Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

Memantine effects on behaviour in moderately severe to severe Alzheimer's disease: A post-marketing surveillance study

The aim of this study is to evaluate memantine effectiveness on behavioural and psychological symptoms of dementia (BPSD) in clinical practice and to identify variables that may predict the therapy effects. The effects of memantine on behaviour were analysed in the database of a post-marketing surveillance study promoted by the Lombardy Region Health Office and involving 43 Alzheimer's disease (AD) Units. From July to December 2005, 399 moderately severe-to-severe AD patients free of cholinergic medications were enrolled, treated with memantine and followed-up for 6 months. BPSD were assessed in a subgroup of 297 patients [mean age 77 ± 8 years; 73% females; mean neuropsychiatric inventory (NPI) score 28 ± 24] for whom the 12-item NPI subscores at baseline, and at 3 and 6 months were available. The 12 BPSD were clustered as follows: affect, physical behaviour, psychosis and hypomania. The main outcome measure was the proportion of individual cluster responders at 6 months of therapy. The proportion of individual cluster responders was 30% affect, 24% physical behaviour, 29% psychosis, 27% hypomania. Patients taking 20 mg memantine daily during the study period had a statistically significant higher probability to experience behavioural improvement than those who discontinued treatment or did not complete memantine titration (affect OR 9.0; 95% CI 3.8-21.6; physical behaviour OR 17.8; 95% CI 5.9-53.6; psychosis OR 23.6; 95% CI 5.1-110.8). The logistic regression analysis was not applicable to the hypomania subsyndrome because of the low cluster prevalence. The standard 20 mg daily memantine treatment regimen was found to be associated with a modest 6-month behavioural improvement in the affect, physical behaviour and psychosis domains in 24-30% of patients. © Springer-Verlag 2011