Arrangements of minors in the positive Grassmannian and a triangulation of the hypersimplex

The structure of zero and nonzero minors in the Grassmannian leads to rich combinatorics of matroids. In this paper, we investigate an even richer structure of possible equalities and inequalities between the minors in the positive Grassmannian. It was previously shown that arrangements of equal minors of largest value are in bijection with the simplices in a certain triangulation of the hypersimplex that was studied by Stanley, Sturmfels, Lam and Postnikov. Here, we investigate the entire set of arrangements and its relations with this triangulation. First, we show that second largest minors correspond to the facets of the simplices. We then introduce the notion of cubical distance on the dual graph of the triangulation and study its relations with the arrangement of t-th largest minors. Finally, we show that arrangements of largest minors induce a structure of a partially ordered set on the entire collection of minors. We use this triangulation of the hypersimplex to describe a two-dimensional grid structure on this poset.     

Preparation,Characterization and Application of Modified Surfaces with 3,5-Bis(3,5-dinitrobenzoyl-amino) benzoic acid

Summary: The spontaneous adsorption of the dendron 3,5-Bis (3,5-dinitrobenzoylamino) benzoic acid (D-NO₂) onto gold and carbon electrodes produced conductive surfaces with electroactive chemical functions. A comparative electrochemical behavior of both electrodes after dendron immobilization led us to conclude that the self-assembly of D-NO₂ on carbon is faster and stronger. Considering this advantage, the surface of magnetic maghemite nanoparticles (MNPs) was modified using D-NO₂. Firstly, MNPs were modified with APS as silane coupling agent and afterwards, D-NO₂ was covalently attached to the surface, achieving nitro-functionalized MNPs. Subsequently, the immobilization of these modified MNPs onto glassy carbon surfaces was explored to generate a novel platform promising for biosensors development.     

Synthesis and Properties of Dendronized Chitosan

Summary: Chitosan films and microspheres were prepared and their surfaces were functionalized with first generation dendritic molecules. The films were modified by Weisocyanate dendron, while Behera's and bis Behera's amine dendrons were used to modify the microspheres. Prior to dendronization films were prepared by blending chitosan with 18% of polyvinyl pyrrolidone (PVP), and casting the resulting mixture. The degree of dendronization reached was 28%. The microspheres were prepared by coacervation/precipitation, after which the surfaces were activated with either epychlorohydrine (ECH) or 1,4-butanediol diglycidyl ether (BDGE). The oxirane groups were utilized to form covalent bonds between chitosan and dendrons. The degree of dendronization yielded with Behera's amine was 60% for both activating agents. When bis Behera's amine was used, the dendronization reached values of 15 and 21% when ECH or BDGE were used, respectively. The dendronized products were characterized through spectroscopic and microscopic studies and by determination of swelling indexes. Only one of the surfaces was dendronized in every film, which therefore presented a hydrophobic and a hydrophilic surface. Since these films maintain the properties of chitosan, they offer interesting potential as dressings for exuding wounds. The different surfaces make the microspheres potentially applicable as carriers for delivery and controlled release of drugs.     

Conjugacy Classes,Class Sums and Character Tables for Hopf Algebras

We extend the notion of conjugacy classes and class sums from finite groups to semisimple Hopf algebras and show that the conjugacy classes are obtained from the factorization of H as irreducible left D(H)-modules. For quasitriangular semisimple Hopf algebras H, we prove that the product of two class sums is an integral combination of the class sums up to d ^?2 where d = dim H. We show also that in this case the character table is obtained from the S-matrix associated to D(H). Finally, we calculate explicitly the generalized character table of D(kS ₃), which is not a character table for any group. It moreover provides an example of a product of two class sums which is not an integral combination of class sums.     

Group graded rings

Let R be a group graded ring . The map ( , ): R × R →₁ defined by: (x,y) = (xy)₁ , is an inner product on R. In this paper we investigate aspects of nondegeneracy of the product, which is a generalization of the notion of strongly G —graded rings,introduced by Dade. We show that various chain conditions are satisfied by R if and only if they are satisfied by R₁ , and that when R₁ is simple artinian, then R is a crossed product R₁ ^* G. We give conditions for simple R-modules to be completely reducible R₁ -modules . Finally, we prove an incomparability theorem,when G is finite abelian.     

On the nature of ion-stabilized cytosine pairs in DNA i-motifs: The importance of charge transfer processes

Recent experimental results indicate that the stability of non-Watson-Crick DNA i-motif structures can be influenced by the presence of various metal cations. Whereas Au⁺, Cu⁺, and Ag⁺ are stabilizing agents, alkali metal ions like Na⁺ or Li⁺ are known to destabilize the i-motif. In terms of reduced ion-cytosine complexes, we rationalize the experimental observations with the help of standard and conceptual density functional theory (DFT) calculations. Our results highlight the importance of coordinating electrostatic bonds with partially covalent character for the stability of the ion-cytosine complex. The occurrence of these bonds can be mainly attributed to charge transfer processes between two cytosines and the transition metal ions, which can be either explained by frontier molecular orbital theory in combination with a bond critical point analysis, or by the concept of chemical reactivity indices within a conceptual DFT approach. The results of our calculations establish a consistent theoretical framework to understand the experimentally observed behavior, and are also important in order to achieve more detailed insights into nucleobase pairing mechanisms in general.     

Catenation and Aggregation of Multi‐Cavity Coordination Cages

A series of metal‐mediated cages, having multiple cavities, was synthesized from Pd^II cations and tris‐ or tetrakis‐monodentate bridging ligands and characterized by NMR spectroscopy, mass spectrometry, and X‐ray methods. The peanut‐shaped [Pd₃L¹₄] cage deriving from the tris‐monodentate ligand L¹ could be quantitatively converted into its interpenetrated [5Cl@Pd₆L¹₈] dimer featuring a linear {[Pd‐Cl‐]₅Pd} stack as an unprecedented structural motif upon addition of chloride anions. Small‐angle neutron scattering (SANS) experiments showed that the cigar‐shaped assembly with a length of 3.7 nm aggregates into mono‐layered discs of 14 nm diameter via solvophobic interactions between the hexyl sidechains. The hepta‐cationic [5Cl@Pd₆L¹₈] cage was found to interact with polyanionic oligonucleotide double‐strands under dissolution of the aggregates in water, rendering the compound class interesting for applications based on non‐covalent DNA binding.     

Dynamic Covalent Identification of an Efficient Heparin Ligand

Despite heparin being the most widely used macromolecular drug, the design of small‐molecule ligands to modulate its effects has been hampered by the structural properties of this polyanionic polysaccharide. Now a dynamic covalent selection approach is used to identify a new ligand for heparin, assembled from extremely simple building blocks. The amplified molecule strongly binds to heparin (K_D in the low μm range, ITC) by a combination of electrostatic, hydrogen bonding, and CH–π interactions as shown by NMR and molecular modeling. Moreover, this ligand reverts the inhibitory effect of heparin within an enzymatic cascade reaction related to blood coagulation. This study demonstrates the power of dynamic covalent chemistry for the discovery of new modulators of biologically relevant glycosaminoglycans.