The entropy rate of Linear Additive Markov Processes.

This work derives a theoretical value for the entropy of a Linear Additive Markov Process (LAMP), an expressive but simple model able to generate sequences with a given autocorrelation structure. Our research establishes that the theoretical entropy rate of a LAMP model is equivalent to the theoretical entropy rate of the underlying first-order Markov Chain. The LAMP model captures complex relationships and long-range dependencies in data with similar expressibility to a higher-order Markov process. While a higher-order Markov process has a polynomial parameter space, a LAMP model is characterised only by a probability distribution and the transition matrix of an underlying first-order Markov Chain. This surprising result can be explained by the information balance between the additional structure imposed by the next state distribution of the LAMP model, and the additional randomness of each new transition. Understanding the entropy of the LAMP model provides a tool to model complex dependencies in data while retaining useful theoretical results. To emphasise the practical applications, we use the LAMP model to estimate the entropy rate of the LastFM, BrightKite, Wikispeedia and Reuters-21578 datasets. We compare estimates calculated using frequency probability estimates, a first-order Markov model and the LAMP model, also considering two approaches to ensure the transition matrix is irreducible. In most cases the LAMP entropy rates are lower than those of the alternatives, suggesting that LAMP model is better at accommodating structural dependencies in the processes, achieving a more accurate estimate of the true entropy.

Does the time to surgery influence outcomes for patients with a hip fracture who undergo total hip arthroplasty?

Aims: Surgery is often delayed in patients who sustain a hip fracture and are treated with a total hip arthroplasty (THA), in order to await appropriate surgical expertise. There are established links between delay and poorer outcomes in all patients with a hip fracture, but there is little information about the impact of delay in the less frail patients who undergo THA. The aim of this study was to investigate the influence of delayed surgery on outcomes in these patients. Methods: A retrospective cohort study was undertaken using data from the Scottish Hip Fracture Audit between May 2016 and December 2020. Only patients undergoing THA were included, with categorization according to surgical treatment within 36 hours of admission (≤ 36 hours = 'acute group' vs > 36 hours = 'delayed' group). Those with delays due to being "medically unfit" were excluded. The primary outcome measure was 30-day survival. Costs were estimated in relation to the differences in the lengths of stay. Results: A total of 1,375 patients underwent THA, with 397 (28.9%) having surgery delayed by > 36 hours. There were no significant differences in the age, sex, residence prior to admission, and Scottish Index of Multiple Deprivation for those with, and those without, delayed surgery. Both groups had statistically similar 30-day (99.7% vs 99.3%; p = 0.526) and 60-day (99.2% vs 99.0%; p = 0.876) survival. There was, however, a significantly longer length of stay for the delayed group (acute: 7.0 vs delayed: 8.9 days; p < 0.001; overall: 8.7 vs 10.2 days; p = 0.002). Delayed surgery did not significantly affect the rates of 30-day readmission (p = 0.085) or discharge destination (p = 0.884). The results were similar following adjustment for potential confounding factors. The estimated additional cost due to delayed surgery was £1,178 per patient. Conclusion: Delayed surgery does not appear to be associated with increased mortality in patients with an intracapsular hip fracture who undergo THA, compared with those who are treated with a hemiarthroplasty or internal fixation. Those with delayed surgery, however, have a longer length of stay, with financial consequences. Clinicians must balance ethical considerations, the local provision of orthopaedic services, and optimization of outcomes when determining the need to delay surgery in a patient with a hip fracture awaiting THA.

Markov modeling of phase singularity interaction effects in human atrial and ventricular fibrillation.

