Directed percolation with incubation times

We introduce a model for directed percolation with a long-range temporal diffusion, while the spatial diffusion is kept short ranged. In an interpretation of directed percolation as an epidemic process, this non-Markovian modification can be understood as incubation times, which are distributed accordingly to a Levy distribution. We argue that the best approach to find the effective action for this problem is through a generalization of the Cardy-Sugar method, adding the non-Markovian features into the geometrical properties of the lattice. We formulate a field theory for this problem and renormalize it up to one loop in a perturbative expansion. We solve the various technical difficulties that the integrations possess by means of an asymptotic analysis of the divergences. We show the absence of field renormalization at one-loop order, and we argue that this would be the case to all orders in perturbation theory. Consequently, in addition to the characteristic scaling relations of directed percolation, we find a scaling relation valid for the critical exponents of this theory. In this universality class, the critical exponents vary continuously with the Levy parameter.Comment: 17 pages, 7 figures. v.2: minor correction

Long-range epidemic spreading with immunization

We study the phase transition between survival and extinction in an epidemic process with long-range interactions and immunization. This model can be viewed as the well-known general epidemic process (GEP) in which nearest-neighbor interactions are replaced by Levy flights over distances r which are distributed as P(r) ~ r^(-d-sigma). By extensive numerical simulations we confirm previous field-theoretical results obtained by Janssen et al. [Eur. Phys. J. B7, 137 (1999)].Comment: LaTeX, 14 pages, 4 eps figure

Contact processes with long-range interactions

A class of non-local contact processes is introduced and studied using mean-field approximation and numerical simulations. In these processes particles are created at a rate which decays algebraically with the distance from the nearest particle. It is found that the transition into the absorbing state is continuous and is characterized by continuously varying critical exponents. This model differs from the previously studied non-local directed percolation model, where particles are created by unrestricted Levy flights. It is motivated by recent studies of non-equilibrium wetting indicating that this type of non-local processes play a role in the unbinding transition. Other non-local processes which have been suggested to exist within the context of wetting are considered as well.Comment: Accepted with minor revisions by Journal of Statistical Mechanics: Theory and experiment

Confronting the trans-Planckian question of inflationary cosmology with dissipative effects

We provide a class of QFTs which exhibit dissipation above a threshold energy, thereby breaking Lorentz invariance. Unitarity is preserved by coupling the fields to additional degrees of freedom (heavy fields) which introduce the rest frame. Using the Equivalence Principle, we define these theories in arbitrary curved spacetime. We then confront the trans-Planckian question of inflationary cosmology. When dissipation increases with the energy, the quantum field describing adiabatic perturbations is completely damped at the onset of inflation. However it still exists as a composite operator made with the additional fields. And when these are in their ground state, the standard power spectrum obtains if the threshold energy is much larger that the Hubble parameter. In fact, as the energy redshifts below the threshold, the composite operator behaves as if it were a free field endowed with standard vacuum fluctuations. The relationship between our models and the Brane World scenarios studied by Libanov and Rubakov displaying similar effects is discussed. The signatures of dissipation will be studied in a forthcoming paper.Comment: 30 pages, 1 Figure, to appear in CQ

Type I interferon responses of common carp strains with different levels of resistance to koi herpesvirus disease during infection with CyHV-3 or SVCV

Carp from breeding strains with different genetic background present diverse levels of resistance to viral pathogens. Carp strains of Asian origin, currently being treated as Cyprinus rubrofuscus L., especially Amur wild carp (AS), were proven to be more resistant to koi herpesvirus disease (KHVD; caused by cyprinid herpesvirus 3, CyHV-3) than strains originating from Europe and belonging to Cyprinus carpio L., like the Prerov scale carp (PS) or koi carp from a breed in the Czech Republic. We hypothesised that it can be associated with a higher magnitude of type I interferon (IFN) response as a first line of innate defence mechanisms against viral infections. To evaluate this hypothesis, four strains of common carp (AS, Rop, PS and koi) were challenged using two viral infection models: Rhabdovirus SVCV (spring viremia of carp virus) and alloherpesvirus CyHV-3. The infection with SVCV induced a low mortality rate and the most resistant was the Rop strain (no mortalities), whereas the PS strain was the most susceptible (survival rate of 78%). During CyHV-3 infection, Rop and AS strains performed better (survival rates of 78% and 53%, respectively) than PS and koi strains (survival rates of 35% and 10%, respectively). The evaluation of virus loads and virus replication showed significant differences between the carp strains, which correlated with the mortality rate. The evaluation of type I IFN responses showed that there were fundamental differences between the virus infection models. While responses to the SVCV were high, the CyHV-3 generally induced low responses. Furthermore, the results demonstrated that the magnitude of type I IFN responses did not correlate with a higher resistance in infected carp. In the case of a CyHV-3 infection, reduced type I IFN responses could be related to the potential ability of the virus to interfere with cellular sensing of foreign nucleic acids. Taken together, the results broaden our understanding of how common carp from different genetic lines interact with various viral pathogens

