We study a random matching problem on closed compact $2$-dimensional Riemannian manifolds (with respect to the squared Riemannian distance), with samples of random points whose common law is absolutely continuous with respect to the volume measure with strictly positive and bounded density. We show that given two sequences of numbers $n$ and $m=m(n)$ of points, asymptotically equivalent as $n$ goes to infinity, the optimal transport plan between the two empirical measures $μ^n$ and $ν^{m}$ is quantitatively well-approximated by $\big(\mathrm{Id},\exp(\nabla h^{n})\big)_\#μ^n$ where $h^{n}$ solves a linear elliptic PDE obtained by a regularized first-order linearization of the Monge-Ampère equation. This is obtained in the case of samples of correlated random points for which a stretched exponential decay of the $α$-mixing coefficient holds and for a class of discrete-time Markov chains having a unique absolutely continuous invariant measure with respect to the volume measure.

In this article we propose a new deep learning approach to approximate operators related to parametric partial differential equations (PDEs). In particular, we introduce a new strategy to design specific artificial neural network (ANN) architectures in conjunction with specific ANN initialization schemes which are tailor-made for the particular approximation problem under consideration. In the proposed approach we combine efficient classical numerical approximation techniques with deep operator learning methodologies. Specifically, we introduce customized adaptions of existing ANN architectures together with specialized initializations for these ANN architectures so that at initialization we have that the ANNs closely mimic a chosen efficient classical numerical algorithm for the considered approximation problem. The obtained ANN architectures and their initialization schemes are thus strongly inspired by numerical algorithms as well as by popular deep learning methodologies from the literature and in that sense we refer to the introduced ANNs in conjunction with their tailor-made initialization schemes as Algorithmically Designed Artificial Neural Networks (ADANNs). We numerically test the proposed ADANN methodology in the case of several parametric PDEs. In the tested numerical examples the ADANN methodology significantly outperforms existing classical approximation algorithms as well as existing deep operator learning methodologies from the literature.

Given a convex domain $C$, a $C$-polygon is an intersection of $n\geq 2$ homothets of $C$. If the homothets are translates of $C$ then we call the intersection a translative $C$-polygon. This paper proves that if $C$ is a strictly convex domain with $m$ singular boundary points, then the number of singular boundary points a $C$-polygon has is between $n$ and $2(n-1)+m$. For a translative $C$-polygon we show the number of singular boundary points is between $n$ and $n+m$.

Researchers frequently wish to assess the equality or inequality of groups, but this poses the challenge of adequately adjusting for multiple comparisons. Statistically, all possible configurations of equality and inequality constraints can be uniquely represented as partitions of groups, where any number of groups are equal if they are in the same subset of the partition. In a Bayesian framework, one can adjust for multiple comparisons by constructing a suitable prior distribution over all possible partitions. Inspired by work on variable selection in regression, we propose a class of flexible beta-binomial priors for multiple comparison adjustment. We compare this prior setup to the Dirichlet process prior suggested by Gopalan and Berry (1998) and multiple comparison adjustment methods that do not specify a prior over partitions directly. Our approach not only allows researchers to assess pairwise equality constraints but simultaneously all possible equalities among all groups. Since the space of possible partitions grows rapidly -- for ten groups, there are already 115,975 possible partitions -- we use a stochastic search algorithm to efficiently explore the space. Our method is implemented in the Julia package EqualitySampler, and we illustrate it on examples related to the comparison of means, standard deviations, and proportions.

