The spectral gap for some spin chains with discrete symmetry breaking

We prove that for any finite set of generalized valence bond solid (GVBS) states of a quantum spin chain there exists a translation invariant finite-range Hamiltonian for which this set is the set of ground states. This result implies that there are GVBS models with arbitrary broken discrete symmetries that are described as combinations of lattice translations, lattice reflections, and local unitary or anti-unitary transformations. We also show that all GVBS models that satisfy some natural conditions have a spectral gap. The existence of a spectral gap is obtained by applying a simple and quite general strategy for proving lower bounds on the spectral gap of the generator of a classical or quantum spin dynamics. This general scheme is interesting in its own right and therefore, although the basic idea is not new, we present it in a system-independent setting. The results are illustrated with an number of examples.Comment: 48 pages, Plain TeX, BN26/Oct/9

Longevity Risk

longevity risk, risk quantification, risk management,

The role of small airways in lung disease

AbstractThe small airways constitute one of the least understood areas of the lungs. They play a role in many lung diseases, and small airway pathology results in significant morbidity. New approaches to their evaluation may provide insights into this major area of lung disease. Asthma is well recognized as a disease of both large and small airways. Physiological and pathological evidence, from techniques such as post-mortem tissue histological analysis, induced sputum and transbronchial biopsies, has reinforced the concept of the involvement of the entire bronchial tree in the inflammatory process in asthma. In addition to describing the airway pathology in asthma, this review focuses on the pathogenesis and role of small airway obstruction in other diseases, including chronic obstructive pulmonary disease (COPD), idiopathic pulmonary fibrosis (IPF), sarcoidosis and obliterative bronchiolitis (OB). COPD is characterized by the presence of airflow obstruction resulting from lesions in the small airways. In addition, features compatible with small airways disease are common in IPF, sarcoidosis and OB. Recent advances in pulmonary imaging, such as high-resolution computed tomography (HRCT) and magnetic resonance imaging (MRI) with hyperpolarized3 He, have allowed non-invasive reproducible measurements of structure–function relationships to be made for the small airways. These techniques have great potential for diagnosing changes in small airway function and for assessing responses to treatment. New insights into the contribution of small airways to a range of lung diseases may lead to the development of therapies targeted at this part of the bronchial anatomy

Origin and spread of human mitochondrial DNA haplogroup U7

Human mitochondrial DNA haplogroup U is among the initial maternal founders in Southwest Asia and Europe and one that best indicates matrilineal genetic continuity between late Pleistocene hunter-gatherer groups and present-day populations of Europe. While most haplogroup U subclades are older than 30 thousand years, the comparatively recent coalescence time of the extant variation of haplogroup U7 (∼16-19 thousand years ago) suggests that its current distribution is the consequence of more recent dispersal events, despite its wide geographical range across Europe, the Near East and South Asia. Here we report 267 new U7 mitogenomes that - analysed alongside 100 published ones - enable us to discern at least two distinct temporal phases of dispersal, both of which most likely emanated from the Near East. The earlier one began prior to the Holocene (∼11.5 thousand years ago) towards South Asia, while the later dispersal took place more recently towards Mediterranean Europe during the Neolithic (∼8 thousand years ago). These findings imply that the carriers of haplogroup U7 spread to South Asia and Europe before the suggested Bronze Age expansion of Indo-European languages from the Pontic-Caspian Steppe region. © The Author(s) 2017