arXiv subjects

Alexander P. Kartun-Giles

Publications and source records attributed to Alexander P. Kartun-Giles.

13 recordsLinked to original sources

arXiv2025

Uncovering the network geometry of green bonds

With the rapid growth of the green bond market amid increasing emphasis on sustainable development, understanding its structural properties and potential systemic risks has become essential. This study applies Minimum Spanning Tree (MST) and Hierarchical Tree (HT) methods introduced by Mantegna, which gives a minimum spanning tree of bonds whose mutual distance corresponds to the correlation coefficient of the synchronous time evolution of the difference of the logarithm of their monthly price. Our analysis reveals that green bonds exhibit tighter ultrametric distances on average compared to stocks and conventional bonds, indicating a highly interconnected market structure. We also identify strong sectorial clustering, with green bonds in the utilities sector emerging as the most central nodes by average total betweenness centrality, suggesting their critical role in potential risk propagation. These findings highlight both the opportunities and vulnerabilities inherent in the green bond market, offering insights for investors and policymakers on monitoring concentration, enhancing transparency, and mitigating systemic risks as the market continues to evolve.

physics.soc-ph↗

arXiv2023

An Introduction to Complex Networks in Climate Finance

In this perspective, we introduce recent research into the structure and function of complex investor networks supporting sustainability efforts. Using the case of solar, wind and hydro energy technologies, this perspective explores the complexity in low-carbon finance markets, defined as markets that direct capital flows towards low-carbon technologies, using network approaches to study their structure and dynamics. Investors are modeled as nodes which form a network or higher-order network connected by edges representing projects in which joint funding or security-related insurance was provided or other investment-related interaction occurred. We review the literature on investor networks generally, particularly in the case of complex networks, and address areas where these ideas were applied in this emerging field. The complex investor dynamics which emerge from the extant funding scenarios are not well understood. These dynamics have the potential to result in interesting non-linear behaviour, growth, and decline, which can be studied, explained and controlled using the tools of network science.

physics.soc-ph↗

arXiv2022

Two-Hop Connectivity to the Roadside in a VANET Under the Random Connection Model

In this paper, we compute the expected number of vehicles with at least one two-hop path to a fixed roadside unit (RSU) in a multi-hop, one-dimensional vehicular ad hoc network (VANET) where other cars can act as relays. The pairwise channels experience Rayleigh fading in the random connection model, and so exist, with a probability given by a function of the mutual distance between the cars, or between the cars and the RSU. We derive exact expressions for the expected number of cars with a two-hop connection to the RSU when the car density $ρ$ tends to zero and infinity, and determine its behaviour using an infinite oscillating power series in $ρ$, which is accurate for all regimes of traffic density. We also corroborate those findings with a realistic scenario, using snapshots of actual traffic data. Finally, a normal approximation is discussed for the probability mass function of the number of cars with a two-hop connection to the RSU.

cs.NI↗

arXiv2022

Meta Distribution of SIR in the Internet of Things Modelled as a Euclidean Matching

The Poisson bipolar model considers user-base station pairs distributed at random on a flat domain, similar to matchsticks scattered onto a table. Though this is a simple and tractable setting in which to study dense networks, it doesn't properly characterise the stochastic geometry of user-base station interactions in some dense deployment scenarios, which may involve short and long range links, with some paired very nearby optimally, and others sub-optimally due to local crowding. Since the users will pair one-to-one with base stations, we can consider using the popular bipartite Euclidean matching (BEM) from spatial combinatorics, and study the corresponding (meta) distribution of the signal-to-interference-ratio (SIR). This provides detailed information about the proportion of links in the network meeting a target reliability constraint. We can then observe via comparison the impact of taking into account the variable/correlated short-range distances between the transmitter-receiver pairs on the communication statistics. We illustrate and quantify how the widely-accepted bipolar model fails to capture the network-wide reliability of communication in a typical ultra-dense setting based on a binomial point process. We also show how assuming a Gamma distribution for link distances may be a simple improvement on the bipolar model. Overall, BEMs provide good grounds for understanding more sophisticated pairing features in ultra-dense networks.

