Topological phases of fermions in one dimension

In this paper we show how the classification of topological phases in insulators and superconductors is changed by interactions, in the case of 1D systems. We focus on the TR-invariant Majorana chain (BDI symmetry class). While the band classification yields an integer topological index $k$, it is known that phases characterized by values of $k$ in the same equivalence class modulo 8 can be adiabatically transformed one to another by adding suitable interaction terms. Here we show that the eight equivalence classes are distinct and exhaustive, and provide a physical interpretation for the interacting invariant modulo 8. The different phases realize different Altland-Zirnbauer classes of the reduced density matrix for an entanglement bipartition into two half-chains. We generalize these results to the classification of all one dimensional gapped phases of fermionic systems with possible anti-unitary symmetries, utilizing the algebraic framework of central extensions. We use matrix product state methods to prove our results.Comment: 14 pages, 3 figures, v2: references adde

Pathogen burden, inflammation, proliferation and apoptosis in human in-stent restenosis - Tissue characteristics compared to primary atherosclerosis

Pathogenic events leading to in-stent restenosis (ISR) are still incompletely understood. Among others, inflammation, immune reactions, deregulated cell death and growth have been suggested. Therefore, atherectomy probes from 21 patients with symptomatic ISR were analyzed by immunohistochemistry for pathogen burden and compared to primary target lesions from 20 stable angina patients. While cytomegalovirus, herpes simplex virus, Epstein-Barr virus and Helicobacter pylori were not found in ISR, acute and/or persistent chlamydial infection were present in 6/21 of these lesions (29%). Expression of human heat shock protein 60 was found in 8/21 of probes (38%). Indicated by distinct signals of CD68, CD40 and CRP, inflammation was present in 5/21 (24%), 3/21 (14%) and 2/21 (10%) of ISR cases. Cell density of ISR was significantly higher than that of primary lesions ( 977 +/- 315 vs. 431 +/- 148 cells/mm(2); p < 0.001). There was no replicating cell as shown by Ki67 or PCNA. TUNEL+ cells indicating apoptosis were seen in 6/21 of ISR specimens (29%). Quantitative analysis revealed lower expression levels for each intimal determinant in ISR compared to primary atheroma (all p < 0.05). In summary, human ISR at the time of clinical presentation is characterized by low frequency of pathogen burden and inflammation, but pronounced hypercellularity, low apoptosis and absence of proliferation. Copyright (C) 2004 S. Karger AG, Basel

Existential questions in (relatively) hyperbolic groups {\it and} Finding relative hyperbolic structures

This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". The first part is entitled "Existential questions in (relatively) hyperbolic groups". We study there the existential theory of torsion free hyperbolic and relatively hyperbolic groups, in particular those with virtually abelian parabolic subgroups. We show that the satisfiability of systems of equations and inequations is decidable in these groups. In the second part, called "Finding relative hyperbolic structures", we provide a general algorithm that recognizes the class of groups that are hyperbolic relative to abelian subgroups.Comment: Two independant parts 23p + 9p, revised. To appear separately in Israel J. Math, and Bull. London Math. Soc. respectivel

Topological entropy and secondary folding

A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is exactly equal to the growth induced by the map on the fundamental group of the torus. However, in many situations the numerically-computed topological entropy is greater than the bound implied by this action. We associate this gap between the bound and the true entropy with 'secondary folding': material lines undergo folding which is not homologically forced. We examine this phenomenon both for physical rod-stirring devices and toral linked twist maps, and show rigorously that for the latter secondary folds occur.Comment: 13 pages, 8 figures. pdfLaTeX with RevTeX4 macro

Peripheral fillings of relatively hyperbolic groups

A group theoretic version of Dehn surgery is studied. Starting with an arbitrary relatively hyperbolic group $G$ we define a peripheral filling procedure, which produces quotients of $G$ by imitating the effect of the Dehn filling of a complete finite volume hyperbolic 3--manifold $M$ on the fundamental group $\pi_1(M)$. The main result of the paper is an algebraic counterpart of Thurston's hyperbolic Dehn surgery theorem. We also show that peripheral subgroups of $G$ 'almost' have the Congruence Extension Property and the group $G$ is approximated (in an algebraic sense) by its quotients obtained by peripheral fillings. Various applications of these results are discussed.Comment: The difference with the previous version is that Proposition 3.2 is proved for quasi--geodesics instead of geodesics. This allows to simplify the exposition in the last section. To appear in Invent. Mat

