Signals with varying periodicity frequently appear in real-world phenomena, necessitating the development of efficient modelling techniques to map the measured nonlinear timeline to linear time. Here we propose a regression model that allows for a representation of periodic and dynamic patterns observed in time series data. The model incorporates a hidden strictly positive stochastic process that represents the instantaneous frequency, allowing the model to adapt and accurately capture varying time scales. A case study focusing on age estimation of narwhal tusks is presented, where cyclic element signals associated with annual growth layer groups are analyzed. We apply the methodology to data from one such tusk collected in West Greenland and use the fitted model to estimate the age of the narwhal. The proposed method is validated using simulated signals with known cycle counts and practical considerations and modelling challenges are discussed in detail. This research contributes to the field of time series analysis, providing a tool and valuable insights for understanding and modeling complex cyclic patterns in diverse domains.

Multivariate Pearson diffusions, also known as polynomial diffusions, are characterized by a linear drift vector and a diffusion matrix that is quadratic in the state variables. We derive exact closed-form expressions for the mean and covariance matrix of this class by using results on matrix exponential integrals. We then extend this framework to a broader class of nonlinear diffusions with Pearson-type multiplicative noise. The main contribution of this paper is a new parameter estimator for these nonlinear models based on Strang splitting (SS). The proposed method decomposes the stochastic system into a deterministic nonlinear ordinary differential equation (ODE) and a multivariate Pearson diffusion. We construct the SS estimator by composing their respective flows and applying a Gaussian transition approximation parameterized by the exact moments of the Pearson component. We prove that the SS estimator is consistent and asymptotically efficient. Furthermore, we introduce a new model within this broader class, which we call the Student Kramers oscillator, and we prove existence and uniqueness of the strong solution as well as existence of an invariant measure. We evaluate the SS estimator through simulation studies on this new oscillator and on the multivariate Wright-Fisher diffusion from population genetics. These simulations demonstrate that the SS estimator outperforms the standard Euler-Maruyama estimator, the Gaussian approximation estimator, and the local linearization estimator. Finally, we apply the SS estimator to fit the Student Kramers oscillator to Greenland ice core data.

Advances in tracking technologies for animal movement require new statistical tools to better exploit the increasing amount of data. Animal positions are usually calculated using the GPS or Argos satellite system and include potentially complex non-Gaussian and heavy-tailed measurement error patterns. Errors are usually handled through a Kalman filter algorithm, which can be sensitive to non-Gaussian error distributions. In this paper, we introduce a realistic latent movement model through an underdamped Langevin stochastic differential equation (SDE) that includes an additional drift term to ensure that the animal remains in a known spatial domain of interest. This can be applied to aquatic animals moving in water or terrestrial animals moving in a restricted zone delimited by fences or natural barriers. We demonstrate that the incorporation of these spatial constraints into the latent movement model improves the accuracy of filtering for noisy observations of the positions. We implement an Extended Kalman Filter as well as a particle filter adapted to non-Gaussian error distributions. Our filters are based on solving the SDE through splitting schemes to approximate the latent dynamic.

The stochastic FitzHugh-Nagumo (FHN) model is a two-dimensional nonlinear stochastic differential equation with additive degenerate noise, whose first component, the only one observed, describes the membrane voltage evolution of a single neuron. Due to its low-dimensionality, its analytical and numerical tractability and its neuronal interpretation, it has been used as a case study to test the performance of different statistical methods in estimating the underlying model parameters. Existing methods, however, often require complete observations, non-degeneracy of the noise or a complex architecture (e.g., to estimate the transition density of the process, ‘‘recovering’’ the unobserved second component) and they may not (satisfactorily) estimate all model parameters simultaneously. Moreover, these studies lack real data applications for the stochastic FHN model. The proposed method tackles all challenges (non-globally Lipschitz drift, non-explicit solution, lack of available transition density, degeneracy of the noise and partial observations). It is an intuitive and easy-to-implement sequential Monte Carlo approximate Bayesian computation algorithm, which relies on a recent computationally efficient and structure-preserving numerical splitting scheme for synthetic data generation and on summary statistics exploiting the structural properties of the process. All model parameters are successfully estimated from simulated data and, more remarkably, real action potential data of rats. The presented novel real-data fit may broaden the scope and credibility of this classic and widely used neuronal model.

