We present the calculation of the so far missing ${\cal O}(α^2α_\mathrm{s})$ corrections to the quantity $Δr$, which relates the Fermi constant to the W-boson mass, and enables precision predictions of the latter. While the ${\cal O}(α^2α_\mathrm{s})$ corrections from diagrams with two closed fermion loops are already known, we here focus on the subset with one closed fermion loop, which is a substantially more complex problem. The calculation has been carried out through a combination of analytical and numerical techniques for the three-loop integrals and the on-shell renormalization. The impact of the new corrections is numerically significant, raising the Standard Model prediction for the W-boson mass by more than 3 MeV.

We build upon our previously developed multi-ion radiative transfer (RT) framework, PEACOCK, to investigate the kinematic and energetic structure of cool-to-warm galactic winds in a sample of 50 nearby star-forming galaxies. Using self-consistent constraints derived from joint modeling of Ly-alpha and multiple ultraviolet metal lines, we analyze how bulk outflows and turbulent motions contribute to the dynamics and energy budget of galactic winds in the circumgalactic medium (CGM). We find that macroscopic turbulent velocities are often comparable to, and sometimes exceed, the coherent bulk outflow velocity. The associated turbulent pressure frequently dominates over both microscopic pressure and ram pressure, indicating that turbulence is a major contributor to the kinetic energy budget of the CGM wind. Wind kinematics, ionic column densities, and metal mass outflow rates all scale systematically with stellar mass and star formation rate, demonstrating a strong coupling between stellar feedback and CGM structure. Including turbulent motions strengthens these CGM-galaxy scaling relations and favors an energy-driven feedback regime. The total kinetic energy flux of the cool-to-warm CGM correlates tightly with the mechanical energy injection rate from star formation, implying that stellar feedback provides sufficient power to sustain both coherent outflows and turbulence. Comparisons with phenomenological line-profile fitting methods further show that simplified treatments can introduce systematic biases in inferred wind properties. Together these results support a turbulence-regulated picture of galactic winds in which a substantial fraction of feedback energy is stored in turbulent motions within a multiphase CGM.

The rapidly expanding Gravitational-Wave Transient Catalog (GWTC) necessitates the development of model-independent techniques to uncover trends and subpopulations within the binary black hole (BBH) population. We present the first usage of the Uniform Manifold Approximation and Projection (UMAP) algorithm, a novel dimensionality-reduction technique, for the purpose of analyzing BBH mergers in GWTC-3. We show that UMAP, paired with a clustering algorithm, effectively partitions the population into four well-segregated subgroups principally via their primary and secondary mass components along with an outlier event, GW$190521\_030229$. UMAP clearly identifies objects in the ${\sim}10~M_\odot$ buildup in the BBH mass spectrum as their own group with aligned spins and mass ratios of ${\sim}0.2{-}0.7$ while objects in or above the ${\sim}35~M_\odot$ overdensity are all in the same, largest group and display typically lower effective spins as well as larger mass ratios (${\sim}0.5{-}0.9$) on average. With the aid of hierarchical population inference, we interpret these as subpopulations from different formation pathways, consistent with previous findings. We also find a transitional group of a handful of objects with masses in between the aforementioned buildups and broad support for anti-aligned spins. We examine the low-mass UMAP subgroup, which exhibits anti-correlation between the mass ratio and effective spin, and show that it drives such anti-correlation for the entire GWTC-3 sample. Overall, we demonstrate that UMAP is an interpretable, non-parametric framework that can not only be used for visualization but also for probing the astrophysics of the BBH population.

