244,781 research outputs found
On Convergence of Approximate Message Passing
Approximate message passing is an iterative algorithm for compressed sensing
and related applications. A solid theory about the performance and convergence
of the algorithm exists for measurement matrices having iid entries of zero
mean. However, it was observed by several authors that for more general
matrices the algorithm often encounters convergence problems. In this paper we
identify the reason of the non-convergence for measurement matrices with iid
entries and non-zero mean in the context of Bayes optimal inference. Finally we
demonstrate numerically that when the iterative update is changed from parallel
to sequential the convergence is restored.Comment: 5 pages, 3 figure
Testing the well-posedness of characteristic evolution of scalar waves
Recent results have revealed a critical way in which lower order terms affect
the well-posedness of the characteristic initial value problem for the scalar
wave equation. The proper choice of such terms can make the Cauchy problem for
scalar waves well posed even on a background spacetime with closed lightlike
curves. These results provide new guidance for developing stable characteristic
evolution algorithms. In this regard, we present here the finite difference
version of these recent results and implement them in a stable evolution code.
We describe test results which validate the code and exhibit some of the
interesting features due to the lower order terms.Comment: 22 pages, 15 figures Submitted to CQ
Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices
Compressed sensing is a signal processing method that acquires data directly
in a compressed form. This allows one to make less measurements than what was
considered necessary to record a signal, enabling faster or more precise
measurement protocols in a wide range of applications. Using an
interdisciplinary approach, we have recently proposed in [arXiv:1109.4424] a
strategy that allows compressed sensing to be performed at acquisition rates
approaching to the theoretical optimal limits. In this paper, we give a more
thorough presentation of our approach, and introduce many new results. We
present the probabilistic approach to reconstruction and discuss its optimality
and robustness. We detail the derivation of the message passing algorithm for
reconstruction and expectation max- imization learning of signal-model
parameters. We further develop the asymptotic analysis of the corresponding
phase diagrams with and without measurement noise, for different distribution
of signals, and discuss the best possible reconstruction performances
regardless of the algorithm. We also present new efficient seeding matrices,
test them on synthetic data and analyze their performance asymptotically.Comment: 42 pages, 37 figures, 3 appendixe
Searching for continuous gravitational wave signals: the hierarchical Hough transform algorithm
It is well known that matched filtering techniques cannot be applied for
searching extensive parameter space volumes for continuous gravitational wave
signals. This is the reason why alternative strategies are being pursued.
Hierarchical strategies are best at investigating a large parameter space when
there exist computational power constraints. Algorithms of this kind are being
implemented by all the groups that are developing software for analyzing the
data of the gravitational wave detectors that will come online in the next
years. In this talk we will report about the hierarchical Hough transform
method that the GEO 600 data analysis team at the Albert Einstein Institute is
developing. The three step hierarchical algorithm has been described elsewhere.
In this talk we will focus on some of the implementational aspects we are
currently concerned with.Comment: 9 pages, 1 figure. To appear in the proceedings of the conference
``Gravitational waves: a challenge to theoretical astrophysics'', (June 5-9
2000, Trieste), ICTP Lecture Notes Serie
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Evolutionary Covariant Positions within Calmodulin EF-hand Sequences Promote Ligand Binding
Intracellular calcium signaling is an essential regulatory mechanism through calcium-mediated signal transduction pathways involved in many cell processes, such as exocytosis, motility, apoptosis, excitability, transcription, and muscle contraction. The calcium-binding, ubiquitous, and highly conserved protein calmodulin (CaM) is an important regulator of hundreds of target proteins involved in cellular calcium signaling. CaM comprises of two pairs of EF-hand calcium-binding domains and these structural regions of the protein are highly conserved. Studying the molecular mechanisms underlying the binding of calcium to the EF-hands of CaM is critical in understanding the calcium-mediated cellular processes and how improper binding of calcium can lead to various human pathologies. Previous site-specific binding measurements indicate that each of the four EF-hands of CaM have distinct affinities for calcium. In this study, we have utilized covariance patterns and site-specific mutagenesis to analyze calcium affinity in the two EF-hands of the N-lobe of CaM in order to determine the specific amino acids that are evolutionarily conserved to coordinate calcium. The specific amino acids in CaM that we studied are theorized to coevolve, which means that in their protein coding genes, when a mutation occurs, a compensatory mutation is likely to follow to conserve structure and function of CaM. Since CaM is a highly conserved protein with a known structure, covariance analyses will help in understanding which amino acid contacts are most important for the coordination of calcium in the EF-hands of CaM and to determine which amino acids are under evolutionary constraint. Covariance algorithms, multiple sequence analyses and accompanied protein structure analyses were used to identify the two high scoring amino acid pairs in the N-lobe EF-hands: positions 22 and 24 in EF-hand site 1 and positions 58 and 60 in EF-hand site 2. The amino acids in these locations were mutated and accompanied calcium binding was measured to better understand the effects of the mutations on calcium binding. We have found that both the D24N mutation in site 1 and the D58N mutation in site 2 disrupt binding likely due to the removal of a necessary aspartate in the binding site. However, the combined D58N and N60D mutations restore binding in site 2 by providing the necessary aspartate in the covariant location. The N60D mutation by itself has little impact on calcium binding in site 2. Therefore, it is evident that evolution conserves at least one aspartate in the covariant positions of the binding site and the presence of two aspartates in the covariant positions of the binding site has little affect on calcium binding. We are currently studying the covariant positions in site 1 and future work includes structurally analyzing the covariant positions in the C-lobe of CaM and studying covariance patterns of other calcium-binding proteins with EF-hand binding domains.Biochemistr
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