cond-mat.dis-nn↗

arXiv2021

Connectivity of 1d random geometric graphs

A 1d random geometric graph (1d RGG) is built by joining a random sample of $n$ points from an interval of the real line with probability $p$. We count the number of $k$-hop paths between two vertices of the graph in the case where the space is the 1d interval $[0,1]$. We show how the $k$-hop path count between two vertices at Euclidean distance $|x-y|$ is in bijection with the volume enclosed by a uniformly random $d$-dimensional lattice path joining the corners of a $(k-1)$-dimensional hyperrectangular lattice. We are able to provide the probability generating function and distribution of this $k$-hop path count as a sum over lattice paths, incorporating the idea of restricted integer partitions with limited number of parts. We therefore demonstrate and describe an important link between spatial random graphs, and lattice path combinatorics, where the $d$-dimensional lattice paths correspond to spatial permutations of the geometric points on the line.

math.CO↗

arXiv2019

Connectivity and Centrality in Dense Random Geometric Graphs

Due to shorter range communication becoming more prevalent with the development of multiple-input, multiple-output antennas (MIMO) and millimeter wave communications, multi-hop, intra-cell communication is anticipated to play a major role in 5G. This is developed in this thesis. Our analysis involves a stochastic spatial network model called a random geometric graph, which we use to model a network of interconnected devices communicating wirelessly without any separate, pre-established infrastructure. [The remaining abstract is available in the front matter of this thesis.]

math.PR↗

arXiv2019

The shape of shortest paths in random spatial networks

In the classic model of first passage percolation, for pairs of vertices separated by a Euclidean distance $L$, geodesics exhibit deviations from their mean length $L$ that are of order $L^χ$, while the transversal fluctuations, known as wandering, grow as $L^ξ$. We find that when weighting edges directly with their Euclidean span in various spatial network models, we have two distinct classes defined by different exponents $ξ=3/5$ and $χ= 1/5$, or $ξ=7/10$ and $χ= 2/5$, depending only on coarse details of the specific connectivity laws used. Also, the travel time fluctuations are Gaussian, rather than Tracy-Widom, which is rarely seen in first passage models. The first class contains proximity graphs such as the hard and soft random geometric graph, and the $k$-nearest neighbour random geometric graphs, where via Monte Carlo simulations we find $ξ=0.60\pm 0.01$ and $χ= 0.20\pm 0.01$, showing a theoretical minimal wandering. The second class contains graphs based on excluded regions such as $β$-skeletons and the Delaunay triangulation and are characterised by the values $ξ=0.70\pm 0.01$ and $χ= 0.40\pm 0.01$, with a nearly theoretically maximal wandering exponent. We also show numerically that the KPZ relation $χ= 2ξ-1$ is satisfied for all these models. These results shed some light on the Euclidean first passage process, but also raise some theoretical questions about the scaling laws and the derivation of the exponent values, and also whether a model can be constructed with maximal wandering, or non-Gaussian travel fluctuations, while embedded in space.

cond-mat.stat-mech↗

arXiv2019

Euclidean Matchings in Ultra-Dense Networks

In order to study the fundamental limits of network densification, we look at the spatial spectral efficiency gain achieved when densely deployed communication devices embedded in the $d$-dimensional Euclidean space are optimally `matched' in near-neighbour pairs. In light of recent success in probabilisitc modelling, we study devices distributed uniformly at random in the unit cube which enter into one-on-one contracts with each another. This is known in statistical physics as an Euclidean `matching'. Communication channels each have their own maximal data capacity given by Shannon's theorem. The length of the shortest matching then corresponds to the maximum one-hop capacity on those points. Interference is then added as a further constraint, which is modelled using shapes as guard regions, such as a disk, diametral disk, or equilateral triangle, matched to points, in a similar light to computational geometry. The disk, for example, produces the Delaunay triangulation, while the diametral disk produces a beta-skeleton. We also discuss deriving the scaling limit of both models using the replica method from the physics of disordered systems.

