Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

Eimeria species (Apicomplexa: Eimeriidae) of podocnemis expansa (Schweigger) and geochelone denticulata (LINN.) from Amazonian Brazil (Reptilia: Chelonia)

Eimeria lagunculata, Eimeria mammiformis and Eimeria podocnemis n. spp., are described from the faeces of the fresh-water turtle Podocnemis expansa, in Pará State, north Brasil. Oocysts of E. lagunculata are ellipsoidal, 19.2 x 12.8 (17.0-20.7 x 11.8-14.1) mum, shape-index (= length/ width) 1.5 (1.4-1.7). Oocyst wall about 0.5-0.7 mum thick, with a prominent stopper-like micropyle at one pole. No oocyst residuum and no polar body. Sporocysts elongate ellipsoidal, 11.0 x 5.4 (10.4-11.8 x 5.2-6.0) mum, shape-index 2.0 (1.8-2.1): no Stieda body. A compact, ellipsoidal sporocyst residuum lies between the two sporozoites, which possess a posterior and an anterior refractile body. Oocysts of E. mammiformis broadly ellipsoidal, 30.0 x 19.4 (23.0-37.0 x 16.3-21.5) mum, shape-index 1.5 (1.1-1.9). Oocyst wall about 0.7 mum thick, with a prominent micropyle: no oocyst residuum and rarely a single polar body. Sporocysts ellipsoidal, 15.3 x 7.9 (14.8-17.0 x 7.4-9.6) mum, shape-index 2.0 (1.8-2.2), with a tiny Stieda body. Sporocyst residuum bulky, ellipsoidal: sporozoites with two conspicuous refractile bodies. E. podocnemis has broadly ellipsoidal oocysts, 17.0 x 12.8 (14.8-19.2 x 11.8-14.1) mum, shape-index 1.3 (1.1-1.4). Oocyst wall about 0.5-0.7 mum thick, with no micropyle. No oocyst residuum, but always a single polar body. Sporocysts ellipsoidal, 9.7 x 5.2 (8.9-10.4 x 4.4-6.0) mum, shape-index 1.9 (1.6-2.0), with no Stieda body. Sporocyst residuum bulky, ellipsoidal: sporocysts with 2 refractile bodies. Eimeria carinii n. sp., is recorded from the tortoise Geochelone denticulata, also from Pará. Oocyst wall about 1.2 mum thicl. No micropyle. Oocyst residuum limited to a number (about 10-20) of scattered granules: no polar body. Sporocysts broadly ellipsoidal, and with no Stieda body: they measure 8,8 x 7.3 (8.0-9.0 x 7.0-7.5) mum, shape-index 1.2 (1.1-1.3). Sporocyst residuum bulky, spherical to ellipsoidal: sporozoites possess both posterior and anterior refractile bodies.

Sparse regularization for fiber ODF reconstruction: from the suboptimality of ℓ2 and ℓ1 priors to ℓ0.

Diffusion MRI is a well established imaging modality providing a powerful way to probe the structure of the white matter non-invasively. Despite its potential, the intrinsic long scan times of these sequences have hampered their use in clinical practice. For this reason, a large variety of methods have been recently proposed to shorten the acquisition times. Among them, spherical deconvolution approaches have gained a lot of interest for their ability to reliably recover the intra-voxel fiber configuration with a relatively small number of data samples. To overcome the intrinsic instabilities of deconvolution, these methods use regularization schemes generally based on the assumption that the fiber orientation distribution (FOD) to be recovered in each voxel is sparse. The well known Constrained Spherical Deconvolution (CSD) approach resorts to Tikhonov regularization, based on an ℓ(2)-norm prior, which promotes a weak version of sparsity. Also, in the last few years compressed sensing has been advocated to further accelerate the acquisitions and ℓ(1)-norm minimization is generally employed as a means to promote sparsity in the recovered FODs. In this paper, we provide evidence that the use of an ℓ(1)-norm prior to regularize this class of problems is somewhat inconsistent with the fact that the fiber compartments all sum up to unity. To overcome this ℓ(1) inconsistency while simultaneously exploiting sparsity more optimally than through an ℓ(2) prior, we reformulate the reconstruction problem as a constrained formulation between a data term and a sparsity prior consisting in an explicit bound on the ℓ(0)norm of the FOD, i.e. on the number of fibers. The method has been tested both on synthetic and real data. Experimental results show that the proposed ℓ(0) formulation significantly reduces modeling errors compared to the state-of-the-art ℓ(2) and ℓ(1) regularization approaches.

