Our study connects the physics of disordered integer-dimensional systems and regular self-similar objects by studying spectral properties of fractal agglomerates with tunable dimension. The latter is controlled by parameter $α$ of the algorithm that generates the agglomerates. We consider the nearest-neighbor tight-binding model on the agglomerates embedded in 2D and 3D, and observe that all eigenstates are localized in the 2D case, whereas in the 3D case, there is a localization--non-ergodic transition upon increasing $α$,i.e., going from sparse to dense fractals: a sub-extensive number of critical states emerge in the spectrum at a certain critical value of $α$. The complex geometry of the agglomerates is also responsible for a peculiar hierarchy of compact localized states and singularities in the density of states, which are typical for ordered fractals.

This paper presents a pilot study exploring the effects of an olfactory stimulus (smoke) for a Virtual Reality game designed to support wildfire evacuation preparedness. Participants (N=18) were split evenly into either a smoke or a control condition, and both completed the same evacuation task. Post-task surveys assessed the participants' perceived preparedness and overall experience. Initial findings suggest participants in the smoke condition reported significantly higher immersion compared to those in the control condition. Across both groups, participants expressed an increased sense of preparedness for real-world wildfire evacuations following the experience.

Consider the following nonlinear one-dimensional stochastic fractional heat equation $$\frac{\partial }{\partial t}u(t, x)= -(-Δ)^{α/2}u(t, x) +σ(t,x,u(t,x)) \dot{W}(t, x), $$ where $-(-Δ)^{α/2}$ is the fractional Laplacian on $\mathbb R$ for $1<α<2$, and $\dot{W}$ is a Gaussian noise that is white in time and behaves in space as a fractional Brownian motion with Hurst index $H$ satisfying $\frac{3-α}{4}<H<\frac12$. When $α=2$, Hu and Wang ({\it Ann. Inst. Henri Poincaré Probab. Stat.} {\bf 58} (2022) 379-423) studied the well-posedness of the solution and its Hölder continuity, removing the technical condition $σ(0)=0$ that was previously assumed in Hu et al. ({\it Ann. Probab.} {\bf 45} (2017) 4561-4616). Their approach relied on working in a weighted space with a suitable power decay function. For the case $α\in (1,2)$, inspired by Hu and Wang, we investigate the well-posedness of the stochastic fractional heat equation without imposing the technical condition of $σ(0)=0$, which was required in the earlier work of Liu and Mao ({\it Bull. Sci. Math.} {\bf181} (2022) 103207). In our analysis, precise estimates of the heat kernel associated with the fractional Laplacian $-(-Δ)^{α/2}$ play a crucial role.

In this paper, we are concerned with the initial-Neumann boundary value problem of the Schrödinger flow for maps from a smooth bounded domain in an Euclidean space into $\mathbb{S}^2$. By adopting a novel method due to B. Chen and Y.D. Wang, we prove the existence of short-time regular solutions to this flow within the framework of Sobolev spaces when the underlying space is a smooth bounded domain in $\mathbb{R}^m$ with $m\leq 3$. Moreover, we also utilize the ``complex structure approximation method" to establish the global existence of weak solutions to the incompressible Schrödinger flow in a smooth bounded domain of $\mathbb{R}^m$ (where $m\geq 1$).

Temporal hypergraphs capture time-resolved group interactions among nodes. Empirical data support that time-stamped group interactions show bursty event sequences and non-trivial temporal correlations. In the present study, we introduce node-driven temporal hypergraph models in which each node stochastically alternates between low- and high-activity states, and a hyperedge produces time-stamped events with a probability that depends on the number of high-state nodes in the hyperedge. For two event-generation rules, we analytically derive interevent time distributions and autocorrelation functions of event sequences, both for hyperedges and nodes. Despite Markovian node-state dynamics, the induced event processes become mixtures of Poissonian, short-tailed components, resulting in longer-tailed interevent time distributions and slowly decaying autocorrelation. The theory further shows the dependence of these features on the size of hyperedge, which largely agrees with various empirical data. We expect our models to provide a simple, interpretable framework for connecting individual-level activity fluctuations to the timing patterns observed in real group interactions.

