Multiplicity of limit cycles and analytic m-solutions for planar differential systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach

Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equilibrium point with the discontinuity surface. Generically, these bifurcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible collision of a non-hyperbolic equilibrium with the boundary in a two-parameter framework and the nonlinear phenomena associated with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of such phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding bi-parametric bifurcation sets is developed.

The fourth extracellular loop of the alpha subunit of Na,K-ATPase. Functional evidence for close proximity with the second extracellular loop.

Na,K-ATPase is the main active transport system that maintains the large gradients of Na(+) and K(+) across the plasma membrane of animal cells. The crystal structure of a K(+)-occluding conformation of this protein has been recently published, but the movements of its different domains allowing for the cation pumping mechanism are not yet known. The structure of many more conformations is known for the related calcium ATPase SERCA, but the reliability of homology modeling is poor for several domains with low sequence identity, in particular the extracellular loops. To better define the structure of the large fourth extracellular loop between the seventh and eighth transmembrane segments of the alpha subunit, we have studied the formation of a disulfide bond between pairs of cysteine residues introduced by site-directed mutagenesis in the second and the fourth extracellular loop. We found a specific pair of cysteine positions (Y308C and D884C) for which extracellular treatment with an oxidizing agent inhibited the Na,K pump function, which could be rapidly restored by a reducing agent. The formation of the disulfide bond occurred preferentially under the E2-P conformation of Na,K-ATPase, in the absence of extracellular cations. Using recently published crystal structure and a distance constraint reproducing the existence of disulfide bond, we performed an extensive conformational space search using simulated annealing and showed that the Tyr(308) and Asp(884) residues can be in close proximity, and simultaneously, the SYGQ motif of the fourth extracellular loop, known to interact with the extracellular domain of the beta subunit, can be exposed to the exterior of the protein and can easily interact with the beta subunit.

Improved temporal resolution for functional studies with reduced number of segments with three-dimensional echo planar imaging.

PURPOSE: To introduce a new k-space traversal strategy for segmented three-dimensional echo planar imaging (3D EPI) that encodes two partitions per radiofrequency excitation, effectively reducing the number excitations used to acquire a 3D EPI dataset by half. METHODS: The strategy was evaluated in the context of functional MRI applications for: image quality compared with segmented 3D EPI, temporal signal-to-noise ratio (tSNR) (the ability to detect resting state networks compared with multislice two-dimensional (2D) EPI and segmented 3D EPI, and temporal resolution (the ability to separate cardiac- and respiration-related fluctuations from the desired blood oxygen level-dependent signal of interest). RESULTS: Whole brain images with a nominal voxel size of 2 mm isotropic could be acquired with a temporal resolution under half a second using traditional parallel imaging acceleration up to 4× in the partition-encode direction and using novel data acquisition speed-up of 2× with a 32-channel coil. With 8× data acquisition speed-up in the partition-encode direction, 3D reduced excitations (RE)-EPI produced acceptable image quality without introduction of noticeable additional artifacts. Due to increased tSNR and better characterization of physiological fluctuations, the new strategy allowed detection of more resting state networks compared with multislice 2D-EPI and segmented 3D EPI. CONCLUSION: 3D RE-EPI resulted in significant increases in temporal resolution for whole brain acquisitions and in improved physiological noise characterization compared with 2D-EPI and segmented 3D EPI. Magn Reson Med 72:786-792, 2014. © 2013 Wiley Periodicals, Inc.

The loop group and the cobar construction

"Vegeu el resum a l'inici del document del fitxer adjunt."

Destruction of invariant curves in the restricted circular planar three body problem using comparison of action

"Vegeu el resum a l'inici del document del fitxer adjunt."

Symmetric planar central configurations of five bodies: Euler plus two

We study planar central configurations of the five-body problem where three of the bodies are collinear, forming an Euler central configuration of the three-body problem, and the two other bodies together with the collinear configuration are in the same plane. The problem considered here assumes certain symmetries. From the three bodies in the collinear configuration, the two bodies at the extremities have equal masses and the third one is at the middle point between the two. The fourth and fifth bodies are placed in a symmetric way: either with respect to the line containing the three bodies, or with respect to the middle body in the collinear configuration, or with respect to the perpendicular bisector of the segment containing the three bodies. The possible stacked five-body central configurations satisfying these types of symmetries are: a rhombus with four masses at the vertices and a fifth mass in the center, and a trapezoid with four masses at the vertices and a fifth mass at the midpoint of one of the parallel sides.

A gamma camera count rate saturation correction method for whole-body planar imaging.