Atrial and ventricular fibrillation (AF/VF) are characterized by the repetitive regeneration of topological defects known as phase singularities (PSs). The effect of PS interactions has not been previously studied in human AF and VF. We hypothesized that PS population size would influence the rate of PS formation and destruction in human AF and VF, due to increased inter-defect interaction. PS population statistics were studied in computational simulations (Aliev-Panfilov), human AF and human VF. The influence of inter-PS interactions was evaluated by comparison between directly modeled discrete-time Markov chain (DTMC) transition matrices of the PS population changes, and M/M/∞ birth-death transition matrices of PS dynamics, which assumes that PS formations and destructions are effectively statistically independent events. Across all systems examined, PS population changes differed from those expected with M/M/∞. In human AF and VF, the formation rates decreased slightly with PS population when modeled with the DTMC, compared with the static formation rate expected through M/M/∞, suggesting new formations were being inhibited. In human AF and VF, the destruction rates increased with PS population for both models, with the DTMC rate increase exceeding the M/M/∞ estimates, indicating that PS were being destroyed faster as the PS population grew. In human AF and VF, the change in PS formation and destruction rates as the population increased differed between the two models. This indicates that the presence of additional PS influenced the likelihood of new PS formation and destruction, consistent with the notion of self-inhibitory inter-PS interactions.

The inspection paradox: An important consideration in the evaluation of rotor lifetimes in cardiac fibrillation.

Background and Objective: Renewal theory is a statistical approach to model the formation and destruction of phase singularities (PS), which occur at the pivots of spiral waves. A common issue arising during observation of renewal processes is an inspection paradox, due to oversampling of longer events. The objective of this study was to characterise the effect of a potential inspection paradox on the perception of PS lifetimes in cardiac fibrillation. Methods: A multisystem, multi-modality study was performed, examining computational simulations (Aliev-Panfilov (APV) model, Courtmanche-Nattel model), experimentally acquired optical mapping Atrial and Ventricular Fibrillation (AF/VF) data, and clinically acquired human AF and VF. Distributions of all PS lifetimes across full epochs of AF, VF, or computational simulations, were compared with distributions formed from lifetimes of PS existing at 10,000 simulated commencement timepoints. Results: In all systems, an inspection paradox led towards oversampling of PS with longer lifetimes. In APV computational simulations there was a mean PS lifetime shift of +84.9% (95% CI, ± 0.3%) (p < 0.001 for observed vs overall), in Courtmanche-Nattel simulations of AF +692.9% (95% CI, ±57.7%) (p < 0.001), in optically mapped rat AF +374.6% (95% CI, ± 88.5%) (p = 0.052), in human AF mapped with basket catheters +129.2% (95% CI, ±4.1%) (p < 0.05), human AF-HD grid catheters 150.8% (95% CI, ± 9.0%) (p < 0.001), in optically mapped rat VF +171.3% (95% CI, ±15.6%) (p < 0.001), in human epicardial VF 153.5% (95% CI, ±15.7%) (p < 0.001). Conclusion: Visual inspection of phase movies has the potential to systematically oversample longer lasting PS, due to an inspection paradox. An inspection paradox is minimised by consideration of the overall distribution of PS lifetimes.

Promoting and countering misinformation during Australia's 2019-2020 bushfires: a case study of polarisation.

During Australia's unprecedented bushfires in 2019-2020, misinformation blaming arson surfaced on Twitter using #ArsonEmergency. The extent to which bots and trolls were responsible for disseminating and amplifying this misinformation has received media scrutiny and academic research. Here, we study Twitter communities spreading this misinformation during the newsworthy event, and investigate the role of online communities using a natural experiment approach-before and after reporting of bots promoting the hashtag was broadcast by the mainstream media. Few bots were found, but the most bot-like accounts were social bots, which present as genuine humans, and trolling behaviour was evident. Further, we distilled meaningful quantitative differences between two polarised communities in the Twitter discussion, resulting in the following insights. First, Supporters of the arson narrative promoted misinformation by engaging others directly with replies and mentions using hashtags and links to external sources. In response, Opposers retweeted fact-based articles and official information. Second, Supporters were embedded throughout their interaction networks, but Opposers obtained high centrality more efficiently despite their peripheral positions. By the last phase, Opposers and unaffiliated accounts appeared to coordinate, potentially reaching a broader audience. Finally, the introduction of the bot report changed the discussion dynamic: Opposers only responded immediately, while Supporters countered strongly for days, but new unaffiliated accounts drawn into the discussion shifted the dominant narrative from arson misinformation to factual and official information. This foiled Supporters' efforts, highlighting the value of exposing misinformation. We speculate that the communication strategies observed here could inform counter-strategies in other misinformation-related discussions. Supplementary Information: The online version contains supplementary material available at 10.1007/s13278-022-00892-x.