When an optimal control problem is solved for all possible initial conditions at once, the initial-state space splits into critical regions, each carrying a closed-form control law that can be evaluated online without solving any optimization. This is the multiparametric approach to explicit control. In the continuous-time setting, the boundaries between these regions are determined by extrema of Lagrange multipliers and constraint functions along the optimal trajectory. Whether a boundary is a hyperplane, computable analytically, or a curved manifold that requires numerical methods has a direct effect on how the partition is built. We show that a boundary is a hyperplane if and only if the relevant extremum is attained at either the initial time or the terminal time, regardless of the initial condition. The reason is that the costate is a linear function of the initial state at any fixed time, so when the extremum is tied to a fixed endpoint, the boundary condition is linear and the boundary normal follows directly from two matrix exponentials and a linear solve. When the extremum occurs at a time that shifts with the initial condition, such as a switching time or an interior stationary point, the boundary is generally curved. We demonstrate the result on a third-order system, obtaining the complete three-dimensional critical-region partition analytically for the first time in this problem class. A comparison with a discrete-time formulation shows how sharply the region count grows under discretization, while the continuous-time partition remains unchanged.

Annotation is a central mechanism in visualization design that enables people to communicate key insights. Prior research has provided essential accounts of the visual forms annotations take, but less attention has been paid to the decisions behind them. This paper examines how annotations are designed in practice and how educators reflect on those practices. We conducted a two-phase qualitative study: interviews with ten practitioners from diverse backgrounds revealed the heuristics they draw on when creating annotations, and interviews with seven visualization educators offered complementary perspectives situated within broader concerns of clarity, guidance, and viewer agency. These studies provide a systematic account of annotation design knowledge in professional settings, highlighting the considerations, trade-offs, and contextual judgments that shape the use of annotations. By making this tacit expertise explicit, our work complements prior form-focused studies, strengthens understanding of annotation as a design activity, and points to opportunities for improved tool and guideline support.

Belnap's four-valued logic, distinguished by its inherent bilattice structure, provides a natural algebraic bridge between discrete Four-valued logic (4VL) in circuit and continuous catastrophe theory (CT). Building on the rigorous verification of the bilattice-catastrophe isomorphism theorem, we establish a categorical correspondence spanning the catastrophe category, interlaced bilattice category, and 4VL category, with the cusp catastrophe emerging as the canonical CT counterpart to 4VL.This unification provides a foundational framework for explaining 4VL's robustness. Crucially, we demonstrate that the four-valued algebra FOUR is the minimal complete algebraic structure capable of describing continuous-discrete interfaces with involution symmetry. Unlike the empirical adoption of X and Z in engineering practice, our work reveals their mathematical necessity: X and Z are topological invariants of discretized continuous dynamical systems, encoding fundamental properties of catastrophe-induced discontinuities. The work enables cross-disciplinary extensions to uncertainty propagation, complex system modeling, and fault-tolerant design.

The advancement of antiferromagnetic spintronics depends on quantum materials with target symmetry-dictated functionalities, however, their systematic discovery is hindered by the immense configurational complexity of the available material space. Here, we introduce a symmetry-guided, AI-accelerated framework incorporating graph neural networks with high generalization ability to overcome this bottleneck. Based on fully intercalated transition metal dichalcogenides (iTMDs) and using only 200 relaxed partially intercalated structures for transfer learning, our model effectively explores more than 100,000 partially intercalated configurations and identifies 35 altermagnetic and 20 $Tτ$-antiferromagnetic ground-state candidates. Interestingly, we show that tuning spin-group symmetry through intercalant arrangement or magnetic ordering realizes a series of d-wave altermagnets in these hexagonal systems with high spin-charge conversion efficiency. Furthermore, we reveal plentiful $Tτ$-antiferromagnets enabling efficient Néel spin-orbit torque switching, driven by giant $T$-odd spin Edelstein susceptibilities. These results establish iTMDs as a versatile platform for spintronics and provide a general strategy for the accelerated design of symmetry-enforced quantum materials.

We show that Villadsen algebras, which are not Z-stable, are singly generated. More generally, we show that any simple unital AH algebra with diagonal maps is singly generated.

Eli, Hom, and Lidman showed that the manifolds produced by attaching the simplest positive Casson handle $CH^+$ to a slice disc complement of the ribbon knot $T_{2,n}\#T_{2,-n}$ for $n\ge3$ and odd, and removing the boundary, form a countably infinite family of exotic $\mathbb{R}^4$'s. They provided a Kirby diagram for the case $n=3$. In this short note, we extend this for $n\ge3$ and odd, and provide Kirby diagrams for two such families of exotic $\mathbb{R}^4$'s, which are then shown to be equivalent. We then generalise these diagrams to a family of exotic $\mathbb{R}^4$'s built using ribbon disc complements of the pretzel knots $P(n,-n,2k)$.