We develop a neural-network framework for multi-period risk--reward stochastic control problems with constrained two-step feedback policies that may be discontinuous in the state. We allow a broad class of objectives built on a finite-dimensional performance vector, including terminal and path-dependent statistics, with risk functionals admitting auxiliary-variable optimization representations (e.g.\ Conditional Value-at-Risk and buffered probability of exceedance) and optional moment dependence. Our approach parametrizes the two-step policy using two coupled feedforward networks with constraint-enforcing output layers, reducing the constrained control problem to unconstrained training over network parameters. Under mild regularity conditions, we prove that the empirical optimum of the NN-parametrized objective converges in probability to the true optimal value as network capacity and training sample size increase. The proof is modular, separating policy approximation, propagation through the controlled recursion, and preservation under the scalarized risk--reward objective. Numerical experiments confirm the predicted convergence-in-probability behavior, show close agreement between learned and reference control heat maps, and demonstrate out-of-sample robustness on a large independent scenario set.

Analogously to classical computers, quantum processors exhibit side channels that may give attackers access to potentially proprietary algorithms. We identify and exploit a previously unexplored side channel in trapped-ion quantum processors that arises from the radio-frequency (RF) signals used to modulate lasers for ion cooling, gate execution, and readout. In these quantum processors, acousto-optical modulators (AOMs) imprint phase and frequency modulations onto laser fields interacting with the ions to implement individual and collective unitaries. The AOMs are driven by strong RF signals, a fraction of which leaks out of the device. We discuss general strategies to exploit this side channel and demonstrate how to detect RF leakage from a state-of-the-art qudit-based quantum processor using off-the-shelf components. From this data, we extract pulse characteristics of single-ion and entangling gates, thereby implementing a proof-of-principle exploitation of the novel attack vector. Finally, we outline ways to mitigate the information leakage through the presented side channel.

Chaotic BKL dynamics provides a canonical description of the approach to spacelike singularities as a sequence of Kasner epochs grouped into eras. While this paradigm is well established for cosmological singularities, explicit realizations inside black holes have been scarce, despite renewed interest from holography. Here, we construct a broad class of asymptotically AdS black holes in $D\ge 4$ whose interiors exhibit bona fide BKL dynamics as the singularity is approached. In the near-singularity regime, the evolution reduces to billiard-like motion in a compact domain that forms a regular $(D-2)$-simplex. We derive closed-form bouncing rules for the Kasner exponents in arbitrary dimension and prove the ensuing chaotic dynamics. A key novelty for $D\ge 5$ is a richer internal organization of eras: inequivalent transitions between epochs lead to distinct Kasner seasons, yielding new patterns of epoch/era structure for both electric and gravitational walls. Finally, we investigate a holographic diagnostic, the thermal $a$-function, whose monotonic flow captures individual epochs and eras and can display near-walking behavior in suitable Kasner regimes.

Designing messenger RNA (mRNA) sequences for a fixed target protein requires searching an exponentially large synonymous space while optimizing properties that affect stability and downstream performance. This is challenging because practical mRNA design involves multiple coupled objectives beyond classical folding criteria, and different applications prefer different trade-offs. We propose a general sampling-based continuous optimization framework, inspired by SamplingDesign, that iteratively samples candidate synonymous sequences, evaluates them with black-box metrics, and updates a parameterized sampling distribution. Across a diverse UniProt protein set and the SARS-CoV-2 spike protein, our method consistently improves the chosen objective, with particularly strong gains on average unpaired probability and accessible uridine percentage compared to LinearDesign and EnsembleDesign. Moreover, our multi-objective COMBO formulation enables weight-controlled exploration of the design space and naturally extends to incorporate additional computable metrics.

Temporal modes of photons are a promising encoding scheme for high-dimensional quantum networks due to their high channel capacity and fiber compatibility. However, realizing their full potential requires devices capable of synchronizing, processing and interfacing these modes across photonic and atomic bandwidths. In this work, we demonstrate a programmable high-dimensional temporal mode processor using a Raman quantum memory in warm cesium vapor. We exploit the single-mode nature of the Raman interaction kernel, dynamically shaping the control field to synthesize a tunable coherent filter that selectively addresses specific temporal waveforms. This mechanism enables on-demand storage, filtering, and conversion, providing a coherent interface between MHz- and GHz-bandwidth modes. We validate the platform's selectivity across a basis of 30 orthogonal Hermite-Gaussian modes and certify high-fidelity quantum operation via 5-dimensional process tomography. By combining deterministic mode conversion with bidirectional bandwidth interfacing, we establish the Raman memory as a critical active node for scalable quantum information processing.