Large Bayesian VARMAs

Vector Autoregressive Moving Average (VARMA) models have many theoretical properties which should make them popular among empirical macroeconomists. However, they are rarely used in practice due to over-parameterization concerns, difficulties in ensuring identification and computational challenges. With the growing interest in multivariate time series models of high dimension, these problems with VARMAs become even more acute, accounting for the dominance of VARs in this field. In this paper, we develop a Bayesian approach for inference in VARMAs which surmounts these problems. It jointly ensures identification and parsimony in the context of an efficient Markov chain Monte Carlo (MCMC) algorithm. We use this approach in a macroeconomic application involving up to twelve dependent variables. We find our algorithm to work successfully and provide insights beyond those provided by VARs.

Observations on some Avian Coccidia (Apicomplexa: Eimeriidae) in Amazonian Brazil

Oocysts of Eimeria porphyrulae n. sp. are described in faeces of Porphyrula martinica (Aves: Gruiformes: Rallidae). They are ellipsoidal to oval, 22.4 x 17.7 (20.0-23.7 x 16.2-18.7) µm, shape-index (length/width) 1.3. Oocyst wall about 1.25 µm thick, colourless, with two layers: inner one prominently striated. Micropyle and sub-micropylar granule present: no oocyst residuum. Sporocysts 17.5 x 9.0 (17.0-19.0 x 8.0-10.0) µm, shape-index 1.9, with inconspicuous Stieda/sub-Stieda bodies. Sporocyst residuum of scattered granules, sometimes a compact mass: sporozoites with two refractile bodies. Eimeria crypturelli n. sp. is described in faeces of Crypturellus soiu (Tinamiformes: Tinamidae). Oocysts ellipsoidal-oval, 20.75 x 14.5 (17.5-25.0 x 11.25-21.25) µm, shape-index 1.4. Oocysts wall about 1.25 µm thick and bi-layered: inner layer faintly striated. Micropyle present, with oocyst residuum immediately below: single polar body rarely present. Sporocysts 13.0 x 7.5 (12.5-13.75 x 7,5-8.1) µm, shape-index 1.7, with a Stieda body but seemingly no sub-Stieda. Sporocyst residuum compact: sporozoites with two refractile bodies. Isospora cacici n. sp. is recorded from faeces of Cacicus cela cela (Passeriformes: Icteridae). Oocysts subspherical-spherical, 26.5 x 23.7 (22.5-27.5 x 20.0-26.2) µm, shape-index 1.1. Wall a single, colourless layer about 1.5 µm thick. No micropyle or oocyst residuum: 1-2 polar bodies. Sporocysts ellipsoidal, 17.7 x 12.5 (17.5-18.75 x 11.25-13.75) µm, shape-index 1.4, with pronounced Stieda/sub-Stieda bodies: residuum compact and sporozoites with two refractile bodies. Isospora thraupis n. sp. is described from faeces of Thraupis palmarum melanoptera (Passeriformes: Thraupidae). Oocysts subspherial-spherical, 19.9 x 19.0 (18.7-21.2 x 18.75-20.0) µm, shape-index 1.0. Wall about 0.6 µm thick, smooth, colourless and a single layer: no micropyle, oocyst residuum or polar bodies. Sporocysts 14.2 x 9.2 (13.7-16.2 x 8.7-10.0) µm, shape-index 1.5: Stied/sub-Stieda bodies inconspicuous. Residuum compact: sporozoites with two refractile bodies.

