Probing the fuzzy sphere regularisation in simulations of the 3d \lambda \phi^4 model

We regularise the 3d \lambda \phi^4 model by discretising the Euclidean time and representing the spatial part on a fuzzy sphere. The latter involves a truncated expansion of the field in spherical harmonics. This yields a numerically tractable formulation, which constitutes an unconventional alternative to the lattice. In contrast to the 2d version, the radius R plays an independent r\^{o}le. We explore the phase diagram in terms of R and the cutoff, as well as the parameters m^2 and \lambda. Thus we identify the phases of disorder, uniform order and non-uniform order. We compare the result to the phase diagrams of the 3d model on a non-commutative torus, and of the 2d model on a fuzzy sphere. Our data at strong coupling reproduce accurately the behaviour of a matrix chain, which corresponds to the c=1-model in string theory. This observation enables a conjecture about the thermodynamic limit.Comment: 31 pages, 15 figure

Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere

We address a detailed non-perturbative numerical study of the scalar theory on the fuzzy sphere. We use a novel algorithm which strongly reduces the correlation problems in the matrix update process, and allows the investigation of different regimes of the model in a precise and reliable way. We study the modes associated to different momenta and the role they play in the ``striped phase'', pointing out a consistent interpretation which is corroborated by our data, and which sheds further light on the results obtained in some previous works. Next, we test a quantitative, non-trivial theoretical prediction for this model, which has been formulated in the literature: The existence of an eigenvalue sector characterised by a precise probability density, and the emergence of the phase transition associated with the opening of a gap around the origin in the eigenvalue distribution. The theoretical predictions are confirmed by our numerical results. Finally, we propose a possible method to detect numerically the non-commutative anomaly predicted in a one-loop perturbative analysis of the model, which is expected to induce a distortion of the dispersion relation on the fuzzy sphere.Comment: 1+36 pages, 18 figures; v2: 1+55 pages, 38 figures: added the study of the eigenvalue distribution, added figures, tables and references, typos corrected; v3: 1+20 pages, 10 eps figures, new results, plots and references added, technical details about the tests at small matrix size skipped, version published in JHE

Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term

Fuzzy spheres appear as classical solutions in a matrix model obtained via dimensional reduction of 3-dimensional Yang-Mills theory with the Chern-Simons term. Well-defined perturbative expansion around these solutions can be formulated even for finite matrix size, and in the case of $k$ coincident fuzzy spheres it gives rise to a regularized U($k$) gauge theory on a noncommutative geometry. Here we study the matrix model nonperturbatively by Monte Carlo simulation. The system undergoes a first order phase transition as we change the coefficient ($\alpha$) of the Chern-Simons term. In the small $\alpha$ phase, the large $N$ properties of the system are qualitatively the same as in the pure Yang-Mills model ($\alpha =0$), whereas in the large $\alpha$ phase a single fuzzy sphere emerges dynamically. Various `multi fuzzy spheres' are observed as meta-stable states, and we argue in particular that the $k$ coincident fuzzy spheres cannot be realized as the true vacuum in this model even in the large $N$ limit. We also perform one-loop calculations of various observables for arbitrary $k$ including $k=1$. Comparison with our Monte Carlo data suggests that higher order corrections are suppressed in the large $N$ limit.Comment: Latex 37 pages, 13 figures, discussion on instabilities refined, references added, typo corrected, the final version to appear in JHE

Sequential Broadening of CTL Responses in Early HIV-1 Infection Is Associated with Viral Escape

BACKGROUND: Antigen-specific CTL responses are thought to play a central role in containment of HIV-1 infection, but no consistent correlation has been found between the magnitude and/or breadth of response and viral load changes during disease progression. METHODS AND FINDINGS: We undertook a detailed investigation of longitudinal CTL responses and HIV-1 evolution beginning with primary infection in 11 untreated HLA-A2 positive individuals. A subset of patients developed broad responses, which selected for consensus B epitope variants in Gag, Pol, and Nef, suggesting CTL-induced adaptation of HIV-1 at the population level. The patients who developed viral escape mutations and broad autologous CTL responses over time had a significantly higher increase in viral load during the first year of infection compared to those who did not develop viral escape mutations. CONCLUSIONS: A continuous dynamic development of CTL responses was associated with viral escape from temporarily effective immune responses. Our results suggest that broad CTL responses often represent footprints left by viral CTL escape rather than effective immune control, and help explain earlier findings that fail to show an association between breadth of CTL responses and viral load. Our results also demonstrate that CTL pressures help to maintain certain elements of consensus viral sequence, which likely represent viral escape from common HLA-restricted CTL responses. The ability of HIV to evolve to escape CTL responses restricted by a common HLA type highlights the challenges posed to development of an effective CTL-based vaccine

Numerical taxonomy of proteolytic psychrotrophs from Queensland raw milks

Eighty‐seven proteolytic psychrotrophic micro‐organisms were isolated from 11 bulk milk supplies of two Queensland factories from different climatic regions, before and after storage at 4°C for 7 d. These isolates together with 15 reference strains formed the basis of a numerical taxonomic study involving 81 attributes. All but six isolates were pseudomonads. The strains clustered into nine groups, of which one group consisted of four yeasts. One group, containing 39 isolates, was designated as Pseudomonas fluorescens biovar 1; three groups, containing 27 isolates, as Ps. fluorescens biovar 5; and one group, containing 10 isolates, as Ps. putida biovar A. This study showed that the proteolytic psychrotrophic microflora of the 11 milks supplying the two factories was substantially different and that the proteolytic flora of 7 d refrigerated milk could not be estimated by examining the flora before storage. Copyrigh