5,094 research outputs found
Product Hardy spaces associated to operators with heat kernel bounds on spaces of homogeneous type
The aim of this article is to develop the theory of product Hardy spaces
associated with operators which possess the weak assumption of Davies--Gaffney
heat kernel estimates, in the setting of spaces of homogeneous type. We also
establish a Calder\'on--Zygmund decomposition on product spaces, which is of
independent interest, and use it to study the interpolation of these product
Hardy spaces. We then show that under the assumption of generalized Gaussian
estimates, the product Hardy spaces coincide with the Lebesgue spaces, for an
appropriate range of~.Comment: Accepted by Math.
Brain mapping and detection of functional patterns in fMRI using wavelet transform; application in detection of dyslexia
Background
Functional Magnetic Resonance Imaging (fMRI) has been proven to be useful for studying brain functions. However, due to the existence of noise and distortion, mapping between the fMRI signal and the actual neural activity is difficult. Because of the difficulty, differential pattern analysis of fMRI brain images for healthy and diseased cases is regarded as an important research topic. From fMRI scans, increased blood ows can be identified as activated brain regions. Also, based on the multi-sliced images of the volume data, fMRI provides the functional information for detecting and analyzing different parts of the brain. Methods
In this paper, the capability of a hierarchical method that performed an optimization algorithm based on modified maximum model (MCM) in our previous study is evaluated. The optimization algorithm is designed by adopting modified maximum correlation model (MCM) to detect active regions that contain significant responses. Specifically, in the study, the optimization algorithm is examined based on two groups of datasets, dyslexia and healthy subjects to verify the ability of the algorithm that enhances the quality of signal activities in the interested regions of the brain. After verifying the algorithm, discrete wavelet transform (DWT) is applied to identify the difference between healthy and dyslexia subjects. Results
We successfully showed that our optimization algorithm improves the fMRI signal activity for both healthy and dyslexia subjects. In addition, we found that DWT based features can identify the difference between healthy and dyslexia subjects. Conclusion
The results of this study provide insights of associations of functional abnormalities in dyslexic subjects that may be helpful for neurobiological identification from healthy subject
A Hybrid Mechanism Forming a 2:1 Librating-Circulating Resonant Configuration in the Planetary System
A diversity of resonance configurations may be formed under different
migration of two giant planets. And the researchers show that the HD 128311 and
HD 73526 planetary systems are involved in a 2:1 mean motion resonance but not
in apsidal corotation, because one of the resonance argument circulates over
the dynamical evolution. In this paper, we investigate potential mechanisms to
form the 2:1 librating-circulating resonance configuration.
In the late stage of planetary formation, scattering or colliding among
planetesimals and planetary embryos can frequently occur. Hence, in our model,
we consider a planetary configuration of two giants together with few
terrestrial planets. We find that both colliding or scattering events at very
early stage of dynamical evolution can influence the configurations trapped
into resonance. A planet-planet scattering of a moderate terrestrial planet, or
multiple scattering of smaller planets in a crowded planetary system can change
the resonant configuration. In addition, collision or merging can alter the
masses and location of the giant planets, which also play an important role in
shaping the resonant configuration during the dynamical evolution. In this
sense, the librating-circulating resonance configuration is more likely to form
by a hybrid mechanism of scattering and collision.Comment: 8 pages, 5 figures, 2 Tables, accepted for publication in MNRA
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