Stephen E. Moore

Jiayi Wang, David Ifeoluwa Adelani, Sweta Agrawal et al.

Despite the recent progress on scaling multilingual machine translation (MT) to several under-resourced African languages, accurately measuring this progress remains challenging, since evaluation is often performed on n-gram matching metrics such as BLEU, which typically show a weaker correlation with human judgments. Learned metrics such as COMET have higher correlation; however, the lack of evaluation data with human ratings for under-resourced languages, complexity of annotation guidelines like Multidimensional Quality Metrics (MQM), and limited language coverage of multilingual encoders have hampered their applicability to African languages. In this paper, we address these challenges by creating high-quality human evaluation data with simplified MQM guidelines for error detection and direct assessment (DA) scoring for 13 typologically diverse African languages. Furthermore, we develop AfriCOMET: COMET evaluation metrics for African languages by leveraging DA data from well-resourced languages and an African-centric multilingual encoder (AfroXLM-R) to create the state-of-the-art MT evaluation metrics for African languages with respect to Spearman-rank correlation with human judgments (0.441).

Stephen E. Moore

We present and analyze an interior penalty discontinuous Galerkin Isogeometric Analysis (dG-IgA) method for the biharmonic equation in computational domain in $\mathbb{R}^d$ with $d =2,3.$ The computational domain consist of several non-overlapping sub-domains or patches. We construct B-Spline approximation spaces which are discontinuous across patch interfaces. We present a priori error estimate in a discrete norm and numerical experiments to confirm the theory.

Stephen E. Moore, Mich-Seth Owusu, Akwasi Asare et al.

Large language models (LLMs) have demonstrated impressive multilingual capabilities for well-resourced languages, yet their performance on low-resource African languages remains poorly understood and largely unevaluated. This paper presents Nsanku, a systematic benchmark that evaluates the zero-shot machine translation performance of 19 open-weight and proprietary LLMs across 43 Ghanaian languages paired with English. Evaluation sentences were sourced from the YouVersion Bible platform, providing 300 sentence pairs per language. Two complementary automatic metrics are employed: Bilingual Evaluation Understudy (BLEU) and Character n-gram F-Score (chrF), alongside an average accuracy score and a cross-language consistency dimension. Nsanku represents the most comprehensive LLM translation evaluation for Ghanaian languages conducted to date. Results show that gemini-2.5-flash achieves the highest overall average score of 26.88 (BLEU: 24.60, chrF: 29.16), followed by claude-sonnet-4-5 at 24.87 (BLEU: 22.46, chrF: 27.28) and gpt-4.1 at 23.20 (BLEU: 21.15, chrF: 25.24). Among open-weight models, kimi-k2-instruct-0905 leads at an average score of 20.87. A critical finding from the consistency analysis is that no model and no language reached the Leaders quadrant of high performance and high consistency simultaneously, indicating that current LLMs are not yet reliably usable for Ghanaian language translation at scale. Siwu achieved the highest per-language average score at 25.73 while Nkonya scored lowest at 11.65. Nsanku establishes a publicly available, community-extensible evaluation infrastructure for African language NLP research.

Ulrich Langer, Angelos Mantzaflaris, Stephen E. Moore et al.

This paper is concerned with the construction of graded meshes for approximating so-called singular solutions of elliptic boundary value problems by means of multipatch discontinuous Galerkin Isogeometric Analysis schemes. Such solutions appear, for instance, in domains with re-entrant corners on the boundary of the computational domain, in problems with changing boundary conditions, in interface problems, or in problems with singular source terms. Making use of the analytic behavior of the solution, we construct the graded meshes in the neighborhoods of such singular points following a multipatch approach. We prove that appropriately graded meshes lead to the same convergence rates as in the case of smooth solutions with approximately the same number of degrees of freedom. Representative numerical examples are studied in order to confirm the theoretical convergence rates and to demonstrate the efficiency of the mesh grading technology in Isogeometric Analysis.

Ulrich Langer, Stephen E. Moore, Martin Neumüller

We present and analyze a new stable space-time Isogeometric Analysis (IgA) method for the numerical solution of parabolic evolution equations in fixed and moving spatial computational domains. The discrete bilinear form is elliptic on the IgA space with respect to a discrete energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the IgA spaces yields an a priori discretization error estimate with respect to the discrete norm. The theoretical results are confirmed by several numerical experiments with low- and high-order IgA spaces.

Ulrich Langer, Angelos Mantzaflaris, Stephen E. Moore et al.

Isogeometric analysis (IgA) uses the same class of basis functions for both, representing the geometry of the computational domain and approximating the solution. In practical applications, geometrical patches are used in order to get flexibility in the geometrical representation. This multi-patch representation corresponds to a decomposition of the computational domain into non-overlapping subdomains also called patches in the geometrical framework. We will present discontinuous Galerkin (dG) methods that allow for discontinuities across the subdomain (patch) boundaries. The required interface conditions are weakly imposed by the dG terms associated with the boundary of the sub-domains. The construction and the corresponding discretization error analysis of such dG multi-patch IgA schemes will be given for heterogeneous diffusion model problems in volumetric 2d and 3d domains as well as on open and closed surfaces. The theoretical results are confirmed by numerous numerical experiments which have been performed in G+SMO. The concept and the main features of the IgA library G+SMO are also described.