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 transport and ocean ice extent on biogenic aerosol sulfur in the Arctic atmosphere

The recent decline in sea ice cover in the Arctic Ocean could affect the regional radiative forcing via changes in sea ice-atmosphere exchange of dimethyl sulfide (DMS) and biogenic aerosols formed from its atmospheric oxidation, such as methanesulfonic acid (MSA). This study examines relationships between changes in total sea ice extent north of 70 degrees N and atmospheric MSA measurement at Alert, Nunavut, during 1980-2009; at Barrow, Alaska, during 1997-2008; and at Ny-Alesund, Svalbard, for 1991-2004. During the 1980-1989 and 1990-1997 periods, summer (July-August) and June MSA concentrations at Alert decreased. In general, MSA concentrations increased at all locations since 2000 with respect to 1990 values, specifically during June and summer at Alert and in summer at Barrow and Ny-Alesund. Our results show variability in MSA at all sites is related to changes in the source strengths of DMS, possibly linked to changes in sea ice extent as well as to changes in atmospheric transport patterns. Since 2000, a late spring increase in atmospheric MSA at the three sites coincides with the northward migration of the marginal ice edge zone where high DMS emissions from ocean to atmosphere have previously been reported. Significant negative correlations are found between sea ice extent and MSA concentrations at the three sites during the spring and June. These results suggest that a decrease in seasonal ice cover influencing other mechanisms of DMS production could lead to higher atmospheric MSA concentrations