Fractional embeddings and stochastic time

As a model problem for the study of chaotic Hamiltonian systems, we look for the effects of a long-tail distribution of recurrence times on a fixed Hamiltonian dynamics. We follow Stanislavsky's approach of Hamiltonian formalism for fractional systems. We prove that his formalism can be retrieved from the fractional embedding theory. We deduce that the fractional Hamiltonian systems of Stanislavsky stem from a particular least action principle, said causal. In this case, the fractional embedding becomes coherent.Comment: 11 page

Irreversibility, least action principle and causality

The least action principle, through its variational formulation, possesses a finalist aspect. It explicitly appears in the fractional calculus framework, where Euler-Lagrange equations obtained so far violate the causality principle. In order to clarify the relation between those two principles, we firstly remark that the derivatives used to described causal physical phenomena are in fact left ones. This leads to a formal approach of irreversible dynamics, where forward and backward temporal evolutions are decoupled. This formalism is then integrated to the Lagrangian systems, through a particular embedding procedure. In this set-up, the application of the least action principle leads to distinguishing trajectories and variations dynamical status. More precisely, when trajectories and variations time arrows are opposed, we prove that the least action principle provides causal Euler-Lagrange equations, even in the fractional case. Furthermore, the embedding developped is coherent.Comment: 14 page

Discrete embeddings for Lagrangian and Hamiltonian systems

The general topic of the present paper is to study the conservation for some structural property of a given problem when discretising this problem. Precisely we are interested with Lagrangian or Hamiltonian structures and thus with variational problems attached to a least action principle. Considering a partial differential equation (PDE) deriving from such a variational principle, a natural question is to know whether this structure at the continuous level is preserved at the discrete level when discretising the PDE. To address this question a concept of \textit{coherence} is introduced. Both the differential equation (the PDE translating the least action principle) and the variational structure can be embedded at the discrete level. This provides two discrete embeddings for the original problem. In case these procedures finally provide the same discrete problem we will say that the discretisation is \textit{coherent}. Our purpose is illustrated with the Poisson problem. Coherence for discrete embeddings of Lagrangian structures is studied for various classical discretisations (finite elements, finite differences and finite volumes). Hamiltonian structures are shown to provide coherence between a discrete Hamiltonian structure and the discretisation of the mixed formulation of the PDE, both for mixed finite elements and mimetic finite differences methods.Comment: Acta Mathematica Vietnamica, Springer Singapore, A Para{\^i}tr

Variational integrators of fractional Lagrangian systems in the framework of discrete embeddings

International audienceThis paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a variational structure called Lagrangian structure. We are specially interested in the conservation at the discrete level of this Lagrangian structure by discrete embeddings. We then replace in this framework the variational integrators developed in [10, Chapter VI.6] and in [12]. Finally, we extend the notion of discrete embeddings and variational integrators to fractional Lagrangian systems

Variational integrator for fractional Euler–Lagrange equations

International audienceWe extend the notion of variational integrator for classical Euler-Lagrange equations to the fractional ones. As in the classical case, we prove that the variational integrator allows to preserve Noether-type results at the discrete level

Multitemporal Observations of Sugarcane by TerraSAR-X Images

The objective of this study is to investigate the potential of TerraSAR-X (X-band) in monitoring sugarcane growth on Reunion Island (located in the Indian Ocean). Multi-temporal TerraSAR data acquired at various incidence angles (17°, 31°, 37°, 47°, 58°) and polarizations (HH, HV, VV) were analyzed in order to study the behaviour of SAR (synthetic aperture radar) signal as a function of sugarcane height and NDVI (Normalized Difference Vegetation Index). The potential of TerraSAR for mapping the sugarcane harvest was also studied. Radar signal increased quickly with crop height until a threshold height, which depended on polarization and incidence angle. Beyond this threshold, the signal increased only slightly, remained constant, or even decreased. The threshold height is slightly higher with cross polarization and higher incidence angles (47° in comparison with 17° and 31°). Results also showed that the co-polarizations channels (HH and VV) were well correlated. High correlation between SAR signal and NDVI calculated from SPOT-4/5 images was observed. TerraSAR data showed that after strong rains the soil contribution to the backscattering of sugarcane fields can be important for canes with heights of terminal visible dewlap (htvd) less than 50 cm (total cane heights around 155 cm). This increase in radar signal after strong rains could involve an ambiguity between young and mature canes. Indeed, the radar signal on TerraSAR images acquired in wet soil conditions could be of the same order for fields recently harvested and mature sugarcane fields, making difficult the detection of cuts. Finally, TerraSAR data at high spatial resolution were shown to be useful for monitoring sugarcane harvest when the fields are of small size or when the cut is spread out in time. The comparison between incidence angles of 17°, 37° and 58° shows that 37° is more suitable to monitor the sugarcane harvest. The cut is easily detectable on TerraSAR images for data acquired less than two or three months after the cut. The radar signal decreases about 5dB for images acquired some days after the cut and 3 dB for data acquired two month after the cut (VV-37°). The difference in radar signal becomes negligible (<1 dB) between harvested fields and mature canes for sugarcane harvested since three months or more

