Entropy-Based Strategies for Multi-Bracket Pools.

Much work in the parimutuel betting literature has discussed estimating event outcome probabilities or developing optimal wagering strategies, particularly for horse race betting. Some betting pools, however, involve betting not just on a single event, but on a tuple of events. For example, pick six betting in horse racing, March Madness bracket challenges, and predicting a randomly drawn bitstring each involve making a series of individual forecasts. Although traditional optimal wagering strategies work well when the size of the tuple is very small (e.g., betting on the winner of a horse race), they are intractable for more general betting pools in higher dimensions (e.g., March Madness bracket challenges). Hence we pose the multi-brackets problem: supposing we wish to predict a tuple of events and that we know the true probabilities of each potential outcome of each event, what is the best way to tractably generate a set of n predicted tuples? The most general version of this problem is extremely difficult, so we begin with a simpler setting. In particular, we generate n independent predicted tuples according to a distribution having optimal entropy. This entropy-based approach is tractable, scalable, and performs well.

Memantine Improves Attentional Processes in Fragile X-Associated Tremor/Ataxia Syndrome: Electrophysiological Evidence from a Randomized Controlled Trial.

Progressive cognitive deficits are common in patients with fragile X-associated tremor/ataxia syndrome (FXTAS), with no targeted treatment yet established. In this substudy of the first randomized controlled trial for FXTAS, we examined the effects of NMDA antagonist memantine on attention and working memory. Data were analyzed for patients (24 in each arm) who completed both the primary memantine trial and two EEG recordings (at baseline and follow-up) using an auditory "oddball" task. Results demonstrated significantly improved attention/working memory performance after one year only for the memantine group. The event-related potential P2 amplitude elicited by non-targets was significantly enhanced in the treated group, indicating memantine-associated improvement in attentional processes at the stimulus identification/discrimination level. P2 amplitude increase was positively correlated with improvement on the behavioral measure of attention/working memory during target detection. Analysis also revealed that memantine treatment normalized the P2 habituation effect at the follow-up visit. These findings indicate that memantine may benefit attentional processes that represent fundamental components of executive function/dysfunction, thought to comprise the core cognitive deficit in FXTAS. The results provide evidence of target engagement of memantine, as well as therapeutically relevant information that could further the development of specific cognitive or disease-modifying therapies for FXTAS.