Excitation Spectrum and Correlation Functions of the Z_3-Chiral Potts Quantum Spin Chain

We study the excitation spectrum and the correlation functions of the Z_3- chiral Potts model in the massive high-temperature phase using perturbation expansions and numerical diagonalization. We are mainly interested in results for general chiral angles but we consider also the superintegrable case. For the parameter values considered, we find that the band structure of the low- lying part of the excitation spectrum has the form expected from a quasiparticle picture with two fundamental particles. Studying the N-dependence of the spectrum, we confirm the stability of the second fundamental particle in a limited range of the momentum, even when its energy becomes so high that it lies very high up among the multiparticle scattering states. This is not a phenomenon restricted to the superintegrable line. Calculating a non-translationally invariant correlation function, we give evidence that it is oscillating. Within our numerical accuracy we find a relation between the oscillation length and the dip position of the momentum dispersion of the lightest particle which seems to be quite independent of the chiral angles.Comment: 19 pages + 6 PostScript figures (LaTeX); BONN-TH-94-2

Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities

We compute the one-dimensional configuration sums of the ABF model using the fermionic technique introduced in part I of this paper. Combined with the results of Andrews, Baxter and Forrester, we find proof of polynomial identities for finitizations of the Virasoro characters $\chi_{b,a}^{(r-1,r)}(q)$ as conjectured by Melzer. In the thermodynamic limit these identities reproduce Rogers--Ramanujan type identities for the unitary minimal Virasoro characters, conjectured by the Stony Brook group. We also present a list of additional Virasoro character identities which follow from our proof of Melzer's identities and application of Bailey's lemma.Comment: 28 pages, Latex, 7 Postscript figure

Adaptation of the carbamoyl-phosphate synthetase (CPS) enzyme in an extremophile fish

Tetrapods and fish have adapted distinct carbamoyl-phosphate synthase (CPS) enzymes to initiate the ornithine urea cycle during the detoxification of nitrogenous wastes. We report evidence that in the ureotelic subgenus of extremophile fish Oreochromis Alcolapia, CPS III has undergone convergent evolution and adapted its substrate affinity to ammonia which is typical of terrestrial vertebrate CPS I. Unusually, unlike in other vertebrates, the expression of CPS III in Alcolapia is localised to the skeletal muscle and is activated in the myogenic lineage during early embryonic development with expression remaining in mature fish. We propose that adaptation in Alcolapia included both convergent evolution of CPS function to that of terrestrial vertebrates, as well as changes in development mechanisms redirecting CPS III gene expression to the skeletal muscle

Exploring the expression of cardiac regulators in a vertebrate adapted to an extreme environment: the cichlid fish Oreochromis (Alcolapia) alcalica

Although it is widely accepted that the cellular and molecular mechanisms of vertebrate cardiac development are evolutionarily conserved, this is on the basis of data from only a few model organisms suited to laboratory studies. Here, we investigate gene expression during cardiac development in the extremophile, non-model fish species, Oreochromis (Alcolapia) alcalica. We first characterise the early development of O. alcalica and observe extensive vascularisation across the yolk prior to hatching. We further investigate heart development by identifying and cloning O. alcalica orthologues of conserved cardiac transcription factors gata4, tbx5, and mef2c for analysis by in situ hybridisation. Expression of these three key cardiac developmental regulators also reveals other aspects of O. alcalica development, as these genes are expressed in developing blood, limb, eyes, and muscle, as well as the heart. Our data support the notion that O. alcalica is a direct-developing vertebrate that shares the highly conserved molecular regulation of the vertebrate body plan. However, the expression of gata4 in O. alcalica reveals interesting di erences in the development of the circulatory system distinct from that of the well-studied zebrafish. Understanding the development of O. alcalica embryos is an important step towards providing a model for future research into the adaptation to extreme conditions; this is particularly relevant given that anthropogenic-driven climate change will likely result in more freshwater organisms being exposed to less favourable conditions

Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4\nu)

