This is the last article in a series of three initiated by the second author. We elaborate on the concepts and theorems constructed in the previous articles. In particular, we prove that the GH and the GGH uniformities previously introduced on the moduli space of isometry classes of globally hyperbolic spacetimes are different, but the Cauchy sequences which give rise to well-defined limit spac...

The GGH Graded Encoding Scheme [10], based on ideal lattices, is the first plausible approximation to a cryptographic multilinear map. Unfortunately, using the security analysis in [10], the scheme requires very large parameters to provide security for its underlying “encoding re-randomization” process. Our main contributions are to formalize, simplify and improve the efficiency and the securit...

Cosmeceuticals represent a marriage between cosmetics and pharmaceuticals. There are numerous cosmeceutically active products which can be broadly classified into the following categories: antioxidants, oligopeptides, growth factors and pigment lightning agents. Much attention has been focused on the tripeptides such as Gly-His-Lys (GHK) and Gly-Gly-His (GGH) and their copper complexes, which h...

AIMS Cervical cancer is the third most frequent cancer in women worldwide, mostly treated with cisplatin-based chemoradiotherapy. Since it is known that folate metabolism might interfere with cisplatin effectiveness, we intended to study the influence of the Gamma Glutamyl Hydrolase -401C>T polymorphism in treatment response in cervical cancer. METHODS We retrospectively reviewed the clinical...

In Crypto 1997, Goldreich, Goldwasser and Halevi (GGH) proposed a lattice analogue of McEliece public key cryptosystem, which security is related to the hardness of approximating the closest vector problem (CVP) in a lattice. Furthermore, they also described how to use the same principle of their encryption scheme to provide a signature scheme. Practically, this cryptosystem uses the euclidean ...

Let h and g be polynomials of bounded Euclidean norm in the ring Z[X]/⟨X+1⟩. Given polynomial [h/g]q ∈ Zq[X]/⟨X+1⟩, the NTRU problem is to find a, b ∈ Z[X]/⟨X + 1⟩ with small Euclidean norm such that [a/b]q = [h/g]q. We propose an algorithm to solve the NTRU problem which runs in 2 2 q) time when ∥g∥, ∥h∥ and ∥g−1∥ are in some range. The main technique of our algorithm is to reduce a problem on...

the growth hormone gene could be an attractive candidate gene for milk production in goats. single-strand conformation polymorphism was used to identify polymorphism at the goat growth hormone (ggh) gene. for this purpose, genotyping of 90 talli goat breeds was performed. nine conformational patterns were observed in exon 4 of the ggh gene, with frequencies of 27.7% for the homozygous pattern (...