The Birkhoff theorem for unitary matrices of arbitrary dimensions

It was shown recently that Birkhoff's theorem for doubly stochastic matrices can be extended to unitary matrices with equal line sums whenever the dimension of the matrices is prime. We prove a generalization of the Birkhoff theorem for unitary matrices with equal line sums for arbitrary dimension.Comment: This manuscript presents a proof for the general unitary birkhoff theorem, conjectured in arXiv:1509.0862

Paxillin facilitates timely neurite initiation on soft-substrate environments by interacting with the endocytic machinery.

Neurite initiation is the first step in neuronal development and occurs spontaneously in soft tissue environments. Although the mechanisms regulating the morphology of migratory cells on rigid substrates in cell culture are widely known, how soft environments modulate neurite initiation remains elusive. Using hydrogel cultures, pharmacologic inhibition, and genetic approaches, we reveal that paxillin-linked endocytosis and adhesion are components of a bistable switch controlling neurite initiation in a substrate modulus-dependent manner. On soft substrates, most paxillin binds to endocytic factors and facilitates vesicle invagination, elevating neuritogenic Rac1 activity and expression of genes encoding the endocytic machinery. By contrast, on rigid substrates, cells develop extensive adhesions, increase RhoA activity and sequester paxillin from the endocytic machinery, thereby delaying neurite initiation. Our results highlight paxillin as a core molecule in substrate modulus-controlled morphogenesis and define a mechanism whereby neuronal cells respond to environments exhibiting varying mechanical properties

Eta absorption by mesons

Using the $[SU(3)_{\mathrm{L}} \times SU(3)_{\mathrm{R}}]_{\mathrm{global}}\times [SU(3)_V]_{\mathrm{local}}$ chiral Lagrangian with hidden local symmetry, we evaluate the cross sections for the absorption of eta meson ($\eta$) by pion ($\pi$), rho ($\rho$), omega ($\omega$), kaon ($K$), and kaon star ($K^*$) in the tree-level approximation. With empirical masses and coupling constants as well as reasonable values for the cutoff parameter in the form factors at interaction vertices, we find that most cross sections are less than 1 mb, except the reactions $\rho\eta\to K\bar K^*(\bar KK^*)$, $\omega\eta\to K\bar K^*(\bar KK^*)$, $K^*\eta\to\rho K$, and $K^*\eta\to\omega K$, which are a few mb, and the reactions $\pi\eta\to K\bar K$ and $K\eta\to\pi K$, which are more than 10 mb. Including these reactions in a kinetic model based on a schematic hydrodynamic description of relativistic heavy ion collisions, we find that the abundance of eta mesons likely reaches chemical equilibrium with other hadrons in nuclear collisions at the Relativistic Heavy Ion Collider.Comment: 29 pages, 10 figures, version to appear in Nucl. Phys.

Matrix Model in a Class of Time Dependent Supersymmetric Backgrounds

We discuss the matrix model in a class of 11D time dependent supersymmetric backgrounds as obtained in hep-th/0508191 . We construct the matrix model action through the matrix regularization of the membrane action in the background. We show that the action is exact to all order of fermionic coordinates. Furthermore We discuss the fuzzy sphere solutions in this background.Comment: 16 pages, 4 figures; references added, modifications of some comments in introduction, version to appear in PL