The cover polynomial introduced by Chung and Graham is a twovariate graph polynomial for directed graphs. It counts the (weighted) number of ways to cover a graph with disjoint directed cycles and paths, it is an interpolation between determinant and permanent, and it is believed to be a directed analogue of the Tutte polynomial. Jaeger, Vertigan, and Welsh showed that the Tutte polynomial is #...

We investigate the complexity of counting the number of integer points in tropical polytopes, and the complexity of calculating their volume. We study the tropical analogue of the outer parallel body and establish bounds for its volume. We deduce that there is no approximation algorithm of factor α = 2 for the volume of a tropical polytope given by n vertices in a space of dimension m, unless P...

The Black-Box Hypothesis, introduced by Barak et al. [BGI12], states that any property of boolean functions decided efficiently (e.g., in BPP) with inputs represented by circuits can also be decided efficiently in the black-box setting, where an algorithm is given an oracle access to the input function and an upper bound on its circuit size. If this hypothesis is true, then P 6= NP. We focus on...

Investigating the kinetics of catalytic reactions with surface-enhanced Raman scattering (SERS) on a single particle remains a significant challenge. In this study, the single particle of the constructed hierarchical peony-like silver microflowers (SMFs) with highly roughened surface led to the coupling of high catalytic activity with a strong SERS effect, which acts as an excellent bifunctiona...

Microorganisms are important components of soil. Some soil filamentous fungi such asPenicilium produce many bioactive small molecules, or secondary metabolites, that range frombeneficial bioactive compounds to harmful toxins. In this study, the metabolites of threepenicillium species (P. goditanum, P. moldavicum and P. corylophilum) were extracted byadding ethyl acetate to liquid cultures. The ...