A backward particle interpretation of Feynman-Kac formulae

We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals "on-the-fly" as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We provide uniform convergence results with respect to the time horizon parameter as well as functional central limit theorems and exponential concentration estimates. Our results have important consequences for online parameter estimation for non-linear non-Gaussian state-space models. We show how the forward filtering backward smoothing estimates of additive functionals can be computed using a forward only recursion.

The MHP36 line of murine neural stem cells expresses functional CXCR1 chemokine receptors that initiate chemotaxis in vitro.

Chemokines help to establish cerebral inflammation after ischemia, which comprises a major component of secondary brain injury. The CXCR4 chemokine receptor system induces neural stem cell migration, and hence has been implicated in brain repair. We show that CXCR1 and interleukin-8 also stimulate chemotaxis in murine neural stem cells from the MHP36 cell line. The presence of CXCR1 was confirmed by reverse transcriptase PCR and immunohistochemistry. Interleukin-8 evoked intracellular calcium currents, upregulated doublecortin (a protein expressed by migrating neuroblasts), and elicited positive chemotaxis in vitro. Therefore, effectors of the early innate immune response may also influence brain repair mechanisms.