Recent works have proposed linear programming relaxations of variational optimization problems subject to nonlinear PDE constraints based on the occupation measure formalism. The main appeal of these methods is the fact that they rely on convex optimization, typically semidefinite programming. In this work we close an open question related to this approach. We prove that the classical and relaxed minima coincide when the dimension of the codomain of the unknown function equals one, both for calculus of variations and for optimal control problems, thereby complementing analogous results that existed for the case when the dimension of the domain equals one. In order to do so, we prove a generalization of the Hardt-Pitts decomposition of normal currents applicable in our setting. We also show by means of a counterexample that, if both the dimensions of the domain and of the codomain are greater than one, there may be a positive gap. The example we construct to show the latter serves also to show that sometimes relaxed occupation measures may represent a more conceptually-satisfactory "solution" than their classical counterparts, so that -- even though they may not be equivalent -- algorithms rendering accessible the minimum in the larger space of relaxed occupation measures remain extremely valuable. Finally, we show that in the presence of integral constraints, a positive gap may occur at any dimension of the domain and of the codomain.

Inferential models (IMs) are data-dependent, imprecise-probabilistic structures designed to quantify uncertainty about unknowns. As the name suggests, the focus has been on uncertainty quantification for inference and on its reliability properties in that context. Focusing on a likelihood-based possibilistic IM formulation, the present paper develops a corresponding framework for decision making, and investigates the decision-theoretic implications of the IM's reliability guarantees. Here we show that the possibilistic IM's assessment of an action's quality, defined by a simple Choquet integral, tends not be too optimistic compared to that of an oracle. This ensures that the IM tends not to favor actions that the oracle doesn't also favor, hence the IM is also reliable for decision making. We also establish a complementary, large-sample efficiency result that says the IM's reliability isn't achieved by being grossly conservative. In the special case of equivariant statistical models, further connections can be made between the IM's and Bayesian's recommended actions, from which certain optimality conclusions can be drawn.

In this work, we explore interesting consequences arising from the coupling between a clean non-Hermitian chain with skin localization and a delocalized chain of the same length under various boundary conditions (BCs). We reveal that in the ladder with weak rung coupling, the nonHermitian skin localization could induce a pseudo mobility edge in the complex energy plane, which separates states with extended and localized profiles yet allowing unidirectional transport of signals. We also demonstrate the gradual takeover of the non-Hermitian skin effect in the entire system with the increase of the rung coupling under conventional open BC. When taking open BC for the nonHermitian chain and periodic BC for the other, it is discovered that a quantized winding number defined under periodic BC could characterize the transition from the pseudo mobility edge to the trivial extended phases, establishing a "bulk-defect correspondence" in our quasi-1D non-Hermitian system. This work hence unveils more subtle properties of non-Hermitian skin effects and sheds light on the topological nature of the non-Hermitian localized modes in the proximity to systems with dissimilar localization properties.

The illumination number $I(K)$ of a convex body $K$ in Euclidean space $\mathbb{E}^d$ is the smallest number of directions that completely illuminate the boundary of a convex body. A cap body $K_c$ of a ball is the convex hull of a Euclidean ball and a countable set of points outside the ball under the condition that each segment connecting two of these points intersects the ball. The main results of this paper are the sharp estimates $I(K_c)\leq6$ for centrally symmetric cap bodies of a ball in $\mathbb{E}^3$, and $I(K_c)\leq 8$ for unconditionally symmetric cap bodies of a ball in $\mathbb{E}^4$.

The irrelevant vertex technique provides a powerful tool for the design of parameterized algorithms for a wide variety of problems on graphs. A common characteristic of these problems, permitting the application of this technique on surface-embedded graphs, is the fact that every graph of large enough treewidth contains a vertex that is irrelevant, in the sense that its removal yields an equivalent instance of the problem. The straightforward application of this technique yields algorithms with running time that is quadratic in the size of the input graph. This running time is due to the fact that it takes linear time to detect one irrelevant vertex and the total number of irrelevant vertices to be detected is linear as well. Using advanced techniques, sub-quadratic algorithms have been designed for particular problems, even in general graphs. However, designing a general framework for linear-time algorithms has been open, even for the bounded-genus case. In this paper we introduce a general framework that enables finding in linear time an entire set of irrelevant vertices whose removal yields a bounded-treewidth graph, provided that the input graph has bounded genus. Our technique consists of decomposing any surface-embedded graph into a tree-structured collection of bounded-treewidth subgraphs where detecting globally irrelevant vertices can be done locally and independently. Our method is applicable to a wide variety of known graph containment or graph modification problems where the irrelevant vertex technique applies. Examples include the (Induced) Minor Folio problem, the (Induced) Disjoint Paths problem, and the $\mathcal{F}$-Minor-Deletion problem.

