Clinicopathological correlation in erythema induratum

Background - Erythema induratum (EI) is a reactive disorder to mycobacterium tuberculosis infection, a diagnosis not to be missed. Erythema nodosum (EN) is the main clinical differential of EI, but a distinctly different pathological condition that can be difficult to distinguish from EI. Methods – In this retrospective review we assess clinical and histological features of 40 EI cases and 16 EN cases. Six experienced dermatologists blindly diagnosed these cases based on clinical images, thereafter the histology was revealed, and they adjusted their diagnoses accordingly. Fleiss Kappa statistics were applied to determine inter-rater variability. A multi-variate logistic regression model determined the clinical and histological features that contribute most to an accurate diagnosis. Results - After assessing the clinical picture 48.8% of the EI cases and 74% of the EN cases were correctly diagnosed. With added histology results 67.1% EI and 81.2% EN cases were correct. EI cases showed inter-rater variability of 0.478 (pvalue < 0.01) before and 0.469 (p-value < 0.01) after histology was revealed. These features combined in a logistic regression model had a higher diagnostic accuracy than the assessors with regard to EI cases. The model was accurate in 100% and 80% of EI and EN cases respectively. Conclusions - While the study was limited by its retrospective nature and small sample size, valuable features (ulceration, vasculitis and lobular or septal panniculitis) were identified. A biopsy of the lower leg markedly increased the diagnostic accuracy, but there was less concordance between assessors, more research is needed to confirm these results

A Noncommutative Sigma Model

We replaced the classical string theory notions of parameter space and world-time with noncommutative tori and consider maps between these spaces. The dynamics of mappings between different noncommutative tori were studied and a noncommutative generalization of the Polyakov action was derived. The quantum torus was studied in detail as well as *-homomorphisms between different quantum tori. A finite dimensional representation of the quantum torus was studied and the partition function and other path integrals were calculated. At the end we proved existence theorems for mappings between different noncommutative tori.Comment: The thesis was based on an article by Vargese Mathai and Jonathan Rosenberg with the same titl

Interplay of Soundcone and Supersonic Propagation in Lattice Models with Power Law Interactions

We study the spreading of correlations and other physical quantities in quantum lattice models with interactions or hopping decaying like $r^{-\alpha}$ with the distance $r$. Our focus is on exponents $\alpha$ between 0 and 6, where the interplay of long- and short-range features gives rise to a complex phenomenology and interesting physical effects, and which is also the relevant range for experimental realizations with cold atoms, ions, or molecules. We present analytical and numerical results, providing a comprehensive picture of spatio-temporal propagation. Lieb-Robinson-type bounds are extended to strongly long-range interactions where $\alpha$ is smaller than the lattice dimension, and we report particularly sharp bounds that are capable of reproducing regimes with soundcone as well as supersonic dynamics. Complementary lower bounds prove that faster-than-soundcone propagation occurs for $\alpha<2$ in any spatial dimension, although cone-like features are shown to also occur in that regime. Our results provide guidance for optimizing experimental efforts to harness long-range interactions in a variety of quantum information and signaling tasks.Comment: 20 pages, 8 figure

Relaxation timescales and decay of correlations in a long-range interacting quantum simulator

We study the time evolution of correlation functions in long-range interacting quantum Ising models. For a large class of initial conditions, exact analytic results are obtained in arbitrary lattice dimension, both for ferromagnetic and antiferromagnetic coupling, and hence also in the presence of geometric frustration. In contrast to the nearest-neighbour case, we find that correlations decay like stretched or compressed exponentials in time. Provided the long-range character of the interactions is sufficiently strong, pronounced prethermalization plateaus are observed and relaxation timescales are widely separated. Specializing to a triangular lattice in two spatial dimensions, we propose to utilize these results for benchmarking of a recently developed ion-trap based quantum simulator.Comment: 19 pages, 6 figures; v2: one section removed, appendices added; v3: upper bound corrected + minor corrections; v4: as publishe

