We propose an SIS competition model describing the propagation of conflicting rumors, such as fake news and its corrections. This simple model captures the interaction between rumor propagation and opinion dynamics, where rumors drive opinion changes and, conversely, individuals' opinions determine the infection rates of rumors. We analytically derive all steady states and their stability. These results uncover a novel coexistence mechanism. This coexistence corresponds to a scenario where belief in one rumor (e.g., fake news) paradoxically aids the spread of the opposing rumor (e.g., corrective information). Due to this mechanism, a nontrivial but realistic phenomenon occurs where a lower infection rate actually enhances the spread of a rumor. Furthermore, although the model does not explicitly incorporate majority conformity, a phenomenon where the majority gains an advantage emerges spontaneously. Consequently, even if one rumor has a higher infection rate, it may be eliminated by the other if its initial share fails to exceed a critical threshold. We analytically derive this threshold using the singular perturbation method.

We present the first systematic census of quenching mechanisms using kinematic asymmetries in a large sample of $\sim$6,700 galaxies from the MaNGA survey, providing a unified view of what halts star formation in the local Universe ($z<0.2$). We quantify stellar and nebular gas disturbances through the higher-order terms of a Fourier series expansion. These asymmetries serve as powerful diagnostics, as different quenching mechanisms leave distinct kinematic signatures on gas and stars. Our analysis reveals that the most effective quenching pathways leave minimal kinematic imprints by the time galaxies are fully quenched. This "kinematic regularity" points toward slow-acting processes (>3 Gyr) such as starvation and maintenance feedback. A striking finding emerges from our mass-matched analysis: quenched symmetric satellites are significantly more compact than their asymmetric counterparts ($3.4σ$), a trend that is even more pronounced for symmetric centrals ($12.3σ$). Our results suggest that environment drives the dominant satellite quenching pathway through rapid gas stripping followed by long-term starvation. These compact, kinematically undisturbed satellites (the most representative case within our sample) have undergone intense gas stripping and central compaction, creating bulge-like structures with old, metal-rich stellar populations. Combined with halo gas cut-off and the prevention of cosmological accretion due to starvation, this creates an irreversible quenching path. Conversely, the larger sizes of disturbed, quenched centrals are consistent with merger-driven growth. Internal processes, likely driven by the AGN cycle over 1-3 Gyr that prevents hot halo gas cooling, sustain quenching maintenance in this population. The absence of asymmetric satellites in the star-forming regime suggests environmental quenching operates without significant kinematic perturbation.

We present magnetization and dilatometry measurements on the honeycomb cobaltate Na$_3$Co$_2$SbO$_6$ and map out its detailed field-temperature phase diagram down to sub-Kelvin temperatures. Our data for in-plane magnetic fields show a strongly anisotropic $c^{*}$-axis lattice response, which is dominated by the variation of Co--O--Co bond angles according to \textit{ab initio} calculations. At $T = 0.4$~K, the magnetization $M(B)$ exhibits step-like features that are also highly anisotropic. In the case of $B \parallel b$, a small hysteresis observed around the second field-induced magnetic transition ($B_{c2}$) indicates its first-order character, whereas divergence of the magnetic Grüneisen parameter at $B_{c2}$ is suppressed upon cooling and signals the absence of quantum critical behavior upon entering the field-polarized state. None of our thermodynamic measurements provide evidence for a field-induced quantum spin liquid state near or above $B_{c2}$.

