A Position-Space Renormalization-Group Approach for Driven Diffusive Systems Applied to the Asymmetric Exclusion Model

This paper introduces a position-space renormalization-group approach for nonequilibrium systems and applies the method to a driven stochastic one-dimensional gas with open boundaries. The dynamics are characterized by three parameters: the probability $\alpha$ that a particle will flow into the chain to the leftmost site, the probability $\beta$ that a particle will flow out from the rightmost site, and the probability $p$ that a particle will jump to the right if the site to the right is empty. The renormalization-group procedure is conducted within the space of these transition probabilities, which are relevant to the system's dynamics. The method yields a critical point at $\alpha_c=\beta_c=1/2$,in agreement with the exact values, and the critical exponent $\nu=2.71$, as compared with the exact value $\nu=2.00$.Comment: 14 pages, 4 figure

Breakdown of thermodynamic equilibrium for DNA hybridization in microarrays

Test experiments of hybridization in DNA microarrays show systematic deviations from the equilibrium isotherms. We argue that these deviations are due to the presence of a partially hybridized long-lived state, which we include in a kinetic model. Experiments confirm the model predictions for the intensity vs. free energy behavior. The existence of slow relaxation phenomena has important consequences for the specificity of microarrays as devices for the detection of a target sequence from a complex mixture of nucleic acids.Comment: 4 pages, 4 figure

Thermodynamics of histories for the one-dimensional contact process

The dynamical activity K(t) of a stochastic process is the number of times it changes configuration up to time t. It was recently argued that (spin) glasses are at a first order dynamical transition where histories of low and high activity coexist. We study this transition in the one-dimensional contact process by weighting its histories by exp(sK(t)). We determine the phase diagram and the critical exponents of this model using a recently developed approach to the thermodynamics of histories that is based on the density matrix renormalisation group. We find that for every value of the infection rate, there is a phase transition at a critical value of s. Near the absorbing state phase transition of the contact process, the generating function of the activity shows a scaling behavior similar to that of the free energy in an equilibrium system near criticality.Comment: 16 pages, 7 figure

Real-space renormalisation group approach to driven diffusive systems

We introduce a real-space renormalisation group procedure for driven diffusive systems which predicts both steady state and dynamic properties. We apply the method to the boundary driven asymmetric simple exclusion process and recover exact results for the steady state phase diagram, as well as the crossovers in the relaxation dynamics for each phase.Comment: 10 pages, 5 figure

Nonequilibrium effects in DNA microarrays: a multiplatform study

It has recently been shown that in some DNA microarrays the time needed to reach thermal equilibrium may largely exceed the typical experimental time, which is about 15h in standard protocols (Hooyberghs et al. Phys. Rev. E 81, 012901 (2010)). In this paper we discuss how this breakdown of thermodynamic equilibrium could be detected in microarray experiments without resorting to real time hybridization data, which are difficult to implement in standard experimental conditions. The method is based on the analysis of the distribution of fluorescence intensities I from different spots for probes carrying base mismatches. In thermal equilibrium and at sufficiently low concentrations, log I is expected to be linearly related to the hybridization free energy $\Delta G$ with a slope equal to $1/RT_{exp}$, where $T_{exp}$ is the experimental temperature and R is the gas constant. The breakdown of equilibrium results in the deviation from this law. A model for hybridization kinetics explaining the observed experimental behavior is discussed, the so-called 3-state model. It predicts that deviations from equilibrium yield a proportionality of $\log I$ to $\Delta G/RT_{eff}$. Here, $T_{eff}$ is an effective temperature, higher than the experimental one. This behavior is indeed observed in some experiments on Agilent arrays. We analyze experimental data from two other microarray platforms and discuss, on the basis of the results, the attainment of equilibrium in these cases. Interestingly, the same 3-state model predicts a (dynamical) saturation of the signal at values below the expected one at equilibrium.Comment: 27 pages, 9 figures, 1 tabl

Finite size scaling of current fluctuations in the totally asymmetric exclusion process