Virtual Reality (VR) enables users to engage with capabilities beyond human limitations, but it is not always obvious how to trigger these capabilities. Taking the lens of Affordance, we believe avatar design is the key to solving this issue, which ideally should communicate its capabilities and how to activate them. To understand the current practice, we selected eight capabilities across four categories and invited twelve professional designers to design avatars that communicate the capabilities and their corresponding interactions. From the resulting designs, we formed 16 guidelines to provide general and category-specific recommendations. Then, we validated these guidelines by letting two groups of twelve participants design avatars with and without guidelines. Participants rated the guidelines' clarity and usefulness highly. External judges confirmed that avatars designed with the guidelines were more intuitive in conveying the capabilities and interaction methods. Finally, we demonstrated the applicability of the guidelines in avatar design for four VR applications.

For each integer $n\ge 2$, we construct infinitely many $n$-component Brunnian links of 3-balls in $S^4$. Our main tool is the third author's result on the existence of splitting spheres for the trivial two-component link of $2$-spheres in $S^{4}$; we also give a new proof of this.

In this short note, we settle a problem posed by Wickstead in ~\cite{W:24}, arising from the study of the Riesz completion of spaces of regular operators between Banach lattices.

Just-in-time (JIT) compilers are key components for many popular programming languages with managed runtimes (e.g., Java and JavaScript). JIT compilers perform optimizations and generate native code at runtime based on dynamic profiling data, to improve the execution performance of the running application. Like other software systems, JIT compilers might have software bugs, and prior work has developed a number of automated techniques for detecting functional bugs (i.e., generated native code does not semantically match that of the original code). However, no prior work has targeted JIT compiler performance bugs, which can cause significant performance degradation while an application is running. These performance bugs are challenging to detect due to the complexity and dynamic nature of JIT compilers. In this paper, we present the first work on demystifying JIT performance bugs. First, we perform an empirical study across four popular JIT compilers for Java and JavaScript. Our manual analysis of 191 bug reports uncovers common triggers of performance bugs, patterns in which these bugs manifest, and their root causes. Second, informed by these insights, we propose layered differential performance testing, a lightweight technique to automatically detect JIT compiler performance bugs, and implement it in a tool called Jittery. We incorporate practical optimizations into Jittery such as test prioritization, which reduces testing time by 92.40% without compromising bug-detection capability, and automatic filtering of false-positives and duplicates, which substantially reduces manual inspection effort. Using Jittery, we discovered 12 previously unknown performance bugs in the Oracle HotSpot and Graal JIT compilers, with 11 confirmed and 6 fixed by developers.

We reveal a striking correspondence between electron- and phonon-driven pairing in twisted bilayer graphene (TBG) by mapping an atomistic electronically driven pairing model onto an effective inter-valley, intra-Chern description, originally proposed for phonon-mediated superconductivity. Within the unified framework of intra-Chern pairing, we analyze the competition between nematic and chiral superconducting states. The latter corresponds to the extreme Chern-polarized limit and thus hosts unpaired flat bands within the superconducting gap, which generally disfavors it relative to the nematic states. Crucially, nematic order is locally preferred at each momenta, but the optimal nematic directions are incompatible across the Brillouin zone due to the broken rotation symmetry. This momentum-space frustration enables a chiral ground state at large fillings or weak interactions. Our results thereby both provide a unified understanding of superconductivity in TBG, with a natural cooperation of electron- and phonon-mediated pairing, and clarify the microscopic origin of the competition between the chiral and nematic superconducting states.

In order to meet the precision requirements for the LHC and future colliders, next-to-next-to-leading order corrections to a wide range of processes are essential, making general automated tools highly desirable. Extending the strategy of the widespread one-loop program OpenLoops to two loops, there are three major ingredients: process-dependent tensor coefficients, tensor integrals, and process-independent counterterms. In these proceedings, we focus on the second part and present a new recursive algorithm to reduce arbitrary two-loop tensor integrals to scalar integrals numerically.

