Structural Vulnerability Analysis of Electric Power Distribution Grids

Power grid outages cause huge economical and societal costs. Disruptions in the power distribution grid are responsible for a significant fraction of electric power unavailability to customers. The impact of extreme weather conditions, continuously increasing demand, and the over-ageing of assets in the grid, deteriorates the safety of electric power delivery in the near future. It is this dependence on electric power that necessitates further research in the power distribution grid security assessment. Thus measures to analyze the robustness characteristics and to identify vulnerabilities as they exist in the grid are of utmost importance. This research investigates exactly those concepts- the vulnerability and robustness of power distribution grids from a topological point of view, and proposes a metric to quantify them with respect to assets in a distribution grid. Real-world data is used to demonstrate the applicability of the proposed metric as a tool to assess the criticality of assets in a distribution grid

Inference of Ancestral Recombination Graphs through Topological Data Analysis

The recent explosion of genomic data has underscored the need for interpretable and comprehensive analyses that can capture complex phylogenetic relationships within and across species. Recombination, reassortment and horizontal gene transfer constitute examples of pervasive biological phenomena that cannot be captured by tree-like representations. Starting from hundreds of genomes, we are interested in the reconstruction of potential evolutionary histories leading to the observed data. Ancestral recombination graphs represent potential histories that explicitly accommodate recombination and mutation events across orthologous genomes. However, they are computationally costly to reconstruct, usually being infeasible for more than few tens of genomes. Recently, Topological Data Analysis (TDA) methods have been proposed as robust and scalable methods that can capture the genetic scale and frequency of recombination. We build upon previous TDA developments for detecting and quantifying recombination, and present a novel framework that can be applied to hundreds of genomes and can be interpreted in terms of minimal histories of mutation and recombination events, quantifying the scales and identifying the genomic locations of recombinations. We implement this framework in a software package, called TARGet, and apply it to several examples, including small migration between different populations, human recombination, and horizontal evolution in finches inhabiting the Gal\'apagos Islands.Comment: 33 pages, 12 figures. The accompanying software, instructions and example files used in the manuscript can be obtained from https://github.com/RabadanLab/TARGe

Analysing Human Mobility Patterns of Hiking Activities through Complex Network Theory

The exploitation of high volume of geolocalized data from social sport tracking applications of outdoor activities can be useful for natural resource planning and to understand the human mobility patterns during leisure activities. This geolocalized data represents the selection of hike activities according to subjective and objective factors such as personal goals, personal abilities, trail conditions or weather conditions. In our approach, human mobility patterns are analysed from trajectories which are generated by hikers. We propose the generation of the trail network identifying special points in the overlap of trajectories. Trail crossings and trailheads define our network and shape topological features. We analyse the trail network of Balearic Islands, as a case of study, using complex weighted network theory. The analysis is divided into the four seasons of the year to observe the impact of weather conditions on the network topology. The number of visited places does not decrease despite the large difference in the number of samples of the two seasons with larger and lower activity. It is in summer season where it is produced the most significant variation in the frequency and localization of activities from inland regions to coastal areas. Finally, we compare our model with other related studies where the network possesses a different purpose. One finding of our approach is the detection of regions with relevant importance where landscape interventions can be applied in function of the communities.Comment: 20 pages, 9 figures, accepte

The SIMIAN architecture-an object-orientated framework for integrated power system modelling, analysis and control

This paper details the work conducted by the Brunel Institute of Power Systems, UK, into an object orientated framework for power systems modelling, analysis and control. Based around a central OODBMS (object orientated database management system), the architecture provides a framework for the construction of analysis and control applications and the sharing of calculated or real-time data between the applications. Although the paper details the architecture only in so far as its applicability to two applications, the framework is designed such that further applications, either client output (such as control applications) or input(such as SCADA systems) may easily be added to the basic structure. To illustrate the architecture, a load flow simulation application is presented, along with the strategy for incorporating other applications. The mechanism by which these `applications' interact with the OODBMS and core structure of the architecture is illustrate

ELASTICITY: Topological Characterization of Robustness in Complex Networks

Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex networks defines the resolve of a network to maintain functionality in the advent of classical component failures and at the onset of cryptic malicious attacks. To date, robustness metrics are deficient and unfortunately the following dilemmas exist: accurate models necessitate complex analysis while conversely, simple models lack applicability to our definition of robustness. In this paper, we define robustness and present a novel metric, elasticity- a bridge between accuracy and complexity-a link in the chain of network robustness. Additionally, we explore the performance of elasticity on Internet topologies and online social networks, and articulate results

Topological fluid mechanics of point vortex motions

Topological techniques are used to study the motions of systems of point vortices in the infinite plane, in singly-periodic arrays, and in doubly-periodic lattices. The reduction of each system using its symmetries is described in detail. Restricting to three vortices with zero net circulation, each reduced system is described by a one degree of freedom Hamiltonian. The phase portrait of this reduced system is subdivided into regimes using the separatrix motions, and a braid representing the topology of all vortex motions in each regime is computed. This braid also describes the isotopy class of the advection homeomorphism induced by the vortex motion. The Thurston-Nielsen theory is then used to analyse these isotopy classes, and in certain cases strong conclusions about the dynamics of the advection can be made