In this paper, we introduce a collection of purely loxodromic free Kleinian groups, called infinite Schottky group, which are defined by a suitable collection of simple loops in a similar way as in the case for Schottky groups of finite rank. An infinite Schottky group $Γ$ admits a $Γ$-invariant connected component $Ω$ of its region of discontinuity, such that every other component is a topological disc and has trivial $Γ$-stabilizer, and $Ω/Γ$ is an infinite type Riemann surface without planar ends. Every infinite type Riemann surface $Σ_{F}$ without planar ends can be so obtained (retrosection theorem). If $G < {\rm Aut}(Σ_{F})$ acts freely and $Σ_{F}/G$ is of finite type, then we observe that it lifts to a group of automorphisms of $Ω$, for a suitable infinite Schottky uniformization of it by a infinite Schottky group $Γ$, if and only if there is a $G$-invariant collection ${\mathcal F}$ of pairwise disjoint essential simple loops on $Σ_{F}$ such that each connected component of $Σ_{F} \setminus {\mathcal F}$ is a finite planar surface, generalizing the situation for the case of Schottky groups of finite rank.

Executing a logical quantum circuit fault-tolerantly incurs a large spacetime overhead. Recent work has proposed and investigated phantom codes, defined by the property that every in-block logical $\mathrm{CNOT}$ circuit can be implemented with a physical permutation, a property that has the potential to greatly reduce the depth of compiled circuits. Here we show that phantomness comes at the cost of low encoding rate. Specifically, we prove that any binary phantom code encoding $k$ logical qubits into $n$ physical qubits with distance $d\geq 2$ obeys the bound $k\leq \log_2(n+1)$ for all $k\neq 4$. For $k=4$ we explicitly construct a nonstabiliser $(\!(8, 2^4, 2)\!)$ phantom code that violates the bound and has a transversal non-Clifford gate. We further show that, within the class of nontrivial CSS phantom codes with $k\neq 4$, there is a unique family of codes saturating this bound. In addition, we prove that this logarithmic ceiling cannot be circumvented by permitting additional local unitary gates, or by making use of subsystem codes: any subspace or subsystem code admitting a $\mathrm{SWAP}$-transversal implementation of every logical $\mathrm{CNOT}$ circuit is constrained to satisfy the same bound. These bounds follow from a general theorem relating the length of a quantum code to the structure of its automorphism group, a result which may find applications beyond phantom codes.

Regulated enterprises in the United States -- banks, telecommunications providers, large technology companies -- operate across heterogeneous systems that were rarely designed to interoperate. ERP platforms, billing engines, supply chain tools, and financial reporting infrastructure coexist within the same organization, but they do not talk to each other well. The resulting fragmentation produces familiar problems: transactions recorded in one system but unreconciled in another, asset inventories drifting from their systems of record, and audit-readiness that depends on manual effort. The PCAOB's 2024 inspection cycle put a number on the consequences: a 39% aggregate Part I.A deficiency rate across all inspected firms. This paper introduces the GERA Framework (Governed Enterprise Reconciliation Architecture) -- a vendor-neutral, four-layer data architecture that integrates deterministic cross-system reconciliation, statistical anomaly detection (baseline Z-Score with robust alternatives), governed semantic standardization, and NIST CSF 2.0-aligned security controls into a single methodology. The architecture spans four layers (ingestion, staging, core models, and semantic serving), following the multi-layer pattern now common in modern data platforms. The patterns are demonstrated through U.S. broadband operations -- where billing reconciliation, inventory aging, and governance are tightly coupled -- and draw on the author's implementation experience across three regulated enterprise environments: a regional bank, a national broadband provider, and a Fortune 500 technology company's central finance organization. This is a practitioner reference -- an architectural framework paper documenting field-tested patterns -- not a controlled experiment or benchmark study. No proprietary systems, datasets, or internal implementations are disclosed.

