arXiv subjects

Samuel Johnson

Publications and source records attributed to Samuel Johnson.

At least 19 recordsLinked to original sources

arXiv2026

Spin Qubits in Photon-Coupled Microwave Cavities

Electron spin qubits in microwave cavities provide a promising platform for scalable quantum computing hardware, leveraging long coherence times, charge-noise robustness and cavity mediated qubit-qubit interactions. While the strong spin-photon coupling regime is accessible via on-chip micromagnets, scaling conventional architectures by placing multiple qubits within a single shared resonator degrades transmission amplitudes, hence limiting large-scale efficiency. To overcome this limitation, we analyze a modular architecture where individual cavities containing a limited number of qubits are coupled via single-photon-exchange waveguides. Using input/output theory, we compute the transmission amplitudes for networks of two and three coupled cavities in various configurations. We map out the distinct physical regimes accessible by tuning key system parameters, offering a viable pathway for scalable cavity-based quantum spin qubit networks.

cond-mat.mes-hall↗

arXiv2026

Types and collapse for cuspidal representations of groups acting on trees

In a previous paper, the second author proved that every supercuspidal representation of a rank-one p-adic group is induced from a compact-mod-center open subgroup. The method was geometric, localizing representations to obtain equivariant sheaves on trees. Here we provide two refinements. The first is a geometric description of the inducing data, via a geometrically minimal K-type. Second is a proof that the equivariant sheaves collapse onto injective sheaves. The two notions of geometrically minimal K-types and collapsibility generalize to higher rank groups, suggesting a pair of conjectures.

math.RT↗

arXiv2026

Trophic structure predicts seizure propagation in brain network models

Epilepsy is widely regarded as a disorder driven by connectivity in the brain. We use a model of seizure dynamics on directed networks to investigate how structural properties affect seizure propensity. We find that properties such as trophic coherence, spectral radius, strong connectivity and non-normality are closely related to seizure propensity, and present a proof of a theoretical relationship between spectral radius and cycle structure. Our simulated results are robust to the kind of coupling used in the model and become stronger as network size is increased. They suggest that the overall directionality of information processing in the brain may be related to a propensity for epileptic seizures.

q-bio.NC↗

arXiv2025

Supernova Siblings and Spectroscopic Host-Galaxy Properties

Over the past century, supernova (SN) searches have detected multiple supernovae (SNe) in hundreds of individual galaxies. So-called SN siblings discovered in the same galaxy present an opportunity to constrain the dependence of the properties of SNe on those of their host galaxies. To investigate whether there is a connection between sibling SNe in galaxies that have hosted multiple SNe and the properties of galaxies, we have acquired integrated optical spectroscopy of 59 galaxies with multiple core-collapse SNe. Perhaps surprisingly, a strong majority of host-galaxy spectra fall within the composite region of the Baldwin-Phillips-Terlevich (BPT) diagram. We find a statistically significant difference (KS test p-value = 0.044) between the distributions of the [NII] $\lambda$6583/H$\alpha$ of galaxies that have hosted a majority SN Ibc and those that have hosted a majority SN II, where the majority SN Ibc galaxies have, on average, higher ratios. The difference between the distributions of [NII] $\lambda$6583/H$\alpha$ may arise from either increased contribution from AGN or LINERs in SN Ibc host galaxies, greater metallicity for SN Ibc host galaxies, or both. When comparing the inferred oxygen abundance and the ionization parameter for the galaxies in the Star-Forming region on the BPT diagram, we find statistically significant differences between the distributions for SN Ibc hosts and SN II hosts (p=0.008 and p=0.001, respectively), as well as SN Ib hosts and SN II hosts (p=0.030 and p=0.006, respectively). We also compare the H$\alpha$ equivalent width distributions, also integrated across the galaxies, and find no significant difference.

