First order convergence of matroids

The model theory based notion of the first order convergence unifies the notions of the left-convergence for dense structures and the Benjamini-Schramm convergence for sparse structures. It is known that every first order convergent sequence of graphs with bounded tree-depth can be represented by an analytic limit object called a limit modeling. We establish the matroid counterpart of this result: every first order convergent sequence of matroids with bounded branch-depth representable over a fixed finite field has a limit modeling, i.e., there exists an infinite matroid with the elements forming a probability space that has asymptotically the same first order properties. We show that neither of the bounded branch-depth assumption nor the representability assumption can be removed.Comment: Accepted to the European Journal of Combinatoric

An analysis of interactions between three structurally diverse anthocyanidins, as well as their glucosides, and model biological membranes, albumin, and plasmid DNA

Abstract The aim of the study is to investigate the differences in the interaction of three structurally diverse anthocyanidins, namely peonidin, petunidin, and delphinidin, as well as their glucosides with model biological membranes, human albumin, and plasmid DNA in order to look into their structure–activity relationships. Fluorimetric studies, as well as ATR-FTIR analyses, were jointly used in order to determine the changes observed in both the hydrophilic and hydrophobic layers of cell-mimic membranes (MM) which reflected the membrane lipid composition of tumour cells and red blood cell membranes (RBCM). Our results showed that anthocyanins and anthocyanidins can cause an increase in the packing order of the polar heads of lipids, as well as interact with their deeper layers by reducing the fluidity of lipid chains. The results presented here indicate that all compounds tested here possessed the ability to bind to human serum albumin (HSA) and the presence of a glucose molecule within the structures formed by anthocyanidin reduces their ability to bind to proteins. Using fluorescence correlation spectroscopy, it was demonstrated that the compounds tested here were capable of forming stable complexes with plasmid DNA and, particularly, strong DNA conformational changes were observed in the presence of petunidin and corresponding glucoside, as well as delphinidin. The results we obtained can be useful in comprehending the anthocyanins therapeutic action as molecular antioxidants and provide a valuable insight into their mechanism of action