Critical endpoint and analytical phase diagram of attractive hard-core Yukawa spheres

We analytically calculate the gas-liquid critical endpoint (cep) for hard spheres with a Yukawa attraction. This cep is a boundary condition for the existence of a liquid. We use an analytical Helmholtz energy expression for the attractive Yukawa (hard) spheres based on the first-order mean spherical approximation to the attractive Yukawa potential by Tang and Lu (J. Chem. Phys. 1993, 99, 9828). This theory and our analytical simplification of it predict the gas-liquid and fluid-solid phase behavior, as found from computer simulations, very accurately as long as the range 1/kappa of attraction is not too short. We find that the cep is situated at kappasigma approximately 6 and at a contact potential around 2 kT. It follows that a liquid state is only possible when the attraction range is longer than (1/6) of the particle diameter sigma, and the attraction strength is smaller than 2 kT. The liquid region does not span more than 0.6 kT in strength, and there is also a relatively narrow window for the attraction range.     

Mesoscopic scales in hierarchical configuration models

To understand mesoscopic scaling in networks, we study the hierarchical configuration model (HCM), a random graph model with community structure. Connections between communities are formed as in a configuration model. We study the component sizes of HCM at criticality, and we study critical bond percolation. We find the conditions on the community sizes such that the critical component sizes of HCM behave similarly as in the configuration model. We show that the ordered components of a critical HCM on $N$ vertices are $O\left(N^{2∕3}\right)$. More specifically, the rescaled component sizes converge to the excursions of a Brownian motion with parabolic drift.     

Random subgraphs of the 2D Hamming graph: the supercritical phase

We study random subgraphs of the 2-dimensional Hamming graph H(2,n), which is the Cartesian product of two complete graphs on n vertices. Let p be the edge probability, and write ${p={(1+\varepsilon)}/{(2(n-1))}}$ for some ${\varepsilon \in \mathbb{R}}$ . In Borgs et al. (Random Struct Alg 27:137–184, 2005; Ann Probab 33:1886–1944, 2005), the size of the largest connected component was estimated precisely for a large class of graphs including H(2,n) for ${\varepsilon \leq \Lambda V^{-1/3}}$ , where Λ >  0 is a constant and V = n ² denotes the number of vertices in H(2,n). Until now, no matching lower bound on the size in the supercritical regime has been obtained. In this paper we prove that, when ${\varepsilon \gg (\log{V})^{1/3} V^{-1/3}}$ , then the largest connected component has size close to ${2 \varepsilon V}$ with high probability. We thus obtain a law of large numbers for the largest connected component size, and show that the corresponding values of p are supercritical. Barring the factor ${(\log{V})^{1/3}}$ , this identifies the size of the largest connected component all the way down to the critical p window.     

Monotonicity for excited random walk in high dimensions

We prove that the drift θ(d, β) for excited random walk in dimension d is monotone in the excitement parameter ${\beta \in [0,1]}$ , when d is sufficiently large. We give an explicit criterion for monotonicity involving random walk Green’s functions, and use rigorous numerical upper bounds provided by Hara (Private communication, 2007) to verify the criterion for d ≥ 9.     

Approximate analysis of single-server tandem queues with finite buffers

In this paper, we study single-server tandem queues with general service times and finite buffers. Jobs are served according to the Blocking-After-Service protocol. To approximately determine the throughput and mean sojourn time, we decompose the tandem queue into single-buffer subsystems, the service times of which include starvation and blocking, and then we iteratively estimate the unknown parameters of the service times of each subsystem. The crucial feature of this approach is that in each subsystem successive service times are no longer assumed to be independent, but a successful attempt is made to include dependencies due to blocking by employing the concept of Markovian Arrival Processes. An extensive numerical study shows that this approach produces very accurate estimates for the throughput and mean sojourn time, outperforming existing methods, especially for longer tandem queues and for tandem queues with service times with a high variability.     