We develop an analytic, fully field-theoretic description of how a hadronic medium can induce photon condensation in a cavity. Starting from leading-order Chiral Perturbation Theory minimally coupled to Maxwell theory, we construct a consistent truncation to the lowest hadronic and gauge modes that still supports a non-vanishing baryon (topological) density. The resulting reduced dynamics is an effective \(1+1\) theory whose couplings retain memory of the three-dimensional cavity through discrete winding and transverse holonomy data. Integrating out the heavy hadronic mode at one loop yields a gauge-invariant effective potential for the lowest photonic cavity mode, from which we derive analytic criteria for a condensed window. In the opposite hierarchy, integrating out the gauge mode produces a one-loop deformation of a sine--Gordon-type EFT for the chiral mode and makes explicit where scale separation fails and the full coupled system must be kept. Upon quantization, the reduced theory maps onto standard nonlinear quantum-optics Hamiltonians, including a two-photon Rabi limit and quartic single-mode photonic models whose trivial and condensed branches obey distinct selection rules. This provides a concrete bridge between finite-density hadronic physics and experimentally familiar nonlinear-cavity diagnostics.

We present PEACOCK, a three-dimensional Monte Carlo radiative transfer (RT) framework designed to self-consistently model rest-frame ultraviolet emission and absorption lines arising from multiphase, clumpy galactic winds. Applied to deep HST/COS spectra of 50 nearby star-forming galaxies, PEACOCK reproduces 220 observed profiles of Ly-alpha, Si II, C II, Si III, Si IV, and C IV spanning absorption, emission, and P-Cygni-like morphologies within a single CGM model. By combining Monte Carlo RT with deep-learning acceleration and nested sampling, the framework enables fully converged multi-line inference at a small fraction of the cost of traditional RT grids. Systematic experiments show that ion column densities, bulk outflow velocities, and turbulent motions leave distinct imprints on line profiles, allowing the underlying gas properties to be constrained with minimal degeneracy. Purely radial accelerating flows often fail to reproduce the observed absorption morphologies, whereas macroscopic velocity dispersion naturally produces the broad asymmetric troughs seen in the data, indicating that turbulent motions are a key component of outflow kinematics. The inferred kinematics reveal strong coherence among low- and high-ionization metal lines in both bulk and turbulent velocities, consistent with a dynamically coupled multiphase wind. In contrast, neutral hydrogen shows weaker correspondence with metals, suggesting incomplete mixing and a distinct kinematic structure. By unifying emission and absorption diagnostics across multiple ions, PEACOCK provides a physically grounded bridge between UV observations and theoretical models of galactic winds.

In our previous work [2], we introduced a hardware- and power-efficient architecture for hybrid digital-analog (HDA) multiuser MIMO (MU-MIMO) based on stacking identical basic modules. Each module consists of a small active multi-antenna feeder (AMAF) placed in the near field of a larger reflective intelligent surface (RIS). Each AMAF is driven by one RF chain and conveys one spatial stream, achieving a multiplexing gain of $K$ with $K$ stacked modules. While [2] focused on module design and efficiency compared to active arrays, performance was evaluated only under pure line-of-sight (LOS) conditions. This work extends our approach in several ways. First, we propose a simple, pragmatic method for designing phase-only flat-top beams for the AMAF-RIS module, enabling wide angular coverage with low ripple and sidelobes. This design supports hierarchical beamforming codebooks for efficient beam acquisition. Second, we evaluate MU-MIMO performance under realistic mmWave multipath channels including both LOS and non-LOS (NLOS) components modeled using a 3D von Mises-Fisher distribution. We propose a low-complexity HDA MU-MIMO framework with: user-beam association via standard beam acquisition; dynamic user grouping (one user per beam); effective baseband MIMO channel estimation using 3GPP-compliant pilots; and downlink transmission with zero-forcing precoding under per-antenna power constraints. Results show high spectral efficiency and multiplexing gain while preserving hardware simplicity and power efficiency. Crucially, the approach is fully compliant with 3GPP 5GNR beam acquisition and sounding reference signaling mechanisms.

