The filtering equations revisited

The problem of nonlinear filtering has engendered a surprising number of mathematical techniques for its treatment. A notable example is the change-of--probability-measure method originally introduced by Kallianpur and Striebel to derive the filtering equations and the Bayes-like formula that bears their names. More recent work, however, has generally preferred other methods. In this paper, we reconsider the change-of-measure approach to the derivation of the filtering equations and show that many of the technical conditions present in previous work can be relaxed. The filtering equations are established for general Markov signal processes that can be described by a martingale-problem formulation. Two specific applications are treated

Primed T Cell Responses to Chemokines Are Regulated by the Immunoglobulin-Like Molecule CD31

CD31, an immunoglobulin-like molecule expressed by leukocytes and endothelial cells, is thought to contribute to the physiological regulation T cell homeostasis due to the presence of two immunotyrosine-based inhibitory motifs in its cytoplasmic tail. Indeed, loss of CD31 expression leads to uncontrolled T cell-mediated inflammation in a variety of experimental models of disease and certain CD31 polymorphisms correlate with increased disease severity in human graft-versus-host disease and atherosclerosis. The molecular mechanisms underlying CD31-mediated regulation of T cell responses have not yet been clarified. We here show that CD31-mediated signals attenuate T cell chemokinesis both in vitro and in vivo. This effect selectively affects activated/memory T lymphocytes, in which CD31 is clustered on the cell membrane where it segregates to the leading edge. We provide evidence that this molecular segregation, which does not occur in naïve T lymphocytes, might lead to cis-CD31 engagement on the same membrane and subsequent interference with the chemokine-induced PI3K/Akt signalling pathway. We propose that CD31-mediated modulation of memory T cell chemokinesis is a key mechanism by which this molecule contributes to the homeostatic regulation of effector T cell immunity

Insights into pathogenic events of HIV-associated Kaposi sarcoma and immune reconstitution syndrome related Kaposi sarcoma

A decrease in the incidence of human immune deficiency virus-associated Kaposi sarcoma (HIV-KS) and regression of some established HIV-KS lesions is evident after the introduction of highly active anti-retroviral treatment (HAART), and is attributed to generalized immune restoration, to the reconstitution of human herpesvirus (HHV)-8 specific cellular immune responses, and to the decrease in HIV Tat protein and HHV-8 loads following HAART. However, a small subset of HIV-seropositive subjects with a low CD4+ T cell count at the time of introduction of HAART, may develop HIV-KS as immune reconstitution inflammatory syndrome (IRIS) within 8 weeks thereafter