Kleinian groups and the complex of curves

We examine the internal geometry of a Kleinian surface group and its relations to the asymptotic geometry of its ends, using the combinatorial structure of the complex of curves on the surface. Our main results give necessary conditions for the Kleinian group to have `bounded geometry' (lower bounds on injectivity radius) in terms of a sequence of coefficients (subsurface projections) computed using the ending invariants of the group and the complex of curves. These results are directly analogous to those obtained in the case of punctured-torus surface groups. In that setting the ending invariants are points in the closed unit disk and the coefficients are closely related to classical continued-fraction coefficients. The estimates obtained play an essential role in the solution of Thurston's ending lamination conjecture in that case.Comment: 32 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol4/paper3.abs.htm

Disordered mixed spin Ising system in a random field

The diluted mixed spin Ising system consisting of spin-1/2 and spin-1 in a random field is studied by the use of finite cluster approximation the framework of a single-site cluster theory. The equations are derived using a probability distribution method based on the use of Van der Waerden identities. The complete phase diagrams are investigated in the case of the simple cubic lattice (z=6), where the random field is bimodally and trimodally distributed. In particular, the influence of the magnetic sites concentration on the tricritical behaviour is examined in detail.The diluted mixed spin Ising system consisting of spin-1/2 and spin-1 in a random field is studied by the use of finite cluster approximation the framework of a single-site cluster theory. The equations are derived using a probability distribution method based on the use of Van der Waerden identities. The complete phase diagrams are investigated in the case of the simple cubic lattice (z=6), where the random field is bimodally and trimodally distributed. In particular, the influence of the magnetic sites concentration on the tricritical behaviour is examined in detail

The transverse mixed spin Ising model in a longitudinal random field

The transverse mixed spin Ising system consisting of spin-1/2 and spin-1 with a longitudinal random field is studied within the finite cluster approximation based on single-site cluster theory. The equations are derived using a probability distribution method based on the use of Van der Waerden identities. In the absence of the transverse field, the complete phase diagram in the case of simple cubic lattice is investigated and exhibits interesting behaviours, where the longitudinal field is bimodally and trimodally distributed. The influence of the transverse field on these behaviours are also examined.The transverse mixed spin Ising system consisting of spin-1/2 and spin-1 with a longitudinal random field is studied within the finite cluster approximation based on single-site cluster theory. The equations are derived using a probability distribution method based on the use of Van der Waerden identities. In the absence of the transverse field, the complete phase diagram in the case of simple cubic lattice is investigated and exhibits interesting behaviours, where the longitudinal field is bimodally and trimodally distributed. The influence of the transverse field on these behaviours are also examined

Unravelling undifferentiated soft tissue sarcomas: insights from genomics

Undifferentiated pleomorphic sarcoma now falls under the broader rubric of undifferentiated soft tissue sarcoma (USTS) in the 2020 World Health Organization classification of bone and soft tissue tumours. These rare cancers remain a diagnosis of exclusion, and show genomic complexity manifesting as extreme forms of aneuploidy and genetic rearrangement. This review covers some of the recent advances in the diagnosis and treatment of USTS based on genomic sequencing, cancer evolution and heterogeneity studies, and immunotherapy. We highlight the critical role that pathologists have to play in the diagnosis and treatment of patients with USTS, viewed through the lens of the hallmarks of cancer

Risk factors of delayed pre-hospital treatment seeking in patients with acute coronary syndrome: A prospective study

Objectives: Despite enormous efforts in public education, treatment seeking time still remains more than optimal in patients with acute coronary syndrome. This prospective study tries to determine the risk factors of pre-hospital delay in patients with acute coronary syndrome. Methods: Descriptive data of 190 patients with diagnosis of acute coronary syndrome attending in 2 tertiary level teaching hospital emergency departments were analyzed to determine risk factors of delayed pre-hospital treatment seeking. Demographic, social and clinical characteristics of patients were obtained and they were asked to fully describe their symptoms and the actions they had done after their symptoms onset. Results: Thirty nine (20.52) of patients were arrived in emergency department in 6 h. Sex, route of transport, scene-to-hospital distance, attributing the symptoms to non-cardiac causes and outpatient physician consultation and cigarette smoking were the risk factors of delayed treatment seeking in our studied patients with acute coronary syndrome. Patients with previous history of ischemic heart disease and Coronary Care Unit admission and patients with underlying diseases like diabetes mellitus, hypertension and hyperlipidemia showed a trend to have more delayed treatment seeking behavior but not with a statistically significant difference. Patients with positive family history of acute coronary syndrome arrived in emergency department earlier than other patients but again with not a statistically significant difference. Conclusion: Most patients with acute coronary syndrome arrived in emergency department in >6 h of their symptoms onset. Sex, route of transport, scene-to-hospital distance, attributing the symptoms to non-cardiac origins, outpatient physician consultation and cigarette smoking were risk factors of delayed treatment seeking in studied patients. © 2016 The Emergency Medicine Association of Turkey