The caloron correspondence and higher string classes for loop groups

We review the caloron correspondence between $G$-bundles on $M \times S^1$ and $\Omega G$-bundles on $M$, where $\Omega G$ is the space of smooth loops in the compact Lie group $G$. We use the caloron correspondence to define characteristic classes for $\Omega G$-bundles, called string classes, by transgression of characteristic classes of $G$-bundles. These generalise the string class of Killingback to higher dimensional cohomology.Comment: 21 pages. Author addresses adde

Curvature in Noncommutative Geometry

Our understanding of the notion of curvature in a noncommutative setting has progressed substantially in the past ten years. This new episode in noncommutative geometry started when a Gauss-Bonnet theorem was proved by Connes and Tretkoff for a curved noncommutative two torus. Ideas from spectral geometry and heat kernel asymptotic expansions suggest a general way of defining local curvature invariants for noncommutative Riemannian type spaces where the metric structure is encoded by a Dirac type operator. To carry explicit computations however one needs quite intriguing new ideas. We give an account of the most recent developments on the notion of curvature in noncommutative geometry in this paper.Comment: 76 pages, 8 figures, final version, one section on open problems added, and references expanded. Appears in "Advances in Noncommutative Geometry - on the occasion of Alain Connes' 70th birthday

Wodzicki Residue for Operators on Manifolds with Cylindrical Ends

We define the Wodzicki Residue TR(A) for A in a space of operators with double order (m_1,m_2). Such operators are globally defined initially on R^n and then, more generally, on a class of non-compact manifolds, namely, the manifolds with cylindrical ends. The definition is based on the analysis of the associate zeta function. Using this approach, under suitable ellipticity assumptions, we also compute a two terms leading part of the Weyl formula for a positive selfadjoint operator belonging the mentioned class in the case m_1=m_2.Comment: 24 pages, picture changed, added references, corrected typo

Authors' reply to Rozin and Quinn et al

Rheumatoid arthritis (RA) is the most common chronic inflammatory disease affecting about 1% of the white population, particularly female patients, and has considerable physical, psychological, and social repercussions.1 In a paper published previously in the Annals, Dadoniene et al described and compared two cohorts of patients with RA from Vilnius (Lithuania) and Oslo (Norway).2 There were no significant differences in sex, age, extra-articular manifestations, education, or family history of RA between the groups. None the less, there were important differences in disease activity, disability, pain, emotional, mental and general health, with patients in the Vilnius group having the worst scores. The number of patients who had never used a disease modifying antirheumatic drug (DMARD) was similar in both groups. Vilnius patients had more commonly used azathioprine, sulfasalazine, and antimalarial drugs, whereas Oslo patients had used methotrexate, gold salts, cyclosporin, and D-penicillamine. Surgery was more common in the Oslo patients. That study was developed to compare the evolution and outcomes of two different populations with RA and was the first to include health related quality of life. The authors attributed the differences between these groups to differences in economic status, medical care, drugs used and, to a lesser extent, genetic differences

Bone metastasis : mechanisms, therapies and biomarkers

Skeletal metastases are frequent complications of many cancers, causing bone complications (fractures, bone pain, disability), which negatively affect the patient's quality of life. Here, we first discuss the burden of skeletal complications in cancer bone metastasis. We then describe the pathophysiology of bone metastasis. Bone metastasis is a multistage process; long before the development of clinically detectable metastases, circulating tumor cells settle and enter a dormant state in normal vascular and endosteal niches present in the bone marrow, which provide immediate attachment and shelter, and only become active years later as they proliferate and alter the functions of bone-resorbing (osteoclasts) and bone-forming (osteoblasts) cells, promoting skeletal destruction. The molecular mechanisms involved in mediating each of these steps are described and we also explain how tumor cells interact with a myriad of interconnected cell populations in the bone marrow, including a rich vascular network, immune cells, adipocytes and nerves. We discuss metabolic programs that tumor cells could engage with to specifically grow in bone. We also describe the progress and future directions of existing bone-targeted agents and report emerging therapies that have arisen from recent advances in our understanding of the pathophysiology of bone metastases. Finally, we discuss the value of bone turnover biomarkers in detection and monitoring of progression and therapeutic effects in patients with bone metastasis