Understanding the origins of the basic equations of statistical fibrillatory dynamics.

The mechanisms governing cardiac fibrillation remain unclear; however, it most likely represents a form of spatiotemporal chaos with conservative system dynamics. Renewal theory has recently been suggested as a statistical formulation with governing equations to quantify the formation and destruction of wavelets and rotors in fibrillatory dynamics. In this perspective Review, we aim to explain the origin of the renewal theory paradigm in spatiotemporal chaos. The ergodic nature of pattern formation in spatiotemporal chaos is demonstrated through the use of three chaotic systems: two classical systems and a simulation of cardiac fibrillation. The logistic map and the baker's transformation are used to demonstrate how the apparently random appearance of patterns in classical chaotic systems has macroscopic parameters that are predictable in a statistical sense. We demonstrate that the renewal theory approach developed for cardiac fibrillation statistically predicts pattern formation in these classical chaotic systems. Renewal theory provides governing equations to describe the apparently random formation and destruction of wavelets and rotors in atrial fibrillation (AF) and ventricular fibrillation (VF). This statistical framework for fibrillatory dynamics provides a holistic understanding of observed rotor and wavelet dynamics and is of conceptual significance in informing the clinical and mechanistic research of the rotor and multiple-wavelet mechanisms of AF and VF.

A governing equation for rotor and wavelet number in human clinical ventricular fibrillation: Implications for sudden cardiac death.

BACKGROUND: Ventricular fibrillation (VF) is characterized by multiple wavelets and rotors. No equation to predict the number of rotors and wavelets observed during fibrillation has been validated in human VF. OBJECTIVE: The purpose of this study was to test the hypothesis that a single equation derived from a Markov M/M/∞ birth-death process could predict the number of rotors and wavelets occurring in human clinical VF. METHODS: Epicardial induced VF (256-electrode) recordings obtained from patients undergoing cardiac surgery were studied (12 patients; 62 epochs). Rate constants for phase singularity (PS) (which occur at the pivot points of rotors) and wavefront (WF) formation and destruction were derived by fitting distributions to PS and WF interformation and lifetimes. These rate constants were combined in an M/M/∞ governing equation to predict the number of PS and WF in VF episodes. Observed distributions were compared to those predicted by the M/M/∞ equation. RESULTS: The M/M/∞ equation accurately predicted average PS and WF number and population distribution, demonstrated in all epochs. Self-terminating episodes of VF were distinguished from VF episodes requiring termination by a trend toward slower PS destruction, slower rates of PS formation, and a slower mixing rate of the VF process, indicated by larger values of the second largest eigenvalue modulus of the M/M/∞ birth-death matrix. The longest-lasting PS (associated with rotors) had shorter interactivation time intervals compared to shorter-lasting PS lasting <150 ms (∼1 PS rotation in human VF). CONCLUSION: The M/M/∞ equation explains the number of wavelets and rotors observed, supporting a paradigm of VF based on statistical fibrillatory dynamics.

Dataset of seized wildlife and their intended uses.

The illegal wildlife trade (IWT) threatens conservation and biosecurity efforts. The Internet has greatly facilitated the trade of wildlife, and researchers have increasingly examined the Internet to uncover illegal trade. However, most efforts to locate illegal trade on the Internet are targeted to one or few taxa or products. Large-scale efforts to find illegal wildlife on the Internet (e-commerce, social media, dark web) may be facilitated by a systematic compilation of illegally traded wildlife taxa and their uses. Here, we provide such a dataset. We used seizure records from three global wildlife trade databases to compile the identity of seized taxa along with their intended usage (i.e., use-type). Our dataset includes c. 4.9k distinct taxa representing c. 3.3k species and contains c. 11k taxa-use combinations from 110 unique use-types. Further, we acquired over 45k common names for seized taxa from over 100 languages. Our dataset can be used to conduct large-scale broad searches of the Internet to find illegally traded wildlife. Further, our dataset can be filtered for more targeted searches of specific taxa or derived products.