astro-ph.GA↗

arXiv2024

The connection between non-normality and trophic coherence in directed graphs

Trophic coherence and non-normality are both ways of describing the overall directionality of directed graphs, or networks. Trophic coherence can be regarded as a measure of how neatly a graph can be divided into distinct layers, whereas non-normality is a measure of how unlike a matrix is with its transpose. We explore the relationship between trophic coherence and non-normality by first considering the connections that exist in the literature and calculating the trophic coherence and non-normality for some toy networks. We then explore how persistence of an epidemic in an SIS model depends on coherence, and how this relates to the non-normality. A similar effect on dynamics governed by a linear operator suggests that it may be useful to extend the concept of trophic coherence to matrices which do not necessarily represent graphs.

physics.soc-ph↗

arXiv2024

Fitness-Based Growth of Directed Networks with Hierarchy

Growing attention has been brought to the fact that many real directed networks exhibit hierarchy and directionality as measured through techniques like Trophic Analysis and non-normality. We propose a simple growing network model where the probability of connecting to a node is defined by a preferential attachment mechanism based on degree and the difference in fitness between nodes. In particular, we show how mechanisms such as degree-based preferential attachment and node fitness interactions can lead to the emergence of the spectrum of hierarchy and directionality observed in real networks. In this work, we study various features of this model relating to network hierarchy, as measured by Trophic Analysis. This includes (I) how preferential attachment can lead to network hierarchy, (II) how scale-free degree distributions and network hierarchy can coexist, (III) the correlation between node fitness and trophic level, (IV) how the fitness parameters can predict trophic incoherence and how the trophic level difference distribution compares to the fitness difference distribution, (V) the relationship between trophic level and degree imbalance and the unique role of nodes at the ends of the fitness hierarchy and (VI) how fitness interactions and degree-based preferential attachment can interplay to generate networks of varying coherence and degree distribution. We also provide an example of the intuition this work enables in the analysis of a real historical network. This work provides insight into simple mechanisms which can give rise to hierarchy in directed networks and quantifies the usefulness and limitations of using Trophic Analysis as an analysis tool for real networks.

physics.soc-ph↗

arXiv2024

Epidemic modelling requires knowledge of the social network

Compartmental models of epidemics are widely used to forecast the effects of communicable diseases such as COVID-19 and to guide policy. Although it has long been known that such processes take place on social networks, the assumption of random mixing is usually made, which ignores network structure. However, super-spreading events have been found to be power-law distributed, suggesting that the underlying networks may be scale free or at least highly heterogeneous. The random-mixing assumption would then produce an overestimation of the herd-immunity threshold for given $R_0$; and a (more significant) overestimation of $R_0$ itself. These two errors compound each other, and can lead to forecasts greatly overestimating the number of infections. Moreover, if networks are heterogeneous and change in time, multiple waves of infection can occur, which are not predicted by random mixing. A simple SIR model simulated on both Erd\H{o}s-R\'enyi and scale-free networks shows that details of the network structure can be more important than the intrinsic transmissibility of a disease. It is therefore crucial to incorporate network information into standard models of epidemics.

physics.soc-ph↗

arXiv2023

Modeling the extracellular matrix in cell migration and morphogenesis: A guide for the curious biologist

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.

q-bio.TO↗

arXiv2022

Influence and Influenceability: Global Directionality in Directed Complex Networks

Knowing which nodes are influential in a complex network and whether the network can be influenced by a small subset of nodes is a key part of network analysis. However, many traditional measures of importance focus on node level information without considering the global network architecture. We use the method of Trophic Analysis to study directed networks and show that both "influence" and "influenceability" in directed networks depend on the hierarchical structure and the global directionality, as measured by the trophic levels and trophic coherence, respectively. We show that in directed networks trophic hierarchy can explain: the nodes that can reach the most others; where the eigenvector centrality localises; which nodes shape the behaviour in opinion or oscillator dynamics; and which strategies will be successful in generalised rock-paper-scissors games. We show, moreover, that these phenomena are mediated by the global directionality. We also highlight other structural properties of real networks related to influenceability, such as the pseudospectra, which depend on trophic coherence. These results apply to any directed network and the principles highlighted, that node hierarchy is essential for understanding network influence, mediated by global directionality, are applicable to many real-world dynamics.