The standard approach to fault-tolerant quantum computation is to store information in a quantum error correction code, such as the surface code, and process information using a strategy that can be summarized as distill-then-synthesize. In the distill step, one performs several rounds of distillation to create high-fidelity logical qubits in a magic state. Each such magic state provides one good T gate. In the synthesize step, one seeks the optimal decomposition of an algorithm into a sequence of many T gates interleaved with Clifford gates. This gate-synthesis problem is well understood for multiqubit gates that do not use any Hadamards. We present an in-depth analysis of a unified framework that realises one round of distillation and multiqubit gate synthesis in a single step. We call these synthillation protocols, and show they lead to a large reduction in resource overheads. This is because synthillation can implement a general class of circuits using the same number of T-states as gate synthesis, yet with the benefit of quadratic error suppression. This general class includes all circuits primarily dominated by control-control-Z gates, such as adders and modular exponentiation routines used in Shor's algorithm. Therefore, synthillation removes the need for a costly round of magic state distillation. We also present several additional results on the multiqubit gate-synthesis problem. We provide an efficient algorithm for synthesizing unitaries with the same worst-case resource scaling as optimal solutions. For the special case of synthesizing controlled-unitaries, our techniques are not just efficient but exactly optimal. We observe that the gate-synthesis cost, measured by T-count, is often strictly subadditive. Numerous explicit applications of our techniques are also presented.

This article introduces and solves a general class of fully coupled forward-backward stochastic dynamics by investigating the associated system of functional differential equations. As a consequence, we are able to solve many different types of forward-backward stochastic differential equations (FBSDEs) that do not fit in the classical setting. In our approach, the equations are running in the same time direction rather than in a forward and backward way, and the conflicting nature of the structure of FBSDEs is therefore avoided.

We study the celestial three-gluon amplitude in a dilaton background through the Mellin-Liouville formulation proposed by Stieberger, Taylor and Zhu (STZ). The original map contains an ambiguity in the identification of Liouville and Mellin variables; we resolve it by requiring global conformal covariance and compatibility with the semiclassical expansion of Liouville theory. This uniquely fixes the operator normalization and the parameter dictionary, and leads to a controlled expansion in the Liouville coupling $b$. Starting from the full Liouville DOZZ three-point function, we derive the leading and first subleading terms in the $b^2$ expansion. The leading term reproduces the tree-level Yang-Mills amplitude in the small total momentum limit, as anticipated in the STZ proposal. The one-loop correction can be written in closed form using modified Bessel functions, and its soft limit exhibits a clear separation into geometric and logarithmic contributions. The resulting framework extends the STZ proposal to finite-$b$ corrections in a consistent and computable way.

High-order methods offer superior dispersion and dissipation properties compared to low-order schemes but require robust stabilization for discontinuities. To ensure stability, local artificial viscosity is common, but often degrades sub-element resolution. Conversely, subcell resolution preserving limiting strategies such as the finite volume subcell method are typically restricted to uniform topologies, such as purely hexahedral, or simplex meshes. This leaves a significant gap in treating the hybrid-element topologies necessary for complex engineering geometries. This paper presents a robust shock-capturing approach for the discontinuous Galerkin spectral element method on mixed curvilinear meshes containing hexahedral, prismatic, tetrahedral, and pyramid elements. Non-hexahedral elements are handled via collapsed coordinate transformations. The proposed method utilizes an h-adaptive finite volume subcell scheme with arbitrary subcell resolution; 2N + 1 in this work. The schemes essential properties, including conservation, spatial convergence, and the shock capturing capabilities are verified. Finally, the method's applicability to complex configurations is demonstrated through a simulation of the flow around a NACA 0012 airfoil.