Endplate calcification and cervical intervertebral disc degeneration: the role of endplate marrow contact channel occlusion

Background: The aim of this study was to determine the fundamental relationships between cervical intervertebral disc (IVD) degeneration, endplate calcification, and the patency of endplate marrow contact channels (MCC). Materials and methods: Sixty cervical IVDs were excised from 30 human cadavers. After sectioning the specimens underwent micro computed tomography (microCT) — from all images the number, calibre, diameter and distribution of endplate openings were measured using ImageJ. Next, the specimens were scored for macroscopic degeneration (Thompson’s classification), and subsequently underwent histological analysis for both IVD and endplate degeneration (Boos’s classification) and calcification. Results: The study group comprised 30 female and 30 male IVDs (mean age ± SD: 51.4 ± 19.5). Specimen’s age, macroscopic and microscopic degeneration correlated negatively with the number of MCCs (r = –0.33–(–0.95); p < 0.0001), apart from the MCCs > 300 μm in diameter (r = 0.66–0.79; p < 0.0001). The negative relationship was strongest for the MCCs 10–50 μm in diameter. Conclusions: There is a strong negative correlation between the number of endplate MCCs, and both macroscopic and microscopic cervical IVD and endplate degeneration. This could further support the thesis that endplate calcification, through the occlusion of MCCs, leads to a fall in nutrient transport to the IVD, and subsequently causes its degeneration

Non-equilibrium Phase Transitions with Long-Range Interactions

This review article gives an overview of recent progress in the field of non-equilibrium phase transitions into absorbing states with long-range interactions. It focuses on two possible types of long-range interactions. The first one is to replace nearest-neighbor couplings by unrestricted Levy flights with a power-law distribution P(r) ~ r^(-d-sigma) controlled by an exponent sigma. Similarly, the temporal evolution can be modified by introducing waiting times Dt between subsequent moves which are distributed algebraically as P(Dt)~ (Dt)^(-1-kappa). It turns out that such systems with Levy-distributed long-range interactions still exhibit a continuous phase transition with critical exponents varying continuously with sigma and/or kappa in certain ranges of the parameter space. In a field-theoretical framework such algebraically distributed long-range interactions can be accounted for by replacing the differential operators nabla^2 and d/dt with fractional derivatives nabla^sigma and (d/dt)^kappa. As another possibility, one may introduce algebraically decaying long-range interactions which cannot exceed the actual distance to the nearest particle. Such interactions are motivated by studies of non-equilibrium growth processes and may be interpreted as Levy flights cut off at the actual distance to the nearest particle. In the continuum limit such truncated Levy flights can be described to leading order by terms involving fractional powers of the density field while the differential operators remain short-ranged.Comment: LaTeX, 39 pages, 13 figures, minor revision

Formation of convective cells in the scrape-off layer of the CASTOR tokamak

Understanding of the scrape-off layer (SOL) physics in tokamaks requires diagnostics with sufficient temporal and spatial resolution. This contribution describes results of experiments performed in the SOL of the CASTOR tokamak (R=40 cm, a = 6 cm) by means of a ring of 124 Langmuir probes surrounding the whole poloidal cross section. The individual probes measure either the ion saturation current of the floating potential with the spatial resolution up to 3 mm. Experiments are performed in a particular magnetic configuration, characterized by a long parallel connection length in the SOL, L_par ~q2piR. We report on measurements in discharges, where the edge electric field is modified by inserting a biased electrode into the edge plasma. In particular, a complex picture is observed, if the biased electrode is located inside the SOL. The poloidal distribution of the floating potential appears to be strongly non-uniform at biasing. The peaks of potential are observed at particular poloidal angles. This is interpreted as formation of a biased flux tube, which emanates from the electrode along the magnetic field lines and snakes q times around the torus. The resulting electric field in the SOL is 2-dimensional, having the radial as well as the poloidal component. It is demonstrated that the poloidal electric field E_pol convects the edge plasma radially due to the E_pol x B_T drift either inward or outward depending on its sign. The convective particle flux is by two orders of magnitude larger than the fluctuation-induced one and consequently dominates.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

Non Sequential Recursive Pair Substitution: Some Rigorous Results

We present rigorous results on some open questions on NSRPS, non sequential recursive pairs substitution method (see Grassberger in \cite{G}). In particular, starting from the action of NSRPS on finite strings we define a corresponding natural action on measures and we prove that the iterated measure becomes asymptotically Markov. This certify the effectiveness of NSRPS as a tool for data compression and entropy estimation.Comment: 20 page