A Framework to Control Functional Connectivity in the Human Brain

In this paper, we propose a framework to control brain-wide functional connectivity by selectively acting on the brain's structure and parameters. Functional connectivity, which measures the degree of correlation between neural activities in different brain regions, can be used to distinguish between healthy and certain diseased brain dynamics and, possibly, as a control parameter to restore healthy functions. In this work, we use a collection of interconnected Kuramoto oscillators to model oscillatory neural activity, and show that functional connectivity is essentially regulated by the degree of synchronization between different clusters of oscillators. Then, we propose a minimally invasive method to correct the oscillators' interconnections and frequencies to enforce arbitrary and stable synchronization patterns among the oscillators and, consequently, a desired pattern of functional connectivity. Additionally, we show that our synchronization-based framework is robust to parameter mismatches and numerical inaccuracies, and validate it using a realistic neurovascular model to simulate neural activity and functional connectivity in the human brain.Comment: To appear in the proceedings of the 58th IEEE Conference on Decision and Contro

Discrete-Time Networks with Diagonal Controllability Gramian

The controllability Gramian of a dynamical network carries rich information of the fundamental properties of the network. How to identify the connections from these fundamental properties to the network topology and weights is of great interest. It is, however, very challenging to do that because the Gramian is an extremely complicated function of the network topology and weights. In this paper, we consider the simplest case where the Gramian is diagonal. One of the main contributions of this paper is to prove the necessary and sufficient graphical conditions for a discrete-time dynamical network to feature a diagonal Gramian. The explicit relations between the values of the diagonal entries of the Gramian and the network weights are also established. The proposed results may be used to design networks with desired control energy and robustness performance

Synchronization Patterns in Networks of Kuramoto Oscillators: A Geometric Approach for Analysis and Control

Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal conditions on the network weights and structure and on the oscillators' natural frequencies that allow the phases of a group of oscillators to evolve cohesively, yet independently from the phases of oscillators in different clusters. Our conditions are applicable to general directed and weighted networks of heterogeneous oscillators. Surprisingly, although the oscillators exhibit nonlinear dynamics, our approach relies entirely on tools from linear algebra and graph theory. Further, we develop a control mechanism to determine the smallest (as measured by the Frobenius norm) network perturbation to ensure the formation of a desired synchronization pattern. Our procedure allows us to constrain the set of edges that can be modified, thus enforcing the sparsity structure of the network perturbation. The results are validated through a set of numerical examples

Morphological and molecular identification of a strain of the unicellular green alga Dunaliella sp. isolated from Tarquinia Salterns

1 - Algae of the genus Dunaliella are among the most studied micro-algae. They are used for the production of feed, for nutritional reinforcement as a vitamin A precursor and for pharmaceuticals and fine chemicals. 2 - The current taxonomy of the genus is based on morphological and physiological attributes including the ability of some species to grow over wide salinity ranges and at extreme salinities, as well as the accumulation of high levels of â-carotene. The taxonomic status of the genus Dunaliella involves some uncertainty, moreover it is very difficult to compare results from different authors, owing to uncertainty on names and species. 3 - In this work, we compare morphological and molecular analysis to characterize a strain of Dunaliella isolated from Tarquinia salt ponds. Samples of natural populations of the unicellular green alga, were collected at various times during the study period to detail the vegetative motile cells and the different stages of its life cycle microscopically. The ITS1 and ITS2 regions were used for the molecular identification analysis. Conserved oligonucleotides of 18S rDNAs (MA3) and speciesspecific primers (DSs), designed from variable sequences, were used to corroborate the identification. 4 - Blast results indicated that our sequences matched at the 100% level with Dunaliella salina Teod reported in Gen Bank. Consequently, based on comparative cell morphology and molecular analysis, the new Dunaliella isolate from Tarquinia salt ponds was classified as D. salina