Let $G$ be a simple graph on $n$ vertices and $I(G)\subseteq R$ be its edge ideal. In this paper, we initiate the study of determining lattice points in $\mathbb{N}^2$ that appear as a pair $(\mathrm{reg}(R/I(G)), \mathrm{v}(I(G)))$, where $G$ ranges over all connected graphs on $n$ vertices, and we denote this set by $\mathcal{RV}(n)$. Here `$\mathrm{reg}$' denotes the (Castelnuovo-Mumford) regularity and `$\mathrm{v}$' denotes the $\mathrm{v}$-number. We establish general bounds for $\mathcal{RV}(n)$ by identifying two sets $A(n)$ and $B(n)$ satisfying $A(n)\subseteq \mathcal{RV}(n)\subseteq B(n)$. Furthermore, we explicitly determine the subsets of $\mathcal{RV}(n)$ consisting of all possible pairs $(\mathrm{reg}(R/I(G)), \mathrm{v}(I(G)))$ arising from whisker graphs and Cameron-Walker graphs on $n$ vertices. Finally, we propose a conjecture on the subset of $\mathcal{RV}(n)$ arising from connected chordal graphs.

We introduce a new resource-efficient scheme for fault-tolerant quantum computation known as `macroscale multiplexing' (or simply `Macromux'), that utilizes scalable postselection to significantly improve the threshold of a given fault-tolerant protocol against both Pauli and erasure errors. Macromux is a hierarchical method for postselecting on constant-size space-time windows of a fault tolerant protocol, requiring only constant additional overheads. The method can be straightforwardly implemented for any fault-tolerant protocol and in any architecture that has access to routing and memory, such as linear-optical fusion-based architectures. We construct fault-tolerant protocols that, to our knowledge, have the highest thresholds in the literature; we perform simulations of fusion-based schemes based on the surface code, showing a maximum possible increase in Pauli thresholds of up to a factor of $\sim6$ (from $1.0\%$ to $5.9\%$). Our schemes are highly-resource efficient, and can for example, double the loss thresholds of some photonic fusion-based protocols using as little as $3 \times$ overhead.

We revisit the determination of the age of the Universe from galactic globular clusters, extending previous analyses by explicitly accounting for the presence of multiple stellar populations within each cluster. Using high--quality \textit{Hubble Space Telescope} color--magnitude diagrams for 69 globular clusters, we relax the standard single--population assumption, and model two stellar populations with independent ages, metallicities, helium abundances, and population fractions. The inference is performed using the full color--magnitude diagram morphology, an explicit treatment of field contamination, and a hierarchical framework that propagates non--Gaussian age posteriors. Allowing for multiple stellar populations has a negligible impact on globular cluster age estimates. The ages of the oldest populations remain fully consistent with those obtained under the single--population assumption, with differences at the $0.6σ$ level. Restricting to the metal--poor subsample ([Fe/H] $< -1.5$), we infer a dominant old component with mean age $t_{\rm GC}=13.61\pm0.25\,\mathrm{(stat)}\,\pm0.23 \mathrm{(sys)}\,\mathrm{Gyr}$. Adopting a conservative delay between the Big Bang and the formation of the first globular clusters, we obtain an age of the Universe of $t_{\rm U}=13.81\pm0.25\,\mathrm{(stat)}\,\pm0.23 \mathrm{(sys)}\,\mathrm{Gyr}$. In addition to age constraints, our analysis yields simultaneous measurements of metallicity and helium content for the different populations, including constraints on helium enrichment and population fractions which are consistent with independent determinations from the literature. These results demonstrate that globular--cluster--based cosmic chronometry is robust to stellar population complexity, reinforcing its role as a precise and largely cosmological model--independent probe of the age of the Universe.

