Agenesis of the corpus callosum (AgCC), a failure to develop the large bundle of fibres that connect the cerebral hemispheres, occurs in 1:4000 individuals. Genetics, animal models and detailed structural neuroimaging are now providing insights into the developmental and molecular bases of AgCC. Studies using neuropsychological, electroencephalogram and functional MRI approaches are examining the resulting impairments in emotional and social functioning, and have begun to explore the functional neuroanatomy underlying impaired higher-order cognition. The study of AgCC could provide insight into the integrated cerebral functioning of healthy brains, and may offer a model for understanding certain psychiatric illnesses, such as schizophrenia and autism.

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This paper presents an elementary treatment of the theory of subresultants, and examines the relationship of the subresultants of a given pair of polynomials to their polynomial remainder sequence as determined by Euclid's algorithm. Two important versions of Euclid's algorithm are discussed. The results are essentially the same as those of Collins, but the presentation is briefer, simpler, and somewhat more general.

Twenty-four patients with chronic renal failure, stabilized on hemodialysis, were treated with recombinant human erythropoietin. Before treatment, all patients were anemic (mean Hct = 23.7%). Hematocrits reached normal levels (36.5%) after three months of treatment. Brain event-related potentials and neuropsychological tests were used to assess changes in brain and cognitive functions associated with the correction of anemia. Assessments were done prior to and after three and twelve months of rHuEPO treatment. The P3 component of the event-related potential increased in amplitude significantly with treatment, while its latency was unaffected. Of the four neuropsychological tests administered, scores on two improved significantly with treatment, and the other two approached significance. Taken together, these findings suggest that the correction of anemia to hematocrits near normal in uremic patients by rHuEPO treatment improves brain and cognitive function by raising levels of sustained attention, thus increasing speed and efficiency of scanning and perceptual-motor functions and enhancing learning and memory. These findings also suggest that anemia, either directly or indirectly, may impair brain function.

The corpus callosum is hypothesized to play a fundamental role in integrating information and mediating complex behaviors. Here, we demonstrate that lack of normal callosal development can lead to deficits in functional connectivity that are related to impairments in specific cognitive domains. We examined resting-state functional connectivity in individuals with agenesis of the corpus callosum (AgCC) and matched controls using magnetoencephalographic imaging (MEG-I) of coherence in the alpha (8–12 Hz), beta (12–30 Hz) and gamma (30–55 Hz) bands. Global connectivity (GC) was defined as synchronization between a region and the rest of the brain. In AgCC individuals, alpha band GC was significantly reduced in the dorsolateral pre-frontal (DLPFC), posterior parietal (PPC) and parieto-occipital cortices (PO). No significant differences in GC were seen in either the beta or gamma bands. We also explored the hypothesis that, in AgCC, this regional reduction in functional connectivity is explained primarily by a specific reduction in interhemispheric connectivity. However, our data suggest that reduced connectivity in these regions is driven by faulty coupling in both inter- and intrahemispheric connectivity. We also assessed whether the degree of connectivity correlated with behavioral performance, focusing on cognitive measures known to be impaired in AgCC individuals. Neuropsychological measures of verbal processing speed were significantly correlated with resting-state functional connectivity of the left medial and superior temporal lobe in AgCC participants. Connectivity of DLPFC correlated strongly with performance on the Tower of London in the AgCC cohort. These findings indicate that the abnormal callosal development produces salient but selective (alpha band only) resting-state functional connectivity disruptions that correlate with cognitive impairment. Understanding the relationship between impoverished functional connectivity and cognition is a key step in identifying the neural mechanisms of language and executive dysfunction in common neurodevelopmental and psychiatric disorders where disruptions of callosal development are consistently identified.

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Archival data from a survey of parent observations was used to determine the prevalence of social and behavioral problems in children with agenesis of the corpus callosum (ACC). Parent observations were surveyed using the Child Behavior Checklist (CBCL) for 61 children with ACC who were selected from the archive based on criteria of motor development suggesting a relatively high general level of functioning. Younger children with ACC (ages 2-5) were rated as primarily having problems with sleep. Older children with ACC (ages 6-11) manifested problems in attention, social function, thought, and somatic complaints. The older children with ACC were also compared to CBCL data from 52 children with autism who were selected from a previous study. Children with ACC were generally less impaired than children with autism on nearly all scales, with significantly less severe problems in the areas of attention, anxiety/depression, social function, and unusual thoughts. A further questionnaire related to diagnostic criteria for autism indicated that some children with ACC had traits that are among those that contribute to the diagnosis of autism within the domains of social interaction and social communication, but fewer who manifest repetitive and restricted behaviors.

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