratsch, Marx, and Schlotter [JCSS'13] proved that this time cannot be improved to $(nT)^{o(k / \log k)}$ assuming the Exponential Time Hypothesis (ETH). Their result has become an important building block, explaining the hardness of many problems in parameterised complexity. Note that their result is one log-factor short of being tight. In this paper, we prove a tight ETH-based lower bound for Bin Packing, ruling out time $2^{o(n)} T^{o(k)}$. This answers an open problem of Jansen et al. and yields improved lower bounds for many applications in parameterised complexity. Since Bin Packing is an example of multi-machine scheduling, it is natural to next study other scheduling problems. We prove tight lower bounds based on the Strong Exponential Time Hypothesis (SETH) for several classic $k$-machine scheduling problems, including makespan minimisation with release dates ($P_k|r_j|C_{\max}$), minimizing the number of tardy jobs ($P_k||ΣU_j$), and minimizing the weighted sum of completion times ($P_k || Σw_j C_j$). For all these problems, we rule out time $2^{o(n)} T^{k-1-\varepsilon}$ for any $\varepsilon > 0$ assuming SETH, where $T$ is the total processing time; this matches classic $n^{\mathcal O(1)} T^{k-1}$-time algorithms from the 60s and 70s. Moreover, we rule out time $2^{o(n)} T^{k-\varepsilon}$ for minimizing the total processing time of tardy jobs ($P_k||Σp_jU_j$), which matches a classic $\mathcal O(n T^{k})$-time algorithm and answers an open problem of Fischer and Wennmann [TheoretiCS'25].

We present a novel augmented Lagrangian (AL) preconditioner for the solution of linear systems arising from finite element discretizations of elliptic interface problems with jump coefficients. The method is based on the Fictitious Domain with Distributed Lagrange Multipliers formulation and it is designed to improve the convergence of the Flexible Generalized Minimal Residual (FGMRES) method in the presence of large coefficient jumps. To reduce the computational cost, we also introduce a cheaper block-triangular variant of the preconditioner. We prove eigenvalue clustering for the ideal AL preconditioner and study the limiting behavior of the spectrum for the modified variant in terms of parameters and the size of the jumps. Numerical experiments on different immersed geometries confirm mesh-independent iteration counts and robustness over large coefficient jumps, with substantial reductions in wall-clock time for the modified approach.

The eruption of Nova Persei 1901 (GK Per) occurred 125 yrs ago; remarkably it still holds major surprises. Using data from the Spectro-Photometer for the History of the Universe, Epoch of Reionization, and Ices Explorer (SPHEREx), we find it has a bipolar molecular hydrogen shell. This shell, which has dimensions 18'x10', is co-spatial with the Halpha nebulosity surrounding the nova, which is purported to be an ancient planetary nebula (PN). The shell is detected most strongly in the 0--0 S(9) 4.6947 micron line. A filament of emission in the S(9) 4.6947 micron line is seen 45" SW of GKPer. This coincides, over much of its length, with the site of X-ray and non-thermal radio emission where the 1901 nova ejecta impinges on the ambient medium. We propose that the H_2 emission from the filament arises from the predicted neutral zone between the forward and reverse shocks. Since it is common for bipolar PNe to be accompanied by H_2 envelopes, it ostensibly suggests that the 18'x10' nebulosity is a conventional PN with a luminous, ionizing central source. We show this is not the case, and that the H$α$ nebulosity may be surrounding gas belonging to pre-existing material that was ionized during the 1901 eruption. The ionized gas is presently undergoing recombination on a timescale of ~3000 years, explaining why the nebulosity is still visible.

Cryptocurrency exchanges use proofs of liabilities (PoLs) to prove to their customers their liabilities committed on-chain, thereby enhancing their trust in the service. Unfortunately, a close examination of currently deployed and academic PoLs reveals significant shortcomings in their designs. For instance, existing schemes cannot resist realistic attack scenarios in which the provider colludes with an existing user. In this paper, we propose a new model, dubbed permissioned PoL, that addresses this gap by not requiring cooperation from users to detect a dishonest provider's potential misbehavior. At the core of our proposal lies a novel primitive, which we call Permissioned Vector Commitment (PVC), to ensure that a committed vector only contains values that users have explicitly signed. We provide an efficient PVC and PoL construction that carefully combines homomorphic properties of KZG commitments and BLS-based signatures. Our prototype implementation shows that, despite the stronger security, our proposal also improves server performance (by up to $10\times$) compared to prior PoLs.

