Functional roles of Phe12 of deacetyl-thymosin β4 in the impaired blastogenic response of uraemic T-lymphocytes

Phe12 of deacetyl-thymosin β4 is one of the structural essentials for restorative effect on the impaired blastogenic response of uraemic T-lymphocytes. In order to evaluate the functional roles of this phenyl group in the restorative effect on impaired T-lymphocytes, two analogues, [1- Nal12]deacetyl-thymosin β4 and [Cha12]deacetyl4 thymosin β4, were synthesized by a solid-phase method and evaluated for restorative effect on the impaired blastogenic response of uraemic T-lymphocytes. The results indicated that [1-Nal12]deacetyl-thymosin β4 which had a bulky naphthyl ring showed a stronger restorative effect than that of deacetyl-thymosin β4, but it was slightly weaker than that of [Phe(4F)12]deacetyl-thymosin β4. However, [Cha12]deacetyl-thymosin β4 showed no restorative effect on the impaired blastogenic response of uraemic T-lymphocytes

Syntheses of two deacetyl-thymosin α1 analogues and their effects on low E-rosette-forming lymphocytes of uraemic patients

Two deacetyl-thymosin α1 analogues containing Phe (4Br) or D-Phe (4Br) residue—[D-Phe(4Br)21]deacetyl-thymosin α1 and [Phe(4Br)21]deacetyl-thymosin α1, respectively—were synthesized by the manual solid-phase method and their immunological effects on the low E-rosette-forming lymphocytes of uraemic patients were examined. One of the synthetic analogues, [Phe(4Br)21deacetyl-thymosin α1, demonstrated a restorative effect on the low E-rosette-forming lymphocytes of uraemic patients, which was stronger than that of deacetyl-thymosin α1, but the other analogue, [D-Phe(4Br)21]deacetyl-thymosin α1, showed no restorative effect under the same conditions

Semidefinite Representation of the kk-Ellipse

The $k$-ellipse is the plane algebraic curve consisting of all points whose sum of distances from $k$ given points is a fixed number. The polynomial equation defining the $k$-ellipse has degree $2^k$ if $k$ is odd and degree $2^k{-}\binom{k}{k/2}$ if $k$ is even. We express this polynomial equation as the determinant of a symmetric matrix of linear polynomials. Our representation extends to weighted $k$-ellipses and $k$-ellipsoids in arbitrary dimensions, and it leads to new geometric applications of semidefinite programming.Comment: 16 pages, 5 figure

Future Foam

We study pocket universes which have zero cosmological constant and non-trivial boundary topology. These arise from bubble collisions in eternal inflation. Using a simplified dust model of collisions we find that boundaries of any genus can occur. Using a radiation shell model we perform analytic studies in the thin wall limit to show the existence of geometries with a single toroidal boundary. We give plausibility arguments that higher genus boundaries can also occur. In geometries with one boundary of any genus a timelike observer can see the entire boundary. Geometries with multiple disconnected boundaries can also occur. In the spherical case with two boundaries the boundaries are separated by a horizon. Our results suggest that the holographic dual description for eternal inflation, proposed by Freivogel, Sekino, Susskind and Yeh, should include summation over the genus of the base space of the dual conformal field theory. We point out peculiarities of this genus expansion compared to the string perturbation series.Comment: 23 pages, 6 figure

Scalar Three-point Functions in a CDL Background

Motivated by the FRW-CFT proposal by Freivogel, Sekino, Susskind and Yeh, we compute the three-point function of a scalar field in a Coleman-De Luccia instanton background. We first compute the three-point function of the scalar field making only very mild assumptions about the scalar potential and the instanton background. We obtain the three-point function for points in the FRW patch of the CDL instanton and take two interesting limits; the limit where the three points are near the boundary of the hyperbolic slices of the FRW patch, and the limit where the three points lie on the past lightcone of the FRW patch. We expand the past lightcone three-point function in spherical harmonics. We show that the near boundary limit expansion of the three-point function of a massless scalar field exhibits conformal structure compatible with FRW-CFT when the FRW patch is flat. We also compute the three-point function when the scalar is massive, and explain the obstacles to generalizing the conjectured field-operator correspondence of massless fields to massive fields.Comment: 42 pages + appendices, 10 figures; v2, v3: minor correction