Device logs are essential for forensic investigations, enterprise monitoring, and fraud detection; however, they often leak personally identifiable information (PII) when exported for third-party analysis. Existing approaches either fail to minimize PII exposure across all stages of log collection and analysis or sacrifice data fidelity, resulting in less effective analysis. We present Proteus, a privacy-preserving device logging framework that enables forensic analysis without disclosing plaintext PII or compromising fidelity, even when facing adversaries with access to multiple snapshots of the log files. To achieve this, Proteus proposes a two-layer scheme that employs keyed-hash pseudonymization of PII fields and time-rotating encryption with ratcheted ephemeral keys to prevent multi-snapshot correlation. For controlled sharing, clients export ratchet states that grant time-bounded access, permitting decryption of pseudonymized tokens that enable linkage and timeline reconstruction without exposing the underlying PII. Subsequent ratchet rotations ensure forward secrecy, while DICE-based attestation authenticates device provenance. We implement Proteus as a transparent extension to Android's logcat and evaluate it across three generations of hardware. Our results demonstrate a median latency of 0.2 ms per message and an average per-PII-field size overhead of only 97.1 bytes.

Understanding how local structural order governs electronic correlations is essential for revealing the microscopic mechanism underlying emergent behavior in two-dimensional magnets. In the layered van der Waals ferromagnet Fe\textsubscript{5-x}GeTe\textsubscript{2}, intrinsic Fe-site disorder provides a natural platform to probe this interplay. Here, we establish a direct atomic scale correlation between Fe-site ordering and local electronic structure by combining high-resolution scanning tunneling microscopy with density functional theory calculations. Scanning tunneling microscopy resolves two coexisting surface phases, a $\sqrt{3} \times \sqrt{3}$ superstructure associated with ordered Fe(1) configurations and an undistorted $1 \times 1$ hexagonal Te lattice in Fe(1)-deficient regions. Spatially resolved spectroscopy shows that the $\sqrt{3}$-ordered domains exhibit metallic behavior, whereas Fe(1) vacant areas display a suppressed density of states(DOS) near the Fermi level, indicative of pseudogapped electronic states. The nanoscale coexistence of these distinct electronic responses provides direct evidence of electronic phase separation driven by Fe-site ordering. First-principles calculations reveal that symmetry allowed hybridization between Fe 3d and Te 5p orbitals reconstructs the low-energy electronic structure, giving rise to the contrasting tunneling signatures of ordered and disordered phases. Bias-dependent local DOS simulations reproduce the experimentally observed contrast evolution and reveal that hybridization induced out of plane orbital character governs the spatial modulation of tunneling conductance. These results provide a microscopic framework linking atomic-scale structural order to nanoscale electronic inhomogeneity in van der Waals magnets.

In this paper, we propose an adaptive data-driven min-max model predictive control (MPC) scheme for discrete-time linear time-varying (LTV) systems. We assume that prior knowledge of the system dynamics and bounds on the variations are known, and that the states are measured online. Starting from an initial state-feedback gain derived from prior knowledge, the algorithm updates the state-feedback gain using online input-state data. To this end, a semidefinite program (SDP) is solved to minimize an upper bound on the infinite-horizon optimal cost and to derive a corresponding state-feedback gain. We prove that the resulting closed-loop system is exponentially stabilized and satisfies the constraints. Further, we extend the proposed scheme to LTV systems with process noise. The resulting closed-loop system is shown to be robustly stabilized to a robust positive invariant (RPI) set. Finally, the proposed methods are demonstrated by numerical simulations.

We show that the geometric and homological finiteness properties of group pairs are invariant under a suitable notion of quasi-isometry for group pairs.

