Exact solution of A-D Temperley-Lieb Models

We solve for the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups {\cal U}_q(X_n } for X_n = A_1,B_n,C_n$and$D_n$. We employ a generalization of the coordinate Bethe-Ansatz developed previously for the deformed biquadratic spin one chain. As expected, all these models have equivalent spectra, i.e. they differ only in the degeneracy of their eigenvalues. This is true for finite length and open boundary conditions. For periodic boundary conditions the spectra of the lower dimensional representations are containded entirely in the higher dimensional ones. The Bethe states are highest weight states of the quantum group, except for some states with energy zero

Recording from two neurons: second order stimulus reconstruction from spike trains and population coding

We study the reconstruction of visual stimuli from spike trains, recording simultaneously from the two H1 neurons located in the lobula plate of the fly Chrysomya megacephala. The fly views two types of stimuli, corresponding to rotational and translational displacements. If the reconstructed stimulus is to be represented by a Volterra series and correlations between spikes are to be taken into account, first order expansions are insufficient and we have to go to second order, at least. In this case higher order correlation functions have to be manipulated, whose size may become prohibitively large. We therefore develop a Gaussian-like representation for fourth order correlation functions, which works exceedingly well in the case of the fly. The reconstructions using this Gaussian-like representation are very similar to the reconstructions using the experimental correlation functions. The overall contribution to rotational stimulus reconstruction of the second order kernels - measured by a chi-squared averaged over the whole experiment - is only about 8% of the first order contribution. Yet if we introduce an instant-dependent chi-square to measure the contribution of second order kernels at special events, we observe an up to 100% improvement. As may be expected, for translational stimuli the reconstructions are rather poor. The Gaussian-like representation could be a valuable aid in population coding with large number of neurons

On the Uq[sl(2)]{\cal{U}}_{q}[sl(2)] Temperley-Lieb reflection matrices

This work concerns the boundary integrability of the spin-s ${\cal{U}}_{q}[sl(2)]$ Temperley-Lieb model. A systematic computation method is used to constructed the solutions of the boundary Yang-Baxter equations. For $s$ half-integer, a general $2s(s+1)+3/2$ free parameter solution is presented. It turns that for $s$ integer, the general solution has $2s(s+1)+1$ free parameters. Moreover, some particular solutions are discussed.Comment: LaTex 17 page

Quantum spin chains of Temperley-Lieb type: periodic boundary conditions, spectral multiplicities and finite temperature

We determine the spectra of a class of quantum spin chains of Temperley-Lieb type by utilizing the concept of Temperley-Lieb equivalence with the S=1/2 XXZ chain as a reference system. We consider open boundary conditions and in particular periodic boundary conditions. For both types of boundaries the identification with XXZ spectra is performed within isomorphic representations of the underlying Temperley-Lieb algebra. For open boundaries the spectra of these models differ from the spectrum of the associated XXZ chain only in the multiplicities of the eigenvalues. The periodic case is rather different. Here we show how the spectrum is obtained sector-wise from the spectra of globally twisted XXZ chains. As a spin-off, we obtain a compact formula for the degeneracy of the momentum operator eigenvalues. Our representation theoretical results allow for the study of the thermodynamics by establishing a TL-equivalence at finite temperature and finite field.Comment: 29 pages, LaTeX, two references added, redundant figures remove

Fungal Chitin Dampens Inflammation through IL-10 Induction Mediated by NOD2 and TLR9 Activation

Funding: JW and NARG thank the Wellcome Trust (080088, 086827, 075470), The Wellcome Trust Strategic Award in Medical Mycology and Fungal Immunology (097377) and the European Union ALLFUN (FP7/2007 2013, HEALTH-2010-260338) for funding. MGN was supported by a Vici grant of the Netherlands Organisation for Scientific Research. AJPB and DMM were funded by STRIFE, ERC-2009-AdG-249793 and AJPB additionally by FINSysB, PITN-GA-2008-214004 and the BBSRC [BB/F00513X/1]. MDL was supported by the MRC (MR/J008230/1). GDB and SV were funded by the Wellcome Trust (086558) and TB and MK were funded by the Deutsche Forschungsgemeinschaft (Bi 696/3-1; Bi 696/5-2; Bi 696/10-1). MS was supported by the Deutsche Forschungsgemeinschaft (Sch 897/1-3) and the National Institute of Dental and Craniofacial Research (R01 DE017514-01). TDK and RKSM were funded by the National Institute of Health (AR056296, AI101935) and the American Lebanese Syrian Associated Charities (ALSAC). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD

Correlation Functions in 2-Dimensional Integrable Quantum Field Theories

In this talk I discuss the form factor approach used to compute correlation functions of integrable models in two dimensions. The Sinh-Gordon model is our basic example. Using Watson's and the recursive equations satisfied by matrix elements of local operators, I present the computation of the form factors of the elementary field $\phi(x)$ and the stress-energy tensor $T_{\mu\nu}(x)$ of the theory.Comment: 19pp, LATEX version, (talk at Como Conference on ``Integrable Quantum Field Theories''