In this work, the effects of the cosmological constant on dark energy stars in Finch-Skea spacetime are systematically investigated within the framework of Einstein gravity. A static and anisotropic stellar configuration composed of ordinary matter and dark energy is constructed by employing the complexity factor formalism to obtain the temporal metric potential. The interior solution is smoothly matched to the exterior Schwarzschild-(anti-)de Sitter spacetime through appropriate boundary conditions. The influence of positive and negative cosmological constants on the structural and stability properties of the compact star candidate Vela X-1 is investigated in detail. The results show that positive values of the cosmological constant produce larger and less compact configurations, whereas negative values lead to denser and more compact stars with stronger gravitational effects. The energy conditions are satisfied throughout the stellar interior for all considered cases. However, sufficiently large values of the cosmological constant introduce deviations from hydrostatic equilibrium and affect the causal and dynamical stability behavior of the model. Overall, the results demonstrate that the cosmological constant plays an important role in determining the compactness, equilibrium and stability behavior of dark energy stars in Finch-Skea spacetime.

Modular Invariant Theory is a branch of mathematics that explores the behavior of polynomial functions invariant under group actions, particularly over fields with positive characteristic. Overall, modular invariant theory serves as a vital link connecting algebraic methods with combinatorial and topological applications. Based on the existing literature, this undergraduate thesis aims to investigate conjectures and problems emerging from the work of Macdonald (1992), and the recent work of Lewis, Reiner, and Stanton (2017), as well as subsequent developments by L. M. Ha, N. D. H. Hai, and N. V. Nghia (2024). In particular, we state and prove a generalization of Conjecture (7.25) by Macdonald (1992), leading to an extension of the Stong-Tamagawa formula, which is a basis-free characterization of Schur functions over finite fields. Besides, we examine conjectures by Lewis-Reiner-Stanton (2017) about invariant spaces of truncated polynomial algebras under the action of parabolic subgroups, and the proof for the Borel subgroups by Ha, Hai, and Nghia (2024), from which we extend the investigation to the invariant rings under the unipotent group's action. Additionally, we consider the delta operators-a pivotal family of operators used in the proof of Ha, Hai, and Nghia (2024)-with particular attention to their polynomiality properties.

The regolith of rocky bodies, such as planets or asteroids, generally settles under gravity conditions different from those of Earth. The behavior of granular material is not easily scalable for different gravities. To predict these highly complex systems where cohesive inter particle forces can be comparable to gravitational forces, we need simulations and experiments. We did experiments on settling of three different granular samples in varying reduced gravities and examined their packing densities. We used a high precision linear stage to artificially induce reduced gravities inside the zero $g$ environment provided by the ZARM drop tower and observe the settling of our samples. The three samples were fine basalt with particle diameters of $1\text{-}200\,μ$m, coarse basalt with $2\text{-}5\,$mm and glass beads with $750\text{-}1000\,μ$m. The artificial gravities were $150,\,250,\,500,\,750$ and $1000\,$mm/s$^2$ and therefore ranged from large asteroid gravity to almost moon gravity. We saw the granular samples have higher volumes in lower gravities and therefore lower packing densities, we also saw the fine basalt be the most sensitive to changes in gravity, up to $+19.6\,\%$ in volume for $250\,$mm/s$^2$, followed by the coarse basalt particles, up to $+12.2\,\%$ for $150\,$mm/s$^2$ and the glass beads packing density being the least sensitive to changes in gravity, up to $+4.25\,\%$ for $250\,$mm/s$^2$. With these experiments we show change in volume is not solely dependent of particle size but also roughness and uniformity, we provide real life experimental data to validate theoretical works and highlight the role of cohesive forces in low gravity environments.