Dipole-radiation-like deviations from general relativity are most prominent during the early inspiral of compact binaries, making space-ground multiband observations a potential probe of such effects. In the same regime, orbital eccentricity can leave a significant imprint on the waveform and is therefore essential for robust dipole-radiation constraints. For the first time we present a multiband Bayesian inference pipeline for stellar-mass binary black holes that simultaneously incorporates eccentricity and a theory-agnostic dipole-radiation correction. We find strong degeneracies among the dipole parameter, chirp mass, and eccentricity, which substantially weaken the inferred dipole constraints when eccentricity is included. Even so, for a GW231123-like source, one year of TianQin or LISA observation with ground-informed priors from a next-generation detector network can still constrain the dipole parameter to $|b|\lesssim\mathcal{O}(10^{-7})$ under inference with noisy data. Our results show that multiband binary black hole observations provide a promising and distinct channel for testing theory-agnostic dipole radiation, while also highlighting the need for more complete waveform modeling in future precision tests of gravity.

Claims reserving is one of the most important actuarial tasks in non-life insurance modeling. There are several popular methods to perform claims reserving such as the chain-ladder (CL), the Bornhuetter--Ferguson (BF) or the generalized Cape Cod (GCC) methods. These methods have originally been introduced as deterministic algorithms, and only in a later step, they have been lifted to stochastic models allowing for analyzing claims prediction uncertainty. This holds true for the CL and the BF methods, but not for the GCC method. The purpose of this article is to close this gap and derive an analytical formula for the mean squared error of prediction (MSEP) of the GCC method.

As an alternative to PINNs, a Deep Ritz framework is proposed to solve fully nonlinear PDEs. A least-squares algorithm is advocated to decouple the nonlinearities from the variational features of several fully nonlinear PDEs. A splitting method allows to iteratively solve local nonlinear problems and linear variational problems at each iteration. While existing nonlinear solvers are applied to solve for nonlinearities, we propose a novel coupling with a Deep Ritz neural network approach that is well-suited to the variational flavor of the linear variational problems. An adaptive sampling strategy for the selection of collocation points is incorporated to increase the efficiency of the algorithm without sacrificing its accuracy. Numerical experiments are presented to solve the Dirichlet problem for several fully nonlinear equations, starting with the prototypical Monge-Ampère equation, showing the flexibility of the approach. Numerical results are compared with results obtained using a full PINNs approach. Finally, numerical experiments are extended to address the optimal transport Monge-Ampère problem with transport boundary conditions.

We consider non-equilibrium evolution of non-Gaussian fluctuations in a hydrodynamic system undergoing a boost-invariant expansion described by Bjorken flow. We derive the evolution equations for two- and three-point velocity correlators using the effective field theory framework and present analytical solutions for them. We show that the average Landau frame is better suited for studying non-Gaussian fluctuations of velocity when relativistic effects are important. In the Bjorken background, the average Landau frame corresponds to the density frame. We demonstrate that the three-point correlators depend nonlinearly on the non-equilibrium dynamics of the two-point functions, and exhibit non-trivial effects such as memory. The importance of these effects in the context of the search for the QCD critical point via fluctuations is discussed.

We discuss modulation phasons as a possible source of unusual elastic behavior of five-layer modulated (10\,M) martensite of the Ni-Mn-Ga shape memory alloy. This material exhibits anomalous macroscopic shear compliance along specific planes perpendicular to the modulation vector, and this compliance disappears when the modulations become incommensurate. Using a simple mechanical model, we show that modulation phasons in Ni-Mn-Ga can have macroscopic mechanical manifestations, and that the resulting 'mechanical phasons' can relax external shear loadings for commensurate and weakly incommensurate modulations, but not for strongly incommensurate modulations. The model merges ideas from the adaptive martensite theory and electronic-structure considerations, and enables straightforward explanations of several properties of the 10\,M lattice, such as spontaneous monoclinic distortion or easy formation and propagation of $a/b$ twins.

