Diffusion and flow models have become the dominant paradigm for generative modeling on Riemannian manifolds, with successful applications in protein backbone generation and DNA sequence design. However, these methods require tens to hundreds of neural network evaluations at inference time, which can become a computational bottleneck in large-scale scientific sampling workflows. We introduce Riemannian MeanFlow~(RMF), a framework for learning flow maps directly on manifolds, enabling high-quality generations with as few as one forward pass. We derive three equivalent characterizations of the manifold average velocity (Eulerian, Lagrangian, and semigroup identities), and analyze parameterizations and stabilization techniques to improve training on high-dimensional manifolds. In promoter DNA design and protein backbone generation settings, RMF achieves comparable sample quality to prior methods while requiring up to 10$\times$ fewer function evaluations. Finally, we show that few-step flow maps enable efficient reward-guided design through reward look-ahead, where terminal states can be predicted from intermediate steps at minimal additional cost.

<p>Abstract:Mediterranean coasts have one of the world’s richest concentrations of cultural heritage, yet this legacy is increasingly threatened by sea-level rise (SLR), coastal erosion and storm impacts. Despite a growing number of local and thematic studies, regional syntheses remain scarce. This paper presents a semi-quantitative review of more than sixty peer-reviewed publications and in-stitutional reports (2010–2024) addressing coastal heritage vulnerability in the Mediterranean. Drawing on a harmonised database, each study has been classified by country, heritage type, threat, temporal horizon and methodological approach, and evaluated through standardised se-verity (0–5) and risk (1–3) scales. Results reveal three interrelated dimensions of imbalance—geo-graphical,methodological and temporal. Geographically, a pronounced north–south asymmetry persists: Italy, Spain and Greece concentrate more than half of all studies, while North Africa and the eastern Mediterranean remain under-represented. Methodologically, about45% of works em-ploy DEM-based geospatial modelling, 25% rely on field evidence, and only 10% address manage-ment or policy dimensions. Prospectively, most analyses project impacts to 2100 under high-emis-sion scenarios, with more than 70% of assessed sites showing moderate-to-high vulnerability. Alt-hough comprehensive, the sample is not systematic, and geographic patterns partly reflect differ-ences in research capacity rather than exposure. A critical weakness identified across the literature is the limited transfer of scientific results into usable frameworks for planners and heritage man-agers, underscoring the need for performance and usability assessment in future climate-adapta-tion research. Advancing this field requires standardised indicators, broader regional coverage, and stronger interdisciplinary integration between coastal science, archaeology and heritage manage-ment to inform effective adaptation strategies for safeguarding Mediterranean coastal heritage under accelerating climate change.</p>

We present a high-order accurate fully discrete numerical scheme for solving Initial Boundary Value Problems (IBVPs) within the Continuous Galerkin (CG)-based Finite Element framework. Both the spatial and time approximation in Summation-By-Parts (SBP) form are considered here. The initial and boundary conditions are imposed weakly using the Simultaneous Approximation Term (SAT) technique. The resulting SBP-SAT formulation yields an energy estimate in terms of the initial and external boundary data, leading to an energy-stable discretization in both space and time. The proposed method is evaluated numerically using the Method of Manufactured Solutions (MMS). The scheme achieves super-convergence in both spatial and temporal direction with accuracy $\mathcal{O}(p+2)$ for $p\geq 2$, where $p$ refers to the degree of the Lagrange basis. In an application case, we show that the fully discrete formulation efficiently captures space-time variations even on coarse meshes, demonstrating the method's computational effectiveness.

RPB2 distance matrix

Figure 4 Distribution of Najas major in Lithuania: A main map view; B within the red square in A; C within the blue square in A. Different colours represent different periods: dark green – the site only recorded in the I period (until 1850); brown – the site only recorded in the II period (1950–1989); purple – the sites only recorded in the III period (1990–2025); light green – the sites recorded in the II and III periods (1950–2025).

Polygonatum simizui Kitag. and Polygonatum dabieshanense

Figure 10 Cerodontha (Dizygomyza) tumefacta sp. nov. Paratype male. A. Habitus, lateral view; B, C. Head, lateral and dorsal view; D, E. Thorax, dorsal and lateral view; F. Abdomen, lateral view; G, J. Genitalia, lateral and ventral view; H, K. Epandrial complex, posterolateral and posterior view; I, L. Ejaculatory apodeme, lateral and ventral view. Scale bars: 0.5 mm (A–F); 0.1 mm (G–L).

Figure 5 Microlaimus parakoreanus sp. nov. A. Lateral view of the male anterior region, showing buccal cavity; B. Lateral view of the male anterior region, showing amphidial fovea; C. Lateral view of the male posterior body, showing spicules and gubernaculum; D. Lateral view of the male posterior body, showing tail. Scale bars: 20 µm (A–D).

Figure 12 External morphology of Cloeon viridulum in Thailand: A. Female imago; B. Male subimago; C. Wing of female imago; D. Wing of male subimago.

Figure 4a Adult morphology of egg parastoids: - Trichogramma chilonis;