We introduce a boundary--residue incidence coalgebra associated with the face poset of a positive geometry and apply it to associahedral scattering forms. The construction is motivated by the analogy between the Connes--Kreimer coproduct on Feynman graphs and the recursive residue structure of canonical forms. For the Stasheff associahedron \(K_n\), whose faces are indexed by non-crossing dissections of an \((n+1)\)-gon, we prove that the incidence coproduct records all intermediate nested planar factorisation channels of the corresponding tree-level scalar amplitude. The residue of the canonical form on a face labelled by a dissection factorises as the exterior product of canonical forms on the lower associahedra associated with the resulting subpolygons. We illustrate the construction explicitly for the pentagon associahedron \(K_4\), corresponding to the five-point planar scalar amplitude. We then formulate a loop-level extension: whenever a planar loop integrand is represented by a positive geometry, the associahedral face poset is replaced by the boundary poset of the corresponding loop geometry. The one-loop halohedron gives a concrete scalar example, while in the non-planar case we define the associated incidence coalgebra at the level of logarithmic singularity strata. Finally, we compare the boundary--residue coalgebra with the cellular incidence coalgebra of a triangulated or regular CW spacetime. The face poset of a finite regular CW complex reconstructs its barycentric subdivision, and hence its underlying polyhedron, while in positive geometry the same incidence mechanism organises canonical-form residues. This yields an incidence-first bridge between cellular spacetime topology and positive-geometric amplitude factorisation, without assuming that metric or causal data are determined by topology.

The harmonic oscillator is the universal Hamiltonian of stable equilibrium. Its counterpart, the inverted harmonic oscillator (IHO), is the Hamiltonian of unstable equilibrium: the saddle point of physical systems. It appears across disciplines, from condensed matter, quantum optics, and quantum chemistry to the Standard Model Higgs instability and quantum field theory near gravitational horizons. Its mathematical depth is further reflected in its relation to the non-trivial zeros of the Riemann zeta function through the Berry-Keating Hamiltonian. Remarkably, a dual Hamiltonian to the IHO has recently been shown to govern the additional spin-2 sector of the unique unitary perturbatively renormalizable theory of quantum gravity in four dimensions, with that sector remaining purely virtual and regularizing gravitational interactions at the Planck scale. This paper argues that the universal physics of the saddle point course-corrects the history of quantum gravity approaches that abandoned renormalizability, uniqueness, and predictivity. Its consequences include a non-singular Universe, Starobinsky inflation, and possible implications for large-scale CMB features and primordial gravitational waves.

We present the EPS Research Astro-RAG Platform (v1.0), an open-science research infrastructure providing four machine-readable, cross-epoch astrophysical corpora, 120 verified executable Jupyter notebook examples, a QuickStart reproducibility pathway, an educational High-School Exploration Track, and a roadmap for LLM-assisted retrieval-augmented generation (RAG) research workflows. The platform spans the full observable cosmic epoch from the local universe (z = 0) to the epoch approaching reionization (z ~ 6), providing the first unified kinematic dataset connecting HI 21cm rotation curves, Milky Way globular cluster dynamics, and high-redshift ALMA [CII] morpho-kinematics under a common schema and analysis framework. The four corpora contain 772 total objects: 438 HI-traced galaxies (Unified HI Rotation Curve Corpus v7.0), 129 dwarf/irregular galaxies (Dwarf/Irregular HI Corpus v1.0), 174 Milky Way globular clusters (GC Corpus v1.3.1), and 31 star-forming galaxies at z = 4.26-5.68 (High-z Kinematic Corpus Z1). The Unified HI corpus preserves the full fidelity of the Case Western Reserve University SPARC database (Lelli et al. 2016), including all photometric decomposition components and surface brightness profiles, augmented with THINGS, LITTLE THINGS, and WALLABY DR2 data. The unifying scientific framework is the omega kinematic correction of Flynn & Cannaliato (2025), which reveals a robust sign reversal in the boundary-point angular velocity omega from positive values at z = 0 (SPARC mean +7.06 +/- 3.26 rad/Gyr) to negative values at z ~ 5 (Z1 median -13.05 rad/Gyr), motivating future RAMSES cosmological simulations. All corpora are released under CC BY 4.0 at Zenodo with permanent DOIs, and the platform is archived at https://github.com/eps-research/rag-corpus-series (DOI: 10.5281/zenodo.20398430).