LLMs are increasingly employed both as judges for evaluating open-ended outputs and as co-creation partners in AI-assisted programming; yet rigorous evaluation in human-AI co-creation settings remains underdeveloped as judgments must be reliable, comparable across models, and interpretable over multi-turn interaction. To address this gap, a rubric-driven LLM-as-a-Judge framework is presented for contest-style human-AI co-creation in coding and software engineering (SE). The framework is built around schema-constrained judge outputs, validation and repair mechanisms, grouped and split by user and problem to prevent trajectory leakage, and participant-level NONBLIND context. Multiple LLM judges are assessed through a multi-metric protocol covering discrimination (ROC-AUC, PR-AUC), thresholded decision quality (MCC), probabilistic reliability (LogLoss, Brier score, ECE), and inter-judge agreement (Cohen's and Fleiss' k). Human-AI co-creation is further examined through trajectory-level signals, including turn-wise confidence, Success-at-Turn, time-to-success, revision churn, and CodeBLEU. Co-creation success is found to concentrate early, with Success-at-Turn rising to 0.8533 at the first observed turn and stabilizing at 0.8641 by turn 6. Revision behavior, however, remains heterogeneous, suggesting that productive progress can emerge through either incremental refinement or broader restructuring. On the judging side, the best held-out scores reach 0.5937 for ROC-AUC, 0.6904 for PR-AUC, and 0.5000 for MCC test, while inter-judge consistency remains modest overall (mean pairwise Cohen's k = 0.1592, Fleiss' k = 0.0696). Taken together, this work offers an auditable and reproducible evaluation methodology that links reliability-aware LLM judging with trajectory-based analysis of human-AI co-creation, providing a practical evaluation template for future AI-assisted coding and SE.

Fabricating brightly fluorescent layers with nanometric thickness and digitally controlled lateral structuration remains a challenge for next-generation photonic devices, optical calibration standards, and biocompatible interfaces. Here, we introduce Nano-Bead Emitters (NBEs), hydrogel nanoparticles covalently functionalized with fluorophores, as a universal, water-processable ink platform for fabricating programmable nanometric fluorescent architectures. By immobilizing fluorophores within a charged nanohydrogel scaffold, the platform entirely decouples film morphology from dye solubility. This molecule-independent strategy enables spectrally distinct, inherently water-insoluble dyes to be processed using a single, standardized aqueous ink formulation. Combined with laser-induced forward transfer (LIFT) printing, this additive approach yields highly uniform fluorescent layers (~7 nm thickness, sub-nanometric roughness). This structural invariance produces complex multicolor patterns sharing identical thickness and surface morphology across all spectral channels, a critical requirement for quantitative optical calibration. Furthermore, LIFT printing provides programmable, layer-by-layer control over fluorescence intensity via successive deposition cycles, yielding precisely tunable brightness without aggregation-caused quenching. This maskless technique enables rapid, high-fidelity printing of both monochromatic and multicolor patterns over macroscopic areas with absolute spatial resolution. Finally, these universally compatible NBE inks stably deposit onto diverse substrates (glass, polymers, semiconductors, metasurfaces), effectively bridging scalable manufacturing with high-performance integrated photonic systems.

