517 research outputs found
Could You Read My Heart
https://digitalcommons.library.umaine.edu/mmb-vp/5388/thumbnail.jp
Chemical master equation and Langevin regimes for a gene transcription model
Gene transcription models must take account of intrinsic stochasticity. The Chemical Master Equation framework is based on modelling assumptions that are highly appropriate for this context, and the Stochastic Simulation Algorithm (also known as Gillespie's algorithm) allows for practical simulations to be performed. However, for large networks and/or fast reactions, such computations can be prohibitatively expensive. The Chemical Langevin regime replaces the massive ordinary dierential equation system with a small stochastic dierential equation system that is more amenable to computation. Although the transition from Chemical Master Equation to Chemical Langevin Equation can be justied rigorously in the large system size limit, there is very little guidance available about how closely the two models match for a xed system. Here, we consider a transcription model from the recent literature and show that it is possible to compare rst and second moments in the two stochastic settings. To analyse the Chemical Master Equation we use some recent work of Gadgil, Lee and Othmer, and to analyse the Chemical Langevin Equation we use Ito's Lemma. We nd that there is a perfect match|both modelling regimes give the same means, variances and correlations for all components in the system. The model that we analyse involves 'unimolecular reactions', and we nish with some numerical simulations involving dimerization to show that the means and variances in the two regimes can also be close when more general 'bimolecular reactions' are involved
It Makes A Lot Of Diff\u27rence When You\u27re With The Girl You Love
https://digitalcommons.library.umaine.edu/mmb-vp/1912/thumbnail.jp
Diagonally Neighbour Transitive Codes and Frequency Permutation Arrays
Constant composition codes have been proposed as suitable coding schemes to
solve the narrow band and impulse noise problems associated with powerline
communication. In particular, a certain class of constant composition codes
called frequency permutation arrays have been suggested as ideal, in some
sense, for these purposes. In this paper we characterise a family of neighbour
transitive codes in Hamming graphs in which frequency permutation arrays play a
central rode. We also classify all the permutation codes generated by groups in
this family
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Writ(h)ing Images: Imagination, the Human Form, and the Divine in William Blake, Salman Rushdie, and Simon Louvish
In this paper, we address issues in segmentation Of remotely sensed LIDAR (LIght Detection And Ranging) data. The LIDAR data, which were captured by airborne laser scanner, contain 2.5 dimensional (2.5D) terrain surface height information, e.g. houses, vegetation, flat field, river, basin, etc. Our aim in this paper is to segment ground (flat field)from non-ground (houses and high vegetation) in hilly urban areas. By projecting the 2.5D data onto a surface, we obtain a texture map as a grey-level image. Based on the image, Gabor wavelet filters are applied to generate Gabor wavelet features. These features are then grouped into various windows. Among these windows, a combination of their first and second order of statistics is used as a measure to determine the surface properties. The test results have shown that ground areas can successfully be segmented from LIDAR data. Most buildings and high vegetation can be detected. In addition, Gabor wavelet transform can partially remove hill or slope effects in the original data by tuning Gabor parameters
Breathing dynamics in heteropolymer DNA
While the statistical mechanical description of DNA has a long tradition,
renewed interest in DNA melting from a physics perspective is nourished by
measurements of the fluctuation dynamics of local denaturation bubbles by
single molecule spectroscopy. The dynamical opening of DNA bubbles (DNA
breathing) is supposedly crucial for biological functioning during, for
instance, transcription initiation and DNA's interaction with selectively
single-stranded DNA binding proteins. Motivated by this, we consider the bubble
breathing dynamics in a heteropolymer DNA based on a (2+1)-variable master
equation and complementary stochastic Gillespie simulations, providing the
bubble size and the position of the bubble along the sequence as a function of
time. We utilize new experimental data that independently obtain stacking and
hydrogen bonding contributions to DNA stability. We calculate the spectrum of
relaxation times and the experimentally measurable autocorrelation function of
a fluorophore-quencher tagged base-pair, and demonstrate good agreement with
fluorescence correlation experiments. A significant dependence of opening
