116,789 research outputs found
Motif Statistics and Spike Correlations in Neuronal Networks
Motifs are patterns of subgraphs of complex networks. We studied the impact
of such patterns of connectivity on the level of correlated, or synchronized,
spiking activity among pairs of cells in a recurrent network model of integrate
and fire neurons. For a range of network architectures, we find that the
pairwise correlation coefficients, averaged across the network, can be closely
approximated using only three statistics of network connectivity. These are the
overall network connection probability and the frequencies of two second-order
motifs: diverging motifs, in which one cell provides input to two others, and
chain motifs, in which two cells are connected via a third intermediary cell.
Specifically, the prevalence of diverging and chain motifs tends to increase
correlation. Our method is based on linear response theory, which enables us to
express spiking statistics using linear algebra, and a resumming technique,
which extrapolates from second order motifs to predict the overall effect of
coupling on network correlation. Our motif-based results seek to isolate the
effect of network architecture perturbatively from a known network state
Model selection and sensitivity analysis for sequence pattern models
In this article we propose a maximal a posteriori (MAP) criterion for model
selection in the motif discovery problem and investigate conditions under which
the MAP asymptotically gives a correct prediction of model size. We also
investigate robustness of the MAP to prior specification and provide guidelines
for choosing prior hyper-parameters for motif models based on sensitivity
considerations.Comment: Published in at http://dx.doi.org/10.1214/193940307000000301 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
Spectral flow in the supersymmetric - model with a interaction
The spectral flow in the supersymmetric {\it t-J} model with
interaction is studied by analyzing the exact spectrum with twisted boundary
conditions. The spectral flows for the charge and spin sectors are shown to
nicely fit in with the motif picture in the asymptotic Bethe ansatz. Although
fractional exclusion statistics for the spin sector clearly shows up in the
period of the spectral flow at half filling, such a property is generally
hidden once any number of holes are doped, because the commensurability
condition in the motif is not met in the metallic phase.Comment: 8 pages, revtex, Phys. Rev. B54 (1996) August 15, in pres
Equi-energy sampler with applications in statistical inference and statistical mechanics
We introduce a new sampling algorithm, the equi-energy sampler, for efficient
statistical sampling and estimation. Complementary to the widely used
temperature-domain methods, the equi-energy sampler, utilizing the
temperature--energy duality, targets the energy directly. The focus on the
energy function not only facilitates efficient sampling, but also provides a
powerful means for statistical estimation, for example, the calculation of the
density of states and microcanonical averages in statistical mechanics. The
equi-energy sampler is applied to a variety of problems, including exponential
regression in statistics, motif sampling in computational biology and protein
folding in biophysics.Comment: This paper discussed in: [math.ST/0611217], [math.ST/0611219],
[math.ST/0611221], [math.ST/0611222]. Rejoinder in [math.ST/0611224].
Published at http://dx.doi.org/10.1214/009053606000000515 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
DNA Motif Match Statistics Without Poisson Approximation
Transcription factors (TFs) play a crucial role in gene regulation by binding to specific regulatory sequences. The sequence motifs recognized by a TF can be described in terms of position frequency matrices. Searching for motif matches with a given position frequency matrix is achieved by employing a predefined score cutoff and subsequently counting the number of matches above this cutoff. In this article, we approximate the distribution of the number of motif matches based on a novel dynamic programming approach, which accounts for higher order sequence background (e.g., as is characteristic for CpG islands) and overlapping motif matches on both DNA strands. A comparison with our previously published compound Poisson approximation and a binomial approximation demonstrates that in particular for relaxed score thresholds, the dynamic programming approach yields more accurate results
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