Black spot diseases in seven commercial fish species from the English Channel and the North Sea: infestation levels, identification and population genetics of Cryptocotyle spp.

Fish are often speckled with “black spots” caused by metacercarial trematode infection, inducing a host response. Cryptocotyle spp. (Opisthorchiidae) are among the parasites responsible for this phenomenon. So far, the impact on human health is still unknown. In addition, few publications dealing with black spot recovery, identification, distribution and diversity among commercially important fish are available. Moreover, “black spots” have been observed by fishermen on marine fish, revealing an appreciable but unquantified presence in consumed fish. An epidemiological survey of 1,586 fish from seven commercial species (herring, sprat, whiting, pout, dab, flounder, and plaice) was conducted in the Eastern English Channel and the North Sea in January 2019 and 2020. Encysted metacercariae were found in 325 out of 1,586 fish, with a total prevalence of 20.5%. Intensity of infection varied from 1 to 1,104 parasites. The recorded encysted metacercariae were identified either by microscopic examination or with molecular tools. Partial sequences of the mtDNA cox1 gene and of the rDNA ITS region were obtained. Two species of Cryptocotyle, Cryptocotyle lingua (Creplin, 1825) and Cryptocotyle concava (Creplin, 1825) were found. Metacercariae belonging to other trematode families were also identified. Molecular phylogenetic analysis and haplotype network construction were performed to confirm the identification and to study the potential presence of different populations of Cryptocotyle spp. This survey enabled us to describe the distribution of two species of Cryptocotyle in the English Channel and North Sea ecosystems. The observed differences in infestation levels between fish species and geographical areas will contribute to better understanding of the ecology of these parasites

Investigation of 3D glenohumeral displacements from 3D reconstruction using biplane X-ray images: Accuracy and reproducibility of the technique and preliminary analysis in rotator cuff tear patients

Rotator cuff (RC) tears may be associated with increased glenohumeral instability; however, this instability is difficult to quantify using currently available diagnostic tools. Recently, the three-dimensional (3D) reconstruction and registration method of the scapula and humeral head, based on sequences of low-dose biplane X-ray images, has been proposed for glenohumeral displacement assessment. This research aimed to evaluate the accuracy and reproducibility of this technique and to investigate its potential with a preliminary application comparing RC tear patients and asymptomatic volunteers. Accuracy was assessed using CT scan model registration on biplane X-ray images for five cadaveric shoulder specimens and showed differences ranging from 0.6 to 1.4 mm depending on the direction of interest. Intra- and interobserver reproducibility was assessed through two operators who repeated the reconstruction of five subjects three times, allowing defining 95% confidence interval ranging from ±1.8 to ±3.6 mm. Intraclass correlation coefficient varied between 0.84 and 0.98. Comparison between RC tear patients and asymptomatic volunteers showed differences of glenohumeral displacements, especially in the superoinferior direction when shoulder was abducted at 20 and 45 . This study thus assessed the accuracy of the low-dose 3D biplane X-ray reconstruction technique for glenohumeral displacement assessment and showed potential in biomechanical and clinical research.Fondation Paris-Tech Programme BIOMECAM Chaire ParisTech Institut de Recherche Robert-Sauvé en Santé et Sécurité du Travail du Québec Natural Science and Engineering Research Council of Canada Fonds de Recherche sur la Nature et les Technologies du Québec Fonds de Recherche en Santé du Québec, EOS Imaging, and French pôle de compétitivité MEDICEN (STEREOS + program)