Fuelled by a desire for greater connectivity, networked systems now pervade our society at an unprecedented level that will affect it in ways we do not yet understand. In contrast, nature has already developed efficient networks that can instigate rapid response and consensus when key elements are stimulated. We present a technique for identifying these key elements by investigating the relationships between a system’s most dominant eigenvectors. This approach reveals the most effective vertices for leading a network to rapid consensus when stimulated, as well as the communities that form under their dynamical influence. In applying this technique, the effectiveness of starling flocks was found to be due, in part, to the low outdegree of every bird, where increasing the number of outgoing connections can produce a less responsive flock. A larger outdegree also affects the location of the birds with the most influence, where these influentially connected birds become more centrally located and in a poorer position to observe a predator and, hence, instigate an evasion manoeuvre. Finally, the technique was found to be effective in large voxel-wise brain connectomes where subjects can be identified from their influential communities.

No abstract

This version is available at https://strathprints.strath.ac.uk/65072/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. Consensus Speed Optimisation with Finite Leadership Perturbation in k-Nearest Neighbour Networks Ruaridh Clark, Giuliano Punzo and Malcolm MacdonaldAbstract-Near-optimal convergence speeds are found for perturbed networked systems, with N interacting agents that conform to k-nearest neighbour (k-NNR) connection rules, by allocating a finite leadership resource amongst selected nodes. These nodes continue averaging their state with that of their neighbours while being provided with the resources to drive the network to a new state. Such systems are represented by a directed graph Laplacian with two newly presented semianalytical approaches used to maximise the consensus speed. The two methods developed typically produce near-optimal results and are highly efficient when compared with conventional numerical optimisation, where the asymptotic computational complexity is O(n 3 ) and O(n 4 ) respectively. The upper limit for the convergence speed of a perturbed k-NNR network is identified as the largest element of the first left eigenvector (FLE) of a graph's adjacency matrix. The first semi-analytical method exploits this knowledge by distributing leadership resources amongst the most prominent nodes highlighted by this FLE. The second method relies on the FLEs of manipulated versions of the adjacency matrix to expose different communities of influential nodes. These are shown to correspond with the communities found by the Leicht-Newman detection algorithm, with this method enabling optimal leadership selection even in low outdegree (< 12 connections) graphs, where the first semianalytical method is less effective.

Eigenvector alignment, introduced herein to investigate human brain functional networks, is adapted from methods developed to detect influential nodes and communities in networked systems. It is used to identify differences in the brain networks of subjects with Alzheimer’s disease (AD), amnestic Mild Cognitive Impairment (aMCI) and healthy controls (HC). Well-established methods exist for analysing connectivity networks composed of brain regions, including the widespread use of centrality metrics such as eigenvector centrality. However, these metrics provide only limited information on the relationship between regions, with this understanding often sought by comparing the strength of pairwise functional connectivity. Our holistic approach, eigenvector alignment, considers the impact of all functional connectivity changes before assessing the strength of the functional relationship, i.e. alignment, between any two regions. This is achieved by comparing the placement of regions in a Euclidean space defined by the network’s dominant eigenvectors. Eigenvector alignment recognises the strength of bilateral connectivity in cortical areas of healthy control subjects, but also reveals degradation of this commissural system in those with AD. Surprisingly little structural change is detected for key regions in the Default Mode Network, despite significant declines in the functional connectivity of these regions. In contrast, regions in the auditory cortex display significant alignment changes that begin in aMCI and are the most prominent structural changes for those with AD. Alignment differences between aMCI and AD subjects are detected, including notable changes to the hippocampal regions. These findings suggest eigenvector alignment can play a complementary role, alongside established network analytic approaches, to capture how the brain’s functional networks develop and adapt when challenged by disease processes such as AD.

Across the world, many coastal tidal regions are unsafe to navigate due to shifting mud and sand pushed by water currents. Ability to regularly map the current location of a channel will aid safe passage for commercial, leisure and rescue craft. This work investigates the use of synthetic aperture radar data derived from satellites to provide accurate mapping of moving channels in coastal regions. As images must be collected at low tide, data availability is assessed considering the relationship between the orbital motion of the satellites and the tides. Change detection methods are applied to suitable images to map changes in the location of navigable channels. Pixels that undergo similar changes over time (e.g. from water covered to exposed sand) are grouped together by examining the principal component of the covariance matrix, for a vector composed of pixel values from the same location at different times. The Solway Firth in Great Britain is selected as a trial site as it is exposed to some of Europe's fastest tidal movements and ranges, and hence is one of Great Britain's most treacherous stretches of coastline.