Identification of Two Palmitoyl Groups in Octopus Rhodopsin

Abstract— We determined the structure and site of fatty acid incorporated in octopus rhodopsin using a combination of fluorescence label and enzymatic cleavage methods in conjunction with fast-atom bombardment (FAB) mass spectrometry. A single peptide containing two adjacent cysteines, Cys337 and Cys338, was successfully isolated using the fluorescence from a dye conjugated to Cys345. The FAB mass spectrometric analysis of the peptide (323phe-³⁴⁰phe) revealed that two palmitoyl groups are linked to Cys337 and Cys338 via thioester bonds in octopus rhodopsin as in bovine rhodopsin.     

The 2-primary torsion on elliptic curves in the Z p -extensions of Q

Let E be an elliptic curve over Q and p a prime number. Denote by Q_p,∞ the Z_p-extension of Q. In this paper, we show that if p≠3, then where E(Q_p,∞)₍₂₎ is the 2-primary part of the group E(Q_p,∞) of Q_p,∞-rational points on E. More precisely, in case p=2, we completely classify E(Q_2,∞)₍₂₎ in terms of E(Q)₍₂₎; in case p≥5 (or in case p=3 and E(Q)₍₂₎≠{O}), we show that E(Q_p,∞)₍₂₎=E(Q)₍₂₎.     

Computer-Aided Detection of Quantitative Signatures for Breast Fibroepithelial Tumors Using Label-Free Multi-Photon Imaging

Fibroadenomas (FAs) and phyllodes tumors (PTs) are major benign breast tumors, pathologically classified as fibroepithelial tumors. Although the clinical management of PTs differs from FAs, distinction by core needle biopsy diagnoses is still challenging. Here, a combined technique of label-free imaging with multi-photon microscopy and artificial intelligence was applied to detect quantitative signatures that differentiate fibroepithelial lesions. Multi-photon excited autofluorescence and second harmonic generation (SHG) signals were detected in tissue sections. A pixel-wise semantic segmentation method using a deep learning framework was used to separate epithelial and stromal regions automatically. The epithelial to stromal area ratio and the collagen SHG signal strength were investigated for their ability to distinguish fibroepithelial lesions. An image segmentation analysis with a pixel-wise semantic segmentation framework using a deep convolutional neural network showed the accurate separation of epithelial and stromal regions. A further investigation, to determine if scoring the epithelial to stromal area ratio and the SHG signal strength within the stromal area could be a marker for differentiating fibroepithelial tumors, showed accurate classification. Therefore, molecular and morphological changes, detected through the assistance of computational and label-free multi-photon imaging techniques, enable us to propose quantitative signatures for epithelial and stromal alterations in breast tissues.     

Any Diophantine quintuple contains a regular Diophantine quadruple

A set {a₁,…,am} of m distinct positive integers is called a Diophantine m-tuple if aiaj+1 is a perfect square for all i, j with 1?i<j?m. It is conjectured that if {a,b,c,d} is a Diophantine quadruple with a<b<c<d, then d=d₊, where d₊=a+b+c+2abc+2rst and , , . In this paper, we show that if {a,b,c,d,e} is a Diophantine quintuple with a<b<c<d<e, then d=d₊.     

Synthesis of novel nocathiacin-class antibiotics. Condensation of glycolaldehyde with primary amides and tandem reductive amination of amadori-rearranged 2-oxoethyl intermediates

Nocathiacin I (1) and nocathiacin IV (2) are novel indole-containing thiazolyl peptide antibiotics, which exhibit potent activity against key Gram-positive bacterial pathogens, including multi drug-resistant Staphylococcus aureus, Streptococcus pneumoniae, and Enterococcus faecium. New nocathiacins 7-12 were prepared from 2 by a condensation with glycolaldehyde followed by tandem reductive amination of the 2-oxoethyl intermediate 4. The latter was formed via Amadori rearrangement from initial 2-hydroxyethylideneamide 3. This transformation readily tolerates the complex architecture of nocathiacins and allows selective incorporation of water solubilizing groups to the primary amide in 2 without protecting group manipulation.     

Torsion on elliptic curves in isogeny classes

Let be an elliptic curve over a number field and its -isogeny class. We are interested in determining the orders and the types of torsion groups in . For a prime , we give the range of possible types of -primary parts of when runs over . One of our results immediately gives a simple proof of a theorem of Katz on the order of maximal -primary torsion in .

     

Extensions of the D(?k2)-triples {k2, k2 ± 1, 4k2 ± 1}

Let n be a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the product of any two of them increased by n is a perfect square. Let k be a positive integer. In this paper, we show that if {k ², k ² + 1, 4k ² + 1, d} is a D(−k ²)-quadruple, then d = 1, and that if {k ² − 1, k ², 4k ² − 1, d} is a D(k ²)-quadruple, then d = 8k ²(2k ² − 1).     

Two-parameter families of uniquely extendable Diophantine triples

Let A and K be positive integers and ε∈ {-2,-1,1,2}. The main contribution of the paper is a proof that each of the D(ε~2)-triples {K, A~2 K+2εA,(A +1)~2 K + 2ε(A+1)} has uniqui extension to a D(ε~2)-quadruple. This is used to slightly strengthen the conditions required for the existencc of a D(1)-quintuple whose smallest three elements form a regular triple.