Interstrain Variability of Human Vaginal Lactobacillus crispatus for Metabolism of Biogenic Amines and Antimicrobial Activity against Urogenital Pathogens

Lactobacillus crispatus is the dominant species in the vagina of many women. With the potential for strains of this species to be used as a probiotic to help prevent and treat dysbiosis, we investigated isolates from vaginal swabs with Lactobacillus-dominated and a dysbiotic microbiota. A comparative genome analysis led to the identification of metabolic pathways for synthesis and degradation of three major biogenic amines in most strains. However, targeted metabolomic analysis of the production and degradation of biogenic amines showed that certain strains have either the ability to produce or to degrade these compounds. Notably, six strains produced cadaverine, one produced putrescine, and two produced tyramine. These biogenic amines are known to raise vaginal pH, cause malodour, and make the environment more favourable to vaginal pathogens. In vitro experiments confirmed that strains isolated from women with a dysbiotic vaginal microbiota have higher antimicrobial effects against the common urogenital pathogens Escherichia coli and Enterococcus faecium. The results indicate that not all L. crispatus vaginal strains appear suitable for probiotic application and the basis for selection should not be only the overall composition of the vaginal microbiota of the host from which they came, but specific biochemical and genetic traits.     

The Constants in the Central Limit Theorem for the One-Dimensional Edwards Model

The Edwards model in one dimension is a transformed path measure for one-dimensional Brownian motion discouraging self-intersections. We study the constants appearing in the central limit theorem (CLT) for the endpoint of the path (which represent the mean and the variance) and the exponential rate of the normalizing constant. The same constants appear in the weak-interaction limit of the one-dimensional Domb–Joyce model. The Domb–Joyce model is the discrete analogue of the Edwards model based on simple random walk, where each self-intersection of the random walk path recieves a penalty e ^–2. We prove that the variance is strictly smaller than 1, which shows that the weak interaction limits of the variances in both CLTs are singular. The proofs are based on bounds for the eigenvalues of a certain one-parameter family of Sturm–Liouville differential operators, obtained by using monotonicity of the zeros of the eigen-functions in combination with computer plots.     

Isoform separation of a multi-acetylated protein using capillary polystyrene-divinylbenzene monolithic columns

Capillary polystyrene-divinylbenzene (PS-DVB) monolithic columns were used to separate differentially acetylated intact IM9 protein isoforms. Compared to the unmodified form, the hydrophobic shift for intact acetylated isoforms was significant under standard reversed-phase conditions (32.5-45% acetonitrile in 10 min). The high chromatographic resolution of the PS-DVB monolithic columns resulted in peak widths at half height of 4-5s. This allowed us to nearly completely resolve a number of peaks greater than the number of possible acetylation sites. This observation suggested that not only the number, but also the location of the acetylations on the protein had a significant effect on the retention. Matrix-assisted laser desorption ionization time-of-flight MS and MS/MS were used to confirm the chromatographic separation of isoforms. It was found that the acetylations site, especially on the N-terminus, has an effect on the retention on the PS-DVB column.     

Weak distance dependence of through-bond interactions in tetrahydro-4H-thiopyran-4-ylidene end-capped oligo(cyclohexylidenes); a computational survey

Calculations on members of the oligo(cyclohexylidene) series [(n), n = 1-5)] and related tetrahydro-4H-thiopyran end-capped analogues [(n), n = 1-4)] show a strong through-bond coupling between their pi bonds and sulfur lone pairs (Lp(pi)S). This coupling is mediated by an interaction between the H(ax)-C-C-H(ax) structural sub-units and the pi bonds connecting the cyclohexyl moieties. A comparison of the length dependency of the through-bond coupling via an oligo(cyclohexylidene) and an alkane bridge [divinyl alkanes (n)] shows that oligo(cyclohexylidenes) are more efficient in mediating through-bond couplings over large distances. Oligo(cyclohexylidene) bridges exhibit molecular wire characteristics.