We present a study of minimal unsatisfiable subsets (MUSs) of 2-CNF Boolean formulas, building on the Abbasizanjani-Kullmann classification of minimally unsatisfiable 2-CNFs (2-MUs). We start by giving a linear-time procedure for recognising 2-MUs. Then we study the problem of finding one simple MUS. On the one hand we extend the results by Kleine Buening et al, which showed NP-completeness of the decision, whether a deficiency-1 MUS exists. On the other hand we show that deciding/finding an MUS containing one or two unit-clauses (which are special deficiency-1 MUSs) can be done in polynomial time. Finally we present an incremental polynomial time algorithm for some special type of MUSs, namely those MUSs containing at least one unit-clause. We conclude by discussing the main open problem, developing a deeper understanding of the landscape of easy/hard MUSs of 2-CNFs.

The SUPerconduction AXion search experiment (Supax) is a future haloscope-type detector designed to probe axion-like particles (ALPs) as candidates for dark matter and solutions to the strong-CP problem in the mass range between $8\,μ$eV and $30\,μ$eV. In the course of the preparation of Supax, a prototype experiment was built and operated. Using a copper cavity, cooled down to a temperature of 2 K and operated in a magnetic field of 12 T, we probe axion masses around $34\,μ$eV and exclude axion-photon couplings down to $|g_{aγγ}|> 1.6\cdot 10^{-13}$GeV$^{-1}$. The data was also used to exclude dark photons in the same mass range with a kinetic mixing parameter of $χ> 1.4\cdot 10^{-12}$. Details of the experimental setup and the analysis strategy are summarized in this paper.

Nuclear quantum effects (NQEs) are often central to a predictive understanding of chemical reactions and rates. While their incorporation in gas-phase reactions is well established, studies involving condensed matter often neglect or approximate such effects. To clarify the role of NQEs in multi-step, multi-molecular reactions in a molecular crystal, we compare atomistic simulations of the thermal decomposition of the energetic material TATB using path integral molecular dynamics (PIMD), the more approximate quantum thermal bath (QTB), and classical MD (ClMD). PIMD samples the quantum canonical distribution by representing each atom as a string of beads (replicas), while QTB uses a frequency-dependent thermostat to reproduce the Bose-Einstein distribution. We find that PIMD results in faster chemical decomposition of the TATB crystal compared to ClMD, as the initial steps involve hydrogen transfer processes. Interestingly, some of the subsequent reactions (e.g. the formation of N2) occur on identical timescales. The PIMD simulations also predict a reduction in overall activation energy by ~8% as compared to the classical result. As observed in model systems and simple unimolecular gas-phase reactions, the QTB significantly overestimates quantum acceleration of chemical reactions and the reduction in activation energy. A comparison of the kinetic energy operator in PIMD and the centroid dynamics provides insight into the physics behind the differences between the QTB and PIMD results.

We present a constructive formalization of Abstract Rewriting Systems (ARS) in the Agda proof assistant, focusing on standard results in term rewriting. We define a taxonomy of concepts related to termination and confluence and investigate the relationships between them and their classical counterparts. We identify, and eliminate where possible, the use of classical logic in the proofs of standard ARS results. Our analysis leads to refinements and mild generalizations of classical termination and confluence criteria. We investigate logical relationships between several notions of termination, arising from different formulations of the concept of a well-founded relation. We illustrate general applicability of our ARS development with an example formalization of the lambda calculus.

Current research on three-dimensional metamaterial has largely focused on conventional strut, plate, and shell-based lattice designs. Although these designs offer several advantages, they possess inherent limitations that can restrict their performance in certain applications, motivating the exploration of alternative structural topologies. Here, we present a large-scale, symmetry guided framework for the generation and analysis of architected metamaterials based on all 36 cubic space groups. Using a voxel-based representation, we construct a database of approximately 1.95 million periodic unit cells spanning a broad range of relative densities and topological complexity. This dataset reveals a rich elastic property landscape shaped by crystallographic symmetry, including rare pentamode designs with high bulk to shear ratios such as $K/G \approx 166$ , isotropic-auxetic architectures with Poisson's ratio as low as $ν=-0.76$, and structures achieving up to 93% of the Hashin-Shtrikman upper bound on stiffness. Complementing the dataset, we develop a three-dimensional convolutional neural network surrogate model trained and evaluated on the full database to predict strain-energy density values under uniaxial, shear, and hydrostatic loading. Together, this work establishes a comprehensive atlas of cubic symmetric metamaterials and provides a pre-trained model for the accelerated discovery and design of 3D architected materials with extreme mechanical properties.