We prove polynomial identities for the N=1 superconformal model SM(2,4\nu) which generalize and extend the known Fermi/Bose character identities. Our proof uses the q-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations for q-series on the fermionic side. We use these polynomials to demonstrate a dual relation under q \rightarrow q^{-1} between SM(2,4\nu) and M(2\nu-1,4\nu). We also introduce a generalization of the Witten index which is expressible in terms of the Rogers false theta functions.Comment: 41 pages, harvmac, no figures; new identities, proofs and comments added; misprints eliminate

sl(N) Onsager's Algebra and Integrability

We define an $sl(N)$ analog of Onsager's Algebra through a finite set of relations that generalize the Dolan Grady defining relations for the original Onsager's Algebra. This infinite-dimensional Lie Algebra is shown to be isomorphic to a fixed point subalgebra of $sl(N)$ Loop Algebra with respect to a certain involution. As the consequence of the generalized Dolan Grady relations a Hamiltonian linear in the generators of $sl(N)$ Onsager's Algebra is shown to posses an infinite number of mutually commuting integrals of motion

Integrating ecology into macroevolutionary research

On 9 March, over 150 biologists gathered in London for the Centre for Ecology and Evolution spring symposium, ‘Integrating Ecology into Macroevolutionary Research’. The event brought together researchers from London-based institutions alongside others from across the UK, Europe and North America for a day of talks. The meeting highlighted methodological advances and recent analyses of exemplar datasets focusing on the exploration of the role of ecological processes in shaping macroevolutionary patterns

Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models

We present fermionic sum representations of the characters $\chi^{(p,p')}_{r,s}$ of the minimal $M(p,p')$ models for all relatively prime integers $p'>p$ for some allowed values of $r$ and $s$. Our starting point is binomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin ${1\over 2}$ chain of anisotropy $-\Delta=-\cos(\pi{p\over p'})$. We use the Takahashi-Suzuki method to express the allowed values of $r$ (and $s$) in terms of the continued fraction decomposition of $\{{p'\over p}\}$ (and ${p\over p'}$) where $\{x\}$ stands for the fractional part of $x.$ These values are, in fact, the dimensions of the hermitian irreducible representations of $SU_{q_{-}}(2)$ (and $SU_{q_{+}}(2)$) with $q_{-}=\exp (i \pi \{{p'\over p}\})$ (and $q_{+}=\exp ( i \pi {p\over p'})).$ We also establish the duality relation $M(p,p')\leftrightarrow M(p'-p,p')$ and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.Comment: Several references, one further explicit result and several discussion remarks adde

Random Matrix Theory and higher genus integrability: the quantum chiral Potts model

We perform a Random Matrix Theory (RMT) analysis of the quantum four-state chiral Potts chain for different sizes of the chain up to size L=8. Our analysis gives clear evidence of a Gaussian Orthogonal Ensemble statistics, suggesting the existence of a generalized time-reversal invariance. Furthermore a change from the (generic) GOE distribution to a Poisson distribution occurs when the integrability conditions are met. The chiral Potts model is known to correspond to a (star-triangle) integrability associated with curves of genus higher than zero or one. Therefore, the RMT analysis can also be seen as a detector of ``higher genus integrability''.Comment: 23 pages and 10 figure

The use of porcine small intestinal submucosa mesh (SURGISIS) as a pelvic sling in a man and a woman with previous pelvic surgery: two case reports

<p>Abstract</p> <p>Introduction</p> <p>Closing the pelvic peritoneum to prevent the small bowel dropping into the pelvis after surgery for locally recurrent rectal cancer is important to prevent adhesions deep in the pelvis or complications of adjuvant radiotherapy. Achieving this could be difficult because sufficient native tissue is unavailable; we report on the use of small intestine submucosa extra-cellular matrix mesh in the obliteration of the pelvic brim.</p> <p>Case presentation</p> <p>We describe two cases in which submucosa extra-cellular matrix mesh was used to obliterate the pelvic brim following resection of a recurrent rectal tumour; the first patient, a 78-year-old Caucasian man, presented with small bowel obstruction caused by adhesions to a recurrent rectal tumour. The second patient, an 84-year-old Caucasian woman, presented with vaginal discharge caused by an entero-vaginal fistula due to a recurrent rectal tumour.</p> <p>Conclusion</p> <p>We report on the use of submucosa extra-cellular matrix mesh as a pelvic sling in cases where primary closure of the pelvic peritoneum is unfeasible. Its use had no infective complications and added minimal morbidity to the postoperative period. This is an original case report that would be of interest to general and colorectal surgeons.</p