The agrin gene codes for a family of basal lamina proteins that differ in function and distribution

We isolated two cDNAs that encode isoforms of agrin, the basal lamina protein that mediates the motor neuron-induced aggregation of acetylcholine receptors on muscle fibers at the neuromuscular junction. Both proteins are the result of alternative splicing of the product of the agrin gene, but, unlike agrin, they are inactive in standard acetylcholine receptor aggregation assays. They lack one (agrin-related protein 1) or two (agrin-related protein 2) regions in agrin that are required for its activity. Expression studies provide evidence that both proteins are present in the nervous system and muscle and that, in muscle, myofibers and Schwann cells synthesize the agrin-related proteins while the axon terminals of motor neurons are the sole source of agrin

Agrin isoforms and their role in synaptogenesis

Agrin is thought to mediate the motor neuron-induced aggregation of synaptic proteins on the surface of muscle fibers at neuromuscular junctions. Recent experiments provide direct evidence in support of this hypothesis, reveal the nature of agrin immunoreactivity at sites other than neuromuscular junctions, and have resulted in findings that are consistent with the possibility that agrin plays a role in synaptogenesis throughout the nervous system

The geometry of a vorticity model equation

We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics describes the geodesic flow on the subgroup of orientation-preserving diffeomorphisms fixing one point, with respect to right-invariant metric induced by the homogeneous Sobolev norm $H^{1/2}$ and show the local existence of the geodesics in the extended group of diffeomorphisms of Sobolev class $H^{k}$ with $k\ge 2$.Comment: 24 page

Determining (n,f) cross sections for actinide nuclei indirectly: An examination of the Surrogate Ratio Method

The validity of the Surrogate Ratio method for determining (n,f) cross sections for actinide nuclei is examined. This method relates the ratio of two compound-nucleus reaction cross sections to a ratio of coincidence events from two measurements in which the same compound nuclei are formed via a direct reaction. With certain assumptions, the method allows one of the cross sections to be inferred if the other is known. We develop a nuclear reaction-model simulation to investigate whether the assumptions underlying the Ratio approach are valid and employ these simulations to assess whether the cross sections obtained indirectly by applying a Ratio analysis agree with the expected results. In particular, we simulate Surrogate experiments that allow us to determine fission cross sections for selected actinide nuclei. The nuclei studied, {sup 233}U and {sup 235}U, are very similar to those considered in recent Surrogate experiments. We find that in favorable cases the Ratio method provides useful estimates of the desired cross sections, and we discuss some of the limitations of the approach

Reaction cross-section predictions for nucleon induced reactions

A microscopic calculation of the optical potential for nucleon-nucleus scattering has been performed by explicitly coupling the elastic channel to all the particle-hole (p-h) excitation states in the target and to all relevant pickup channels. These p-h states may be regarded as doorway states through which the flux flows to more complicated configurations, and to long-lived compound nucleus resonances. We calculated the reaction cross sections for the nucleon induced reactions on the targets $^{40,48}$Ca, $^{58}$Ni, $^{90}$Zr and $^{144}$Sm using the QRPA description of target excitations, coupling to all inelastic open channels, and coupling to all transfer channels corresponding to the formation of a deuteron. The results of such calculations were compared to predictions of a well-established optical potential and with experimental data, reaching very good agreement. The inclusion of couplings to pickup channels were an important contribution to the absorption. For the first time, calculations of excitations account for all of the observed reaction cross-sections, at least for incident energies above 10 MeV.Comment: 6 pages, 6 figures. Submitted to INPC 2010 Conference Proceeding

Many-body approach to proton emission and the role of spectroscopic factors

The process of proton emission from nuclei is studied by utilizing the two-potential approach of Gurvitz and Kalbermann in the context of the full many-body problem. A time-dependent approach is used for calculating the decay width. Starting from an initial many-body quasi-stationary state, we employ the Feshbach projection operator approach and reduce the formalism to an effective one-body problem. We show that the decay width can be expressed in terms of a one-body matrix element multiplied by a normalization factor. We demonstrate that the traditional interpretation of this normalization as the square root of a spectroscopic factor is only valid for one particular choice of projection operator. This causes no problem for the calculation of the decay width in a consistent microscopic approach, but it leads to ambiguities in the interpretation of experimental results. In particular, spectroscopic factors extracted from a comparison of the measured decay width with a calculated single-particle width may be affected.Comment: 17 pages, Revte

Determining Compound-Nuclear Reaction Cross Sections Via Surrogate Reactions: Approximation Schemes for (n,f) Reactions

The validity of the Surrogate Nuclear Reactions method in the Weisskopf-Ewing limit and the Surrogate Ratio method are examined for neutron-induced fission of uranium nuclei. Both methods are approximations to the full Surrogate Nuclear Reactions approach, which aims at determining cross sections for compound-nuclear reactions. A nuclear-reaction model is employed to simulate physical quantities that are typically measured in Surrogate experiments and to test commonly-used assumptions underlying the analyses of Surrogate experiments