In the paper we study transformations of the interval $[0;1)$ and functions that preserve the asymptotic mean $r$ of the digits in the $s$--adic representation of a number $x$, $$r(x)=\lim\limits_{n\to\infty}\frac{1}{n}\sum\limits^{n}_{i=1}α_i(x)$$ specify the necessary and sufficient conditions for a transformation to belong to this class

In this paper we discuss a classical geometrical problem of estimating an unknown point's location in $\Real{n}$ from several noisy measurements of the Euclidean distances from this point to a set of known reference points (anchors). We approach the problem via a set-mem\-ber\-ship methodology, in which we assume the distance measurements to be affected by unknown-but-bounded errors, and we characterize the set of all points that are consistent with the measurements and their assumed error model. This set is nonconvex, but we show in the paper that it is contained in a region given by the intersection of certain closed balls and a polytope, which we call the {\em localization set}. Then, we develop efficient methods, based on convex programming, for computing a tight outer-bounding set of simple structure (a box, or an ellipsoid) for the localization set, which then acts as a guaranteed set-valued location estimate. % The center of the bounding set also serves as a point location estimate. Related problems of inner approximation of the localization set via balls and ellipsoids are also posed as convex programming problems. Different from existing methods based on semidefinite programming relaxations of a nonconvex cost minimization problem, our approach is direct, geometric and based on a polyhedral set of points that satisfy pairwise differences of the measurement equations.

The explosive growth of the low-altitude economy, driven by eVTOLs and UAVs, demands a unified digital infrastructure to ensure safety and scalability. However, the current aviation vertical references are dangerously fragmented: manned aviation relies on barometric pressure, cartography uses Mean Sea Level (MSL), and obstacle avoidance depends on Above Ground Level (AGL). This fragmentation creates significant ambiguity for autonomous systems and hinders cross-stakeholder interoperability. In this article, we propose Height Above Ellipsoid (HAE) as the standardized vertical reference for lower airspace. Unlike legacy systems prone to environmental drift and inconsistent datums, HAE provides a globally consistent, GNSS-native, and mathematically stable reference. We present a pragmatic bidirectional transformation framework to bridge HAE with legacy systems and demonstrate its efficacy through (1) real-world implementation in Shenzhen's partitioned airspace management, and (2) a probabilistic risk assessment driven by empirical flight logs from the PX4 ecosystem. Results show that transitioning to HAE reduces the required vertical separation minimum, effectively increasing dynamic airspace capacity while maintaining a target safety level. This work offers a roadmap for transitioning from analog height keeping to a digital-native vertical standard.

Given a set of $m$ points and a set of $n$ lines in the plane, we consider the problem of computing the faces of the arrangement of the lines that contain at least one point. In this paper, we present an $O(m^{2/3}n^{2/3}+(n+m)\log n)$ time algorithm for the problem. We also show that this matches the lower bound under the algebraic decision tree model and thus our algorithm is optimal. In particular, when $m=n$, the runtime is $O(n^{4/3})$, which matches the worst case combinatorial complexity $Ω(n^{4/3})$ of all output faces. This is the first optimal algorithm since the problem was first studied more than three decades ago [Edelsbrunner, Guibas, and Sharir, SoCG 1988].

Time series classification underpins applications such as human activity recognition, healthcare monitoring, and gesture detection in the IoT domain. Tiny Machine Learning enables models to run directly on low-power microcontroller units, improving efficiency, ensuring privacy, and reducing cost by avoiding reliance on cloud or edge computing. While Long Short-Term Memory networks are widely used for capturing temporal dependencies, their high computational and memory demands make real-time MCU deployment impractical. In this work, we conduct a hardware-aware feasibility study of LSTM versus 1D Convolutional Neural Networks across five benchmark datasets. Results show that 1D-CNN consistently achieves comparable or higher accuracy around 95% than LSTM which is around 89%, while requiring 35% less RAM, approx. 25% less Flash, and enabling real-time inference that is 27.6 ms vs. 2038 ms. Being so lightweight, 1D-CNN is particularly suitable for on-device processing in wearables and other low-power, battery-operated systems, establishing it as a practical and resource-efficient choice for TinyML deployment.

