Statistical model for dynamically-changing correlation matrices with application to brain connectivity

BACKGROUND

Recent studies have indicated that functional connectivity is dynamic even during rest. A common approach to modeling the dynamic functional connectivity in whole-brain resting-state fMRI is to compute the correlation between anatomical regions via sliding time windows. However, the direct use of the sample correlation matrices is not reliable due to the image acquisition and processing noises in resting-sate fMRI.

NEW METHOD

To overcome these limitations, we propose a new statistical model that smooths out the noise by exploiting the geometric structure of correlation matrices. The dynamic correlation matrix is modeled as a linear combination of symmetric positive-definite matrices combined with cosine series representation. The resulting smoothed dynamic correlation matrices are clustered into disjoint brain connectivity states using the k-means clustering algorithm.

RESULTS

The proposed model preserves the geometric structure of underlying physiological dynamic correlation, eliminates unwanted noise in connectivity and obtains more accurate state spaces. The difference in the estimated dynamic connectivity states between males and females is identified.

COMPARISON WITH EXISTING METHODS

We demonstrate that the proposed statistical model has less rapid state changes caused by noise and improves the accuracy in identifying and discriminating different states.

CONCLUSIONS

We propose a new regression model on dynamically changing correlation matrices that provides better performance over existing windowed correlation and is more reliable for the modeling of dynamic connectivity.

From Chilean Patagonia to Galapagos, Ecuador: novel insights on blue whale migratory pathways along the Eastern South Pacific

Background

The most traditional scheme for migration among baleen whales comprises yearly migrations between productive waters at high latitude summer feeding grounds and warmer waters at lower latitudes where whales calve and mate, but rarely feed. Evidence indicates, however, that large departures from this scheme exist among populations and individuals. Furthermore, for some populations there is virtually no information on migratory pathways and destinations. Such is the case of Chilean blue whales throughout the Eastern South Pacific; hence, the goal of this study was to assess its migratory behavior.

Methods

Dedicated marine surveys and satellite tagging efforts were undertaken during the austral summer and early autumn on blue whale feeding grounds off Chilean Northern Patagonia (CNP) during 2013, 2015 and 2016. Positional data derived from satellite tags regarding movement patterns and behavior were analyzed using Bayesian switching first-difference correlated random walk models.

Results

We instrumented 10 CNP blue whales with satellite transmitters and documented individual variation in departure time, northbound migratory routes and potential wintering grounds. The onset of migration occurred from mid/late austral autumn to well into the austral winter. Blue whales moved in various directions, but ultimately converged toward a general NW movement direction along a wide corridor exceeding 2,000 km. Area-Restricted Search behavior was exhibited within fjords and channels of CNP and also South of Galapagos Archipelago (GA) and northern Peru, but never during migration. Interestingly, dive profiles for one whale that reached GA showed a sharp and consistent increase in depth north of 5°S and extreme deep dives of up to 330 m.

Discussion

Information derived from satellite tagged blue whales in this study is the first of its kind off the Eastern Southern Pacific. Our results provide valuable information on their migratory timing, routes and behavior on their northbound migration, particularly regarding the varied migratory plasticity for this particular population. Our results also highlight the first record of two complete migratory paths between CNP and GA and strengthen the hypothesis that GA waters correspond to a potential wintering destination for CNP blue whales. We further hypothesize that this area might be selected because of its biological productivity, which could provide feeding opportunities during the breeding season. Our results suggest that special efforts should be put forward to identify blue whale critical areas and understand key behavioral aspects in order to provide the basis for their conservation on a regional context (i.e., reducing potential ship strike and promote Marine Protected Area (MPA) implementation in Chile, Ecuador and Peru). Indeed, we suggest joint blue whale conservation efforts at the regional level in order to identify and determine potential threats and impacts and, most importantly, implement prospective management actions.

Improved design of constrained model predictive tracking control for batch processes against unknown uncertainties

In this paper, an improved constrained tracking control design is proposed for batch processes under uncertainties. A new process model that facilitates process state and tracking error augmentation with further additional tuning is first proposed. Then a subsequent controller design is formulated using robust stable constrained MPC optimization. Unlike conventional robust model predictive control (MPC), the proposed method enables the controller design to bear more degrees of tuning so that improved tracking control can be acquired, which is very important since uncertainties exist inevitably in practice and cause model/plant mismatches. An injection molding process is introduced to illustrate the effectiveness of the proposed MPC approach in comparison with conventional robust MPC.