Patients with Alzheimer's disease have reduced activities in midlife compared with healthy control-group members

The development of Alzheimer's disease (AD) later in life may be reflective of environmental factors operating over the course of a lifetime. Educational and occupational attainments have been found to be protective against the development of the disease but participation in activities has received little attention. In a case-control study, we collected questionnaire data about 26 nonoccupational activities from ages 20 to 60. Participants included 193 people with probable or possible AD and 358 healthy control-group members. Activity patterns for intellectual, passive, and physical activities were classified by using an adaptation of a published scale in terms of “diversity” (total number of activities), “intensity” (hours per month), and “percentage intensity” (percentage of total activity hours devoted to each activity category). The control group was more active during midlife than the case group was for all three activity categories, even after controlling for age, gender, income adequacy, and education. The odds ratio for AD in those performing less than the mean value of activities was 3.85 (95% confidence interval: 2.65–5.58, P < 0.001). The increase in time devoted to intellectual activities from early adulthood (20–39) to middle adulthood (40–60) was associated with a significant decrease in the probability of membership in the case group. We conclude that diversity of activities and intensity of intellectual activities were reduced in patients with AD as compared with the control group. These findings may be because inactivity is a risk factor for the disease or because inactivity is a reflection of very early subclinical effects of the disease, or both.

Ergodic theorems along sequences and Hardy fields.

Let a(x) be a real function with a regular growth as x --> infinity. [The precise technical assumption is that a(x) belongs to a Hardy field.] We establish sufficient growth conditions on a(x) so that the sequence ([a(n)])(infinity)(n=1) is a good averaging sequence in L2 for the pointwise ergodic theorem. A sequence (an) of positive integers is a good averaging sequence in L2 for the pointwise ergodic theorem if in any dynamical system (Omega, Sigma, m, T) for f [symbol, see text] in L2(Omega) the averages [equation, see text] converge for almost every omicron in. Our result implies that sequences like ([ndelta]), where delta > 1 and not an integer, ([n log n]), and ([n2/log n]) are good averaging sequences for L2. In fact, all the sequences we examine will turn out to be good averaging for Lp, p > 1; and even for L log L. We will also establish necessary and sufficient growth conditions on a(x) so that the sequence ([a(n)]) is good averaging for mean convergence. Note that for some a(x) (e.g., a(x) = log2 x), ([a(n)]) may be good for mean convergence without being good for pointwise convergence.