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Deterministic Constructions of Binary Measurement Matrices from Finite Geometry
Deterministic constructions of measurement matrices in compressed sensing
(CS) are considered in this paper. The constructions are inspired by the recent
discovery of Dimakis, Smarandache and Vontobel which says that parity-check
matrices of good low-density parity-check (LDPC) codes can be used as
{provably} good measurement matrices for compressed sensing under
-minimization. The performance of the proposed binary measurement
matrices is mainly theoretically analyzed with the help of the analyzing
methods and results from (finite geometry) LDPC codes. Particularly, several
lower bounds of the spark (i.e., the smallest number of columns that are
linearly dependent, which totally characterizes the recovery performance of
-minimization) of general binary matrices and finite geometry matrices
are obtained and they improve the previously known results in most cases.
Simulation results show that the proposed matrices perform comparably to,
sometimes even better than, the corresponding Gaussian random matrices.
Moreover, the proposed matrices are sparse, binary, and most of them have
cyclic or quasi-cyclic structure, which will make the hardware realization
convenient and easy.Comment: 12 pages, 11 figure
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The Emerging Role of Ten-Eleven Translocation 1 in Epigenetic Responses to Environmental Exposures.
Mounting evidence from epidemiological studies and animal models has linked exposures to environmental factors to changes in epigenetic markers, especially in DNA methylation. These epigenetic changes may lead to dysregulation of molecular processes and functions and mediate the impact of environmental exposures in complex diseases. However, detailed molecular events that result in epigenetic changes following exposures remain unclear. Here, we review the emerging evidence supporting a critical role of ten-eleven translocation 1 (TET1) in mediating these processes. Targeting TET1 and its associated pathways may have therapeutic potential in alleviating negative impacts of environmental exposures, preventing and treating exposure-related diseases
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