This note aims to continue our study about the applications of Poisson quasi-Nijenhuis geometry to the theory of classical completely integrable systems. More precisely, we will present new versions of the deformation and involutivity theorems, under the hypothesis that the closed 2-form triggering the deformation and the closed 3-form defining the Poisson quasi-Nijenhuis structure are factorized. These results will be supplemented by several examples of involutive Poisson quasi- Nijenhuis manifolds.

We present a method for calculating the ground state energy of the Fermi-Hubbard model leveraging Rydberg atom processors and sample-based quantum diagonalization (SQD). By exploiting the perturbative relationship between the Fermi-Hubbard and Heisenberg models, the procedure samples from the Heisenberg model as prepared on the Rydberg atom processor, and uses the samples to diagonalize the Fermi-Hubbard model for large U. We include anisotropy and next-nearest-neighbor interactions and discuss the relevant regime for quasi-superconductivity in the 1-dimensional Fermi- Hubbard model. Numerical and experimental results on the Aquila quantum processor are presented for ground state energy calculations as well as the chemical potential. We find that the Heisenberg model sampling in the studied regime is sufficient to converge near to the ground state for up to 56 qubits, and we see a clear advantage of Rydberg atom sampling as opposed to random sampling even with 10x more samples for diagonalization. We also present a gate-based implementation of the gate-based SQD algorithm on IBM Quantum hardware for 56-qubit Hubbard model as a benchmark. Finally, we provide a gap analysis for studying emergent superconductivity using this method.

Numerous cell types relate to their immediate environment by exerting a three-dimensional pressure field on their environment, with components both longitudinal and transverse to the cell membrane. This pressure field can in principle be measured by traction force microscopy experiments. Compared to other approaches, the technique of Protrusion Force Microscopy gives access with high spatial resolution to the pressure field by measuring the deformation of a thin elastic membrane using atomic force microscopy (AFM). However, while the pressure field under interest is three-dimensional, the height profile measured by AFM is only one-dimensional. We propose a solution to this inverse problem and we explore its regime of applicability in the experimental context.

We present a reanalysis of archived data from the ALEPH experiment at LEP in the $\mathrm{Z \to q\bar{q}}$ final state. We apply modern jet flavour tagging techniques to improve the separation between the different hadronic decay channels of the Z boson, achieving up to one order of magnitude improvement in misidentification rate for b- and c-quark jets compared to the legacy algorithms used for the most recent ALEPH results, for the same identification efficiency. We also present the first implementation of strange quark jet tagging with LEP data, which allows for the selection of a $\mathrm{Z \to s\bar{s}}$ enriched event sample. These improvements in the flavour tagging performance are achieved by leveraging the lifetime, particle identification, and secondary vertex information, as well as modern classifiers based on a deep learning approach. We also demonstrate the calibration of the tagger in data using a tag-and-probe method, obtaining good data to simulation agreement for all quark flavours. These results pave the way for improved measurements of electroweak precision observables with LEP archived data, and can serve as a guidance for the development of detectors and algorithms for future electron-positron colliders.

The calculation of the error threshold of quantum error correcting codes typically proceeds as follows. First, syndromes are measured. Then, a decoder infers the error chain and the corresponding correction is applied. The threshold is then defined as the largest correctable error rate, with the maximum-likelihood decoder corresponding to the ``optimal'' threshold. However, a broader set of operations could be used to recover quantum information. The true optimal threshold should be optimised over all possible recovery schemes, which can be described by quantum channels. Here, we study such optimal recovery channels and their thresholds $p_\mathrm{th}^\mathrm{opt}$. We introduce an information-theoretic quantity, mutual trace distance, which provides a necessary and sufficient diagnostic for sharply determining $p_\mathrm{th}^\mathrm{opt}$ without explicit optimisation. In contrast, previous works give a lower bound on $p_\mathrm{th}^\mathrm{opt}$ by specifying particular recovery schemes, e.g. Schumacher-Westmoreland (SW) which provides coherent information as a diagnostic to lower bound $p^\mathrm{opt}_\mathrm{th}$. We prove that the Petz and SW recovery schemes are optimal, i.e. their threshold is $p_\mathrm{th}^\mathrm{opt}$. With their optimality established, we explore the structure of optimal and non-optimal recovery schemes and their phase diagrams.

