On Multiplicative Sidon Sets

Fix integers $b>a\geq1$ with $g:=\gcd(a,b)$. A set $S\subseteq\mathbb{N}$ is \emph{$\{a,b\}$-multiplicative} if $ax\neq by$ for all $x,y\in S$. For all $n$, we determine an $\{a,b\}$-multiplicative set with maximum cardinality in $[n]$, and conclude that the maximum density of an $\{a,b\}$-multiplicative set is $\frac{b}{b+g}$. For $A, B \subseteq \mathbb{N}$, a set $S\subseteq\mathbb{N}$ is \emph{$\{A,B\}$-multiplicative} if $ax=by$ implies $a = b$ and $x = y$ for all $a\in A$ and $b\in B$, and $x,y\in S$. For $1 < a < b < c$ and $a, b, c$ coprime, we give an O(1) time algorithm to approximate the maximum density of an $\{\{a\},\{b,c\}\}$-multiplicative set to arbitrary given precision

Can enlightenment be traced to specific neural correlates, cognition, or behavior? No, and (a qualified) Yes

The field of contemplative science is rapidly growing and integrating into the basic neurosciences, psychology, clinical sciences, and society-at-large. Yet the majority of current research in the contemplative sciences has been divorced from the soteriological context from which these meditative practices originate and has focused instead on clinical applications with goals of stress reduction and psychotherapeutic health. In the existing research on health outcomes of mindfulness-based clinical interventions, for example, there have been almost no attempts to scientifically investigate the goal of enlightenment. This is a serious oversight, given that such profound transformation across ethical, perceptual, emotional, and cognitive domains are taken to be the natural outcome and principle aim of mindfulness practice in the traditional Buddhist contexts from which these practices are derived. If short-term interventions as short as a few sessions are now beginning to produce neuroplastic changes, it may be that even in secular contexts, practitioners are already developing states and traits that are associated with progress toward enlightenment. In order to carefully assess the potential effects of meditative interventions it is of singular importance to ask whether enlightenment can be traced to specific neural correlates, cognition, or behavior

The Impact of a Regulatory Intervention on Resident-Centered Nursing Home Care: Rhode Island's Individualized Care Pilot

Evaluates a pilot project to promote resident-centered care through activities integrated with recertification inspections, including visits from a nonregulatory entity, and its impact on understanding, consideration, and implementation of practices

Estimating Functions of Probability Distributions from a Finite Set of Samples, Part 1: Bayes Estimators and the Shannon Entropy

We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint distribution, we present finite sample estimators for the mutual information, covariance, and chi-squared functions of that probability distribution.Comment: uuencoded compressed tarfile, submitte

Driven Polymer Translocation Through a Narrow Pore

Motivated by experiments in which a polynucleotide is driven through a proteinaceous pore by an electric field, we study the diffusive motion of a polymer threaded through a narrow channel with which it may have strong interactions. We show that there is a range of polymer lengths in which the system is approximately translationally invariant, and we develop a coarse-grained description of this regime. From this description, general features of the distribution of times for the polymer to pass through the pore may be deduced. We also introduce a more microscopic model. This model provides a physically reasonable scenario in which, as in experiments, the polymer's speed depends sensitively on its chemical composition, and even on its orientation in the channel. Finally, we point out that the experimental distribution of times for the polymer to pass through the pore is much broader than expected from simple estimates, and speculate on why this might be.Comment: 16 pages, 8 figures, RevTex and harvard citation style, submitted to Biophysical Journa