Recent advances in the use of High-Resolution Cross-Correlation Spectroscopy (HRCCS) to detect molecular species in exoplanet atmospheres, presents a new challenge for the accuracy of reference spectroscopic line lists. While parent isotopologues of key atmospheric tracers are often well-characterized, minor isotopologues, crucial for diagnosing planetary formation histories and evolution, suffer from a scarcity of experimental data, often leading to reliance on less accurate theoretical predictions. In this work, a comprehensive machine learning framework is designed to mitigate these inaccuracies by modelling the residual errors of the isotopologue extrapolation (IE) method used within the ExoMol project. A fully connected neural network architecture for carbon dioxide (CO$_2$) is shown to predict energy corrections with high fidelity, reducing the mean absolute error (MAE) relative to the original IE approach for more than 87\% of the levels when benchmarked against empirical (\Marvel) energies. Furthermore, development of a novel hybrid, molecule-aware transfer learning architecture is presented that successfully propagates correction patterns from the data-rich CO$_2$ system to the data-poor carbon monoxide (CO) system. This transfer learning approach yields MAE improvements in over 93\% of CO samples, demonstrating that physical correction factors related to isotopic substitution can be generalized across chemically related molecular systems. Updated and improved line lists are presented for 11 CO$_2$ isotopologues and energy levels for excited states of CO isotopologues are predicted. The methodology establishes a scalable, data-driven paradigm for refining molecular line lists, helping to bridge the gap between theoretical calculations and experimental precision.

We develop an operator-theoretic formulation of hereditary constitutive models and characterize optimal finite-rank internal-variable approximations in the sense of Kolmogorov $N$-widths. The history operator is shown to be compact under natural assumptions on the relaxation kernel, thereby admitting optimal low-rank approximations. The resulting reduced models inherit thermodynamic consistency, stability, and provable approximation bounds. An analysis clarifies the structural relation between hereditary representations and internal-variable theories and provides a rigorous basis for reduced-order modeling in computational mechanics. Selected numerical examples showcase optimal convergence of approximations with respect to rank and sampling.

Distance-bounding (DB) protocols let a verifier upper-bound a prover's physical distance by timing rapid challenge-response exchanges. Quantum communication promises simpler DB protocols with stronger security guarantees, yet existing quantum distance-bounding (QDB) proposals are analysed in ad-hoc models and, to the best of our knowledge, lack a common game-based treatment of standard fraud attacks. We contribute (i) a reusable security framework for QDB that fixes system and timing assumptions, specifies a quantum-capable adversary model, formalises distance-, mafia-, and terrorist-fraud experiments, and includes a simple i.i.d. depolarizing noise model; and (ii) an application of this framework to a published QDB protocol. For this protocol we characterise the honest per-round acceptance probability under noise and lift it to the multi-round setting, yielding explicit completeness guarantees as a function of the number of fast rounds, the acceptance threshold, and the noise parameter. For active adversaries we bound the per-round success probability of distance-fraud attacks and analyse the best known mafia-fraud strategy, deriving corresponding multi-round soundness bounds. We also show that the protocol is inherently insecure against terrorist-fraud in our model. The framework cleanly separates protocol-independent definitions from protocol-specific analysis and can be used to evaluate existing and future QDB protocols on a common basis.

This paper proposes the LiFE-CD algorithm for convergence time analysis of the max-consensus algorithm in multi-agent systems under Bernoulli-distributed link failures. Unlike existing approaches, which either assume ideal communication or provide asymptotic upper bounds on the expected convergence time, LiFE-CD deterministically computes the full probability distribution of the convergence time from network topology and individual link failure probabilities, without simulation. The full probability distribution enables deadline-aware protocol design with specified reliability guarantees. Based on geometrically distributed link delays, the proposed algorithm iteratively reduces the given network topology considering both unicast and broadcast transmissions. LiFE-CD yields exact results for acyclic networks and, for cyclic networks, tight upper bounds on the convergence time via shortest-path spanning tree construction. Numerical results confirm analytical exactness for acyclic networks, validate tightness for cyclic networks, and demonstrate improvement over existing approaches. Our complexity analysis shows reduced computational cost compared to Monte Carlo simulations, while eliminating stochastic variability and enhancing reproducibility. All results extend directly to min-consensus by structural equivalence.