Text classification to streamline online wildlife trade analyses.

Automated monitoring of websites that trade wildlife is increasingly necessary to inform conservation and biosecurity efforts. However, e-commerce and wildlife trading websites can contain a vast number of advertisements, an unknown proportion of which may be irrelevant to researchers and practitioners. Given that many wildlife-trade advertisements have an unstructured text format, automated identification of relevant listings has not traditionally been possible, nor attempted. Other scientific disciplines have solved similar problems using machine learning and natural language processing models, such as text classifiers. Here, we test the ability of a suite of text classifiers to extract relevant advertisements from wildlife trade occurring on the Internet. We collected data from an Australian classifieds website where people can post advertisements of their pet birds (n = 16.5k advertisements). We found that text classifiers can predict, with a high degree of accuracy, which listings are relevant (ROC AUC ≥ 0.98, F1 score ≥ 0.77). Furthermore, in an attempt to answer the question 'how much data is required to have an adequately performing model?', we conducted a sensitivity analysis by simulating decreases in sample sizes to measure the subsequent change in model performance. From our sensitivity analysis, we found that text classifiers required a minimum sample size of 33% (c. 5.5k listings) to accurately identify relevant listings (for our dataset), providing a reference point for future applications of this sort. Our results suggest that text classification is a viable tool that can be applied to the online trade of wildlife to reduce time dedicated to data cleaning. However, the success of text classifiers will vary depending on the advertisements and websites, and will therefore be context dependent. Further work to integrate other machine learning tools, such as image classification, may provide better predictive abilities in the context of streamlining data processing for wildlife trade related online data.

Exploring the effect of streamed social media data variations on social network analysis.

To study the effects of online social network (OSN) activity on real-world offline events, researchers need access to OSN data, the reliability of which has particular implications for social network analysis. This relates not only to the completeness of any collected dataset, but also to constructing meaningful social and information networks from them. In this multidisciplinary study, we consider the question of constructing traditional social networks from OSN data and then present several measurement case studies showing how variations in collected OSN data affect social network analyses. To this end, we developed a systematic comparison methodology, which we applied to five pairs of parallel datasets collected from Twitter in four case studies. We found considerable differences in several of the datasets collected with different tools and that these variations significantly alter the results of subsequent analyses. Our results lead to a set of guidelines for researchers planning to collect online data streams to infer social networks.

The acceptability and uptake of smartphone tracking for COVID-19 in Australia.

In response to the COVID-19 pandemic, many Governments are instituting mobile tracking technologies to perform rapid contact tracing. However, these technologies are only effective if the public is willing to use them, implying that their perceived public health benefits must outweigh personal concerns over privacy and security. The Australian federal government recently launched the 'COVIDSafe' app, designed to anonymously register nearby contacts. If a contact later identifies as infected with COVID-19, health department officials can rapidly followup with their registered contacts to stop the virus' spread. The current study assessed attitudes towards three tracking technologies (telecommunication network tracking, a government app, and Apple and Google's Bluetooth exposure notification system) in two representative samples of the Australian public prior to the launch of COVIDSafe. We compared these attitudes to usage of the COVIDSafe app after its launch in a further two representative samples of the Australian public. Using Bayesian methods, we find widespread acceptance for all tracking technologies, however, observe a large intention-behaviour gap between people's stated attitudes and actual uptake of the COVIDSafe app. We consider the policy implications of these results for Australia and the world at large.

Risk mapping for COVID-19 outbreaks in Australia using mobility data.

