Rate of convergence of truncated stochastic approximation procedures with moving bounds

The paper is concerned with stochastic approximation procedures having three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. We study convergence and rate of convergence. Main results are supplemented with corollaries to establish various sets of sufficient conditions, with the main emphases on the parametric statistical estimation. The theory is illustrated by examples and special cases.Comment: 30 page

Interaction of inflammatory cytokines and erythropoeitin in iron metabolism and erythropoiesis in anaemia of chronic disease

In chronic inflammatory conditions increased endogenous release of specific cytokines (TNFα, IL-1, IL-6, IFNγ and others) is presumed. It has been shown that those of monocyte lineage play a key role in cytokine expression and synthesis. This may be associated with changes in iron metabolism and impaired erythropoiesis and may lead to development of anaemia in patients with rheumatoid arthritis. Firstly, increased synthesis of acute phase proteins, like ferritin, during chronic inflammation is proposed as the way by which the toxic effect of iron and thereby the synthesis of free oxy-radicals causing the damage on the affected joints, may be reduced. This is associated with a shift of iron towards the mononuclear phagocyte system which may participate in the development of anaemia of chronic disease. Secondly, an inhibitory action of inflammatory cytokines (TNFα, IL-1), on proliferation and differentiation of erythroid progenitors as well as on synthesis of erythropoietin has been shown, thereby also contributing to anaemia. Finally, chronic inflammation causes multiple, complex disturbances in the delicate physiologic equilibrium of interaction between cytokines and cells (erythroid progenitors, cells of mononuclear phagocyte system and erythropoietin producing cells) leading to development of anaemia of chronic disease (Fig. 1)

On differential games with long-time-average cost

The paper deals with the ergodicity of deterministic zero-sum differential games with long-time-average cost. Some new sufficient conditions are given, as well as a class of games that are not ergodic. In particular, we settle the issue of ergodicity for the simple games whose associated Isaacs equation is a convex-concave eikonal equation