cond-mat.dis-nn↗

arXiv2019

Beyond the clustering coefficient: A topological analysis of node neighbourhoods in complex networks

In Network Science node neighbourhoods, also called ego-centered networks have attracted large attention. In particular the clustering coefficient has been extensively used to measure their local cohesiveness. In this paper, we show how, given two nodes with the same clustering coefficient, the topology of their neighbourhoods can be significantly different, which demonstrates the need to go beyond this simple characterization. We perform a large scale statistical analysis of the topology of node neighbourhoods of real networks by first constructing their clique complexes, and then computing their Betti numbers. We are able to show significant differences between the topology of node neighbourhoods of real networks and the stochastic topology of null models of random simplicial complexes revealing local organisation principles of the node neighbourhoods. Moreover we observe that a large scale statistical analysis of the topological properties of node neighbourhoods is able to clearly discriminate between power-law networks, and planar road networks.

physics.soc-ph↗

arXiv2018

Counting k-Hop Paths in the Random Connection Model

We study, via combinatorial enumeration, the probability of k-hop connection between two nodes in a wireless multi-hop network. This addresses the difficulty of providing an exact formula for the scaling of hop counts with Euclidean distance without first making a sort of mean field approximation, which in this case assumes all nodes in the network have uncorrelated degrees. We therefore study the mean and variance of the number of k-hop paths between two vertices x,y in the random connection model, which is a random geometric graph where nodes connect probabilistically rather than deterministically according to a critical connection range. In the example case where Rayleigh fading is modelled, the variance of the number of three hop paths is in fact composed of four separate decaying exponentials, one of which is the mean, which decays slowest as the Euclidean distance between the endpoints goes to infinity. These terms each correspond to one of exactly four distinct sub-structures with can form when pairs of paths intersect in a specific way, for example at exactly one node. Using a sum of factorial moments, this relates to the path existence probability. We also discuss a potential application of our results in bounding the broadcast time.

math.PR↗

arXiv2016

Connectivity of Soft Random Geometric Graphs Over Annuli

Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present analytic formulas for the connection probability of these spatially embedded graphs, describing the connectivity behaviour as a dense-network limit is approached. This extends recent work modelling ad hoc networks in non-convex domains.

math.CO↗

arXiv2016

Betweenness Centrality in Dense Random Geometric Networks

Random geometric networks consist of 1) a set of nodes embedded randomly in a bounded domain $\mathcal{V} \subseteq \mathbb{R}^d$ and 2) links formed probabilistically according to a function of mutual Euclidean separation. We quantify how often all paths in the network characterisable as topologically `shortest' contain a given node (betweenness centrality), deriving an expression in terms of a known integral whenever 1) the network boundary is the perimeter of a disk and 2) the network is extremely dense. Our method shows how similar formulas can be obtained for any convex geometry. Numerical corroboration is provided, as well as a discussion of our formula's potential use for cluster head election and boundary detection in densely deployed wireless ad hoc networks.

cs.SI↗

arXiv2016

Counting Geodesic Paths in 1D VANETs

In the IEEE 802.11p standard addressing vehicular communications, Basic Safety Messages (BSMs) can be bundled together and relayed as to increase the effective communication range of transmitting vehicles. This process forms a vehicular ad hoc network (VANET) for the dissemination of safety information. The number of "shortest multihop paths" (or geodesics) connecting two network nodes is an important statistic which can be used to enhance throughput, validate threat events, protect against collusion attacks, infer location information, and also limit redundant broadcasts thus reducing interference. To this end, we analytically calculate for the first time the mean and variance of the number of geodesics in 1D VANETs.

cs.NI↗