PSBF: p-adic Integer Scalable Bloom Filter.

Given the challenges associated with the dynamic expansion of the conventional bloom filter's capacity, the prevalence of false positives, and the subpar access performance, this study employs the algebraic and topological characteristics of p-adic integers to introduce an innovative approach for dynamically expanding the p-adic Integer Scalable Bloom Filter (PSBF). The proposed method involves converting the target element into an integer using a string hash function, followed by the conversion of said integer into a p-adic integer through algebraic properties. This process automatically establishes the topological tree access structure of the PSBF. The experiment involved a comparison of access performance among the standard bloom filter, dynamic bloom filter, and scalable bloom filter. The findings indicate that the PSBF offers advantages such as avoidance of a linear storage structure, enhanced efficiency in element insertion and query, improved storage space utilization, and reduced likelihood of false positives. Consequently, the PSBF presents a novel approach to the dynamic extensibility of bloom filters.

Chiral Self-Assembly of Nonplanar 10,10'-Dibromo-9,9'-bianthryl Molecules on Ag(111).

We report on the low-temperature scanning tunneling microscopy (STM) measurements of the self-assembly of nonplanar 10,10'-dibromo-9,9'-bianthryl (DBBA) molecules on Ag(111) combined with density functional theory (DFT) calculations. DBBA molecules have two enantiomorphous adsorption configurations, from which more chiral structures can be formed. At a low coverage [0.4 monolayer (ML)], DBBA forms racemic netlike islands consisting of molecular chains along ⟨1 2 3̅⟩Ag. Moreover, the gliding between the molecular chains gives rise to chiral windmill-like patterns in the islands. At 0.8 ML, DBBA forms a racemic row phase and a homochiral hexamer phase. The molecular appearance difference between the two coexisted phases and the DFT calculated molecular adsorption configuration reveal a decrease in the molecular dihedral angle of DBBA, which implies an enhancement in the intermolecular interactions via CH···π and halogen bonds. The transition from a racemic packing mode to a homochiral one suggests that the suitability of steric configurations is dominant in the close-packing mode under enhanced intermolecular interactions.