ISAC systems introduce new privacy risks because an unintended sensing node may exploit the shared radio waveform to infer transmitter-related information even when the communication payload remains secure. This paper investigates transmitter privacy, defined as limiting unauthorized inference of transmitter-related information through channel estimation, in a RIS-aided multi-antenna wireless system with a transmitter, a legitimate receiver, a malicious sensor, and a RIS. The malicious sensor is assumed to estimate the transmitter--sensor channel, and the resulting channel state information can then support unauthorized sensing, inference, or related signal processing. To mitigate this threat, we consider a privacy-oriented design in which the transmitter adopts superposition-based signaling with a message signal and transmit-side artificial noise, while the RIS shapes the propagation environment in a privacy-aware manner. The channel-estimation performance at the malicious sensor is first analyzed under imperfect prior knowledge, and both the true and predicted mean-square-error expressions are derived. Based on this analysis, we formulate a joint active--passive beamforming design problem that maximizes the malicious sensor's predicted channel-estimation error subject to a communication quality-of-service constraint, a transmit-power budget, and the unit-modulus constraints of the RIS. The resulting non-convex problem is handled through a numerically efficient alternating-optimization framework based on an augmented Lagrangian reformulation. Numerical results show that RIS-assisted propagation shaping can substantially degrade unauthorized channel estimation relative to the non-RIS case while preserving reliable communication, and further show that the privacy gains also improve a more direct sensing metric, namely the malicious sensor's angle-of-arrival estimation accuracy.

We describe the prismatic F-gauge associated to a finite flat height one group scheme over a smooth variety of positive characteristic. As applications, we derive the description of the crystalline Dieudonné module of Berthelot-Breen-Messing in this case and recover results of Bragg-Olsson describing flat cohomology using a Hoobler-type sequence.

Statistical physics can describe the behavior of microbial populations consisting of many heterogeneous individuals. A direct consequence is the existence of phase transitions, where the behavior of a population changes discontinuously upon a small perturbation. While such phase transitions have often been proposed in biology, connecting observed behavior to the underlying physics has remained challenging. We show how phase transitions naturally arise in microbial population dynamics and highlight their connection with genealogies. We rigorously demonstrate the existence of a first-order phase transition in a model of bacterial plasmid engineering and find a strict lower bound on the number of plasmids that can be stably maintained in a population.

Temporal dependencies between customer visits, such as synchronization constraints, pose a fundamental challenge in vehicle routing. These dependencies, which arise in applications such as home healthcare routing, aircraft scheduling, and technician routing, introduce inter-route constraints that make the resulting problems significantly harder to solve. We present an exact solution method for vehicle routing problems with temporal dependencies capable of handling all types of temporal dependencies studied in the literature, unlike most existing approaches that target specific subclasses. Our approach is based on a fragment-based formulation in which routes are represented as sequences of a new type of fragment, designed to handle temporal dependency constraints. This formulation is solved via a price-cut-and-enumerate algorithm that computes a lower bound using alternating column-and-row generation, obtains an initial upper bound, and iteratively refines both bounds through fragment enumeration and branch-and-cut, supported by several new classes of valid inequalities. Computational experiments show that our method significantly outperforms state-of-the-art benchmark methods and is able to solve previously intractable instances while covering a wider range of temporal dependencies.

