An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem

Let (lambda_d)(p) be the p monomer-dimer entropy on the d-dimensional integer lattice Z^d, where p in [0,1] is the dimer density. We give upper and lower bounds for (lambda_d)(p) in terms of expressions involving (lambda_(d-1))(q). The upper bound is based on a conjecture claiming that the p monomer-dimer entropy of an infinite subset of Z^d is bounded above by (lambda_d)(p). We compute the first three terms in the formal asymptotic expansion of (lambda_d)(p) in powers of 1/d. We prove that the lower asymptotic matching conjecture is satisfied for (lambda_d)(p).Comment: 15 pages, much more about d=1,2,

Collective polarization exchanges in collisions of photon clouds

The one-loop "vacuum" Heisenberg-Euler coupling of four electromagnetic fields can lead to interesting collective effects in the collision of two photon clouds, on a time scale orders of magnitude faster than one estimates from the cross-section and density. We estimate the characteristic time for macroscopic transformation of positive to negative helicity in clouds that are initially totally polarized and for depolarization of a polarized beam traversing an unpolarized cloud.Comment: Recapitulates much that is in hep-ph/0402127, with new results in the last section, and the first section drastically reduced in view of the previous work of Kotkin and Serbo. Typo corrected in eq. 1

Quantum versus classical phase-locking transition in a driven-chirped oscillator

Classical and quantum-mechanical phase locking transition in a nonlinear oscillator driven by a chirped frequency perturbation is discussed. Different limits are analyzed in terms of the dimensionless parameters $/\sqrt{2m\hbar \omega_{0}\alpha}$ and $P_{2}=(3\hbar \beta)/(4m\sqrt{\alpha})$ ($\epsilon,$ $\alpha,$ $\beta$ and $\omega_{0}$ being the driving amplitude, the frequency chirp rate, the nonlinearity parameter and the linear frequency of the oscillator). It is shown that for $P_{2}\ll P_{1}+1$, the passage through the linear resonance for $P_{1}$ above a threshold yields classical autoresonance (AR) in the system, even when starting in a quantum ground state. In contrast, for $$, the transition involves quantum-mechanical energy ladder climbing (LC). The threshold for the phase-locking transition and its width in $P_{1}$ in both AR and LC limits are calculated. The theoretical results are tested by solving the Schrodinger equation in the energy basis and illustrated via the Wigner function in phase space

Integrin α2β1 Expression Regulates Matrix Metalloproteinase-1-Dependent Bronchial Epithelial Repair in Pulmonary Tuberculosis.

Pulmonary tuberculosis (TB) is caused by inhalation of Mycobacterium tuberculosis, which damages the bronchial epithelial barrier to establish local infection. Matrix metalloproteinase-1 plays a crucial role in the immunopathology of TB, causing breakdown of type I collagen and cavitation, but this collagenase is also potentially involved in bronchial epithelial repair. We hypothesized that the extracellular matrix (ECM) modulates M. tuberculosis-driven matrix metalloproteinase-1 expression by human bronchial epithelial cells (HBECs), regulating respiratory epithelial cell migration and repair. Medium from monocytes stimulated with M. tuberculosis induced collagenase activity in bronchial epithelial cells, which was reduced by ~87% when cells were cultured on a type I collagen matrix. Matrix metalloproteinase-1 had a focal localization, which is consistent with cell migration, and overall secretion decreased by 32% on type I collagen. There were no associated changes in the specific tissue inhibitors of metalloproteinases. Decreased matrix metalloproteinase-1 secretion was due to ligand-binding to the α2β1 integrin and was dependent on the actin cytoskeleton. In lung biopsies, samples from patients with pulmonary TB, integrin α2β1 is highly expressed on the bronchial epithelium. Areas of lung with disrupted collagen matrix showed an increase in matrix metalloproteinases-1 expression compared with areas where collagen was comparable to control lung. Type I collagen matrix increased respiratory epithelial cell migration in a wound-healing assay, and this too was matrix metalloproteinase-dependent, since it was blocked by the matrix metalloproteinase inhibitor GM6001. In summary, we report a novel mechanism by which α2β1-mediated signals from the ECM modulate matrix metalloproteinase-1 secretion by HBECs, regulating their migration and epithelial repair in TB

Natural ventilation for the prevention of airborne contagion.

