Homogeneous cosmologies and the Maupertuis-Jacobi principle

A recent work showing that homogeneous and isotropic cosmologies involving scalar fields are equivalent to the geodesics of certain effective manifolds is generalized to the non-minimally coupled and anisotropic cases. As the Maupertuis-Jacobi principle in classical mechanics, such result permits us to infer some dynamical properties of cosmological models from the geometry of the associated effective manifolds, allowing us to go a step further in the study of cosmological dynamics. By means of some explicit examples, we show how the geometrical analysis can simplify considerably the dynamical analysis of cosmological models.Comment: 5 page

Trailing Edge Unification via an Intermediate Pati-Salam Group

We demonstrate to two-loop order that an intermediate symmetrically embedded Pati-Salam $SU(2)_L \times SU(2)_R \times SU(4)$ level of symmetry is all that is necessary to accommodate empirical values of $\alpha(M_z), \alpha_s(M_z)$ and $\sin^2\theta_w(M_z)$ within a grand unification context but with a high (10^{14} GeV) intermediate mass scale and with a concomitant higher GUT scale.Comment: 7 pages, 4 embedded eps figur

Erythroid anion transporter assembly is mediated by a developmentally regulated recruitment onto a preassembled membrane cytoskeleton

Analysis of the expression and assembly of the anion transporter by metabolic pulse-chase and steady-state protein and RNA measurements reveals that the extent of association of band 3 with the membrane cytoskeleton varies during chicken embryonic development. Pulse-chase studies have indicated that band 3 polypeptides do not associate with the membrane cytoskeleton until they have been transported to the plasma membrane. At this time, band 3 polypeptides are slowly recruited, over a period of hours, onto a preassembled membrane cytoskeletal network and the extent of this cytoskeletal assembly is developmentally regulated. Only 3% of the band 3 polypeptides are cytoskeletal-associated in 4-d erythroid cells vs. 93% in 10-d erythroid cells and 36% in 15-d erythroid cells. This observed variation appears to be regulated primarily at the level of recruitment onto the membrane cytoskeleton rather than by different transport kinetics to the membrane or differential turnover of the soluble and insoluble polypeptides and is not dependent upon the lineage or stage of differentiation of the erythroid cells. Steady-state protein and RNA analyses indicate that the low levels of cytoskeletal band 3 very early in development most likely result from limiting amounts of ankyrin and protein 4.1, the membrane cytoskeletal binding sites for band 3. As embryonic development proceeds, ankyrin and protein 4.1 levels increase with a concurrent rise in the level of cytoskeletal band 3 until, on day 10 of development, virtually all of the band 3 polypeptides are cytoskeletal bound. After day 10, the levels of total and cytoskeletal band 3 decline, whereas ankyrin and protein 4.1 continue to accumulate until day 18, indicating that the cytoskeletal association of band 3 is not regulated solely by the availability of membrane cytoskeletal binding sites at later stages of development. Thus, multiple mechanisms appear to regulate the recruitment of band 3 onto the erythroid membrane cytoskeleton during chicken embryonic development

Startling Equivalences in the Higgs-Goldstone Sector between Radiative and Lowest-Order Conventional Electroweak Symmetry Breaking

For the Higgs boson mass of $\sim 220$ GeV expected to arise from radiative electroweak symmetry breaking, we find the same lowest-order expressions as would be obtained from conventional electroweak symmetry breaking, given the same Higgs boson mass, for Higgs-Goldstone sector scattering processes identified with $W_L^ + W_L^- \to W_L^+ W_L^-$, $W_L^+ W_L^- \to Z_L Z_L$, as well as for Higgs boson decay widths $H \to W_L^+ W_L^-$, $H \to Z_L Z_L$. The radiatively broken case, however, leads to an order of magnitude enhancement over lowest-order conventional symmetry breaking for scattering processes $W_L^+ W_L^+ \to H H$, $Z_L Z_L \to H H$, as well as a factor of $\sim 30$ enhancement for $H H \to H H$.Comment: 6 pages, uses ws-ijmpa.cls written in Latex2E. Major revision in text and conclusions--different enhanced scattering processes found than the earlier version. To appear in the IJMPA proceedings issue for MRST 2005, Utica, N