We introduce the Huffman-Bucket Sketch (HBS), a simple, mergeable data structure that losslessly compresses a HyperLogLog (HLL) sketch with $m$ registers to optimal space $O(m+\log n)$ bits, with amortized constant-time updates, acting as a drop-in replacement for HLL that retains mergeability and substantially reduces memory requirements. We partition registers into small buckets and encode their values with a global Huffman codebook derived from the strongly concentrated HLL rank distribution, using the current cardinality estimate for determining the mode of the distribution. We prove that the Huffman tree needs rebuilding only $O(\log n)$ times over a stream, roughly when cardinality doubles. The framework can be extended to other sketches with similar strongly concentrated distributions. We provide preliminary numerical evidence that suggests that HBS is practical and can potentially be competitive with state-of-the-art in practice.

The influence of chiral molecular potentials on phase-coherent transport in superconducting Josephson junctions is investigated. Within a Bogoliubov-de Gennes tight-binding framework, an SNS junction functionalized by adsorbed chiral molecules is modeled, where electrostatic gradients generated by the molecules induce spin-orbit coupling in the normal region. The equilibrium charge current-phase relation is found to remain largely insensitive to molecular chirality in symmetric, zero-field configurations. In contrast, the spin supercurrent exhibits a pronounced chirality-dependent response, with opposite enantiomers producing distinct and anisotropic spin-polarized Josephson currents. The resulting handedness contrast can be enhanced through control parameters such as molecular orientation and the strength of the induced spin-orbit coupling. The temperature dependence of these currents further shows that the chirality-dependent signatures persist across a range of temperatures well below the superconducting critical temperature. These results establish Josephson interferometry as a phase-sensitive and accessible platform for detecting molecular chirality and highlight spin-polarized superconducting transport as a promising route toward integrating chiral molecular functionality into superconducting spintronic devices.

Tolerance intervals provide bounds that contain a specified proportion of a population with a given confidence level, yet their construction remains challenging when parametric assumptions fail or sample sizes are small. Traditional nonparametric methods, such as Wilks' intervals, lack flexibility and often require large samples to be valid. We propose a fully nonparametric approach for constructing one-sided and two-sided tolerance intervals using a calibrated Gibbs posterior. Leveraging the connection between tolerance limits and population quantiles, we employ a Gibbs posterior based on the asymmetric Laplace (check) loss function. A key feature of our method is the calibration of the learning rate, which ensures nominal frequentist coverage across diverse distributional shapes. Simulation studies show that the proposed approach often yields shorter intervals than classical nonparametric benchmarks while maintaining reliable coverage. The framework's practical utility is illustrated through applications in ecology, biopharmaceutical manufacturing, and environmental monitoring, demonstrating its flexibility and robustness across diverse applications.

We study the long-time dynamics of a bulk-surface convective Cahn--Hilliard system describing phase separation processes with bulk-surface interaction. The presence of convection terms leads to a non-autonomous dynamical system and prevents the associated free energy from being a Lyapunov functional, which makes the analysis of the asymptotic behavior considerably more challenging. First, we establish an instantaneous regularization property for weak solutions. Next, interpreting the evolution as a continuous two-parameter process, we prove the existence of a minimal pullback attractor. Finally, under suitable decay assumptions on the velocity fields, we show that every solution converges as $t\to\infty$ to a single steady state. The proof of this convergence relies on the Łojasiewicz--Simon inequality combined with customized decay estimates that compensate for the lack of a monotone energy functional.

We introduce the notion of F-convexity as a general extension of power convexity. We characterize the F-convexities preserved under the heat flow in the n-dimensional Euclidean space, and identify the strongest and the weakest ones among them. We also characterize the F-convexities preserved under the Dirichlet heat flow in convex domains.

