Optimal nonlinear filtering using the finite-volume method.

Optimal sequential inference, or filtering, for the state of a deterministic dynamical system requires simulation of the Frobenius-Perron operator, that can be formulated as the solution of a continuity equation. For low-dimensional, smooth systems, the finite-volume numerical method provides a solution that conserves probability and gives estimates that converge to the optimal continuous-time values, while a Courant-Friedrichs-Lewy-type condition assures that intermediate discretized solutions remain positive density functions. This method is demonstrated in an example of nonlinear filtering for the state of a simple pendulum, with comparison to results using the unscented Kalman filter, and for a case where rank-deficient observations lead to multimodal probability distributions.

Polymorphism at codon 72 of p53 is not associated with cervical cancer risk.

P53 allelic polymorphism at codon 72 has been studied as a possible predisposing factor for cervical carcinogenesis with inconsistent results. Storey and colleagues recently published the interesting finding of a 7-fold increased risk for cervical cancer in women homozygous for the arginine allele at codon 72. This stimulated a number of independent investigations, the majority of which found no association of cervical cancer and arginine homozygosity. With the use of a modified Storey method for determining codon 72 allelotypes, DNA was examined from 431 microdissected, formalin-fixed, archival cervical conization specimens ranging from low-grade squamous lesions to invasive cancer. An alternative independent method using restriction fragment length polymorphism analysis was performed on all arginine homozygotes and all indeterminate cases for confirmation and final allelotype assignment. With the use of Storey's method alone, logistic regression suggested an association (odds ratio, 1.42) between arginine homozygosity and invasive disease. However, with the use of the combined method for accurate allelotyping, this trend disappeared (odds ratio, 1.00), the discordance was clearly resolvable as being due to methodologic variables. With the use of two separate methods for codon 72 allelotyping and accounting for a number of the issues raised in previously published reports, there is no increased risk for invasive cervical cancer associated with arginine homozygosity at codon 72 of p53.