Limit Cycles for a class of three dimensional polynomial differential systems

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Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

Vaccination of Callithrix jacchus (Linné, 1758) marmosets with the PF strain of Trypanosoma cruzi

Callithrix jacchus marmosets, vaccinated more than once with high doses of the PF strain of Trypanosoma cruzi, showed a certain degree of parasitemia related to the number of parasites injected. Thirty days after vaccination, all animals were alive and showed no apparent morbid symptoms. The relationship between the dose of injected trypanosomes and the observed parasitemias is discussed and analysed as well as the immunologic incompetence of the experimental animals used.

The existence of periodic solutions of a two dimensional Lattice

We consider a two dimensional lattice coupled with nearest neighbor interaction potential of power type. The existence of infinite many periodic solutions is shown by using minimax methods.

MB-MDR: Model-Based Multifactor Dimensionality Reduction for detecting interactions in high-dimensional genomic data

L’anàlisi de l’efecte dels gens i els factors ambientals en el desenvolupament de malalties complexes és un gran repte estadístic i computacional. Entre les diverses metodologies de mineria de dades que s’han proposat per a l’anàlisi d’interaccions una de les més populars és el mètode Multifactor Dimensionality Reduction, MDR, (Ritchie i al. 2001). L’estratègia d’aquest mètode és reduir la dimensió multifactorial a u mitjançant l’agrupació dels diferents genotips en dos grups de risc: alt i baix. Tot i la seva utilitat demostrada, el mètode MDR té alguns inconvenients entre els quals l’agrupació excessiva de genotips pot fer que algunes interaccions importants no siguin detectades i que no permet ajustar per efectes principals ni per variables confusores. En aquest article il•lustrem les limitacions de l’estratègia MDR i d’altres aproximacions no paramètriques i demostrem la conveniència d’utilitzar metodologies parametriques per analitzar interaccions en estudis cas-control on es requereix l’ajust per variables confusores i per efectes principals. Proposem una nova metodologia, una versió paramètrica del mètode MDR, que anomenem Model-Based Multifactor Dimensionality Reduction (MB-MDR). La metodologia proposada té com a objectiu la identificació de genotips específics que estiguin associats a la malaltia i permet ajustar per efectes marginals i variables confusores. La nova metodologia s’il•lustra amb dades de l’Estudi Espanyol de Cancer de Bufeta.

Hopf bifurcation in higher dimensional differential systems via the averaging method

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Plasmodium falciparum merozoite surface protein 2: epitope mapping and biological activity analysis of specific antibodies

Background: Plasmodium falciparum(P. falciparum) merozoite surfaceprotein 2 (MSP-2) is one of bloodstage proteins that are associated withprotection from malaria. MSP-2 consistsof a highly polymorphic centralrepeat region flanked by a dimorphicregion that defines the two allelicfamilies, 3D7 and FC27; N- and Cterminalregions are conserved domains.Long synthetic peptides (LSP)representing the two allelic familiesof MSP-2 and constant regions arerecognized by sera from donors livingin endemic areas; and specific antibodies(Abs) are associated with protectionand active in antibody dependentcellular inhibition (ADCI) in vitro.However, the fine specificity ofAb response to the two allelic familiesof MSP-2 is unknown. Methods: Peptidesrepresenting dimorphic regionof 3D7 and FC27 families and theirC-terminal (common fragment to thetwo families) termed 3D7-D (88 aa),FC27-D (48 aa) and C (40 aa) respectivelywere synthesized. Overlapping20 mer peptides covering dimorphicand constant regions of two familieswere also synthesized for epitopemapping. Human sera were obtainedfrom donors living in malaria endemicareas. SpecificDand CregionsAbs were purified from single or poolhuman sera. Sera from mice were obtainedafter immunization with thetwo families LSP mixture in three differentadjuvants: alhydrogel (Alum),Glucopyranosyl Lipid Adjuvant-Stableoil-in-water Emulsion (GLA-SE)and Virosome. For ADCI, P. falciparum(strain 3D7) parasite wasmaintained in culture at 0.5% parasitemiaand 4% hematocrit in air tightbox at love oxygen (2%) and 37 ºC.Results: We identified several epitopesfrom the dimorphic and constantregions of both families of MSP-2, inmice and humans (adults and children).In human, most recognizedepitopes were the same in differentendemic regions for each domain ofthe two families of MSP-2. In mice,the differential recognition of epitopewas depending on the strain of mouseand interestingly on the adjuvantused. GLA-SE and alum as adjuvantswere more often associated with therecognition of multiple epitopes thanvirosomes. Epitope-specific Abs recognizednative merozoites of P.falciparum and were active in ADCIto block development of parasite.Conclusion: The delineation of a limitednumber of epitopes could be exploitedto develop MSP-2 vaccinesactive on both allelic families ofMSP-2.