During pandemics, public health agencies need to rapidly assess whether a new viral variant is more transmissible than existing lineages. For co-circulating variants, relative fitness can be expressed as a selective coefficient, as the differential population growth rate (DPGR) estimated from genomic surveillance, or, with additional assumptions, as a contrast in epidemic reproduction numbers $R_t$. We show that DPGR estimates a pairwise growth-rate difference. Under a specified generation-interval model, this difference can be transformed into reproduction-number space; in the equal-generation-time SIR special case, it reduces to a scaled difference in variant-specific $R_t$. Related growth-rate contrasts also appear in multinomial logistic and growth-advantage random-walk models, although those methods differ from DPGR in likelihood, smoothing, priors, and data inputs. We evaluate the theory across five SARS-CoV-2 and influenza analyses totaling more than 2,200 matched data points. SIR simulation recovers the expected mapping when the true $R_t$ is known, and retrospective SARS-CoV-2 analyses show sustained DPGR signals 43 to 65 days before variant dominance, with 95\% sign accuracy in our analysis. DPGR is approximately transitive across lineage triplets, near zero for selected functionally similar sublineages, and directionally consistent across countries. These results connect sequence-count-based fitness estimates to reproduction-number contrasts through an assumption-explicit growth-rate bridge.

We provide a lower bound for a weighted ratio of $Γ-$functions and its $\log{}-$derivative. Then we apply this result to estimate the norm of the operator associated with the Cesáro operator in the Hardy space $H^p({\mathbb C}_+)$, $1<p<\infty$

FREESS (Free Educational Superscalar Simulator) is an open-source teaching environment for instruction-level parallelism in a RISC-V-inspired superscalar processor. It provides a compact, cycle-by-cycle view of register renaming, issue, execution, write-back, commit, and memory ordering in a Tomasulo-style machine. The simulator exposes the register map, free pool, instruction window, reorder buffer, and load/store queues in one textual representation, so the evolution of the hardware state can be followed on screen and reproduced on paper. Runtime parameters such as issue width, queue sizes, and functional-unit latencies can be changed easily, enabling direct comparison among alternative superscalar organizations. The tool has supported Advanced Computer Architecture teaching for about fifteen years and is publicly available on GitHub.

Apple-Peel Unfolding is a greedy algorithm that selects the faces (or cells) of a polyhedron (or polytope) one at a time in a spiral order, producing a net analogous to peeling an apple in a single continuous strip. We define two face-selection rules -- RS (Spiral rule: minimum signed determinant, i.e.\ sharpest clockwise turn) and RZ (Zonal rule: maximum coordinate along the peeling axis) -- and systematically evaluate their unfolding success rates on (i)~the five Platonic solids, (ii)~the thirteen Archimedean solids, and (iii)~the six regular convex 4-polytopes. A principal contribution is a three-way classification of each solid as \emph{Perfect} (every starting pair yields a complete net), \emph{Possible} (at least one pair succeeds), or \emph{Impossible} (no pair succeeds), together with an equivariance argument showing that face-transitive solids are confined to the $0/100\%$ dichotomy. RZ achieves the highest success rates in most cases; for the regular 4-polytopes it is the only rule yielding non-zero results for the 120-cell, where it achieves a Perfect result (1,440/1,440 pairs). We note that \emph{ordering success} (completing the greedy traversal) and \emph{geometric validity} (no self-intersection in the 3D realization) are distinct: every 120-cell ordering produces a self-intersecting 3D net, so the 120-cell has zero valid 3D nets despite its Perfect ordering result. The 600-cell is Impossible under all rules tested.

We show that the GW170817-GW190814 tension can be reconciled within General Relativity by a structured causal EoS basin found with a Constrained Evolutionary TOV Discovery pipeline (CETD). The basin contains ~1.4x10^4 unique EoS with M_max = 2.3-2.8 M_sun, R_1.4 = 11.97-12.29 km, Lambda_1.4 <= 580, and double-peaked sound speeds reaching c_s^2/c^2 = 0.86-0.99.

Distributed systems must frequently keep track of many different types of performance metrics across many different computers. For example, the latency distribution of certain operations may be computed for a large combination of computers, users, and operations. These empirical distributions need to be collected at minimal expense on the individual software components, efficiently aggregated across multiple dimensions, and stored in a compact representation for a variety of downstream data analysis applications. We describe an information loss metric for binned data that allows us to optimize cost of information loss from different histogram representations. We explore the use of polynomial histograms where each bin of a histogram is annotated with moments of the underlying distribution in that bin. These polynomial histograms are compared to traditional histograms using the same storage cost for additional bins instead of annotations in each bin. We describe an application of these techniques for file system metrics for a large production system, and analytically characterize when polynomial histograms offer more information at lower cost.