COVID-19 is highly transmissible and containing outbreaks requires a rapid and effective response. Because infection may be spread by people who are pre-symptomatic or asymptomatic, substantial undetected transmission is likely to occur before clinical cases are diagnosed. Thus, when outbreaks occur there is a need to anticipate which populations and locations are at heightened risk of exposure. In this work, we evaluate the utility of aggregate human mobility data for estimating the geographical distribution of transmission risk. We present a simple procedure for producing spatial transmission risk assessments from near-real-time population mobility data. We validate our estimates against three well-documented COVID-19 outbreaks in Australia. Two of these were well-defined transmission clusters and one was a community transmission scenario. Our results indicate that mobility data can be a good predictor of geographical patterns of exposure risk from transmission centres, particularly in outbreaks involving workplaces or other environments associated with habitual travel patterns. For community transmission scenarios, our results demonstrate that mobility data add the most value to risk predictions when case counts are low and spatially clustered. Our method could assist health systems in the allocation of testing resources, and potentially guide the implementation of geographically targeted restrictions on movement and social interaction.

A guide to using the internet to monitor and quantify the wildlife trade.

The unrivaled growth in e-commerce of animals and plants presents an unprecedented opportunity to monitor wildlife trade to inform conservation, biosecurity, and law enforcement. Using the internet to quantify the scale of the wildlife trade (volume and frequency) is a relatively recent and rapidly developing approach that lacks an accessible framework for locating relevant websites and collecting data. We produced an accessible guide for internet-based wildlife trade surveillance. We detailed a repeatable method involving a systematic internet search, with search engines, to locate relevant websites and content. For data collection, we highlight web-scraping technology as an efficient way to collect data in an automated fashion at regularly timed intervals. Our guide is applicable to the multitude of trade-based contexts because researchers can tailor search keywords for specific taxa or derived products and locations of interest. We provide information for working with the diversity of websites used in wildlife trade. For example, to locate relevant content on social media (e.g., posts or groups), each social media platform should be examined individually via the site's internal search engine. A key advantage of using the internet to study wildlife trade is the relative ease of access to an increasing amount of trade-related data. However, not all wildlife trade occurs online and it may occur on unobservable sections of the internet.

Resumen Una Guía para Usar el Internet para Monitorear y Cuantificar el Mercado de Fauna El crecimiento incomparable del comercio en línea de animales y plantas representa una oportunidad sin precedentes para monitorear el mercado de fauna y así orientar a la conservación, la bioseguridad y la aplicación de la ley. El uso del internet para cuantificar la escala del mercado de fauna (volumen y frecuencia) es una estrategia relativamente reciente y de rápido desarrollo que carece de un marco de trabajo accesible para la localización de sitios web relevantes y para la recolección de datos. Realizamos una guía accesible para la vigilancia del mercado de fauna en internet. Detallamos un método repetible que involucra una búsqueda sistemática por internet, por medio de buscadores, para localizar sitios web y contenidos relevantes. Para la recolección de datos, resaltamos la tecnología de web scraping como una manera eficiente de obtener datos de manera automatizada a intervalos regulares de tiempo. Nuestra guía puede aplicarse a la multitud de contextos basados en el mercado porque los investigadores pueden adaptar las palabras de búsqueda a taxones específicos o productos derivados y a localidades de interés. Proporcionamos información para poder trabajar con la diversidad de sitios web que se usan para el mercado de fauna. Por ejemplo, para localizar contenido relevante en las redes sociales (p. ej.: publicaciones o grupos), cada plataforma social debería ser examinada individualmente por medio del buscador interno del sitio. Una ventaja importante de usar el internet para estudiar el mercado de fauna es el acceso relativamente sencillo a una creciente cantidad de datos relacionados con el mercado. Sin embargo, no todo el mercado de fauna ocurre en línea y puede que suceda en secciones inobservables del internet.

Complex Contagion Features without Social Reinforcement in a Model of Social Information Flow.

