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Abstract Low‐lying islands in tropical regions are vulnerable to near‐term sea‐level rise and hurricane‐induced flooding, with substantial human impact. These risks motivate researchers to elucidate the processes and timescales involved in the formation, growth and stabilization of coastlines through the study of Holocene shoreline dynamics. Little Ambergris Cay (Turks and Caicos Islands) is a low‐lying carbonate island that provides a case study in the nucleation and growth of such islands. This study investigates the sedimentology and radiocarbon chronology of the island's lithified sediments to develop a model for its history. The island's lithified rim encloses a tidal swamp populated by microbial mats and mangroves. Preliminary radiocarbon data supported a long‐standing inference that the island is Holocene in age. This study integrates petrographic, sedimentological and new radiocarbon data to quantify the age of the island and develop a model for its evolution. Results indicate that the ages of most lithified sediments on the island are <1000 cal yrbp, and the generation and lithification of carbonate sediment in this system supports coastline growth of at least 5 cm/year. The lithification of anthropogenic detritus was documented, consistent with other evidence that in recent centuries the lithified rim has grown by rates up to tens of centimetres per year. A unit of mid‐Holocene age was identified and correlated with a similar unit of early transgressive aeolianite described from San Salvador, The Bahamas. It is proposed that this antecedent feature played an important role in the nucleation and formation of the modern island. Results extend an established Bahamian stratigraphic framework to the south‐western extreme of the Lucayan archipelago, and highlight the dynamism of carbonate shorelines, which should inform forward‐looking mitigation strategies to increase coastal resiliency to sea‐level rise. These results inform interpretation of the palaeoenvironmental record of carbonate environments, underscoring their geologically rapid pace of lithification. 

Given an image u_0, the aim of minimising the Mumford-Shah functional is to find a decomposition of the image domain into sub-domains and a piecewise smooth approximation u of u_0 such that u varies smoothly within each sub-domain. Since the Mumford-Shah functional is highly non- smooth, regularizations such as the Ambrosio-Tortorelli approximation can be considered, which is one of the most computationally efficient approximations of the Mumford-Shah functional for image segmentation. While very impressive numerical results have been achieved in a large range of applications when minimising the functional, no analytical results are currently available for minimizers of the functional in the piece- wise smooth setting, and this is the goal of this work. Our main result is the Γ-convergence of the Ambrosio-Tortorelli approximation of the Mumford-Shah functional for piecewise smooth approximations. This requires the introduction of an appropriate function space. As a consequence of our Gamma-convergence result, we can infer the convergence of minimizers of the respective functionals. 

The extended cleavage specificities of two hematopoietic serine proteases originating from the ray-finned fish, the spotted gar (Lepisosteus oculatus), have been characterized using substrate phage display. The preference for particular amino acids at and surrounding the cleavage site was further validated using a panel of recombinant substrates. For one of the enzymes, the gar granzyme G, a strict preference for the aromatic amino acid Tyr was observed at the cleavable P1 position. Using a set of recombinant substrates showed that the gar granzyme G had a high selectivity for Tyr but a lower activity for cleaving after Phe but not after Trp. Instead, the second enzyme, gar DDN1, showed a high preference for Leu in the P1 position of substrates. This latter enzyme also showed a high preference for Pro in the P2 position and Arg in both P4 and P5 positions. The selectivity for the two Arg residues in positions P4 and P5 suggests a highly specific substrate selectivity of this enzyme. The screening of the gar proteome with the consensus sequences obtained by substrate phage display for these two proteases resulted in a very diverse set of potential targets. Due to this diversity, a clear candidate for a specific immune function of these two enzymes cannot yet be identified. Antisera developed against the recombinant gar enzymes were used to study their tissue distribution. Tissue sections from juvenile fish showed the expression of both proteases in cells in Peyer’s patch-like structures in the intestinal region, indicating they may be expressed in T or NK cells. However, due to the lack of antibodies to specific surface markers in the gar, it has not been possible to specify the exact cellular origin. A marked difference in abundance was observed for the two proteases where gar DDN1 was expressed at higher levels than gar granzyme G. However, both appear to be expressed in the same or similar cells, having a lymphocyte-like appearance.