Hybrid quantum computing systems that combine discrete-variable qubits with continuous-variable qumodes offer promising advantages for quantum simulation, error correction, and sensing applications. However, existing quantum software frameworks lack native support for expressing and manipulating hybrid circuits, forcing developers to work with fragmented toolchains or rely on simulation-coupled representations that limit scalability. We present Hybridlane, an open-source software development kit providing a unified frontend for hybrid continuous-discrete variable quantum computing. Hybridlane introduces automatic wire type inference to distinguish qubits from qumodes without manual annotations, enabling compile-time validation of circuit correctness. By decoupling gate semantics from matrix representations, Hybridlane can describe wide and deep circuits with minimal memory consumption and without requiring simulation. The framework implements a comprehensive library of hybrid gates and decompositions following established instruction set architectures, while remaining compatible with PennyLane's extensive qubit algorithm library. Furthermore, it supports multiple backends including classical simulation with Bosonic Qiskit and hardware compilation to Sandia National Laboratories' QSCOUT ion trap. We demonstrate Hybridlane's capabilities through bosonic quantum phase estimation and ion trap calibration workflows.

Meta-analytic methods tend to take all-or-nothing approaches to study-level heterogeneity, assuming all studies are heterogeneous or homogeneous, leading to inefficiency and/or bias in estimation and inference. In this paper, we develop a heterogeneity-adaptive meta-analysis in linear models that adapts to the amount of information shared between datasets. The primary mechanism for the information-sharing is a shrinkage of dataset-specific distributions towards a new "centroid" distribution through a Kullback-Leibler divergence penalty. The Kullback-Leibler divergence is uniquely geometrically suited for measuring relative information between datasets, and leads to relatively simple closed form estimators with intuitive interpretations. We establish our estimator's desirable inferential properties without assuming homogeneity of dataset parameters. Among other results, we show that our estimator has a provably smaller mean squared error than the dataset-specific maximum likelihood estimators, and establish asymptotically valid inference procedures. A comprehensive set of simulations highlights our estimator's versatility, and an analysis of data from the eICU Collaborative Research Database illustrates its performance in a real-world setting.

Quantum hypergraph states extend the well-studied class of graph states by taking into account multi-qubit interactions through hyperedges. They provide a powerful framework to represent a family of quantum states with genuine multipartite entanglement. In this review, we provide a compact overview of the formal structure, entanglement characteristics, and operational relevance of hypergraph states in quantum information theory. We begin by introducing their mathematical foundations and generalizations of the stabilizer formalism. A central focus is placed on their entanglement properties, including the classification under local unitary (LU) and stochastic local operations with classical communication (SLOCC), the quantification of multipartite entanglement, and detection techniques via entanglement witnesses. We also explore other nonclassical features of hypergraph states, such as contextuality and genuine multipartite nonlocality, derived from stabilizer-based Bell-type inequalities. Additional attention is given to the role of hypergraph states in error correction, and as a computational resource in measurement-based quantum computation (MBQC), and to their non-stabilizer character - quantified via resource-theoretic measures of quantum magic. Finally we review their generalization to higher dimensions, i.e. to qudits and continuous variables.

Protoclusters represent sites of accelerated galaxy formation and extreme astrophysical activity characteristic of dense environments. Identifying massive protoclusters and mapping their spatial structures are therefore crucial first steps in understanding how the large-scale environment influences galaxy evolution. We combine wide-field Ly$α$ imaging from the ODIN survey with extensive DESI and ancillary spectroscopy across the extended COSMOS and XMM-LSS fields ($\approx$14 deg$^2$) to search for massive protoclusters. We confirm six systems at $z\approx 2.4$ and $z\approx 3.1$, reconstruct their three-dimensional structures, estimate descendant halo masses, and, for one structure at $z\approx 3.12$, demonstrate that overlapping narrowband filters ($NB497$ and $N501$) provide accurate redshift tomography for emission-line galaxies. One protocluster at $z\approx 2.45$ overlaps with one of the LATIS tomographic fields, enabling direct comparison between galaxy and H {\sc i} overdensities traced by Ly$α$ forest absorption. Another at $z\approx 3.12$ hosts a massive quiescent galaxy ($M_{\ast} \approx 1.2 \times 10^{11}M_\odot$), indicating early quenching in a dense environment. By comparing Ly$α$ emission properties across environments, we find that protocluster galaxies exhibit higher median line fluxes and a deficit of faint emitters relative to the field. The effect is strongest when both 2D and 3D density information are combined, indicating that galaxies in the densest protocluster cores are most affected by environmental processes. This effect is stronger at $z\approx3.1$ than at $z\approx2.4$, suggesting possible redshift evolution.

