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

Myocardial infarct extension during reperfusion after coronary artery occlusion: Pathologic evidence

AbstractObjectives. The goal of this study was to demonstrate myocardial infarct extension during reperfusion within the same animal.Background. Whether myocardial reperfusion can result in the extension of myocardial necrosis remains controversial. The transformation of reversibly injured myocytes into irreversibly damaged cells after reperfusion has been difficult to demonstrate pathologically.Methods. New Zealand White rabbits (Group I, n = 10) were subjected to 30 min of coronary artery occlusion and 180 min of reperfusion. Horseradish peroxidase, a tracer protein that permeates the sarcolemma of irreversibly injured myocytes, was used to quantitate myocyte necrosis at the beginning of reperfusion. Within the same heart, infarct size was measured after 180 min of reperfusion by triphenyttetrazolium chloride (TTC) staining. In separate experiments to demonstrate the validity of the model, rabbits were subjected to 30 min of coronary occlusion, followed by intravenous infusion of horseradish peroxidase and rapid induction of death (Group II) or 30 min of occlusion, 180 min of reperfusion with horseradish peroxidase administered after 180 min of reperfusion and TTC staining after induced death (Group III).Results. In Group I, infarct size at the onset of reperfusion, delineated by horseradish peroxidase, measured 45.3 ± 2.8% of the area of risk and was significantly less than TTC-delineated infarct size after 189 min of re perfusion (59.8 ± 33%, p = 0.0002). By electron microscopy, border areas within the ischemic bed demonstrated irreversibly injured horseradish peroxidasepositive myocytes adjacent to irreversibly injured horseradish peroxidase-negative myocytes, suggesting that farther cell death occurred during reperfusion. In Group II, infarcts delineated by horseradish peroxidase after 30 min of coronary occlusion were similar in size to infarcts measured by this tracer in Group I. In Group III, infarcts delineated by horseradish peroxidase at 180 min of reperfusion were similar in size to infarcts measured by TTC and similar to TTC-delineated infarcts measured at 180 min of reperfusion in Group I.Conclusions. These results provide evidence that there is a subset of myocytes in border areas within the ischemic region that are viable at the beginning of reperfusion but subsequently progress to irreversible injury during the reperfusion period

Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t = -1

We prove that the hyperelliptic Torelli group is generated by Dehn twists about separating curves that are preserved by the hyperelliptic involution. This verifies a conjecture of Hain. The hyperelliptic Torelli group can be identified with the kernel of the Burau representation evaluated at t = −1 and also the fundamental group of the branch locus of the period mapping, and so we obtain analogous generating sets for those. One application is that each component in Torelli space of the locus of hyperelliptic curves becomes simply connected when curves of compact type are added

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

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

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

On the number of excursion sets of planar Gaussian fields

37 pages, 14 figures37 pages, 14 figures37 pages, 14 figure

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