The evolution of planet-forming disks and the processes of planet formation influence each other, and both of them are possibly impacted by the local environment. Extensive high-resolution imagery of disks across space and time is the best tool for determining their evolution. We compiled a comprehensive list of disk-bearing young stars with near-IR high-contrast images available. The sample sums up to 268 sources, including 51 targets with no prior publications, which makes this study the largest of its kind and the most extensive release of IR disk images to date. Our census reveals very diverse disk and ambient morphologies. Disks in Lupus are bright, in Chamaeleon are faint, in Corona Australis and Taurus are frequently surrounded by ambient emission. Disks experience an abrupt increase in IR brightness between 2 Myr and 5 Myr. The earliest IR disk cavities around single stars arise after 2-3 Myr explaining why are young disks faint in the near-IR, and determining which disks can live longer. Well-known, high-longevity disks (>8 Myr) are always bright. Ambient material is detected in more than 20% of young sources but the fraction drops with time. We find a clear correspondence for the presence of ambient material with the stellar variability, near-IR excess, and mass accretion rate as well as, in turn, with spirals and shadows in disks. Half of the disks with ambient material show spirals while none of them show rings. We therefore propose that the spirals and the disk warps responsible for shadows are generally induced by late infall from the medium, and that this also affects the stellar accretion. The emerging picture proves the fundamental role of the environment for the disk evolution and planet formation.

The anisotropic influence on the $f$-mode frequency of oscillations and dimensionless tidal deformability of neutron stars is analyzed by employing the nonradial oscillation equations for the complete general relativity frame and tidal deformability equations, which are derived and modified from their standard form to introduce the anisotropic factor. The fluid inside the compact star obeys an equation of state constructed by matching microscopic nuclear and perturbative QCD calculations through a piecewise polytropic interpolating scheme. For the anisotropic profile, we use a local anisotropy which is regular along the whole star and vanishes both at the center and on the star's surface. We show that the \(f\)-mode oscillation frequency and dimensionless tidal deformability are noticeably affected by anisotropy. Finally, we investigate the correlation between the dimensionless tidal deformability inferred from the GW$170817$ event and the anisotropy parameter.

Nowadays, the convergence of mobile edge computing (MEC) and vehicular networks has emerged as a vital enabler for the ever-increasing intelligent onboard applications. This paper proposes a multi-tier task offloading mechanism for MEC-enabled vehicular networks leveraging vehicle-to-everything (V2X) communications. The study focuses on applications with sequential subtasks and explores the collaboration of two tiers. In the Vehicle Tier, the requesting vehicle (RV)-service vehicle (SV) matching scheme and the inter-vehicle collaborative computation are studied, with joint optimization of task offloading decision, communication, and computing resource allocation to minimize energy consumption while satisfying delay requirements. In the Roadside Unit (RSU) Tier, collaboration among RSUs is investigated to further address multi-access issues of uplink subchannels and computing resources for serving unmatched RVs. To tackle this intricate problem, a layered optimization framework is first proposed to obtain task offloading decisions and optimal continuous resource allocation, after which a subchannel allocation scheme is designed to recover the discrete solution with low complexity. Extensive experiments are conducted to demonstrate that the proposed method reduces average energy consumption by at least 15% compared with recent utility maximization and energy cost minimization benchmarks under varying task delay requirements and vehicle scales.

We revisit black hole mass estimates for high-redshift broad-line active galactic nuclei (AGNs) discovered with JWST by jointly analysing their broad emission lines and their systematic non-detections in deep Chandra imaging. Building upon a self-shadowed, super-Eddington accretion framework in which the corona undergoes efficient radiative over-cooling, we couple funnel-dependent Comptonisation physics with slim-disc spectral models and explore the resulting parameter space through a full MCMC inference. Using a recently compiled sample of JWST high-redshift broad-line AGNs, we show that the observed X-ray weakness - manifested as extreme bolometric corrections, suppressed 2-10 keV luminosities, and non-detections in the 0.5-5 keV Chandra band - naturally arises when the corona is confined and radiatively over-cooled inside a narrow super-Eddington funnel. The combined broad line+X-ray analysis yields strongly bimodal posteriors: either very massive, very low-Eddington black holes (physically disfavoured), or a population of low-mass ($\sim 10^{6}$-$10^{7} M_{\odot}$) black holes accreting at $f_{\rm Edd} \gg 1$. The latter solution is strongly preferred for nearly all objects and returns masses consistent with, or lower than, local $M_{\rm BH}$-$M_{\star}$ relations, mitigating the extreme mass ratios implied by single-epoch virial estimators. The predicted intrinsic spectra are redder and exhibit reduced hard-X-ray output but higher bolometric luminosities, implying bolometric corrections larger than those typical of the local AGN population, yet consistent with low-redshift highly accreting counterparts. These results support a picture in which many JWST broad-line AGNs are powered by rapidly growing, super-Eddington black holes whose suppressed coronal emission and self-shadowed BLR geometry combine to mimic overmassive black holes at $z \gtrsim 6$.