A class of models with inverse seesaw mechanism is considered for arbitrary numbers p and q of new neutral fermions for each generation of leptons. The models containing a candidate particle for the role of warm dark matter are sorted using the inversion technique of an arbitrary block matrix in terms of Schur complement. Unlike the seesaw type I and II models with keV sterile dark matter neutrinos, in the inverse seesaw models mixing does not depend on the mass of dark matter particle, but depends only on the mass of heavy sterile pseudo-Dirac neutrinos.

We show how the computer algebra system OSCAR can be used to obtain topologically correct or visually pleasing drawings of real plane algebraic curves.

The ground state of the negatively charged NV center forms a spin-1 manifold providing a versatile platform for sensing and information processing. Here we present a scheme for implementing fast arbitrary qutrit gates in the low-field regime using monochromatic microwave pulses of constant intensity tuned to the zero-field transition. By concatenating pulses with appropriate phases and durations, the NV-ERC scheme is extended from SU(2) operations in the double-quantum subspace to the full three-level structure. We show that arbitrary SU(3) operations can be decomposed into rotations in the double-quantum subspace together with effective implementations of the generators related to $\hatλ_5$ and $\hatλ_8$. We illustrate this decomposition with a use case: performing quantum state tomography of the complete three-level density matrix.

The Nancy Grace Roman Space Telescope currently plans to survey nearly 6000 square degrees of the sky, mainly in the High-Latitude Wide-Area Survey (HLWAS) and Galactic Plane Survey (GPS). Although these surveys are optimized for other science, they are also a treasure trove for studying the nearby universe. The foreground of the HLWAS includes 59 known stellar streams, 14 known satellite galaxies, and 9 globular clusters in the Milky Way, and an additional 63 galaxies within 10 Mpc spanning several orders of magnitude in stellar mass. The GPS includes an additional 38 globular clusters in its footprint. We summarize and visualize these populations and discuss some of the relevant characteristics of the planned Roman observations. We also examine the expected astrometric performance of the core surveys based on the anticipated time-baselines between observations, and point out the substantial improvement provided by longer time intervals between repeat observations. In particular, the plan for a 6-month revisit timescale in the HLWAS is a missed opportunity from the perspective of proper motions. These data will nonetheless be a powerful new resource for studying the Milky Way and its neighborhood.

Let $E_n$ be Morava $E$-theory of height $n$. Let $R$ be a $p$-adically flat commutative ring spectrum. Then the Tate-valued Frobenius map endows $π_0 R$ with the structure of a $δ$-ring. On the other hand, we may form the $K(n)$-completed tensor product $L_{K(n)}(R \otimes E_n)$, which is a $K(n)$-local $E_n$-algebra. Then $π_0(L_{K(n)}(R \otimes E_n)) = LT_n \widehat{\otimes} π_0 R$ admits the structure of an algebra over the monad $\mathbb{T}(n)$ defined by Rezk. The $\mathbb{T}(n)$-algebra structure encodes the power operations of $L_{K(n)}(R \otimes E_n)$. In this paper we describe the $\mathbb{T}(n)$-algebra structure on $π_0(L_{K(n)}(R \otimes E_n))$.

We investigate the acceleration of stationary iterations for multi-term Sylvester equation by means of reduced rank extrapolation (RRE). Theoretical convergence results and implementations are provided for both small and large-scale problems. For the large-scale problems, an inexact non-stationary iteration is discussed, which makes use of low-rank matrix approximations. Numerical experiments illustrate the potential of the RRE acceleration which often leads to a substantial gain in convergence speed and therefore reducing the consumption of storage and computing time.

Carbon ion therapy is one of the most advanced forms of radiotherapy, promising improved efficacy against resistant cancers. However, the high precision offered by the carbon ion Bragg peak requires precise knowledge of the beam range inside the patient. We report the first experimental realization of range monitoring and portal imaging with a mixed ion beam, where carbon ions are treating the tumor while helium ions simultaneously accelerated to the same velocity fully traverse the patient and provide treatment feedback. Using the GSI synchrotron, a beam of 12C3+ and 4He1+ ions is accelerated, exploiting their nearly identical charge-to-mass ratios. Stable extraction with controlled helium fractions down to 7% is demonstrated. Beam characterization reveals that the helium ion Bragg peak can be cleanly separated from the carbon ion fragment background which enables accurate detection of sub-millimeter Bragg peak displacements. Mixed-beam radiographs of a lung-cancer-like phantom offer target position detection to better than 0.5 mm accuracy. This establishes mixed beams as a powerful modality for real-time image guidance in carbon ion therapy, uniquely providing simultaneous treatment delivery, range probing, and portal imaging. By overcoming range uncertainty inside the patient, mixed beams will enable to fully exploit the precision of carbon ion therapy.