Due to its ability to summarise 'real-time' epidemic behaviour, the time-dependent reproduction number, Rt, is a useful metric for tracking pathogen transmission and quantifying the effects of interventions during infectious disease outbreaks. The predominant models underlying inferred Rt trajectories are renewal equations, their success owing in part to the relatively few assumptions they require. One necessary assumption is the generation time distribution, which summarises the time periods between infections in infector-infectee transmission pairs. This distribution is typically assumed to be the same across all members of a population. In reality, however, it may vary systematically between population groups. In this study, we consider two Rt inference frameworks based on renewal equation models: one for a single, homogeneous group and another accounting for a structured population. We compare the estimates of Rt generated by the two models and investigate, both analytically and through simulations, under which conditions the conclusions drawn from these modelling paradigms differ. We also demonstrate a methodology for selecting the generation time for the one-group model that correctly encapsulates variations between different population groups; this allows us to use a renewal framework for a one-group model to infer Rt when, in fact, the population is structured. Finally, we use real epidemic data to demonstrate that practical Rt estimates can differ depending on whether the underlying model is the one-group model or the multi-group model. Our results motivate the need for rigorous collection of detailed epidemic data and consideration of differences between population groups to improve the accuracy of Rt estimates that are used to guide public health policy responses.

Using Vakarelov's theory of lattice logics with negation, we introduce the (co)quasiintuitionistic logic, and prove its soundness and completeness with respect to the class of (co)quasiintuitionistic algebras. Combining these algebras together, we obtain biquasiintuitionistic algebras and the biquasiintuitionistic logic. Their further extension with the Skolem algebra structure defines Akchurin algebras and the respective logic, which is a product of biquasiintuitionistic and biintuitionistic logics, featuring four distinct negations. Next we generalise the framework of spectral presheaves (which is a main object in the Butterfield--Isham--Döring topos theoretic approach to quantum mechanics) to arbitrary complete orthocomplemented lattices, and show that the orthocomplementation determines two negation operators on the spectral presheaf (one paraconsistent, another paracomplete), equipping the set of all closed-and-open subpresheaves of a spectral presheaf with the structure of a biquasiintuitionistic algebra. Combined with the generic Skolem (i.e. Heyting and Brouwer) algebra structure of this set, this gives a particular instance of an Akchurin algebra. We also show that the underlying orthocomplemented lattice can be reconstructed as an internal object of the spectral presheaf, resulting as the image of a double coquasiintuitionistic (resp., quasiintuitionistic) negation monad (resp., comonad). Finally, we prove a no-go theorem for the claim that the spectral presheaf is a model of a dialectical (or any other) relevance logic.

This paper presents a study of the charmless three-body decays ${B^0_{(s)} \to K_{\mathrm{S}}^0 h^+ h^{\prime -}}$ (where $h^{(\prime)} = π, K$), using a sample of $pp$ collision data collected by the LHCb experiment, corresponding to an integrated luminosity of $9\mbox{\,fb}^{-1}$. The decay ${B^0_s \to K_{\mathrm{S}}^0 K^+ K^-}$ is observed for the first time, and the following ratios of branching fractions are measured: \begin{alignat*}{6} &\frac{{\cal B}(B^0 \to K^0_{\mathrm{S}} K^+ K^-)}{{\cal B}(B^0 \to K^0_{\mathrm{S}} π^+π^-)} &&= 0.578 &&\pm 0.007 &&\pm 0.017\,, &\frac{{\cal B}(B^0 \to K^0_{\mathrm{S}} K^\pmπ^\mp)}{{\cal B}(B^0 \to K^0_{\mathrm{S}} π^+π^-)} &&= 0.1363 &&\pm 0.0035 &&\pm 0.0051\,, &\frac{{\cal B}(B^0_s \to K^0_{\mathrm{S}} π^+π^-)}{{\cal B}(B^0 \to K^0_{\mathrm{S}} π^+π^-)} &&= 0.269 &&\pm 0.011 &&\pm 0.015 && \pm 0.008\,, &\frac{{\cal B}(B^0_s \to K^0_{\mathrm{S}} K^+ K^-)}{{\cal B}(B^0 \to K^0_{\mathrm{S}} π^+π^-)} &&= 0.0303 &&\pm 0.0041 &&\pm 0.0025 && \pm 0.0009\,, &\frac{{\cal B}(B^0_s \to K^0_{\mathrm{S}} K^\pmπ^\mp)}{{\cal B}(B^0 \to K^0_{\mathrm{S}} π^+π^-)} &&= 1.818 &&\pm 0.021 &&\pm 0.031 && \pm 0.056\,, \end{alignat*} where the uncertainties are statistical, systematic, and due to knowledge of the ratio of hadronisation fractions of the $B^0_s$ and $B^0$ mesons, respectively.

