In this paper, we focus on a hypercube-like structure, the folded hypercube, which is basically a standard hypercube with some extra links between its nodes. Let f be a faulty vertex in an n-dimensional folded hypercube FQn. We show that FQn−{f } contains a faultfree cycle of every even length from 4 to 2n−2 if n ≥ 3 and, furthermore, every odd length from n+ 1 to 2n − 1 if n ≥ 2 and n is even....

Let p > 3 be a prime, ζp a pth primitive root of 1, and ∆ the Galois group of Q(ζp) over Q. Let q 6= p be a prime and n the order of q modulo p. Assume q 6≡ 1 mod p and so n ≥ 2, p(q− 1)|qn − 1, and n|p− 1. Set f = (q − 1)/p and e = (p− 1)/n. Let Q be a prime ideal of Z[ζp] above q and let F = Z[ζp]/Q. Thus F ∼= Fqn , the finite field with q elements. Let α ∈ Z[ζp] be a generator of F such that...

Efficient multiplication in finite fields Fqn requires Fq-bases of low density,i.e., such that the products of the basis elements have a sparse expression in the basis. In this paper we introduce a new family of bases: the quasi-normal bases. These bases generalize the notion of normal bases and provide simple exponentiation to the power q in Fqn . For some extension fields Fqn over Fq, we cons...

The University Center for Academic Learning and Teaching (UOCG) provides the University of Groningen with an educational program to train fully qualified secondary school teachers in many secondary school subjects including computer science. This two-year Master’s in Education Program consists of teacher training that includes a large internship component and teacher training courses, in additi...

In light of the shortage of healthcare professionals, many developing countries operate a de facto two-tiered system of healthcare provision, in which Community Health Workers (CHWs) supplement service provision by fully qualified physicians. CHWs are relatively inexpensive to train but can treat only a limited range of medical conditions. This paper explicitly models a two-tiered structure of ...

In the methods on page 112, we report a “cytological” estimate of 710 Mb based flow cytometry for Melaleuca alternifolia. For clarity, this should have been qualified as “2C” or diploid genome size.

BACKGROUND The transition from medical school to the workplace can be demanding, with high expectations placed on newly qualified doctors. The provision of up-to-date and accurate information is essential to support doctors at a time when they are managing increased responsibility for patient care. In August 2012, the Wales Deanery issued the Dr.Companion© software with five key medical textboo...

This paper presents the construction of an explicit, optimal-access, high-rate MSR code for any (n, k, d = k + 1, k + 2, k + 3) parameters over the finite field FQ having sub-packetization α = qd n q e, where q = d − k + 1 and Q = O(n). The sub-packetization of the current construction meets the lower bound proven in a recent work by Balaji et al. in [1]. To our understanding the codes presente...