Synchronization conditions in networks of Hindmarsh-Rose systems

The algebraic connectivity is crucial parameter in studying of synchronization of diffusively coupled networks. This paper studies the synchronization in networks of Hindmarsh-Rose systems, which is one of the most used neuron models. It presents sufficient condition for synchronization in these networks using the Lyapunov function method. This is a simple condition which depends on the algebraic connectivity and on the parameters of the individual system. Numerical examples are presented to illustrate the obtained results.

From single layer to multilayer networks in Mild Cognitive Impairment and Alzheimer’s Disease

We investigate the alterations of functional networks of patients suffering from mild cognitive impairment (MCI) and Alzheimer’s disease (AD) when compared to healthy individuals. Departing from the magnetoencephalographic recordings of these three groups, we construct and analyse the corresponding single layer functional networks at different frequency bands, both at the sensors and the ROIs (regions of interest) levels. Different network parameters show statistically significant differences, with global efficiency being the one having the most pronounced differences between groups. Next, we extend the analyses to the frequency-band multilayer networks of the same dataset. Using the mutual information as a metric to evaluate the coordination between brain regions, we construct the αβ multilayer networks and analyse their algebraic connectivity at baseline λ2−BSL (i.e., the second smallest eigenvalue of the corresponding Laplacian matrices). We report statistically significant differences at the sensor level, despite the fact that these differences are not clearly observed when networks are obtained at the ROIs level (i.e., after a source reconstruction procedure). Next, we modify the weights of the inter-links of the multilayer network to identify the value of the algebraic connectivity λ2−T leading to a transition where layers can be considered to be fully merged. However, differences between the values of λ2−T of the three groups are not statistically significant. Finally, we developed nested multinomial logistic regression models (MNR models), with the aim of predicting group labels with the parameters extracted from the multilayer networks (λ2−BSL and λ2−T ). Using these models, we are able to quantify how age influences the risk of suffering AD and how the algebraic connectivity of frequency-based multilayer functional networks could be used as a biomarker of AD in clinical contexts.

Speeding Up Velocity Consensus Control with Small World Communication Topology for Unmanned Aerial Vehicle Swarms

This study addressed a problem of rapid velocity consensus within a swarm of unmanned aerial vehicles. Our analytical framework was based on tools using matrix theory and algebraic graph theory. We established connections between algebraic connectivity and the speed of converging on a velocity. The relationship between algebraic connectivity and communication cost was established. To deal with the trade-off among algebraic connectivity, convergence speed and communication cost, we propose a distributed small world network construction method. The small world network characteristics expedite the convergence speed toward consensus in the unmanned aerial vehicle swarm. Eventually, our method greatly sped up the consensus velocities in the unmanned aerial vehicle swarms at a lower communication cost than other methods required.

Algebraic Connectivity Control in Distributed Networks by Using Multiple Communication Channels

The effectiveness of collaboration in distributed networks, such as sensor networks and multi-agent systems, relies on nodes’ ability to exchange information. The availability of various communication protocols with different technical properties opens the possibility to guarantee connectivity during a system’s operation in any condition. A communication network can be represented by a graph on which connectivity can be expressed by a well-known algebraic connectivity value or Fiedler value. It is one of the most important tools used in many applications where connectivity preservation is required. In this paper, a trust-based consensus algorithm for algebraic connectivity estimation has been implemented. To guarantee the accomplishment of the global objective and the system’s performance, our contributions include: (i) a novel decentralized framework for combining multiple communication channels in a resulting channel and (ii) a decentralized algebraic connectivity control law that dynamically changes the number of agents in the system during operation. The proposed algebraic connectivity control strategy has been evaluated in simulations and in a real multi-robot system using two channels with different properties and initial topologies.

Comparative transcriptomics of leaves of five mulberry accessions and cataloguing structural and expression variants for future prospects

Bombyx mori, a monophagous insect, prefers leaves of the certain species of Morus more than others. The preference has been attributed to morphological and anatomical features and biochemical compounds. In the present manuscript a comparison has been made among the transcriptome of leaves of the two preferred cultivated varieties and three wild types species. While assembling, high quality transcriptomes of five genotypes were constructed with a total of 100930, 151245, 89724, 181761 and 102908 transcripts from ML, MN, MS, K2 and V1 samples respectively. Further, to compare them, orthologs were identified from these assembled transcriptome. A total of 22462, 23413, 23685, 24371, 18362, 22326, 20058, 18049, 17567 and 20518 clusters of orthologs were found in one to one comparison in KvsN, KvsL, KvsS, KvsV, LvsN, LvsS, LvsV, NvsS, NvsV, and SvsV respectively. 4236 orthologs with algebraic connectivity of 1.0 were then used to compare and to find out differentially expressed transcripts from all the genotypes. A total of 1037 transcripts expressed that include some of the important morphology, anatomy and biochemical pathways regulating transcription factors (AP2/ERFs and C2H2 Zinc fingers) and signalling components were identified to express differentially. Further, these transcriptomes were used find out markers (SSR) and variants and a total of 1101013, 537245, 970877, 310437, 675772, 338400, 581189, 751477, 514999 and 257107 variants including SNP, MNP, Insertions and deletions were found in one to one comparisons. Taken together, our data could be highly useful for mulberry community worldwide as it could be utilized in mulberry breeding programs.

On Consensus Index of Triplex Star-Like Networks: A Graph Spectra Approach

In this article, the consensus-related performances of the triplex multi-agent systems with star-related structures, which can be measured by the algebraic connectivity and network coherence, have been studied by the characterization of Laplacian spectra. Some notions of graph operations are introduced to construct several triplex networks with star substructures. The methods of graph spectra are applied to derive the network coherence, and some asymptotic behaviors of the indices have been derived. It is found that the operations of adhering star topologies will make the first-order coherence increase a constant value under the triplex structures as parameters tend to infinity, and the second-order coherence have some equality relations as the node related parameters tend to infinity. Finally, the consensus related indices of the triplex systems with the same number of nodes but non-isomorphic graph structures have been compared and simulated to verify the results.