New Solutions to the Yang--Baxter Equation from Two--Dimensional Representations of Uq(sl(2))U_q(sl(2)) at Roots of Unit

We present particularly simple new solutions to the Yang--Baxter equation arising from two--dimensional cyclic representations of quantum $SU(2)$. They are readily interpreted as scattering matrices of relativistic objects, and the quantum group becomes a dynamical symmetry.Comment: 11 page

Quantum Groups

These notes correspond rather accurately to the translation of the lectures given at the Fifth Mexican School of Particles and Fields, held in Guanajuato, Gto., in December~1992. They constitute a brief and elementary introduction to quantum symmetries from a physical point of view, along the lines of the forthcoming book by C. G\'omez, G. Sierra and myself.Comment: 37 pages, plain.te

Stretched Horizon for Non-Supersymmetric Black Holes

We review the idea of stretched horizon for extremal black holes in supersymmetric string theories, and we compute it for non-supersymmetric black holes in four dimensions. Only for small masses of the order of the Veneziano wavelength is the stretched horizon bigger than the event horizon.Comment: 4 pages, 2 figures, to appear in the Proceedings of the VIII Mexican School, Oaxaca, AI

Pion Scattering Revisited

Chiral Ward identities lead to consistent accounting for the sigma's width in the linear sigma model's Feynman rules. Reanalysis of pion scattering data at threshold imply a mass for the sigma of 600+ 200 - 100 MeV.Comment: latex; VIII EMPC (Oaxaca, Nov 98) Proceeding

A GLI1-p53 inhibitory loop controls neural stem cell and tumour cell numbers

How cell numbers are determined is not understood. Hedgehog-Gli activity is involved in precursor cell proliferation and stem cell self-renewal, and its deregulation sustains the growth of many human tumours. However, it is not known whether GLI1, the final mediator of Hh signals, controls stem cell numbers, and how its activity is restricted to curtail tumourigenesis. Here we have altered the levels of GLI1 and p53, the major tumour suppressor, in multiple systems. We show that GLI1 expression in Nestin+ neural progenitors increases precursor and clonogenic stem cell numbers in vivo and in vitro. In contrast, p53 inhibits GLI1-driven neural stem cell self-renewal, tumour growth and proliferation. Mechanistically, p53 inhibits the activity, nuclear localisation and levels of GLI1 and in turn, GLI1 represses p53, establishing an inhibitory loop. We also find that p53 regulates the phosphorylation of a novel N' truncated putative activator isoform of GLI1 in human cells. The balance of GLI1 and p53 functions, thus, determines cell numbers, and prevalence of p53 restricts GLI1-driven stem cell expansion and tumourigenesis