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k-Universality of Regular Languages
No full texthttp://dx.doi.org/10.13039/501100000275 Leverhulme Trusthttp://dx.doi.org/10.13039/501100001659 Deutsche Forschungsgemeinschaf
Latest Oligocene–earliest Miocene Australasian freshwater sponges (Demospongiae: Spongillida) from a maar paleolake in southern New Zealand
No full textAbstract The evolutionary history of freshwater sponges (Porifera: Spongillida) in Australasia is poorly understood due to a paucity of fossils. A new genus and new species, Protooncosclera zealandiae n. gen. n. sp., family Potamolepidae, was discovered in southern New Zealand from lacustrine diatomites/spiculites of latest Oligocene–earliest Miocene of the Fossil-Lagerstätte at Foulden Maar. The fossil spicular complement is similar to that of the extant genus Oncosclera but differs from that and all other Spongillida genera by possessing a structured gemmular architecture armed by ornamented strongyles and strongyloxeas, with theca surrounded by a spicular cage of slender acanthoxeas, and a skeletal spicular complement of stout, smooth to spiny oxeas. This is the first fossil (pre-Quaternary) record of freshwater sponges from Australasia and fits into the Gondwana-like distribution of potamolepid freshwater sponges. Its discovery in a subtropical maar lake on the southwestern margin of Zealandia confirms a formerly wider geographic distribution of Potamolepidae in the Cenozoic, followed by range retractions related to post-Early Miocene climate cooling. The stratigraphic distribution of sponge remains at Foulden Maar demonstrates that sponges colonized the isolated maar lake soon after its formation, most likely by passive dispersal by water birds, and then thrived in the shallow water margins of the paleolake for ca. 130,000 years. Sponge remains, skeletal spicules and gemmules, frequently associated with coprolites indicate that sponges were consumed by one or more spongivorous taxa, presumably fish belonging to the Southern Hemisphere family Galaxiidae. UUID: http://zoobank.org/72a81923-9766-4ae0-b980-28b2e3d98ebeFondazione di Sardegna https://doi.org/10.13039/100014810Deutsche Forschungsgemeinschaft https://doi.org/10.13039/50110000165
Semi-discrete unbalanced optimal transport and quantization
No full textAbstract In this paper we study the class of optimal entropy-transport problems introduced by Liero, Mielke and Savaré in Inventiones Mathematicae 211 in 2018. This class of unbalanced transport metrics allows for transport between measures of different total mass, unlike classical optimal transport where both measures must have the same total mass. In particular, we develop the theory for the important subclass of semi-discrete unbalanced transport problems, where one of the measures is diffuse (absolutely continuous with respect to the Lebesgue measure) and the other is discrete (a sum of Dirac masses). We characterize the optimal solutions and show they can be written in terms of generalized Laguerre diagrams. We use this to develop an efficient method for solving the semi-discrete unbalanced transport problem numerically. As an application, we study the unbalanced quantization problem, where one looks for the best approximation of a diffuse measure by a discrete measure with respect to an unbalanced transport metric. We prove a type of crystallization result in two dimensions – optimality of a locally triangular lattice with spatially varying density – and compute the asymptotic quantization error as the number of Dirac masses tends to infinity
Membrane-Permeable 5-Fluorodeoxyuridine Triphosphate Derivatives Inhibit the Proliferation of Plasmodium falciparum
No full textLeft-handed DNA for efficient highly multiplexed imaging at single-protein resolution
No full textAbstract Multiplexed super-resolution microscopy enables spatial proteomics at single-protein resolution, but current methods often depend on secondary labels, complicating implementation and limiting throughput. We introduce a streamlined approach that combines speed-optimized DNA-PAINT sequences with their mirror-image analogs (left-handed DNA), enabling rapid and efficient 12-plex imaging. Validated on synthetic and cellular benchmarks, our method maps dense neuronal interactomes in 3D with 15 nm spatial resolution across a 200 × 200 µm 2 field of view
Physics of droplet regulation in biological cells
No full textAbstract Droplet formation has emerged as an essential concept for the spatiotemporal organisation of biomolecules in cells. However, classical descriptions of droplet dynamics based on passive liquid-liquid phase separation cannot capture the complex situation inside cells. This review discusses three distinct aspects that are crucial in cells: (i) biomolecules are diverse and individually complex, implying that cellular droplets posses complex internal behaviour, e.g., in terms of their material properties; (ii) the cellular environment contains many solid-like structures that droplets can wet; (iii) cells are alive and use fuel to drive processes out of equilibrium. We illustrate how these principles control droplet nucleation, growth, position, and count to unveil possible regulatory mechanisms in biological cells and other applications of phase separation