We study the fluctuations of the current J(t) of the totally asymmetric exclusion process with open boundaries. Using a density matrix renormalization group approach, we calculate the cumulant generating function of the current. This function can be interpreted as a free energy for an ensemble in which histories are weighted by exp(-sJ(t)). We show that in this ensemble the model has a first order space-time phase transition at s=0. We numerically determine the finite size scaling of the cumulant generating function near this phase transition, both in the non-equilibrium steady state and for large times.Comment: 18 pages, 11 figure

Bovine tuberculosis surveillance alternatives in Belgium

&lt;p&gt;Belgium obtained the bovine tuberculosis (bTB) officially free status in 2003 (EC Decision 2003/467/EC). This study was carried out to evaluate the components of the current bTB surveillance program in Belgium and to determine the sensitivity of this program. Secondly, alternatives to optimize the bTB surveillance in accordance with European legislation (Council Directive 64/432/EEC) were evaluated. Separate scenario trees were designed for each active surveillance component of the bTB surveillance program. Data from 2005 to 2009 regarding cattle population, movement and surveillance were collected to feed the stochastic scenario tree simulation model. A total of 7,403,826 cattle movement history records were obtained for the 2,678,020 cattle from 36,059 cattle herds still active in 2009. The current surveillance program sensitivity as well as the impact of alternative surveillance protocols was simulated in a stochastic model using 10,000 iterations per simulation. The median (50% percentile) of the component sensitivities across 10,000 iterations was 0.83, 0.85, 0.99, 0.99, respectively, for (i) testing the cattle only during the winter screening, (ii) testing only imported cattle, (iii) testing only purchased cattle and (iv) testing only all slaughtered cattle. The sensitivity analysis showed that the most influential input parameter explaining the variability around the output came from the uncertainty distribution around the sensitivity of the diagnostic tests used within the bTB surveillance. Providing all animals are inspected and post mortem inspection is highly sensitive, slaughterhouse surveillance was the most effective surveillance component. If these conditions were not met, the uncertainty around the mean sensitivity of this component was important. Using an antibody ELISA at purchase and an interferon gamma test during winter screening and at import would increase greatly the sensitivity and the confidence level of Belgium&#039;s freedom from bTB infection status.&lt;/p&gt;</p

Low-density series expansions for directed percolation IV. Temporal disorder

We introduce a model for temporally disordered directed percolation in which the probability of spreading from a vertex $(t,x)$, where $t$ is the time and $x$ is the spatial coordinate, is independent of $x$ but depends on $t$. Using a very efficient algorithm we calculate low-density series for bond percolation on the directed square lattice. Analysis of the series yields estimates for the critical point $p_c$ and various critical exponents which are consistent with a continuous change of the critical parameters as the strength of the disorder is increased.Comment: 11 pages, 3 figure

The effects of mismatches on hybridization in DNA microarrays: determination of nearest neighbor parameters

Quantifying interactions in DNA microarrays is of central importance for a better understanding of their functioning. Hybridization thermodynamics for nucleic acid strands in aqueous solution can be described by the so-called nearest-neighbor model, which estimates the hybridization free energy of a given sequence as a sum of dinucleotide terms. Compared with its solution counterparts, hybridization in DNA microarrays may be hindered due to the presence of a solid surface and of a high density of DNA strands. We present here a study aimed at the determination of hybridization free energies in DNA microarrays. Experiments are performed on custom Agilent slides. The solution contains a single oligonucleotide. The microarray contains spots with a perfect matching complementary sequence and other spots with one or two mismatches: in total 1006 different probe spots, each replicated 15 times per microarray. The free energy parameters are directly fitted from microarray data. The experiments demonstrate a clear correlation between hybridization free energies in the microarray and in solution. The experiments are fully consistent with the Langmuir model at low intensities, but show a clear deviation at intermediate (non-saturating) intensities. These results provide new interesting insights for the quantification of molecular interactions in DNA microarrays.Comment: 31 pages, 5 figure