The rapid proliferation of artificial intelligence, connected devices, and high speed mobile networks is driving unprecedented computational demands that challenge traditional sensor architectures. This article explores the shift toward edge computing, where computation is performed directly at the data source, and highlights the key architectures and performance metrics that may define the next generation of intelligent sensor systems.

Existing collaborative WiFi sensing systems rely on perfect node synchronization and complete data availability. However, real-world edge deployments suffer from heterogeneous computing and network dropouts, leading to asynchronous and incomplete features. We propose CREWS, a robust collaborative sensing framework that inherently resists these network volatility. First, CREWS employs a topology-agnostic aggregator invariant to the arrival order and subset size of incoming features. Second, rather than discarding delayed observations, it utilizes a staleness-aware adaptive replay mechanism. By treating stale features from lagging nodes as system-induced hard samples, CREWS transforms synchronization delays into beneficial training regularization. We theoretically prove the joint convergence of this architecture and demonstrate how replay bounds the bias-variance trade-off. Extensive evaluations and an 8-node heterogeneous hardware testbed demonstrate its superior resilience. Under severe conditions i.e., 50\% transient dropout rate or out-of-distribution jitter, CREWS restricts accuracy degradation to merely 2.2 percentage points, substantially outperforming state-of-the-art baselines.

The numerical simulation of electromagnetic transients in fusion devices is essential for analyzing plasma stability and disruptive events. However, it remains computationally demanding due to the large-scale dense systems arising from integral formulations. This work proposes a model order reduction (MOR) strategy for transient electromagnetic problems based on integral formulations. Unlike operator-based compression techniques (such as $\mathcal{H}$-matrix approaches), the reduced space is constructed directly from the transient excitation. In contrast to classical snapshot- and transfer-function-based MOR approaches, the proposed formulation avoids repeated explicit inversions or factorizations of the dense integral operator during the MOR basis-construction stage. By combining wavelet-based temporal compression with source-driven Krylov projections, the method generates reduced models tailored to the dynamically reachable responses of the prescribed excitation families. Numerical validations on various plasma events and fusion-relevant scenarios demonstrate the robustness of the strategy, achieving substantial computational speedups while accurately preserving the transient electromagnetic response. Finally, the method is successfully applied to the null-field problem to efficiently generate training data for neural-network surrogates, contributing toward physics-consistent AI-enabled fusion modelling.

Estimating time-resolved velocity and pressure fields from Particle Image Velocimetry (PIV) remains challenging due to its limited temporal resolution in many applications. Data-driven approaches that combine snapshot PIV with high-frequency probe data have shown great promise in reconstructing the flow dynamics for advection-dominated flows; however, they typically exploit only the probe measurements directly synchronized with the PIV frames, leaving a large volume of probe-only data acquired between snapshots unused. In this work, we propose a framework that enriches the original PIV training dataset by time-marching a simple advection model and then exploits unlabelled probe data through a semi-supervised learning strategy. Two neural networks are trained to predict the temporal coefficients of Proper Orthogonal Decomposition (POD) modes of the flow fields, and their temporal derivatives, respectively. Unlabelled probe samples are leveraged to enforce temporal consistency and expand the coverage of flow scenarios beyond those captured by snapshot PIV, which is crucial for obtaining physically consistent temporal gradients required for pressure field reconstruction. A least-squares regularization step is further employed to reconcile the predictions and enforce consistency between temporal coefficients and their derivatives. The proposed approach is validated on both synthetic turbulent channel flow data and experimental PIV measurements of an airfoil wake. Results demonstrate that incorporating unlabelled probe data significantly improves the accuracy and temporal smoothness of velocity reconstruction, leading to more reliable pressure estimation via the Navier-Stokes equations, without increasing the experimental cost.