We address parameter estimation in second-order stochastic differential equations (SDEs), which are prevalent in physics, biology, and ecology. The second-order SDE is converted to a first-order system by introducing an auxiliary velocity variable, which raises two main challenges. First, the system is hypoelliptic since the noise affects only the velocity, making the Euler-Maruyama estimator ill-conditioned. We propose an estimator based on the Strang splitting scheme to overcome this. Second, since the velocity is rarely observed, we adapt the estimator to partial observations. We present four estimators for complete and partial observations, using the full pseudo-likelihood or only the velocity-based partial pseudo-likelihood. These estimators are intuitive, easy to implement, and computationally fast, and we prove their consistency and asymptotic normality. Our analysis demonstrates that using the full pseudo-likelihood with complete observations reduces the asymptotic variance of the diffusion estimator. With partial observations, the asymptotic variance increases as a result of information loss but remains unaffected by the likelihood choice. However, a numerical study on the Kramers oscillator reveals that using the partial pseudo-likelihood for partial observations yields less biased estimators. We apply our approach to paleoclimate data from the Greenland ice core by fitting the Kramers oscillator model, capturing transitions between metastable states reflecting observed climatic conditions during glacial eras.

Narwhals in the Arctic are increasingly exposed to human activities that can temporarily or permanently threaten their survival by modifying their behavior. We examine GPS data from a population of narwhals exposed to ship and seismic airgun noise during a controlled experiment in 2018 in the Scoresby Sound fjord system in Southeast Greenland. The fjord system has a complex shore line, restricting the behavioral response options for the narwhals to escape the threats. We propose a new continuous-time correlated velocity model with varying coefficients that includes spatial constraints on movement. To assess the sound exposure effect we compare a baseline model for the movement before exposure to a response model for the movement during exposure. Our model, applied to the narwhal data, suggests increased tortuosity of the trajectories as a consequence of the spatial constraints, and further indicates that sound exposure can disturb narwhal motion up to a couple of tens of kilometers. Specifically, we found an increase in velocity and a decrease in the movement persistence.

Epidemic models are used to understand the dynamics of disease transmission and explore the possible measures for preventing the spread of infection in the population. Disease transmission is intrinsically random and severely affected by environmental factors. We investigated a stochastic population model of the susceptible-infected-susceptible (SIS) type, in which infection spreads via both vertical and horizontal transmission routes. To incorporate stochasticity to the system, white multiplicative noise was taken into account in the horizontal disease transmission term. We proved that noise intensity, disease transmission, and recovery rates are potential routes for eradicating the disease. Furthermore, the parasite population reduces its fitness for some fixed noise if the relative fecundity of infected hosts and the disease transmission are low. However, if either of these is increased, it observes enhanced fitness. A simulation study illustrated the system's analytically dynamic properties and provided different insights. A case study for the imperfect vertical and horizontal infection transmission is also presented, supporting some of our observed theoretical results.

IntroductionAge estimation is an important tool for understanding the life history of animal populations, and several techniques have been developed, each with its own strengths and limitations.MethodsIn this study, we apply a novel age estimation method that utilizes trace element signals with seasonal components obtained through laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) on tusks of 16 narwhals. We model tusk growth as a stochastic process that, by hypothesis, tracks the number of elapsed annual cycles. For each tusk, we estimate this process in order to derive model-based age estimates. ResultsWe show that this method provides objective and reproducible age estimates without requiring visually distinguishable growth layers. Age estimates are compared with those from other methods, specifically manual counting (visual reading) of growth layers, radiocarbon dating, and using aspartic acid racemization. Our model provided age estimates ranging from 16 to 60 years of age and showed strong agreement with manual counts for 14 of 16 individuals, with two critical exceptions differing by 9 and 14 years, respectively. DiscussionWe end with a discussion of modeling challenges and deficiencies related to this particular tusk dataset. Although demonstrated on narwhal tusks, we discuss how this method can be generalized to other mineralized materials with a layered structure.

We develop several statistical tests of the determinant of the diffusion coefficient of a stochastic differential equation, based on discrete observations on a time interval [0,T] sampled with a time step Δ. Our main contribution is to control the test Type I and Type II errors in a non asymptotic setting, i.e. when the number of observations and the time step are fixed. The test statistics are calculated from the process increments. In dimension 1, the density of the test statistic is explicit. In dimension 2, the test statistic has no explicit density but upper and lower bounds are proved. We also propose a multiple testing procedure in dimension greater than 2. Every test is proved to be of a given non-asymptotic level and separability conditions to control their power are also provided. A numerical study illustrates the properties of the tests for stochastic processes with known or estimated drifts.