physics.soc-ph↗

arXiv2022

Strong Connectivity in Real Directed Networks

In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean degree and degree-degree correlations. And it has important implications for other properties of real networks and the dynamical behaviour of many complex systems. We find that strong connectivity depends crucially on the extent to which the network has an overall direction or hierarchical ordering -- a property measured by trophic coherence. Using percolation theory, we find the critical point separating weakly and strongly connected regimes, and confirm our results on many real-world networks, including ecological, neural, trade and social networks. We show that the connectivity structure can be disrupted with minimal effort by a targeted attack on edges which run counter to the overall direction. And we illustrate with example dynamics -- the SIS model, majority vote, Kuramoto oscillators and the voter model -- how a small number of edge deletions can utterly change dynamical processes in a wide range of systems.

cond-mat.dis-nn↗

arXiv2022

Network Hierarchy and Pattern Recovery in Directed Sparse Hopfield Networks

Many real-world networks are directed, sparse and hierarchical, with a mixture of feed-forward and feedback connections with respect to the hierarchy. Moreover, a small number of 'master' nodes are often able to drive the whole system. We study the dynamics of pattern presentation and recovery on sparse, directed, Hopfield-like neural networks using Trophic Analysis to characterise their hierarchical structure. This is a recent method which quantifies the local position of each node in a hierarchy (trophic level) as well as the global directionality of the network (trophic coherence). We show that even in a recurrent network, the state of the system can be controlled by a small subset of neurons which can be identified by their low trophic levels. We also find that performance at the pattern recovery task can be significantly improved by tuning the trophic coherence and other topological properties of the network. This may explain the relatively sparse and coherent structures observed in the animal brain, and provide insights for improving the architectures of artificial neural networks. Moreover, we expect that the principles we demonstrate, through numerical analysis, here will be relevant for a broad class of system whose underlying network structure is directed and sparse, such as biological, social or financial networks.

cond-mat.dis-nn↗

arXiv2020

A look at generalized perfect shuffles

Standard perfect shuffles involve splitting a deck of $2n$ cards into two stacks and interlacing the cards from the stacks. There are two ways that this interlacing can be done, commonly referred to as an in shuffle and an out shuffle, respectively. In 1983, Diaconis, Graham, and Kantor determined the permutation group generated by in and out shuffles on a deck of $2n$ cards for all $n$. Diaconis et al. concluded their work by asking whether similar results can be found for so-called generalized perfect shuffles. For these new shuffles, we split a deck of $mn$ cards into $m$ stacks and similarly interlace the cards with an in $m$-shuffle or out $m$-shuffle (denoted $I_m$ and $O_m$, respectively). In this paper, we find the structure of the group generated by these two shuffles for a deck of $m^k$ cards, together with $m^y$-shuffles, for all possible values of $m$, $k$, and $y$. The group structure is completely determined by $k/\gcd(y,k)$ and the parity of $y/\gcd(y,k)$. In particular, the group structure is independent of the value of $m$.

math.CO↗

arXiv2019

Organisational Social Influence on Directed Hierarchical Graphs, from Tyranny to Anarchy

Coordinated human behaviour takes place within a diverse range of social organisational structures, which can be thought of as power structures with "managers" who influence "subordinates". A change in policy in one part of the organisation can cause cascades throughout the structure, which may or may not be desirable. As organisations change in size, complexity and structure, the system dynamics also change. Here, we consider majority rule dynamics on organisations modelled as hierarchical directed graphs, where the directed edges indicate influence. We utilise a topological measure called the trophic incoherence parameter, q, which effectively gauges the stratification of power structure in an organisation. We show that this measure bounds regimes of behaviour. There is fast consensus at low q (e.g. tyranny), slow consensus at mid q (e.g. democracy), and no consensus at high q (e.g. anarchy). These regimes are investigated analytically, numerically and empirically with diverse case studies in the Roman Army, US Government, and a healthcare organisation. Our work demonstrates the usefulness of the trophic incoherence parameter when considering models of social influence dynamics, with widespread consequences in the design and analysis of organisations.

