We apply the Hecke operators T (p) and T̃j(p 2) (1 ≤ j ≤ n, p prime) to a degree n theta series attached to a rank 2k Z-lattice L, n ≤ k, equipped with a positive definite quadratic form in the case that L/pL is hyperbolic. We show that the image of the theta series under these Hecke operators can be realized as a sum of theta series attached to certain closely related lattices, thereby generali...

In the last decade, many papers highlighted that the histone variant H2AX and its phosphorylation on Ser 139 (γH2AX) cannot be simply considered a specific DNA double-strand-break (DSB) marker with a role restricted to the DNA damage response, but rather as a 'protagonist' in different scenarios. This review will present and discuss an up-to-date view regarding the 'non-canonical' H2AX roles, f...

Common intronic variants in the Human fat mass and obesity-associated gene (FTO) are found to be associated with an increased risk of obesity. Overexpression of FTO correlates with increased food intake and obesity, whilst loss-of-function results in lethality and severe developmental defects. Despite intense scientific discussions around the role of FTO in energy metabolism, the function of FT...

Coordinated morphogenetic cell movements during gastrulation are crucial for establishing embryonic axes in animals. Most recently, the non-canonical Wnt signaling cascade (PCP pathway) has been shown to regulate convergent extension movements in Xenopus and zebrafish. Heparan sulfate proteoglycans (HSPGs) are known as modulators of intercellular signaling, and are required for gastrulation mov...

Transcription factor binding sites are short DNA sequences that interact with transcription factors and the proper control of gene expression appears to require the mechanisms including the regulation through the genome context around the transcription factor binding sites. The MYC proteins are central regulators of cell growth. Many genes have been reported to be regulated by MYC through E-box...

Finite affine groups are given by groups of translations and di- lations on finite cyclic groups. For cyclic groups of prime order we develop a time-scale (wavelet) analysis and show that for a large class of non-zero window signals/vectors, the generated full cyclic wavelet system constitutes a frame whose canonical dual is a cyclic wavelet frame.