Asymptotic enumeration of sparse 2‐connected graphs

We determine an asymptotic formula for the number of labelled 2‐connected (simple) graphs on n vertices and m edges, provided that m ‐ n →∞ and m = O(nlog n) as n →∞. This is the entire range of m not covered by previous results. The proof involves determining properties of the core and kernel of random graphs with minimum degree at least 2. The case of 2‐edge‐connectedness is treated similarly. We also obtain formulae for the number of 2‐connected graphs with given degree sequence for most (“typical”) sequences. Our main result solves a problem of Wright from 1983. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013     

Structure Results for Multiple Tilings in 3D

We study multiple tilings of 3-dimensional Euclidean space by a convex body. In a multiple tiling, a convex body $P$ is translated with a discrete multiset $\Lambda $ in such a way that each point of ${\mathbb {R}}^d$ gets covered exactly $k$ times, except perhaps the translated copies of the boundary of $P$ . It is known that all possible multiple tilers in ${\mathbb {R}}^3$ are zonotopes. In ${\mathbb {R}}^2$ it was known by the work of Kolountzakis (Discrete Comput Geom 23(4):537–553, 2000) that, unless $P$ is a parallelogram, the multiset of translation vectors $\Lambda $ must be a finite union of translated lattices (also known as quasi periodic sets). In that work (Kolountzakis, Discrete Comput Geom 23(4):537–553, 2000) the author asked whether the same quasi-periodic structure on the translation vectors would be true in ${\mathbb {R}}^3$ . Here we prove that this conclusion is indeed true for ${\mathbb {R}}^3$ . Namely, we show that if $P$ is a convex multiple tiler in ${\mathbb {R}}^3$ , with a discrete multiset $\Lambda $ of translation vectors, then $\Lambda $ has to be a finite union of translated lattices, unless $P$ belongs to a special class of zonotopes. This exceptional class consists of two-flat zonotopes $P$ , defined by the Minkowski sum of two 2-dimensional symmetric polygons in ${\mathbb {R}}^3$ , one of which may degenerate into a single line segment. It turns out that rational two-flat zonotopes admit a multiple tiling with an aperiodic (nonquasi-periodic) set of translation vectors $\Lambda $ . We note that it may be quite difficult to offer a visualization of these 3-dimensional non-quasi-periodic tilings, and that we discovered them by using Fourier methods.     

Diffusion of Myelin Oligodendrocyte Glycoprotein in Living OLN-93 Cells Investigated by Raster-Scanning Image Correlation Spectroscopy (RICS)

Many membrane proteins and lipids are partially confined in substructures ranging from tens of nanometers to micrometers in size. Evidence for heterogeneities in the membrane of oligodendrocytes, i.e. the myelin-producing cells of the central nervous system, is almost exclusively based on detergent methods. However, as application of detergents can alter the membrane phase behaviour, it is important to investigate membrane heterogeneities in living cells. Here, we report on the first investigations of the diffusion behavior of the myelin-specific protein MOG (myelin oligodendrocyte glycoprotein) in OLN-93 as studied by the recently developed RICS (raster-scanning image correlation spectroscopy) technique. We implemented RICS on a standard confocal laser-scanning microscope with one-photon excitation and analog detection. Measurements on FITC-dextran were used to evaluate the performance of the system and the data analysis procedure. Ellen Gielen and Nick Smisdom contributed equally to this work.     

Power-output regularization in global sound equalization

The purpose of equalization in room acoustics is to compensate for the undesired modification that an enclosure introduces to signals such as audio or speech. In this work, equalization in a large part of the volume of a room is addressed. The multiple point method is employed with an acoustic power-output penalty term instead of the traditional quadratic source effort penalty term. Simulation results demonstrate that this technique gives a smoother decline of the reproduction performance away from the control points.     

