arXiv subjects

Kevin P. O'Keeffe

Publications and source records attributed to Kevin P. O'Keeffe.

At least 19 recordsLinked to original sources

arXiv2026

Rare but stable: hidden states in the 1D swarmalator model

The one-dimensional swarmalator model is usually understood through three macroscopic states: synchrony, the phase wave, and asynchrony. We show that the identical model also contains a much larger set of hidden stable equilibria - families of q-twisted and m-clustered states - which random initial conditions almost never reach, because many are embedded in a degenerate neutral manifold of vanishing global basin. They are nonetheless locally robust: under Gaussian perturbations of per-coordinate amplitude ε their survival radii shrink only algebraically, as 1/q and 1/m, in sharp contrast to the Gaussian basins and winding ceiling of twisted states on a nearest-neighbour Kuramoto ring, both removed by mean-field coupling. A block-circulant Jacobian fixes the stability in closed form, and far-kick experiments indicate the basins are compact cores rather than tentacled sets. Several patterns reported in extended swarmalator models thus already exist, stable or neutrally stable, in the minimal one.

nlin.AO↗

arXiv2026

A solvable normal form for coupled swarmalators

Swarmalators are mobile generalizations of phase oscillators. Introduced to model systems in which sync and self-assembly interact, they remain poorly understood theoretically. Unlike the Kuramoto model for coupled oscillators, existing swarmalator models lack a normal-form foundation, and their basic stabilities and bifurcations remain largely unsolved. Here we address both problems. Building on Tanaka's reduction of chemotactic oscillators, we show that the canonical one-dimensional swarmalator model -- previously introduced as an ad hoc toy model -- is recovered in the first-harmonic, zero-lag limit, implying its behavior is generic. We then derive the stability boundaries organizing its four collective states, show they meet at a single cusp, correct a previously published order-parameter formula, and uncover a non-monotonic sync response absent in the Kuramoto model.

nlin.AO↗

arXiv2026

Self-propulsion in the 1D swarmalator model

We study the 1D swarmalator model augmented with self-propulsion. Each swarmalator swims along the ring at a speed $v_0\sinθ_i$ fixed by its orientation $θ_i$. Self-propulsion unfolds the static states of the ordinary model into traveling, breathing, split-wave, and chaotic states. Several of these states admit analytic reductions: an exact drifting two-cluster branch with a closed-form stability spectrum, and a four-cluster split-wave ansatz whose active pair reduces, in a constant-orientation approximation, to an Adler equation. Our numerical evidence suggests that the transition to chaos under broad random initial conditions is not caused by local destabilization of the ordered cluster branches, but by basin reorganization among coexisting attractors. The resulting states may serve as qualitative signatures for confined active oscillator arrays.

nlin.AO↗

arXiv2026

Unsteady phase waves in the 1D swarmalator model with inertia

We study a one-dimensional swarmalator model with inertia. Previous studies have focused almost exclusively on the overdamped limit. We find inertia introduces a new unsteady collective state in which the rainbow order parameters undergo multiharmonic oscillations. This "thrashing" phase wave bifurcates from the model's static phase wave state through a subcritical Hopf bifurcation that coincides with a saddle-node of limit cycles. The wave itself exists in clockwise and counterclockwise symmetric pairs. For small populations we observe attractor switching between these chiral states, while for larger systems the dynamics settle onto a single branch.

nlin.AO↗

arXiv2025

Curiosity-driven RL for symbolic equation solving

We explore if RL can be useful for symbolic mathematics. Previous work showed contrastive learning can solve linear equations in one variable. We show model-free PPO \cite{schulman2017proximal} augmented with curiosity-based exploration and graph-based actions can solve nonlinear equations such as those involving radicals, exponentials, and trig functions. Our work suggests curiosity-based exploration may be useful for general symbolic reasoning tasks.

cs.LG↗

arXiv2024

Global synchronization theorem for coupled swarmalators

The global stability of oscillator networks has attracted much recent attention. Ordinarily, the oscillators in such studies are motionless; their spatial degrees of freedom are either ignored (e.g. mean field models) or inactive (e.g geometrically embedded networks like lattices). Yet many real-world oscillators are mobile, moving around in space as they synchronize in time. Here we prove a global synchronization theorem for such swarmalators for a simple model where the units' movements are confined to a 1d ring. This can be thought of as a generalization from oscillators connected on random networks to oscillators connected on temporal networks, where the edges are determined by the oscillators' movements.

nlin.AO↗

arXiv2023

Order, chaos, and dimensionality transition in a system of swarmalators

Similar to sperm, where individuals self-organize in space while also striving for coherence in their tail swinging, several natural and engineered systems exhibit the emergence of swarming and synchronization. The arising and interplay of these phenomena have been captured by collectives of hypothetical particles named swarmalators, each possessing a position and a phase whose dynamics are affected reciprocally and also by the space-phase states of their neighbors. In this work, we introduce a solvable model of swarmalators able to move in two-dimensional spaces. We show that several static and active collective states can emerge and derive necessary conditions for each to show up as the model parameters are varied. These conditions elucidate, in some cases, the displaying of multistability among states. Notably, in the active regime, individuals behave chaotically, maintaining spatial correlation under certain conditions, and breaking it under others on what we interpret as a dimensionality transition.