Contagion models are a primary lens through which we understand the spread of information over social networks. However, simple contagion models cannot reproduce the complex features observed in real-world data, leading to research on more complicated complex contagion models. A noted feature of complex contagion is social reinforcement that individuals require multiple exposures to information before they begin to spread it themselves. Here we show that the quoter model, a model of the social flow of written information over a network, displays features of complex contagion, including the weakness of long ties and that increased density inhibits rather than promotes information flow. Interestingly, the quoter model exhibits these features despite having no explicit social reinforcement mechanism, unlike complex contagion models. Our results highlight the need to complement contagion models with an information-theoretic view of information spreading to better understand how network properties affect information flow and what are the most necessary ingredients when modeling social behavior.

Elucidating user behaviours in a digital health surveillance system to correct prevalence estimates.

Estimating seasonal influenza prevalence is of undeniable public health importance, but remains challenging with traditional datasets due to cost and timeliness. Digital epidemiology has the potential to address this challenge, but can introduce sampling biases that are distinct to traditional systems. In online participatory health surveillance systems, the voluntary nature of the data generating process must be considered to address potential biases in estimates. Here we examine user behaviours in one such platform, FluTracking, from 2011 to 2017. We build a Bayesian model to estimate probabilities of an individual reporting in each week, given their past reporting behaviour, and to infer the weekly prevalence of influenza-like-illness (ILI) in Australia. We show that a model that corrects for user behaviour can substantially affect ILI estimates. The model examined here elucidates several factors, such as the status of having ILI and consistency of prior reporting, that are strongly associated with the likelihood of participating in online health surveillance systems. This framework could be applied to other digital participatory health systems where participation is inconsistent and sampling bias may be of concern.

Prospective cross-sectional study using Poisson renewal theory to study phase singularity formation and destruction rates in atrial fibrillation (RENEWAL-AF): Study design.

BACKGROUND: Unstable functional reentrant circuits known as rotors have been consistently observed in atrial fibrillation and are mechanistically believed critical to the maintenance of the arrhythmia. Recently, using a Poisson renewal theory-based quantitative framework, we have demonstrated that rotor formation (λf) and destruction rates (λd) can be measured using in vivo electrophysiologic data. However, the association of λf and λd with clinical, electrical, and structural markers of atrial fibrillation phenotype is unknown. METHODS: RENEWAL-AF is a multicenter prospective cross-sectional study recruiting adult patients with paroxysmal or persistent atrial fibrillation undergoing clinically indicated catheter ablation. Patients will undergo intraprocedural electrophysiologic atrial fibrillation mapping, with λf and λd to be determined from 2-minute unipolar electrogram recordings acquired before ablation. The primary objective will be to determine the association of λf and λd as markers of fibrillatory dynamics with clinical, electrical, and structural markers of atrial fibrillation clinical phenotype, measured by preablation transthoracic echocardiogram and cardiac magnetic resonance imaging. An exploratory objective is the noninvasive assessment of λf and λd using surface ECG characteristics via a machine learning approach. RESULTS: Not applicable. CONCLUSION: This pilot study will provide insight into the correlation between λf/λd with clinical, electrophysiological, and structural markers of atrial fibrillation phenotype and provide a foundation for the development of noninvasive assessment of λf/λd using surface ECG characteristics will help expand the use of λf/λd in clinical practice.

How the Avengers assemble: Ecological modelling of effective cast sizes for movies.

The number of characters in a movie is an important feature. However, it is non-trivial to measure directly, for example naive metrics such as the number of credited characters vary wildly. Here, we show that a metric based on the notion of ecological diversity as expressed through a Shannon-entropy based metric can characterise the number of characters in a movie, and is useful in taxonomic classification. We also show how the metric can be generalised using Jensen-Shannon divergence to provide a measure of the similarity of characters appearing in different movies, for instance of use in recommendation systems, e.g., Netflix. We apply our measures to the Marvel Cinematic Universe (MCU), and show what they teach us about this highly successful franchise of movies. In particular, these measures provide a useful predictor of success for films in the MCU, as well as a natural means to understand the relationships between the stories in the overall film arc.