Ultrafast laser writing of single lattice defects in wide-bandgap semiconductors is shown to present a new physical setting in which deeply subwavelength laser-writing positioning precision is attainable, but where the whole notion of positioning can only be understood in a statistical sense. We outline a framework for the analysis of this class of laser - matter interactions, grounding the concepts of optical super-resolution and subdiffraction positioning in statistical optics. Working along these lines, we derive closed-form solutions for physically meaningful quantifiers of laser-matter interactions on a subwavelength scale, suggesting a physically clear view of how deeply subdiffraction resolution can emerge from the interplay between determinism and stochasticity. We show that subdiffraction positioning precision in single-lattice-defect laser writing is achieved at the cost of a lower throughput, setting physical bounds on the scalability of integrated quantum photonic systems fabricated by means of super-resolving laser writing.

We investigate the spatial profile of the curvature perturbation generated in multi-waterfall hybrid inflation models, which are known to produce various topological defects. Using the lattice simulation code \acl{STOLAS}, based on the stochastic formalism of inflation, we analyse six cases by varying the number of waterfall fields $n$ and the functional form of the inflaton potential (``Quadratic'' and ``Cubic'' cases). Our statistical analysis shows that the \acp{PDF} and power spectra are broadly consistent with the so-called stochastic-$δN$ algorithm. The ``Cubic'' case also exhibits a characteristic upper bound in the \ac{PDF}, as discovered in our previous work, that suppresses \acl{PBH} formation while potentially affecting halo formation. Furthermore, we employ the Euler characteristic as a topological diagnostic tool to identify the structures of the waterfall fields as well as the curvature perturbation. We find that the topological defects, such as domain walls ($n=1$), cosmic strings ($n=2$), and monopoles ($n=3$), are reconnected during inflation into finer structures by the stochastic noise, making their correlation lengths much smaller than the Hubble scale at the critical point of the waterfall phase transition counterintuitively. The Euler characteristic also implies global structures of the curvature perturbation for $n=1$, though we do not conclude if they are due to the domain wall, because neither the strings ($n=2$) nor monopoles ($n=3$) leave such structures. The global structures of the curvature perturbation will provide a novel probe for the physics of the early universe.

We study the effects of spatially inhomogeneous diffusion on the non-equilibrium phase transition in the contact process. The directed-percolation critical point in the contact process is known to be stable against the addition of a spatially uniform diffusion term. Correspondingly, we find quenched randomness in the diffusion rates to be irrelevant by power counting in the field-theory of the contact process. However, large-scale Monte Carlo simulations demonstrate that such diffusion disorder destabilizes the clean directed percolation critical point. Instead, the transition belongs to the same infinite-randomness universality class as the contact process with disorder in the infection or healing rates. To explain these results, we develop an effective model with an infinite diffusion rate; it shows that diffusion disorder generates an effective disorder in the healing rates. The same mechanism also appears in the field-theoretic description: Whereas diffusion disorder is irrelevant by power-counting, it generates standard random-mass disorder under renormalization. We discuss the validity of this mechanism for other absorbing state transitions and non-equilibrium phase transitions in general.

Mixed H2/H-infinity control balances performance and robustness by minimizing an H2 cost bound subject to an H-infinity constraint. However, classical Riccati/LMI solutions offer limited insight into the nonconvex optimization landscape and do not readily scale to large-scale or data-driven settings. In this paper, we revisit mixed H2/H-infinity control from a modern policy optimization viewpoint, including the general two-channel and single-channel cases. One central result is that both cases enjoy a benign nonconvex structure: every stationary point is globally optimal. We characterize the H-infinity-constrained feasible set, which is open, path-connected, with boundary given exactly by policies saturating the H-infinity constraint. We also show that the mixed objective is real analytic in the interior with explicit gradient formulas. Our key analysis builds on an Extended Convex Lifting (ECL) framework that bridges nonconvex policy optimization and convex reformulations. The ECL constructions rely on non-strict Riccati inequalities that allow us to characterize global optimality. These insights reveal hidden convexity in mixed H2/H-infinity control and facilitate the design of scalable policy iteration methods in large-scale settings.

We show that the Bergman kernel of a finite-volume quotient of a Hermitian manifold $\widetilde{X}$ with bounded geometry by a discrete group $Γ$ of its isometries is the same as the averaging over $Γ$ of the Bergman kernel on $\widetilde{X}$. We then use these results when $\widetilde{X}$ is a Hermitian symmetric space to show that a large class of relative Poincaré series does not vanish. This extends the results of Borthwick-Paul-Uribe and Barron (formerly Foth) to the case of general locally symmetric spaces of finite volume.