Tyzzeria boae n. sp., (Apicomplexa: Eimeriidae), a New Coccidium from the Kidney of the snake Boa constrictor constrictor (Serpentes: Boidae)

A new species of Tyzzeria is described from the kidney of the snake Boa constrictor constrictor Linnaeus, from the State of Pará, north Brazil. Oocysts from the coacal contents matured in eight days, at approximately 24°C. They measured 19.0 x 18.0 (15.0 x 15.0 - 22.5 x 21.5) µm, shape-index (length/width) 1.0 (1.0 - 1.1). The oocyst wall is of an extremely delicate single, colourless layer, with no micropyle. Division of the oocyst contents into the 8 naked sporozoites leaves a bulky, spherical oocyst residuum averaging 15.5 x 14.8 (13.5 x 13.5 - 18.5 x 17.5) µm; the sporozoites measure an average of 11.0 x 1.8 (8.5 x 1.25 - 12.5 x 2.0) µm, and possess both anterior and posterior refractile bodies. Tyzzeria boae n.sp. is unique among the recorded species of the genus by virtue of its development in the epithelial cells of the distal convoluted tubules and collecting tubules of the kidney: stages in the merogony and gametogony of the parasite are described and figured.

Occurrence of "Nuages" and "Lamellae Anulata" during spermatogenesis in Dermatobia hominis (Diptera: Cuterebridae)

Various types of "nuages" and "lamellae anulata" can be found during Dermatobia hominis spermatogenesis. In spermatogonia, the "nuages" occur as granules juxtaposed to the cytoplasmic face of the nuclear envelope or as cytoplasmic granules similar to glycogen granules. In spermatocytes, in addition to the "nuages", dense spherical bodies of approximately 1.0 µm in diameter are also observed. In the spermatids the "nuages" can be of the following types: perinuclear granules, spherical granules with diameters varying in length from 0.5 to 1.0 µm, granules similar to glycogen granules, granules with variable diameters which accumulate at the flagellum base forming the centriole adjunct, or remain in the cytoplasm. "Nuages" can also be observed in these cellular types as dense masses, without a definite outline and are common to animal germinal cells in general. The "lamellae anulata" on the other hand, are observed only in spermatocytes I and in early spermatids, being always immersed in electron-dense material of indefinite outline. In spermatids, the "lamellae anulata" are close to the nuclear envelope suggesting, in spite of opposing opinions, that these cells are envolved in the synthesis and transport of material from the nucleus to the cytoplasm.

Using a NPWE model observer to assess suitable image quality for a digital mammography quality assurance programme.

A method of objectively determining imaging performance for a mammography quality assurance programme for digital systems was developed. The method is based on the assessment of the visibility of a spherical microcalcification of 0.2 mm using a quasi-ideal observer model. It requires the assessment of the spatial resolution (modulation transfer function) and the noise power spectra of the systems. The contrast is measured using a 0.2-mm thick Al sheet and Polymethylmethacrylate (PMMA) blocks. The minimal image quality was defined as that giving a target contrast-to-noise ratio (CNR) of 5.4. Several evaluations of this objective method for evaluating image quality in mammography quality assurance programmes have been considered on computed radiography (CR) and digital radiography (DR) mammography systems. The measurement gives a threshold CNR necessary to reach the minimum standard image quality required with regards to the visibility of a 0.2-mm microcalcification. This method may replace the CDMAM image evaluation and simplify the threshold contrast visibility test used in mammography quality.

