Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Functional education of invariant NKT cells by dendritic cell tuning of SHP-1.

Invariant NKT (iNKT) cells play key roles in host defense by recognizing lipid Ags presented by CD1d. iNKT cells are activated by bacterial-derived lipids and are also strongly autoreactive toward self-lipids. iNKT cell responsiveness must be regulated to maintain effective host defense while preventing uncontrolled stimulation and potential autoimmunity. CD1d-expressing thymocytes support iNKT cell development, but thymocyte-restricted expression of CD1d gives rise to Ag hyperresponsive iNKT cells. We hypothesized that iNKT cells require functional education by CD1d(+) cells other than thymocytes to set their correct responsiveness. In mice that expressed CD1d only on thymocytes, hyperresponsive iNKT cells in the periphery expressed significantly reduced levels of tyrosine phosphatase SHP-1, a negative regulator of TCR signaling. Accordingly, heterozygous SHP-1 mutant mice displaying reduced SHP-1 expression developed a comparable population of Ag hyperresponsive iNKT cells. Restoring nonthymocyte CD1d expression in transgenic mice normalized SHP-1 expression and iNKT cell reactivity. Radiation chimeras revealed that CD1d(+) dendritic cells supported iNKT cell upregulation of SHP-1 and decreased responsiveness after thymic emigration. Hence, dendritic cells functionally educate iNKT cells by tuning SHP-1 expression to limit reactivity.

Hand detection in cluttered scene images using Fourier-Mellin invariant features

This paper proposes an automatic hand detection system that combines the Fourier-Mellin Transform along with other computer vision techniques to achieve hand detection in cluttered scene color images. The proposed system uses the Fourier-Mellin Transform as an invariant feature extractor to perform RST invariant hand detection. In a first stage of the system a simple non-adaptive skin color-based image segmentation and an interest point detector based on corners are used in order to identify regions of interest that contains possible matches. A sliding window algorithm is then used to scan the image at different scales performing the FMT calculations only in the previously detected regions of interest and comparing the extracted FM descriptor of the windows with a hand descriptors database obtained from a train image set. The results of the performed experiments suggest the use of Fourier-Mellin invariant features as a promising approach for automatic hand detection.

Hand detection in cluttered scene images using Fourier-Mellin invariant features

This paper proposes an automatic hand detection system that combines the Fourier-Mellin Transform along with other computer vision techniques to achieve hand detection in cluttered scene color images. The proposed system uses the Fourier-Mellin Transform as an invariant feature extractor to perform RST invariant hand detection. In a first stage of the system a simple non-adaptive skin color-based image segmentation and an interest point detector based on corners are used in order to identify regions of interest that contains possible matches. A sliding window algorithm is then used to scan the image at different scales performing the FMT calculations only in the previously detected regions of interest and comparing the extracted FM descriptor of the windows with a hand descriptors database obtained from a train image set. The results of the performed experiments suggest the use of Fourier-Mellin invariant features as a promising approach for automatic hand detection.

Enrichment of human CD4+ V(alpha)24/Vbeta11 invariant NKT cells in intrahepatic malignant tumors.

Invariant NKT cells (iNKT cells) recognize glycolipid Ags via an invariant TCR alpha-chain and play a central role in various immune responses. Although human CD4(+) and CD4(-) iNKT cell subsets both produce Th1 cytokines, the CD4(+) subset displays an enhanced ability to secrete Th2 cytokines and shows regulatory activity. We performed an ex vivo analysis of blood, liver, and tumor iNKT cells from patients with hepatocellular carcinoma and metastases from uveal melanoma or colon carcinoma. Frequencies of Valpha24/Vbeta11 iNKT cells were increased in tumors, especially in patients with hepatocellular carcinoma. The proportions of CD4(+), double negative, and CD8alpha(+) iNKT cell subsets in the blood of patients were similar to those of healthy donors. However, we consistently found that the proportion of CD4(+) iNKT cells increased gradually from blood to liver to tumor. Furthermore, CD4(+) iNKT cell clones generated from healthy donors were functionally distinct from their CD4(-) counterparts, exhibiting higher Th2 cytokine production and lower cytolytic activity. Thus, in the tumor microenvironment the iNKT cell repertoire is modified by the enrichment of CD4(+) iNKT cells, a subset able to generate Th2 cytokines that can inhibit the expansion of tumor Ag-specific CD8(+) T cells. Because CD4(+) iNKT cells appear inefficient in tumor defense and may even favor tumor growth and recurrence, novel iNKT-targeted therapies should restore CD4(-) iNKT cells at the tumor site and specifically induce Th1 cytokine production from all iNKT cell subsets.