Convergence of the maximum a posteriori path estimator in hiddenMarkov models

In a hidden Markov model (HMM) the underlying finite-state Markov chain cannot be observed directly but only by an additional process. We are interested in estimating the unknown path of the Markov chain. The most widely used estimator is the maximum a posteriori path estimator (MAP path estimator). It can be calculated effectively by the Viterbi (1967) algorithm as is, e.g., frequently done in the field of coding theory, correction of intersymbol interference, and speech recognition. We investigate (component-wise) convergence of the MAP path estimator. Convergence is shown under the condition of unbounded likelihood ratios. This condition is satisfied in the important case of HMMs with additive white Gaussian noise. We also prove convergence, if the Markov chain has two states. The so-called Viterbi paths are an important tool for obtaining these results     

Sonographically detected fetal and placental abnormalities associated with trisomy 16 confined to the placenta. A case report and review of the literature

Previous studies have demonstrated that cortical spreading depression (CSD) induces neuronal tolerance to a subsequent episode of ischemia. The objective of the present investigation was to determine whether CSD alters levels of mRNA coding for putative neuroprotective proteins. Unilateral CSD was evoked in male Wistar rats by applying 2 mol/L KCl over the frontal cortex for 2 hours. After recovery for 0, 2, or 24 hours, levels of several mRNA coding for neuroprotective proteins were measured bilaterally in parietal cortex using Northern blot analysis. Levels of c-fos mRNA and brain-derived neurotrophic factor (BDNF) mRNA were markedly elevated at 0 and 2 hours, but not 24 hours after CSD. Tissue plasminogen activator (tPA) mRNA levels were also significantly increased at 0 and 2 hours, but not 24 hours after CSD. Levels of the 72-kDa heat-shock protein (hsp72) mRNA were not significantly increased by CSD, except for a small elevation (20%) at 2 hours recovery. Levels of the 73-kDa heat-shock cognate (hsc73) mRNA were slightly, but significantly, increased at 2 and 24 hours of recovery. Finally, levels of mRNA for protease nexin-1 and glutamine synthetase were not significantly altered by CSD at any time studied. The current results support the hypothesis that neuronal tolerance to ischemia after CSD may be mediated by increased expression of FOS, BDNF, or tPA, but not by increased expression of hsp72, hsc73, nexin-1, or glutamine synthetase.