Inter-event times of various human behaviour are apparently non-Poissonian and obey long-tailed distributions as opposed to exponential distributions, which correspond to Poisson processes. It has been suggested that human individuals may switch between different states, in each of which they are regarded to generate events obeying a Poisson process. If this is the case, inter-event times should approximately obey a mixture of exponential distributions with different parameter values. In the present study, we introduce the minimum description length principle to compare mixtures of exponential distributions with different numbers of components (i.e. constituent exponential distributions). Because these distributions violate the identifiability property, one is mathematically not allowed to apply the Akaike or Bayes information criteria to their maximum-likelihood estimator to carry out model selection. We overcome this theoretical barrier by applying a minimum description principle to joint likelihoods of the data and latent variables. We show that mixtures of exponential distributions with a few components are selected, as opposed to more complex mixtures in various datasets, and that the fitting accuracy is comparable to that of state-of-the-art algorithms to fit power-law distributions to data. Our results lend support to Poissonian explanations of apparently non-Poissonian human behaviour.
Download full-text PDF |
Source |
---|---|
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7062064 | PMC |
http://dx.doi.org/10.1098/rsos.191643 | DOI Listing |
Nanoscale Adv
December 2024
Department of Mechanical Engineering, IIT Bombay Mumbai Maharashtra India 400076
Using the spectral energy density method, we predict the phonon scattering mean lifetimes of polycrystalline graphene (PC-G) having polycrystallinity only along the -axis with seven different misorientation (tilt) angles at room temperature. Contrary to other studies on PC-G samples, our results indicate a strong dependence of the thermal conductivity (TC) on the tilt angles which we attribute to careful preparation of our grain boundaries-based samples without introducing any local strains and ensuring periodic boundary conditions for the supercells along the and axes. We also show that the square of the group velocity components along and axes and the phonon lifetimes are uncorrelated and the phonon density of states are almost the same for all samples with different tilt angles.
View Article and Find Full Text PDFSci Rep
January 2025
Department of Infection Biology, London School of Hygiene and Tropical Medicine, Keppel St, London, WC1E 7HT, UK.
The significance of multiplication rate variation in malaria parasites needs to be determined, particularly for Plasmodium falciparum, the species that causes most virulent infections. To investigate this, parasites from cases presenting to hospital in The Gambia and from local community infections were culture-established and then tested under exponential growth conditions in a standardised six-day multiplication rate assay. The multiplication rate distribution was lower than seen previously in clinical isolates from another area in West Africa where infection is more highly endemic.
View Article and Find Full Text PDFPLoS One
January 2025
Department of Mathematics, College of Science, University of Hafr Al Batin, Hafar Al-Batin, Saudi Arabia.
In this paper, we propose a new flexible statistical distribution, the Topp-Leone Exponentiated Chen distribution, to model real-world data effectively, with a particular focus on COVID-19 data. The motivation behind this study is the need for a more flexible distribution that can capture various hazard rate shapes (e.g.
View Article and Find Full Text PDFISA Trans
December 2024
School of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, China. Electronic address:
This paper addresses the event-based sliding mode control problem for singularly perturbed systems with switching parameters. Unlike traditional Markovian switching systems, singularly perturbed S-MSSs allow more flexible state transitions, which can be described by a general distribution rather than the exponential distribution assumed in Markovian switching systems. To enhance the performance of such systems, a novel memory-based dynamic event-triggered protocol (DETP) is proposed, incorporating a memory term for the auxiliary offset variable.
View Article and Find Full Text PDFFront Neurol
December 2024
Department of Head and Neck Surgery and Brain Research Institute, David Geffen School of Medicine at UCLA, Los Angeles, CA, United States.
The relative accessibility and simplicity of vestibular sensing and vestibular-driven control of head and eye movements has made the vestibular system an attractive subject to experimenters and theoreticians interested in developing realistic quantitative models of how brains gather and interpret sense data and use it to guide behavior. Head stabilization and eye counter-rotation driven by vestibular sensory input in response to rotational perturbations represent natural, ecologically important behaviors that can be reproduced in the laboratory and analyzed using relatively simple mathematical models. Models drawn from dynamical systems and control theory have previously been used to analyze the behavior of vestibular sensory neurons.
View Article and Find Full Text PDFEnter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!