We study the full evolution of a 1.313 Msun white dwarf star that descended from a 9 Msun main-sequence progenitor with an initial metallicity of Z=0.02. Using MESA r24.08.01, we calculate its entire evolution from pre-ZAMS to the WD cooling curve, including both the evolution through 139 thermal pulses and the post-AGB phase. The resulting remnant is an ultramassive H-deficient WD, for which the composition, in mass fraction, is 47.7% O16, 39.7% Ne20, 4.2% Mg24, 3.3% Na23 and 0.386% C12 -- corresponding to a total mass of 5 x 10^-3 Msun of C --, surrounded by a 1.5 x 10^-5 Msun He layer. We also investigate the effects of fully suppressing the TP-SAGB stage by adopting a high mass-loss rate only after the second dredge-up, and find only minor differences in the final mass and composition. In addition, we calculate models with and without phase separation during the WD stage, estimating a cooling delay of only 16 Myr. This is the first ultramassive white dwarf sequence for which both the TP-SAGB and post-AGB stages are calculated and, to our knowledge, the most massive WD model from complete evolution for which cooling times and detailed abundance profiles are published

Motivated by the results for Magic: The Gathering presented in [CBH20] and [Bid20], we study a (different) computability problem about winning strategies in Yu-Gi-Oh! Trading Card Game, a popular card game developed and published by Konami. We show that the problem of establishing whether, from a given game state, a given computable strategy is winning is undecidable. In particular, not only do we prove that the Halting Problem can be reduced to this problem, but also that this problem is actually $Π^1_1$-complete. We extend this last result to all strategies with a reduction on the set of countable well orders, a classic $\boldsymbolΠ^1_1$-complete set. For these reductions, we present two legal decks (according to the current Forbidden & Limited List of Yu-Gi-Oh! Trading Card Game) that can be used by the player who goes first to perform them.

Loops of portal matter (PM) fields carrying both dark and Standard Model (SM) quantum numbers can lead to the kinetic mixing (KM) of the SM photon and the analogous dark photon (DP) of a phenomenologically interesting magnitude. However, in specific frameworks, different loops of these same PM fields can also lead to other new types of interactions between some of the SM fields and the DP via the generation of `dark moment'-like couplings, even though the SM fields carry a zero dark charge at tree-level. In recent work, this possibility has been explored for the case when these SM fields are fermionic. In this paper, we extend this idea to the case of the SM $W$ boson employing a previously examined model wherein PM consists of a complex scalar triplet plus a complex singlet, both of which obtain vevs and thus also generate the DP mass. While this setup results in a somewhat stronger interaction between the DP and the $W$ than in the familiar KM setup, the rate for $W+$DP production at the LHC is shown to still be rather small and is very difficult to observe due to large SM backgrounds. The direct production of the scalar PM itself, however, is shown to lead to similar new physics signatures but with much larger rates and are considered here in their own right. The properties of such new PM states may already be constrained by LHC searches in both the $W^\pm+$MET and $W^+W^-+$MET channels.

A comparison of the {\it ab initio} calculations using the i-DMFT Method by Di Liu et al. (2025) with benchmark potential curves for three HX(F,Cl,Br) halides shows their inaccuracy in the domain around equilibrium - they do not reproduce quantitatively the results of the Born-Oppenheimer approximation - and also they predict a qualitatively wrong behavior in the Van der Waals region of large distances, thus, contradict the multipole expansion.