Exceptional points, where two or more eigenstates of a non-Hermitian system coalesce, are now of interest across many fields of physics, from the perspective of open-system dynamics, sensing, nonreciprocal transport, and topological phase transitions. In this work, we investigate exceptional points in cavity optomechanics, a platform of interest to diverse communities working on gravitational-wave detection, macroscopic quantum mechanics, quantum transduction, etc. Specifically, we clarify the role of quantum jumps in making a clear distinction between Liouvillian and Hamiltonian exceptional points in optomechanical systems. While the Liouvillian exceptional point arises from the unconditional Lindblad dynamics and is independent of the phonon-bath temperature, the Hamiltonian exceptional point emerges from the conditional no-jump evolution and acquires a thermal shift due to an enhanced conditional damping. Employing the thermofield formalism, we derive a unified spectral framework that interpolates between these regimes via an analytical hybrid-Liouvillian description. Remarkably, in the weak-quantum-jump regime, the exceptional point is perturbed only at the second order, highlighting the robustness of the Hamiltonian exceptional point under small hybrid perturbations. Our work reveals a continuous family of hybrid exceptional points, clarifies the operational and physical differences between the conditional and unconditional dissipative dynamics in optomechanical systems, and provides a probe for thermal baths.

Repeating partial tidal disruption events (pTDEs) provide a direct probe of stellar orbits and episodic mass loss around supermassive black holes, but robust identification requires multi-band and multi-epoch evidence. %consistent with a single physical origin. We investigate whether the late-time radio rebrightening of the nuclear transient IGR~J12580+0134 in NGC~4845 can be explained as a repeating pTDE, using multi-epoch Karl G.\ Jansky VLA observations together with X-ray constraints from \textit{Swift}/XRT and \textit{NICER}. Through a systematic analysis of the radio data, we identify two well-defined radio flares and a possible third late-time rebrightening flare. Modeling the second flare with a synchrotron afterglow framework using Markov Chain Monte Carlo fitting is consistent with a sub-relativistic outflow with a characteristic velocity of order ${v \simeq 0.3c}$, an isotropic-equivalent kinetic energy of order ${10^{50}}$ erg, and an approximately constant-density circumnuclear medium. No significant contemporaneous brightening is detected by \textit{Swift}/XRT during the 2016 radio flare, while faint \textit{NICER} flares in 2023 suggest intermittent low-level accretion. We also considered several possible interpretations for the late-time radio rebrightening, and found that the repeated pTDE scenario provides a more natural overall explanation for the observed phenomenology. Given the currently sparse data coverage, continued sensitive radio and X-ray monitoring will be essential to test this interpretation and to search for future reactivations.

An RGD system $\mathcal{D}$ is called \emph{linear w.r.t. a root basis $\mathcal{B}$} if the commutation relations between the root groups of $\mathcal{D}$ are `linear' in a certain sense. Moreover, $\mathcal{D}$ is called \emph{linearizable}, if there exists a root basis $\mathcal{B}$ such that $\mathcal{D}$ is linear w.r.t. $\mathcal{B}$. For many examples of RGD systems it is easy to see that they are linear w.r.t. a concrete root basis. To the best of our knowledge, it was unclear whether RGD systems exist which are not linearizable. In this article we show that there exist uncountably many RGD systems which are not linearizable. In particular, we provide the first explicit example of such an RGD system. This expands the quote from Rémy that axiom (RGD$1$)$_{\mathrm{lin}}$ is not only a strengthening of axiom (RGD$1$), but is in fact stronger than it. We show that non-linearizability appears in examples of universal type, and also in examples of $2$-spherical type. For the examples of universal type we construct an uncountable family of non-linearizable RGD systems, and for the examples of $2$-spherical type we show that the RGD systems of type $(4, 4, 4)$ recently constructed by the author provide uncountably many non-linearizable RGD systems.

