Principal 22-Blocks and Sylow 22-Subgroups

Let $G$ be a finite group with Sylow $2$-subgroup $P \leqslant G$. Navarro-Tiep-Vallejo have conjectured that the principal $2$-block of $N_G(P)$ contains exactly one irreducible Brauer character if and only if all odd-degree ordinary irreducible characters in the principal $2$-block of $G$ are fixed by a certain Galois automorphism $\sigma \in \mathrm{Gal}(\mathbb{Q}_{|G|}/\mathbb{Q})$. Recent work of Navarro-Vallejo has reduced this conjecture to a problem about finite simple groups. We show that their conjecture holds for all finite simple groups, thus establishing the conjecture for all finite groups.Comment: 12 page

Phosphotyrosines in the killer cell inhibitory receptor motif of NKB1 are required for negative signaling and for association with protein tyrosine phosphatase 1C.

NKB1 is one member of a growing family of killer cell inhibitory receptors (KIR). It is expressed on natural killer (NK) cells and T cells, and has been shown to inhibit cytolytic functions of these cells upon interacting with its ligand, HLA-B (Bw4). We demonstrate here that the cytoplasmic region of NKB1 is capable of inhibiting T cell activation in Jurkat cells. The tyrosine phosphorylation of the NKB1 KIR consensus motif, YxxL(x)26 YxxL, induces an association with the protein tyrosine phosphatase 1C (PTP1C). Importantly, mutation of both tyrosines in the motif abolished the inhibitory functions of NKB1 and abrogated PTP1C association. Mutational analysis of the individual tyrosines suggest that the membrane proximal tyrosine may play a crucial role in mediating the inhibitory signal. These results demonstrate that KIR can not only inhibit cytolytic activity, but can also negatively regulate T cell receptor activation events that lead to downstream gene activation, and further supports a model that implicates PTP1C as a mediator in the KIR inhibitory signal

Fast and adaptive fractal tree-based path planning for programmable bevel tip steerable needles

© 2016 IEEE. Steerable needles are a promising technology for minimally invasive surgery, as they can provide access to difficult to reach locations while avoiding delicate anatomical regions. However, due to the unpredictable tissue deformation associated with needle insertion and the complexity of many surgical scenarios, a real-time path planning algorithm with high update frequency would be advantageous. Real-time path planning for nonholonomic systems is commonly used in a broad variety of fields, ranging from aerospace to submarine navigation. In this letter, we propose to take advantage of the architecture of graphics processing units (GPUs) to apply fractal theory and thus parallelize real-time path planning computation. This novel approach, termed adaptive fractal trees (AFT), allows for the creation of a database of paths covering the entire domain, which are dense, invariant, procedurally produced, adaptable in size, and present a recursive structure. The generated cache of paths can in turn be analyzed in parallel to determine the most suitable path in a fraction of a second. The ability to cope with nonholonomic constraints, as well as constraints in the space of states of any complexity or number, is intrinsic to the AFT approach, rendering it highly versatile. Three-dimensional (3-D) simulations applied to needle steering in neurosurgery show that our approach can successfully compute paths in real-time, enabling complex brain navigation

1D to 3D Crossover of a Spin-Imbalanced Fermi Gas

We have characterized the one-dimensional (1D) to three-dimensional (3D) crossover of a two-component spin-imbalanced Fermi gas of 6-lithium atoms in a 2D optical lattice by varying the lattice tunneling and the interactions. The gas phase separates, and we detect the phase boundaries using in situ imaging of the inhomogeneous density profiles. The locations of the phases are inverted in 1D as compared to 3D, thus providing a clear signature of the crossover. By scaling the tunneling rate with respect to the pair binding energy, we observe a collapse of the data to a universal crossover point at a scaled tunneling value of 0.025(7).Comment: 5 pages, 4 figure