Whole-body (WB) planar imaging has long been one of the staple methods of dosimetry, and its quantification has been formalized by the MIRD Committee in pamphlet no 16. One of the issues not specifically addressed in the formalism occurs when the count rates reaching the detector are sufficiently high to result in camera count saturation. Camera dead-time effects have been extensively studied, but all of the developed correction methods assume static acquisitions. However, during WB planar (sweep) imaging, a variable amount of imaged activity exists in the detector's field of view as a function of time and therefore the camera saturation is time dependent. A new time-dependent algorithm was developed to correct for dead-time effects during WB planar acquisitions that accounts for relative motion between detector heads and imaged object. Static camera dead-time parameters were acquired by imaging decaying activity in a phantom and obtaining a saturation curve. Using these parameters, an iterative algorithm akin to Newton's method was developed, which takes into account the variable count rate seen by the detector as a function of time. The algorithm was tested on simulated data as well as on a whole-body scan of high activity Samarium-153 in an ellipsoid phantom. A complete set of parameters from unsaturated phantom data necessary for count rate to activity conversion was also obtained, including build-up and attenuation coefficients, in order to convert corrected count rate values to activity. The algorithm proved successful in accounting for motion- and time-dependent saturation effects in both the simulated and measured data and converged to any desired degree of precision. The clearance half-life calculated from the ellipsoid phantom data was calculated to be 45.1 h after dead-time correction and 51.4 h with no correction; the physical decay half-life of Samarium-153 is 46.3 h. Accurate WB planar dosimetry of high activities relies on successfully compensating for camera saturation which takes into account the variable activity in the field of view, i.e. time-dependent dead-time effects. The algorithm presented here accomplishes this task.

Access of extracellular cations to their binding sites in Na,K-ATPase: role of the second extracellular loop of the alpha subunit.

Na,K-ATPase, the main active transport system for monovalent cations in animal cells, is responsible for maintaining Na(+) and K(+) gradients across the plasma membrane. During its transport cycle it binds three cytoplasmic Na(+) ions and releases them on the extracellular side of the membrane, and then binds two extracellular K(+) ions and releases them into the cytoplasm. The fourth, fifth, and sixth transmembrane helices of the alpha subunit of Na,K-ATPase are known to be involved in Na(+) and K(+) binding sites, but the gating mechanisms that control the access of these ions to their binding sites are not yet fully understood. We have focused on the second extracellular loop linking transmembrane segments 3 and 4 and attempted to determine its role in gating. We replaced 13 residues of this loop in the rat alpha1 subunit, from E314 to G326, by cysteine, and then studied the function of these mutants using electrophysiological techniques. We analyzed the results using a structural model obtained by homology with SERCA, and ab initio calculations for the second extracellular loop. Four mutants were markedly modified by the sulfhydryl reagent MTSET, and we investigated them in detail. The substituted cysteines were more readily accessible to MTSET in the E1 conformation for the Y315C, W317C, and I322C mutants. Mutations or derivatization of the substituted cysteines in the second extracellular loop resulted in major increases in the apparent affinity for extracellular K(+), and this was associated with a reduction in the maximum activity. The changes produced by the E314C mutation were reversed by MTSET treatment. In the W317C and I322C mutants, MTSET also induced a moderate shift of the E1/E2 equilibrium towards the E1(Na) conformation under Na/Na exchange conditions. These findings indicate that the second extracellular loop must be functionally linked to the gating mechanism that controls the access of K(+) to its binding site.

Reciprocal regulation of brain and muscle Arnt-like protein 1 and peroxisome proliferator-activated receptor alpha defines a novel positive feedback loop in the rodent liver circadian clock.

Recent evidence has emerged that peroxisome proliferator-activated receptor alpha (PPARalpha), which is largely involved in lipid metabolism, can play an important role in connecting circadian biology and metabolism. In the present study, we investigated the mechanisms by which PPARalpha influences the pacemakers acting in the central clock located in the suprachiasmatic nucleus and in the peripheral oscillator of the liver. We demonstrate that PPARalpha plays a specific role in the peripheral circadian control because it is required to maintain the circadian rhythm of the master clock gene brain and muscle Arnt-like protein 1 (bmal1) in vivo. This regulation occurs via a direct binding of PPARalpha on a potential PPARalpha response element located in the bmal1 promoter. Reversely, BMAL1 is an upstream regulator of PPARalpha gene expression. We further demonstrate that fenofibrate induces circadian rhythm of clock gene expression in cell culture and up-regulates hepatic bmal1 in vivo. Together, these results provide evidence for an additional regulatory feedback loop involving BMAL1 and PPARalpha in peripheral clocks.

Monocular-based 3-D seafloor reconstruction and ortho-mosaicing by piecewise planar representation

Photo-mosaicing techniques have become popular for seafloor mapping in various marine science applications. However, the common methods cannot accurately map regions with high relief and topographical variations. Ortho-mosaicing borrowed from photogrammetry is an alternative technique that enables taking into account the 3-D shape of the terrain. A serious bottleneck is the volume of elevation information that needs to be estimated from the video data, fused, and processed for the generation of a composite ortho-photo that covers a relatively large seafloor area. We present a framework that combines the advantages of dense depth-map and 3-D feature estimation techniques based on visual motion cues. The main goal is to identify and reconstruct certain key terrain feature points that adequately represent the surface with minimal complexity in the form of piecewise planar patches. The proposed implementation utilizes local depth maps for feature selection, while tracking over several views enables 3-D reconstruction by bundle adjustment. Experimental results with synthetic and real data validate the effectiveness of the proposed approach