The likelihood functions for discretely observed nonlinear continuous-time models based on stochastic differential equations are not available except for a few cases. Various parameter estimation techniques have been proposed, each with advantages, disadvantages, and limitations depending on the application. Most applications still use the Euler-Maruyama discretization, despite many proofs of its bias. More sophisticated methods, such as Kessler's Gaussian approximation, Ozaki's Local Linearization, Aït-Sahalia's Hermite expansions, or MCMC methods, might be complex to implement, do not scale well with increasing model dimension, or can be numerically unstable. We propose two efficient and easy-to-implement likelihood-based estimators based on the Lie-Trotter (LT) and the Strang (S) splitting schemes. We prove that S has $L^p$ convergence rate of order 1, a property already known for LT. We show that the estimators are consistent and asymptotically efficient under the less restrictive one-sided Lipschitz assumption. A numerical study on the 3-dimensional stochastic Lorenz system complements our theoretical findings. The simulation shows that the S estimator performs the best when measured on precision and computational speed compared to the state-of-the-art.

Over recent years, positive airway pressure (PAP) remote monitoring has transformed the management of OSA and produced a large amount of data. Accumulated PAP data provide valuable and objective information regarding patient treatment adherence and efficiency. However, the majority of studies that have analyzed longitudinal PAP remote monitoring have summarized data trajectories in static and simplistic metrics for PAP adherence and the residual apnea-hypopnea index by the use of mean or median values. The aims of this article are to suggest directions for improving data cleaning and processing and to address major concerns for the following data science applications: (1) conditions for residual apnea-hypopnea index reliability, (2) lack of standardization of indicators provided by different PAP models, (3) missing values, and (4) consideration of treatment interruptions. To allow fair comparison among studies and to avoid biases in computation, PAP data processing and management should be conducted rigorously with these points in mind. PAP remote monitoring data contain a wealth of information that currently is underused in the field of sleep research. Improving the quality and standardizing data handling could facilitate data sharing among specialists worldwide and enable artificial intelligence strategies to be applied in the field of sleep apnea. Over recent years, positive airway pressure (PAP) remote monitoring has transformed the management of OSA and produced a large amount of data. Accumulated PAP data provide valuable and objective information regarding patient treatment adherence and efficiency. However, the majority of studies that have analyzed longitudinal PAP remote monitoring have summarized data trajectories in static and simplistic metrics for PAP adherence and the residual apnea-hypopnea index by the use of mean or median values. The aims of this article are to suggest directions for improving data cleaning and processing and to address major concerns for the following data science applications: (1) conditions for residual apnea-hypopnea index reliability, (2) lack of standardization of indicators provided by different PAP models, (3) missing values, and (4) consideration of treatment interruptions. To allow fair comparison among studies and to avoid biases in computation, PAP data processing and management should be conducted rigorously with these points in mind. PAP remote monitoring data contain a wealth of information that currently is underused in the field of sleep research. Improving the quality and standardizing data handling could facilitate data sharing among specialists worldwide and enable artificial intelligence strategies to be applied in the field of sleep apnea.

Cet article propose une revue de la littérature nationale et internationale sur les effets causaux des campagnes de vaccination menées dans les pays de l’OCDE. Qu’elles prennent la forme de recommandations ou d’une obligation vaccinale, les campagnes de vaccination, et notamment celles menées en milieu scolaire ou ciblant les jeunes enfants, ont un effet direct très positif : elles contribuent à augmenter très fortement les taux de vaccination contre la maladie ciblée, pour la population visée par la campagne. Par ailleurs, la littérature met en évidence l’existence d’effets indirects de ces campagnes, c’est-à-dire d’effets collatéraux, qui s’étendent au-delà de la population ou du vaccin ciblés par la campagne. Certains de ces effets externes, négatifs, conduisent naturellement à s’interroger sur l’effet net de la campagne. Au total, notre revue de littérature montre l’importance, mais également la difficulté, d’évaluer les campagnes de vaccination, comme toute politique publique, dans leur globalité, en ne se focalisant pas seulement sur l’impact direct qu’elles peuvent avoir sur la population ciblée et le vaccin concerné.

