The homotopy type of spaces of locally convex curves in the sphere

A smooth curve \gamma: [0,1] \to \Ss^2 is locally convex if its geodesic curvature is positive at every point. J. A. Little showed that the space of all locally convex curves $\gamma$ with $\gamma(0) = \gamma(1) = e_1$ and $\gamma'(0) = \gamma'(1) = e_2$ has three connected components $L_{-1,c}$, $L_{+1}$, $L_{-1,n}$. The space \cL_{-1,c} is known to be contractible. We prove that \cL_{+1} and \cL_{-1,n} are homotopy equivalent to (\Omega\Ss^3) \vee \Ss^2 \vee \Ss^6 \vee \Ss^{10} \vee \cdots and (\Omega\Ss^3) \vee \Ss^4 \vee \Ss^8 \vee \Ss^{12} \vee \cdots, respectively. As a corollary, we deduce the homotopy type of the components of the space \Free(\Ss^1,\Ss^2) of free curves \gamma: \Ss^1 \to \Ss^2 (i.e., curves with nonzero geodesic curvature). We also determine the homotopy type of the spaces \Free([0,1], \Ss^2) with fixed initial and final frames.Comment: 47 pages, 13 figure

Introgression of Brown Norway \u3cem\u3eCYP4A\u3c/em\u3e Genes onto the Dahl Salt-Sensitive Background Restores Vascular Function in SS-5\u3csup\u3eBN\u3c/sup\u3e Consomic Rats

The present study tested the hypothesis that the Dahl SS (salt-sensitive) rat has vascular dysfunction due, in part, to the up-regulation of the CYP4A/20-HETE (cytochrome P450 ω-hydroxylase 4A)/20-hydroxyeicosatetraenoic acid) system. To assess the role of vascular 20-HETE, SS rats were compared with SS-5BN consomic rats, carrying CYP4A alleles on chromosome 5 from the normotensive BN (Brown Norway) introgressed on to the SS genetic background. Cerebral arteries from SS-5BN rats had less CYP4A protein than arteries from SS rats fed either NS (normal-salt, 0.4% NaCl) or HS (high-salt, 4.0% NaCl) diet. ACh (acetylcholine)-induced dilation of MCAs (middle cerebral arteries) from SS and SS-5BN rats was present in SS-5BN rats fed on either an NS or HS diet, but absent in SS rats. In SS rats fed on either diet, ACh-induced dilation was restored by acute treatment with the CYP4A inhibitor DDMS (N-methyl-sulfonyl-12,12-dibromododec-11-enamide) or the 20-HETE antagonist 20-HEDE [20-hydroxyeicosa-6(Z),15(Z)-dienoic acid]. The restored response to ACh in DDMS-treated SS rats was inhibited by L-NAME (NGnitro-L-arginine methyl ester) and unaffected by indomethacin or MS-PPOH [N-methylsulfonyl-6-(2-propargyloxyphenyl)hexanamide]. Vascular relaxation responses to the NO donor C5FeN6Na2O were intact in both SS and SS-5BN rats and unaffected by the acute addition of DDMS, indicating that the vascular dysfunction of the SS rat is due to a reduced bioavailability of NO instead of failure of the VSMCs (vascular smooth muscle cells) to respond to the vasodilator. Superoxide levels in cerebral arteries of SS-5BN rats [evaluated semi-quantitatively by DHE (dihydroethidium) fluorescence] were lower than those in the arteries of SS rats. These findings indicate that SS rats have an up-regulation of the CYP4A/20-HETE pathway resulting in elevated ROS (reactive oxygen species) and reduced NO bioavailability causing vascular dysfunction

Blood and skin-derived Sezary cells: differences in proliferation-index, activation of PI3K/AKT/mTORC1 pathway and its prognostic relevance

Sézary syndrome (SS) is a rare and aggressive variant of Cutaneous T-Cell Lymphoma characterized by neoplastic distribution mainly involving blood, skin, and lymph-node. Although a role of the skin microenvironment in SS pathogenesis has long been hypothesized, its function in vivo is poorly characterized. To deepen this aspect, here we compared skin to blood-derived SS cells concurrently obtained from SS patients highlighting a greater proliferation-index and a PI3K/AKT/mTORC1 pathway activation level, particularly of mTOR protein, in skin-derived-SS cells. We proved that SDF-1 and CCL21 chemokines, both overexpressed in SS tissues, induce mTORC1 signaling activation, cell proliferation and Ki67 up-regulation in a SS-derived cell line and primary-SS cells. In a cohort of 43 SS cases, we observed recurrent copy number variations (CNV) of members belonging to this cascade, namely: loss of LKB1 (48%), PTEN (39%) and PDCD4 (35%) and gains of P70S6K (30%). These alterations represent druggable targets unraveling new therapeutic treatments as metformin here evaluated in vitro. Moreover, CNV of PTEN, PDCD4, and P70S6K, evaluated individually or in combination, are associated with reduced survival of SS patients. These data shed light on effects in vivo of skin-SS cells interaction underlying the prognostic and therapeutic relevance of mTORC1 pathway in SS

