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).     

Phospholipid Polymer Hydrogel Matrices with Dually Immobilized Cytokines for Accelerating Secretion of the Extracellular Matrix by Encapsulated Cells

Construction of 3D tissues by various types of cells with specific characteristics is an important and fundamental technology in tissue reconstruction medicine and animal‐free diagnosis system. To do so, an excellent extracellular matrix (ECM) is needed for encapsulation of cells and maintaining cell activity. Spontaneously forming hydrogel matrix is used by complexation between two water‐soluble polymers, 2‐methacryloyloxyethyl phosphorylcholine polymer bearing phenylboronic acid groups and poly(vinyl alcohol). Two cytokines for cell proliferation are immobilized in the hydrogel matrix to control the activities of the encapsulated cells. The cytokine‐immobilized hydrogel matrix can encapsulate both L929 fibroblasts and normal human dermal fibroblasts under mild condition. The physical properties of the hydrogel matrix can follow the proliferation process of the encapsulated cells. The encapsulated cells secrete ECM in the polymer hydrogel networks upon 3D culturing for 7 days. Consequently, the tissue‐mimicking ECM hybrid hydrogels are fabricated successfully.     

Analytical applications of second-order calibration methods

Second-order calibration methods are gaining widespread acceptance among the analytical community mainly because: (1) a wide range of analytical instrumentation is available that enables high dimensionality data to be obtained; (2) the chemometric techniques for treating these data are highly developed; and (3) they have the so-called “second-order advantage”, i.e. they can predict the concentration of the analyte of interest even in the presence of unknown interferents. This also enables several analytes to be determined simultaneously.In this paper we describe the most common instrumental and chemometric techniques used in second-order calibration and discuss their applications since 2000. First, we introduce briefly the techniques and then we comment the applications. Given the practical nature of this paper, we have classified the techniques according to five fields of application: pharmaceuticals, biological matrices, foods, environmental matrices and synthetic matrices.     

Global fluctuations in general Dyson’s Brownian motion

We consider a system of diffusing particles on the real line in a quadratic external potential and with a logarithmic interaction potential. The empirical measure process is known to converge weakly to a deterministic measure-valued process as the number of particles tends to infinity. Provided the initial fluctuations are small, the rescaled linear statistics of the empirical measure process converge in distribution to a Gaussian limit for sufficiently smooth test functions. For a large class of analytic test functions, we derive explicit general formulae for the mean and covariance in this central limit theorem by analyzing a partial differential equation characterizing the limiting fluctuations.     

Contractions with rank one defect operators and truncated CMV matrices

The main issue we address in the present paper are the new models for completely nonunitary contractions with rank one defect operators acting on some Hilbert space of dimension N?∞. These models complement nicely the well-known models of Livšic and Sz.-Nagy-Foias. We show that each such operator acting on some finite-dimensional (respectively, separable infinite-dimensional Hilbert space) is unitarily equivalent to some finite (respectively semi-infinite) truncated CMV matrix obtained from the “full” CMV matrix by deleting the first row and the first column, and acting in CN (respectively ?²(N)). This result can be viewed as a nonunitary version of the famous characterization of unitary operators with a simple spectrum due to Cantero, Moral and Velázquez, as well as an analog for contraction operators of the result from [Yu. Arlinski?, E. Tsekanovski?, Non-self-adjoint Jacobi matrices with a rank-one imaginary part, J. Funct. Anal. 241 (2006) 383-438] concerning dissipative non-self-adjoint operators with a rank one imaginary part. It is shown that another functional model for contractions with rank one defect operators takes the form of the compression f(ζ)→PK(ζf(ζ)) on the Hilbert space L²(T,dμ) with a probability measure μ onto the subspace K=L²(T,dμ)?C. The relationship between characteristic functions of sub-matrices of the truncated CMV matrix with rank one defect operators and the corresponding Schur iterates is established. We develop direct and inverse spectral analysis for finite and semi-infinite truncated CMV matrices. In particular, we study the problem of reconstruction of such matrices from their spectrum or the mixed spectral data involving Schur parameters. It is pointed out that if the mixed spectral data contains zero eigenvalue, then no solution, unique solution or infinitely many solutions may occur in the inverse problem for truncated CMV matrices. The uniqueness theorem for recovered truncated CMV matrix from the given mixed spectral data is established. In this part the paper is closely related to the results of Hochstadt and Gesztesy-Simon obtained for finite self-adjoint Jacobi matrices.     

Geometry of 2×2 Hermitian matrices over any division ring

Let D be a division ring with an involution-,H2(D) be the set of 2 × 2 Hermitian matrices over D. Let ad(A,B) = rank(A-B) be the arithmetic distance between A,B ∈ H2(D) . In this paper,the fundamental theorem of the geometry of 2 × 2 Hermitian matrices over D(char(D) = 2) is proved:if  :H2(D) → H2(D) is the adjacency preserving bijective map,then  is of the form (X) = tP XσP +(0) ,where P ∈ GL2(D) ,σ is a quasi-automorphism of D. The quasi-automorphism of D is studied,and further results are obtained.     

The structure of matrices with a maximum multiplicity eigenvalue

There is remarkable and distinctive structure among Hermitian matrices, whose graph is a given tree T and that have an eigenvalue of multiplicity that is a maximum for T. Among such structure, we give several new results: (1) no vertex of T may be “neutral”; (2) neutral vertices may occur if the largest multiplicity is less than the maximum; (3) every Parter vertex has at least two downer branches; (4) removal of a Parter vertex changes the status of no other vertex; and (5) every set of Parter vertices forms a Parter set. Statements (3), (4) and (5) are also not generally true when the multiplicity is less than the maximum. Some of our results are used to give further insights into prior results, and both the review of necessary background and the development of new structural lemmas may be of independent interest.     

Superstochastic matrices and magic Markov chains

A brief account of the conceptual formulation of the two entities in this paper’s title, plus an initial preliminary investigation of some of their mathematical properties, is given.     

On a class of signals and matrices giving very fast algorithms for linear problems

In this paper is presented a class of stochastic signals and of correlation matrices introducing very fast algorithms for solving linear problems. These signals are derived from white noise by using three kinds of operations combined in various orders: summation, difference and instantaneous modulation. The discrete time Brownian motion is a particular example of such signals.     

On the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree

A different approach is given to recent results due mainly to R. C. Johnson and A. Leal Duarte on the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree. The techniques developed are based on some results of matching polynomials and used a work by O. L. Heilmann and E. H. Lieb on an apparently unrelated topic.