We investigate a generalized Ising action containing nearest neighbour, next to nearest neighbour and plaquette terms that has been suggested as a potential string worldsheet discretization on cubic lattices by Savvidy and Wegner. We use both mean field techniques and Monte-Carlo simulations to sketch out the phase diagram. The Gonihedric (Savvidy-Wegner) model has a symmetry that allows any pl...

where the sum is over the edges of some triangulated surface, θ(αij) = |π − αij | ζ , ζ is some exponent, and αij is the dihedral angle between neighbouring triangles with common link < ij >. This definition of the action was inspired by the geometrical notion the linear size of a surface, originally defined by Steiner. In equ.(1) it is the surface itself that is discretized, rather than the sp...

We introduce the notion of sofic measurable equivalence relations. Using them we prove that Connes’ Embedding Conjecture as well as the Measurable Determinant Conjecture of Lück, Sauer and Wegner hold for treeable equivalence relations.

Wegener's granulomatosis is a disease characterised by a necrotising vasculitis and granulomatous inflammation. The localised form involves the upper and/or lower respiratory tracts while in the commoner generalised form there is a widespread necrotising vasculitis and renal involvement. Intestinal involvement, which may be severe, has been detected at necropsy in 24% of cases. Gastrointestinal...

Antineutrophil-cytoplasm antibody (ANCA)-associated vasculitides (AAV), classified as small-sized vessel vasculitides, include: granulomatosis with polyangiitis (GPA) (formerly Wegener’s granulomatosis disease), microscopic polyangiitis (MPA), and eosinophilic granulomatosis with polyangiitis (EGPA) (formerly Churg–Strauss syndrome) [1]. Although they share some common features, EGPA has certai...

Inhalation of cosmetic talc can lead to pulmonary foreign-body granulomatosis, though fewer than 10 cases of inhaled cosmetic talc-related pulmonary granulomatosis have been reported in adults. We report the case of a 64-year-old man with diffuse, bilateral pulmonary nodules and ground glass opacities associated with chronic inhalation of cosmetic talc. Transbronchial biopsy showed peribronchio...

Antineutrophil cytoplasmic antibody (ANCA)–associated vasculitis encompasses 3 conditions: eosinophilic granulomatosis with polyangiitis (EGPA; formerly named Churg-Strauss syndrome), granulomatosis with polyangiitis (GPA; formerly named Wegener granulomatosis), and microscopic polyangiitis.1 Diagnosing ANCA-associated small-vessel vasculitis is challenging for clinicians because of its infrequ...

Background: Alveolar hemorrhage can be seen in many vasculitic disorders. However, granulomatosis polyangiitis (formerly Wegener’s granulomatosis) uncommonly presents with life threatening alveolar hemorrhage and has only been discussed in a few case reports [1]. Case Presentation: A 53 year old Caucasian male presented with hemoptysis and profound anemia. Two weeks prior, he had presented with...