70,734 research outputs found
Linear Transformations for Randomness Extraction
Information-efficient approaches for extracting randomness from imperfect
sources have been extensively studied, but simpler and faster ones are required
in the high-speed applications of random number generation. In this paper, we
focus on linear constructions, namely, applying linear transformation for
randomness extraction. We show that linear transformations based on sparse
random matrices are asymptotically optimal to extract randomness from
independent sources and bit-fixing sources, and they are efficient (may not be
optimal) to extract randomness from hidden Markov sources. Further study
demonstrates the flexibility of such constructions on source models as well as
their excellent information-preserving capabilities. Since linear
transformations based on sparse random matrices are computationally fast and
can be easy to implement using hardware like FPGAs, they are very attractive in
the high-speed applications. In addition, we explore explicit constructions of
transformation matrices. We show that the generator matrices of primitive BCH
codes are good choices, but linear transformations based on such matrices
require more computational time due to their high densities.Comment: 2 columns, 14 page
Coarse-graining in retrodictive quantum state tomography
Quantum state tomography often operates in the highly idealised scenario of
assuming perfect measurements. The errors implied by such an approach are
entwined with other imperfections relating to the information processing
protocol or application of interest. We consider the problem of retrodicting
the quantum state of a system, existing prior to the application of random but
known phase errors, allowing those errors to be separated and removed. The
continuously random nature of the errors implies that there is only one click
per measurement outcome -- a feature having a drastically adverse effect on
data-processing times. We provide a thorough analysis of coarse-graining under
various reconstruction algorithms, finding dramatic increases in speed for only
modest sacrifices in fidelity
Bacterial Community Reconstruction Using A Single Sequencing Reaction
Bacteria are the unseen majority on our planet, with millions of species and
comprising most of the living protoplasm. While current methods enable in-depth
study of a small number of communities, a simple tool for breadth studies of
bacterial population composition in a large number of samples is lacking. We
propose a novel approach for reconstruction of the composition of an unknown
mixture of bacteria using a single Sanger-sequencing reaction of the mixture.
This method is based on compressive sensing theory, which deals with
reconstruction of a sparse signal using a small number of measurements.
Utilizing the fact that in many cases each bacterial community is comprised of
a small subset of the known bacterial species, we show the feasibility of this
approach for determining the composition of a bacterial mixture. Using
simulations, we show that sequencing a few hundred base-pairs of the 16S rRNA
gene sequence may provide enough information for reconstruction of mixtures
containing tens of species, out of tens of thousands, even in the presence of
realistic measurement noise. Finally, we show initial promising results when
applying our method for the reconstruction of a toy experimental mixture with
five species. Our approach may have a potential for a practical and efficient
way for identifying bacterial species compositions in biological samples.Comment: 28 pages, 12 figure
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