Discrete embedded solitons

We address the existence and properties of discrete embedded solitons (ESs), i.e., localized waves existing inside the phonon band in a nonlinear dynamical-lattice model. The model describes a one-dimensional array of optical waveguides with both the quadratic (second-harmonic generation) and cubic nonlinearities. A rich family of ESs was previously known in the continuum limit of the model. First, a simple motivating problem is considered, in which the cubic nonlinearity acts in a single waveguide. An explicit solution is constructed asymptotically in the large-wavenumber limit. The general problem is then shown to be equivalent to the existence of a homoclinic orbit in a four-dimensional reversible map. From properties of such maps, it is shown that (unlike ordinary gap solitons), discrete ESs have the same codimension as their continuum counterparts. A specific numerical method is developed to compute homoclinic solutions of the map, that are symmetric under a specific reversing transformation. Existence is then studied in the full parameter space of the problem. Numerical results agree with the asymptotic results in the appropriate limit and suggest that the discrete ESs may be semi-stable as in the continuous case.Comment: A revtex4 text file and 51 eps figure files. To appear in Nonlinearit

On Optimal Two-Impulse Earth-Moon Transfers in a Four-Body Model

In this paper two-impulse Earth-Moon transfers are treated in the restricted four-body problem with the Sun, the Earth, and the Moon as primaries. The problem is formulated with mathematical means and solved through direct transcription and multiple shooting strategy. Thousands of solutions are found, which make it possible to frame known cases as special points of a more general picture. Families of solutions are defined and characterized, and their features are discussed. The methodology described in this paper is useful to perform trade-off analyses, where many solutions have to be produced and assessed

Correlation between CD105 expression and postoperative recurrence and metastasis of hepatocellular carcinoma

BACKGROUND: Angiogenesis is one of the mechanisms most critical to the postoperative recurrence and metastasis of hepatocellular carcinoma (HCC). Thus, finding the molecular markers associated with angiogenesis may help identify patients at increased risk for recurrence and metastasis of HCC. This study was designed to investigate whether CD105 or CD34 could serve as a valid prognostic marker in patients with HCC by determining if there is a correlation between CD105 or CD34 expression and postoperative recurrence or metastasis. METHODS: Immunohistochemical staining for the CD105, CD34 and vascular endothelial growth factor (VEGF) antibodies was performed in 113 HCC tissue specimens containing paracarcinomatous tissue and in 14 normal liver tissue specimens. The quantitation of microvessels identified by anti-CD105 and anti-CD34 monoclonal antibodies and the semiquantitation of VEGF expression identified by anti-VEGF monoclonal antibody were analyzed in conjunction with the clinicopathological characteristics of the HCC and any available follow-up information about the patients from whom the specimens were obtained. RESULTS: CD105 was not expressed in the vascular endothelial cells of any normal liver tissue or paracarcinomatous liver tissue but was expressed in the vascular endothelial cells of all HCC tissue. In contrast, CD34 was expressed in the vascular endothelial cells of normal liver tissue, paracarcinomatous tissue, and HCC tissue in the following proportions of specimens: 86.7%, 93.8%, and 100%, respectively. The microvascular densities (MVDs) of HCC determined by using an anti-CD105 mAb (CD105-MVD) and an anti-CD34 mAb (CD34-MVD), were 71.7 ± 8.3 (SD) and 106.3 ± 10.4 (SD), respectively. There was a significant correlation between CD105-MVD and CD34-MVD (r = 0.248, P = 0.021). Although CD34-MVD was significantly correlated with VEGF expression (r = 0.243, P = 0.024), CD105-MVD was more closely correlated (r = 0.300, P= 0.005). The correlation between microscopic venous invasion and CD105-MVD, but not CD34-MVD, was also statistically significant (r = 0.254, P = 0.018). Univariate analysis showed that CD105-MVD was significantly correlated with the 2-year overall survival rate (P = 0.014); CD34-MVD was not (P = 0.601). Multivariate analysis confirmed that CD105-MVD was an independent prognostic factor and that CD34-MVD was not. CONCLUSION: The anti-CD105 mAb is an ideal instrument to quantify new microvessels in HCC as compared with anti-CD34 mAb. CD105-MVD as compared with CD34-MVD is relevant a significant and independent prognostic indicator for recurrence and metastasis in HCC patients

Overexpression of β2-microglobulin is associated with poor survival in patients with oral cavity squamous cell carcinoma and contributes to oral cancer cell migration and invasion

β2-Microglobulin (β2M), a component of MHC class I molecules, is believed to be associated with tumour status in various cancers. In this study, we examined the expression of β2M at different malignant stages of oral cavity squamous cell carcinoma (OCSCC). To determine the possible correlation between β2M expression and various clinical characteristics, 256 samples from patients with OCSCC were evaluated by immunohistochemical staining. Strong β2M expression was significantly correlated with a relatively advanced tumour stage (P<0.001), positive nodal status (P<0.001), and TNM stage (P<0.001). The cumulative 5-year survival rate was significantly correlated with a relatively advanced tumour stage (P<0.001), positive nodal status (P<0.001), TNM stage (P<0.001), and strong expression of β2M (P<0.001). Thus, elevated β2M expression is an indicator of poor survival (P<0.001). In addition, we extended our analysis of β2M expression to the FaDu and SCC25 oral cancer cell lines. β2-Microglobulin expression was positively correlated with cell migration and invasion in β2M-overexpressing transfectants in Transwell chambers. The suppression of β2M expression using small interfering RNA (siRNA) was sufficient to decrease cell migration and invasion in vitro. Taken together, our results suggest that β2M expression in the tissues is associated with survival and may be involved in tumour progression and metastasis in OCSCC

Anomalous Peak Effect in CeRu2 and NbSe2 : Fracturing of a Flux Line Lattice?

CeRu2 and 2H-NbSe2 display remarkable similarities in their magnetic response, reflecting the manner in which the weakly pinned flux line lattice (FLL) loses spatial order in the Peak Effect (PE) regime. The discontinuous change in screening response near the onset of PE and the history dependence in it are attributed to a disorder-induced fracturing transition of the FLL, as an alternative to the scenario involving the appearance of a spatial modulation in superconducting order parameter in CeRu2.Comment: 4 pages of text and figures in ps for