We establish scaling limit results for fluid dynamics equations driven by pseudo-transport noise. The behaviour of noise at small scales is governed by a parameter a. This extends previous results by Flandoli and Luo (2020) and Galeati (2020), which correspond to a=0 in our setting. Depending on the value of a, we prove that the noise delays the potential blow-up of both the 3D Euler and Navier-Stokes (NS) equations with high probability.

Large language models (LLMs) have recently been adopted for recommendations due to their ability to understand user intent and item semantics. However, LLM-based recommender systems often rely on parametric knowledge and suffer from outdated knowledge, motivating knowledge graph retrieval-augmented generation (KG-RAG) to ground recommendations on structured, up-to-date KGs. Despite this promise, effective KG-RAG in recommendations faces great challenges. First, users' queries vary in complexity and require KG knowledge at different granularities, whereas existing methods adopt a one-size-fits-all retrieval strategy, leading to over-retrieval for simple queries and under-retrieval for complex ones. In addition, augmenting LLMs with KG knowledge requires translating graph-structured data into linear text, which may introduce noise and cause structural information loss. Moreover, the selection of retrieval granularity lacks direct supervision and must be inferred from the final recommendation after alignment and downstream utilization, making query-aware retrieval hard to learn end-to-end. To address these issues, we propose MixRAGRec, a cooperative multi-agent framework for KG-RAG recommendations. MixRAGRec integrates a Mixture-of-Experts Retrieval Agent that routes each query to a KG retrieval expert with different granularities, a Knowledge Preference Alignment Agent that converts structured knowledge into LLM-friendly natural language, and a Contrastive Learning-reinforced Recommendation Agent trained with contrastive preference feedback. Notably, we introduce Mixture-of-Experts Multi-Agent Policy Optimization (MMAPO) to train three agents under a unified objective. Extensive experiments on real-world datasets demonstrate the effectiveness of our framework.

Motivated by the COLT 2023 open problem of Criscitiello, Martínez-Rubio, and Boumal on deterministic first-order methods for Lipschitz geodesically convex optimization on Hadamard manifolds, we study hyperbolic space \[ \HH^d_{-\kappaC^2} =\{X\in\R^{d+1}:\ipL{X}{X}=-1,\ X_0>0\}, \qquad \ip{U}{V}_X=\kappaC^{-2}\ipL{U}{V}. \] For every geodesically convex $M$-Lipschitz function \[ f:\bar B_{\HH}(x_0,r)\to\R,\qquad s=\kappaC r, \] we give a one-shot Klein cutting-plane method returning a queried point $\hat x$ such that \[ f(\hat x)-\min_{\bar B_{\HH}(x_0,r)}f\le \eps Mr \] after at most \[ \left\lceil 2d(d+1)\log\!\left(\frac{16\sinh s\cosh s}{s\eps}\right) \right\rceil \] oracle calls. For $d\ge2$, each localization step costs $O(d^2)$ arithmetic operations; for $d=1$, an interval variant gives the same oracle bound. Hence \[ N=O\bigl(d^2(s+\log(e/\eps))\bigr) =O\bigl(d^2ζ_s\log(e/\eps)\bigr), \qquad ζ_s=s/\tanh s . \] Compared with the constant-curvature construction associated with the COLT problem, this replaces chained curvature--accuracy dependence by additive dependence. The proof does not rely on convexity of the Klein pullback, which is generally only quasiconvex. Instead, every Riemannian subgradient halfspace becomes an exact Euclidean central cut: for $θ=\kappaC\dist(X,Y)$, \[ \ip{g}{\log_XY}_X =\fracθ{\kappaC^2\sinhθ}\ipL{g}{Y}, \] and tangency at $X$ converts $\ipL{g}{Y}\le0$ into \[ \gbar^{\mathsf T}(u-c)\le0,\qquad u=Φ(Y),\ c=Φ(X). \] Thus one fixed Euclidean ellipsoid localizes the hyperbolic ball, and curvature enters only through \[ \log\!\left(\frac{\sinh s\cosh s}{s\eps}\right) =\log(1/\eps)+2s-\log(4s)+O(e^{-4s}). \] The general Hadamard-manifold problem remains open.