nlin.AO↗

arXiv2019

Digraphs are different: Why directionality matters in complex systems

Many networks describing complex systems are directed: the interactions between elements are not symmetric. Recent work has shown that these networks can display properties such as trophic coherence or non-normality, which in turn affect stability, percolation and other dynamical features. I show here that these topological properties have a common origin, in that the edges of directed networks can be aligned - or not - with a global direction. And I illustrate how this can lead to rich and unexpected dynamical behaviour even in the simplest of models.

physics.soc-ph↗

arXiv2018

Resilience or Robustness: Identifying Topological Vulnerabilities in Rail Networks

Many critical infrastructure systems have network structure and are under stress. Despite their national importance, the complexity of large-scale transport networks means we do not fully understand their vulnerabilities to cascade failures. The research in this paper examines the interdependent rail networks in Greater London and surrounding commuter area. We focus on the morning commuter hours, where the system is under the most demand stress. There is increasing evidence that the topological shape of the network plays an important role in dynamic cascades. Here, we examine whether the different topological measures of resilience (stability) or robustness (failure) are more appropriate for understanding poor railway performance. The results show that resilience and not robustness has a strong correlation to the consumer experience statistics. Our results are a way of describing the complexity of cascade dynamics on networks without the involvement of detailed agent-based-models, showing that cascade effects are more responsible for poor performance than failures. The network science analysis hints at pathways towards making the network structure more resilient by reducing feedback loops.

physics.soc-ph↗

arXiv2018

Gang Confrontation: The case of Medellin (Colombia)

Protracted conflict is one of the largest human challenges that have persistently undermined economic and social progress. In recent years, there has been increased emphasis on using statistical and physical science models to better understand both the universal patterns and the underlying mechanics of conflict. Whilst macroscopic power-law fractal patterns have been shown for death-toll in wars and self-excitation models have been shown for roadside ambush attacks, very few works deal with the challenge of complex dynamics between gangs at the intra-city scale. Here, based on contributions to the historical memory of the conflict in Colombia, Medellin's gang-confrontation-network is presented. It is shown that socio-economic and violence indexes are moderate to highly correlated to the structure of the network. Specifically, the death-toll of conflict is strongly influenced by the leading eigenvalues of the gangs' conflict adjacency matrix, which serves a proxy for unstable self-excitation from revenge attacks. The distribution of links based on the geographic distance between gangs in confrontation leads to the confirmation that territorial control is a main catalyst of violence and retaliation among gangs. Additionally, the Boltzmann-Lotka-Volterra (BLV) dynamic interaction network analysis is applied to quantify the spatial embeddedness of the dynamic relationship between conflicting gangs in Medellin, results suggest that more involved and comprehensive models are needed to described the dynamics of Medellin's armed conflict.

physics.soc-ph↗

arXiv2017

Relaxation dynamics of maximally clustered networks

We study the relaxation dynamics of fully clustered networks (maximal number of triangles) to an unclustered state under two different edge dynamics---the double-edge swap, corresponding to degree-preserving randomization of the configuration model, and single edge replacement, corresponding to full randomization of the Erd\H{o}s--R\'enyi random graph. We derive expressions for the time evolution of the degree distribution, edge multiplicity distribution and clustering coefficient. We show that under both dynamics networks undergo a continuous phase transition in which a giant connected component is formed. We calculate the position of the phase transition analytically using the Erd\H{o}s--R\'enyi phenomenology.

physics.soc-ph↗

arXiv2017

Urban Analytics: Multiplexed and Dynamic Community Networks

In the past decade, cities have experienced rapid growth, expansion, and changes in their community structure. Many aspects of critical urban infrastructure are closely coupled with the human communities that they serve. Urban communities are composed of a multiplex of overlapping factors which can be distinguished into cultural, religious, social-economic, political, and geographical layers. In this paper, we review how increasingly available heterogeneous mobile big data sets can be leveraged to detect the community interaction structure using natural language processing and machine learning techniques. A number of community layer and interaction detection algorithms are then reviewed, with a particular focus on robustness, stability, and causality of evolving communities. The better understanding of the structural dynamics and multiplexed relationships can provide useful information to inform both urban planning policies and shape the design of socially coupled urban infrastructure systems.

cs.SI↗