This paper studies reliability-guaranteed decoding for variable-length stop-feedback (VLSF) codes over correlated noncoherent fading channels. The decoding rule is based on the evolution of the information density associated with a given channel input-output realization. Due to channel memory, exact evaluation of this information density is intractable. To enable constructive decoding, computable finite-blocklength lower and upper bounds on the information density that hold uniformly over time along each input-output sequence are derived. The lower bound enables a stopping-time analysis for VLSF decoding and has an operational meaning, while the upper bound provides a reference for the relaxation gap, which is explicitly characterized. As a concrete application, the Gauss-Markov fading channel with Gaussian signaling is considered to numerically investigate the stopping-time distribution and the impact of fading correlation on decoding performance.

Laser-plasma wakefield acceleration (LWFA) offers ultrahigh accelerating gradients in compact setups, but the complex non-linear nature of the process makes it challenging to generate high-quality beams. Injection of electron bunches from an external source into a plasma accelerator provides a promising route to improved performance; however, electron bunches from conventional radio-frequency (RF)-based injectors suffer from non-linear compression and laser-beam asynchrony, leading to energy jitter and emittance growth. We present a fundamental concept of terahertz-controlled electron bunches for external injection into LWFA. This terahertz-frequency approach provides temporal locking between the electron beam and the drive laser, and enables the compression of high-quality beams to sub-10-fs durations before injection into the LWFA. Numerical simulations demonstrate that GeV-scale acceleration with excellent beam quality and stability -- energy jitter and energy spread around 0.2% -- can be achieved using this method. This concept opens new opportunities for stable, multi-stage laser-driven accelerators and supports the development of next-generation applications such as free-electron lasers (FELs).

Scale-resolving simulations of high Reynolds number incompressible flows are often limited by the Courant-Friedrichs-Lewy (CFL) stability restriction imposed by explicit time-stepping schemes, resulting in small time step sizes and long time-to-solution. In this work, we systematically compare two implicit formulations of the velocity correction scheme -- a linear-implicit approach and a sub-stepping (or semi-Lagrangian) method -- against a standard semi-implicit formulation within a high-order spectral/hp element framework. The schemes are assessed in terms of stability limits, temporal accuracy, and computational performance for implicit large-eddy simulation of the Imperial Front Wing benchmark, a complex high Reynolds number geometry with curved surfaces that imposes strict CFL constraints. Both implicit schemes extend the stability limit by up to two orders of magnitude in time step size. While increasing the cost per time step, they reduce the overall time-to-solution by up to a factor of eleven. Accuracy analysis shows that time step sizes up to twenty times larger than the explicit limit have only minor impact on resolving laminar-turbulent transition and key flow statistics. The results quantify the trade-off between stability, accuracy, and computational cost for implicit velocity correction schemes on complex geometries and provide guidance for selecting time integration strategies in large-scale scale-resolving simulations.

We study projective one-parameter conifold degenerations whose central fiber has finitely many ordinary double points. Existing finite-node theory isolates one rank-one local sector per node on the perverse-sheaf, mixed-Hodge-module, and categorical sides, but does not determine which global extension classes are actually realized by geometry. We show that when the nodes are linked by common cycle geometry or homological relations, the corrected extension is not free nodewise data, but is forced into a smaller relation-controlled subspace. To formalize this, we introduce a cycle-node incidence datum and the associated geometrically realized subspace of the ambient nodewise extension space. Under geometrically admissible and block-adapted incidence hypotheses, we prove that the corrected perverse extension factors through this subspace, with incidence compatibility derived from propagation of local variation data along admissible cycle components, and we show that the same relation law lifts compatibly to the mixed-Hodge-module setting. We then compare this relation law with the resolution and smoothing sides and, in the block-separated cycle family, obtain $R_{\mathrm{res}}=R_{\mathrm{sm}}=R_{\mathrm{ext}}=R_{\mathrm{blk}}$.