We report the theoretical prediction and measurement of a tune-out wavelength for the ground state of the thulium atom in a linearly polarized optical dipole trap with a wavelength of approximately 576 nm. The measurements were conducted using a combination of trap frequency and RF loss spectroscopy, thus making it possible to separate the scalar and tensor parts of the total polarizability without measurements in the range of negative total polarizability. The calculated tune-out wavelength is consistent with the measured one of $575.646_{-0.014}^{+0.016}$ nm in air. The existence of the zero in the polarizability for the Tm ground state was confirmed by the trap loss experiment, which also made it possible to refine the tune-out wavelength to $575.646_{-0.004}^{+0.004}$. Despite the presence of an imaginary part of the polarizability at some wavelengths, it was experimentally demonstrated that, with a proper choice of the dipole trap polarization, it was possible to achieve Bose-Einstein condensation of thulium atoms in the range from 575.348 to 575.689 nm, covering the tune-out wavelength.

In modern interconnected societies, opinions and beliefs can quickly spread across large populations, giving rise to collective behaviors such as the adoption of social norms or polarization. These phenomena have motivated many models aimed at reproducing emergent properties from simple interaction mechanisms. In particular, opinion dynamics models describe how individual opinions evolve through interactions and study the conditions for global consensus or polarization. Most models assume that these interactions occur between pairs of agents, typically on a fixed network structure. However, opinion changes can occur in groups, which may also undergo adaptive changes if disagreement arises. Here, we propose a bounded confidence model that incorporates both mechanisms: group discussions can lead to global agreement among members, while strong internal disagreement causes groups to split, with resulting subgroups merging with others. We systematically study the model outcomes as a function of agents' tolerance for agreement. Strikingly, adaptivity suppresses key effects of group interactions, restoring a phenomenology close to that of pairwise interactions. In particular, adaptivity enables the formation of large groups and prevents fragmentation at small tolerance. It also restores a phase transition from polarization to consensus, which would otherwise disappear in a non-adaptive group-based model. Overall, our work shows that both adaptivity and group interactions shape the structure of social ties and global opinion dynamics in a population.

Non-fungible tokens (NFTs) on Ethereum currently follow a binary mobility paradigm: ERC-721 enables unrestricted transfers, whereas SBTs (ERC-5192) prohibit transfers entirely. We identify a design gap in which no standard mechanism supports bounded transferability, where ownership mobility is allowed but limited to a finite number of programmable transfers. We study counted NFT transfers and introduce ERC-7634 as a minimal realization compatible with ERC-721. The design augments each token with a transfer counter and configurable cap L, allowing ownership to evolve under a finite transfer budget. ERC-7634 defines a minimal extension interface with three lightweight functions (transferCountOf, setTransferLimit, and transferLimitOf), two events, and native-transfer hooks, requiring fewer than 60 additional lines of Solidity while preserving full backward compatibility with existing NFT infrastructure. We analyze behavioral and economic consequences of counted transfers. Our results reveal (i) a mobility premium induced by remaining transfer capacity, (ii) a protocol-level costing signal that can deter wash trading in cap-aware markets through irreversible budget consumption, (iii) bounded recursive collateralization enabled by limited ownership turnover, and (iv) associated security and gas-cost implications, including wrapper-bypass trade-offs. Evaluation on calibrated simulations shows that moderate limits (e.g., L = 10) affect fewer than 15% of tokens under representative transfer distributions, while repeated manipulation becomes unprofitable after a few cycles in a cap-aware pricing model; the additional gas overhead remains below 11% per transfer. We further position ERC-7634 within the NFT mobility design space, derive practical cap-selection guidelines, and discuss post-cap ownership outcomes including soulbound conversion, auto-burn, and provenance freeze.