Cellwise Robust Twoblock (CRTB) is introduced, the first cellwise robust method for simultaneous dimension reduction of multivariate predictor and response blocks, in both a dense and a sparse variable-selecting variant. Classical robust methods protect against casewise outliers by downweighting or removing entire observations, a strategy that becomes inefficient -- and eventually breaks down -- when contamination is scattered across individual cells rather than concentrated in whole rows. CRTB combines a column-wise pre-filter for cellwise outlier detection with model-based imputation of flagged cells inside an iteratively reweighted M-estimation loop, retaining the clean cells of partially contaminated rows instead of discarding the observation. An efficient algorithm is provided that uses the classical twoblock SVD as a warm start and converges in a handful of IRLS iterations at a moderate computational cost. The method resists settings where more than $50\%$ of rows contain contaminated cells while retaining comparable efficiency on clean data. A simulation study confirms these properties and shows that CRTB additionally recovers the underlying cellwise outlier pattern with high fidelity and, in the sparse setting, the correct set of informative variables. Two compelling examples illustrate CRTB's practical utility. In each of these, CRTB is shown to be conducive to results that are highly interpretable in the respective domains in the presence of cellwise outliers. As a by-product, the corresponding cells are identified with high fidelity.

In propensity score weighted analysis, robust variance that does not account for weight estimation is commonly used. In propensity score weighted Cox models (CoxPSW), the robust variance is known to be conservative when weights for the average treatment effect (ATE) are used, but it remains unclear whether this conservativeness also holds for other weighting schemes. This study evaluated the performance of the robust variance in CoxPSW when weights other than ATE are applied. We conducted an asymptotic comparison between the robust variance and a variance estimator that accounts for weight estimation under non-ATE weights. Their performance was further evaluated through simulation studies and real data analysis. The analytical results, simulations, and real data analysis indicated that the robust variance is not necessarily conservative in CoxPSW when weights other than ATE are used. These findings suggest that variance estimators that account for weight estimation should be used when applying non-ATE weights in CoxPSW.

Omega Centauri is the most massive and chemically complex multi-population globular cluster with a wide metallicity range that has been extensively studied photometrically and spectroscopically. Using the wide metallicity range of omega Cen, HST photometry (F275W, F336W, F435W, F625W), and MUSE spectroscopy ([M/H]), we derive [M/H]- and M_{F625W}-dependent stellar loci to estimate photometric metallicities from HST colors. Our tests yield metallicity precisions of 0.10\,dex for giants and 0.22\,dex for fainter dwarfs. We construct a photometric metallicity catalog from simultaneous F336W, F435W, and F625W observations (plus F275W where available), containing 20,778 giants and 346,546 dwarfs. A subsample of 20,533 giants is used to study the spatial metallicity distribution and gradient. We find no significant metallicity gradient within the half-light radius, consistent with previous work. Moreover, the previously reported ring-like structure is less pronounced in our data, and no physically significant, irregular two-dimensional metallicity pattern is detected, indicating that the stellar subpopulations are well mixed within the half-light radius. Our catalog significantly extends the metallicity sample of omega Cen, and this approach can be applied to other HST data to estimate photometric metallicities.

We present a framework based on the determinantal geometry of two-qubit gates. Combining the Weyl chamber representation with operator Schmidt theory, we interpret gate synthesis as a distance problem to determinantal varieties. This gives an operational geometry to the Weyl chamber, quantifying nonlocal complexity. We show that the square root iSWAP gate is the closest perfect entangler to the variety of local operations, and that no perfect entangler can be approximated by a local gate with average gate fidelity above 79.8%. The three different determinantal costs form a synthesis-adapted coordinate system that encodes nonlocal complexity and generally reconstructs the Weyl chamber.

