DNA storage is one of the most promising ways for future information storage due to its high data storage density, durable storage time and low maintenance cost. However, errors are inevitable during synthesizing, storing and sequencing. Currently, many error correction algorithms have been developed to ensure accurate information retrieval, but they will decrease storage density or increase computing complexity.Here,we apply the Bloom Filter,a space-efficient probabilistic data structure,to DNA storage to achieve the anti-error, or anti-contamination function. This method only needs the original correct DNA sequences (referred to as target sequences) to produce a corresponding data structure, which will filter out almost all the incorrect sequences (referred to as non-target sequences) during sequencing data analysis. Experimental results demonstrate the universal and efficient filtering capabilities of our method. Furthermore, we employ the Counting Bloom Filter to achieve the file version control function, which significantly reduces synthesis costs when modifying DNA-form files. To achieve cost-efficient file version control function, a modified system based on yin-yang codec is developed.

An essential component of the coral reef animal diversity is the species hidden in crevices within the reef matrix, referred to as the cryptobiome. These organisms play an important role in nutrient cycling and provide an abundant food source for higher trophic levels, yet they have been largely overlooked. Here, we analyzed the distribution patterns of the mobile cryptobiome (>2000 μm) along the latitudinal gradient of the Saudi Arabian coast of the Red Sea. Analysis was conducted based on 54 Autonomous Reef Monitoring Structures. We retrieved a total of 5273 organisms, from which 2583 DNA sequences from the mitochondrially encoded cytochrome c oxidase I were generated through sanger sequencing. We found that the cryptobiome community is variable over short geographical distances within the basin. Regression tree models identified sea surface temperature (SST), percentage cover of hard coral and turf algae as determinant for the number of operational taxonomic units present per Autonomous Reef Monitoring Structures (ARMS). Our results also show that the community structure of the cryptobiome is associated with the energy available (measured as photosynthetic active radiation), sea surface temperature, and nearby reef habitat characteristics (namely hard corals, turf and macroalgae). Given that temperature and reef benthic characteristics affect the cryptobiome, current scenarios of intensive climate change are likely to modify this fundamental biological component of coral reef functioning. However, the trajectory of change is unknow and can be site specific, as for example, diversity is expected to increase above SST of 28.5°C, and with decreasing hard coral and turf cover. This study provides a baseline of the cryptobenthic community prior to major coastal developments in the Red Sea to be used for future biodiversity studies and monitoring projects. It can also contribute to better understand patterns of reef biodiversity in a period where Marine Protected Areas are being discussed in the region.

Most studies of droplet impact on liquid pools focus on droplet diameters up to the capillary length (0.27 cm). We break from convention and study extremely large water droplets (1 to 6 cm diameter) falling into a pool of water. We demonstrate that the depth and width of the cavity formed by large droplet impact is greatly influenced by the deformed shape of the droplet at impact (i.e., prolate, spherical, and oblate), and larger droplets amplify this behavior by flattening before impact. In particular, the maximum cavity depth is a function of the Froude number and axis ratio of the droplet just before impact. Further, the cavity depth is more dependent on the droplet height than width, and the maximum cavity diameter is independent of the droplet height. In general, we observe that more oblate droplets result in decreasing cavity depths for a fixed liquid volume. This is because an increase in horizontal droplet diameter results in a reduced impact energy flux and therefore reduced cavity depth.

In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of deterministic mean field games and master equations, where the interaction of the agents happens only at the terminal time. The point of view via this transport equation has two important consequences. First, this equation reveals a new monotonicity condition that is sufficient both for the uniqueness of MFG Nash equilibria and for the global in time well-posedness of master equations. Interestingly, this condition is in general in dichotomy with both the Lasry–Lions and displacement monotonicity conditions, studied so far in the literature. Second, in the absence of monotonicity, the conservative form of the transport equation can be used to define weak entropy solutions to the master equation. We construct several concrete examples to demonstrate that MFG Nash equilibria, whether or not they actually exist, may not be selected by the entropy solutions of the master equation.

In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of deterministic mean field games and master equations, where the interaction of the agents happens only at the terminal time. The point of view via this transport equation has two important consequences. First, this equation reveals a new monotonicity condition that is sufficient both for the uniqueness of MFG Nash equilibria and for the global in time well-posedness of master equations. Interestingly, this condition is in general in dichotomy with both the Lasry–Lions and displacement monotonicity conditions, studied so far in the literature. Second, in the absence of monotonicity, the conservative form of the transport equation can be used to define weak entropy solutions to the master equation. We construct several concrete examples to demonstrate that MFG Nash equilibria, whether or not they actually exist, may not be selected by the entropy solutions of the master equation.