We construct a finite-dimensional algebra derived equivalent to the example of Kershaw--Rickard. For the Kershaw--Rickard example the delooping level and the sub-derived delooping level are both infinite, while for our algebra both invariants are $0$. Thus the finiteness of these invariants is not preserved under derived equivalences.

In this paper, we first discuss the optimal convergence of the adaptive finite element methods for non-self-adjoint eigenvalue problems. We present new theoretical error estimators and computable error estimators for multiple and clustered eigenvalues with the help of the error estimators of finite element solutions for the corresponding source problems, and prove the equivalence between these two estimators. We propose an adaptive algorithm for the eigenvalue cluster and demonstrate that it achieves the optimal convergence rate.We also provide numerical experiments to support our theoretical findings.

The RAPTOR code is used to model how the time required for controlled termination of Ohmic plasmas scales from present tokamaks like TCV and JET, to reactor-grade tokamaks like ITER and DEMO. We show that ramping the plasma current $I_p$ down to 20% of the flat-top value over a time $Δt_{ramp-down}=τ_{LR}=L_i/R$, with internal inductance $L_i$ and resistance $R$ evaluated at flat-top conditions, results in an approximately self-similar peaking of the current density for these four tokamaks, indicating the adequacy of $τ_{LR}$ as a relevant timescale for cross-machine comparison, yielding $τ_{LR} =$ 0.033s (TCV), 2.87s (JET), 63.2s (ITER) and 166.9s (DEMO). Note that $τ_{LR}$ is easy to evaluate, both in systems codes and on a real-time control system. For the simulated ramp-downs with $Δt_{ramp-down}=τ_{LR}$, the end-of-ramp-down normalized internal inductance $\ell_{i3}$ is limited below 2. An $I_p$ ramp-down faster than $τ_{LR}=L_i/R$ requires a reversal of the boundary loop voltage and leads to the formation of a broad plasma layer carrying current in the direction opposite to the total plasma current, concomitant with $\ell_{i3}>2$, a central region with low magnetic shear and strongly peaked pressure profiles. Significant reduction of plasma volume and elongation, as foreseen for ITER and DEMO, is shown to counteract the reversal of current density and the $\ell_{i3}$ increase, while easing vertical stability control, potentially enabling faster $I_p$ ramp-down scenarios. Experimental and theoretical studies should be performed to test the feasibility of such fast termination scenarios, notably with respect to vertical position control, shape control and (resistive) beta limits. A simple analytical model is proposed and applied to estimate $τ_{LR}$ based on 0D engineering parameters for different tokamaks and for different operating points.

Context. Multi-element phased-array radio telescopes use digital beamforming to widen their field-of-view with numerous tied-array beams (TABs). These beams share bandpass variations and radio frequency interference (RFI). Yet, most pulsar and transient pipelines process each beam independently, ignoring shared spatial information. This leads to many RFI-dominated false positives that require extensive later sifting. Aims. We exploit multi-beam spatial information to stabilize bandpasses, suppress red noise and broad-band RFI, and drastically reduce false positives without degrading genuine astrophysical signals. Methods. We derive tied-array gain against residual phase dispersion, showing off-beam sources converge to the incoherent limit. Using chi-squared statistics, we analyze dividing a TAB by a beam-averaged reference and quantify the necessary smoothing. We test these predictions using LOFAR high-band antenna voltages (PSR B0329+54), simulations, and LOTAAS survey data (PSR J0250+5854). Results. Off-beam sources contribute nearly uniform power across beams once primary-beam effects are handled. Dividing by a smoothed multi-beam reference yields flatter dynamic spectra and equal or higher pulse signal-to-noise ratios compared to incoherent subtraction. Applied to LOTAAS data, this "beam flatfielding" cuts single-pulse false triggers by a factor of ~200 while preserving profile morphology and peak S/N. Conclusions. Beam flatfielding is a computationally cheap, simple post-beamforming step. For current and future multi-beam facilities, it provides stable bandpasses, closer-to-Gaussian noise statistics, and drastically fewer false positives, easing downstream classification without sacrificing sensitivity.

