Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Tumour infiltrating lymphocytes and apoptosis are independent features in colorectal cancer stratified according to microsatellite instability status

Background-The presence of high level DNA microsatellite instability (MSI-H) in colorectal cancer is associated with an improved prognosis, as is the presence of tumour infiltrating lymphocytes (TILs). It is not clear if TILs contribute directly to the survival advantage associated with MSI-H cancers through activation of an antitumour immune response. Aims-To correlate TIL and apoptosis rates in colorectal cancer stratified by MSI status. Methods-The distribution of TILs was characterised and quantified in a selected series of 102 sporadic colorectal cancers classified according to levels of MSI as 32 MSI-H, 30 MSI-low (MSI-L), and 40 microsatellite stable (MSS). Archival blocks were immunostained using the T cell markers CD3 and CD8, and the B cell marker CD20. Apoptosis of malignant epithelial cells was quantified by immunohistochemistry with the M30 CytoDEATH antibody. Results-Positive staining with anti-CD3 and negative staining with anti-CD20 identified virtually all TILs as T cells. The majority of CD3(+) TILs (>75%) also stained with anti-CDS. TILs were most abundant in MSI-H colorectal cancers in which 23/32 (72%) scored as TIL positive. Only 5/40 (12.5%) MSS tumours and 9/30 (30%) MSI-L cancers were TIL positive (p

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

Comparison of differentiated dendritic cell infiltration of autoimmune and osteoarthritis synovial tissue

Objective. Infiltration of rheumatoid arthritis (RA) synovial tissue (ST) by differentiated dendritic cells (DC) is a consistent feature in patients with active disease. However, mononuclear cells (MNC), including DC, may be nonspecifically chemoattracted to inflammatory sites regardless of etiology, Therefore, to evaluate the specificity of ST infiltration by differentiated DC, synovial biopsies from patients with RA, spondylarthropathy (SpA), osteoarthritis (OA), and gout were examined. Methods. Formalin-fixed ST sections were analyzed by double immunohistochemical staining for vascularity and infiltration by differentiated DC, lymphocytes, and macrophages. Results, DC containing nuclear RelB were found in perivascular MNC aggregates from patients with all arthritides studied. Infiltration by differentiated DC was similar in RA and SpA ST, but reduced in OA ST. Differentiated DC were always observed in close association with lymphocytes, and the correlation between these variables suggested that the infiltration of inflammatory sites by DC and lymphocytes was associated. Conclusion, Perivascular infiltration by DC, lymphocytes, and macrophages is nonspecifically related to inflammation, but signals present in RA and SpA ST lead to more intense cellular infiltration and accumulation.

Relationship of glycosaminoglycan and matrix changes to vascular smooth cell phenotype modulation in rabbit arteries after acute injury

Purpose: The phenotype of vascular smooth muscle cells (SMCs) is altered in several arterial pathologies, including the neointima formed after acute arterial injury. This study examined the time course of this phenotypic change in relation to changes in the amount and distribution of matrix glycosaminoglycans. Methods: The immunochemical staining of heparan sulphates (HS) and chondroitin sulphates (CS) in the extracellular matrix of the arterial wall was examined at early points after balloon catheter injury of the rabbit carotid artery. SMC phenotype was assessed by means of ultrastructural morphometry of the cytoplasmic volume fraction of myofilaments. The proportions of cell and matrix components in the media were analyzed with similar morphometric techniques. Results: HS and CS were shown in close association with SMCs of the uninjured arterial media as well as being more widespread within the matrix. Within 6 hours after arterial injury, there was loss of the regular pericellular distribution of both HS and CS, which was associated with a significant expansion in the extracellular space. This preceded the change in ultrastructural phenotype of the SMCs. The glycosaminoglycan loss was most exaggerated at 4 days, after which time the HS and CS reappeared around the medial SMCs. SMCs of the recovering media were able to rapidly replace their glycosaminoglycans, whereas SMCs of the developing neointima failed to produce HS as readily as they produced CS. Conclusions: These studies indicate that changes in glycosaminoglycans of the extracellular matrix precede changes in SMC phenotype after acute arterial injury. In the recovering arterial media, SMCs replace their matrix glycosaminoglycans rapidly, whereas the newly established neointima fails to produce similar amounts of heparan sulphates.