In many traditional social choice problems, analyzing the voting power of the voters in a given profile is an important part. Usually the voting power of an agent is measured by whether the agent is pivotal. In this paper, we introduce two extensions of the set of pivotal agents to measure agents’ voting power in a given profile. The first, which is called hierarchical pivotal sets, captures th...

LLactic acid bacteria (LAB) are used widely in food microbiology as probiotics and biopreservatives to extend shelf life of items. Lactic produced by LAB strains precursor polylactic acid(PLA) that has growing demand bioplastics biodegradable nature replacing traditional plastics. have the potential utilize polysaccharides from various sources produce lactic acid. The aim this study is identify...