When Learners Surpass Their Models: Mathematical Modeling of Learning from an Inconsistent Source

It has been reported in the literature that both adults and children can, to a different degree, modify and regularize the often-inconsistent linguistic input they receive. We present a new algorithm to model and investigate the learning process of a learner mastering a set of (grammatical or lexical) forms from an inconsistent source. The algorithm is related to reinforcement learning and drift-diffusion models of decision making, and possesses several psychologically relevant properties such as fidelity, robustness, discounting, and computational simplicity. It demonstrates how a learner can successfully learn from or even surpass its imperfect source. We use the data collected by Singleton and Newport (Cognit Psychol 49(4):370-407, 2004) on the performance of a 7-year-boy Simon, who mastered the American Sign Language (ASL) by learning it from his parents, both of whom were imperfect speakers of ASL. We show that the algorithm possesses a frequency boosting property, whereby the frequency of the most common form of the source is increased by the learner. We also explain several key features of Simon's ASL. © 2014 Society for Mathematical Biology

Association of Immunosuppression and Human Immunodeficiency Virus (HIV) Viremia with Anal Cancer Risk in Persons Living with HIV in the United States and Canada

Background: People living with human immunodeficiency virus (HIV; PLWH) have a markedly elevated anal cancer risk, largely due to loss of immunoregulatory control of oncogenic human papillomavirus infection. To better understand anal cancer development and prevention, we determined whether recent, past, cumulative, or nadir/peak CD4+ T-cell count (CD4) and/or HIV-1 RNA level (HIV RNA) best predict anal cancer risk. Methods: We studied 102 777 PLWH during 1996-2014 from 21 cohorts participating in the North American AIDS Cohort Collaboration on Research and Design. Using demographics-adjusted, cohort-stratified Cox models, we assessed associations between anal cancer risk and various time-updated CD4 and HIV RNA measures, including cumulative and nadir/peak measures during prespecified moving time windows. We compared models using the Akaike information criterion. Results: Cumulative and nadir/peak CD4 or HIV RNA measures from approximately 8.5 to 4.5 years in the past were generally better predictors for anal cancer risk than their corresponding more recent measures. However, the best model included CD4 nadir (ie, the lowest CD4) from approximately 8.5 years to 6 months in the past (hazard ratio [HR] for <50 vs ≥500 cells/μL, 13.4; 95% confidence interval [CI], 3.5-51.0) and proportion of time CD4 <200 cells/μL from approximately 8.5 to 4.5 years in the past (a cumulative measure; HR for 100% vs 0%, 3.1; 95% CI, 1.5-6.6). Conclusions: Our results are consistent with anal cancer promotion by severe, prolonged HIV-induced immunosuppression. Nadir and cumulative CD4 may represent useful markers for identifying PLWH at higher anal cancer risk