Chemical Synthesis and Immunological Evaluation of a Pentasaccharide Bearing Multiple Rare Sugars as a Potential Anti-pertussis Vaccine

With the infection rate of Bordetella pertussis at a 60-year high, there is an urgent need for new anti-pertussis vaccines. The lipopolysaccharide (LPS) of B. pertussis is an attractive antigen for vaccine development. With the presence of multiple rare sugars and unusual glycosyl linkages, the B. pertussis LPS is a highly challenging synthetic target. In this work, aided by molecular dynamics simulation and modeling, a pertussis-LPS-like pentasaccharide was chemically synthesized for the first time. The pentasaccharide was conjugated with a powerful carrier, bacteriophage Qβ, as a vaccine candidate. Immunization of mice with the conjugate induced robust anti-glycan IgG responses with IgG titers reaching several million enzyme-linked immunosorbent assay (ELISA) units. The antibodies generated were long lasting and boostable and could recognize multiple clinical strains of B. pertussis, highlighting the potential of Qβ-glycan as a new anti-pertussis vaccine.     

Mass Spectrometric Identification of [4Fe–4S](NO)x Intermediates of Nitric Oxide Sensing by Regulatory Iron–Sulfur Cluster Proteins

Nitric oxide (NO) can function as both a cytotoxin and a signalling molecule. In both cases, reaction with iron–sulfur (Fe–S) cluster proteins plays an important role because Fe–S clusters are reactive towards NO and so are a primary site of general NO-induced damage (toxicity). This sensitivity to nitrosylation is harnessed in the growing group of regulatory proteins that function in sensing of NO via an Fe–S cluster. Although information about the products of cluster nitrosylation is now emerging, detection and identification of intermediates remains a major challenge, due to their transient nature and the difficulty in distinguishing spectroscopically similar iron-NO species. Here we report studies of the NO-sensing Fe–S cluster regulators NsrR and WhiD using non-denaturing mass spectrometry, in which non-covalent interactions between the protein and Fe/S/NO species are preserved. The data provide remarkable insight into the nitrosylation reactions, permitting identification, for the first time, of protein-bound mono-, di- and tetranitrosyl [4Fe–4S] cluster complexes ([4Fe–4S](NO), [4Fe–4S])(NO)₂ and [4Fe–4S](NO)₄) as intermediates along pathways to formation of product Roussin's red ester (RRE) and Roussin's black salt (RBS)-like species. The data allow the nitrosylation mechanisms of NsrR and WhiD to be elucidated and clearly distinguished.     

Synthesis and characterisation of low density porous polymers by reversible addition-fragmentation chain transfer (RAFT)

PolyHIPE foams with densities of 0.05–0.1 g cm^?3 have been prepared by the polymerisation of the continuous phase of high internal phase emulsions (HIPEs). The internal aqueous phase in HIPE occupies more than 74 % of the total volume, which leads to highly porous and open-cell morphologies. In this paper a method of preparing polyHIPE foams by using reversible addition-fragmentation chain transfer (RAFT) polymerisation has been investigated. Polystyrene-co-polymethyl methacrylate (PS-co-PMMA) has been studied and by using a variety of characterisation methods, it was possible to compare the polyHIPEs prepared by the conventional free radical polymerisation (FRP) to those by RAFT polymerisation. Scanning electron microscopy images have confirmed the presence of a cellular polyHIPE structure. PS-co-PMMA polyHIPEs made by RAFT have significantly narrower molecular weight distribution with values for the polydispersity index (PDI) for PS-co-PMMA between 1.46 and 2.08 compared to 4.68 observed by FRP. The effects of different concentrations of the RAFT agent on structure, glass transition temperature (T _g) and PDI of PS-co-PMMA polyHIPE foams are presented.     

On time regularity and related conditions for power-bounded operators

Let T be a bounded linear operator in a complex Banach space.Our main result gives various characterizations of the condition:T is power-bounded and an estimate ||(I – T)Tⁿ || cn^–1/2 holds for all positive integers n. In particular, this conditionholds if and only if T = β S + (1 – β)I, forsome β (0, 1) and some power-bounded operator S; or ifand only if T is power-bounded and the discrete semigroup (Tⁿ)is dominated by the continuous semigroup (e^{– t(I –T)})_{t 0} in a natural sense. As a consequence of our main results,for 1/2 < 1 we characterize the condition that T is power-boundedand ||(I – T)Tⁿ || c n^– for all n, in terms ofestimates on the semigroup e^{–t(I – T)}.