A renormalization group study of a class of reaction-diffusion model, with particles input

We study a class of reaction-diffusion model extrapolating continuously between the pure coagulation-diffusion case ($A+A\to A$) and the pure annihilation-diffusion one ($A+A\to\emptyset$) with particles input ($\emptyset\to A$) at a rate $J$. For dimension $d\leq 2$, the dynamics strongly depends on the fluctuations while, for $d >2$, the behaviour is mean-field like. The models are mapped onto a field theory which properties are studied in a renormalization group approach. Simple relations are found between the time-dependent correlation functions of the different models of the class. For the pure coagulation-diffusion model the time-dependent density is found to be of the form $c(t,J,D) = (J/D)^{1/\delta}{\cal F}[(J/D)^{\Delta} Dt]$, where $D$ is the diffusion constant. The critical exponent $\delta$ and $\Delta$ are computed to all orders in $\epsilon=2-d$, where $d$ is the dimension of the system, while the scaling function $\cal F$ is computed to second order in $\epsilon$. For the one-dimensional case an exact analytical solution is provided which predictions are compared with the results of the renormalization group approach for $\epsilon=1$.Comment: Ten pages, using Latex and IOP macro. Two latex figures. Submitted to Journal of Physics A. Also available at http://mykonos.unige.ch/~rey/publi.htm

Equilibrium statistical mechanics on correlated random graphs

Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists and/or, typically, such interactions are essentially (weighted) imitative. Despite such aspects are widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a-priori assumptions and in most cases still implement constant intensities for links. Here we propose a simple shift in the definition of patterns in an Hopfield model to convert frustration into dilution: By varying the bias of the pattern distribution, the network topology -which is generated by the reciprocal affinities among agents - crosses various well known regimes (fully connected, linearly diverging connectivity, extreme dilution scenario, no network), coupled with small world properties, which, in this context, are emergent and no longer imposed a-priori. The model is investigated at first focusing on these topological properties of the emergent network, then its thermodynamics is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality. At least at equilibrium, dilution simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations and a naive picture is that within our approach replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible sub-graphs belonging to the main one investigated: As a consequence, for these objects a closure for a self-consistent relation is achieved.Comment: 30 pages, 4 figure

Transcriptional Dynamics Reveal Critical Roles for Non-coding RNAs in the Immediate-Early Response

<div><p>The immediate-early response mediates cell fate in response to a variety of extracellular stimuli and is dysregulated in many cancers. However, the specificity of the response across stimuli and cell types, and the roles of non-coding RNAs are not well understood. Using a large collection of densely-sampled time series expression data we have examined the induction of the immediate-early response in unparalleled detail, across cell types and stimuli. We exploit cap analysis of gene expression (CAGE) time series datasets to directly measure promoter activities over time. Using a novel analysis method for time series data we identify transcripts with expression patterns that closely resemble the dynamics of known immediate-early genes (IEGs) and this enables a comprehensive comparative study of these genes and their chromatin state. Surprisingly, these data suggest that the earliest transcriptional responses often involve promoters generating non-coding RNAs, many of which are produced in advance of canonical protein-coding IEGs. IEGs are known to be capable of induction without de novo protein synthesis. Consistent with this, we find that the response of both protein-coding and non-coding RNA IEGs can be explained by their transcriptionally poised, permissive chromatin state prior to stimulation. We also explore the function of non-coding RNAs in the attenuation of the immediate early response in a small RNA sequencing dataset matched to the CAGE data: We identify a novel set of microRNAs responsible for the attenuation of the IEG response in an estrogen receptor positive cancer cell line. Our computational statistical method is well suited to meta-analyses as there is no requirement for transcripts to pass thresholds for significant differential expression between time points, and it is agnostic to the number of time points per dataset.</p></div