Niche-conservative species are especially susceptible to changes in their environment, and detecting the negative effects of new stressors in their habitats is vital for safeguarding of these species. In the Arctic, human disturbance including marine traffic and exploration of resources is increasing rapidly due to climate change–induced reduction of sea ice. Here, we show that the narwhal, Monodon monoceros , is extremely sensitive to human-made noise. Narwhals avoided deep diving (> 350 m) with simultaneous reduction of foraging and increased shallow diving activity as a response to either ship sound alone or ship sound with concurrent seismic airgun pulses. Normal behavior decreased by 50 to 75% at distances where received sound levels were below background noise. Narwhals were equally responsive to both disturbance types, hence demonstrating their acute sensitivity to ship sound. This sensitivity coupled with their special behavioral-ecological strategy including a narrow ecological niche and high site fidelity makes them thus especially vulnerable to human impacts in the Arctic.

Over recent years, positive airway pressure (PAP) remote monitoring has transformed the management of OSA and produced a large amount of data. Accumulated PAP data provide valuable and objective information regarding patient treatment adherence and efficiency. However, the majority of studies that have analyzed longitudinal PAP remote monitoring have summarized data trajectories in static and simplistic metrics for PAP adherence and the residual apnea-hypopnea index by the use of mean or median values. The aims of this article are to suggest directions for improving data cleaning and processing and to address major concerns for the following data science applications: (1) conditions for residual apnea-hypopnea index reliability, (2) lack of standardization of indicators provided by different PAP models, (3) missing values, and (4) consideration of treatment interruptions. To allow fair comparison among studies and to avoid biases in computation, PAP data processing and management should be conducted rigorously with these points in mind. PAP remote monitoring data contain a wealth of information that currently is underused in the field of sleep research. Improving the quality and standardizing data handling could facilitate data sharing among specialists worldwide and enable artificial intelligence strategies to be applied in the field of sleep apnea.CHEST 2023; 163(5):1279-1291

The so-called Rayleigh-Plateau instability of fluid jets has been widely studied and is extensively used in the Continuous InkJet (CIJ) printing process. The present dataset contains the numerically-generated interfaces of Newtonian fluids jets in CIJ jetting conditions for low to moderately high stimulation amplitudes. We used Basilisk, an open-source Computational Fluid Dynamics (CFD) software specialized in multiphase flow to compute thousands of jets of fluids for Reynolds numbers ranging from 100 to 1000. The dataset gives raw data of CFD simulations liquid-air interfaces, for each Reynolds – stimulation amplitude pair. The present 10 GB dataset contains ≈110000 interfaces which allows to use novel machine learning and deep-learning approaches to explore jet morphologies evolution that can’t be addressed with the classical Rayleigh’s theory.

In this article, we construct and analyse an explicit numerical splitting method for a class of semi-linear stochastic differential equations (SDEs) with additive noise, where the drift is allowed to grow polynomially and satisfies a global one-sided Lipschitz condition. The method is proved to be mean-square convergent of order 1 and to preserve important structural properties of the SDE. First, it is hypoelliptic in every iteration step. Second, it is geometrically ergodic and has an asymptotically bounded second moment. Third, it preserves oscillatory dynamics, such as amplitudes, frequencies and phases of oscillations, even for large time steps. Our results are illustrated on the stochastic FitzHugh-Nagumo model and compared with known mean-square convergent tamed/truncated variants of the Euler-Maruyama method. The capability of the proposed splitting method to preserve the aforementioned properties may make it applicable within different statistical inference procedures. In contrast, known Euler-Maruyama type methods commonly fail in preserving such properties, yielding ill-conditioned likelihood-based estimation tools or computationally infeasible simulation-based inference algorithms.

The understanding of flowing properties of fluids and the knowledge of the related rheological properties are crucial from both a research and industrial point of view. To determine the complex rheological properties of fluids, many devices have thus been developed, the so-called rheometers. The main objective of the present paper is to identify the rheological properties of a fluid jetted using continuous inkjet (CIJ) printing process by comparing the morphology of the aforementioned jetted fluid to a dataset of known (rheologically speaking) fluid jet morphologies and properties of a fluid by the viscosity, the surface tension, and the density of fluids using large datasets and a CIJ printing process. When ejecting a fluid, the CIJ ejection process competes among several forces: inertial, viscous, surface tension, and elasticity, which affect the morphology of the resulting jet. Also, under certain conditions, the morphology of the jet is unique and directly related to the rheological properties of the fluid. We want to use this uniqueness to identify the fluid among a large dataset of known fluid jet morphologies to be compared with, to obtain its rheological properties. Using a large numerically generated dataset of Newtonian fluid jets, we show in this article that the identification of the viscosity using neural network is not only feasible but also proves to be very accurate with an average error of less than 1% for a large range of viscosities.