probability and waiting time between bubble events on the local DNA sequence is
revealed and quantified for a promoter sequence of the T7 phage. The strong
dependence on sequence, temperature and salt concentration for the breathing
dynamics of DNA found here points at a good potential for nanosensing
applications by utilizing short fluorophore-quencher dressed DNA constructs.Comment: 11 pages, 8 figure
Molecular Distributions in Gene Regulatory Dynamics
We show how one may analytically compute the stationary density of the
distribution of molecular constituents in populations of cells in the presence
of noise arising from either bursting transcription or translation, or noise in
degradation rates arising from low numbers of molecules. We have compared our
results with an analysis of the same model systems (either inducible or
repressible operons) in the absence of any stochastic effects, and shown the
correspondence between behaviour in the deterministic system and the stochastic
analogs. We have identified key dimensionless parameters that control the
appearance of one or two steady states in the deterministic case, or unimodal
and bimodal densities in the stochastic systems, and detailed the analytic
requirements for the occurrence of different behaviours. This approach
provides, in some situations, an alternative to computationally intensive
stochastic simulations. Our results indicate that, within the context of the
simple models we have examined, bursting and degradation noise cannot be
distinguished analytically when present alone.Comment: 14 pages, 12 figures. Conferences: "2010 Annual Meeting of The
Society of Mathematical Biology", Rio de Janeiro (Brazil), 24-29/07/2010.
"First International workshop on Differential and Integral Equations with
Applications in Biology and Medicine", Aegean University, Karlovassi, Samos
island (Greece), 6-10/09/201
Markovian Dynamics on Complex Reaction Networks
Complex networks, comprised of individual elements that interact with each
other through reaction channels, are ubiquitous across many scientific and
engineering disciplines. Examples include biochemical, pharmacokinetic,
epidemiological, ecological, social, neural, and multi-agent networks. A common
approach to modeling such networks is by a master equation that governs the
dynamic evolution of the joint probability mass function of the underling
population process and naturally leads to Markovian dynamics for such process.
Due however to the nonlinear nature of most reactions, the computation and
analysis of the resulting stochastic population dynamics is a difficult task.
This review article provides a coherent and comprehensive coverage of recently
developed approaches and methods to tackle this problem. After reviewing a
general framework for modeling Markovian reaction networks and giving specific
examples, the authors present numerical and computational techniques capable of
evaluating or approximating the solution of the master equation, discuss a
recently developed approach for studying the stationary behavior of Markovian
reaction networks using a potential energy landscape perspective, and provide
an introduction to the emerging theory of thermodynamic analysis of such
networks. Three representative problems of opinion formation, transcription
regulation, and neural network dynamics are used as illustrative examples.Comment: 52 pages, 11 figures, for freely available MATLAB software, see
http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.htm
Induction level determines signature of gene expression noise in cellular systems
Noise in gene expression, either due to inherent stochasticity or to varying
inter- and intracellular environment, can generate significant cell-to-cell
variability of protein levels in clonal populations. We present a theoretical
framework, based on stochastic processes, to quantify the different sources of
gene expression noise taking cell division explicitly into account. Analytical,
time-dependent solutions for the noise contributions arising from the major
steps involved in protein synthesis are derived. The analysis shows that the
induction level of the activator or transcription factor is crucial for the
characteristic signature of the dominant source of gene expression noise and
thus bridges the gap between seemingly contradictory experimental results.
Furthermore, on the basis of experimentally measured cell distributions, our
simulations suggest that transcription factor binding and promoter activation
can be modelled independently of each other with sufficient accuracy
The Dynamics of Health and Return Migration
In the final article in a six-part PLoS Medicine; series on Migration & Health, Anita Davies and colleagues from the International Organization for Migration (IOM) discuss the specific health risks and policy needs associated with return migratio
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