Generalised Perk--Schultz models: solutions of the Yang-Baxter equation associated with quantised orthosymplectic superalgebras

The Perk--Schultz model may be expressed in terms of the solution of the Yang--Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra $U_q[sl(m|n)]$, with a multiparametric co-product action as given by Reshetikhin. Here we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras $U_q[osp(m|n)]$. In this manner we obtain generalisations of the Perk--Schultz model.Comment: 10 pages, 2 figure

Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)]

Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so contains a \textit{universal $R$-matrix} in the tensor product algebra which satisfies the Yang-Baxter equation. Applying the vector representation $\pi$, which acts on the vector module $V$, to one side of a universal $R$-matrix gives a Lax operator. In this paper a Lax operator is constructed for the $C$-type quantum superalgebras $U_q[osp(2|n)]$. This can in turn be used to find a solution to the Yang-Baxter equation acting on $V \otimes V \otimes W$ where $W$ is an arbitrary $U_q[osp(2|n)]$ module. The case $W=V$ is included here as an example.Comment: 15 page

SU(3) monopoles and their fields

Some aspects of the fields of charge two SU(3) monopoles with minimal symmetry breaking are discussed. A certain class of solutions look like SU(2) monopoles embedded in SU(3) with a transition region or ``cloud'' surrounding the monopoles. For large cloud size the relative moduli space metric splits as a direct product AH\times R^4 where AH is the Atiyah-Hitchin metric for SU(2) monopoles and R^4 has the flat metric. Thus the cloud is parametrised by R^4 which corresponds to its radius and SO(3) orientation. We solve for the long-range fields in this region, and examine the energy density and rotational moments of inertia. The moduli space metric for these monopoles, given by Dancer, is also expressed in a more explicit form.Comment: 17 pages, 3 figures, latex, version appearing in Phys. Rev.

Visitor effects on zoo-housed Sulawesi crested macaque (Macaca nigra) behaviour: Can signs with ‘watching eyes’ requesting quietness help?

Visiting public can cause changes in the behaviour of zoo-housed primates. These effects, if indicative of stress, can be of welfare concern. However, few options to mitigate visitor effects through modulating visitor behaviour have been explored. Here we evaluated the effects of visitor number and visitor noise level on the behaviour of five UK groups of Sulawesi crested macaques. We also investigated whether visitor behaviour can be effectively modulated through targeted signage requesting visitors to be quiet, and assessed the use of signs incorporating salient ‘watching’ human eyes, novel to a zoo setting, alongside ‘control’ signs lacking eyes. We used scan sampling to collect over 100 h of behavioural observation data, analysis of which indicated that Sulawesi crested macaques were significantly affected by both visitor number and noise level at all five zoos. We found that active behaviours, such as locomotion or foraging, and behaviours identified as negative for welfare, such as vigilance, increased with increasing visitor number and noise levels, whereas resting and social huddling decreased. The extent to which these behavioural changes reflect welfare, particularly the increase seen in active behaviours, is not clear. We also found that both sign treatments, with and without salient eyes, slightly but significantly reduced visitor noise levels compared with no sign, although signs displaying human eyes were not more effective than the control signs. Our results highlight a need for further research into active behaviours to assess whether increases in these behaviours are associated with stress. While we found signage to be a promising tool to mitigate against these visitor effects, our results also suggest areas in which signs incorporating salient human eyes could be adapted for the zoo environment in order to realise their full potential

Properties of non-BPS SU(3) monopoles

This paper is concerned with magnetic monopole solutions of SU(3) Yang-Mills-Higgs system beyond the Bogomol'nyi-Prasad-Sommerfield limit. The different SU(2) embeddings, which correspond to the fundamental monopoles, as well the embedding along composite root are studied. The interaction of two different fundamental monopoles is considered. Dissolution of a single fundamental non-BPS SU(3) monopole in the limit of the minimal symmetry breaking is analysed.Comment: 19 pages, 7 figures. Typos corrected, reference added. Final version published in Physica Script

Fungal infections of the central nervous system: A review of fungal pathogens and treatment

Multiple factors influence the outcome of fungal infection of the central nervous system (CNS). The host and the pathogen in concert with drug delivery across the blood-brain barrier and drug activity are key factors in outcome. Drug costs can be prohibitively expensive. Drug toxicity with standard antifungal agents such as amphotericin B (infusion rate toxicity) can be reduced using simple techniques such as slower infusion and appropriate saline loading. Continuous infusion can allow relatively large doses of amphotericin B (up to 2 mg/kg/day, remaining below 0.08 mg/kg/hour) to be given with toxicity profiles comparable to expensive lipid formulations of amphotericin B. Dedicated peripherally inserted central catheters can remain in situ for weeks to months and are safe and relatively inexpensive. Correction of metabolic pathology in the case of mucormycosis and resolution of neutropenia are essential to effective treatment of filamentous fungal infections such as Mucor, Aspergillus and Scedosporium. The pharmacology and pharmacokinetics of the current major antifungal agents used to treat fungal infections of the CNS are reviewed. Tables that provide information about achievable CNS drug levels, antifungal susceptibilities and the likelihood of intrinsic drug resistance of significant fungal pathogens have been included to help the clinician with therapy. Treatment recommendations for Cryptococcal and Candida meningitis and for rhinocerebral infection with Mucor and Aspergillus have been included

On the structure of the set of bifurcation points of periodic solutions for multiparameter Hamiltonian systems

This paper deals with periodic solutions of the Hamilton equation with many parameters. Theorems on global bifurcation of solutions with periods $2\pi/j,$ $j\in\mathbb{N},$ from a stationary point are proved. The Hessian matrix of the Hamiltonian at the stationary point can be singular. However, it is assumed that the local topological degree of the gradient of the Hamiltonian at the stationary point is nonzero. It is shown that (global) bifurcation points of solutions with given periods can be identified with zeros of appropriate continuous functions on the space of parameters. Explicit formulae for such functions are given in the case when the Hessian matrix of the Hamiltonian at the stationary point is block-diagonal. Symmetry breaking results concerning bifurcation of solutions with different minimal periods are obtained. A geometric description of the set of bifurcation points is given. Examples of constructive application of the theorems proved to analytical and numerical investigation and visualization of the set of all bifurcation points in given domain are provided. This paper is based on a part of the author's thesis [W. Radzki, ``Branching points of periodic solutions of autonomous Hamiltonian systems'' (Polish), PhD thesis, Nicolaus Copernicus University, Faculty of Mathematics and Computer Science, Toru\'{n}, 2005].Comment: 35 pages, 4 figures, PDFLaTe

Calibrated Sub-Bundles in Non-Compact Manifolds of Special Holonomy

This paper is a continuation of math.DG/0408005. We first construct special Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on the cotangent bundle of S^n by looking at the conormal bundle of appropriate submanifolds of S^n. We find that the condition for the conormal bundle to be special Lagrangian is the same as that discovered by Harvey-Lawson for submanifolds in R^n in their pioneering paper. We also construct calibrated submanifolds in complete metrics with special holonomy G_2 and Spin(7) discovered by Bryant and Salamon on the total spaces of appropriate bundles over self-dual Einstein four manifolds. The submanifolds are constructed as certain subbundles over immersed surfaces. We show that this construction requires the surface to be minimal in the associative and Cayley cases, and to be (properly oriented) real isotropic in the coassociative case. We also make some remarks about using these constructions as a possible local model for the intersection of compact calibrated submanifolds in a compact manifold with special holonomy.Comment: 20 pages; for Revised Version: Minor cosmetic changes, some paragraphs rewritten for improved clarit