We provide a self-contained derivation of the Hamiltonian formulation of General Relativity in vielbein variables in $d=D+1$ dimensions. Starting from the Einstein--Hilbert action in a standard metric $D+1$ decomposition, we derive Lorentz- and $\mathrm{SO}(D)$-covariant phase-space actions, identify the primary Lorentz constraints, and obtain the Hamiltonian and momentum constraints. We compute the resulting first-class constraint algebra, relate the vielbein and metric phase-space formulations, and discuss the rotation/boost decomposition. In particular, we construct the boost generator in the $\mathrm{SO}(D)$-covariant formulation, thereby recovering full local Lorentz symmetry.

Decentralized AI systems, such as federated learning, can play a critical role in further unlocking AI asset marketplaces (e.g., healthcare data marketplaces) thanks to increased asset privacy protection. Unlocking this big potential necessitates governance mechanisms that are transparent, scalable, and verifiable. However current governance approaches rely on bespoke, infrastructure-specific policies that hinder asset interoperability and trust among systems. We are proposing a Technical Policy Blueprint that encodes governance requirements as policy-as-code objects and separates asset policy verification from asset policy enforcement. In this architecture the Policy Engine verifies evidence (e.g., identities, signatures, payments, trusted-hardware attestations) and issues capability packages. Asset Guardians (e.g. data guardians, model guardians, computation guardians, etc.) enforce access or execution solely based on these capability packages. This core concept of decoupling policy processing from capabilities enables governance to evolve without reconfiguring AI infrastructure, thus creating an approach that is transparent, auditable, and resilient to change.

In this paper, we study problems related to harmonic analysis on hypersurfaces in $\mathbb{R}^4 $ with zero Gaussian curvature and given as graphs of polynomial functions. We derive sharp uniform estimates with respect to the direction of frequencies for the Fourier transform of measures supported on such hypersurfaces. Additionally, we study the $L^p$-boundedness problem of maximal operators associated with hypersurfaces. We determine the exact value of the boundedness exponent in terms of the heights of these hypersurfaces.

We investigate charge and energy transport in monolayer graphene with smooth finite-range disorder, modeled by soft impurity potentials. Using a continuum Dirac model, we go beyond the Born approximation by computing the exact scattering matrix for individual impurities. This captures the full nonperturbative physics of smooth disorder. From the exact scattering data, we evaluate transport coefficients by solving the Boltzmann equation with energy-resolved phase shifts. We analyze electrical and electronic thermal conductivities versus carrier density and temperature, including deviations from the Wiedemann-Franz law. Our results reveal that finite-range disorder nontrivially modifies charge and heat currents, especially at low energies where perturbative methods fail. These findings provide a more accurate transport characterization for disordered Dirac materials and clarify how smooth disorder governs energy flow in graphene.

Parquet is the de facto columnar file format in modern analytical systems, yet its configuration guidelines have largely been shaped by CPU-centric execution models. As GPU-accelerated data processing becomes increasingly prevalent, Parquet files generated with CPU-oriented defaults can severely underutilize GPU parallelism, turning GPU scans into a performance bottleneck. In this work, we systematically study how Parquet configurations affect GPU scan performance. We show that Parquet's poor GPU performance is not inherent to the format itself but rather a consequence of suboptimal configuration choices. By applying GPU-aware configurations, we increase effective read bandwidth up to 125 GB/s without modifying the Parquet specification.

We study the existence of solutions of the following nonlinear Schrödinger equation $$ -Δu+V(x)u-\frac{(N-2)^2}{4|x|^2}u=f(x,u) $$ where $V:\mathbb{R}^N\to\mathbb{R}$ and $f:\mathbb{R}^N\times \mathbb{R}\to \mathbb{R}$ are periodic with respect to $x\in\mathbb{R}^N.$ We assume that $V$ has positive essential infimum, $f$ satisfies weak growth conditions and $N\geq 3$. The approach to the problem uses variational methods with nonstandard functional setting. We obtain the existence of the ground state solution using the new profile decomposition.

