The effect of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class is studied by a strong disorder renormalization group approach and by density matrix renormalization group calculations. We show that for sufficiently strong disorder the critical behavior is controlled by a strong disorder fixed point and in one dimension the critical exponents are conjectured to be exact: beta=(3-sqrt[5])/2 and nu( perpendicular )=2. For disorder strengths outside the attractive region of this fixed point, disorder dependent critical exponents are detected. Existing numerical results in two dimensions can be interpreted within a similar scenario.

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Quenched disorder -in the sense of the Harris criterion -is generally a relevant perturbation at an absorbing state phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class. For strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point, which is isomorph with the fixed point of random quantum Ising systems. In this fixed point dynamical correlations are logarithmically slow and the static critical exponents are conjecturedly exact for one-dimensional systems. The renormalization group scenario is confronted with numerical results on the random contact process in one and two dimensions and satisfactory agreement is found. For weaker disorder the numerical results indicate static critical exponents which vary with the strength of disorder, whereas the dynamical correlations are compatible with two possible scenarios. Either they follow a power-law decay with a varying dynamical exponent, like in random quantum systems, or the dynamical correlations are logarithmically slow even for weak disorder. For models in the parity conserving universality class there is no strong disorder fixed point according to our renormalization group analysis.

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Cumulants of a fluctuating current can be obtained from a free energy-like generating function which for Markov processes equals the largest eigenvalue of a generalized generator. We determine this eigenvalue with the DMRG for stochastic systems. We calculate the variance of the current in the different phases, and at the phase transitions, of the totally asymmetric exclusion process. Our results can be described in the terms of a scaling ansatz that involves the dynamical exponent z. We also calculate the generating function of the activity near the absorbing state transition of the contact process. Its scaling properties can be expressed in terms of known critical exponents. PACS numbers:Physical systems that are in contact with two reservoirs at a different temperature or chemical potential, develop a heat or particle current [1]. In macroscopic systems, fluctuations of these currents can often be neglected. As is the case in equilibrium systems, one can however expect that such fluctuations become important in mesoscopic systems and in the vicinity of a nonequilibrium critical point [2].The statistics of current fluctuations in mesoscopic conductors have received a lot of attention in the past decade [3], since they can, for example, give insight on correlated electron transport. It is nowadays possible to measure experimentally third and higher order cumulants of the current in problems of charge transport [4,5]. Theoretically, these cumulants can be obtained as derivatives of a generating function. This function has many similarities to the free energy in equilibrium systems.In the present Letter, we focus on the scaling of the current distribution in one-dimensional (classical) stochastic models such as the (a)symmetric exclusion process. This stochastic process is a standard model of non-equilibrium statistical mechanics [6,7]. Rigorous results are known for the current distribution in this model both on a ring and for open boundaries [8,9,10,11]. Moreover, several approximate and numerical approaches to this problem have been developped: simulation techniques that sample rare events [12,13], renormalisation approaches [14] and perturbation techniques [15]. Here we apply for the first time the density matrix renormalisation group (DMRG) to the investigation of current fluctuations. We illustrate the method for the current of the totally asymmetric exclusion process, but the technique is more general. As an example we also present results on the total number of changes of configuration (a quantity that has been called activity [16]) in the contact process [2].In the totally asymmetric exclusion process (TASEP), each site of a one-dimensional lattice of L sites can be empty or occupied by at most one particle. The dynamics of the model is a continuous time Markov process in which a particle hops to its right neighbor with unit rate provided that site is empty. At the left boundary particles enter the system with rate α, while at the right boundary they leave it with rate β. Asymptotically, the TASEP reache...

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 (PM) complementary sequence and other spots with one or two mismatches (MM) : 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.

Although the exact role in the disease development or physiological state of the airways of the proteins described in the presented pattern is not clear at this moment, this is an important step in the search for exhaled biomarkers for asthma. This study shows that EBC contains proteins that are of interest for future non-invasive asthma diagnosis or follow-up.

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