nlin.AO↗

arXiv2023

Swarmalators with thermal noise

We investigate a population of swarmalators, a mobile version of phase oscillators that both sync in time and swarm through space. We focus on a XY-type model of identical swarmalators running on a one-dimensional ring and subject to thermal noise. We uncover four distinct collective states, some of which capture the behavior of real-world swarmalators such as vinegar eels and sperm. Among these, the most intriguing is the `mixed state', which blends two of the other states. We present a comprehensive phase diagram from the Fourier mode analysis with a high accuracy, which is in excellent agreement with numerical simulation results. Our model serves as a tractable toy model for thermal systems that both self-synchronize and self-assemble interdependently.

cond-mat.stat-mech↗

arXiv2022

Travel distance, frequency of return and the spread of disease

In 2020 and 2021, the spread of COVID-19 was globally addressed by imposing restrictions on the distance of individual travel. Recent literature has uncovered a clear pattern in human mobility that underlies the complexity of urban mobility: $r \cdot f$, the product of distance traveled $r$ and frequency of return $f$ per user to a given location, is invariant across space. This paper asks whether the invariant $r\cdot f$ also serves as a driver for epidemic spread, so that the risk associated with human movement can be modeled by a unifying variable $r\cdot f$. We use two large-scale datasets of individual human mobility to show that there is in fact a simple relation between $r$ and $f$ and both speed and spatial dispersion of disease spread. This discovery could assist in modeling spread of disease and inform travel policies in future epidemics -- based not only on travel distance $r$ but also on frequency of return $f$.

physics.soc-ph↗

arXiv2021

Modeling the interplay between seasonal flu outcomes and individual vaccination decisions

Seasonal influenza presents an ongoing challenge to public health. The rapid evolution of the flu virus necessitates annual vaccination campaigns, but the decision to get vaccinated or not in a given year is largely voluntary, at least in the United States, and many people decide against it. In early attempts to model these yearly flu vaccine decisions, it was often assumed that individuals behave rationally, and do so with perfect information -- assumptions that allowed the techniques of classical economics and game theory to be applied. However, the usual assumptions are contradicted by the emerging empirical evidence about human decision-making behavior in this context. We develop a simple model of coupled disease spread and vaccination dynamics that instead incorporates experimental observations from social psychology to model annual vaccine decision-making more realistically. We investigate population-level effects of these new decision-making assumptions, with the goal of understanding whether the population can self-organize into a state of herd immunity, and if so, under what conditions. Our model agrees with established results while also revealing more subtle population-level behavior, including biennial oscillations about the herd immunity threshold.

q-bio.PE↗

arXiv2020

The darkweb: a social network anomaly

We analyse the darkweb and find its structure is unusual. For example, $ \sim 87 \%$ of darkweb sites \emph{never} link to another site. To call the darkweb a "web" is thus a misnomer -- it's better described as a set of largely isolated dark silos. As we show through a detailed comparison to the World Wide Web (www), this siloed structure is highly dissimilar to other social networks and indicates the social behavior of darkweb users is much different to that of www users. We show a generalized preferential attachment model can partially explain the strange topology of the darkweb, but an understanding of the anomalous behavior of its users remains out of reach. Our results are relevant to network scientists, social scientists, and other researchers interested in the social interactions of large numbers of agents.

physics.soc-ph↗

arXiv2019

On the Use of ArXiv as a Dataset

The arXiv has collected 1.5 million pre-print articles over 28 years, hosting literature from scientific fields including Physics, Mathematics, and Computer Science. Each pre-print features text, figures, authors, citations, categories, and other metadata. These rich, multi-modal features, combined with the natural graph structure---created by citation, affiliation, and co-authorship---makes the arXiv an exciting candidate for benchmarking next-generation models. Here we take the first necessary steps toward this goal, by providing a pipeline which standardizes and simplifies access to the arXiv's publicly available data. We use this pipeline to extract and analyze a 6.7 million edge citation graph, with an 11 billion word corpus of full-text research articles. We present some baseline classification results, and motivate application of more exciting generative graph models.

