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 ...

We review in this paper some recent yet fundamental results on evaluating queries over probabilistic databases. While one can see this problem as a special instance of general purpose probabilistic inference, we describe in this paper two key database specific techniques that significantly reduce the complexity of query evaluation on probabilistic databases. The first is the separation of the q...

where ∧ denotes exterior product. The above expression is the exterior product of M two-forms of rank two, which produces a volume form D2,2(v1, . . . , v4M ) in the 2M -dimensional linear space. If we fix a basis e1, . . . , e2M in the linear space, then each of the vectors vi can be expressed as a sequence of 2M numbers, and D2,2(v1, . . . , v4M ) is also a number (the coefficient at e1∧. . ....

Phases of the 600 km. deep earthquake of April 16, 1957, which have not been reflected at the earth's surface show very sharp beginnings arriving within the limits of error of a few seconds at the cMculated times. However, phases which have been reflected at the surface, for example PP, pP', pPP, have more or less emergent beginnings which arrive between a few seconds and as much as 30 seconds ...