Nonlinear trend removal should be carefully performed in heart rate variability analysis

$\bullet$ Background : In Heart rate variability analysis, the rate-rate time series suffer often from aperiodic non-stationarity, presence of ectopic beats etc. It would be hard to extract helpful information from the original signals. 10 $\bullet$ Problem : Trend removal methods are commonly practiced to reduce the influence of the low frequency and aperiodic non-stationary in RR data. This can unfortunately affect the signal and make the analysis on detrended data less appropriate. $\bullet$ Objective : Investigate the detrending effect (linear \& nonlinear) in temporal / nonliear analysis of heart rate variability of long-term RR data (in normal sinus rhythm, atrial fibrillation, 15 congestive heart failure and ventricular premature arrhythmia conditions). $\bullet$ Methods : Temporal method : standard measure SDNN; Nonlinear methods : multi-scale Fractal Dimension (FD), Detrended Fluctuation Analysis (DFA) \& Sample Entropy (Sam-pEn) analysis. $\bullet$ Results : The linear detrending affects little the global characteristics of the RR data, either 20 in temporal analysis or in nonlinear complexity analysis. After linear detrending, the SDNNs are just slightly shifted and all distributions are well preserved. The cross-scale complexity remained almost the same as the ones for original RR data or correlated. Nonlinear detrending changed not only the SDNNs distribution, but also the order among different types of RR data. After this processing, the SDNN became indistinguishable be-25 tween SDNN for normal sinus rhythm and ventricular premature beats. Different RR data has different complexity signature. Nonlinear detrending made the all RR data to be similar , in terms of complexity. It is thus impossible to distinguish them. The FD showed that nonlinearly detrended RR data has a dimension close to 2, the exponent from DFA is close to zero and SampEn is larger than 1.5 -- these complexity values are very close to those for 30 random signal. $\bullet$ Conclusions : Pre-processing by linear detrending can be performed on RR data, which has little influence on the corresponding analysis. Nonlinear detrending could be harmful and it is not advisable to use this type of pre-processing. Exceptions do exist, but only combined with other appropriate techniques to avoid complete change of the signal's intrinsic dynamics. 35 Keywords $\bullet$ heart rate variability $\bullet$ linear / nonlinear detrending $\bullet$ complexity analysis $\bullet$ mul-tiscale analysis $\bullet$ detrended fluctuation analysis $\bullet$ fractal dimension $\bullet$ sample entropy

Comparison of the Mechanical Behavior of Railroad Ballast in a Box Test under Sinusoidal and Realistic Train Loadings Using Discrete Element Method

A ballasted track is a popular type of railway track and its use is increasing all over the world. A ballasted track consists of different structural elements like rails, fasteners, sleepers, ballast layer, sub-ballast layer and subgrade. A ballast layer is considered as the main structural element of ballasted tracks; it has a significant contribution to track stability and alignment. After service, periodical maintenance of ballast layer is required to maintain its functionality. Ballast maintenance is a cost and time expensive operation. Better understanding of ballast mechanical behavior leads to better ballast design and efficient maintenance. Discrete Element Method has been used extensively in the literature to understand the mechanical behavior of railroad ballast in a box test. Nevertheless, in the literature most of the studies simulate train loading as pure continuous sinusoidal loading unlike the real train loading. This paper aims to investigate the influence of the simulated train loading on the mechanical behavior of railroad ballast after 1000 loading cycles. There are two simulated train-loading cases used in this study for comparison purposes; continuous sinusoidal loading and a more realistic train loading utilizing the Beam on Elastic Foundation theory. The results show a difference of ballast vertical settlement up to 14% between the two simulated train-loading cases

On the Ulam-Hyers-Rassias stability for a boundary value problem of implicit ψ-Caputo fractional integro-differential equation

The main purpose of this paper is to study the existence and uniqueness of a nonlinear implicit ψ-Caputo fractional order integro-differential boundary value problem using Schauder’s and Banach’s fixed point theorems. Besides, we study its stability using Ulam-Hyers-Rassias stability type. Finally, we demonstrate our main findings, with a particular case example included to show the significance of our results.Publisher's Versio

The fall of the reentry paradigm of cardiac fibrillation

International audienceCardiac fibrillation a ects the atria or the ventricles and, in both cases, poses major challenges to public health management. Atrial fibrillation is the predominant cause of embolic stroke while ventricular fibrillation leads to sudden cardiac arrest and death. The medical community of cardiac electro-physiologists consider cardiac fibrillation as a disease of known cause, namely a chaotic multiplication of electric pulse reentries, but of unknown trigger. Putative triggers are targeted in an e ort to solve this riddle by a combination of safe therapies including anti-arrhythmic drugs and catheter radio-frequency ablation. In two recent works (10.3389/fphys.2017.01139 and 10.3389/fphys.2019.00480), with Evgeniya Gerasimova Françoise Argoul and Alain Arneodo, we have provided evidence and modeling which clash with the accepted wisdom. We give here the main argument for the incompatibility of the random multifractal scaling, revealed in recordings of the electrical activity of fibrillating human hearts, with the reentry paradigm. In the model, pulse dynamics is akin to a random branching birth and death process due to a highly fluctuating conductance. In this respect, we sketch a calculation of the multifractal spectrum for our cardiac modeling, which underlines how the multifractal parameter is related to the variance of the abnormal capacitive electric field at the gap junction channels. Those new observations and modeling raise a number of theoretical and practical possibilities and new challenges, such as electric recording interpretation from the level of cell-to-cell coupling up to the level of neural modulations. Gray area Is atrial fibrillation characterized only by spatio-temporal irregularity of local beat-to-beat cycles? Figure 1: Left: Atrial fibrillation schematic mechanisms. Right: High density mapping of activation times