Supernova remnants (SNRs) can strongly affect the chemical composition of the interstellar dust. In this paper we investigate to what degree the dust and ices are modified by observing four stars expected to be absorbed by a giant molecular cloud interacting with SNR W44, using medium-resolution spectroscopy in 2-5 $μ$m. Absorption from H2O ice around 3.0 $μ$m and aliphatic hydrocarbon dust around 3.4 $μ$m were detected towards two stars, while probable CO ice at 4.67 $μ$m towards one of them. Millimeter gas-phase CO J = 1-0 lines and three-dimensional dust extinction maps show that the dense molecular gas associated with W44 dominates (> 60%) the total interstellar extinction (A_K ~ 2.6) along these two sightlines. The H2O ice column densities are a factor of 1.5-3 lower than nearby MCs at similar extinctions, possibly because of the destruction of ice by shocks and cosmic rays (CRs) from W44, consistent with the low CO ice abundance relative to H2O (< 12%). One of the sightlines shows an unusually strong 3.4 $μ$m aliphatic hydrocarbon absorption. If the carriers are located in diffuse dust along the sightline, unrelated to W44, its strength is ~ 4 times larger than those typically observed for diffuse dust clouds. Alternatively, the carriers may be enhanced in the W44 environment. We discuss several possible explanations, including shock formation of aliphatic hydrocarbons in diffuse clouds associated with W44, contribution from aliphatic hydrocarbons in shocked and CR-bombarded molecular clouds, and changes in the extinction law due to the SNR interaction.

Precise environmental-noise characterisation in open quantum systems is a key step toward high-fidelity quantum control and targeted decoherence suppression in computing and sensing applications. Non-parametric quantum noise spectroscopy (QNS) provides a general-purpose, model-agnostic framework for estimating the spectral properties of an environment. The ability to perform such protocols under realistic constraints is key to their practical applicability. Notably, it is important to account for control constraints and understand how they limit the ability to learn about noise correlations as experiment-agnostic objects. We show how adopting a control-centric point of view allows one to recast the noise spectroscopy problem in such a way that (i) the central objects are now the time-ordered polyspectra, (ii) control filter functions are no longer encumbered by time-ordering. In particular, we show that this approach enables the seamless generalisation of frequency-comb QNS protocols to arbitrary control scenarios without introducing additional control symmetries that effectively remove time-ordering from filter functions, improving estimation in typically pathological scenarios. We demonstrate the targeted reconstruction of the time-ordered polyspectra across classical Gaussian and quantum non-Gaussian environments via simulations.

Affine frequency division multiplexing (AFDM) has emerged as a promising waveform for high-mobility communications. However, its equalization remains a practical challenge under general physical channels with off-grid delay and Doppler effects. In this paper, we investigate frequency domain equalization for AFDM by considering a practical filtered-AFDM waveform. We analyze the input-output relations of filtered-AFDM across various domains and show that off-grid effects lead to severe inter-symbol interference in the DAFT domain, limiting the effectiveness of DAFT domain equalization. Motivated by the compactness of the frequency domain channel matrix in wideband systems, we propose a low-complexity two-stage frequency domain equalization scheme. Numerical results demonstrate that the proposed approach achieves performance close to full-block LMMSE equalization with significantly reduced computational complexity, and offers clear advantages over time domain equalization in wideband scenarios.

We study the asymptotic behavior of the continuum Kuramoto model with a fractional Laplacian-type kernel. For this, we construct global weak solutions via a two-parameter regularization procedure using a kernel truncation with fractional dissipation. Using a priori uniform estimates derived in fractional Sobolev spaces, we employ compactness arguments to construct global weak solutions to the singular continuum Kuramoto model. Furthermore, we also establish an exponential relaxation toward the initial phase average in $L^2$-norm under suitable assumptions on initial data and system parameters. These findings provide a rigorous characterization of the existence of solutions and the emergent dynamics of Kuramoto ensembles under physically important strongly singular interactions, including power-law singular kernels and Coulomb-type kernels.

Light in the mode of a Fabry-Pérot cavity heats the mirror surfaces via optical absorption, causing thermoelastic deformation of the mirror substrates, which in turn dictates the shape of the mode. We develop an analytical model which predicts that this effect limits the maximum focal intensity of the mode. Using two near-concentric Fabry-Pérot cavities -- one with 4.5-fold higher mirror absorption than the other -- we measure the thermoelastic properties of the cavity mirrors and demonstrate that it is possible to achieve at least 70% of this predicted limit (in the high-absorption cavity), and that the predicted limit is 2.9 TW/cm^2 (in the low-absorption cavity).

