5,062 research outputs found

    Rapid polynomial approximation in L2L_2-spaces with Freud weights on the real line

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    The weights Wα(x)=exp(xα)W_\alpha(x)=\exp{(-|x|^{\alpha})} (α>1)(\alpha>1) form a subclass of Freud weights on the real line. Primarily from a functional analytic angle, we investigate the subspace of L2(R,Wα2(x)dx)L_2(\mathbb R, W_\alpha^2(x)\,dx) consisting of those elements that can be rapidly approximated by polynomials. This subspace has a natural Fr\'echet topology, in which it is isomorphic to the space of rapidly decreasing sequences. We show that it consists of smooth functions and obtain concrete results on its topology. For α=2\alpha=2 there is a complete and elementary description of this topological vector space in terms of the Schwartz functions.Comment: 18 page

    Evaluation of genome-wide chromatin library of Stat5 binding sites in human breast cancer

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    BACKGROUND: There is considerable interest in identifying target genes and chromatin binding sites for transcription factors in a genome-wide manner. Such information may become useful in diagnosis and treatment of disease, drug target identification, and for prognostication. In cancer diagnosis, patterns of transcription factor binding to specific regulatory chromatin elements are expected to complement and enhance current diagnostic predictions of tumor behavior based on protein and mRNA analyses. Signal transducer and activator of transcription-5 (Stat5) is a cytokine-activated transcription factor implicated in growth and progression of many malignancies, including hematopoietic, prostate, and breast cancer. We have explored immunoaffinity purification of Stat5-bound chromatin from breast cancer cells to identify Stat5 target sites in an unbiased, genome-wide manner. RESULTS: In this report, we evaluate the efficacy of a Stat5-bound chromatin library to identify valid Stat5 chromatin binding sites within the oncogenome of T-47D human breast cancer cells. A general problem with cloning of immunocaptured, transcription factor-bound chromatin fragments is contamination with non-specific chromatin. However, using an optimized strategy, five out of ten randomly selected clones could be experimentally verified to bind Stat5 both in vitro and in vivo as tested by electrophoretic mobility shift assay and chromatin immunoprecipitation, respectively. While there was no binding to fragments lacking a Stat5 consensus binding sequence, presence of a Stat5 binding sequence did not assure binding. CONCLUSION: A chromatin library coupled with experimental validation may productively identify novel in vivo Stat5 chromatin binding sites in cancer, including abnormal regulatory sites in tumor-specific neochromatin

    Research on vertical relationships of enterprises in the shipping industrial chain

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    Efficient Non-parametric Bayesian Hawkes Processes

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    In this paper, we develop an efficient nonparametric Bayesian estimation of the kernel function of Hawkes processes. The non-parametric Bayesian approach is important because it provides flexible Hawkes kernels and quantifies their uncertainty. Our method is based on the cluster representation of Hawkes processes. Utilizing the stationarity of the Hawkes process, we efficiently sample random branching structures and thus, we split the Hawkes process into clusters of Poisson processes. We derive two algorithms -- a block Gibbs sampler and a maximum a posteriori estimator based on expectation maximization -- and we show that our methods have a linear time complexity, both theoretically and empirically. On synthetic data, we show our methods to be able to infer flexible Hawkes triggering kernels. On two large-scale Twitter diffusion datasets, we show that our methods outperform the current state-of-the-art in goodness-of-fit and that the time complexity is linear in the size of the dataset. We also observe that on diffusions related to online videos, the learned kernels reflect the perceived longevity for different content types such as music or pets videos
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