E[n] ' { Z/nZ⊕ Z/nZ if p = 0 or p n, Z/nZ or {0} if p > 0 and n is a power of p. Proof. Assume p n and let ` be a prime dividing n. Then the multiplication-by-` map [`] is separable of degree `2, and therefore E[`] = ker[`] has order `2. Every nonzero element of E[`] has order `, and it follows that E[`] ' Z/`Z ⊗ Z/`Z. Thus the `-rank of E[`], and hence of E[n], is 2. If `e is the largest power...

This is the so-called Second Moment Method, since it uses the second moment, i.e. the variance of X. As an application of the above inequality, we presented some thresholds in the Erdős-Rényi Gn,p model. We extend that example here to show something that at first looks like a paradox. So, we consider a random graph G ∼ Gn,p and let Z1 be the number of copies of K4 in G, and Z2 be the number of ...

The 2013 "Vaccine and Drug Ontology Studies" (VDOS 2013) international workshop series focuses on vaccine- and drug-related ontology modeling and applications. Drugs and vaccines have contributed to dramatic improvements in public health worldwide. Over the last decade, tremendous efforts have been made in the biomedical ontology community to ontologically represent various areas associated wit...

For certain courses in the bachelor program, students have to write C++ programs to solve problems. Unfortunately it sometimes happens that students copy code from their fellow classmates, which is not allowed. Currently Moss2 is used to detect this plagiarism, but it does not find all plagiarized files. Therefore we experiment with a few new methods to improve upon Moss2. These methods are bas...