Haemodynamics and flow modification stents for peripheral arterial disease:a review

Endovascular stents are widely used for the treatment of peripheral arterial disease (PAD). However, the development of in-stent restenosis and downstream PAD progression remain a challenge. Stent revascularisation of PAD causes arterial trauma and introduces abnormal haemodynamics, which initiate complicated biological processes detrimental to the arterial wall. The interaction between stent struts and arterial cells in contact, and the blood flow field created in a stented region, are highly affected by stent design. Spiral flow is known as a normal physiologic characteristic of arterial circulation and is believed to prevent the development of flow disturbances. This secondary flow motion is lost in atheromatous disease and its re-introduction after endovascular treatment of PAD has been suggested as a method to induce stabilised and coherent haemodynamics. Stent designs able to generate spiral flow may support endothelial function and therefore increase patency rates. This review is focused on secondary flow phenomena in arteries and the development of flow modification stent technologies for the treatment of PAD

Brain Changes in Long-Term Zen Meditators Using Proton Magnetic Resonance Spectroscopy and Diffusion Tensor Imaging: A Controlled Study

Introduction: This work aimed to determine whether 1H magnetic resonance imaging (MRI), magnetic resonance spectroscopy (MRS), diffusion-weighted imaging (DWI) and diffusion tensor imaging (DTI) are correlated with years of meditation and psychological variables in long-term Zen meditators compared to healthy non-meditator controls. Materials and Methods: Design. Controlled, cross-sectional study. Sample. Meditators were recruited from a Zen Buddhist monastery. The control group was recruited from hospital staff. Meditators were administered questionnaires on anxiety, depression, cognitive impairment and mindfulness. 1H-MRS (1.5 T) of the brain was carried out by exploring four areas: both thalami, both hippocampi, the posterior superior parietal lobule (PSPL) and posterior cingulate gyrus. Predefined areas of the brain were measured for diffusivity (ADC) and fractional anisotropy (FA) by MR-DTI. Results: Myo-inositol (mI) was increased in the posterior cingulate gyrus and Glutamate (Glu), N-acetyl-aspartate (NAA) and N-acetyl-aspartate/Creatine (NAA/Cr) was reduced in the left thalamus in meditators. We found a significant positive correlation between mI in the posterior cingulate and years of meditation (r = 0.518; p = .019). We also found significant negative correlations between Glu (r =20.452; p = .045), NAA (r =20.617; p = .003) and NAA/Cr (r =20.448; P = .047) in the left thalamus and years of meditation. Meditators showed a lower Apparent Diffusion Coefficient (ADC) in the left posterior parietal white matter than did controls, and the ADC was negatively correlated with years of meditation (r =20.4850, p = .0066). Conclusions: The results are consistent with the view that mI, Glu and NAA are the most important altered metabolites. This study provides evidence of subtle abnormalities in neuronal function in regions of the white matter in meditators

The lived experiences of experienced Vipassana Mahasi meditators: an interpretative phenomenological analysis.

Research into the effects and mechanisms of mindfulness training draws predominantly on quantitative research. There is a lack of understanding about the subjective experiences of experienced mindfulness meditators, which may provide additional insights into the effects, processes and context of mindfulness training. This qualitative study explored the lived experiences of a novel group of experienced mindfulness meditators who practise Vipassana Mahasi (VM) meditation. The study aimed to understand how experienced VM practitioners make sense of the effects of practice and what processes they ascribe to it. Participants attended semistructured interviews, and their responses were analysed using interpretative phenomenological analysis. Results yielded overarching themes including (a) improvements in hedonic and eudaimonic well-being; (b) insights into self, others and perception of reality; (c) attaining equanimity; and (d) physical and interpersonal difficulties. Participants perceived VM as a ‘cleansing’ process whereby maladaptive responses were eliminated through mindfulness, other supportive mental qualities, decentering and nonattachment. The findings revealed a complex and dynamic set of interdependent outcomes and processes, which are reinforced by Buddhist teachings and ethical practices. This study highlights the need for additional interdisciplinary research into topics such as insight generation and supportive mental qualities cultivated during VM, novel states of well-being informed by Buddhist constructs and interpersonal difficulties related to long-term practice. Findings also suggest that incorporating Buddhist teachings and ethics into mindfulness-based interventions may enhance practitioner understanding and implementation of meditation techniques.N/