The 19-Vertex Model at critical regime ∣q∣=1|q|=1

We study the 19-vertex model associated with the quantum group $U_q(\hat{sl_2})$ at critical regime $|q|=1$. We give the realizations of the type-I vertex operators in terms of free bosons and free fermions. Using these free field realizations, we give the integral representations for the correlation functions.Comment: LaTEX2e, 19page

SDiff(2) Toda equation -- hierarchy, τ\tau function, and symmetries

A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda equation, is shown to have a Lax formalism and an infinite hierarchy of higher flows. The Lax formalism is very similar to the case of the self-dual vacuum Einstein equation and its hyper-K\"ahler version, however now based upon a symplectic structure and the group SDiff(2) of area preserving diffeomorphisms on a cylinder $S^1 \times \R$. An analogue of the Toda lattice tau function is introduced. The existence of hidden SDiff(2) symmetries are derived from a Riemann-Hilbert problem in the SDiff(2) group. Symmetries of the tau function turn out to have commutator anomalies, hence give a representation of a central extension of the SDiff(2) algebra.Comment: 16 pages (``vanilla.sty" is attatched to the end of this file after ``\bye" command

Commuting difference operators with elliptic coefficients from Baxter's vacuum vestors

For quantum integrable models with elliptic R-matrix, we construct the Baxter Q-operator in infinite-dimensional representations of the algebra of observables.Comment: 31 pages, LaTeX, references adde

Quantum integrable multi atom matter-radiation models with and without rotating wave approximation

New integrable multi-atom matter-radiation models with and without rotating wave approximation (RWA) are constructed and exactly solved through algebraic Bethe ansatz. The models with RWA are generated through ancestor model approach in an unified way. The rational case yields the standard type of matter-radiaton models, while the trigonometric case corresponds to their q-deformations. The models without RWA are obtained from the elliptic case at the Gaudin and high spin limit.Comment: 9 pages, no figure, talk presented in int. conf. NEEDS04 (Gallipoli, Italy, July 2004

Integrable Time-Discretisation of the Ruijsenaars-Schneider Model

An exactly integrable symplectic correspondence is derived which in a continuum limit leads to the equations of motion of the relativistic generalization of the Calogero-Moser system, that was introduced for the first time by Ruijsenaars and Schneider. For the discrete-time model the equations of motion take the form of Bethe Ansatz equations for the inhomogeneous spin-1/2 Heisenberg magnet. We present a Lax pair, the symplectic structure and prove the involutivity of the invariants. Exact solutions are investigated in the rational and hyperbolic (trigonometric) limits of the system that is given in terms of elliptic functions. These solutions are connected with discrete soliton equations. The results obtained allow us to consider the Bethe Ansatz equations as ones giving an integrable symplectic correspondence mixing the parameters of the quantum integrable system and the parameters of the corresponding Bethe wavefunction.Comment: 27 pages, latex, equations.st

Explorations of the Extended ncKP Hierarchy

A recently obtained extension (xncKP) of the Moyal-deformed KP hierarchy (ncKP hierarchy) by a set of evolution equations in the Moyal-deformation parameters is further explored. Formulae are derived to compute these equations efficiently. Reductions of the xncKP hierarchy are treated, in particular to the extended ncKdV and ncBoussinesq hierarchies. Furthermore, a good part of the Sato formalism for the KP hierarchy is carried over to the generalized framework. In particular, the well-known bilinear identity theorem for the KP hierarchy, expressed in terms of the (formal) Baker-Akhiezer function, extends to the xncKP hierarchy. Moreover, it is demonstrated that N-soliton solutions of the ncKP equation are also solutions of the first few deformation equations. This is shown to be related to the existence of certain families of algebraic identities.Comment: 34 pages, correction of typos in (7.2) and (7.5

Cathodoluminescence characterization of Ge-doped CdTe crystals

Cathodoluminescence (CL) microscopic techniques have been used to study the spatial distribution of structural defects and the deep levels in CdTe:Ge bulk crystals. The effect of Ge doping with concentrations of 10(17) and 10(19) cm(-3) on the compensation of V-Cd in CdTe has been investigated. Dependence of the intensity distribution of CL emission bands on the dopant concentration has been studied. Ge doping causes a substantial reduction of the generally referred to 1.40 eV luminescence, which is often present in undoped CdTe crystals, and enhances the 0.91 and 0.81 eV emissions