We investigate how pulsar timing array (PTA) measurements of the nanoHertz gravitational-wave background (GWB) can constrain models for the growth history of supermassive black holes (SMBHs) and how active galactic nucleus (AGN) and stellar feedback models can affect GWB predictions. Feedback regulates supermassive black hole (SMBH) growth, altering the black hole mass function (BHMF). Using BHMFs drawn from multiple cosmological simulation suites including IllustrisTNG, MillenniumTNG, Simba, and CAMELS, and combining these with a quasar-based SMBH binary population framework, we predict the resulting GWB amplitude under a range of different stellar and AGN feedback prescriptions. We find that the choice of both stellar and AGN feedback models alters the high-mass end of the BHMF and changes the predicted GWB amplitude by up to a factor of 2 for the fiducial simulations and a factor 10 for extreme feedback variations in CAMELS. Models with inefficient or absent AGN feedback produce abundant SMBHs and yield GWB amplitudes consistent with PTA data, yet fail in producing realistic galaxies. Fiducial models of AGN and stellar feedback suppress SMBH growth too much and under-predict the expected signal, an effect which could possibly be mitigated by more realistic black hole seeding and growth prescriptions. The mismatch between the GWB amplitudes predicted by cosmological simulations and that inferred by PTA measurements suggests that SMBH growth is more efficient or occurs earlier than captured by current models. This demonstrates that PTA measurements provide a powerful new probe of not only the SMBH population but also feedback physics.

The OCTOPUS project addresses the development and characterization of monolithic active pixel sensors in the TPSCo 65 nm ISC technology in view of vertexing applications at a future lepton collider. Meeting the corresponding requirements -- outlined in the ECFA detector road map -- will necessitate the simulation, design, and testing of prototypes and a demonstrator chip in this very process. This work reviews the literature on existing prototypes, summarizing their design characteristics, properties, and performance in charged-particle detection, and provides an overview of previous simulation efforts. The presented results suggest the feasibility of the endeavor while showcasing challenges, the need for further investigations, and providing a foundation for imminent design choices.

The generation of relativistic vortex electron beams via photoemission requires ultraviolet laser beams with well-controlled orbital angular momentum (OAM) and compatibility with radio-frequency (RF) photoinjector drive-laser systems. High-OAM vortex beams at a wavelength of 266 nm are generated using three fabricated diffractive optical elements integrated into an operational photoinjector beamline: a reflective fork grating, a high-topological-charge spiral phase plate, and binary axicons. The spiral phase plate produces a high-purity Laguerre-Gaussian mode with an OAM of l = 64 and a conversion efficiency of 80%, whereas binary axicons generate low-divergence quasi-Bessel beams forming a superposition of multiple OAM states with a finite OAM bandwidth imposed by their binary phase structure. Fork gratings provide flexible access to lower OAM values and enable robust modal diagnostics. The generated beams are characterized using cylindrical-lens mode conversion and radial intensity analysis, demonstrating practical control of both the OAM content and spectral bandwidth of ultraviolet structured light for accelerator-based applications.

We recast spinful superconductivity as a \textit{quaternion field theory}, where a quaternion is a four-component hypercomplex number with units $(\boldsymbol{e}_x,\boldsymbol{e}_y,\boldsymbol{e}_z)$, that encodes the spin-singlet/triplet gap in a single field $q(\mathbf{k})$. This yields a compact Bogoliubov-de Gennes (BdG) Hamiltonian $H_{\rm BdG}=ξ_{\mathbf{k}}τ_z+τ_+q+τ_-\,q^\ddagger$ and keeps time-reversal symmetry, Altland-Zirnbauer classification, and topological diagnostics in the same variables. In general the mixed singlet--triplet spectrum is branch-split, while the familiar perfect-square form is recovered only for unitary pairing. We introduce a quarteting field $Q\!\propto\!\mathrm{Sc}(q^2)$ and a minimal Ginzburg-Landau (GL) functional with covariant derivatives $(\nabla-2ie\mathbf A)q$ and $(\nabla-4ie\mathbf A)Q$. Analytically, a one-loop evaluation of the fluctuation bubble $Π(0)$ gives a quantitative vestigial charge-$4e$ criterion $μ_{\rm eff}=μ-\frac{g^2}{2}Π(0)<0$. Numerically, we verified: (i) a two-dimensional (2D) class-DIII lattice model whose $\mathbb{Z}_2$ index, computed from the occupied BdG eigenvectors via the standard sewing-matrix (Pfaffian) construction at time-reversal-invariant momenta, matches helical edge spectra; (ii) a GL simulation of a pure-$Q$ vortex carrying $h/4e$ flux within $\sim2\%$ and exhibiting $ξ_Q\!\propto\!\sqrt{η/|μ_{\rm eff}|}$; and (iii) a short-junction current-phase relation with a controlled window where the second harmonic dominates ($I_2\!\gg\!I_1$), together with doubled alternating-current Josephson emission and a Shapiro response consistent with $4e$-dominated transport. The framework provides a compact, symmetry-faithful route from microscopic pairing to device-level charge-$4e$ signatures.