Parametric generation of second sound in superfluid helium: linear stability and nonlinear dynamics

We report the experimental studies of a parametric excitation of a second sound (SS) by a first sound (FS) in a superfluid helium in a resonance cavity. The results on several topics in this system are presented: (i) The linear properties of the instability, namely, the threshold, its temperature and geometrical dependencies, and the spectra of SS just above the onset were measured. They were found to be in a good quantitative agreement with the theory. (ii) It was shown that the mechanism of SS amplitude saturation is due to the nonlinear attenuation of SS via three wave interactions between the SS waves. Strong low frequency amplitude fluctuations of SS above the threshold were observed. The spectra of these fluctuations had a universal shape with exponentially decaying tails. Furthermore, the spectral width grew continuously with the FS amplitude. The role of three and four wave interactions are discussed with respect to the nonlinear SS behavior. The first evidence of Gaussian statistics of the wave amplitudes for the parametrically generated wave ensemble was obtained. (iii) The experiments on simultaneous pumping of the FS and independent SS waves revealed new effects. Below the instability threshold, the SS phase conjugation as a result of three-wave interactions between the FS and SS waves was observed. Above the threshold two new effects were found: a giant amplification of the SS wave intensity and strong resonance oscillations of the SS wave amplitude as a function of the FS amplitude. Qualitative explanations of these effects are suggested.Comment: 73 pages, 23 figures. to appear in Phys. Rev. B, July 1 st (2001

Relationship between social support, quality of life, and Th2 cytokines in a biobehavioral cancer survivorship trial.

ObjectiveBenefits of social support (SS) during cancer survivorship are complex. This study examines change in SS over time in cervical cancer (CXCA) survivors who have completed definitive treatment and how changing SS impacts quality of life (QOL) and T-helper type 2 (Th2) cytokines.MethodsWe conducted a randomized trial in 204 CXCA survivors to test if psychosocial telephone counseling (PTC) could improve QOL compared to usual care (UC). Although PTC did not target SS, data were collected at baseline, 4 and 9 months post-enrollment using the Medical Outcomes Survey Social Support scale. Biospecimens were collected to investigate associations with patient-reported outcomes. Data were analyzed using multivariate linear models and stepwise regression.ResultsParticipants' mean age was 43. PTC participants experienced increasing SS compared to UC at 4 months (PTC-UC = 5.1; p = 0.055) and 9 months (PTC-UC = 6.0; p = 0.046). Higher baseline SS and increasing SS were independently associated with improved QOL at 4 and 9 months after adjusting for patient characteristics (p < 0.05). Differences between study arms were not statistically significant. Improvements in QOL at 4 months were observed with increases in emotional/informational and tangible SS. Increasing SS predicted significant longitudinal decreases in IL-4 and IL-13 at 4 months that were larger in the PTC arm (interactions p = 0.041 and p = 0.057, respectively).ConclusionImproved SS was significantly associated with improved QOL independent of patient characteristics and study arm. Decreasing Th2 cytokines with increasing SS and QOL are consistent with a biobehavioral paradigm in which modulation of the chronic stress response is associated with shifts in immune stance

A new transcript in the TCRB locus unveils the human ortholog of the mouse pre-Dß1 promoter

Introduction: While most transcripts arising from the human T Cell Receptor locus reflect fully rearranged genes, several germline transcripts have been identified. We describe a new germline transcript arising from the human TCRB locus. Methods: cDNA sequencing, promoter, and gene expression analyses were used to characterize the new transcript. Results: The new germline transcript encoded by the human TCRB locus consists of a new exon of 103bp, which we named TRBX1 (X1), spliced with the first exon of gene segments C ss 1 or C ss 2. X1 is located upstream of gene segment D ss 1 and is therefore deleted from a V-DJ rearranged TCRB locus. The X1-C ss transcripts do not appear to code for a protein. We define their transcription start and minimal promoter. These transcripts are found in populations of mature T lymphocytes from blood or tissues and in T cell clones with a monoallelic TCRB rearrangement. In immature thymocytes, they are already detectable in CD1a(-)CD34(+)CD4(-)CD8(-) cells, therefore before completion of the TCRB rearrangements. Conclusions: The X1 promoter appears to be the ortholog of the mouse pre-D ss 1 promoter (PD ss 1). Like PD ss 1, its activation is regulated by E ss in T cells and might facilitate the TCRB rearrangement process by contributing to the accessibility of the D ss 1 locus