Lag-invariant detection of interactions in spatially-extended systems using linear inverse modeling

Measurements on physical systems result from the systems’ activity being converted into sensor measurements by a forward model. In a number of cases, inversion of the forward model is extremely sensitive to perturbations such as sensor noise or numerical errors in the forward model. Regularization is then required, which introduces bias in the reconstruction of the systems’ activity. One domain in which this is particularly problematic is the reconstruction of interactions in spatially-extended complex systems such as the human brain. Brain interactions can be reconstructed from non-invasive measurements such as electroencephalography (EEG) or magnetoencephalography (MEG), whose forward models are linear and instantaneous, but have large null-spaces and high condition numbers. This leads to incomplete unmixing of the forward models and hence to spurious interactions. This motivated the development of interaction measures that are exclusively sensitive to lagged, i.e. delayed interactions. The drawback of such measures is that they only detect interactions that have sufficiently large lags and this introduces bias in reconstructed brain networks. We introduce three estimators for linear interactions in spatially-extended systems that are uniformly sensitive to all lags. We derive some basic properties of and relationships between the estimators and evaluate their performance using numerical simulations from a simple benchmark model.

Mapping of Substrate Categories Changes in Exposure to Coral Reefs Using Alos Avnir-2 and Spot 7 Images in The South Area of Kotabaru District

The South of Pulau Laut is an area in the which is included in the Coral Triangle and Aquatic Conservation Areas. The purpose of this study was to map changes in the extent of coral reefs based on the class of substrate categories and objects on exposure to coral reefs in the southern waters of Sea Island within 6 years from 2011- 2017 using SPOT 7 satellite imagery in 2017 and AVNIR ALOS-2 in 2011. Using the method of Lyzenga Dept Index for basic invariant detection of waters. Based on the results of substrate-based classification using both satellite images overlaye, there has been a decline for the coral category as much as -19.21 ha, seagrass and algae as much as -3.57 ha. On the Contrary, the category of open substrate has Increased by 22.77 ha. Object-based classification results using the Object Based Image Analysis (OBIA) method have a reduction in area for the hard coral category (HC) of -1.66 ha, hard sand mixed with sand (HC S) of -15.99 ha, dead coral overgrown with algae and sand (DCA S) of -0.39 ha, algae and seagrass (FS) covering an area of ​​-1.65 ha, sand-mixed coral fragments (RS) of 4:45 ha. On the other hand, there was an increase of in the area.