Additive Hermitian idempotent preservers between operator algebras

Let L be an additive map between (real or complex) matrix algebras sending $n\times n$ Hermitian idempotent matrices to $m\times m$ Hermitian idempotent matrices. We show that there are nonnegative integers $p,q$ with $n(p+q)=r\le m$ and an $m\times m$ unitary matrix U such that$L(A)=U[(I_p?A)\oplus (I_q?A^t)\oplus 0_{m?r}]U^{?},\text{for any}n\times n\text{Hermitian}A\text{with rational trace}.$ We also extend this result to the (complex) von Neumann algebra setting, and provide a supplement to the Dye-Bunce-Wright Theorem asserting that every additive map of Hermitian idempotents extends to a Jordan ?-homomorphism.     

Linear codes associated to skew-symmetric determinantal varieties

In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum distances of these codes are determined and a recursive formula for the weight of a general codeword in these codes is given.     

Effect of matrices and additives on phosphorylated and ketodeoxyoctonic acid lipids A analysis by matrix‐assisted laser desorption ionization‐mass spectrometry

Lipid A is a major compound of the outer membrane of gram‐negative bacteria and is a key factor of bacterial virulence. As lipid A's structure differs among bacterial species and varies between strains of the same species, knowing its modifications is essential to understand its implications in the infectious process. To analyze these lipids, matrix‐assisted laser desorption ionization‐mass spectrometry (MALDI‐MS) is a well‐suited method that is fast and efficient. However, there are limitations with the matrix and additives used, such as the suppression of signal or prompt fragmentations that could give a false overview of lipid A composition in biological samples. For a comprehensive analysis of the entire lipid A species present in a sample, we tested 16 matrices and 11 additives on two commercial lipids A. The first commercial one contains single phosphorylation group, and the second contains two phosphorylation and two ketodeoxyoctonic acid (KDO) groups. The lipid A containing KDO groups was essentially detected by the 3‐hydroxypicolinic acid (3‐HPA) matrix, whereas the monophosphorylated lipid A could be detected by 13 matrices out of the 16. We also demonstrated that the signal of diphosphorylated lipid A can be enhanced with the use of additives in the matrix. Our study indicated that the best conditions to obtain a clear signal of both lipids A without prompt fragmentation was the use of 3‐HPA with 10mM trifluoroacetic acid (TFA).