A Construction of Almost Steiner Systems

Let n, k, and t be integers satisfying . A Steiner system with parameters t, k, and n is a k‐uniform hypergraph on n vertices in which every set of t distinct vertices is contained in exactly one edge. An outstanding problem in Design Theory is to determine whether a nontrivial Steiner system exists for . In this note we prove that for every and sufficiently large n, there exists an almost Steiner system with parameters t, k, and n; that is, there exists a k‐uniform hypergraph on n vertices such that every set of t distinct vertices is covered by either one or two edges.     

1‐Factorizations of pseudorandom graphs

A 1‐factorization of a graph G is a collection of edge‐disjoint perfect matchings whose union is E(G). In this paper, we prove that for any ?>0, an (n,d,λ)‐graph G admits a 1‐factorization provided that n is even, C₀ ≤ d ≤ n?1 (where C₀=C₀(?) is a constant depending only on ?), and λ ≤ d^1??. In particular, since (as is well known) a typical random d‐regular graph G_n,d is such a graph, we obtain the existence of a 1‐factorization in a typical G_n,d for all C₀ ≤ d ≤ n?1, thereby extending to all possible values of d results obtained by Janson, and independently by Molloy, Robalewska, Robinson, and Wormald for fixed d. Moreover, we also obtain a lower bound for the number of distinct 1‐factorizations of such graphs G, which is better by a factor of 2^nd/2 than the previously best known lower bounds, even in the simplest case where G is the complete graph.     

Constructing near spanning trees with few local inspections

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded‐degree graph. Given an edge e in G we would like to decide whether e belongs to a connected subgraph consisting of edges (for a prespecified constant ), where the decision for different edges should be consistent with the same subgraph . Can this task be performed by inspecting only a constant number of edges in G ? Our main results are:

• We show that if every t‐vertex subgraph of G has expansion then one can (deterministically) construct a sparse spanning subgraph of G using few inspections. To this end we analyze a “local” version of a famous minimum‐weight spanning tree algorithm.
• We show that the above expansion requirement is sharp even when allowing randomization. To this end we construct a family of 3‐regular graphs of high girth, in which every t‐vertex subgraph has expansion . We prove that for this family of graphs, any local algorithm for the sparse spanning graph problem requires inspecting a number of edges which is proportional to the girth.

© 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 183–200, 2017     

Experimental studies on the ring opening polymerization of p-dioxanone using an Al(OPr)3-monosaccharide initiator system

The ring opening polymerization (ROP) of p-dioxanone using a protected monosaccharide (1,2;3,4-di-O-isopropylidene-α-d-galactopyranose)/Al(OⁱPr)₃ initiator system to yield polydioxanone with a protected monosaccharide end-group is described. The products were synthesized at 60-100 °C and characterized by ¹H and ¹³C NMR, and MALDI-TOF mass spectrometry. Besides the desired polydioxanone functionalised with a monosaccharide end-group, also polydioxanone with an OⁱPr end-group was formed (20-30%). Systematic studies showed that the polymer yield is a function of the reaction temperature and the reaction time, with higher temperatures (100 °C) leading to lower yields. The average chain length of the polymers is between 7 and 58 repeating units and may be tuned by the monomer to monosaccharide ratio (at constant Al(OⁱPr)₃ intake). A statistical model has been developed that successfully describes the experimentally observed relation between the average chain length of the functionalized polymer and reaction parameters.     

Interactions of histatin-3 and histatin-5 with actin

Background

Histatins are histidine rich polypeptides produced in the parotid and submandibular gland and secreted into the saliva. Histatin-3 and ?5 are the most important polycationic histatins. They possess antimicrobial activity against fungi such as Candida albicans. Histatin-5 has a higher antifungal activity than histatin-3 while histatin-3 is mostly involved in wound healing in the oral cavity. We found that these histatins, like other polycationic peptides and proteins, such as LL-37, lysozyme and histones, interact with extracellular actin.

Results

Histatin-3 and ?5 polymerize globular actin (G-actin) to filamentous actin (F-actin) and bundle F-actin filaments. Both actin polymerization and bundling by histatins is pH sensitive due to the high histidine content of histatins. In spite of the equal number of net positive charges and histidine residues in histatin-3 and ?5, less histatin-3 is needed than histatin-5 for polymerization and bundling of actin. The efficiency of actin polymerization and bundling by histatins greatly increases with decreasing pH. Histatin-3 and ?5 induced actin bundles are dissociated by 100 and 50 mM NaCl, respectively. The relatively low NaCl concentration required to dissociate histatin-induced bundles implies that the actin-histatin filaments bind to each other mainly by electrostatic forces. The binding of histatin-3 to F-actin is stronger than that of histatin-5 showing that hydrophobic forces have also some role in histatin-3- actin interaction. Histatins affect the fluorescence of probes attached to the D-loop of G-actin indicating histatin induced changes in actin structure. Transglutaminase cross-links histatins to actin. Competition and limited proteolysis experiments indicate that the main histatin cross-linking site on actin is glutamine-49 on the D-loop of actin.

Conclusions

Both histatin-3 and ?5 interacts with actin, however, histatin 3 binds stronger to actin and affects actin structure at lower concentration than histatin-5 due to the extra 8 amino acid sequence at the C-terminus of histatin-3. Extracellular actin might regulate histatin activity in the oral cavity, which should be the subject of further investigation.

     

Optical purification of a mixture of chiral forms by dimer formation

We introduce a readily executable method for the optical purification of "scalemic" (non 50%-50%) mixtures of chiral molecules of opposite handedness ("enantiomers"). The method relies on the formation of two types of dimers, (R-R or S-S) "homodimers" and (R-S) "heterodimers." The selectivity is linked to the difference in sign recently discovered by us to exist between certain transition-dipole matrix elements of opposite enantiomers. This sign difference results in differences in spectral propensity rules: In homodimers, transitions from the ground state can only take place to inversion symmetric excited states, while in the heterodimer the transitions are much more likely to proceed to antisymmetric excited states (although for heterodimers weak transitions to symmetric states might exist). These opposing propensity rules fully explain the observed large differences in the spectra of homodimers vs. heterodimers, which exist despite the almost identical energy levels positions. We illustrate the general concepts by computationally demonstrating the optically induced enantio-purification of scalemic mixtures of the hydropropionic C(3)H(6)O(3) (lactic) acid.     

Color-critical graphs have logarithmic circumference

A graph G is k-critical if every proper subgraph of G is (k−1)-colorable, but the graph G itself is not. We prove that every k-critical graph on n vertices has a cycle of length at least , improving a bound of Alon, Krivelevich and Seymour from 2000. Examples of Gallai from 1963 show that the bound cannot be improved to exceed . We thus settle the problem of bounding the minimal circumference of k-critical graphs, raised by Dirac in 1952 and Kelly and Kelly in 1954.     

Influence of the temperature on the heat of formation of nickel monoxide at high temperature

In order to see whether the heat of formation ΔH⁰ of the insulating transition metal monoxides shows any change at high temperatures, this property has been accurately measured for NiO by the electrochemical method in the temperature range 743–1323 K. The results show that ΔH⁰ changes from ? 56.10 kcal mol^?1 to ? 55.66 ± 0.08 kcal mol^?1 as the temperature is increased through 913 K. The significance of the heat of formation is discussed from the viewpoint of electronic structure of this compound.     

Kinematical scaling violation at fixed energy

We calculate the ξ-scaling corrections to xⁿy^k moments inclusive lepton-hadron cross sections at fixed incident lepton energy.