This paper develops a methodology for representing machine learning models as models of formal theories, grounded in the perspective that machine learning models are a form of database and that databases are models of theories in coherent logic. Two intermediate results support this approach: any functorial database schema has an associated $κ$-coherent theory whose models coincide with its instances, and data may be hard-coded into a coherent category such that any model of the resulting theory necessarily contains it. These tools are used to show that any dense feed-forward neural network architecture over the floating point numbers may be presented as a coherent category $G$ whose $Set$-models are the networks of that architecture, with inference arising as the precomposition functor $Coh(ι, Set)$ along a coherent functor $ι: RSpan(a_0, a_n) \rightarrow G$. This representation is extended to networks with weight and bias fixing and tying, encompassing sparse and convolutional architectures, via a 2-coequaliser construction in $Coh_\sim$. Taken together, these results recast neural network inference as an extension problem in the 2-category $Coh_\sim$ of coherent categories, supporting the interpretation of a network architecture as a formal hypothesis about the structure of data and of model training as a lifting of a dataset into a more constrained theory.

Toward the large-scale, practical realization of quantum computing, quantum error correction is essential. Among various quantum error-correcting codes, the surface code stands out as a leading candidate, and lattice surgery based on surface codes has emerged as a promising technique for fault-tolerant quantum computation (FTQC). However, implementing quantum algorithms using lattice surgery introduces both resource and time overhead. Existing approaches typically focus on large layout designs, with compiler passes aimed primarily at optimizing time overhead. This often overlooks the trade-off between rotation bottlenecks and movement distance, which leads to inefficient resource utilization and prevents further reduction of the quantum computation failure rate. To address these challenges, we introduce O3LS, a framework for optimizing lattice surgery through automatic layout search and loose scheduling. O3LS achieves an optimal balance by automatically generating squeezed data layouts to reduce space requirements and employing loose scheduling algorithms combined with circuit synthesis techniques to reduce time overhead, thereby effectively minimizing overall logical error rates. Numerical results indicate that O3LS can reduce space overhead by 28.0% over standard layouts and 46.7% over sparse layouts without increasing the number of time steps, leading to suppression of logical error rates by up to 16% relative to larger data layout designs. O3LS can also achieve time overhead reductions of 36.07% and 24.76% in compact and standard data layout designs, respectively. It suppresses logical error rates by up to an order of magnitude compared to prior compilers that focus primarily on maximizing parallelism.

We describe the indecomposable components of the tangent bundle of the punctual Hilbert scheme of a smooth projective surface. As an application, we prove a recent conjecture about classification of products of punctual Hilbert schemes of smooth projective surfaces. We also determine when two products of symmetric powers of a smooth variety can be isomorphic.

Kardar-Parisi-Zhang (KPZ) scaling has been observed in discrete polariton lattices, enabled by engineered band structures that stabilize the condensate. Whether this universality extends to intrinsically continuous systems with natural noise regularization remains an open question. We propose and numerically demonstrate KPZ scaling in a continuous quasi-one-dimensional polariton condensate stabilized by optical confinement in the transversal direction. Large-scale simulations of the stochastic Gross-Pitaevskii equation, with experimentally relevant parameters, reveal temporal and spatial scaling exponents of the two-point phase correlation function betaC = 0.30(5) and alfaC =0.46(8), and Tracy-Widom one-point phase fluctuation statistics, yielding robust KPZ dynamics intrinsic to the continuous polariton fluid.

To address the urgent need in the NISQ era for high-performance, scalable quantum compilers and to advance the integration of classical and quantum computing, we present QLLVM, an advanced Quantum-Classical co-compilation framework built on LLVM. To our knowledge, QLLVM delivers an end-to-end, LLVM-based compilation workflow that unifies the build of classical high-performance programs, including CUDA, MPI, and C++, together with quantum programs into a single executable. For quantum program compilation, QLLVM adopts a three-stage design: high-level optimizations are implemented in the MLIR Quantum dialect and then lowered to QIR, an LLVM IR-based representation, for low-level optimization and hardware mapping. Its extensible architecture and seamless interoperability with classical high-performance computing provide an efficient, flexible, industrial-grade compilation infrastructure for future quantum software development. Experimental results show that, on the MQTBench benchmark suite, QLLVM reduces circuit depth and gate counts compared with state-of-the-art compilers and demonstrates clear advantages in compiling hybrid classical-quantum programs.