The effective field theory (EFT) of cosmic acceleration provides a model-independent framework for describing dark energy and modified gravity, yet many of its defining operators remain weakly constrained by existing observations. We show that measurements of horizon-scale metric fluctuations with a lunar laser interferometer can directly probe the kinetic sector of the EFT of dark energy, enabling constraints on operators governing scalar perturbation dynamics rather than only the background expansion history. In particular, we demonstrate sensitivity to the EFT kinetic coefficient $M_2^4$ and the associated sound speed of dark energy, $c_s^2$. This establishes a qualitatively new observational handle on the microphysical consistency conditions of late-time acceleration models, allowing broad regions of EFT parameter space to be probed, constrained, or potentially discovered.

Modern e-commerce search is inherently multimodal: customers make purchase decisions by jointly considering product text and visual informations. However, most industrial retrieval and ranking systems primarily rely on textual information, underutilizing the rich visual signals available in product images. In this work, we study unified text-image fusion for two-tower retrieval models in the e-commerce domain. We demonstrate that domain-specific fine-tuning and two stage alignment between query with product text and image modalities are both crucial for effective multimodal retrieval. Building on these insights, we propose a noval modality fusion network to fuse image and text information and capture cross-modal complementary information. Experiments on large-scale e-commerce datasets validate the effectiveness of the proposed approach.

The Seebeck coefficient in liquids often reaches the mV/K range, yet its microscopic origin remains unclear due to the complexity of electrolyte systems. Here we propose a minimal electrostatic theory focusing on solvation entropy. Using the extended Born equation with temperature ($T$)-dependent dielectric constant ($\varepsilon$), we quantitatively reproduce the experimentally observed magnitude. The theory clarifies that large valence, small cationic radius, small dielectric constant, and large $\frac{d\varepsilon}{dT}$ are key factors for enhanced liquid Seebeck response.

Neighborhood algorithms may take a considerable percentage of computer time in discrete element methods (DEM). While the sort-and-sweep algorithm is ideal in some ways, as it only deal with particles whose relative positions change in one coordinate direction, the other directions must be processed too, for all particles. In contrast, tree-codes deal only with adjacent particles. We compare sort-and-sweep and tree-code neighborhood algorithms for two-dimensional DEM simulations of polygonal particles in a rotating drum with up to 12000 particles. We discuss the effects of system size and inlining on the performance with respect to the cache memory. For the tree code, the performance is slightly better, at the cost of significantly increased cyclomatic complexity. In particular, one benefit is improved possibilities for shared memory parallelization.

This is the final paper in the five-part series The Semantic Arrow of Time. Part I identified the FITO category mistake -- treating forward temporal flow as sufficient for establishing meaning. Part II presented the constructive alternative: the OAE link state machine with its mandatory reflecting phase. Part III showed the FITO fallacy operating at industrial scale in RDMA completion semantics. Part IV traced the same pattern through file synchronization, email, human memory, and language model hallucination. This paper closes the series by constructing the Leibniz Bridge: a unified framework that connects the philosophical foundations (Leibniz's Identity of Indiscernibles, as formalized by Spekkens), the protocol engineering (OAE's bilateral transaction structure), and the physical substrate (indefinite causal order in quantum mechanics). The bridge rests on a single principle: mutual information conservation -- the requirement that every causal exchange preserve the total information accessible to both endpoints, with the direction of time emerging not from axiom but from entropy production when a reversible exchange commits. We show that this principle dissolves the apparent impossibility of the FLP, Two Generals, and CAP theorems by revealing them as theorems about FITO systems, not about physics. We present the triangle network as the minimal topology for semantic consistency without centralized coordination. We conclude with open questions and a reflection on what distributed computing looks like when the FITO assumption is dropped.