BACKGROUND: Institutional transmission of airborne infections such as tuberculosis (TB) is an important public health problem, especially in resource-limited settings where protective measures such as negative-pressure isolation rooms are difficult to implement. Natural ventilation may offer a low-cost alternative. Our objective was to investigate the rates, determinants, and effects of natural ventilation in health care settings. METHODS AND FINDINGS: The study was carried out in eight hospitals in Lima, Peru; five were hospitals of "old-fashioned" design built pre-1950, and three of "modern" design, built 1970-1990. In these hospitals 70 naturally ventilated clinical rooms where infectious patients are likely to be encountered were studied. These included respiratory isolation rooms, TB wards, respiratory wards, general medical wards, outpatient consulting rooms, waiting rooms, and emergency departments. These rooms were compared with 12 mechanically ventilated negative-pressure respiratory isolation rooms built post-2000. Ventilation was measured using a carbon dioxide tracer gas technique in 368 experiments. Architectural and environmental variables were measured. For each experiment, infection risk was estimated for TB exposure using the Wells-Riley model of airborne infection. We found that opening windows and doors provided median ventilation of 28 air changes/hour (ACH), more than double that of mechanically ventilated negative-pressure rooms ventilated at the 12 ACH recommended for high-risk areas, and 18 times that with windows and doors closed (p < 0.001). Facilities built more than 50 years ago, characterised by large windows and high ceilings, had greater ventilation than modern naturally ventilated rooms (40 versus 17 ACH; p < 0.001). Even within the lowest quartile of wind speeds, natural ventilation exceeded mechanical (p < 0.001). The Wells-Riley airborne infection model predicted that in mechanically ventilated rooms 39% of susceptible individuals would become infected following 24 h of exposure to untreated TB patients of infectiousness characterised in a well-documented outbreak. This infection rate compared with 33% in modern and 11% in pre-1950 naturally ventilated facilities with windows and doors open. CONCLUSIONS: Opening windows and doors maximises natural ventilation so that the risk of airborne contagion is much lower than with costly, maintenance-requiring mechanical ventilation systems. Old-fashioned clinical areas with high ceilings and large windows provide greatest protection. Natural ventilation costs little and is maintenance free, and is particularly suited to limited-resource settings and tropical climates, where the burden of TB and institutional TB transmission is highest. In settings where respiratory isolation is difficult and climate permits, windows and doors should be opened to reduce the risk of airborne contagion

Dynamics of Ferromagnetic Walls: Gravitational Properties

We discuss a new mechanism which allows domain walls produced during the primordial electroweak phase transition. We show that the effective surface tension of these domain walls can be made vanishingly small due to a peculiar magnetic condensation induced by fermion zero modes localized on the wall. We find that in the perfect gas approximation the domain wall network behaves like a radiation gas. We consider the recent high-red shift supernova data and we find that the corresponding Hubble diagram is compatible with the presence in the Universe of a ideal gas of ferromagnetic domain walls. We show that our domain wall gas induces a completely negligible contribution to the large-scale anisotropy of the microwave background radiation.Comment: Replaced with revised version, accepted for publication in IJMP

Simulation of Radiation-Induced Damage Distribution to evaluate Models for Higher-Order Chromosome Organisation

The structure of chromatin at the level of the 30 nm fibre has been studied in considerable detail, but little is known about how this fibre is arranged within the interphase chromosome territory. Over the years, various polymer models were developed to simulate chromosome structure, for example the random-walk/giant-loop (RWGL) model, the multi-loop subcompartment (MLS) model, and the interconnected-fibre-loop model (Friedland et al., 1999). These models differ mainly in the size and arrangement of the chromatin loops and, correspondingly, in the predicted distribution of chromatin density within the nucleus. It occurred to us that densely ionising radiation can be used to probe the actual distribution of chromatin density in human interphase cells. In contrast to sparsely ionising radiation (e.g. X-rays), which induces DNA double-strand breaks (DSB) that are distributed randomly within the nucleus, irradiation with densely ionising accelerated ions leads to spatial clustering of DSB. This inhomogeneity in DSB localisation, together with an inhomogeneity of DNA density within the nucleus, causes an over-dispersion in the resulting distribution of DNA fragment sizes that can be detected by pulsed-field gel electrophoresis. Using the above-mentioned chromosome models, we performed computer simulations to predict the DNA fragment size distributions resulting from irradiation with accelerated ions, and compared the predicted distributions with those obtained experimentally. We found that simulations based on the MLS model, in which local variations in chromatin density are higher than in the other models, resulted in the best agreement between calculation and experiment