Effect of Knotting on the Shape of Polymers

Momentary configurations of long polymers at thermal equilibrium usually deviate from spherical symmetry and can be better described, on average, by a prolate ellipsoid. The asphericity and nature of asphericity (or prolateness) that describe these momentary ellipsoidal shapes of a polymer are determined by specific expressions involving the three principal moments of inertia calculated for configurations of the polymer. Earlier theoretical studies and numerical simulations have established that as the length of the polymer increases, the average shape for the statistical ensemble of random configurations asymptotically approaches a characteristic universal shape that depends on the solvent quality. It has been established, however, that these universal shapes differ for linear, circular, and branched chains. We investigate here the effect of knotting on the shape of cyclic polymers modeled as random isosegmental polygons. We observe that random polygons forming different knot types reach asymptotic shapes that are distinct from the ensemble average shape. For the same chain length, more complex knots are, on average, more spherical than less complex knots.

Eimeria peltocephali n. sp., (Apicomplexa:Eimeriidae) from the Freshwater Turtle Peltocephalus dumerilianus (Chelonia:Pelomusidae) and Eimeria molossi n. sp., from the Bat, Molossus ater (Mammalia:Chiroptera)

The oocyst is described of Eimeria peltocephali n.sp. from faeces of the freshwater turtle Peltocephalus dumerilianus from Barcelos, State of Amazonas, Brazil. Sporulation is exogenous and fully developed oocysts are elongate, ellipsoidal or cylindrical, frequently curved to a banana-shape, 54.4 x19.1 (37.5 - 68.7 x 18.7-20.0 µm), shape-index 2.8 (1.8 -3.9). The oocyst wall is a single thin, colourless layer about 1 µm thick, with no micropyle. There is a bulky oocyst residuum, at first spherical to ellipsoidal, 19 x 16 (16. 2 -26.2 x 16 - 21.5µm) , but becoming dispersed on maturation. There are no polar bodies. The sporocysts, 19.1 x 6.8 ( 17.5 -21.2 x 6.2 -7.5 µm), shape- index 2.8 (2.3 -3.2), are usually disposed in pairs at each end of the oocyst, and bear an inconspicuous Stieda body in the form of a flat cap. The sporozoites are elongate and slightly curved around the residuum. No refractile bodies were seen. Eimeria molossi n.sp., is described from the molossid bat Molossus ater. Sporulation is exogenous and the mature oocysts are predominantly broadly ellipsoidal, 23.4 x 17.5 (18-30 x 15-22.5 µm), shape-index 1.3 (1-1.6). The oocyst wall is about 2 µm thick, and of three layers: an inner thin, colourless one and two outer layers which are thicker, yellowish-brown, prominently striated and in close apposition. There is no micropyle or oocyst residuum, but one and occasionally two polar bodies are usually present. Sporocysts are ellipsoidal, 10.2 x 7.5 (10-12.5 x 7.5 µm), shape-index 1.4 (1.3-1.7) with an inconspicuous Stieda body. Endogenous stages are described in the epithelial cells of the small intestine

Cell Adhesion Peptide RGDSP and Laminin Support Proliferation and Migration of Postnatal Retinal Stem Cells in a 3D Hydrogel Culture System

Purpose: Retinal stem cells (RSCs) can be isolated from radial glia population of the newborn mouse retina (Angénieux et al., 2006). These RSCs have great capacity to renew and generate neurons including cells differentiated towards the photoreceptor lineage (Mehri-Soussi et al., 2006). However, our published results showed poor integration and survival rate after cell grafting into the retina. The uncontrollable environment of retina seems to be the problem. To bypass this, we are trying to generate hemi-retinal tissue in vitro that can be used for transplantation. Methods: Expanded RSCs were seeded in a mixture of poly-ethylene-glycol (PEG)-polymer-based hydrogels crosslinked by peptides that also serve as substrates for matrix metalloproteinases. Different doses of crosslinker peptides were tested. Several growth factors were studied to stimulate cell proliferation and differentiation. Results: Cells were trapped in hydrogels and cultured in the presence of FGF2 and EGF. Spherical cell clusters indicating proliferation appeared within several days, but there was no cell migration within the gel. We then added cell adhesion molecules integrin ligand RGDSP, or laminin, or a combination of both, into the gel. Cells grown with laminin showed the best proliferation. Cells grown with RGDSP proliferated a few times and then started to spread out. Cells grown with the combination of RGDSP and laminin showed better proliferation than with RGDSP alone and larger spread-outs than with laminin alone. After stimulations with first FGF2 and EGF, and then only FGF2, some cells showed neuronal morphology after 2 weeks. The neuronal population was assessed by the presence of neuronal marker b-tubulin-III. Glial cells were also present. Further characterizations are undergoing. Conclusions: RSC can grow and migrate in 3D hydrogel with the addition of FGF2, EGF, RGDSP and laminin. Further developments are necessary to form a homogenous tissue containing retinal cells.