This paper introduces an optically controlled 4H-SiC MOSFET designed to avoid the gate-oxide interface unreliability and electromagnetic interference (EMI) susceptibility inherent in conventional voltage-driven devices. By replacing the conventional gate electrode with a semi-transparent optical window, the device enables direct modulation of channel conductivity through ultraviolet illumination. Electrical and optical characterization demonstrates that under an optical power density above 0.1 W/cm^2, the device achieves an on/off current ratio exceeding 10^6 between illuminated and dark states. Notably, at an optical power density of 0.031 W/cm^2, the photogenerated current density exceeds that obtained under a gate bias of 15 V in magnitude. Energy band analysis confirms that the optical switching mechanism operates through direct photogenerated carrier generation and transport, fundamentally differing from conventional gate voltage control and thus circumventing interface-trap and EMI-related limitations. Dynamic measurements further reveal fast switching capability, with a rise time of 1.44 ns. These results validate the feasibility of optically driven switching in SiC-based devices and highlight their potential for high-speed logic applications.

Bound states in the continuum (BICs) have enabled lasers with rich momentum-space textures. However, the output patterns of quasi-BIC lasers remain largely static and confined to a few geometries. Here, a reconfigurable momentum-space vectorial laser was proposed based on two-dimensional photonic crystal. By selectively exciting quasi-BIC modes, we identify the geometric asymmetry factors favoring single BIC, dual-BIC, and radiative mode with BIC operation. This approach yields vectorial lasing with characteristic patterns lasing in momentum space of bidirectional double lobes (BDL), radially polarized ring with BDL, azimuthally polarized ring with BDL, and linearly polarized spot with BDL. Importantly, reversible switching between a single donut and a donut with BDL was achieved in the same device by varying the pump energy density. Our work establishes a compact, versatile platform for reconfigurable vectorial lasers, with potential applications in tunable optical tweezers, super-resolution imaging, and on-chip optical interconnects.

Data from gravitational-wave (GW) detectors often contains a high rate of non-Gaussian transient noise, known as glitches. The parameters estimated from GW signals coinciding with detector glitches are occasionally biased away from their true values. During the first part of the fourth LIGO-Virgo-KAGRA (LVK) observing run, 29% of GW candidates had overlapping or nearby glitches in one or more detectors. In the latter part of the fourth observation run, sensitivity improvements have increased the rates of GW detection. Consequently, scenarios in which GW signals and detector glitches overlap in time are more likely. In this study, we quantify shifts in inferred posterior distributions for short-duration compact binary coalescence GW signals interacting with common LIGO glitches as a function of time between the signal merger time and the glitch. We find statistically significant biases in parameter estimation for mass, spin, and sky position for "blip", "thunder", and "fast-scattering" glitches. Using these results, we provide estimates of what parameters are most affected by overlapping noise sources, as well as what constitutes a "safe" time separation between a gravitational wave signal and a glitch, without requiring glitch subtraction for unbiased source property estimation. We find that in a majority of cases, all parameters are susceptible to significant bias due to glitch interference. Additionally, we find that glitches that occur within the time prior of the GW signal cause more extreme biases than glitches outside of the time prior.

This paper is devoted to the study of the existence of positive and bounded solutions for a Schrödinger type equation defined on the entire Euclidean space, involving a general integro-differential operator. We consider the case where the potential is nonnegative and vanishes at infinity with a nonlinearity exhibiting critical or supercritical growth in the Sobolev sense. To overcome the lack of compactness and the difficulties imposed by the general structure of the nonlinearity, we employ variational methods combined with a penalization technique. Unlike the classical fractional Laplacian framework, where specific regularity results, decay estimates, and the $s$-harmonic extension are available, our approach relies on a weak Maximum Principle combined with the construction of a supersolution based on the truncated fundamental solution of the fractional Laplacian to control the asymptotic behavior of the solutions. We prove that, for sufficiently small perturbation parameters and under suitable decay conditions on the potential, the equation admits a nontrivial solution.