We investigate the nonlinear heat-diffusion equation \( C(u)\,\frac{\partial u}{\partial t} = \frac{\partial}{\partial x}\!\left( K(u)\,\frac{\partial u}{\partial x} \right) \), where \( C(u) \) and \( K(u) \) are coefficients that depend on \( u \). By applying the classical Lie symmetry method, we determine the admitted Lie point symmetries and compute the corresponding infinitesimal generators according to the functional relationship between \( C(u) \) and \( K(u) \). The admitted symmetries are used to reduce the partial differential equation to ordinary differential equations and to construct invariant solutions. Particular cases of physical interest are analyzed in detail, including Storm-type materials and power-law dependence of \( C(u) \) and \( K(u) \) on \( u \). For these cases, similarity solutions are obtained.

Spatially-resolved X-ray observations are the key to understanding electron acceleration in solar flares. Currently, the underlying processes that efficiently energize solar flare particles are poorly constrained. Abundant flare observations suggest that turbulence plays a crucial role in transferring energy between the magnetic field and energetic electrons. For the first time, we connect inhomogeneous acceleration from turbulence and hard X-ray spectroscopy and imaging observations with kinetic modeling to constrain the properties of flare acceleration. Observing three large flares with RHESSI, or Solar Orbiter/STIX, we extract X-ray imaging and spectroscopy observables. We compare with modeling results, mapping observables to electron acceleration and turbulent properties. We determine that extended regions of turbulence are required to match multiple X-ray observables, suggesting electrons are accelerated over a large fraction (~25%) of the flare loop; a property that is usually unconstrained from X-ray observations alone. Additionally, we determine acceleration timescales that vary between 7 and 22s by using fixed values for the turbulent scattering timescale and the velocity dependence of the acceleration diffusion coefficient. These fixed values are effectively unconstrained, but yield acceleration timescales that will help to restrict possible viable stochastic models.

AI weather foundation models now achieve forecast skill comparable to numerical weather prediction at far lower computational cost, yet their predictability for high-impact extremes across dynamical regimes remains uncertain. We evaluate Aurora using an event-based framework spanning tropical cyclones, freezes, heatwaves, atmospheric rivers, and extreme precipitation at lead times from 1 to 21 days. Aurora demonstrates strong short-range (1-7 day) skill across event types, including competitive tropical cyclone track accuracy and high spatial agreement for temperature and moisture extremes. However, a consistent subseasonal failure mode emerges: while large-scale circulation patterns remain moderately skillful at 14-21 day leads, threshold-based extreme intensity collapses as fields regress toward climatology. This divergence indicates that Aurora retains synoptic-scale dynamical structure but loses surface-impact amplitude beyond 7-10 days. The practical predictability horizon for deterministic AI extreme-event forecasting therefore remains constrained by intrinsic atmospheric dynamics.

Next-generation wireless networks require enhanced flexibility, efficiency, and reliability in physical layer waveform design to address the challenges posed by heterogeneous channel conditions and stringent quality-of-service demands. To this end, this paper proposes a unified multicarrier waveform framework that provides a systematic characterization and practical implementation guidelines to facilitate waveform selection for the sixth-generation (6G) mobile networks and beyond. We commence by examining the design principles of the state-of-the-art waveforms, which are categorized into one-dimensional modulation waveforms (e.g., orthogonal frequency division multiplexing (OFDM) and affine frequency division multiplexing (AFDM)) and two-dimensional modulation waveforms (e.g., orthogonal time frequency space (OTFS)). Their inherent resilience against various channel-induced interference is further studied, revealing their distinct suitability in diverse channel conditions. Furthermore, an in-depth performance analysis is presented by comparing their key performance indicators (KPIs), followed by an extensive exploration of these advanced waveforms in various applications. Consequently, this work aims to serve as a pivotal reference for waveform adoption in future 6G standardization and network deployment.