Soft and non-soft structural transitions in disordered nematic networks

Properties of disordered nematic elastomers and gels are theoretically investigated with emphasis on the roles of non-local elastic interactions and crosslinking conditions. Networks originally crosslinked in the isotropic phase lose their long-range orientational order by the action of quenched random stresses, which we incorporate into the affine-deformation model of nematic rubber elasticity. We present a detailed picture of mechanical quasi-Goldstone modes, which accounts for an almost completely soft polydomain-monodomain (P-M) transition under strain as well as a ``four-leaf clover'' pattern in depolarized light scattering intensity. Dynamical relaxation of the domain structure is studied using a simple model. The peak wavenumber of the structure factor obeys a power-law-type slow kinetics and goes to zero in true mechanical equilibrium. The effect of quenched disorder on director fluctuation in the monodomain state is analyzed. The random frozen contribution to the fluctuation amplitude dominates the thermal one, at long wavelengths and near the P-M transition threshold. We also study networks obtained by crosslinking polydomain nematic polymer melts. The memory of initial director configuration acts as correlated and strong quenched disorder, which renders the P-M transition non-soft. The spatial distribution of the elastic free energy is strongly dehomogenized by external strain, in contrast to the case of isotropically crosslinked networks.Comment: 19 pages, 15 EPS figure

WNT signalling in prostate cancer

Genome sequencing and gene expression analyses of prostate tumours have highlighted the potential importance of genetic and epigenetic changes observed in WNT signalling pathway components in prostate tumours-particularly in the development of castration-resistant prostate cancer. WNT signalling is also important in the prostate tumour microenvironment, in which WNT proteins secreted by the tumour stroma promote resistance to therapy, and in prostate cancer stem or progenitor cells, in which WNT-β-catenin signals promote self-renewal or expansion. Preclinical studies have demonstrated the potential of inhibitors that target WNT receptor complexes at the cell membrane or that block the interaction of β-catenin with lymphoid enhancer-binding factor 1 and the androgen receptor, in preventing prostate cancer progression. Some WNT signalling inhibitors are in phase I trials, but they have yet to be tested in patients with prostate cancer

Culture and establishment of self-renewing human and mouse adult liver and pancreas 3D organoids and their genetic manipulation.

Adult somatic tissues have proven difficult to expand in vitro, largely because of the complexity of recreating appropriate environmental signals in culture. We have overcome this problem recently and developed culture conditions for adult stem cells that allow the long-term expansion of adult primary tissues from small intestine, stomach, liver and pancreas into self-assembling 3D structures that we have termed 'organoids'. We provide a detailed protocol that describes how to grow adult mouse and human liver and pancreas organoids, from cell isolation and long-term expansion to genetic manipulation in vitro. Liver and pancreas cells grow in a gel-based extracellular matrix (ECM) and a defined medium. The cells can self-organize into organoids that self-renew in vitro while retaining their tissue-of-origin commitment, genetic stability and potential to differentiate into functional cells in vitro (hepatocytes) and in vivo (hepatocytes and endocrine cells). Genetic modification of these organoids opens up avenues for the manipulation of adult stem cells in vitro, which could facilitate the study of human biology and allow gene correction for regenerative medicine purposes. The complete protocol takes 1-4 weeks to generate self-renewing 3D organoids and to perform genetic manipulation experiments. Personnel with basic scientific training can conduct this protocol.LB is supported by an EMBO Postdoctoral fellowship (EMBO ALTF 794-2014). CH is supported by a Cambridge Stem Cell Institute Seed Fund award and the Herchel Smith Fund. BK is supported by a Sir Henry Dale Fellowship from the Wellcome Trust and the Royal Society. MH is a Wellcome Trust Sir Henry Dale Fellow and is jointly funded by the Wellcome Trust and the Royal Society (104151/Z/14/Z).This is the author accepted manuscript. The final version is available from Nature Publishing Group via http://dx.doi.org/10.1038/nprot.2016.097