Variable-free exploration of stochastic models: a gene regulatory network example

Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these complex systems and (b) characterizing the dynamics of the observables. In a previous paper [13], we assumed that good observables were known a priori, and presented an equation-free approach to approximate coarse-grained quantities (i.e, effective drift and diffusion coefficients) that characterize the long-time behavior of the observables. Here we use diffusion maps [9] to extract appropriate observables ("reduction coordinates") in an automated fashion; these involve the leading eigenvectors of a weighted Laplacian on a graph constructed from network simulation data. We present lifting and restriction procedures for translating between physical variables and these data-based observables. These procedures allow us to perform equation-free coarse-grained, computations characterizing the long-term dynamics through the design and processing of short bursts of stochastic simulation initialized at appropriate values of the data-based observables.Comment: 26 pages, 9 figure

A FLAMINGOS Deep Near Infrared Imaging Survey of the Rosette Complex I: Identification and Distribution of the Embedded Population

We present the results of a deep near-infrared imaging survey of the Rosette Complex. We studied the distribution of young embedded sources using a variation of the Nearest Neighbor Method applied to a carefully selected sample of near-infrared excess (NIRX) stars which trace the latest episode of star formation in the complex. Our analysis confirmed the existence of seven clusters previously detected in the molecular cloud, and identified four more clusters across the complex. We determined that 60% of the young stars in the complex and 86% of the stars within the molecular cloud are contained in clusters, implying that the majority of stars in the Rosette formed in embedded clusters. We compare the sizes, infrared excess fractions and average extinction towards individual clusters to investigate their early evolution and expansion. We found that the average infrared excess fraction of clusters increases as a function of distance from NGC 2244, implying a temporal sequence of star formation across the complex. This sequence appears to be primordial, possibly resulting from the formation and evolution of the molecular cloud and not from the interaction with the HII region.Comment: Accepted by Astrophysical Journa

A Disk Shadow Around the Young Star ASR 41 in NGC 1333

We present images of the young stellar object ASR 41 in the NGC 1333 star forming region at the wavelengths of H_alpha and [SII] and in the I, J, H, and K-bands. ASR 41 has the near-infrared morphology of an edge-on disk object, but appears an order of magnitude larger than typical systems of this kind. We also present detailed models of the scattering and radiative transfer in systems consisting of a young star surrounded by a proto-planetary disk, and the whole system being embedded in either an infalling envelope or a uniform molecular cloud. The best fit to the observed morphology can be achieved with a disk of approx. 200 AU diameter, immersed in a low density cloud. The low cloud density is necessary to stay below the sub-mm flux upper limits and to preserve the shadow cast by the disk via single scattering. The results demonstrate that ASR 41 is probably not inherently different from typical edge-on disk objects, and that its large apparent size is due to the shadow of a much smaller disk being projected into the surrounding dusty molecular material

Directed motion emerging from two coupled random processes: Translocation of a chain through a membrane nanopore driven by binding proteins

We investigate the translocation of a stiff polymer consisting of M monomers through a nanopore in a membrane, in the presence of binding particles (chaperones) that bind onto the polymer, and partially prevent backsliding of the polymer through the pore. The process is characterized by the rates: k for the polymer to make a diffusive jump through the pore, q for unbinding of a chaperone, and the rate q kappa for binding (with a binding strength kappa); except for the case of no binding kappa=0 the presence of the chaperones give rise to an effective force that drives the translocation process. Based on a (2+1) variate master equation, we study in detail the coupled dynamics of diffusive translocation and (partial) rectification by the binding proteins. In particular, we calculate the mean translocation time as a function of the various physical parameters.Comment: 22 pages, 5 figures, IOP styl