Recycling probability and dynamical properties of germinal center reactions

We introduce a new model for the dynamics of centroblasts and centrocytes in a germinal center. The model reduces the germinal center reaction to the elements considered as essential and embeds proliferation of centroblasts, point mutations of the corresponding antibody types represented in a shape space, differentiation to centrocytes, selection with respect to initial antigens, differentiation of positively selected centrocytes to plasma or memory cells and recycling of centrocytes to centroblasts. We use exclusively parameters with a direct biological interpretation such that, once determined by experimental data, the model gains predictive power. Based on the experiment of Han et al. (1995b) we predict that a high rate of recycling of centrocytes to centroblasts is necessary for the germinal center reaction to work reliably. Furthermore, we find a delayed start of the production of plasma and memory cells with respect to the start of point mutations, which turns out to be necessary for the optimization process during the germinal center reaction. The dependence of the germinal center reaction on the recycling probability is analyzed.Comment: 30 pages, 8 figure

Equivariant Deformations of Horospherical Surfaces

The classical Goursat transform for minimal surfaces is interpreted as conformal transformation of the Gauss map, allowing us to bend these surfaces for certain geometric purposes. A simple analogue of this deformation is defined for CMC1 surfaces which makes the Goursat transform equivariant with respect to the Lawson correspondence, thereby increasing the number of explicitly computable examples of minimal/CMC1 cousin pairs. We then indicate how the Goursat transformation law and integrability conditions for the spin curve of a horospherical surface are analogous to the Lorentz transformation law and equations of motion for the wavefunction of a massless fermion

Resonance region neutronics of unit cells in fast and thermal reactors

Originally presented as the first author's thesis, (Ph. D.)--in the M.I.T. Dept. of Nuclear Engineering, 1977Includes bibliographical references (p. 226-229)ERDA research and development E(11-1)--2250 UC-79P LMFBR-Physic

Quantum Optimal Control of Nuclear Spin Qudecimals in 87Sr^{87}\text{Sr}

We study the ability to implement unitary maps on states of the $I=9/2$ nuclear spin in \textsuperscript{87}Sr, a $d=10$ dimensional (qudecimal) Hilbert space, using quantum optimal control. Through a combination of nuclear spin-resonance and a tensor AC-Stark shift, by solely modulating the phase of a radio-frequency magnetic field, the system is quantum controllable. Alkaline earth atoms, such as \textsuperscript{87}Sr, have a very favorable figure-of-merit for such control due to narrow intercombination lines and the large hyperfine splitting in the excited states. We numerically study the quantum speed-limit, optimal parameters, and the fidelity of arbitrary state preparation and full SU(10) maps, including the presence of decoherence due to optical pumping induced by the light-shifting laser. We also study the use of robust control to mitigate some dephasing due to inhomogeneities in the light shift. We find that with an rf-Rabi frequency of $\Omega_\text{rf}$ and 0.5\% inhomogeneity in the the light shift we can prepare an arbitrary Haar-random state in a time $T={4.5}\pi/\Omega_\text{rf}$ with average fidelity $\langle \mathcal{F}_\psi \rangle =0.9992$, and an arbitrary Haar-random SU(10) map in a time $T=24\pi/\Omega_\text{rf}$ with average fidelity $\langle \mathcal{F}_U \rangle = 0.9923$