Analysis of a class of nonlinear and non-separable multiscale representations

In this paper, we introduce a particular class of nonlinear and non-separable multiscale representations which embeds most of these representations. After motivating the introduction of such a class on one-dimensional examples, we investigate the multi-dimensional and non-separable case where the scaling factor is given by a non-diagonal dilation matrix M. We also propose new convergence and stability results in L ^p and Besov spaces for that class of nonlinear and non-separable multiscale representations. We end the paper with an application of the proposed study to the convergence and the stability of some nonlinear multiscale representations.     

Smoothness characterization and stability for nonlinear multiscale representations

The goal of this Note is to present some theoretical results for the nonlinear multiscales representations concerning the smoothness characterization through the rate of decay of multiscales coefficients and stability. We introduce a general framework to analyze such properties. To cite this article: B. Matei, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

A Water-Soluble Polymer-Lumefantrine Conjugate for the Intravenous Treatment of Severe Malaria

Uncomplicated malaria is effectively treated with oral artemisinin-based combination therapy (ACT). Yet, there is an unmet clinical need for the intravenous treatment of the more fatal severe malaria. There is no combination intravenous therapy for uncomplicated due to the nonavailability of a water-soluble partner drug for the artemisinin, artesunate. The currently available treatment is a two-part regimen split into an intravenous artesunate followed by the conventional oral ACT . In a novel application of polymer therapeutics, the aqueous insoluble antimalarial lumefantrine is conjugated to a carrier polymer to create a new water-soluble chemical entity suitable for intravenous administration in a clinically relevant formulation . The conjugate is characterized by spectroscopic and analytical techniques, and the aqueous solubility of lumefantrine is determined to have increased by three orders of magnitude. Pharmacokinetic studies in mice indicate that there is a significant plasma release of lumefantrine and production its metabolite desbutyl-lumefantrine (area under the curve of metabolite is ≈10% that of the parent). In a Plasmodium falciparum malaria mouse model, parasitemia clearance is 50% higher than that of reference unconjugated lumefantrine. The polymer-lumefantrine shows potential for entering the clinic to meet the need for a one-course combination treatment for severe malaria.     

Analysis of motion tracking in echocardiographic image sequences: Influence of system geometry and point-spread function

This paper focuses on motion tracking in echocardiographic ultrasound images. The difficulty of this task is related to the fact that echographic image formation induces decorrelation between the underlying motion of tissue and the observed speckle motion. Since Meunier’s seminal work, this phenomenon has been investigated in many simulation studies as part of speckle tracking or optical flow-based motion estimation techniques. Most of these studies modeled image formation using a linear convolution approach, where the system point-spread function (PSF) was spatially invariant and the probe geometry was linear. While these assumptions are valid over a small spatial area, they constitute an oversimplification when a complete image is considered. Indeed, echocardiographic acquisition geometry relies on sectorial probes and the system PSF is not perfectly invariant, even if dynamic focusing is performed.This study investigated the influence of sectorial geometry and spatially varying PSF on speckle tracking. This was done by simulating a typical 64 elements, cardiac probe operating at 3.5 MHz frequency, using the simulation software Field II. This simulation first allowed quantification of the decorrelation induced by the system between two images when simple motion such as translation or incompressible deformation was applied. We then quantified the influence of decorrelation on speckle tracking accuracy using a conventional block matching (BM) algorithm and a bilinear deformable block matching (BDBM) algorithm. In echocardiography, motion estimation is usually performed on reconstructed images where the initial sectorial (i.e., polar) data are interpolated on a cartesian grid. We therefore studied the influence of sectorial acquisition geometry, by performing block matching on cartesian and polar data.Simulation results show that decorrelation is spatially variant and depends on the position of the region where motion takes place relative to the probe. Previous studies did not consider translation in their experiments, since their simulation model (spatially invariant PSF and linear probe) yields by definition no decorrelation. On the opposite, our realistic simulation settings (i.e., sectorial probe and realistic beamforming) show that translation yields decorrelation, particularly when translation is large (above 6 mm) and when the moving regions is located close to the probe (distance to probe less than 50 mm).The tracking accuracy study shows that tracking errors are larger for the usual cartesian data, whatever the estimation algorithm, indicating that speckle tracking is more reliable when based on the unconverted polar data: for axial translations in the range 0-10 mm, the maximum error associated to conventional block matching (BM) is 4.2 mm when using cartesian data and 1.8 mm for polar data. The corresponding errors are 1.8 mm (cartesian data) and 0.4 mm (polar data) for an applied deformation in the range 0-10%. We also show that accuracy is improved by using the bilinear deformable block matching (BDBM) algorithm. For translation, the maximum error associated to the bilinear deformable block matching is indeed 3.6 mm (cartesian data) and 1.2 mm (polar data). Regarding deformation, the error is 0.7 mm (cartesian data) and 0.3 mm (polar data). These figures also indicates that the larger improvement brought by the bilinear deformable block matching over standard block matching logically takes place when deformation on cartesian data is considered (the error drops from 1.8 to 0.7 mm is this case).We give a preliminary evaluation of this framework on a cardiac sequence acquired with a Toshiba Powervision 6000 imaging system using a probe operating at 3.25 MHz. As ground truth reference motion is not available in this case, motion estimation performance was evaluated by comparing a reference image (i.e., the first image of the sequence) and the subsequent images after motion compensation has been applied. The comparison was quantified by computing the normalized correlation between the reference and the motion-compensated images. The obtained results are consistent with the simulation data: correlation is smaller for cartesian data, whatever the estimation algorithm. The correlation associated to the conventional block matching (BM) is in the range 0.45-0.02 when using cartesian data and in the range 0.65-0.2 for polar data. The corresponding correlation ranges for the bilinear deformable block matching are 0.98-0.2 and 0.98-0.55. In the same way these figures indicate that the bilinear deformable block matching yield a larger improvement when cartesian data are considered (correlation range increases from 0.45-0.02 to 0.98-0.2 in this case).     

Evidence for baryonium exchange in medium and high energy scattering

We review the prominent effects supposed to be associated with the exchange of baryonium Regge trajectories. The experimental presence of all expected effects leads us to suggest that the baryonium exchange mechanism is a correct phenomenological picture and that mesons with isospin 2 or $\text{3}\text{2}$ or with strangeness ?2, strongly coupled to the baryon-antibaryon channels, must be observed. An unexpected enhancement of the pure baryonium channel cross sections in the case of baryon decuplet production is pointed out. We also show that the old ?′ puzzle in π^?p → π⁰n seems to be solved by considering a recent generalization of the baryonium concept.     

Towards a general theory of formallyp-adic fields

The work is devoted to develop a general framework for the theory of formallyp-adic fields and to prove in this context some analogues of certain results of the theory of formallyp-adic fields in the sense of Kochen-Roquette. The general theory is illustrated by examples.