The optimal measure of allelic association

Allelic association between pairs of loci is derived in terms of the association probability ρ as a function of recombination θ, effective population size N, linear systematic pressure v, and time t, predicting both ρrt, the decrease of association from founders and ρct, the increase by genetic drift, with ρt = ρrt + ρct. These results conform to the Malecot equation, with time replaced by distance on the genetic map, or on the physical map if recombination in the region is uniform. Earlier evidence suggested that ρ is less sensitive to variations in marker allele frequencies than alternative metrics for which there is no probability theory. This robustness is confirmed for six alternatives in eight samples. In none of these 48 tests was the residual variance as small as for ρ. Overall, efficiency was less than 80% for all alternatives, and less than 30% for two of them. Efficiency of alternatives did not increase when information was estimated simultaneously. The swept radius within which substantial values of ρ are conserved lies between 385 and 893 kb, but deviation of parameters between measures is enormously significant. The large effort now being devoted to allelic association has little value unless the ρ metric with the strongest theoretical basis and least sensitivity to marker allele frequencies is used for mapping of marker association and localization of disease loci.

A complexity measure for selective matching of signals by the brain.

We have previously derived a theoretical measure of neural complexity (CN) in an attempt to characterize functional connectivity in the brain. CN measures the amount and heterogeneity of statistical correlations within a neural system in terms of the mutual information between subsets of its units. CN was initially used to characterize the functional connectivity of a neural system isolated from the environment. In the present paper, we introduce a related statistical measure, matching complexity (CM), which reflects the change in CN that occurs after a neural system receives signals from the environment. CM measures how well the ensemble of intrinsic correlations within a neural system fits the statistical structure of the sensory input. We show that CM is low when the intrinsic connectivity of a simulated cortical area is randomly organized. Conversely, CM is high when the intrinsic connectivity is modified so as to differentially amplify those intrinsic correlations that happen to be enhanced by sensory input. When the input is represented by an individual stimulus, a positive value of CM indicates that the limited mutual information between sensory sheets sampling the stimulus and the rest of the brain triggers a large increase in the mutual information between many functionally specialized subsets within the brain. In this way, a complex brain can deal with context and go "beyond the information given."

The deferred imitation task as a nonverbal measure of declarative memory.

We tested amnesic patients, patients with frontal lobe lesions, and control subjects with the deferred imitation task, a nonverbal test used to demonstrate memory abilities in human infants. On day 1, subjects were given sets of objects to obtain a baseline measure of their spontaneous performance of target actions. Then different event sequences were modeled with the object sets. On day 2, the objects were given to the subjects again, first without any instructions to imitate the sequences, and then with explicit instructions to imitate the actions exactly as they had been modeled. Control subjects and frontal lobe patients reproduced the events under both uninstructed and instructed conditions. In contrast, performance by the amnesic patients did not significantly differ from that of a second control group who had the same opportunities to handle the objects but were not shown the modeled actions. These findings suggest that deferred imitation is dependent on the brain structures essential for declarative memory that are damaged in amnesia, and they support the view that infants who imitate actions after long delays have an early capacity for long-term declarative memory.