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The computational power of massively parallel networks of simple processing elements resides in the communication bandwidth provided by the hardware connections between elements. These connections can allow a significant fraction of the knowledge of the system to be applied to an instance of a problem in a very short time. One kind of computation for which massively parallel networks appear to be well suited is large constraint satisfaction searches, but to use the connections efficiently two conditions must be met: First, a search technique that is suitable for parallel networks must be found. Second, there must be some way of choosing internal representations which allow the preexisting hardware connections to be used efficiently for encoding the constraints in the domain being searched. We describe a general parallel search method, based on statistical mechanics, and we show how it leads to a general learning rule for modifying the connection strengths so as to incorporate knowledge about a task domain in an efficient way. We describe some simple examples in which the learning algorithm creates internal representations that are demonstrably the most efficient way of using the preexisting connectivity structure.

Vaccine 15, 1114 -1122] concluded that repeat vaccination provided continual protection. We propose an explanation, the antigenic distance hypothesis, and test it by analyzing seven influenza outbreaks that occurred during the Hoskins and Keitel studies. The hypothesis is that variation in repeat vaccine efficacy is due to differences in antigenic distances among vaccine strains and between the vaccine strains and the epidemic strain in each outbreak. To test the hypothesis, antigenic distances were calculated from historical hemagglutination inhibition assay tables, and a computer model of the immune response was used to predict the vaccine efficacy of individuals given different vaccinations. The model accurately predicted the observed vaccine efficacies in repeat vaccinees relative to the efficacy in first-time vaccinees (correlation 0.87). Thus, the antigenic distance hypothesis offers a parsimonious explanation of the differences between and within the Hoskins and Keitel studies. These results have implications for the selection of influenza vaccine strains, and also for vaccination strategies for other antigenically variable pathogens that might require repeated vaccination.original antigenic sin ͉ vaccine efficacy ͉ repeated vaccination ͉ antigenic distance A ntigenic drift of the influenza virus exposes the human population to new but related influenza variants on an annual basis. Thus, components of the influenza vaccine are updated, sometimes yearly, to maintain a reasonable correspondence between the vaccine and epidemic strains. Public health recommendations are for annual vaccination of at-risk individuals (1).Influenza vaccination works effectively in first-time vaccinees (2). However, efficacy in repeat vaccinees has been difficult to determine definitively. A meta-analysis of 19 repeat vaccination studies showed that on average repeat vaccinees were protected at least as well as first-time vaccinees (3). However, in the 12 studies in which protection was measured serologically, there was statistically significant unexplained heterogeneity: In some years repeat vaccinees were better protected than first-time vaccinees; in other years they had worse protection (3). Similarly, two widely cited vaccine efficacy field studies have reached different conclusions: The ''Hoskins study'' (4) concluded that repeat vaccination was not effective, whereas the ''Keitel study'' (5) concluded that repeat vaccination was effective. There was also heterogeneity within the Hoskins (6) and Keitel studies (Fig. 1). Meta-analysis found no factor that explained the heterogeneity among 12 serological studies; among the factors tested were differences in influenza subtype, age, study design, hemagglutination inhibition (HI) assay method, and vaccine type (3).We propose and test a hypothesis to explain the heterogeneity of repeated influenza vaccination. The hypothesis extends the idea that the closeness of the antigenic match between the vaccine strain and the epidemic virus is important for vaccine efficacy in first-time...