Superconductivity is one of the most amazing properties that metallic conductors exhibit. Electrical resistance is completely eliminated below the critical temperature (Tc), which is the most important parameter in superconductivity. Since the discovery of copper oxide superconductors 39 years ago, many solid state chemists have made significant contributions to the field by discovering new compounds and producing high-quality samples for physical measurements. However, superconductivity research remains challenging for most solid state chemists because it requires knowledge of complicated solid state physics. This manuscript aims to provide a simple, intuitive introduction to superconductivity using only fundamental physics concepts that solid state chemists are familiar with. The author investigates a wide range of materials and classifies them according to the superconductivity mechanisms that may drive them. Specifically focusing on a series of copper oxide superconductors with the highest Tc at ambient conditions, the remarkable material dependence of Tc and the underlying, unconventional superconductivity mechanism that leads to the high Tc are thoroughly examined. Although our understanding of cuprate superconductivity is still fragmented, the author believes that once the branches and leaves are removed, the story will be fairly simple, similar to the phonon-based superconductivity mechanism revealed by the BCS theory. Furthermore, potential strategies for raising the Tc of cuprates and other superconductors are discussed. The author hopes that this article will pique interest in superconductors in young solid state chemists and encourage them to pursue the discovery of still unknown and unexplored room-temperature superconductors in the future.

The production of identified hadrons inside jets in $e^+ e^-$ annihilation allows for detailed studies of parton-to-hadron fragmentation functions in a clean environment. We compute hadron-in-jets production cross sections for $e^+e^- \to 2\,\mathrm{jets}$ and $e^+e^- \to 3\,\mathrm{jets}$ to next-to-next-to-leading order (NNLO) in perturbative QCD. By comparing with data from the ALEPH experiment, we demonstrate the implications of the newly computed theory predictions for precision phenomenology.

Based on deep high resolution JWST images of AS1063, and after a careful masking of artifacts, extended features in the cluster, and background galaxies (including known lensed ones), we have identified tens of thousands of unresolved point sources in the central region of the galaxy cluster. We extended the identification of these point sources up to 1.18 Mpc from the center of the cluster using data in the second module. Most of these sources are expected to be globular clusters orbiting in the deep potential well of the cluster, but also the surviving compact cores of satellite galaxies. We study the distribution of the globular clusters and compared it with the distribution of mass from a lens model derived from the same JWST data. We find a very tight correlation between the two distributions, but also some differences, including a more concentrated distribution for the globular clusters than for dark matter. We explored the possibility of using the distribution of globular clusters as a proxy for the lensing mass. We find that a simple smoothing kernel can transform the discrete distribution of point sources into a continuous two-dimensional distribution that matches well the lensing convergence. This suggests that globular clusters can be used as tracers of the dark matter distribution in other massive clusters where gravitational lensing constraints are scarce but globular clusters can be detected more easily, for instance in low redshift galaxy clusters.