Earth's climate is influenced by over a dozen feedbacks, but only three dominate its long-term climate behavior. Models of the exoplanet habitable zone (HZ) assume that this is similar for other Earth-like planets. We used dynamical simulations to study Earth-like planets with a fourth, (potentially strong) generalized climate feedback. Across over 20,000 climate simulations, we find that the addition of the fourth feedback produces novel behaviors, including runaway and chaotic climate trajectories, that are more diverse than one would expect based on Earth's climate configuration. Non-negligible fourth feedbacks -- if negative -- would not lessen the probability of planets with temperate climates. However, positive fourth feedbacks decrease the fraction of exo-Earth candidates that are long-term habitable. Therefore, strong fourth feedbacks will alter (and mostly shrink) the boundaries of the classical habitable zone. When combined with occurrence rates of Earth-sized planets around sun-like stars, our results imply that the fraction of stars hosting rocky planets with temperate climates may be substantially lower than classical estimates under Earth-like climate assumptions. Our results are subject to the validity of the model assumptions and not intended to represent conclusive predictions about exoplanet populations but rather to demonstrate the potential climate diversity that emerges from non-Earth-like model configurations. Our conclusions provide context on sample sizes and science questions for next-generation exoplanet surveys.

We record a folklore theorem that says a partial group embeds in a group if and only if each word has at most one possible multiplication, regardless of choice of parenthesization. We further investigate the partial groups which are exemplars of non-embeddability. Finally we show that a partial groupoid embeds in a groupoid if and only if its reduction embeds in a group.

We investigate some fundamental properties of a peculiar class of special functions strictly related to Bessel, Anger and Weber functions, whose introduction was originally motivated by linear susceptibility tensor calculations in a hot, magnetised plasma. We show that these functions are solutions of an inhomogeneous Bessel ODE, with specified initial conditions and a distinct right-hand-side term fulfilling the Nielsen's requirement. Beside deriving recurrence relations and an alternative representation involving incomplete Anger-Weber functions, we show that these functions admit a simple series expansion in terms of Bessel functions of integer order, obtained by resorting to the Jacobi-Anger formula. In plasma applications this eventually leads to expressions involving infinite sums of products of Bessel functions, not particularly apt to numerical evaluation ought to their slow convergence rate when the particle's gyro-radius is larger than the wavelength. By exploiting the previously determined recurrence properties of the new class of functions we present a particularly simple derivation of the linear susceptibility tensor that enables to avoid this inconvenience.

Communication blackout due to the plasma layer creates a critical telemetry gap for re-entry vehicles. To mitigate this, we present the first fully-coupled simulation of high-voltage pulsed discharges interacting with a Mach 24 flowfield using an advanced numerical framework. The results demonstrate that the applied electric field generates a large, non-neutral plasma sheath near the cathode, depleting electron density by several orders of magnitude over a distance commensurate with the height of the shock layer. This depletion window effectively reduces the attenuation of a 4 GHz signal from 60% to 4% with a manageable power requirement of 66 W per cm$^2$ of exposed cathode surface. Feasibility analysis indicates that this system can be powered by a battery pack weighing less than 3 kg for a typical re-entry trajectory, with further mass reductions possible through intermittent transmission. A sensitivity analysis reveals that the sheath topology is governed principally by ion kinetics; specifically, corrections to ion mobility at high reduced electric fields lead to enhanced space-charge shielding and a subsequent contraction of the sheath. Conversely, the sheath structure is largely insensitive to the electron mobility model. Finally, we argue that the present drift-diffusion model likely yields a conservative lower bound for mitigation performance. A kinetic approach accounting for ballistic ion transport and non-local ionization would likely predict thicker sheaths and lower attenuation for equivalent power deposition.