We elucidate the Bures metric in quantum state space near a rank-changing point of the density matrix and show contrasting behavior for two-level ($N=2$) systems versus higher-level systems. Due to the smooth pure-state boundary for $N=2$, we prove the apparent metric divergences to be merely coordinate artifacts and present three Lindblad processes exhibiting qualitatively different evolution near rank-changing points, showing geodesic approach, power-law scaling, and pure-state escape law. For higher-dimensional ($N\ge 3$) systems, the geometry near a rank-changing point differs fundamentally. Under suitable restrictions of the density matrix and its approach towards a pure state, the Bures metric reduces to a conical metric with the pure state at the cone tip. Such a conic geometry leads to genuine curvature singularities: A two-dimensional cone exhibits a Dirac delta-function curvature near the tip while a higher-dimensional cone shows a power-law divergence of the curvature towards the cone tip. A construction of Lindblad evolution for $N=3$ systems with conic singularities is presented, along with possible implications for future experimental and theoretical research.

We study single-target localization in a group-connected beyond-diagonal reconfigurable intelligent surface (BD-RIS)-assisted monostatic network with K element groups. We propose a Nested Tensor Factorization and Estimation (NTFE) algorithm that models the received signal as a 3rd-order nested Tucker tensor, decoupling the delay-Doppler and angle domains. The resulting two-stage procedure estimates the target-bearing tensor factors and then extracts the other physical parameters using subspace and closed-form steps. We also analyze identifiability and uniqueness conditions. Simulations show that NTFE exploits the group-connected BD-RIS structure and outperforms state-of-the-art sensing benchmarks.

Altermagnetism is a compensated magnetic phase characterized by zero net magnetization and exchange-driven spin splitting. However, identifying altermagnets among collinear antiferromagnets usually requires full magnetic-space-group or spin-group analysis, which is not intuitive. Here we formulate a simple real-space criterion based on how the crystallographic operations of the host nonmagnetic structure permute the two opposite-spin sublattices. For simplicity, we focus on collinear compensated antiferromagnets whose magnetic primitive cell coincides with the host nonmagnetic crystallographic primitive cell. In this class, altermagnetic spin splitting is generally allowed unless an inversion-type operation exists that exchanges the two opposite-spin sublattices. First-principles calculations on representative noncentrosymmetric and centrosymmetric materials demonstrate this criterion. Similar rules can also be applied to low-dimensional crystals or quasicrystals. Our work reduces the identification of altermagnetism to a transparent real-space symmetry test and provides a practical route for discovering altermagnetic crystals.

We give an introduction to the cosmological multiverse, aimed at an audience of artists. We discuss general relativity -- our modern theory of gravity -- and the cosmological constant, which is widely believed to be responsible for the observed accelerated expansion of the universe. We then turn to a big puzzle that the cosmological constant poses, and, eventually, how the multiverse could solve this puzzle. There's no such thing as a free lunch, however: the multiverse can become arbitrarily large and old. The unsolved problem of making unambiguous predictions for observations in eternally accelerating universes is known as the measure problem of eternal inflation.

We show that the Wirtinger criterion cannot be used to investigate the frame set conjecture for the first Hermite function. More generally, for odd functions, it cannot determine regions of the frame set with density less than 2.

This paper establishes new upper bounds for the sum of the $k$ largest eigenvalues of symmetric matrices. When applied to the adjacency matrix of a graph, our results improve upon a related bound due to Mohar {\bf [On the sum of k largest eigenvalues of graphs and symmetric matrices, J. Combin. Theory Ser. B 99 (2009) 306--313]}. Furthermore, in the case of the Laplacian matrix, we prove that the well-known Brouwer's conjecture {\bf [Spectra of Graphs, Springer, New York, 2012]} holds for small values of $k$ for almost all graphs, thereby taking a significant step toward its complete resolution.

