The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is 1+21+\sqrt{2}

In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a. honeycomb) lattice is $\mu=\sqrt{2+\sqrt{2}}.$ A key identity used in that proof was later generalised by Smirnov so as to apply to a general O(n) loop model with $n\in [-2,2]$ (the case $n=0$ corresponding to SAWs). We modify this model by restricting to a half-plane and introducing a surface fugacity $y$ associated with boundary sites (also called surface sites), and obtain a generalisation of Smirnov's identity. The critical value of the surface fugacity was conjectured by Batchelor and Yung in 1995 to be $y_{\rm c}=1+2/\sqrt{2-n}.$ This value plays a crucial role in our generalized identity, just as the value of growth constant did in Smirnov's identity. For the case $n=0$, corresponding to \saws\ interacting with a surface, we prove the conjectured value of the critical surface fugacity. A crucial part of the proof involves demonstrating that the generating function of self-avoiding bridges of height $T$, taken at its critical point $1/\mu$, tends to 0 as $T$ increases, as predicted from SLE theory.Comment: Major revision, references updated, 25 pages, 13 figure

Spatial Point Process Models of Defensive Strategies: Detecting Changes

Poisson point process, kernel smoothing, intensity function, Monte Carlo testing, conditional power, geopolitical tendencies, Primary: 62M30, Secondary: 60G55,

Comparative proteome analysis of Helicobacter pylori clinical strains by two-dimensional gel electrophoresis*

Objective: To investigate the pathogenic properties of Helicobacter pylori by comparing the proteome map of H. pylori clinical strains. Methods: Two wild-type H. pylori strains, YN8 (isolated from biopsy tissue of a gastric cancer patient) and YN14 (isolated from biopsy tissue of a gastritis and duodenal ulcer patient), were used. Proteomic analysis, using a pH range of 3–10 and 5–8, was performed. The individual proteins were identified by quadrupole time-of-flight (Q-TOF) mass spectrometer and protein database search. Results: Variation in spot patterns directed towards differential protein expression levels was observed between the strains. The gel revealed prominent proteins with several protein “families”. The comparison of protein expressions of the two strains reveals a high variability. Differentially present or absent spots were observed. Nine differentially expressed protein spots identified by Q-TOF included adenosine triphosphate (ATP)-binding protein, disulfide oxidoreductase B (DsbB)-like protein, N utilization substance A (NusA), ATP-dependent protease binding subunit/heat shock protein, hydantoin utilization protein A, seryl-tRNA synthetase, molybdenum ABC transporter ModD, and hypothetical proteins. Conclusions: This study suggests that H. pylori strains express/repress protein variation, not only in terms of the virulence proteins, but also in terms of physiological proteins, when they infect a human host. The difference of protein expression levels between H. pylori strains isolated from gastric cancer and gastritis may be the initiator of inflammation, and result in the different clinical presentation. In this preliminary study, we report seven differential proteins between strains, with molecule weights from approximately 10 kDa to approximately 40 kDa. Further studies are needed to investigate those proteins and their function associated with H. pylori colonization and adaptation to host environment stress