Sunitinib and other targeted therapies for renal cell carcinoma

Targeted therapy has radically altered the way metastatic renal cancer is treated. Six drugs are now licensed in this setting, with several other agents under evaluation. Sunitinib is currently the most widely used in the first line setting with impressive efficacy and an established toxicity profile. However, as further randomised studies report and as newer drugs become available this may change. In this review, we address our current understanding of targeted therapy in renal cancer. We also discuss areas in which our knowledge is incomplete, including the identification of correlative biomarkers and mechanisms of drug resistance. Finally, we will describe the major areas of clinical research that will report over the next few years

ANCA-associated vasculitis.

The anti-neutrophil cytoplasmic antibody (ANCA)-associated vasculitides (AAVs) are a group of disorders involving severe, systemic, small-vessel vasculitis and are characterized by the development of autoantibodies to the neutrophil proteins leukocyte proteinase 3 (PR3-ANCA) or myeloperoxidase (MPO-ANCA). The three AAV subgroups, namely granulomatosis with polyangiitis (GPA), microscopic polyangiitis and eosinophilic GPA (EGPA), are defined according to clinical features. However, genetic and other clinical findings suggest that these clinical syndromes may be better classified as PR3-positive AAV (PR3-AAV), MPO-positive AAV (MPO-AAV) and, for EGPA, by the presence or absence of ANCA (ANCA+ or ANCA-, respectively). Although any tissue can be involved in AAV, the upper and lower respiratory tract and kidneys are most commonly and severely affected. AAVs have a complex and unique pathogenesis, with evidence for a loss of tolerance to neutrophil proteins, which leads to ANCA-mediated neutrophil activation, recruitment and injury, with effector T cells also involved. Without therapy, prognosis is poor but treatments, typically immunosuppressants, have improved survival, albeit with considerable morbidity from glucocorticoids and other immunosuppressive medications. Current challenges include improving the measures of disease activity and risk of relapse, uncertainty about optimal therapy duration and a need for targeted therapies with fewer adverse effects. Meeting these challenges requires a more detailed knowledge of the fundamental biology of AAV as well as cooperative international research and clinical trials with meaningful input from patients

On geodesics of the rotation group SO(3)

Geodesics on SO(3) are characterized by constant angular velocity motions and as great circles on a three-sphere. The former interpretation is widely used in optometry and the latter features in the interpolation of rotations in computer graphics. The simplicity of these two disparate interpretations belies the complexity of the corresponding rotations. Using a quaternion representation for a rotation, we present a simple proof of the equivalence of the aforementioned characterizations and a straightforward method to establish features of the corresponding rotations

On the Gibbs–Appell equations for the dynamics of rigid bodies

Since their introduction in the early 20th century, the Gibbs– Appell equations have proven to be a remarkably popular and influential method to formulate the equations of motion of constrained rigid bodies. In particular, when the coordinates and quasi-velocities are chosen appropriately, the resulting equations of motion are reactionless even if the constraints on the system are nonholonomic. Researchers provide a demonstration with the help of a recent treatment. The researchers demonstrate that the developments are also applicable to Kane’s equations of motion. They show that it is straightforward to extend the derivation of the Gibbs–Appell equations from the Newton–Euler balance laws

Gliding motions of a rigid body: The curious dynamics of Littlewood’s rolling hoop

The celebrated mathematician John E. Littlewood noted that a hoop with an attached mass rolling on a ground plane may exhibit self-induced jumping. Subsequent works showed that his analysis was flawed and revealed paradoxical behaviour that can be resolved by incorporating the inertia of the hoop. A comprehensive analysis of this problem is presented in this paper. The analysis illuminates the regularity induced in the model of the hoop when its mass moment of inertia is incorporated, shows that the paradoxical motions of the hoop are consistent with the principles of mechanics and demonstrates the simplest example in the dynamics of rigid bodies that exhibits self-induced jumping

Gliding motions of a rigid body: The curious dynamics of Littlewood’s rolling hoop

The celebrated mathematician John E. Littlewood noted that a hoop with an attached mass rolling on a ground plane may exhibit self-induced jumping. Subsequent works showed that his analysis was flawed and revealed paradoxical behaviour that can be resolved by incorporating the inertia of the hoop. A comprehensive analysis of this problem is presented in this paper. The analysis illuminates the regularity induced in the model of the hoop when its mass moment of inertia is incorporated, shows that the paradoxical motions of the hoop are consistent with the principles of mechanics and demonstrates the simplest example in the dynamics of rigid bodies that exhibits self-induced jumping