Elastic wave propagation is intrinsically sensitive to the mechanical properties of the medium through which it travels. In soft elastomers, this makes guided elastic waves natural probes of viscoelastic and acoustoelastic behavior over a broad frequency range. In this work, we introduce a wave-based mechanical characterization method in which a thin elastomer strip acts as a waveguide supporting multiple in-plane guided modes. By combining stroboscopic measurements of monochromatic wave fields with a theoretical framework that couples frequency-dependent viscoelasticity and elongation-dependent acoustoelasticity, we extract complex-valued dispersion relations for guided modes under controlled static elongation. A dedicated numerical implementation allows these experimental dispersion curves to be quantitatively matched to theory, enabling identification of the material's rheological and hyperelastic parameters. Applied to several commercial silicone elastomers, the method yields mechanical parameters that are consistent with conventional plate-plate rheometry, while extending the accessible frequency range beyond that of conventional techniques. By exploiting the richness of guided-wave dispersion and the sensitivity of waves to both frequency and pre-stress, this approach provides a unified, broadband, and experimentally simple route to the mechanical characterization of soft elastomers.

We develop a coarse-grained theoretical description of the macroscopic emergent electric field generated by phonon-coupled lattice deformations in the breathing and rotational dynamics of a skyrmion lattice under microwave excitation. The analysis identifies the symmetry and dynamical conditions that yield rectified (dc) and oscillating (ac) electric fields, even in the absence of net translational motion of the skyrmion lattice, particularly in the dilute-lattice limit. Using experimentally measurable skyrmion profile parameters such as the equilibrium radius, domain-wall width, and dynamical resonance frequency of skyrmion lattice, the model further enables identification of harmonic components contributing to the observed macroscopic electrodynamic response in the long-wavelength phonon limit ($q \to 0$) and at finite phonon frequency, providing a unified framework for phonon-driven spin-charge-lattice coupling in topological magnets.

Room-temperature single-photon emission (SPE) resulting from a biexciton-exciton cascaded decay is demonstrated for the first time from chemically and photoelectrochemically etched site-controlled In0.14Ga0.86N quantum dots (QDs) embedded in vertical GaN nanowires. Diameter-dependent biexciton-exciton dynamics are analysed to determine the eligibility of QD as a single-photon emitter. The signal-to-noise ratio degrades with increasing QD diameter. Background noise photons pose a bottleneck to achieving SPE. This is also explained from a carrier dynamics perspective. Surface recombination contributes to inhomogeneous broadening at QD diameters larger than 35 nm. Below 35 nm, density-of-states-corrected Auger gradually becomes the principal biexciton-decay route with further reduction in QD diameter, thereby quenching the possibility of thermal broadening and setting a threshold for SPE. Below 9 nm, the Auger recombination rate becomes manyfold of other decay rates, causing multi-photon suppression via single Auger decay to form an exciton. Surface recombination probability of this exciton is minimized while biexciton state filling probability is maximized by reducing sidewall surface states through wet-treatment. These improve biexciton state preparation and enhance the single-photon purity of the exciton towards the exciton Bohr radius (3 nm) regime. Far away from this regime, higher-order autocorrelations to characterize quantum emission involving multi-photon events are discussed. This study establishes a generalized physical framework for predetermining SPE probability as a function of QD surface and geometry down to the exciton Bohr radius regime, with practical implementations. This work shows the pathway to design and develop next-generation semiconductor QDs for high-purity room-temperature SPE.

We construct a Lagrangian Floer homology whose chain complex is generically generated by the inscriptions of isosceles trapezoids in a smooth Jordan curve. This is an extension of Greene and Lobb's Jordan Floer homology (arXiv:2404.05179), which we also call Jordan Floer homology. Its non-triviality re-establishes that every smooth Jordan curve inscribes every isosceles trapezoid. By consideration of the spectral invariants associated with the real filtration known as the action filtration, we establish new cases of non-smooth Jordan curves which admit inscriptions of isosceles trapezoids.

