On perfect hashing of numbers with sparse digit representation via multiplication by a constant

Consider the set of vectors over a field having non-zero coefficients only in a fixed sparse set and multiplication defined by convolution, or the set of integers having non-zero digits (in some base b) in a fixed sparse set. We show the existence of an optimal (or almost-optimal, in the latter case) ‘magic’ multiplier constant that provides a perfect hash function which transfers the information from the given sparse coefficients into consecutive digits. Studying the convolution case we also obtain a result of non-degeneracy for Schur functions as polynomials in the elementary symmetric functions in positive characteristic.     

Comparison of hydrophilic-interaction, reversed-phase and porous graphitic carbon chromatography for glycan analysis

Hydrophilic-interaction liquid chromatography (HILIC), reversed-phase chromatography (RPC) and porous graphitic carbon (PGC) chromatography are typically applied for liquid chromatographic separations of protein N-glycans. Hence the performances of these chromatography modes for the separation of fluorescently labeled standard glycan samples (monoclonal antibody, fetuin, ribonuclease-B) covering high-mannose and a broad range of complex type glycans were investigated. In RPC the retention of sialylated glycans was enhanced by adding an ion-pairing agent to the mobile phase, resulting in improved peak shapes for sialylated glycans compared to methods recently reported in literature. For ion pairing RPC (IP-RPC) and HILIC ultra-high performance stationary phases were utilized to maximize the peak capacity and thus the resolution. But due to the shallow gradient in RPC the peak capacity was lower than on PGC. Retention times in HILIC and IP-RPC could be correlated to the monosaccharide compositions of the glycans by multiple linear regression, whereas no adequate model was obtained for PGC chromatography, indicating the significance of the three-dimensional structure of the analytes for retention in this method. Generally low correlations were observed between the chromatography methods, indicating their orthogonality. The high selectivities, as well as the commercial availability of ultra-high performance stationary phases render HILIC the chromatography method of choice for the analysis of glycans. Even though for complete characterization of complex glycan samples a combination of chromatography methods may be necessary.     

Synthetic Antitumor Vaccines Containing MUC1 Glycopeptides with Two Immunodominant Domains-Induction of a Strong Immune Response against Breast Tumor Tissues

A shot in the arm for cancer treatment: Two MUC1 tetanus toxoid vaccines were synthesized and induced a strong immune response in mice. The antibodies elicited by the vaccines show a high selectivity for the tumor cells in mammary carcinoma tissues and also distinguish between tumor tissues at different stages.     

Nano‐Ruby: A Promising Fluorescent Probe for Background‐Free Cellular Imaging

Bioprobes based on fluorescent ruby nanoparticles, which are suitable for ultrasensitive imaging, are reported. A stable aqueous/buffer colloid, permitting facile conjugation to proteins, is produced by femtosecond laser ablation of ruby and the nanoparticles (mean size 17 nm) are photostable, with long lifetime (1–4 ms) 694 nm emission. With time‐gating complete (>20 dB) suppression of cell autofluorescence and suppression of exogenous fluorophores is observed. Nanoparticles are imaged in as‐grown cells and those immunolabeled with quantum dots. Immunoassay binding to target biomolecules is also demonstrated.     

A long-wavelength biolabeling reagent based on the oxonol fluorophore

A red fluorescent dye of the oxonol class, bis-[1-(carboxymethyl)barbituric acid-(5)]-pentamethinoxonol, has been synthesized and, in the form of the succinimidyl active ester, has been applied to antibody labeling for application to flow cytometry and to imaging of tissue sections. The new dye, named CMOX (for carboxymethyloxonol), shows maximum excitation at 583 nm and emission at 611 nm, with a quantum yield of 0.2 in aqueous buffer and methanol. Antibodies labeled with the new dye show favorable brightness, photostability, and low levels of nonspecific binding.     

Super edge-magic strength of fire crackers, banana trees and unicyclic graphs

A graph G(V,E) is called super edge-magic if there exists a bijection f from V∪E to {1,2,3,…,|V|+|E|} such that f(u)+f(v)+f(uv)=c(f) is constant for any uv∈E and f(V)={1,2,3,…,|V|}. Such a bijection is called a super edge-magic labeling of G. The super edge-magic strength of a graph G is defined as the minimum of all c(f) where the minimum runs over all super edge-magic labelings of G and is denoted by sm(G). The super edge-magic strength of some families of graphs are obtained in this paper.