A famous result of Klee from 1981 is that the Banach space $\ell_1(κ)$ admits a disjoint tiling by balls of radius $1$, for all cardinals $κ$ with $κ^ω=κ$. Klee also observed that the smallest cardinal in which such a tiling might exist is $κ= 2^{\aleph_0}$, leaving open the question whether, for $κ< 2^{\aleph_0}$, $\ell_1(κ)$ might admit a tiling by balls at all. Our main result answers this question in the negative, proving in particular that $\ell_1$ does not admit any tiling by balls. We also give a companion result about star-$n$-finite coverings by balls of $\ell_1(κ)$ and we give a construction of a star-finite tiling of $\mathcal{X} \oplus_\infty c_{00}$, for each space $\mathcal{X}$ whose dimension is at most countable.

Collective spin systems -- spin ensembles coupled to a common reservoir and effectively described by a single macrospin -- play an important role in both atomic and solid-state physics. Their intrinsic nonlinearity gives rise to multiple long-lived metastable states that ultimately relax to a unique most probable state. This dominant state can change with a control parameter, leading to first-order phase transitions. We develop a real-time instanton approach based on quantum quasiprobability dynamics that captures the stationary state in the large-spin limit and the asymptotic scaling of relaxation rates. We further show that these features are not accurately described by the previously applied semiclassical Wigner approach due to its neglect of non-Gaussian fluctuations.

We report on the discovery of an FUor-like Class I protostar in NGC~7538. The source, named NGC~7538~MIR, exhibited a giant luminosity burst ($ΔK_s\sim5$) and a prolonged high-luminosity state lasting at least five years. Its mid-infrared (mid-IR) light curves, constructed from WISE/NEOWISE multiepoch data, presented a rapid rise and slight fading after the peak, placing this event among long-duration eruptive phenomena observed in protostars, for example, FUor-type events. The evolution of W1/W2 luminosity and $W1-W2$ color can be naturally split into three phases, pre-burst, burst and post-burst, suggesting that different physical processes may dominate in the three phases. The evolution of NGC~7538~MIR is consistent with a transition from variability influenced by circumstellar extinction (pre-burst) to a phase with greatly enhanced accretion luminosity (burst), and followed by a gradual relaxation of the circumstellar environment (post-burst). Overall, the observed IR variability of NGC~7538~MIR is consistent with an FUor-like accretion event occurred at an early evolutionary stage, highlighting the importance of long-term IR monitoring for identifying episodic accretion events in deeply embedded protostars.

This article provides a survey of gauge theory for families, with a particular focus on its applications to diffeomorphism groups of $4$-manifolds that were developed during the period 2021--2025.

Twenty-five years have passed since the first experimental demonstration of attosecond pulses, marking the advent of our ability to resolve and control electron motion in real time. What began as a technological breakthrough - generating the shortest flashes ever produced - has evolved into a powerful approach for probing and steering electronic dynamics in atoms, molecules, and solids. This roadmap, authored by leading experts in the field, surveys the recent rapid progress in the generation and characterization of attosecond pulses, emerging attosecond measurement and control techniques, and their expanding range of applications. It reviews current and future developments in attosecond light sources, including novel laser technologies, waveform synthesizers, new schemes for high-order harmonic generation, attosecond pulse generation at free-electron lasers, and structured light. Advances in attosecond measurement methodologies are also discussed, encompassing all-attosecond pump-probe spectroscopy, attosecond four-wave mixing, attosecond microscopy, spectroscopy with light transients, and attosecond interferometry. Furthermore, the roadmap addresses applications of attosecond spectroscopy to reveal electron dynamics in molecules and condensed matter systems from both theoretical and experimental perspectives, and highlights emerging directions at the interface with quantum optics and quantum entanglement. Overall, this work aims to serve as a comprehensive resource for navigating the evolving landscape of attosecond science.