This is the fourth of five papers comprising The Semantic Arrow of Time. Parts I-III established that computing's hidden arrow of time is semantic rather than thermodynamic, that bilateral transaction protocols create causal order through a mandatory reflecting phase, and that RDMA's completion semantics implement the FITO category mistake at industrial scale. This paper traces the consequences of the FITO category mistake beyond the data center, into systems people use every day. We examine three domains where forward-only temporal assumptions destroy meaning: file synchronization, where cloud platforms silently delete user content because last-writer-wins cannot represent distributed causality; email, where timestamp-based ordering produces phantom messages, causality violations, and stuck synchronization; and memory--both human and artificial--where reconstructive processes that operate without transactional guarantees produce systematic semantic corruption. In each domain, we identify the same structural pattern: a system that commits state changes forward in time without a reflecting phase, and that therefore cannot distinguish between successful semantic integration and mere temporal succession. The pattern is not coincidental. It is the FITO category mistake operating at different scales: bytes in a NIC buffer, files in a cloud, messages in an inbox, engrams in a hippocampus, tokens in a transformer. We conclude that the semantic arrow of time is violated whenever a system treats the forward flow of information as sufficient evidence of meaning. Part V will show how the Leibniz Bridge provides a unified framework for closing this gap across all five domains.

We show that a driven-dissipative cavity-magnonic dimer supports multistability with coexisting symmetric and symmetry-broken steady states. The interplay between magnon Kerr nonlinearity and photon tunneling induces magnon self-trapping, leading to a persistent population imbalance between the two resonators. In the vicinity of saddle-node bifurcations, the system exhibits critical slowing down, with relaxation times far exceeding the intrinsic dissipation scale. Focusing on quan- tum correlations, we analyze the quantum fidelity and mutual information between the intercavity magnon modes. We find that both the infidelity and the mutual information increase sharply near the phase boundaries, providing clear quantum signatures of the multistable and symmetry-broken phases. Our results establish cavity magnonic dimers as a versatile platform for exploring nonlinear nonequilibrium physics in hybrid quantum systems.

Cross-language collaborative storytelling plays a vital role in children's language learning and cultural development, fostering both expressive ability and intercultural awareness. Yet, in practice, children's participation is often shallow, and facilitating such sessions places heavy cognitive and organizational burdens on coordinators, who must coordinate language support, maintain children's engagement, and navigate cultural differences. To address these challenges, we conducted a formative study with coordinators to identify their needs and pain points, which guided the design of SparkTales, an intelligent support system for cross-language collaborative storytelling. SparkTales leverages both individual and common characteristics of participating children to provide coordinators with story frameworks, diverse questions, and comprehension-oriented materials, aiming to reduce coordinators' workload while enhancing children's interactive engagement. Evaluation results show that SparkTales not only significantly increases coordinators' efficiency and quality of guidance but also improves children's participation, providing valuable insights for the design of future intelligent systems supporting cross-language collaboration.

Resentencing in California remains a complex legal challenge despite legislative reforms like the Racial Justice Act (2020), which allows defendants to challenge convictions based on statistical evidence of racial disparities in sentencing and charging. Policy implementation lags behind legislative intent, creating a 'second-chance gap' where hundreds of resentencing opportunities remain unidentified. We present Redo.io, an open-source platform that processes 95,000 prison records acquired under the California Public Records Act (CPRA) and generates court-ready statistical evidence of racial bias in sentencing for prima facie and discovery motions. We explore the design of an LLM-powered interpretive layer that synthesizes results from statistical methods like Odds Ratio, Relative Risk, and Chi-Square Tests into cohesive narratives contextualized with confidence intervals, sample sizes, and data limitations. Our evaluations comparing LLM performance to statisticians using the LLM-as-a-Judge framework suggest that AI can serve as a powerful descriptive assistant for real-time evidence generation when ethically incorporated in the analysis pipeline.

We define the Archimedean height pairing for fiberwise cohomologically trivial differential forms on a one-parameter degeneration of Riemann surfaces, and we study its asymptotic behavior. The proof relies on recent work by Dai--Yoshikawa on the asymptotics of small eigenvalues. As an application, we relate this pairing to the current-valued pairing of Filip--Tosatti, extending their construction to broader geometric settings.