Crosstalk noise derives from phenomena in quantum devices which inhibit individual addressability or cause unintended interactions among qubits. It is widely considered one of the major problems to be solved for a quantum computing platform to operate at scales beyond one or two qubits. Despite this, detailed discussion of crosstalk is often neglected when quantum device performance is described both in the context of device benchmarking and individual algorithm execution. Additionally, while the potential for crosstalk exists in all quantum platforms, the mechanisms and severity of crosstalk between platforms varies significantly, increasing the barrier of entry associated with understanding and performing research on unfamiliar quantum platforms. While previous work focused on theoretical formalism or platform specific details, in this review article, we provide a comprehensive overview of crosstalk from quantum computing literature across a range of physical systems focusing on physical origins, methods of mitigation and known consequential security vulnerabilities. We describe multiple crosstalk mechanisms for all major quantum computing platforms, which are usually implicitly addressed through device design, tuning, and mitigation techniques. We also observe accelerating research regarding security implications, however with multiple avenues for further exploration, especially for non-superconducting systems. Together, this review provides a comprehensive entry point for researchers and industry engineers interested in understanding and addressing the challenges arising from crosstalk phenomena in modern quantum computing systems.

We calculate parity non-conservation (PNC) amplitudes for all magnetic-dipole (M1) transitions within the ground $5p^2$ configuration of Sn. Among the transitions considered, the $^1$S$_0$-$^3$P$_1$ transition has the largest PNC amplitude and appears to be the most promising candidate for experiment. We also discuss a measurement method capable of achieving unprecedentedly high precision in a measurement of PNC in this transition. We argue that the most robust test should be based on ratios of PNC amplitudes for different isotopes, since the atomic-structure factor largely cancels in such ratios. We study the effect of the neutron skin on these isotope ratios using available nuclear data for Sn and show that the uncertainty associated with the neutron skin can be reduced to the $10^{-3}$ level relative to the isotopic variation of the PNC effect. Our results indicate that PNC measurements along a chain of Sn isotopes offer a realistic and sensitive probe of new physics.

The rapid proliferation of visual content raises fundamental questions about how different visual formats and features shape perceived credibility. Drawing on processing fluency theory, this research examines how visuals shape credibility judgments. We focus on three popular formats-photos, infographics, and data visualizations-comparing them to text-only posts, and test how two visual features, aesthetic appeal and production quality, influence credibility through processing fluency as a mediating mechanism. Through a preregistered experiment with 1200 US participants, we found that visual posts are generally perceived as more credible than text-only posts but this credibility advantage only applies to photos and infographics, not to data visualizations. Aesthetic appeal increases perceived credibility, partially mediated by processing fluency, while production quality had no significant effect on credibility across formats. These findings differentiate visual formats, advance conceptualizations of visual features, and identify processing fluency as a key mechanism for theorizing credibility across multimodal contexts.

An important evolutionary pathway for planetary atmospheres is escape to space, which has been studied on Earth and Mars for several decades and more recently in exoplanets. A particularly important regime is the hydrodynamic escape, wherein atmospheric mass escapes the planet at high rates in a collisional fluid outflow. This process is used to partly explain the early evolution of rocky planets in and out of the Solar System, as well as key aspects of exoplanet demographics. Hydrodynamic escape is not occurring in the Solar System planets, so our only option for such observations is through exoplanets. The ultraviolet (UV) capabilities of the Hubble Space Telescope (HST) are fundamental to detect hydrodynamic escape and measure the resulting mass-loss rates for a range of planetary systems and to identify targets for surveys with the Habitable Worlds Observatory. We discuss here what kinds of observations and instrument modes are necessary to continue studying atmospheric escape in exoplanets for the next decade, as well as how to advance our understanding of planetary evolution and habitability.

Nonadiabatic molecular dynamics (NAMD) is widely used to describe hot electron relaxation and nonradiative recombination processes, but high computational costs limit its application to large supercells. Here, we implement a nonadiabatic coupling (NAC) module directly into CP2K, enabling on-the-fly NAC calculation during ab-initio molecular dynamics. Unlike conventional approaches relying on interfaces between external NAMD programs and electronic structure codes, this integration streamlines the workflow. Combined with CP2K's inherent Gaussian and Plane Waves (GPW) method, it achieves efficient NAC calculations for large-scale systems. To ensure numerical stability, a phase correction scheme is introduced to remove inconsistencies of wavefunction phases. Benchmark calculations of hot electron relaxation in crystalline pentacene agree with previous studies, while the results of simulations with and without phase correction show significant difference, confirming the necessity of the phase correction. Simulations on larger pentacene supercells further demonstrate the capability of this implementation for large-scale NAMD simulations.