A NORMALLY ELLIPTIC HAMILTONIAN BIFURCATION

A universal local bifurcation analysis is presented of an autonomous Hamiltonian system around a certain equilibrium point. This central equilibrium has a double zero eigenvalue, the other eigenvalues being in general position. Main emphasis is given to the 2 degrees of freedom case where these other eigenvalues are purely imaginary. By normal form techniques and Singularity Theory unfoldings are obtained. having 'integrable' approximations related to the Elliptic and Hyperbolic Umbilic Catastrophes

A NORMALLY ELLIPTIC HAMILTONIAN BIFURCATION

A universal local bifurcation analysis is presented of an autonomous Hamiltonian system around a certain equilibrium point. This central equilibrium has a double zero eigenvalue, the other eigenvalues being in general position. Main emphasis is given to the 2 degrees of freedom case where these other eigenvalues are purely imaginary. By normal form techniques and Singularity Theory unfoldings are obtained. having 'integrable' approximations related to the Elliptic and Hyperbolic Umbilic Catastrophes

A NORMALLY ELLIPTIC HAMILTONIAN BIFURCATION

A universal local bifurcation analysis is presented of an autonomous Hamiltonian system around a certain equilibrium point. This central equilibrium has a double zero eigenvalue, the other eigenvalues being in general position. Main emphasis is given to the 2 degrees of freedom case where these other eigenvalues are purely imaginary. By normal form techniques and Singularity Theory unfoldings are obtained. having 'integrable' approximations related to the Elliptic and Hyperbolic Umbilic Catastrophes

Inflammatory breast cancer: dynamic contrast-enhanced MR in patients receiving bevacizumab. Initial experience

To retrospectively compare three dynamic contrast material-enhanced magnetic resonance (MR) imaging (dynamic MR imaging) analytic methods to determine the parameter or combination of parameters most strongly associated with changes in tumor microvasculature during treatment with bevacizumab alone and bevacizumab plus chemotherapy in patients with inflammatory or locally advanced breast cancer. MATERIALS AND METHODS: This study was conducted in accordance with the institutional review board of the National Cancer Institute and was compliant with the Privacy Act of 1974. Informed consent was obtained from all patients. Patients with inflammatory or locally advanced breast cancer were treated with one cycle of bevacizumab alone (cycle 1) followed by six cycles of combination bevacizumab and chemotherapy (cycles 2-7). Serial dynamic MR images were obtained, and the kinetic parameters measured by using three dynamic analytic MR methods (heuristic, Brix, and general kinetic models) and two region-of-interest strategies were compared by using two-sided statistical tests. A P value of .01 was required for significance. RESULTS: In 19 patients, with use of a whole-tumor region of interest, the authors observed a significant decrease in the median values of three parameters measured from baseline to cycle 1: forward transfer rate constant (Ktrans) (-34% relative change, P=.003), backflow compartmental rate constant extravascular and extracellular to plasma (Kep) (-15% relative change, P<.001), and integrated area under the gadolinium concentration curve (IAUGC) at 180 seconds (-23% relative change, P=.009). A trend toward differences in the heuristic slope of the washout curve between responders and nonresponders to therapy was observed after cycle 1 (bevacizumab alone, P=.02). The median relative change in slope of the wash-in curve from baseline to cycle 4 was significantly different between responders and nonresponders (P=.009). CONCLUSION: The dynamic contrast-enhanced MR parameters Ktrans, Kep, and IAUGC at 180 seconds appear to have the strongest association with early physiologic response to bevacizumab. Clinical trial registration no. NCT0001654

The structure of a major surface antigen SAG19 from Eimeria tenella unifies the Eimeria SAG family

In infections by apicomplexan parasites including Plasmodium, Toxoplasma gondii, and Eimeria, host interactions are mediated by proteins including families of membrane-anchored cysteine-rich surface antigens (SAGs) and SAG-related sequences (SRS). Eimeria tenella causes caecal coccidiosis in chickens and has a SAG family with over 80 members making up 1% of the proteome. We have solved the structure of a representative E. tenella SAG, EtSAG19, revealing that, despite a low level of sequence similarity, the entire Eimeria SAG family is unified by its three-layer αβα fold which is related to that of the CAP superfamily. Furthermore, sequence comparisons show that the Eimeria SAG fold is conserved in surface antigens of the human coccidial parasite Cyclospora cayetanensis but this fold is unrelated to that of the SAGs/SRS proteins expressed in other apicomplexans including Plasmodium species and the cyst-forming coccidia Toxoplasma gondii, Neospora caninum and Besnoitia besnoiti. However, despite having very different structures, Consurf analysis showed that Eimeria SAG and Toxoplasma SRS families each exhibit marked hotspots of sequence hypervariability that map to their surfaces distal to the membrane anchor. This suggests that the primary and convergent purpose of the different structures is to provide a platform onto which sequence variability can be imposed

Control of Rayleigh-Taylor instability by vertical vibration in large aspect ratio containers

We consider a horizontal heavy fluid layer supported by a light, immiscible one in a wide (as compared to depth) container, which is vertically vibrated intending to counterbalance the Rayleigh-Taylor instability of the flat, rigid-body vibrating state. In the simplest case when the density and viscosity of the lighter fluid are small compared to their counterparts in the heavier fluid, we apply a long wave, weakly nonlinear analysis that yields a generalized Cahn-Hilliard equation for the evolution of the fluid interface. This equation shows that the stabilizing effect of vibration is like that of surface tension, and is used to analyze the linear stability of the flat state, the local bifurcation at the instability threshold and some global existence and stability properties concerning the steady states without dry spots. The analysis is extended to two cases of practical interest. Namely, (a) the viscosity of one of the fluids is much smaller than that of the other one, and (b) the densities and viscosities of both fluids are quite close to each other