The algebra of $R$-valued functions on the set of chambers of a real hyperplane arrangement is called the Varchenko-Gelfand (VG) algebra. This algebra carries a natural filtration by the degree with respect to Heaviside functions, giving rise to the associated graded VG algebra. When the coefficient ring $R$ is an integral domain of characteristic $2$, the graded VG algebra is known to be isomorphic to the Orlik-Solomon algebra. In this paper, we study VG algebras over coefficient rings of characteristic different from $2$, and investigate to what extent VG algebras determine the underlying oriented matroid structures. Our main results concern hyperplane arrangements that are generic in codimension $2$. For such arrangements, if $R$ is an integral domain of characteristic not equal to $2$, then the oriented matroid can be recovered from both the filtered and the graded VG algebras. As a byproduct, we prove that, unlike the complexification, the cohomology ring of the complement of a $3$-plexification of a real arrangement is not determined by the intersection lattice. We also formulate an algorithm that is expected to reconstruct oriented matroids from VG algebras in the case of general arrangements.

xAI's large language model, Grok, is called by millions of people each week on the social media platform X. Prior work characterizing how large language models are used has focused on private, one-on-one interactions. Grok's deployment on X represents a major departure from this setting, with interactions occurring in a public social space. In this paper, we systematically sample three months of interaction data to investigate how, when, and to what effect Grok is used on X. At the platform level, we find that Grok responds to 62% of requests, that the majority (51%) are in English, and that engagement is low, with half of Grok's responses receiving 20 or fewer views after 48 hours. We also inductively build a taxonomy of 10 roles that LLMs play in mediating social interactions and use these roles to analyze 41,735 interactions with Grok on X. We find that Grok most often serves as an information provider but, in contrast to LLM use in private one-on-one settings, also takes on roles related to dispute management, such as truth arbiter, advocate, and adversary. Finally, we characterize the population of X users who prompted Grok and find that their self-expressed interests are closely related to the roles the model assumes in the corresponding interactions. Our findings provide an initial quantitative description of human-AI interactions on X, and a broader understanding of the diverse roles that large language models might play in our online social spaces.

Anticipating tipping points in complex systems is a fundamental challenge across domains. Traditional early warning signals (EWSs) based on critical slowing down, such as increasing sample variance, are widely used, but their ability to reliably indicate imminent bifurcations and forecast their timing remains limited. Here, we introduce TIPMOC (TIpping via Power-law fits and MOdel Comparison), a parametric framework designed to statistically detect the approach of a bifurcation and estimate its future location using only the sample variance. TIPMOC exploits the mathematical property that variance diverges with a characteristic power-law form near codimension-one bifurcations. By sequentially monitoring system variance as a control parameter changes, TIPMOC statistically adjudicates between linear and power-law divergence at each step. When evidence favors power-law divergence, TIPMOC forecasts the impending tipping point and estimates its position; otherwise, it avoids false positives. Through numerical simulations, we demonstrate TIPMOC's robustness and accuracy in both detection and timing prediction across different types of dynamics and bifurcation, whereas the accuracy of timing prediction is limited. TIPMOC shows low false positive rates and performs well even with uneven sampling and colored noise. This method thus enhances the interpretability and practical utility of classical EWSs, serving as both a transparent add-on and a stand-alone statistical tool for forecasting regime shifts in diverse complex systems.

Cyberattacks on enterprise networks exploit complex dependencies among infrastructure, services, and applications, which challenge traditional analysis methods that focus on attack paths or network topology in isolation. In this study, we introduce a novel probabilistic multilayer modelling framework, based on influence propagation in networks, that integrates attack graphs with the communication network topology, enabling a service-centric impact analysis of cyberattacks. Our method captures both the vulnerability exploitability and network connectivity, allowing us to assess the likelihood of attack propagation and cumulative impacts across interconnected services. By integrating standard vulnerability metrics (such as CVSS) with the network-level connectivity probabilities, the framework provides a cohesive view of the dynamics of cyberattacks. We validate this approach using a realistic case study of an enterprise network, demonstrating its ability to determine critical nodes, vulnerabilities, and service dependencies that significantly influence attack outcomes. Our findings show that integrating network and attack graph perspectives offers more actionable insights into risk assessment and mitigation planning, advancing the analysis of cyberattacks in complex networked environments.