Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

Non-self-adjoint graphs

On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a Riesz basis of projectors and similarity transforms to self-adjoint Laplacians. Among other things, we describe a simple way to relate the similarity transforms between Laplacians on certain graphs with elementary similarity transforms between matrices defining the boundary conditions.

Transformation of leukocytes by Theileria parva and T. annulata.

Theileria parva and T. annulata provide intriguing models for the study of parasite-host interactions. Both parasites possess the unique property of being able to transform the cells they infect; T. parva transforms T and B cells, whereas T. annulata affects B cells and monocytes/macrophages. Parasitized cells do not require antigenic stimulation or exogenous growth factors and acquire the ability to proliferate continuously. In vivo, parasitized cells undergo clonal expansion and infiltrate both lymphoid and non-lymphoid tissues of the infected host. Theileria-induced transformation is entirely reversible and is accompanied by the expression of a wide range of different lymphokines and cytokines, some of which may contribute to proliferation or may enhance spread and survival of the parasitized cell in the host. The presence of the parasite in the host-cell cytoplasm modulates the state of activation of a number of signal transduction pathways. This, in turn, leads to the activation of transcription factors, including nuclear factor-kappa B, which appear to be essential for the survival of Theileria-transformed T cells.

Interference by the intracellular parasite Theileria parva with T-cell signal transduction pathways induces transformation and protection against apoptosis

The intracellular parasite Theileria parva transforms bovine T-lymphocytes, inducing uncontrolled proliferation. Upon infection, cells cease to require antigenic stimulation and exogenous growth factors to proliferate. Earlier studies have shown that pathways triggered via stimulation of the T-cell receptor are silent in transformed cells. This is reflected by a lack of phosphorylation of key signalling molecules and the fact that proliferation is not inhibited by immunosuppressants such as cyclosporin and ascomycin that target calcineurin. This suggests that the parasite bypasses the normal T-cells activation pathways to induce proliferation. Among the MAP-kinase pathways, ERK and p38 are silent, and only Jun N-terminal kinase is activated. This appears to suffice to induce constitutive activation of the transcription factor AP-1. More recently, it could be shown that the presence of the parasite in the host cell cytoplasm also induces constitutive activation of NF-kappaB, a transcription factor involved in proliferation and protection against apoptosis. Activation is effectuated by parasite-induced degradation of IkappaBs, the cytoplasmic inhibitors which sequester NF-kappaB in the cytoplasm. NF-kappaB activation is resistant to the antioxidant N-acetyl cysteine and a range of other reagents, suggesting that activation might occur in an unorthodox manner. Studies using inhibitors and dominant negative mutants demonstrate that the parasite activates a NF-kappaB-dependent anti-apoptotic mechanism that protects the transformed cell form spontaneous apoptosis and is essential for maintaining the transformed state of the parasitised cell.

Theileria parva: taking control of host cell proliferation and survival mechanisms.

The intracellular parasite Theileria parva infects and transforms bovine T-cells, inducing their uncontrolled proliferation and spread in non-lymphoid as well as lymphoid tissues. This parasite-induced transformation is the predominant factor contributing to the pathogenesis of a lymphoproliferative disease, called East Coast fever. T. parva-transformed cells become independent of antigenic stimulation or exogenous growth factors. A dissection of the signalling pathways that are activated in T. parva-infected cells shows that the parasite bypasses signalling pathways that normally emanate from the T-cell antigen receptor to induce continuous proliferation. This review concentrates on the influence of the parasite on the state of activation of the mitogen-activated protein kinase (MAPK), NF-kappaB and phosphoinositide-3-kinase (PI3-K) pathways in the host cell. Of the MAPKs, JNK, but not ERK or p38, is active, inducing constitutive activation of the transcription factors AP-1 and ATF-2. A crucial step in the transformation process is the persistent activation of the transcription factor NF-kappaB, which protects T. parva-transformed cells from spontaneous apoptosis accompanying the transformation process. Inhibitor studies also suggest an important role for the lipid kinase, PI-3K, in the continuous proliferation of T. parva-transformed lymphocytes.