Determination of displacement, stress- and strain-distribution in the human heart: a FE-model on the basis of MR imaging.

The determination of characteristic cardiac parameters, such as displacement, stress and strain distribution are essential for an understanding of the mechanics of the heart. The calculation of these parameters has been limited until recently by the use of idealised mathematical representations of biventricular geometries and by applying simple material laws. On the basis of 20 short axis heart slices and in consideration of linear and nonlinear material behaviour we have developed a FE model with about 100,000 degrees of freedom. Marching Cubes and Phong's incremental shading technique were used to visualise the three dimensional geometry. In a quasistatic FE analysis continuous distribution of regional stress and strain corresponding to the endsystolic state were calculated. Substantial regional variation of the Von Mises stress and the total strain energy were observed at all levels of the heart model. The results of both the linear elastic model and the model with a nonlinear material description (Mooney-Rivlin) were compared. While the stress distribution and peak stress values were found to be comparable, the displacement vectors obtained with the nonlinear model were generally higher in comparison with the linear elastic case indicating the need to include nonlinear effects.

Bargaining one-dimensional policies and the efficiency of super majority rules

We consider negotiations selecting one-dimensional policies. Individuals have single-peaked preferences, and they are impatient. Decisions arise from a bargaining game with random proposers and (super) majority approval, ranging from the simple majority up to unanimity. The existence and uniqueness of stationary subgame perfect equilibrium is established, and its explicit characterization provided. We supply an explicit formula to determine the unique alternative that prevails, as impatience vanishes, for each majority. As an application, we examine the efficiency of majority rules. For symmetric distributions of peaks unanimity is the unanimously preferred majority rule. For asymmetric populations rules maximizing social surplus are characterized.

Influence of Trypanosoma cruzi strain on the pathogenesis of chronic myocardiopathy in mice

The murine model of chronic Chaga's myocardiopathy was developed in 201 inbred and outbred mice. The experimental groups consisted of 1st: 73 inbred AKR and A/J mice inoculated with one of the following. Trypanosoma cruzi strains: Peruvian (Type I), 12 SF (Type II) or Colombian (Type III); 2nd: 128 outbred Swiss mice, chronically infected either with Type II or Type III strains isolated from human patients from different geographical areas. All T. cruzi strains were previoulsly characterized by their morphobiological behaviour in mice and by isoenzymatic patterns. For the 1st group the inoculum was 5 x 10**4 for the Peruvian strain and 1 x 10**5 for the 12 SF and Colombian strains. In the 2nd group-Swiss mice the inoculum size varied from 2 x 10**4 to 2 x 10**5. The inbred animals were killed at a 3 time-point scale (90, 180 and 240 days) post-infection. The Swiss mice were killed from 180 to 660 days after infection. The evaluation of parasitemia and serology (xeodiagnosis and indirect immunofluorescent test) was performed. The incidence of macroscopic alterations of the heart and cardiac index were evaluated. Histopathological lesions of the myocardium were graded. The influence of T. cruzi strain on the intensity of cardiac lesions was evaluated by the Chi-square test; the incidence of inflammatory lesions and its relationship to the parasite strain was evaluated by the Fisher test. The influence of the duration of infection was evaluated by using the Gamma Coefficient of Kruskal and Goodman and its measure of significance. Slight to severe microscopic alterations occurred in 85% of the chronically infected nice. There were a clear predominance on the incidence and intensity of inflammatory and fibrotic alterations for the mice infected with Type III strains. Statistical analysis has shown significant differences among the infected groups, in the inflammatory and fibrotic lesions. Macroscopic alterations (right cavities dilatation and apex aneurism of left ventricle), differed in incidence according to mice strains; in Swiss and AKR mice, significant differences were seen in mice infected with different T. cruzi strains, but the A/J mice failed to show significant differences correlated with different parasite strains. The duration of infection, from 90 to 240 days, could not be correlated with the degree of lesions in the several groups.