We show for the first time that the low-spin ($J \le 4^+$) six-$α$ condensate candidate states in $^{24}$Mg, recently reported by Fujikawa et al. [Phys. Lett. B 848, 138384 (2024)], are well described by the superfluid $α$-cluster model (SCM). This is achieved by a rigorous treatment of the Nambu-Goldstone (NG) zero mode as the order parameter of condensation in the finite six-$α$ system. We find that a roton rotational band with a large moment of inertia is built on the first excited NG $0^+$ state, analogous to the roton bands observed in three-, four-, and five-$α$ condensates in $^{12}$C, $^{16}$O, and $^{20}$Ne, respectively. Remarkably, our calculated roton band reproduces the well-known molecular resonance with a $^{12}$C($0_2^+$)+$^{12}$C($0_2^+$) structure ($16^+$) observed at $E_{\rm c.m.} = 32.5$ MeV in inelastic $^{12}$C+$^{12}$C scattering. This result provides a unified description of both the low-spin six-$α$ condensate states and the high-spin $^{12}$C($0_2^+$)+$^{12}$C($0_2^+$) molecular resonance. Analysis of the wave functions reveals a large overlap between the SCM states and a geometrical $^{12}$C($0_2^+$)+$^{12}$C($0_2^+$) configuration. This dual nature -the coexistence of superfluidity and crystallinity- identifies these states as a signature of a supersolid.

Large language models (LLMs) have been widely deployed for online generative services, where numerous LLM instances jointly handle workloads with fluctuating request arrival rates and variable request lengths. To efficiently execute coexisting compute-intensive and memory-intensive operators, near-memory processing (NMP) based computing paradigm has been extensively proposed. However, existing NMP designs adopt coarse-grained KV cache management and inflexible attention execution flow. Such limitations hinder these proposals from efficiently handling \textit{highly dynamic} LLM serving workloads, limiting their ability to accelerate LLM serving. To tackle these problems, we propose Helios, a Hybrid-bonding-based \uline{L}LM \uline{S}erving accelerator. Helios aims to bridge the fundamental gap between the dynamic nature of KV cache management in LLM serving and the distributed, non-uniform memory abstraction among NMP processing engines (PEs). To this end, we design both the intra-PE execution flow and the inter-PE communication primitives for distributed tiled attention execution. We further propose \textit{spatially-aware} KV cache allocation mechanism to balance the attention workload distribution while minimizing the inter-PE data transfer overhead. Compared with existing GPU/NMP designs, Helios achieves 3.25 times (geomean) speedup and 3.36 times (geomean) better energy efficiency, along with up to 72%/76% P50/P99 time-between-tokens degradation.

Understanding the internal structure of the proton-including the distributions of quarks and gluons and their contributions to proton properties such as mass-remains a central challenge in quantum chromodynamics (QCD). While quark generalized parton distributions (GPDs) have been studied extensively, a unified approach that simultaneously extracts quark parton distribution functions (PDFs), gravitational form factors (GFFs), and gluon GPDs from experimental constraints is still lacking. Moreover, the role of gluons in proton mass generation, particularly through the trace anomaly mechanism, requires deeper theoretical and phenomenological exploration. In this study, we first extract quark GPDs in protons using parameterization method based on the electromagnetic form factors provided by Light-Front Holographic QCD (LFHQCD) from which we derive both quark PDFs and their GFFs. We then extend this approach to model gluon GPDs. Our calculations show consistency with experimental data and lattice QCD results and successfully reproduce soft Pomeron behavior. Furthermore, we investigate near-threshold $J/ψ$ production using gauge/string duality to quantify the contribution of the trace anomaly to the proton mass. Our results demonstrate that the parameterization method provides a consistent framework for describing both quark and gluon structure, bridging GPDs, PDFs, and GFFs. The analysis of $J/ψ$ production confirms that the trace anomaly contributes significantly ($\sim 23\%$) to the proton mass, with the calculated cross-section dependence on momentum transfer $t$ in agreement with experimental observations. This work advances the understanding of proton structure by integrating quark and gluon degrees of freedom and elucidating the origin of proton mass within QCD.

