Search

Compressed sensing (CS) ensures the recovery of sparse vectors from a number of randomized measurements proportional to their sparsity. The initial theory considers discretized domains, and the randomness makes the physical positions of the grid nodes irrelevant. Most imaging devices, however, operate over some continuous physical domain, and it makes sense to consider Dirac masses with arbitrary positions. In this article, we consider such a continuous setup and analyze the performance of the BLASSO algorithm, which is the continuous extension of the celebrated LASSO [Formula omitted] regularization method. This approach is appealing from a numerical perspective because it avoids to discretize the domain of interest. Previous works considered translation-invariant measurements, such as randomized Fourier coefficients, in which it makes clear that the discrete theory should be extended by imposing a minimum distance separation constraint (often called 'Rayleigh limit') between the Diracs. These prior works, however, rule out many domains and sensing operators of interest, which are not translation invariant. This includes, for instance, Laplace measurements over the positive reals and Gaussian mixture models over the mean-covariance space. Our theoretical advances crucially rely on the introduction of a canonical metric associated with the measurement operator, which is the so-called Fisher geodesic distance. In the case of Fourier measurements, one recovers the Euclidean metric, but this metric can cope with arbitrary (possibly non-translation invariant) domains. Furthermore, it is naturally invariant under joint reparameterization of both the sensing operator and the Dirac locations. Our second and main contribution shows that if the Fisher distance between spikes is larger than a Rayleigh separation constant, then the BLASSO recovers in a stable way a stream of Diracs, provided that the number of measurements is proportional (up to log factors) to the number of Diracs. We measure the stability using an optimal transport distance constructed on top of the Fisher geodesic distance. Our result is (up to log factor) sharp and does not require any randomness assumption on the amplitudes of the underlying measure. Our proof technique relies on an infinite-dimensional extension of the so-called golfing scheme which operates over the space of measures and is of general interest., Author(s): Clarice Poon [sup.1] , Nicolas Keriven [sup.2] , Gabriel Peyré [sup.3] Author Affiliations: (1) grid.7340.0, 0000 0001 2162 1699, Department of Mathematical Sciences, University of Bath, , Bath, UK [...]

Mechanical fatigue under strain controlled tension/tension (T/T) of rectangular un-notched and notched specimens of high density polyethylene and polyamide 6 was performed. Under large amplitude oscillatory elongation, the stress response is nonlinear asymmetric due to a different stress response during loading and unloading and was analyzed via discrete Fourier transform. Dynamic strain ([[epsilon].sub.0]) sweep tests revealed odd ([I.sub.3/1] [alpha] [[epsilon].sub.0.sup.2]) and even ([I.sub.2/1] [alpha] [[epsilon].sub.0.sup.1]) harmonics in the stress, well described by the Neo-Hooke's law. Before crack onset for the Nc specimens, the storage and loss moduli and [I.sub.2/1] are constant, but [I.sub.3/1] increases with fatigue. The first derivative of [I.sub.3/1] (([I.sub.3/1]/dN) and the cumulative nonlinearity [Q.sub.f] parameter (integral of [I.sub.3/1] /[[epsilon].sub.0.sup.2]) were found to be strong criteria predicting fatigue. To break the unnotched specimens in the low and high cycle fatigue regime, large strain amplitudes were applied, resulting for both materials in initial plastic deformation followed by buckling when a critical compression force is exceeded. This results in a different time evolution of the linear and nonlinear parameters, especially as a minimum in the [I.sub.2/1] curve. Finally, a model is proposed to describe the nonlinear viscoelastic specimen response under T/T and the effect of buckling. KEYWORDS buckling, mechanical fatigue, nonlinear stress response, plastic deformation, 1 | INTRODUCTION Failure of a part under a cyclic load or deformation is called mechanical fatigue break-up. It is typically characterized via the average applied stress ([[sigma].sub.0]) or the [...]

Gratings.sup.1 and holograms.sup.2 use patterned surfaces to tailor optical signals by diffraction. Despite their long history, variants with remarkable functionalities continue to be developed.sup.3,4. Further advances could exploit Fourier optics.sup.5, which specifies the surface pattern that generates a desired diffracted output through its Fourier transform. To shape the optical wavefront, the ideal surface profile should contain a precise sum of sinusoidal waves, each with a well defined amplitude, spatial frequency and phase. However, because fabrication techniques typically yield profiles with at most a few depth levels, complex 'wavy' surfaces cannot be obtained, limiting the straightforward mathematical design and implementation of sophisticated diffractive optics. Here we present a simple yet powerful approach to eliminate this design-fabrication mismatch by demonstrating optical surfaces that contain an arbitrary number of specified sinusoids. We combine thermal scanning-probe lithography.sup.6-8 and templating.sup.9 to create periodic and aperiodic surface patterns with continuous depth control and sub-wavelength spatial resolution. Multicomponent linear gratings allow precise manipulation of electromagnetic signals through Fourier-spectrum engineering.sup.10. Consequently, we overcome a previous limitation in photonics by creating an ultrathin grating that simultaneously couples red, green and blue light at the same angle of incidence. More broadly, we analytically design and accurately replicate intricate two-dimensional moiré patterns.sup.11,12, quasicrystals.sup.13,14 and holograms.sup.15,16, demonstrating a variety of previously unattainable diffractive surfaces. This approach may find application in optical devices (biosensors.sup.17, lasers.sup.18,19, metasurfaces.sup.4 and modulators.sup.20) and emerging areas in photonics (topological structures.sup.21, transformation optics.sup.22 and valleytronics.sup.23). Combining thermal scanning-probe lithography with templating enables the production of high-quality gratings that manipulate light through Fourier-spectrum engineering in ways that are not achievable with conventional gratings., Author(s): Nolan Lassaline [sup.1] , Raphael Brechbühler [sup.1] , Sander J. W. Vonk [sup.1] [sup.2] , Korneel Ridderbeek [sup.1] , Martin Spieser [sup.3] , Samuel Bisig [sup.3] , Boris le [...]

