On Linearly Constrained Minimum Variance Beamforming

Beamforming is a widely used technique for source localization in signal processing and neuroimaging. A number of vector-beamformers have been introduced to localize neuronal activity by using magnetoencephalography (MEG) data in the literature. However, the existing theoretical analyses on these beamformers have been limited to simple cases, where no more than two sources are allowed in the associated model and the theoretical sensor covariance is also assumed known. The information about the effects of the MEG spatial and temporal dimensions on the consistency of vector-beamforming is incomplete. In the present study, we consider a class of vector-beamformers defined by thresholding the sensor covariance matrix, which include the standard vector-beamformer as a special case. A general asymptotic theory is developed for these vector-beamformers, which shows the extent of effects to which the MEG spatial and temporal dimensions on estimating the neuronal activity index. The performances of the proposed beamformers are assessed by simulation studies. Superior performances of the proposed beamformers are obtained when the signal-to-noise ratio is low. We apply the proposed procedure to real MEG datasets derived from five sessions of a human face-perception experiment, finding several highly active areas in the brain. A good agreement between these findings and the known neurophysiology of the MEG response to human face perception is shown

Vacuum Stability and Higgs Diphoton Decay Rate in the Zee-Babu Model

Although recent Higgs data from ATLAS and CMS are compatible with a Standard Model (SM) signal at $2\sigma$ level, both experiments see indications for an excess in the diphoton decay channel, which points to new physics beyond the SM. Given such a low Higgs mass $m_H \sim 125 {\rm GeV}$, another sign indicating the existence of new physics beyond the SM is the vacuum stability problem, i.e., the SM Higgs quartic coupling may run to negative values at a scale below the Planck scale. In this paper, we study the vacuum stability and enhanced Higgs diphoton decay rate in the Zee-Babu model, which was used to generate tiny Majorana neutrino masses at two-loop level. We find that it is rather difficult to find overlapping regions allowed by the vacuum stability and diphoton enhancement constraints. As a consequence, it is almost inevitable to introduce new ingredients into the model, in order to resolve these two issues simultaneously.Comment: 19 pages, 6 figure