Twists of newforms

AbstractLet Sk0(N, ψ) denote the subspace generated by newforms in the space of cuspforms of weight k and character ψ on Σ0(N). In this paper we study decompositions of Sk0(N, ψ) into direct sums of twists (by Dirichlet characters) of other spaces of newforms. Applied to individual newforms, these results immediately yield information on the behavior of newforms under character twists. Most of the results follow from applications of the Eichler Selberg formula for the traces of the Hecke operators. A version of this formula is given in the paper. A sample result is: Let p be a prime and let M be a positive integer prime to p. Let ω be a character mod pv with e = ordpf(ω) > v2 and let φ be a character mod M. Then Sk0(pvM, ωφ) = ⊕χ Sk0(peM, ωχ2φ)χ where the sum ⊕χ is over all primitive characters χ modulo pv − e and where Sk0(N, ψ)χ denotes the twist of Sk0(N,ψ) by χ

Efficacy of a Non-Hypercalcemic Vitamin-D2 Derived Anti-Cancer Agent (MT19c) and Inhibition of Fatty Acid Synthesis in an Ovarian Cancer Xenograft Model

BACKGROUND:Numerous vitamin-D analogs exhibited poor response rates, high systemic toxicities and hypercalcemia in human trials to treat cancer. We identified the first non-hypercalcemic anti-cancer vitamin D analog MT19c by altering the A-ring of ergocalciferol. This study describes the therapeutic efficacy and mechanism of action of MT19c in both in vitro and in vivo models. METHODOLOGY/PRINCIPAL FINDING:Antitumor efficacy of MT19c was evaluated in ovarian cancer cell (SKOV-3) xenografts in nude mice and a syngenic rat ovarian cancer model. Serum calcium levels of MT19c or calcitriol treated animals were measured. In-silico molecular docking simulation and a cell based VDR reporter assay revealed MT19c-VDR interaction. Genomewide mRNA analysis of MT19c treated tumors identified drug targets which were verified by immunoblotting and microscopy. Quantification of cellular malonyl CoA was carried out by HPLC-MS. A binding study with PPAR-Y receptor was performed. MT19c reduced ovarian cancer growth in xenograft and syngeneic animal models without causing hypercalcemia or acute toxicity. MT19c is a weak vitamin-D receptor (VDR) antagonist that disrupted the interaction between VDR and coactivator SRC2-3. Genome-wide mRNA analysis and western blot and microscopy of MT19c treated xenograft tumors showed inhibition of fatty acid synthase (FASN) activity. MT19c reduced cellular levels of malonyl CoA in SKOV-3 cells and inhibited EGFR/phosphoinositol-3kinase (PI-3K) activity independently of PPAR-gamma protein. SIGNIFICANCE:Antitumor effects of non-hypercalcemic agent MT19c provide a new approach to the design of vitamin-D based anticancer molecules and a rationale for developing MT19c as a therapeutic agent for malignant ovarian tumors by targeting oncogenic de novo lipogenesis

Underwater Image Processing: State of the Art of Restoration and Image Enhancement Methods

The underwater image processing area has received considerable attention within the last decades, showing important achievements. In this paper we review some of the most recent methods that have been specifically developed for the underwater environment. These techniques are capable of extending the range of underwater imaging, improving image contrast and resolution. After considering the basic physics of the light propagation in the water medium, we focus on the different algorithms available in the literature. The conditions for which each of them have been originally developed are highlighted as well as the quality assessment methods used to evaluate their performance

Verifiable delay functions from supersingular isogenies and pairings

International audienceWe present two new Verifiable Delay Functions (VDF) based on assumptions from elliptic curve cryptography. We discuss both the advantages and drawbacks of our constructions, we study their security and we demonstrate their practicality with a proof-of-concept implementation