A key problem in approximation theory is the recovery of high-dimensional functions from samples. In many cases, the functions of interest exhibit anisotropic smoothness, and, in many practical settings, the nature of this anisotropy may be unknown a priori. Therefore, an important question involves the development of universal algorithms, namely, algorithms that simultaneously achieve optimal or near-optimal rates of convergence across a range of different anisotropic smoothness classes. In this work, we consider universal approximation of periodic functions that belong to anisotropic Sobolev spaces and anisotropic dominating mixed smoothness Sobolev spaces. Our first result is the construction of a universal algorithm. This recasts function recovery as a sparse recovery problem for Fourier coefficients and then exploits compressed sensing to yield the desired approximation rates. Note that this algorithm is nonadaptive, as it does not seek to learn the anisotropic smoothness of the target function. We then demonstrate optimality of this algorithm up to a dimension-independent polylogarithmic factor. We do this by presenting a lower bound for the adaptive $m$-width for the unit balls of such function classes. Finally, we demonstrate the necessity of nonlinear algorithms. We show that universal linear algorithms can achieve rates that are at best suboptimal by a dimension-dependent polylogarithmic factor. In other words, they suffer from a curse of dimensionality in the rate -- a phenomenon which justifies the necessity of nonlinear algorithms for universal recovery.

Extending the Gaussian covariant hydrodynamics approach [1] using torsion as an auxiliary field we formulate a fluctuating hydrodynamics with spin which is covariant with respect to pseudo-gauge transformations as well as generally covariant with respect to foliations. This is done via the second order gravitational Ward identities, derived here in the torsionful case. This ensures that, while angular momentum observables depend covariantly on the pseudo-gauge, the dynamics is pseudo-gauge independent, thus clarifying the role of the pseudo-gauge in hydrodynamics with spin

Globular clusters (GCs) are powerful tracers of galaxy assembly, frequently used to identify accreted substructure and reconstruct hierarchical merger histories. With advances in GC formation models and cosmological simulations, we can now better quantify the information about galaxy evolution encoded in present-day GCs. Here, we investigate how GC kinematics evolve over cosmic time and assess the extent to which GCs retain memory of the past of their host galaxy. Using a GC formation model applied to five Milky Way (MW) analogues from the Latte suite of the FIRE-2 simulations, we track the evolution of kinematic properties. At $z=0$, in-situ and ex-situ GCs exhibit substantial overlap in kinematic space, indicating that these populations are not clearly separable. We find that a subset of kinematic properties evolve in an ordered fashion across both in-situ and ex-situ populations, whereas others are dominated by stochastic variations. As a result, by the present day, most memory of the progenitor of an accreted GC is erased and only a few correlations persist. These correlations link progenitor halo mass to the total mass and number of a GC population, and the galactocentric distance of GC substructure to progenitor maximum circular velocity. These results highlight how both deterministic and stochastic processes driven by galaxy evolution shape GC kinematics and demonstrate the limits of reconstructing the assembly history of a galaxy from present-day GC orbits alone.

Altermagnetism has recently emerged as a distinct class of collinear antiferromagnets that break time-reversal symmetry, exhibiting a host of novel properties. Applied strain has attracted particular attention as a key tuning parameter for altermagnets. Although several experimental studies have demonstrated the preparation of single-domain states through a combination of applied strain and magnetic field, the route to such states remains unclear. Here, we use magneto-optical measurements on single crystals of MnTe under applied strain to show that, in contrast to previous reports, strain acts primarily to rotate the Néel vector L continuously. Since the orientation of L determines the magnetic point group symmetry, this continuous rotation effectively tunes the symmetry and its associated physical properties. Furthermore, we demonstrate that built-in strain in free-standing crystals is sufficient to pin L into continuous textures over millimeter length scales. Together, these results provide guidance for future device design and open the door to leveraging the Néel vector orientation as a tunable degree of freedom in spintronic applications.

We investigate the vacuum-induced current density for a charged scalar field in a $(D+1)$-dimensional cosmic dispiration spacetime threaded by a magnetic flux. This background combines a cosmic string and a screw dislocation, yielding a nontrivial helical geometry. By constructing the normalized mode functions of the Klein--Gordon equation, we evaluate the Wightman function and obtain the vacuum expectation value of the current density. We show that, in addition to the azimuthal component describing a persistent current around the defect, a nonvanishing axial component is induced as a direct consequence of the helical structure of the spacetime. Both components are periodic functions of the magnetic flux, depending only on its fractional part, reflecting the Aharonov--Bohm nature of the effect. Closed expressions are obtained for both massive and massless fields in arbitrary dimensions. We demonstrate that the screw dislocation parameter plays a crucial role in the behavior of the induced currents, leading to the regularization of the axial component at the origin and controlling its magnitude. The asymptotic behavior of both components is analyzed in detail. Our results reduce to known expressions in the absence of the screw dislocation, providing a consistency check. In particular, we examine the physically relevant $(3+1)$-dimensional case, where numerical analysis reveals nontrivial features arising from the interplay between topology and gauge effects.