Processes involving bursts of activity separated by quiescent periods occur across diverse systems and scales. In human dynamics, these phenomena have been described by power-law inter-event time distributions, $P(t)\sim t^{-α}$, with putative universality classes $α=1$ and $α=\frac{3}{2}$ having been proposed. Whether the observed $α= 1$ scaling reflects intrinsic scale-free dynamics or instead emerges from heterogeneous underlying rates has been debated at length. We address this question in a canonical physical system for first-passage dynamics: two-dimensional molecular diffusion detected by the tip of a scanning tunnelling microscope. The resulting inter-pulse time distributions exhibit the same apparent truncated power-law form reported for human activities such as email communication, web browsing, and library loans. Maximum-likelihood estimation and model comparison decisively favor a Kohlrausch-Williams-Watts--tempered power law, $P(t)\propto t^{-α}\exp\left(-(t/t_c)^β\right)$, with $α\sim 1$. Kinetic Monte Carlo simulations reproduce this behavior, showing that the apparent $α\sim 1$ scaling is confined to a finite time window and arises from tip-induced spatial heterogeneity, not scale invariance.

In the sixth generation (6G) wireless communication networks, the device density, antenna number, and the complexity of communication scenarios will significantly increase, which brings great challenges for system design and network optimization. By obtaining channel information in advance, channel map has become a promising solution to these challenges in 6G era. However, conventional channel maps cannot be updated in time as physical environment changes. To solve the problem, a novel dynamic channel map (DCM) is proposed in this work. For DCM construction, we further present a ray tracing (RT) and geometric stochastic hybrid channel model (RT-GSHCM), which pre-constructs the DCM offline by RT and updates it online by geometry-based stochastic channel model (GBSM). By this way, the DCM can provide time-varying channel information and channel properties while matintaining accuracy. Next, a channel measurement campaign is conducted, and the measurement results are compared with the RT-GSHCM, RT, and GBSM. The comparison results validate the accuracy of DCM. Meanwhile, the time cost on DCM update is compared with that of conventional channel maps, illustrating the time-efficiency of DCM. Finally, important statistical channel properties of RT-GSHCM are further derived, analyzed, and compared under different configurations of interaction objects in physical environment.

Since its discovery, ferroelectric hafnia has been extensively studied due to its CMOS-compatibility and ability to remain polarized at sub-10 nm thicknesses. The ferroelectric behaviour is generally attributed to a polar orthorhombic (OIII) phase. However, a second polar phase with rhombohedral symmetry (R-phase) has also been reported in epitaxial films. The nature of the R-phase remains disputed due to the subtle differences with the OIII-phase when probed by standard thin film characterisation techniques. Given the functional properties of ferroelectrics are crucially determined by the crystal symmetry, resolving this matter is imperative. In this work, we settle the controversy through extensive 3D reciprocal space surveys made possible via synchrotron-based grazing incidence diffraction from epitaxial films of both phases. These experiments, together with direct comparison of their temperature dependence and electrical responses, conclusively establish them as two distinct phases and provide insight into their key characteristics.

Products of MDS codes are of major practical importance; for a recent example, they are used in Data Availability Sampling (DAS) in blockchain networks such as Celestia and as part of the Ethereum roadmap. This motivates us to consider subcodes of such codes with the goal of obtaining a larger minimum distance. In this paper, we present explicit constructions of subcodes of Reed--Solomon product codes, along with bounds on their minimum distance. In particular, they achieve an optimal or near-optimal dimension--distance tradeoff. For component codes of dimension $r$, our construction requires a field whose size is bounded linearly by the overall product code length, and attains the maximum possible minimum distance for subcode dimensions $r^2-1$, $r^2-2$, and all dimensions at most $2r-1$. Furthermore, we establish a new upper bound on the minimum distance of subcodes of the product of two codes with identical parameters.