With the continuous expansion of blockchain application scenarios, consortium chains have raised higher performance and security requirements for consensus mechanisms. Unlike public blockchains, consortium chains typically implement an admission mechanism that restricts participation to trusted entities, ensuring that most replicas are honest and the number of faulty nodes remains small under normal circumstances. In such settings, conventional Byzantine Fault Tolerant (BFT) protocols, which are designed for worst-case adversarial scenarios, incur excessive message exchanges and computational overhead, thereby limiting performance and scalability. To address this issue, this paper proposes T-RBFT, a two-layer consensus mechanism inspired by network sharding and enhanced by the trusted execution environment (TEE). In T-RBFT, consensus nodes are first dynamically grouped based on their runtime characteristics. Then, inter-group consensus is achieved through a TEE-assisted BFT protocol, while each group internally reaches agreement using an improved Raft-based mechanism. Experimental evaluation shows that T-RBFT reduces communication overhead and latency, and achieves higher throughput compared to existing two-layer consensus protocols, providing a scalable and communication-efficient consensus protocol for permissioned blockchain networks.

We point out that the method presented in a recent arXiv article by Jia et al. (arXiv:2512.21848) for constructing local hidden-state models closely follows the framework we developed in N. von Selzam & F. Marquardt (PRX Quantum, 2025) for constructing local hidden-variable models. While Jia et al. cite our work, the extent of the methodological overlap and the degree of textual similarity are not adequately reflected by the attribution given. We document this overlap in detail.

We develop embedding formulae for all possible diffraction problems with Dirichlet scatterers on square lattices using the Wiener--Hopf perspective. The embedding formula expresses solutions for arbitrary plane-wave incidence in terms of a finite set of auxiliary problems, eliminating the need to re-solve boundary value problems for each incidence angle. First we derive explicit embedding formulae for canonical geometries including the half-plane, finite strip, and right-angled wedge. We then generalize the method through an operator-based approach, obtaining embedding formula for arbitrary configurations of obstacles on lattices. This general embedding formula is a key difference from the continuous setting where this is currently not possible. To validate the theory, we perform numerical experiments, confirming agreement with the results derived using the embedding formula. The results highlight the efficiency and generality of the Wiener--Hopf approach in discrete diffraction theory, with potential applications in inverse problems and other areas of physics and mathematics.

In this work, we present an optimization framework for sparse variable-length stop-feedback (VLSF) codes based on a saddlepoint approximation, which jointly optimizes the decoding configuration parameters. Thanks to the analytical tractability of the saddlepoint approximation, the framework enables efficient gradient-based optimization of such parameters for common memoryless channels, including the additive white Gaussian noise, binary symmetric, and binary erasure channels. We further propose a refined decoding rule that extends the conventional fixed-threshold rule and leads to a tighter achievability bound. Numerical results demonstrate that our framework provides near-optimal decoding configurations at low computational cost. Moreover, the results from our refined rule demonstrate that the fixed-threshold decoding rule is restrictive and that achievability bounds can be further tightened.

We have studied the domain switching under NIR fs-laser irradiation in MgO:LN single crystals with special attention to the relative positions of the light-induced domains, microtracks and regions with modified refractive index in the vicinity of the focusing point. The optical imaging along X direction of the irradiated sample demonstrated the narrow microtracks and the lens-shaped regions ("lenses") located in the vicinity of the microtracks. The relative positions of light-induced microtracks, domains and lenses were revealed by overlapping of their images. We have found that the domain envelops the microtrack and partially intersects with the lens. The temperature stability of all light-induced objects during annealing was studied. It was shown that the local modification of the refractive index disappeared irreversibly while the microtrack and domain remain unchanged. The obtained local modification of the refractive index has been considered as a result of the photorefractive effect. The disappearance of the lens after annealing is caused by bulk screening of the photoinduced space-charge field by increased bulk conductivity. The generation of photovoltaic field by tightly focused NIR fs-laser irradiation close to the focusing point is reported for the first time to the authors' knowledge. It should be noted that in LN the photovoltaic field is codirectional with spontaneous polarization and thus cannot switch the polarization. However, it is possible in ferroelectrics with the opposite direction of the photovoltaic field and low value of threshold field. The revealed effect can be utilized for creation of 3D nonlinear photonic crystals by in-bulk domain engineering.