We introduce two probabilistic models of random log-concave polynomials, the uniform model and the beta model, and study the asymptotic distribution of their zeros in the complex plane. In the uniform model, we show that the empirical root distribution converges to the uniform probability measure on the unit circle, placing the model in the same universality class as classical Kac polynomials. In contrast, in the beta model log-concavity is amplified through exponential scaling of the coefficients, leading to a new limiting distribution that is rotationally symmetric and absolutely continuous with respect to Lebesgue measure on the plane.

Experienced storytellers decompose stories into local narrative strategies and how these strategies shape higher-level arcs. This decomposition helps writers recognize patterns in others' work and adapt those patterns to tell new stories. Novices, however, struggle to identify these strategies or to reuse them effectively. We present Narrix, a novel writing tool that helps novice writers recognize narrative strategies in example stories and repurpose these strategies in their own writing. Narrix analyzes strategies in example stories, highlights them with color-coded lexical cues and explanations, and situates them on an interactive story arc for exploration by emotional shifts and turning points. Writers then drag strategies onto multi-dimensional tracks and apply block-scoped edits to revise or continue their drafts through controlled generation steered by specified strategies. Through a within-subjects study (N=12), Narrix showed improved participants' retention, confidence, and creative adaptation of narrative strategies compared to a baseline chat-based writing interface.

Entanglement criteria based on variances or Fisher information are well developed for compact collective spin algebras, but their extension to non-compact dynamical sectors is less straightforward. In particular, double-quantum (DQ) observables associated with effective SU(1,1) structures can lead to formally unbounded classical fluctuation estimates unless additional physical constraints are imposed. In this note, we develop a thermodynamic witness framework in which the classically accessible fluctuation sector is strictly bounded by finite-temperature detailed-balance conditions and motionally narrowed sequence-transfer limits. By analyzing the quantum dynamical semigroup of the spin-bath interaction, we demonstrate that spontaneous transient pair correlations generated by a stationary incoherent bath are contractively capped near an amplitude of \(10^{-9}\). Furthermore, classical coherent sequence amplification is empirically bounded to \(\mathcal{O}(10^{-2})\) in motionally narrowed tissue. The resulting functional provides a concrete, theoretically derived bounding framework against which macroscopic DQ anomalies (e.g., fractional amplitudes on the order of \(10\%\) to \(15\%\)) can be rigorously classified as classically inexplicable, provided macro-scale structural stability (constant \(T_2^*\)) is empirically verified.

Flexible random scale-mixture models provide a framework for capturing a broad range of extremal dependence structures. However, likelihood-based inference under the peaks-over-threshold setting is often computationally infeasible, due to the censored likelihood requiring repeated evaluation of high-dimensional Gaussian distribution functions. We propose a multiplicative log-Laplace nugget that yields conditional independence in the censored likelihood, resulting in a joint likelihood function that is the product of univariate densities which are available in closed form. This eliminates multivariate Gaussian distribution function evaluations and thereby enables inference for threshold exceedances in high dimensions, which represents a major shift for spatial extremes modelling as the total computational cost is now primarily driven by standard spatial statistics operations. We further show that a broad class of scale-mixture processes augmented with the proposed nugget preserves the extremal dependence structure of the underlying smooth process. The proposed methodology is illustrated through simulation studies and an application to precipitation extremes.

Girls remain underrepresented in computing, and rural contexts often compound barriers of access, language, and gender norms. Prior work in computing education highlights that confidence and belonging can shape participation, yet most evidence comes from well-resourced, English-dominant settings. Less is known about how locally grounded pathways can build programming self-efficacy and broaden career interest for adolescent girls. We addressed this gap by delivering a curriculum that began with digital foundations and unplugged problem-solving, then progressed to block-based programming activities, supported by parent awareness and teacher training in gender-responsive practices. Pre and post-surveys showed a reliable increase in programming self-efficacy, and career aspirations shifted toward technology. Complementary qualitative data indicate that mastery experiences, peer collaboration, and the creation of personal projects were key drivers of confidence, suggesting design priorities for scalable, locally relevant programmes in low-resource communities that can shift perceptions of who belongs in computing.