In an act of sabotage or terrorism, hazardous material might be released deliberately into the atmosphere to threaten individuals, e.g., those operating critical infrastructure. Hazardous materials in such a scenario include toxic industrial chemicals (TICs), which are often invisible to the human eye, making it difficult to detect and respond to releases in a timely manner. This contribution considers the scenario of an airborne hazardous release requiring rapid and reliable assessment, with a chemical, biological, radiological, and nuclear (CBRN) sensor system providing scarce and local measurements. We present a novel algorithm that couples these data with an advection-diffusion model to detect, localize, and quantify a moving and time-varying contaminant source. Unlike many existing methods, the approach identifies sources with unknown occurrence time and trajectory by incorporating spatial sparsity as prior information. The feasibility of the approach is demonstrated in a two-dimensional computational domain. To further increase the technology readiness level, we additionally propose a calibration methodology for the required three-dimensional flow models based on wind tunnel experiments. Finally, a strategy for coupling the framework with real-time sensor data within a digital twin environment is outlined to enable predictive decision support in emergency scenarios.

Authentication is crucial to confirm that an individual or entity trying to perform an action is actually who or what they claim to be. In dynamic environments such as the Internet of Things (IoT), Internet of Vehicles (IoV), healthcare, and smart cities, security risks can change depending on varying contextual factors (e.g., user attempting to authenticate, location, device type). Thus, authentication methods must adapt to mitigate changing security risks while meeting usability and performance requirements. However, existing adaptive authentication systems provide limited guidance on (a) representing contextual factors, requirements, and authentication methods (b) understanding the influence of contextual factors and authentication methods on the fulfilment of requirements, and (c) selecting effective authentication methods that reduce security risks while maximizing the satisfaction of the requirements. This paper proposes a framework for engineering adaptive authentication systems that dynamically select effective authentication methods to address changes in contextual factors and security risks. The framework leverages a contextual goal model to represent requirements and the influence of contextual factors on security risks and requirement priorities. It uses an extended feature model to represent potential authentication methods and their impacts on mitigating security risks and satisfying requirements. At runtime, when contextual factors change, the framework employs a Fuzzy Causal network encoded using the Z3 SMT solver to analyze the goal and feature models, enabling the selection of effective authentication methods. We demonstrate and evaluate our framework through its application to real-world authentication scenarios in the IoV and the healthcare domains.

Strongly self-absorbing $\mathrm{C}^*$-algebras play a distinguished role in the classification of nuclear $\mathrm{C}^*$-algebras. Their dynamical analogues were introduced and extensively studied by Szabó. In this paper, we propose a conjecture regarding the equivariant $KK$-theory of strongly self-absorbing $\mathrm{C}^*$-dynamical systems of compact groups in the equivariant bootstrap category; an affirmative answer to this conjecture would lead to classification results. We settle this conjecture for all finite EPPO (every element has a prime-power order) groups. In the course of our proof, we establish a Künneth-type formula for the equivariant $K$-theory of $\mathrm{C}^*$-algebras equipped with finite cyclic group actions -- more precisely, for the cyclotomic part of the equivariant $K$-groups introduced by Meyer and Nadareishvili -- under a certain unique divisibility assumption.

Learning under non-smooth objectives remains a fundamental challenge in machine learning, as abrupt changes in conditioning variables can induce highly non-smooth loss landscapes and destabilize optimization. This difficulty is particularly pronounced in non-autonomous dynamical systems driven by discontinuous inputs, where widely used optimization methods, including recent neural smoothing approaches, exhibit unreliable convergence or strong hyperparameter sensitivity. To address this issue, we propose Deep Predictor-Corrector Networks (DePCoN), a multi-scale learning framework that stabilizes optimization by learning scale-consistent parameter update rules across a hierarchy of smoothed inputs. Rather than treating smoothing as a fixed preprocessing choice, DePCoN integrates smoothing into the learning dynamics itself through a learned predictor-corrector mechanism. Across biological and ecological benchmarks with discontinuous inputs, DePCoN consistently achieves more robust and faster convergence than existing methods while substantially reducing sensitivity to hyperparameter choices. Beyond dynamical systems, our approach provides a general learning principle for stabilizing optimization under non-smooth objectives.