We introduce a colorful version of separating path systems, in which two edges can only be separated from each other by two paths of distinct colors. We calculate the minimum sizes of such systems for various standard classes of graphs and numbers of colors. With respect to this setup, we identify three possible asymptotic behaviors for a class of graphs as the number of colors goes to infinity, and we find a wide range of examples that display each of these behaviors.

We present the results for the galaxy NGC 628 observed with the Planetary Nebulae Spectrograph (PN.S) equipped with the H$α$ arm. With the third PN.S arm, the H$α$ arm, we measure the H$α$ fluxes, in addition to fluxes and line-of-sight velocities (LOSV) of monochromatic spatially unresolved [OIII] 5007Å sources. The narrow band color ([OIII] 5007Å-H$α$) vs m5007 magnitude diagram separates planetary nebulae (PNe) from single compact ionized HII regions and supernovae remnants (SNRs), which also emit in [OIII]5007 Å. The goals are to detect bona-fide PNe in the face-on spiral galaxy NGC 628 (M74) so that we can measure the velocity dispersion of the stars perpendicular to the main plane of the disc. This study validates the empirical selection criteria for PNe with the PN.S in star forming discs. We classified 442 PNe and 251 spatially isolated, unresolved HII regions: the PN.S with the H$α$ arm increased the number of known PNe by a factor 4. We find evidence for two kinematically distinct PN populations in the NGC 628 disc. The kinematically cold PN population dominates the PN luminosity function close to the bright cut-off magnitude, indicating that the PN massive, short-lived progenitors dominate the PNLF bright cut-off in NGC 628. The warmer PN component increasingly dominates at fainter magnitudes. The velocity dispersion orthogonal to the disc plane are σz,cold = 8.8 kms-1 and σz,warm =26.1 kms-1 respectively, over a range of radii 80 to 425 arcsec. These components contribute with the ratio 46% (cold) and 54% (warm). Once the velocity dispersion of the old component is matched with the population's scale height, the decomposition of the rotation curve for NGC 628 leads to a maximal disc, with the rotation of the baryonic component accounting for 78% of the total rotational velocity in NGC 628.

High-performance computing (HPC) applications are increasingly executed in heterogeneous environments, introducing new challenges for programming and software portability. SYCL has emerged as a leading model designed to simplify heterogeneous programming and make it more accessible to developers. Intended as a single-source, cross-platform parallel programming framework, SYCL promises portability, productivity, and performance across a variety of architectures. However, these goals have not been consistently defined or realized, leaving developers with varying expectations. This paper addresses this gap by evaluating SYCL from the perspective of application developers. We analyze whether SYCL meets essential criteria for cross-platform development, including code portability, development productivity, and runtime efficiency. Our evaluation draws on benchmarks and illustrative examples and focuses on SYCL's memory management and parallelism abstractions. We provide detailed comparisons between Unified Shared Memory (USM) and buffer-accessor approaches, as well as between NDRange and hierarchical kernel models. In addition to presenting our own benchmark results on Intel platforms, we synthesize findings from recent studies across multiple SYCL implementations and compilers. Our results expose key limitations and inconsistencies in current SYCL implementations and offer insights into the steps needed to improve the framework's reliability and cross-platform usability.

We study the minimality of $n\times n$ Hermitian matrices $A$ respect to a $C^*$-subalgebra $\mathcal{B}$ of $M_n(\mathbb{C})$ in the spectral norm, that is \[\|A\|\leq \|A+B\|,\ \text{ for every } B\in \mathcal{B}.\] We generalize the notion of the moment of a subspace and relate it to the joint numerical range and the subdifferentials of the maximum eigenvalue. We extend results previously known for the subalgebra of diagonal operators and describe the subdifferential of the maximum eigenvalue in terms of the moment of the corresponding eigenspace. We also characterize $\mathcal{B}$-minimality via moments and subdifferentials, and provide examples.