cs.IR↗

arXiv2018

Quantifying the sensing power of crowd-sourced vehicle fleets

Sensors can measure air quality, traffic congestion, and other aspects of urban environments. The fine-grained diagnostic information they provide could help urban managers to monitor a city's health. Recently, a `drive-by' paradigm has been proposed in which sensors are deployed on third-party vehicles, enabling wide coverage at low cost} Research on drive-by sensing has mostly focused on sensor engineering, but a key question remains unexplored: How many vehicles would be required to adequately scan a city? Here, we address this question by analyzing the sensing power of a taxi fleet. Taxis, being numerous in cities and typically equipped with some sensing technology (e.g. GPS), are natural hosts for the sensors. Our strategy is to view drive-by sensing as a spreading process, in which the area of sensed terrain expands as sensor-equipped taxis diffuse through a city's streets. In tandem with a simple model for the movements of the taxis, this analogy lets us analytically determine the fraction of a city's street network sensed by a fleet of taxis during a day. Our results agree with taxi data obtained from nine major cities, and reveal that a remarkably small number of taxis can scan a large number of streets. This finding appears to be universal, indicating its applicability to cities beyond those analyzed here. Moreover, because taxi motions combine randomness and regularity (passengers' destinations being random, but the routes to them being deterministic), the spreading properties of taxi fleets are unusual; in stark contrast to random walks, the stationary densities of our taxi model obey Zipf's law, consistent with the empirical taxi data. Our results have direct utility for town councilors, smart-city designers, and other urban decision makers.

physics.soc-ph↗

arXiv2018

Ring states in swarmalator systems

Synchronization is a universal phenomenon, seen in systems as diverse as superconducting Josephson junctions and discharging pacemaker cells. Here the elements have rhythmic state variables whose mutual influence promotes temporal order. A parallel form of order is seen in swarming systems, such as schools of fish or flocks of birds. Now the degrees of freedom are the individuals' positions, which get redistributed through interactions to form spatial structures. Systems capable of both swarming and synchronizing, dubbed swarmalators, have recently been proposed [O'Keeffe, Kevin P., and Steven H. Strogatz. "Swarmalators: Oscillators that sync and swarm." arXiv preprint arXiv:1701.05670 (2017)] and analyzed in the continuum limit. Here we extend this work by studying finite populations of swarmalators, whose phase similarity affects both their spatial attraction and repulsion. We find ring states, and compute criteria for their existence and stability. Larger populations can form annular distributions, whose density and inner and outer radii we calculate explicitly. These states may be observable in groups of Japanese tree frogs, magnetic colloids, and other systems with an interplay between swarming and synchronization.

nlin.AO↗

arXiv2018

Bayesian approach to uncertainty quantification for cerebral autoregulation index

Cerebral autoregulation refers to the brain's ability to maintain cerebral blood flow at an approximately constant level, despite changes in arterial blood pressure. The performance of this mechanism is often assessed using a ten-scale index called the ARI (autoregulation index). Here, $0$ denotes the absence of, while $9$ denotes the strongest, autoregulation. Current methods to calculate the ARI do not typically provide error estimates. Here, we show how this can be done using a bayesian approach. We use Markov-chain Monte Carlo methods to produce a probability distribution for the ARI, which gives a natural way to estimate error.

physics.med-ph↗

arXiv2017

Oscillators that sync and swarm

Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. A complementary form of self-organization occurs among swarming insects, flocking birds, or schooling fish; now the individuals move through space, but without conspicuously altering their internal states. Here we explore systems in which both synchronization and swarming occur together. Specifically, we consider oscillators whose phase dynamics and spatial dynamics are coupled. We call them swarmalators, to highlight their dual character. A case study of a generalized Kuramoto model predicts five collective states as possible long-term modes of organization. These states may be observable in groups of sperm, Japanese tree frogs, colloidal suspensions of magnetic particles, and other biological and physical systems in which self-assembly and synchronization interact.

nlin.AO↗

arXiv2016

Correlated disorder in the Kuramoto model: Effects on phase coherence, finite-size scaling, and dynamic fluctuations

We consider a mean-field model of coupled phase oscillators with quenched disorder in the natural frequencies and coupling strengths. A fraction $p$ of oscillators are positively coupled, attracting all others, while the remaining fraction $1-p$ are negatively coupled, repelling all others. The frequencies and couplings are deterministically chosen in a manner which correlates them, thereby correlating the two types of disorder in the model. We first explore the effect of this correlation on the system's phase coherence. We find that there is a a critical width $γ_c$ in the frequency distribution below which the system spontaneously synchronizes. Moreover, this $γ_c$ is independent of $p$. Hence, our model and the traditional Kuramoto model (recovered when $p=1$) have the same critical width $γ_c$. We next explore the critical behavior of the system by examining the finite-size scaling and the dynamic fluctuation of the traditional order parameter. We find that the model belongs to the same universality class as the Kuramoto model with deterministically (not randomly) chosen natural frequencies for the case of $p<1$.

cond-mat.stat-mech↗

arXiv2016

Dynamics of a population of oscillatory and excitable elements

We analyze a variant of a model proposed by Kuramoto, Shinomoto, and Sakaguchi for a large population of coupled oscillatory and excitable elements. Using the Ott-Antonsen ansatz, we reduce the behavior of the population to a two-dimensional dynamical system with three parameters. We present the stability diagram and calculate several of its bifurcation curves analytically, for both excitatory and inhibitory coupling. Our main result is that when the coupling function is broad, the system can display bistability between steady states of constant high and low activity, whereas when the coupling function is narrow and inhibitory, one of the states in the bistable regime can show persistent pulsations in activity.

nlin.CD↗