We study the dimension-six SMEFT four-lepton operators in the $μ$--$τ$ sector. These operators control both charged-lepton scattering and neutrino self-interactions, the latter being weakly constrained by direct laboratory probes despite their importance for cosmological tensions. We compare three classes of constraints on the Warsaw-basis coefficients $[C_{\ell\ell}]_{2222}$, $[C_{\ell\ell}]_{2233}$, and $[C_{\ell\ell}]_{2332}$. We use perturbative unitarity from $2\!\to\!2$ partial-wave analysis, spin-summing positivity sum rules, and the experimental bounds from NA64$μ$ and the global fit~\cite{Falkowski:2017pss}. We find that the global fit dominates for $[C_{\ell\ell}]_{2222}$ and $[C_{\ell\ell}]_{2332}$, while NA64$μ$ provides the leading bound on $[C_{\ell\ell}]_{2233}$, with the unitarity line for this direction entering the range of collider energies near $200~\mathrm{GeV}$. Renormalization-group running between $1~\mathrm{GeV}$ and $30~\mathrm{TeV}$ modifies these coefficients by up to $10\%$. Translating these bounds onto the effective four-neutrino coupling $G_\mathrm{eff}$, we find values many orders of magnitude smaller than the strongly interacting regime motivated by the Hubble tension; this excludes heavy-mediator UV completions of strong $ν_μ$--$ν_μ$ and $ν_μ$--$ν_τ$ self-interactions within the validity of the dimension-six SMEFT and in the absence of tuned cancellations between operators, while leaving the cosmologically motivated light-mediator scenarios unconstrained by this analysis. Finally, we comment on the bounds these coefficients place on a leptophilic $L_μ- L_τ$ $Z'$ UV completion. Our SMEFT-based current and projected NA64$μ$ bounds reproduce the dedicated $Z'$ analyses already available in the literature.

How code representation format shapes false positive behaviour in cross-language LLM vulnerability detection remains poorly understood. We systematically vary training intensity and code representation format, comparing raw source text with pruned Abstract Syntax Trees at both training time and inference time, across two 8B-parameter LLMs (Qwen3-8B and Llama 3.1-8B-Instruct) fine-tuned on C/C++ data from the NIST Juliet Test Suite (v1.3) and evaluated on Java (OWASP Benchmark v1.2) and Python (BenchmarkPython v0.1). Cross-language FPR reflects the joint effect of training-time and inference-time representation, not either alone. Text fine-tuning drives FPR upward monotonically (Qwen3-8B: 0.763 zero-shot, 0.866 pilot, 1.000 full-scale) while F1 remains stable (0.637-0.688), masking the collapse. We argue surface-cue memorisation is the primary mechanism: text fine-tuning encodes C/C++-specific API names and syntactic idioms as vulnerability triggers that fire indiscriminately on target-language code. A cross-representation probe, applying text-trained weights to AST-encoded input without retraining, isolates this: Qwen3-8B FPR drops from 0.866 to 0.583, and 37.2% of false positives revert to true negatives under AST input alone. Direct AST fine-tuning does not preserve the benefit (FPR at least 0.970), as flat linearisation introduces structural surface cues of its own. The pattern replicates across both model families. On BenchmarkPython the AST probe yields FPR=0.554, within 2.9 percentage points of the Java result, despite maximal surface-syntax differences, substantially weakening a domain-shift explanation. These findings motivate a pre-deployment consistency gate, running alerts through both text and AST paths, as a retraining-free filter for false-positive-sensitive settings, at the cost of reduced recall.

The rapid diversification of social media platforms and the increasing restrictions on official APIs have significantly complicated cross-platform analysis. Researchers are often forced to rely on heterogeneous datasets obtained through web scraping and historical archives; however they often lack structural consistency. Prior to conducting cross-platform social media analyses, one needs to answer three critical questions: (1) What makes platforms different and similar? (2) How were the datasets collected? (3) How can we align the datasets of different platforms to conduct fair analyses? To address these questions, we introduce the Social Media Data Toolkit (\projectname{}), a comprehensive Python framework designed for the standardization, anonymization, and enrichment of social network datasets. \projectname{} unifies diverse data structures into a generic schema comprising Communities, Accounts, Posts, Actions, and Entities to facilitate multi-platform research. The framework features a configurable anonymization module to secure Personally Identifiable Information (PII) and an extendable enrichment layer that integrates Large Language Models (LLMs) and network analysis tools for downstream tasks such as stance detection and toxicity scoring without creating codebase for different datasets. We demonstrate the versatility of \projectname{} through four case studies spanning from textual analysis of the content to network analysis across platforms. To offer reproducible social media research, \projectname{} is released as an open-source tool featuring detailed documentation and practical guides for researchers at any skill-level. It can be accessed at github.com/ViralLab/SMDT and varollab.com/SMDT.