Photosphere radius expansion (PRE) bursts provide a crucial tool for constraining the mass and radius of neutron stars. In this study, we analyze time-resolved spectroscopic data from XTE J1810-189 in 2008, which exhibit evidence of a PRE event. We report here the possibility of a small-size and low-mass neutron star in XTE J1810-189 with use of the advantage of the direct cooling tail method. We obtained three sets of results, which can be broadly divided into high metal abundance (20 $\rm{Z}_{\odot}$ and 40 $\rm{Z}_{\odot}$), low metal abundance and hydrogen-rich (pure hydrogen, $\rm{Z}_{\odot}$, 0.3 $\rm{Z}_{\odot}$, 0.1 $\rm{Z}_{\odot}$, 0.01 $\rm{Z}_{\odot}$), and pure helium. In the high-metallicity scenario, the inferred neutron star mass is $<1.3\,M_{\odot}$ with a radius $<8\,\rm{km}$. In the low-metallicity, hydrogen-rich case, the mass ranges from 0.3 to 2.1 $M_{\odot}$ with radii of 7-13 km. For a pure-helium composition, we find two mass solutions: $1.08_{-0.22}^{+1.32}M_{\odot}$ (with $R>14\,\rm{km}$) and $2.5-2.9\,M_{\odot}$ (above the highest observed neutron star masses). Additionally, we applied the touchdown method combined with an MCMC analysis, the results are consistent with those from the direct cooling tail method, but with a broader range. Our analysis of the time-resolved spectrum of burst suggests a high-metallicity atmosphere, but new observations are required to confirm this result.

Recent measurements of electroweak phenomena from the Compact Muon Solenoid (CMS) experiment at the Large Hadron Collider are summarized. The standard model of particle physics was tested through highly precise determinations of its key electroweak parameters and through measurements of electroweak processes in proton-proton collisions at unprecedented center-of-mass energies of up to $13.6 \, \mathrm{TeV}$. The performance of the CMS experiment establishes its key role in the study of electroweak physics, with many measurements performed either for the first time or with the best precision at a proton-proton collider, in some cases reaching or even surpassing the precision of legacy results from lepton colliders. Recent electroweak results from the CMS experiment include: measurements of the W and Z bosons production cross sections; high-precision measurements of the forward-backward asymmetry in Drell-Yan production and of the effective leptonic electroweak mixing angle; measurements of tau lepton properties and of multiboson production and vector boson scattering rates.

We propose and analyze a perturbative regularization method to approximate quadratic optimization problems with finite-dimensional degeneracy. The original problem is first approximated by a regularized problem depending on a small positive parameter, and then discretized using the finite element method. The resulting families of continuous and discrete functionals $Γ$-converge to the functional of the original problem and the corresponding minimizers converge as well. Our method generalizes the approach proposed in Kaleem et al. (2026) for numerically approximating pure Neumann problems, which represents the cornerstone of a sparsity-preserving, numerically efficient alternative to the methods developed in Bochev and Lehoucq (2005), Ivanov et al. (2019) and Roccia et al. (2024). References: A. Kaleem, C. Gebhardt, and I. Romero. On the pure traction problem of linear elasticity: a regularized formulation and its robust approximation. arXiv preprint arXiv:2602.04359, 2026. P. Bochev and R. Lehoucq. On the finite element solution of the pure Neumann problem. SIAM Review, 47:50-66, 2005. M. Ivanov, I. Kremer, and M. Urev. Solving the pure Neumann problem by a finite element method. Numerical Analysis and Applications, 12:359-371, 2019. B. Roccia, C. Alturria, F. Mazzone, and C. Gebhardt. On the homogeneous torsion problem for heterogeneous and orthotropic cross-sections: theoretical and numerical aspects. Applied Numerical Mathematics, 201:579-607, 2024.

A vocabulary is a list of words designating subsets from a grand set X. We model a vocabulary as a partition of X and study the aggregation of individual vocabularies into a collective one. We characterize aggregation rules when X is linearly ordered and each word of the vocabulary spans an order interval. We allow for individual vocabularies to differ both in the number and in the span of their words. Under a suitable restriction on agents' preferences, we show that our aggregation rules are strategy-proof.

We present effective a priori adaptive numerical methods for estimating the blow-up time for solutions of autonomous ODEs. The novelty of our approach is to base our adaptive steps on the sensitivity of an auxiliary hitting time. We provide results on the theoretical error rates, and show that there is a benefit in terms of computational effort in choosing our adaptive algorithm over alternative approaches. Numerical experiments support our theoretical results and show how the methods perform in practice.

We consider accelerated versions of the operator Sinkhorn iteration (OSI) for solving scaling problems for completely positive maps. Based on the interpretation of OSI as alternating fixed point iteration, it has been recently proposed to achieve acceleration by means of nonlinear successive overrelaxation (SOR), e.g.~with respect to geodesics in Hilbert metric. The direct implementation of the proposed SOR algorithms, however, can be numerically unstable for ill-conditioned instances, limiting the achievable accuracy. Here we derive equivalent versions of OSI with SOR where, similar to the original OSI formulation, scalings are applied on the fly in order to take advantage of preconditioning effects. Numerical experiments confirm that this modification allows for numerically stable SOR-acceleration of OSI even in ill-conditioned cases.