Simple modifications for stabilization of the finite point method

A stabilized version of the finite point method (FPM) is presented. A source of instability due to the evaluation of the base function using a least square procedure is discussed. A suitable mapping is proposed and employed to eliminate the ill‐conditioning effect due to directional arrangement of the points. A step by step algorithm is given for finding the local rotated axes and the dimensions of the cloud using local average spacing and inertia moments of the points distribution. It is shown that the conventional version of FPM may lead to wrong results when the proposed mapping algorithm is not used. It is shown that another source for instability and non‐monotonic convergence rate in collocation methods lies in the treatment of Neumann boundary conditions. Unlike the conventional FPM, in this work the Neumann boundary conditions and the equilibrium equations appear simultaneously in a weight equation similar to that of weighted residual methods. The stabilization procedure may be considered as an interpretation of the finite calculus (FIC) method. The main difference between the two stabilization procedures lies in choosing the characteristic length in FIC and the weight of the boundary residual in the proposed method. The new approach also provides a unique definition for the sign of the stabilization terms. The reasons for using stabilization terms only at the boundaries is discussed and the two methods are compared. Several numerical examples are presented to demonstrate the performance and convergence of the proposed methods. Copyright © 2005 John Wiley & Sons, Ltd

Role of the IL-23 pathway in the pathogenesis and treatment of enthesitis in psoriatic arthritis

Introduction: Enthesitis is a key feature of spondyloarthritis (SpA). Several studies have underlined the role of interleukin (IL)-23 in SpA development as a crucial cytokine in the pathogenesis of enthesitis. Area covered: This review summarizes recent evidence of the role of IL-23 in the pathogenesis of and as a target of the treatment of enthesitis. We review the definition, diagnosis and clinical impact of enthesitis and its connection with microbial infections, gut dysbiosis, and mechanical stress. We also review clinical trials and real-life studies of drugs targeting the p19 or p40 subunits of IL-23. Expert opinion: Novel therapies targeting the p19 or p40 subunit of IL-23 appear to be promising treatment options for patients with enthesitis. Although we are currently unable to identify the best therapeutic window to target IL-23 in SpA disease evolution, the promising ability of this therapy to control the gut-entheseal axis is increasing our knowledge of SpA pathogenesis