While arrow squid (Nototodarus gouldi) in Australia are currently managed as a single population, biological differences in individuals between locations of capture suggests these are separate stocks requiring stock-specific harvest strategies. We used two techniques to derive information about stock structure from different parts of the life cycle, providing a novel holistic approach to exploring stock structure. This study combined two techniques, statolith shape and statolith elemental composition, to determine dispersal patterns of N. gouldi between regions and evidence of separate stocks. While adult statolith shape provided evidence that adults caught in the two locations belonged to different stocks, statolith elemental composition suggested that N. gouldi caught at each location had hatched throughout their distribution, with egg mass and juvenile drift potentially facilitated by seasonal longitudinal ocean currents. However, there was evidence of asymmetry in ontogenetic movement of N. gouldi, with adults in Victoria contributing more to the Great Australian Bight stock than vice versa and with the implication that the Victorian stock may need to be managed as the source stock. Les encornets eventails (Nototodarus gouldi) en Australie sont actuellement geres comme s'ils constituaient une population unique; toutefois, des differences entre individus d'un lieu de capture a l'autre donnent a penser qu'ils appartiennent a des stocks distincts necessitant leurs strategies d'exploitation propres. Nous avons utilise deux techniques pour obtenir de l'information sur la structure des stocks pour differentes parties du cycle biologique, dans une nouvelle approche holistique d'exploration de la structure des stocks. L'etude combine la determination de la forme et de la composition elementaire des statolithes afin d'etablir les motifs de dispersion de N. gouldi d'une region a l'autre et detecter d'eventuels indices de la presence de stocks distincts. Si la forme des statolithes d'adultes indique que des adultes captures en deux endroits differents appartiennent a des stocks distincts, la composition elementaire des statolithes indiquerait que les N. gouldi captures dans chaque endroit ont eclos a la grandeur de leur aire de repartition, la derive des masses d'reufs et des juveniles etant potentiellement facilitee par des courants oceaniques longitudinaux saisonniers. Des signes d'asymetrie des deplacements ontogeniques de N. gouldi ont toutefois ete notes, les adultes de Victoria ayant une plus grande contribution au stock de la Grande Baie australienne que l'inverse, ce qui donne a penser que le stock de Victoria pourrait devoir etre gere en tant que stock source. [Traduit par la Redaction], Introduction Stock identification and recognition is a fundamental requirement of fisheries assessments and management (Cadrin et al. 2005) and can be relatively straight forward for site-attached species, who once recruited [...]

In a previous paper we used our integro-differential extension of Gaussian transforms to find the closed analytic form for hydrogenic bound-state transitions with arbitrarily high quantum numbers due to projectile impact excitation via Coulomb potentials (in the intermediate representation). Here we extend that result to Yukawa potentials, but do so by utilizing Fourier transforms. The result is used to find the first-order cross section for proton impact excitation of hydrogen to the 2s-7s final states. Because the results hold for any initial and final quantum states, and the amplitude may be easily converted for use with pseudostates, it may be used to automatically calculate sums over intermediate pseudostate propagators whose (bound and free) principal and angular quantum numbers can become very large. This result may be extended to multi-electron transition amplitudes by representing initial and final states by configuration-interaction wave-functions. PACS Nos.: 34.10.+x, 2.90.+p, 34.50.Fa. Precedemment, nous avons utilise une extension integro-differentielle des transformees de Gauss pour trouver la forme analytique pour les transitions entre etats lies hydrogeniques avec nombres quantiques arbitrairement eleves, suite aune excitation par impact via des potentiels de Coulomb (dans la representation intermediaire). Nous etendons ici ce resultat aux potentiels de Yukawa, mais suivant une transformee de Fourier. Nous utilisons le resultat pour trouver la section efficace au premier ordre de l'excitation par impact de proton sur de l'hydrogene vers les etats finals 2s-7s. Parce que ce resultat reste valide pour tous les etats initiaux et finals et que l'amplitude peut facilement etre convertie pour pseudo-etats, il peut etre utilise pour calculer automatiquement des sommes sur des propagateurs de pseudo-etats intermediaires dont les nombres quantiques principaux et angulaires peuvent devenir tres grands. Ce resultat peut meme etre etendu aux amplitudes de transition multielectroniques en representant les etats initial et final par des fonctions d'onde de configuration d'interaction. [Traduit par le Redaction], 1. Introduction Atomic physics is an ideal testing ground for new methods in quantum theory because the interactions (potential functions) are known and the quantum wave functions may often be [...]