Modelling of trends in Twitter using retweet graph dynamics

In this paper we model user behaviour in Twitter to capture the emergence of trending topics. For this purpose, we first extensively analyse tweet datasets of several different events. In particular, for these datasets, we construct and investigate the retweet graphs. We find that the retweet graph for a trending topic has a relatively dense largest connected component (LCC). Next, based on the insights obtained from the analyses of the datasets, we design a mathematical model that describes the evolution of a retweet graph by three main parameters. We then quantify, analytically and by simulation, the influence of the model parameters on the basic characteristics of the retweet graph, such as the density of edges and the size and density of the LCC. Finally, we put the model in practice, estimate its parameters and compare the resulting behavior of the model to our datasets.Comment: 16 pages, 5 figures, presented at WAW 201

A noncommutative sigma model.

We replace the classical string theory notions of mapping between parameter space and world-time with noncommutative tori mapping between these spaces. The dynamics of mappings between different noncommutative tori are studied and noncommutative versions of the Polyakov action and the Euler-Lagrange equations are derived. The quantum torus is studied in detail, as well as C*-homomorphisms between different quantum tori. A finite dimensional representation of the quantum torus is studied, and the partition function and other path integrals are calculated. At the end we prove existence theorems for mappings between different noncommutative tori.This abstract was presented at the ‘Studentesimposium in die Natuurwetenskappe 2011’, presented under the protection of the Suid- Afrikaanse Akademie vir Wetenskap en Kuns. The symposium was held at the University of South Africa on 27–28 October 2011.http://www.satnt.ac.zaam201

Investigations on apocynin, a potent NADPH oxidase inhibitor

Polymorphonuclear neutrophils (PMNs) play a major role in inflammatory diseases. They act as a first line of defense against invading infectious microorganisms. For this purpose, PMNs contain granules filled with proteolytic and other cytotoxic enzymes. Besides releasing enzymes, PMNs are also able to phagocytose and to convert oxygen into highly reactive oxygen species (ROS). Following phagocytosis, ingested microorganisms may be killed inside the phagosome by a combined action of enzyme activity and ROS production. Although the formation of ROS by stimulated PMNs is a physiological response which is advantageous to the host, it can also be detrimental in many inflammatory states in which these radicals give rise to excessive tissue damage. Therefore, there is an ongoing search for anti-inflammatory compounds which are able to prevent this damaging ROS production without affecting the other killing capacities of the PMN. In 1971, the isolation of apocynin from the roots of Picrorhiza kurroa Royle ex Benth. was reported. Picrorhiza kurroa is a small, perennial plant growing at high altitudes in the western Himalayas and which has been used extensively for ages and is still in use in the Ayurvedic system of medicine in India and Sri Lanka. Following experiments showed that apocynin was a potent anti-inflammatory agent, based on the selective inhibition of the production of ROS by activated human PMNs. Although proven to be an active anti-inflammatory compound in several experimental animal models, the exact mechanism of action of apocynin was still not fully understood. In this thesis, experiments are described that have led to a better understanding of the mode of action by which apocynin inhibits the ROS production by activated human PMNs. One of the conclusions is that apocynin itself is not active, but that it is converted into an active dimer inside the phagosomes of activated PMNs

Breakdown of Quasilocality in Long-Range Quantum Lattice Models

We study the nonequilibrium dynamics of correlations in quantum lattice models in the presence of long-range interactions decaying asymptotically as a power law. For exponents larger than the lattice dimensionality, a Lieb-Robinson- type bound effectively restricts the spreading of correlations to a causal region, but allows supersonic propagation. We show that this decay is not only sufficient but also necessary. Using tools of quantum metrology, for any exponents smaller than the lattice dimension, we construct Hamiltonians giving rise to quantum channels with capacities not restricted to a causal region. An analytical analysis of long-range Ising models illustrates the disappearance of the causal region and the creation of correlations becoming distance independent. Numerical results obtained using matrix product state methods for the XXZ spin chain reveal the presence of a sound cone for large exponents and supersonic propagation for small ones. In all models we analyzed, the fast spreading of correlations follows a power law, but not the exponential increase of the long-range Lieb-Robinson bound