We present the results of directed searches for continuous gravitational waves from unknown neutron stars in five Milky Way globular clusters. We carry out the searches in the LIGO data from the first eight months of the fourth LIGO-Virgo-KAGRA observing run using the WEAVE semi-coherent program, which sums matched-filter detection-statistic values over many time segments spanning the observation period. No gravitational wave signal is detected in the search band of 20-475 Hz for assumed source ages greater than 300 years. Injections of simulated continuous wave signals in the data indicate that we achieve the most sensitive results to date across most of the explored parameter space volume, obtaining median 95% confidence level upper limits as low as $\sim 4.2 \times 10^{-26}$ near 282 Hz for NGC 6397.

Accurate modeling of neutron-induced (n,p) reaction cross sections is essential for diverse applications in nuclear physics, including reactor design, nuclear astrophysics, and radionuclide production. However, experimental data are often sparse or incomplete, and theoretical results like TALYS Evaluated Nuclear Data Library (TENDL-2023) data may carry systematic uncertainties. In this work, we present a data-driven framework based on a Bayesian Neural Network (BNN), denoted as BNN-I6, to predict (n,p) reaction cross sections with quantified uncertainties. The model incorporates six physically motivated input features and is trained on Evaluated Nuclear Data from the ENDF/B-VIII.1 library. Leveraging stochastic variational inference, the BNN offers reliable uncertainty estimates in addition to accurate predictions. The performance of BNN-I6 is benchmarked against the TENDL-2023 library and experimental measurements across a wide range of nuclei. Additionally, SHapley Additive exPlanations (SHAP) based feature-importance analysis reveals the dominant role of theoretical cross-section inputs in driving predictions. These results highlight the potential of BNN-based approaches to enhance nuclear data evaluations and support future applications in data-scarce regimes.

Space-air-ground integrated networks (SAGINs) interconnect satellites, uncrewed aerial vehicles (UAVs), and ground devices to enable flexible and ubiquitous wireless services. The integration of reconfigurable intelligent surfaces (RISs) and fluid antenna systems (FASs) further enhances radio environment controllability. However, the tight integration of cross-layer facilities and radio enhancement technologies leads to pronounced environmental dynamics and heterogeneity, posing fundamental challenges for system modeling and optimization in large-scale SAGINs. This paper investigates a SAGIN in which low Earth orbit (LEO) satellite constellations communicate with multiple ground hotspots via RIS-assisted UAV relays, serving both FAS-equipped and conventional users. A system model is developed that explicitly captures satellite mobility, UAV trajectories, RIS phase control, and heterogeneous user reception capabilities. Accordingly, a multi-hotspot downlink rate maximization problem is studied, whose solvability is analyzed through a hierarchical Stackelberg game. To address heterogeneous and time-varying multi-hotspot environments, an adaptive personalized federated reinforcement learning (FRL) algorithm is proposed for adaptive optimization of UAV trajectories and RIS phase controls. Simulation results demonstrate superior performance and validate the effectiveness of personalization in dynamic heterogeneous SAGIN scenarios.

We use a series of global models to investigate the linear and nonlinear interactions between shock cells, Kelvin-Helmholtz waves, guided jet modes, and other fluctuations in a screeching jet. First, we identify a set of lightly damped global eigenmodes of the Navier-Stokes operator linearized about the mean flow and show that they result from interactions with different shock-cell wavenumbers. Second, we use resolvent analysis to study the linear input-output behavior of the jet and obtain a time-periodic representation of the screech mode, which compares favorably with experimental data. Third, we use harmonic resolvent analysis to study triadic interactions, including inter-frequency energy transfer, between the screech mode determined from resolvent analysis and other fluctuations in the jet. The components of the optimal harmonic resolvent mode at harmonics of the screech frequency match experimental observations that have not been previously predicted by global models. Fourth, we leverage a novel bilinear formulation of harmonic resolvent analysis to study the impact of the screech mode's nonlinear self-interaction on other fluctuations in the jet. We show that the forcing provided by this nonlinear self-interaction of the screech mode, along with its triadic interactions with other frequencies embedded within the harmonic resolvent operator, is sufficient to explain the redistribution of energy to other frequencies and the associated experimental observations. In aggregate, these findings underscore the critical role of triadic and nonlinear interactions in shaping screech dynamics and offer a promising workflow for studying similar interactions in other flows dominated by periodic motions.