Statistical symmetries of the Lundgren-Monin-Novikov hierarchy.

It was shown by Oberlack and Rosteck [Discr. Cont. Dyn. Sys. S, 3, 451 2010] that the infinite set of multipoint correlation (MPC) equations of turbulence admits a considerable extended set of Lie point symmetries compared to the Galilean group, which is implied by the original set of equations of fluid mechanics. Specifically, a new scaling group and an infinite set of translational groups of all multipoint correlation tensors have been discovered. These new statistical groups have important consequences for our understanding of turbulent scaling laws as they are essential ingredients of, e.g., the logarithmic law of the wall and other scaling laws, which in turn are exact solutions of the MPC equations. In this paper we first show that the infinite set of translational groups of all multipoint correlation tensors corresponds to an infinite dimensional set of translations under which the Lundgren-Monin-Novikov (LMN) hierarchy of equations for the probability density functions (PDF) are left invariant. Second, we derive a symmetry for the LMN hierarchy which is analogous to the scaling group of the MPC equations. Most importantly, we show that this symmetry is a measure of the intermittency of the velocity signal and the transformed functions represent PDFs of an intermittent (i.e., turbulent or nonturbulent) flow. Interesting enough, the positivity of the PDF puts a constraint on the group parameters of both shape and intermittency symmetry, leading to two conclusions. First, the latter symmetries may no longer be Lie group as under certain conditions group properties are violated, but still they are symmetries of the LMN equations. Second, as the latter two symmetries in its MPC versions are ingredients of many scaling laws such as the log law, the above constraints implicitly put weak conditions on the scaling parameter such as von Karman constant κ as they are functions of the group parameters. Finally, let us note that these kind of statistical symmetries are of much more general type, i.e., not limited to MPC or PDF equations emerging from Navier-Stokes, but instead they are admitted by other nonlinear partial differential equations like, for example, the Burgers equation when in conservative form and if the nonlinearity is quadratic.

Multipotent mesenchymal stem cells with immunosuppressive activity can be easily isolated from dental pulp.

BACKGROUND: Bone marrow mesenchymal stem cells (MSCs) are currently being investigated in preclinical and clinical settings because of their multipotent differentiative capacity or, alternatively, their immunosuppressive function. The aim of this study was to evaluate dental pulp (DP) as a potential source of MSCs instead of bone marrow (BM). METHODS: Flow cytometric analysis showed that DP-MSCs and BM-MSCs were equally SH2, SH3, SH4, CD29 and CD 166 positive. The in vitro proliferative kinetics of MSCs were measured by 3H-thymidine incorporation uptake. The immunosuppressive function of MSCs was then tested by coculturing PHA-stimulated allogeneic T cells with or without MSCs for 3 days. RESULTS: BM-MSCs could be differentiated in vitro into osteogenic, chondrogenic and adipogenic lineages. DP-MSCs showed osteogenic and adipocytic differentiation, but did not differentiate into chondrocytes. Although DP-MSCs grow rapidly in vitro between day 3 and day 8 of culture and then decrease their proliferation by day 15, BM-MSCs have a stable and continuous proliferation over the same period of time. The addition of DP-MSCs or BM-MSCs resulted in 91 +/- 4% and 75 +/- 3% inhibition of T cell response, respectively, assessed by a 3H-thymidine assay. CONCLUSIONS: Dental pulp is an easily accessible and efficient source of MSCs, with different kinetics and differentiation potentialities from MSCs as isolated from the bone marrow. The rapid proliferative capacity together with the immunoregulatory characteristics of DP-MSCs may prompt future studies aimed at using these cells in the treatment or prevention of T-cell alloreactivity in hematopoietic or solid organ allogeneic transplantation.