Construction of the mutually orthogonal extraordinary supersquares

Our purpose is to determine the complete set of mutually orthogonal squares of order d, which are not necessary Latin. In this article, we introduce the concept of supersquare of order d, which is defined with the help of its generating subgroup in $\mathbb{F}_d \times \mathbb{F}_d$ . We present a method of construction of the mutually orthogonal supersquares. Further, we investigate the orthogonality of extraordinary supersquares, a special family of squares, whose generating subgroups are extraordinary. The extraordinary subgroups in $\mathbb{F}_d \times \mathbb{F}_d$ are of great importance in the field of quantum information processing, especially for the study of mutually unbiased bases. We determine the most general complete sets of mutually orthogonal extraordinary supersquares of order 4, which consist in the so-called Type I and Type II. The well-known case of d ? 1 mutually orthogonal Latin squares is only a special case, namely Type I.     

Finite Phase Space,Wigner Functions,and Tomography for Two-Qubit States

We discuss the Wigner functions and tomographic probability distributions of two-qubit states. We give the kernel of the map, which provides the expression of the state tomogram in terms of the Wigner function of the two-qubit state, in an explicit form. Also we obtain the kernel of the inverse map and elucidate the connection of the constructed maps with the star-product scheme of quantization.     

Recent advances in the MS analysis of glycoproteins: Theoretical considerations

Protein glycosylation is involved in a broad range of biological processes that regulate protein function and control cell fate. As aberrant glycosylation has been found to be implicated in numerous diseases, the study and large-scale characterization of protein glycosylation is of great interest not only to the biological and biomedical research community, but also to the pharmaceutical and biotechnology industry. Due to the complex chemical structure and differing chemical properties of the protein/peptide and glycan moieties, the analysis and structural characterization of glycoproteins has been proven to be a difficult task. Large-scale endeavors have been further limited by the dynamic outcome of the glycosylation process itself, and, occasionally, by the low abundance of glycoproteins in biological samples. Recent advances in MS instrumentation and progress in miniaturized technologies for sample handling, enrichment and separation, have resulted in robust and compelling analysis strategies that effectively address the challenges of the glycoproteome. This review summarizes the key steps that are involved in the development of efficient glycoproteomic analysis methods, and the latest innovations that led to successful strategies for the characterization of glycoproteins and their corresponding glycans. As a follow-up to this work, we review innovative capillary and microfluidic-MS workflows for the identification, sequencing and characterization of glycoconjugates.     

Synthesis and characterization of conformationally preorganized, (R)-diethylene glycol-containing γ-peptide nucleic acids with superior hybridization properties and water solubility

Developed in the early 1990s, peptide nucleic acid (PNA) has emerged as a promising class of nucleic acid mimic because of its strong binding affinity and sequence selectivity toward DNA and RNA and resistance to enzymatic degradation by proteases and nucleases; however, the main drawbacks, as compared to other classes of oligonucleotides, are water solubility and biocompatibility. Herein we show that installation of a relatively small, hydrophilic (R)-diethylene glycol ("miniPEG", R-MP) unit at the γ-backbone transforms a randomly folded PNA into a right-handed helix. Synthesis of optically pure (R-MP)γPNA monomers is described, which can be accomplished in a few simple steps from a commercially available and relatively cheap Boc-l-serine. Once synthesized, (R-MP)γPNA oligomers are preorganized into a right-handed helix, hybridize to DNA and RNA with greater affinity and sequence selectivity, and are more water soluble and less aggregating than the parental PNA oligomers. The results presented herein have important implications for the future design and application of PNA in biology, biotechnology, and medicine, as well as in other disciplines, including drug discovery and molecular engineering.     

Correlations and cross-correlations in the Brazilian agrarian commodities and stocks

We investigate the auto-correlations and cross-correlations of the volatility time series in the Brazilian stock and commodity market, using the recently introduced Detrended Cross-Correlation Analysis. We find that the auto-correlations in stock volatilities are weaker than the auto-correlations in the commodity volatility series, contrary to earlier findings for the USA market where commodity volatility exponents were found to be lower than for stocks. We also find that the cross-correlations in the Brazilian stock and commodity market are stronger than what would be expected from simple combinations of auto-correlations of individual series, implying that there may be hidden factors that govern the behavior of the observed volatility series. This enhanced cross-correlation behavior is found in a considerable fraction of Brazilian stocks and agricultural commodities considered in the present work, suggesting that further studies should be directed into investigating these super-cross-correlations, and pinpointing the exogenous variables responsible for such behavior.     

Unprecedented Route to Ordered Polyaniline: Direct Synthesis of Highly Crystalline Fibrillar Films with Strong π‐π Stacking Alignment

Films of polyaniline (PANI) featuring about 80% crystallinity and characterised with strong π‐π stacking alignment parallel to the film surface have been obtained directly after the original synthesis upon simple drying of the aqueous PANI suspension. A strong anisotropy in the growth of the nano‐sized crystals produced during the synthesis results in the formation of micrometer‐length fibrils perpendicular to the film surface in the course of water evaporation. The regular intercalation of water molecules between the PANI chains seems to be crucial for their ordering throughout the synthesis and film formation.