Electrical discharge at the smallest possible length and charge scales is not well understood. Using optical tweezers, we investigate spontaneous discharges of a single micron-scale particle levitated in air. These ``microdischarges'' have a typical size of $\sim$40 $|e|$, but can be as small as a few $|e|$ and as large as several hundred. The absence of a well-defined trigger charge and the weak dependence on particle size suggest events are not classical gaseous breakdown. Instead, we show that microdischarge events arise from the rapid capture of ions left in the tracks of nearby passing ionizing radiation. Our results highlight the role of natural ionizing radiation in initiating micron-scale discharges and provide a platform for studying discharge physics in electrode-free environments and at the smallest scales.

Ground-based gravitational wave detectors are now routinely surveying the dark Universe, finding hundreds of collisions between compact objects such as black holes and neutron stars. However, terrestrial non-Gaussian noise artefacts, commonly known as glitches, reduce the sensitivity to signals and can overlap signals, producing biased astrophysical inferences. We introduce a hierarchical Bayesian model to measure the glitch rate, which improves upon existing trigger-counting methods in its capacity to measure the rate down into the low signal-to-noise regime without contamination from the Gaussian noise background, provided the population is accurately modelled. The methodology builds on standard hierarchical inference, but includes several novel features, including hierarchical inference with quantile compression (HIQC), a generic approximation method for the hierarchical recycled likelihood, and a time-domain rate estimated by fitting basis functions. We validate the methodology using simulated data with injected glitches and then apply it to data from the fourth LIGO-Virgo-KAGRA observing run, demonstrating time-resolved inferences of the glitch rate over a 24 h period. The inferred glitch rate is consistent with estimates from trigger counts, but does not require an arbitrary threshold and provides a more fine-grained view of the temporal behaviour. Finally, we demonstrate how our individual-detector rate estimates can be transformed into a coincident glitch probability and utilise this to validate that the retracted gravitational-wave candidate GW230630_070659 is likely a pair of coincident glitches.

Understanding and anticipating vulnerability-related activity is a major challenge in cyber threat intelligence. This work investigates whether vulnerability sightings, such as proof-of-concept releases, detection templates, or online discussions, can be forecast over time. Building on our earlier work on VLAI, a transformer-based model that predicts vulnerability severity from textual descriptions, we examine whether severity scores can improve time-series forecasting as exogenous variables. We evaluate several approaches for short-term forecasting of sightings per vulnerability. First, we test SARIMAX models with and without log(x+1) transformations and VLAI-derived severity inputs. Although these adjustments provide limited improvements, SARIMAX remains poorly suited to sparse, short, and bursty vulnerability data. In practice, forecasts often produce overly wide confidence intervals and sometimes unrealistic negative values. To better capture the discrete and event-driven nature of sightings, we then explore count-based methods such as Poisson regression. Early results show that these models produce more stable and interpretable forecasts, especially when sightings are aggregated weekly. We also discuss simpler operational alternatives, including exponential decay functions for short forecasting horizons, to estimate future activity without requiring long historical series. Overall, this study highlights both the potential and the limitations of forecasting rare and bursty cyber events, and provides practical guidance for integrating predictive analytics into vulnerability intelligence workflows.

Random matrices provide a well-established statistical model for a range of arithmetic phenomena. In this paper, we investigate the extent to which one- and two-dimensional convolutional neural networks (CNNs) can distinguish between arithmetic data arising from elliptic curves with conductor in a fixed interval and random matrix data drawn from the same Sato-Tate distribution. Inspired by converse theorems in the Langlands program, we represent each elliptic curve together with its twists as a vector field and, subsequently, encode that vector field as a digital image. We observe that a two-dimensional CNN trained on this image data is better able to separate conductor families from random matrix data than a one-dimensional CNN trained on vectors of Frobenius traces without twisting data. We also observe that the same two-dimensional architecture can predict the analytic rank of an elliptic curve, and it does so by factoring through the (untwisted) Frobenius traces.