Handling noise in image deconvolution with local/non-local priors

International audienceNon-blind deconvolution consists in recovering a sharp latent image from a blurred image with a known kernel. Decon-volved images usually contain unpleasant artifacts due to the ill-posedness of the problem even when the kernel is known. Making use of natural sparse priors has shown to reduce ring-ing artifacts but handling noise remains limited. On the other hand, non-local priors have shown to give the best results in image denoising. We propose in this paper to combine both local and non-local priors to handle noise. We show that the blur increases the self-similarity within an image and thus makes non-local priors a good choice for denoising blurred images. However, denoising introduces outliers which are not Gaussian and should be well modeled. Experiments show that our method produces a better image reconstruction both visually and empirically compared to methods some popular methods

Geomechanical Modelling of Railroad Ballast: A Review

Traditional ballasted tracks have been used intensively around the world with ballast as the main material for tracks. Ballast has a significant contribution to the track alignment, stability and sustainability. After service, ballast deforms and degrades. Periodic ballast maintenance is needed which is a time and cost expensive activity. Understanding the mechanical behaviour of railroad ballast leads to better design and efficient maintenance. From the literature, there are two main approaches used to understand the mechanical behaviour of railroad ballast; large scale experimental and modelling. This paper aims to review the state of the art of literature on the modelling approaches used to understand ballast mechanical behaviour. It discusses the key findings from each modelling approach in understanding ballast mechanical behavior. It presents the main concerns and limitations of each modelling approach from different perspectives related to ballast modelling. It summarizes the limitations, gaps and gaps' developments of the researches used to understand ballast behaviour via modelling approach.Open Access funding provided by the Qatar National Library. This work has been carried out under a research project entitled "Framework for Research on Railway Engineering" which is supported by a grant sponsored by Qatar Rail with a grant reference number: QUEX-CENG-Rail 17/18.Scopu

A Non-Local Low-Rank Approach to Enforce Integrability

International audienceWe propose a new approach to enforce integrability using recent advances in non-local methods. Our formulation consists in a sparse gradient data-fitting term to handle outliers together with a gradient-domain non-local low-rank prior. This regularization has two main advantages : 1) the low-rank prior ensures similarity between non-local gradient patches, which helps recovering high-quality clean patches from severe outliers corruption, 2) the low-rank prior efficiently reduces dense noise as it has been shown in recent image restoration works. We propose an efficient solver for the resulting optimization formulation using alternate minimization. Experiments show that the new method leads to an important improvement compared to previous optimization methods and is able to efficiently handle both outliers and dense noise mixed together

Régularisation parcimonieuse pour le problème d'intégration en traitement d'images

International audienceLa reconstruction d'une surface ou image à partir d'un champ de gradient corrompu est une étape primordiale dans plusieurs applications en traitement d'images. Un tel champ peut contenir du bruit et des données aberrantes qui nuisent à la qualité de la reconstruction. On propose dans ce papier d'utiliser la parcimonie pour régulariser le problème, ainsi qu'une méthode efficace pour estimer une bonne solution du problème d'optimisation qui en résulte. Les expériences montrent que la méthode proposée permet d'améliorer considérablement la qualité de la reconstruction comparée aux méthodes précédentes

The role of abnormal inhibitory transmission at the gap junctions of cardiac cells in fibrillation

International audienceThe noisy aspect of data recorded by electrodes, on the inner surface of human atria during episodes of atrial fibrillation, exhibit intriguing features for excitable media. Instead of phase chaos as typically expected, it shares many common traits of non-equilibrium fluctuations in disordered systems or strong turbulence. To assess those peculiar observations we investigate a synaptic plasticity that affects conduction properties. Electrical synapses comprise many different kinds of connexins, which may be affected by diverse factors, so we use a generic approach. Slight detuning of their linear response leads to an instability of the modulating agents, here an excess charge. Acting on slow time scales of repolarisation, it is understood as collective modes propagating through and retroacting on each synapse: The medium is desynchronised. It is not a syncytium. Transient states are here associated with a phenomenon called electrical remodelling, which has not received any accepted description thus far. Moreover, from the properties of the model it is possible to start exploring phase space. Transitions between different regimes could help decipher stages in the evolution of the disease from acute to chronic, one main goal of cardiovascular research