Gravitational waves (GWs) are unique messengers as they travel through the Universe without alteration except for gravitational lensing. Their long wavelengths make them susceptible to diffraction by cosmic structures, providing an unprecedented opportunity to map dark matter substructures. Identifying lensed events requires the analysis of thousands to millions of simulated events to reach high statistical significances. This is computationally prohibitive with standard GW parameter estimation methods. We exploit DINGO-lensing, a deep-learning algorithm that accelerates the inference from CPU days to minutes to thoroughly reanalyze GW231123, the most promising lensing candidate to date. By performing more than 200,000 simulations with 3 different waveform models, we find that its statistical significance is below 4$σ$ and the event cannot be claimed as lensed. We observe that 8% of GW231123-like nonlensed simulations favor lensing, which could be explained by the self-similarity of short-duration signals. Still, 58% of GW231123-like lensed simulations have larger support for lensing, showing that higher detection statistics are possible. We show that analyzing simulations with different waveform models only lowers the significance, highlighting the relevance of waveform systematics. Although GW231123 exposes the challenges of claiming the first GW lensing detection, our deep-learning methods have demonstrated to be powerful enough to enable the upcoming discovery of lensed GWs.

The mechanical response of elastic porous media confined within rigid geometries is central to a wide range of industrial, geological, and biomedical systems. However, current models for these problems typically overlook the role of wall friction, and particularly its interaction with confinement. Here, we develop a theoretical framework to describe the interplay between the mechanics of the medium and Coulomb friction at the confining walls for slow, quasistatic deformations in response to two canonical uniaxial forcings: piston-driven loading (i.e., an imposed effective stress at the top boundary) and fluid-driven loading (i.e., an imposed fluid pressure at the top boundary) followed by unloading. We find that, during compression, the stress field evolves according to a quasistatic advection-diffusion equation, extending classical poroelasticity results. The magnitude of friction is controlled by a single dimensionless number proportional to the friction coefficient and the aspect ratio of the confining geometry. During decompression, a portion of the solid matrix remains stuck due to friction, leading to hysteresis and to the propagation of a slip front. In piston-driven loading, the frictional stress is directly coupled to the solid effective stress, leading to exponential damping of the loading and striking changes to the displacement field. However, this coupling limits the energy dissipated by friction. In fluid-driven loading, the pressure gradient locally adds energy, decoupling elastic energy storage and frictional energy dissipation. The displacement remains qualitatively unchanged but is quantitatively reduced due to large energy dissipation. In both cases, friction can have a substantial impact on the apparent mechanical properties of the medium.

A \emph{disk graph} is the intersection graph of (closed) disks in the plane. We consider the classic problem of finding a maximum clique in a disk graph. For general disk graphs, the complexity of this problem is still open, but for unit disk graphs, it is well known to be in P. The currently fastest algorithm runs in time $O(n^{7/3+ o(1)})$, where $n$ denotes the number of disks~\cite{EspenantKM23, keil_et_al:LIPIcs.SoCG.2025.63}. Moreover, for the case of disk graphs with $t$ distinct radii, the problem has also recently been shown to be in XP. More specifically, it is solvable in time $O^*(n^{2t})$~\cite{keil_et_al:LIPIcs.SoCG.2025.63}. In this paper, we present algorithms with improved running times by allowing for approximate solutions and by using randomization: - for unit disk graphs, we give an algorithm that, with constant success probability, computes a $(1-\varepsilon)$-approximate maximum clique in expected time $\tilde{O}(n/\varepsilon^2)$; and - for disk graphs with $t$ distinct radii, we give a parameterized approximation scheme that, with a constant success probability, computes a $(1-\varepsilon)$-approximate maximum clique in expected time $\tilde{O}(f(t)\cdot (1/\varepsilon)^{O(t)} \cdot n)$, for some (exponential) function $f(t)$.

A well-known principle states that a congruence between objects should give rise to a corresponding congruence between the special values of $L$-functions attached to these objects. We computationally investigate this principle for Rankin--Selberg $L$-functions attached to pairs of holomorphic cuspforms, and formulate a precise conjecture in general.

The time evolution of the Wigner distribution function for a single-particle excitation in a Fermi system was studied within the framework of the diffusion approximation of kinetic theory by numerically solving a nonlinear diffusion equation with constant kinetic coefficients. A method was proposed to separate the dissipative processes into contributions from the relaxation of the single-particle excitation and from the relaxation of the nuclear core, with a distinct relaxation time introduced for each process. The influence of the diffusion and drift coefficients on the characteristic relaxation time scale was analyzed. It was found that the resulting relaxation times exhibit a discrepancy relative to the kinetic coefficient estimates known from previous studies.