We study dense mixtures of passive and active self-aligning disks with isotropic or anisotropic mobility. We find that the passive fraction controls an order-disorder transition that is continuous in the isotropic case and discontinuous in the anisotropic one. A mean-field equation derived from the microscopic heading dynamics captures this dichotomy. Near the transition, both ordered regimes can exhibit multiple metastable oscillating or rotating states, depending on the spatial arrangement of passive particles and lattice defects, but with different transient dynamics: Systems with isotropic mobility visit multiple long-lived attractors during each simulation while systems with anisotropic mobility are trapped by a single attractor. Our results reveal the passive fraction as a physically relevant control parameter in active systems, leading to rich self-organizing dynamics.

Many algorithmic problems can be solved (almost) as efficiently in metric spaces of bounded doubling dimension as in Euclidean space. Unfortunately, the metric space defined by points in a simple polygon equipped with the geodesic distance does not necessarily have bounded doubling dimension. We therefore study the doubling dimension of fat polygons, for two well-known fatness definitions. We prove that locally-fat simple polygons do not always have bounded doubling dimension, while any $(α,β)$-covered polygon does have bounded doubling dimension (even if it has holes). We also study the perimeter of geodesically convex sets in $(α,β)$-covered polygons (possibly with holes), and show that this perimeter is at most a constant times the Euclidean diameter of the set. Using these two results, we obtain new results for several problems on $(α,β)$-covered polygons, including an algorithm that computes the closest pair of a set of $m$ points in an $(α,β)$-covered polygon with $n$ vertices that runs in $O(n + m\log{n})$ expected time.

We establish a decomposition of the intensity-intensity correlation of a scalar optical beam carrying orbital angular momentum (OAM) across multiple modes into intermodal contributions, thereby linking it, within the framework of the Hanbury Brown-Twiss effect, to the underlying modal coherence structure. Upon filtering the spiral phase dependence, the intensity correlations are governed by OAM coherence and orbital anisotropy reflecting classical entanglement between spatial and OAM degrees of freedom. These results extend intensity interferometry to structured light fields and provide direct access to modal coherence properties without phase-sensitive measurements.

We show that the Aligned 2-Higgs Doublet Model (A2HDM) is a framework able to simultaneously accommodate strong first order electro-weak phase transitions, in turn generating detectable gravitational waves as well as a variety of Higgs boson signals (involving both the Standard Model state and its companions, both neutral and charged) accessible at the Large Hadron Collider (LHC). We map the corresponding expanse of parameter space where such a phenomenology is realised in terms of the relative values of the masses of the discovered Higgs boson and the extended Higgs sector states of this model: two neutral ones (a CP-even and a CP-odd) plus a pair of charged ones. We find that both the Laser Interferometer Space Antenna experiment and High-Luminosity LHC can test such a scenario within their lifetime. This study thus sets the stage for a two-prong complementary approach able to scrutinise the extended Higgs sector of the A2HDM in both its high and low temperature manifestations.

Scaling laws are increasingly used as fast surrogate models for high energy laser atmospheric propagation, yet their calibration and comparison still depend on large collections of high-fidelity wave-optics simulations. Existing studies usually rely on privately organized simulation outputs, which makes it difficult to reproduce published fits or evaluate new surrogate formulations on a shared benchmark. We present a public simulation dataset for high energy laser atmospheric propagation with coupled turbulence and thermal blooming. The release contains 226,500 cases spanning target speed, emission geometry, aperture diameter, visibility, aerosol model, beam quality, turbulence strength, and laser power. Data are organized as a case-level main table linked to indexed long-exposure irradiance arrays and centralized metadata, which supports statistical analysis without hiding the underlying field outputs. The simulation pipeline is based on split-step wave-optics propagation with turbulence, attenuation, and thermal-blooming models that have been validated against established propagation references. The dataset is intended for scaling-law calibration, benchmark comparison, surrogate-model training, sensitivity analysis, and inverse studies.