We present a short proof, based on local character expansions, of the celebrated theorem of Harish-Chandra about local integrability of complex characters of $p$-adic reductive groups. The proof gives an algebraic incarnation of the local integrability that works for some coefficients different from $\mathbb{C}$, verifies local integrability in cases that appear not covered in the literature, and shows that a character is locally-$L^α$ for some specified $α>1$ as in [GGH23].

The European Research and Development for Space based High Contrast Imaging II Workshop, held at MPIA in May 2025, advanced Europe strategic coordination in support of future exoplanet imaging missions such as the Habitable Worlds Observatory and the Large Interferometer for Exoplanets mission. Building on the first 2024 workshop, this meeting defined concrete priorities across eight technical areas, including wavefront sensing, coronagraphs, post processing, nulling interferometry, deformable mirrors, detectors, and telescope design. Discussions emphasized Europe strengths in adaptive optics, ground-based facilities, and interferometry, while identifying key gaps, particularly the need for a dedicated European vacuum testbed for high contrast imaging. The community highlighted near infrared or UV coronagraphy as a promising domain for European leadership and called for joint development of advanced data reduction algorithms, detectors, and cross-mission coordination with HWO and LIFE. The workshop outcomes establish a collaborative roadmap to strengthen Europe technological readiness, foster agency partnerships, and ensure its continued leadership in the next generation of space-based exoplanet exploration.

Increasing system-on-chip (SoC) heterogeneity, deep hardware/software integration, and the proliferation of third-party intellectual property (IP) have brought security validation to the forefront of semiconductor design. While simulation and formal verification remain indispensable, they often struggle to expose vulnerabilities that emerge only under realistic execution conditions, long software-driven interactions, and adversarial stimuli. In this context, hardware emulation is emerging as an increasingly important pre-silicon verification technology because it enables higher-throughput execution of RTL designs under realistic hardware/software workloads while preserving sufficient fidelity for security-oriented analysis. This paper presents a comprehensive survey and perspective on emulation-based security verification and validation. We organize the landscape of prior work across assertion-based security checking, coverage-driven exploration, adversarial testing, information-flow tracking, fault injection, and side-channel-oriented evaluation. We provide a structured view of emulation-enabled security verification workflows, including instrumentation, stimulus generation, runtime monitoring, and evidence-driven analysis. We also examine practical challenges related to observability, scalability, property specification, and the definition of security-oriented coverage metrics for emulation-based verification. Finally, we discuss emerging directions such as AI-assisted emulation, digital security twins, chiplet-scale security exploration, automated vulnerability assessment, and cloud-scale secure emulation. Overall, this paper positions emulation as a promising foundation for the next generation of pre-silicon hardware security assurance.

The generalized moment problem (GMP) is an infinite dimensional linear problem over the cone of finite nonnegative Borel measures. When a GMP instance involves finitely many polynomial moment constraints, moment/sum-of-squares hierarchies provide a sequence of bounds converging to the optimal value. We consider GMP instances with measures supported over a compact basic semialgebraic set $X$. We study the case when $X$ has nonempty interior, and the case when $X$ is the vanishing set of prescribed polynomials forming a Gröbner basis of the ideal they generate, which we assume is real radical. Under a relative interior assumption, we show attainment of the infinite dimensional dual problem, and attainment of each associated finite dimensional sum-of-squares strengthening. For the latter we present two disjoint proofs. The first is obtained by adapting results regarding the closedness of quadratic modules, and the second builds on Csiszár's work on exponential density constructions to find a strictly feasible measure. Finally, we discuss the special case where $X$ is the product of spheres, and applications of our results to GMP instances arising from tensor optimization and quantum information theory.