We evaluate the impact of a French vaccination campaign against Hepatitis B (HB) in 1994. Usinga regression discontinuity design, we show that this campaign created an exogenous shock on vaccinationbehavior, increasing the vaccination rate for children aged 11 and above. We also show that this vaccinationscheme led to a decline in the knowledge about HB transmission modes, as well as public confusion aboutthe target population. But our most important result is a drop in measles, mumps, and rubella (MMR)vaccination rate and an increase in the belief that measles is a benign disease. We interpret these results asa salience effect: the focus on HB vaccination may lead to a decrease in the beliefs that other vaccines are asimportant. We find that the decrease in MMR vaccination is mostly due to high-educated parents who aremore likely to substitute MMR with HB for their children, and could have been influenced by their familydoctor. The effect on MMR vaccination was relatively unexpected and may imply a negative externality.Measles is an extremely contagious disease. If the vaccination rate falls, the disease will spread further,raising the question of the net effect of the HB vaccination campaign on the well-being of the population.Overall, it shows the necessity - but also the difficulty- to evaluate the effects of a public policy as a whole,taking into account all potential side effects but also unexpected adverse effects.

Anthropogenic activities are increasing in the Arctic, posing a threat to niche-conservative species with high seasonal site fidelity, such as the narwhal Monodon monoceros. In this controlled sound exposure study, six narwhals were live-captured and instrumented with animal-borne tags providing movement and behavioural data, and exposed to concurrent ship noise and airgun pulses. All narwhals reacted to sound exposure with reduced buzzing rates, where the response was dependent on the magnitude of exposure defined as 1/distance to ship. Buzzing rate was halved at 12 km from the ship, and whales ceased foraging at 7-8 km. Effects of exposure could be detected at distances > 40 km from the ship.At only a few kilometres from the ship, the received high-frequency cetacean weighted sound exposure levels were below background noise indicating extreme sensitivity of narwhals towards sound disturbance and demonstrating their ability to detect signals embedded in background noise. The narwhal's reactions to sustained disturbance may have a plethora of consequences both at individual and population levels. The observed reactions of the whales demonstrate their auditory sensitivity but also emphasize, that anthropogenic activities in pristine narwhal habitats needs to be managed carefully if healthy narwhal populations are to be maintained.

Background Obstructive sleep apnea (OSA) is a chronic disease characterized by recurrent pharyngeal collapses during sleep. In most severe cases, continuous positive airway pressure (CPAP) consists in keeping the airways open by administering mild air pressure. This treatment faces adherence issues. Objectives Eight hundred and forty-eight subjects were equipped with CPAP prescribed at the Grenoble University Hospital between 2016 and 2018. Their daily CPAP uses have been recorded during the first 3 months. Our aim is to cluster these adherence time series. With hierarchical agglomerative clustering, we focused on the choices of the dissimilarity measure and the internal cluster validation index (CVI). Methods The Euclidean distance, the dynamic time warping (DTW) and the generalized summed discrete Frechet dissimilarity were implemented with three linkage strategies ("average," "complete," and "Ward"). The performances of each method (dissimilarity and linkage) were evaluated on a simulation study through the adjusted Rand index (ARI). The Ward linkage with DTW dissimilarity provided the best ARI. Then six different internal CVIs (Silhouette, Calinski Harabasz, Davies Bouldin, Modified Davies Bouldin, Dunn, and COP) were compared on their ability to choose the best number of clusters. The Dunn index beat the others. Results CPAP data were clustered with the Ward linkage, the DTW dissimilarity and the Dunn index. It identified six clusters, from a cluster of patients (N = 29 subjects) whose stopped the therapy early on to a cluster (N = 105) with increasing adherence over time. Other clusters were extremely good users (N = 151), good users (N = 150), moderate users (N = 235), and poor adherers (N = 178).