MAX phases (M$_{n+1}$AX$_n$), precursors to MXenes, span a vast compositional space, motivating efficient computational screening for synthesisable candidates. We employ CrystaLLM$-π$, a large language model fine-tuned on 6,179 double transition-metal MAX phases, and demonstrate its ability to generate out-of-sample structures consistent with known experimental trends. Using a conditioning vector with two dimensions (a statistically derived MXene derivative count and a surrogate for A-site binding energy), the model was able to target MXene-favourable regions of phase space for generation. Specific condition vectors double novel stable structure generation rates versus unconditioned baselines. Of ten compositionally novel candidates, five exhibit DFT-validated stability ($E_{hull} < 0.050$ eV/atom). This work showcases the potential for autoregressive generative models to explore targeted materials' spaces, offering a scalable framework for accelerated discovery in compositionally complex systems.

Artificial intelligence (AI) is now embedded in educational, civic, and economic systems worldwide. For African primary and secondary education, this creates a double imperative: to prepare a young population (over sixty per cent of Africans are under twenty-five) for AI-mediated labour markets without uncritically importing curricula designed for other linguistic, cultural, and socio-political contexts. The African Union's Continental AI Strategy (2024) and the 2025 Africa Declaration on AI have elevated these questions to the continental agenda. This paper proposes a Pan-African, culturally contextualised, and ethically grounded framework for integrating AI education into African primary and secondary schools. The paper is a structured conceptual synthesis of continental and national policy documents, peer-reviewed scholarship on AI ethics, AI literacy, decolonial pedagogy, and Ubuntu-grounded AI governance. We contribute: (i) a framework of six guiding principles, four curriculum domains, five ethical competencies, and an age-banded progression from lower primary to upper secondary; (ii) a comparative analysis of continental and national policy contexts; (iii) an explicit mapping between global AI-ethics principles and Ubuntu-informed relational ethics; (iv) a planned empirical validation programme combining a Delphi study, teacher surveys across anglophone, francophone, lusophone, and arabophone contexts, and multi-country classroom piloting; and (v) targeted recommendations for policymakers, educators, civil society, and international partners. We argue that an ethical AI curriculum can serve as a transformative tool for equity, innovation, and social justice, and outline a research agenda to embed ethics, resilience, and critical thinking at the core of Africa's digital future.

In this study, we present a comprehensive quantitative analysis of the radiation emitted by 855 MeV electrons propagating through an oriented diamond hetero-crystal. The crystal consists of two distinct segments: (i) a straight single-crystal diamond substrate, and (ii) a diamond layer that is periodically doped with boron atoms. The doping profiles were derived from precise experimental measurements of boron concentration obtained during the layer fabrication via Microwave Plasma Chemical Vapor Deposition (MPCVD). Our study systematically investigates the channelling and the crystalline undulator radiation, accounting for the different doping profiles in the undulating region. The simulations were conducted using the advanced MBNExplorer software package, which enables detailed modeling of particle trajectories and radiation emission. We report on good agreement with experiment and discuss remaining discrepancies providing possible explanations for them. The results obtained show that the radiation intensity is significantly affected by a range of factors, including the angular divergence of the incident beam, its orientation with respect to the target, the direction in which the emitted radiation is detected, and the choice of the doping profiles. These findings are important for optimising the design of crystalline undulators as novel gamma radiation light sources.