M/M/Infinity Birth-Death Processes - A Quantitative Representational Framework to Summarize and Explain Phase Singularity and Wavelet Dynamics in Atrial Fibrillation.

RATIONALE: A quantitative framework to summarize and explain the quasi-stationary population dynamics of unstable phase singularities (PS) and wavelets in human atrial fibrillation (AF) is at present lacking. Building on recent evidence showing that the formation and destruction of PS and wavelets in AF can be represented as renewal processes, we sought to establish such a quantitative framework, which could also potentially provide insight into the mechanisms of spontaneous AF termination. OBJECTIVES: Here, we hypothesized that the observed number of PS or wavelets in AF could be governed by a common set of renewal rate constants λ f (for PS or wavelet formation) and λ d (PS or wavelet destruction), with steady-state population dynamics modeled as an M/M/∞ birth-death process. We further hypothesized that changes to the M/M/∞ birth-death matrix would explain spontaneous AF termination. METHODS AND RESULTS: AF was studied in in a multimodality, multispecies study in humans, animal experimental models (rats and sheep) and Ramirez-Nattel-Courtemanche model computer simulations. We demonstrated: (i) that λ f and λ d can be combined in a Markov M/M/∞ process to accurately model the observed average number and population distribution of PS and wavelets in all systems at different scales of mapping; and (ii) that slowing of the rate constants λ f and λ d is associated with slower mixing rates of the M/M/∞ birth-death matrix, providing an explanation for spontaneous AF termination. CONCLUSION: M/M/∞ birth-death processes provide an accurate quantitative representational architecture to characterize PS and wavelet population dynamics in AF, by providing governing equations to understand the regeneration of PS and wavelets during sustained AF, as well as providing insight into the mechanism of spontaneous AF termination.

Renewal Theory as a Universal Quantitative Framework to Characterize Phase Singularity Regeneration in Mammalian Cardiac Fibrillation.

BACKGROUND: Despite a century of research, no clear quantitative framework exists to model the fundamental processes responsible for the continuous formation and destruction of phase singularities (PS) in cardiac fibrillation. We hypothesized PS formation/destruction in fibrillation could be modeled as self-regenerating Poisson renewal processes, producing exponential distributions of interevent times governed by constant rate parameters defined by the prevailing properties of each system. METHODS: PS formation/destruction were studied in 5 systems: (1) human persistent atrial fibrillation (n=20), (2) tachypaced sheep atrial fibrillation (n=5), (3) rat atrial fibrillation (n=4), (5) rat ventricular fibrillation (n=11), and (5) computer-simulated fibrillation. PS time-to-event data were fitted by exponential probability distribution functions computed using maximum entropy theory, and rates of PS formation and destruction (λf/λd) determined. A systematic review was conducted to cross-validate with source data from literature. RESULTS: In all systems, PS lifetime and interformation times were consistent with underlying Poisson renewal processes (human: λf, 4.2%/ms±1.1 [95% CI, 4.0-5.0], λd, 4.6%/ms±1.5 [95% CI, 4.3-4.9]; sheep: λf, 4.4%/ms [95% CI, 4.1-4.7], λd, 4.6%/ms±1.4 [95% CI, 4.3-4.8]; rat atrial fibrillation: λf, 33%/ms±8.8 [95% CI, 11-55], λd, 38%/ms [95% CI, 22-55]; rat ventricular fibrillation: λf, 38%/ms±24 [95% CI, 22-55], λf, 46%/ms±21 [95% CI, 31-60]; simulated fibrillation λd, 6.6-8.97%/ms [95% CI, 4.1-6.7]; R2≥0.90 in all cases). All PS distributions identified through systematic review were also consistent with an underlying Poisson renewal process. CONCLUSIONS: Poisson renewal theory provides an evolutionarily preserved universal framework to quantify formation and destruction of rotational events in cardiac fibrillation.