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 mouse Lyt-2/3 antigen complex--II. Structural analysis of the subunits.

Surface- or biosynthetically labeled Lyt-2/3 antigens were isolated from cell lysates by immunoprecipitation and affinity chromatography with a monoclonal antibody. Tryptic digests of the individual subunits of 37,000, 32,000 and 28,000 apparent mol. wts were analysed by reverse-phase high-performance liquid chromatography and by two-dimensional peptide mapping. The results indicate that the 37,000 and 32,000 mol. wt components are structurally very similar whereas the 28,000 mol. wt component appears as a different molecule.

Persistent bundles over a two dimensional compact set

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Molecular analysis of yellow fever virus 17DD vaccine strain

The Oswaldo Cruz Foundation produces most of the yellow fever (YF) vaccine prepared world wide. As part of a broader approach to determine the genetic variability in YF l7D seeds and vaccines and its relevance to viral attenuation the 17DD virus was purifed directly from chick embryo homogenates which is the source of virus used for vaccination of millions of people in Brazil and other countries for half a century. Neutralization and hemagglutination tests showed that the purified virus is similar to the original stock. Furthermore, radioimmune precipitation of 35S-methionine-labeled viral proteins using mouse hyperimmune ascitic fluid revealed identical patterns for the purified 17DD virus and the YF l7D-204 strain except for the 17DD E protein which migrated slower on SDS-PAGE. This difference is likely to be due to N-linked glycosylation. Finally, comparison by northern blot nybridization of virion RNAs of purified 17DD with two other strains of YF virus only fenome-sized molecules for all three viruses. These observations suggest that vaccine phenotype is primarily associated with the accumulation of mutations.

Differentiation of rat striatal embryonic stem cells in vitro: monolayer culture vs. three-dimensional coculture with differentiated brain cells.

Several groups have demonstrated the existence of self-renewing stem cells in embryonic and adult mouse brain. In vitro, these cells proliferate in response to epidermal growth factor, forming clusters of nestin-positive cells that may be dissociated and subcultured repetitively. Here we show that, in stem cell clusters derived from rat embryonic striatum, cell proliferation decreased with increasing number of passages and in response to elevated concentrations of potassium (30 mM KCl). In monolayer culture, the appearance of microtubule-associated protein type-5-immunoreactive (MAP-5(+)) cells (presumptive neurons) in response to basic fibroblast growth factor (bFGF) was reduced at low cell density and with increasing number of passages. In the presence of bFGF, elevated potassium caused a more differentiated neuronal phenotype, characterized by an increased proportion of MAP-5(+) cells, extensive neuritic branching, and higher specific activity of glutamic acid decarboxylase. Dissociated stem cells were able to invade cultured brain cell aggregates containing different proportions of neurons and glial cells, whereas they required the presence of a considerable proportion of glial cells in the host cultures to become neurofilament H-positive. The latter observation supports the view that astrocyte-derived factors influence early differentiation of the neuronal cell lineage.