Description of the Oocysts of Three New Species of Eimeria (Apicomplexa: Eimeriidae) from Iguanid Lizards (Sauria: Iguanidae) of Central and South America

Three new species of Eimeria are described from iguanid lizards of Central and South America. The oocysts of each species have no micropyles or residua and the sporocysts lack Stieda bodies, but all have a sporocyst residuum. Eimeria sanctaluciae n.sp. was found in the St. Lucia tree lizard, Anolis luciae, collected from the Maria Islands, Lesser Antilles. The oocysts are spherical to subspherical, averaging 17.3 x 16.5 µm, with a single layered colourless wall; about 60% contain polar granules. The sporocysts are ellipsoidal and average 7.7 x 5.5 µm. Eimeria liolaemi n.sp. was recovered from the blue-gold swift, Liolaemus taenius, from Chile. The oocysts are spherical to subspherical, measuring 21 x 20.1 µm with a single-layered colourless wall. The sporocysts are subspherical and average 7.4 x 6.8 µm. Eimeria caesicia n.sp. is described from the Brazilian collared iguanid, Tropidurus torquatus. The oocysts measure 27.4 x 23.7 µm, are spherical to subspherical, with a bilayered wall, the outer surface of which appears pale blue in colour, the thin, inner wall appearing brown, when viewed by direct light under the optical microscope. The sporocysts are subspherical and average 9.4 x 7.2 µm. Unnamed polysporocystid oocysts with dizoic sporocysts are reported from the faeces of the lesser St. Vincent tree lizard, Anolis trinitatis and the possibility of spurious parasitism briefly discussed. In addition, oocysts of an unnamed Isospora sp. with a smooth oocyst wall which closely resembles I. reui were recovered from A. trinitatis.

On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable configurations are generated with positive probability Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.

On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable con gurations are generated with positive probability Lundh calls this percolation di usion. An integral condition for percolation di ffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.

Forces de Casimir i les seves aplicacions

Report for the scientific sojourn carried out at the Darmouth College, from august 2007 until february 2008. It has been very successful, from different viewpoints: scientific, philosophical, human. We have definitely advanced, during the past six months, towards the comprehension of the behaviour of the fluctuations of the quantum vacuum in the presence of boundaries, moving and non-moving, and also in situations where the topology of space-time changes: the dynamical Casimir effect, regularization problems, particle creation statistics, according to different BC, etc. We have solved some longstanding problems and got in this subject quite remarkable results (as we will explain in more detail below). We also pursued a general approach towards a viable modified f(R) gravity in both the Jordan and the Einstein frames (which are known to be mathematically equivalent, but physically not so). A class of exponential, realistic modified gravities has been introduced by us and investigated with care. Special focus was made on step-class models, most promising from the phenomenological viewpoint and which provide a natural way to classify all viable modified gravities. One- and two-steps models were considered, but the analysis is extensible to N-step models. Both inflation in the early universe and the onset of recent accelerated expansion arise in these models in a natural, unified way, what makes them very promising. Moreover, it is monstrated in our work that models in this category easily pass all local tests, including stability of spherical body solution, non-violation of Newton's law, and generation of a very heavy positive mass for the additional scalar degree of freedom.