Exponential Decay of Correlations for Strongly Coupled Toom Probabilistic Cellular Automata

We investigate the low-noise regime of a large class of probabilistic cellular automata, including the North-East-Center model of Toom. They are defined as stochastic perturbations of cellular automata belonging to the category of monotonic binary tessellations and possessing a property of erosion. We prove, for a set of initial conditions, exponential convergence of the induced processes toward an extremal invariant measure with a highly predominant spin value. We also show that this invariant measure presents exponential decay of correlations in space and in time and is therefore strongly mixing.Comment: 21 pages, 0 figure, revised version including a generalization to a larger class of models, structure of the arguments unchanged, minor changes suggested by reviewers, added reference

A Toom rule that increases the thickness of sets

Toom's north-east-self voting cellular automaton rule R is known to suppress small minorities. A variant which we call R^+ is also known to turn an arbitrary initial configuration into a homogenous one (without changing the ones that were homogenous to start with). Here we show that R^+ always increases a certain property of sets called thickness. This result is intended as a step towards a proof of the fast convergence towards consensus under R^+. The latter is observable experimentally, even in the presence of some noise.Comment: 16 pages, 8 figure

Involvement of BMP-2, TGF-ß2 and TGF-ß3 Signaling in Initial and Early Stages of Heterotopic Ossification in a rat Experimental Model

This study focused on the localization and expression of bone morphogenetic protein 2 (BMP-2) and different  isoforms of transforming growth factor s (TGF-s1, TGF-s2 and TGF-s3) in the initial and early stages  of heterotopic ossification (HO) employing an animal model mimicking the situation after total hip arthroplasty  (THA). Bone growth was induced in rats using s-tricalcium phosphate implants immersed either in  osteoinductive rhBMP-2 solution or in saline and implanted at the site where the HO is usually expected  to develop after THA. Implants were removed at 3 or 21 days after the operation and handled according to  stereology principles. mRNA expression and protein staining of growth factors in different types of tissues  was determined by in situ hybridization and immunohistochemistry, respectively. After three days, TGF-s3 content in the undifferentiated mesenchymal-like cells in the rhBMP-2 treated  implants was, as assessed by immunohistochemistry, 49.6% higher compared to the saline treated group  (p=0.024). This was also supported by in situ hybridization of mRNA of TGF-s3, which showed stronger  expression in rhBMP-2 treated group. Immunohistochemical investigation showed that after 21 days the  connective tissue in the rhBMP-2 treated implants contained more TGF-s1, TGF-s2 and TGF-s3, compared  to BMP-2 and osteoblasts contained significantly (27.2%) more TGF-s3 compared to TGF-s1 (p=0.045). In  the formed HO the proportion of the TGF-s2 and TGF-s3 producing bone tissue was increased by 32.1% and  47.8% respectively, compared to the TGF-s1 producing bone tissue (p=0.007 and p=0.006) and although  this difference was not so clear at mRNA level, this suggests that TGF-s2 and TGF-s3 signaling seem to play  an important role during initial and early stages of HO formation.

Invariant Measures and Decay of Correlations for a Class of Ergodic Probabilistic Cellular Automata

We give new sufficient ergodicity conditions for two-state probabilistic cellular automata (PCA) of any dimension and any radius. The proof of this result is based on an extended version of the duality concept. Under these assumptions, in the one dimensional case, we study some properties of the unique invariant measure and show that it is shift-mixing. Also, the decay of correlation is studied in detail. In this sense, the extended concept of duality gives exponential decay of correlation and allows to compute explicitily all the constants involved

Harness processes and harmonic crystals

In the Hammersley harness processes the real-valued height at each site i in Z^d is updated at rate 1 to an average of the neighboring heights plus a centered random variable (the noise). We construct the process "a la Harris" simultaneously for all times and boxes contained in Z^d. With this representation we compute covariances and show L^2 and almost sure time and space convergence of the process. In particular, the process started from the flat configuration and viewed from the height at the origin converges to an invariant measure. In dimension three and higher, the process itself converges to an invariant measure in L^2 at speed t^{1-d/2} (this extends the convergence established by Hsiao). When the noise is Gaussian the limiting measures are Gaussian fields (harmonic crystals) and are also reversible for the process.Comment: 21 pages. Revised version with minor changes. Version almost identical to the one to be published in SP

Quantum memories based on engineered dissipation

Storing quantum information for long times without disruptions is a major requirement for most quantum information technologies. A very appealing approach is to use self-correcting Hamiltonians, i.e. tailoring local interactions among the qubits such that when the system is weakly coupled to a cold bath the thermalization process takes a long time. Here we propose an alternative but more powerful approach in which the coupling to a bath is engineered, so that dissipation protects the encoded qubit against more general kinds of errors. We show that the method can be implemented locally in four dimensional lattice geometries by means of a toric code, and propose a simple 2D set-up for proof of principle experiments.Comment: 6 +8 pages, 4 figures, Includes minor corrections updated references and aknowledgement

Stochastic theory of non-equilibrium wetting

We study a Langevin equation describing non-equilibrium depinning and wetting transitions. Attention is focused on short-ranged attractive substrate-interface potentials. We confirm the existence of first order depinning transitions, in the temperature-chemical potential diagram, and a tricritical point beyond which the transition becomes a non-equilibrium complete wetting transition. The coexistence of pinned and depinned interfaces occurs over a finite area, in line with other non-equilibrium systems that exhibit first order transitions. In addition, we find two types of phase coexistence, one of which is characterized by spatio-temporal intermittency (STI). A finite size analysis of the depinning time is used to characterize the different coexisting regimes. Finally, a stationary distribution of characteristic triangles or facets was shown to be responsible for the structure of the STI phase.Comment: To appear in Europhys. Lett. // 3 figure

Influence of temperature and relative humidity on the survival of <i>Chlamydia pneumoniae</i> in aerosols

The survival of Chlamydia pneumoniae in aerosols was investigated by using a chamber with a capacity of 114.5 liters. We injected 5 x 107 inclusion- forming units (IFU) of C. pneumoniae in aerosols with a droplet size of 3 to 5 μm. Samples were taken after 30 s and every 1 min thereafter. The survival of C. pneumoniae was measured at four temperatures (8.5, 15, 25, and 35°C) and at three different relative humidities (RH) of 5, 50, and 95% for each temperature. The survival rates of Streptococcus pneumoniae, Streptococcus faecalis, Klebsiella pneumoniae, Chlamydia trachomatis LGV2, and cytomegalovirus were also determined at 25°C and 95% RH and compared with that of C. pneumoniae. At the mentioned temperatures and RH, a rapid decrease of C. pneumoniae IFU was observed in the first 30 s. After this the decrease in the number of IFU was more gradual. The survival of C. pneumoniae in aerosols was optimal at 15 to 25°C and 95% RH; it was good compared with those of other microorganisms. A lower death rate was observed only in S. faecalis. In C. trachomatis, the death rate during the first 30 s was higher than that in C. pneumoniae (85 and 53.3%, respectively). After the first 30 s, the death rates in the two organisms were identical. It was concluded that transmission of C. pneumoniae via aerosols was possible. There is probably a direct transmission from person to person, taking into account the relatively short survival period of C. pneumoniae in aerosols.</p