This article surveys gauge theory for families and its applications to the comparison between the diffeomorphism group and the homeomorphism group of $4$-manifolds, up to 2021.

Incorporation of external information into high-dimensional modeling for gene expression data has been shown, both theoretically and empirically, to substantially enhance performance. Such external information, sometimes referred to as prior information or priors, has become increasingly accessible from multiple sources, yet its reliability may vary considerably. Existing approaches often integrate these priors without sufficiently accounting for their quality, which may result in unsatisfactory or even misleading results. To effectively and selectively exploit such priors, we propose adaptive Multi-Prior Lasso, a novel regularization approach that simultaneously identifies reliable prior sources and integrates them to improve model performance. For high-dimensional generalized linear models (GLMs), an adaptive data-driven weight is assigned to each prior, so that more reliable sources are emphasized while less credible ones are downweighted. Theoretical guarantees are established, and the proposed method is shown through extensive simulations to improve estimation, prediction, and variable selection. An application to TCGA breast cancer gene expression data further illustrates the practical value of the proposed method, showing that incorporating prior information from PubMed published studies improves model performance.

Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately. We introduce multitasking formulations of these problems that are an effective way to solve multiple related problems with a single run. In our setting the given problems share a monotone submodular function $f$ but have different knapsack constraints. We examine the case where elements within a constraint have the same cost and show that our multitasking formulations result in small Pareto fronts. This allows the population to share solutions between all problems leading to significant improvements compared to running several classical approaches independently. Using rigorous runtime analysis, we analyze the expected time until the introduced multitasking approaches obtain a $(1-1/e)$-approximation for each of the given problems. Our experimental investigations for the maximum coverage problem give further insight into the dynamics behind how the approach works and doesn't work in practice for problems where elements within a constraint also have varied costs.

Internal climate variability arises from the climate system's inherently chaotic dynamics. Quantifying it is essential for climate science, as it enables risk-based decision-making and differentiates between externally forced change and internal fluctuations. In statistical terms, natural variability corresponds to aleatoric uncertainty, i.e., irreducible stochastic variability. Despite this close conceptual alignment, the link between internal climate variability and aleatoric uncertainty has not yet been formalized. We establish a theoretical link by showing that member-to-member differences in single-model large ensembles provide a direct representation of aleatoric uncertainty. To quantify the spatio-temporal structure of aleatoric uncertainty, we employ generalized additive models. The proposed framework is validated through comparison with ERA5-Land reanalysis data, demonstrating that ensemble-derived estimates reproduce key spatial and temporal patterns of real-world variability. Applied to the water balance over the Iberian Peninsula, our approach reveals coherent variability structures and pronounced regional heterogeneity. We find a decline in variability in drought-prone regions and seasons, a pattern that strengthens under +3 °C global warming, implying an increased risk of persistent summer drought conditions. Beyond this application, the framework is climate-model agnostic and transferable to other variables and spatial scales, providing a statistical basis for quantifying internal climate variability as aleatoric uncertainty.

Actively tunable photonic devices are vital for next-generation optoelectronics requiring rapid switching and high bandwidth. Although organic optoelectronic devices have found wide application, their use as optical modulators has been limited by low absorption in the critical near-infrared (NIR) region, slow response time, and weak nonlinearities. To address these limitations, we developed a scheme based on intermediate exciton-photon coupling in a NIR absorbing squaraine-dye based photonic structure. Using energy-momentum resolved pump-probe spectroscopy, we show that the sign and magnitude of the optical response of our system depends strongly on the energy detuning between the excitonic and photonic modes. These data are analyzed using temporal coupled-mode theory to show that near resonance, a distinct energy exchange process emerges in the cross-over regime between strong and weak light-matter coupling. This effect enables dynamical control over the photoinduced response, providing a pathway for broadband optical signal modulation extending into the NIR spectral region.