This paper is a supplement of our earlier work [1]. We map the vector potential of charged black holes into GEMS and find that its effect on the thermal spectrum is the same as that on the black hole side, i.e., it will induce a chemical potential in the thermal spectrum which is the same as that in the charged black holes. We also argue that the generalization of GEMS approach to non-stationar...

In Lecture 10, we introduced a fundamental object of spectral graph theory: the graph Laplacian, and established some of its basic properties. We then focused on the task of estimating the value of eigenvalues of Laplacians. In particular, we proved the Courant-Fisher theorem that is instrumental in obtaining upper-bounding estimates on eigenvalues. Today, we continue by showing a technique – s...

Today, we will briefly discuss an important technique in probability theory – measure concentration. Roughly speaking, measure concentration corresponds to exploiting a phenomenon that some functions of random variables are highly concentrated around their expectation/median. The main example that will be of our interest here is Johnson-Lindenstrauss (JL) lemma. The JL lemma is a very powerful ...

currently much debate, attention and concern surrounds the use of genetically modified plants or animals. but there has not been much concern about microorganisms, although we all are aware of the place of microorganisms in the circle of life, their abundance and diversity. there are many examples regarding the application of genetically engineered microorganisms (gems), however, like other hig...