Riesz s-Equilibrium Measures on d-Dimensional Fractal Sets as s Approaches d

Let $A$ be a compact set in \Rp of Hausdorff dimension $d$. For $s\in(0,d)$, the Riesz $s$-equilibrium measure $\mu^{s,A}$ is the unique Borel probability measure with support in $A$ that minimizes \Is(\mu):=\iint\Rk{x}{y}{s}d\mu(y)d\mu(x) over all such probability measures. In this paper we show that if $A$ is a strictly self-similar $d$-fractal, then $\mu^{s,A}$ converges in the weak-star topology to normalized $d$-dimensional Hausdorff measure restricted to $A$ as $s$ approaches $d$ from below

The Generalized Asymptotic Equipartition Property: Necessary and Sufficient Conditions

Suppose a string $X_1^n=(X_1,X_2,...,X_n)$ generated by a memoryless source $(X_n)_{n\geq 1}$ with distribution $P$ is to be compressed with distortion no greater than $D\geq 0$, using a memoryless random codebook with distribution $Q$. The compression performance is determined by the ``generalized asymptotic equipartition property'' (AEP), which states that the probability of finding a $D$-close match between $X_1^n$ and any given codeword $Y_1^n$, is approximately $2^{-n R(P,Q,D)}$, where the rate function $R(P,Q,D)$ can be expressed as an infimum of relative entropies. The main purpose here is to remove various restrictive assumptions on the validity of this result that have appeared in the recent literature. Necessary and sufficient conditions for the generalized AEP are provided in the general setting of abstract alphabets and unbounded distortion measures. All possible distortion levels $D\geq 0$ are considered; the source $(X_n)_{n\geq 1}$ can be stationary and ergodic; and the codebook distribution can have memory. Moreover, the behavior of the matching probability is precisely characterized, even when the generalized AEP is not valid. Natural characterizations of the rate function $R(P,Q,D)$ are established under equally general conditions.Comment: 19 page

Data Reduction and Analysis of Photometric Data for 48 Evolved Stars from the All Sky Automated Survey and Valparaiso University Observatory

We are carrying out research to determine the pulsation period of a specific stage in evolved, low-mass stars’ life cycles called Proto-Planetary Nebulae. Our datasets come from The Valparaiso University Observatory (VUO), as well as The All Sky Automated Survey – All Sky Catalogue (ASAS-ASC), and The All Sky Automated Survey for Supernova (ASAS-SN). These datasets complement each other to ensure that we get high-quality data for our very faint objects over long intervals of time in both hemispheres. The VUO has been observing on this project for over 20 years. The ASAS-ASC and ASAS-SN data recently became open to the public and we are using them in our analysis. We are using these three datasets to search for periodic photometric variability in 48 evolved stars. We do this by using a sophisticated period search program called Period04. Our research has found 18 objects that have one or more significant periods ranging from 37 to 208 days

Mortality Salience and Metabolism: Glucose Drinks Reduce Worldview Defense Caused by Mortality Salience

The current work tested the hypothesis that a glucose drink would reduce worldview defense following mortality salience. Participants consumed either a glucose drink or placebo, wrote about either death or dental pain, and then completed a measure of worldview defense (viewing positively someone with pro-US views and viewing negatively someone with anti-US views). Mortality salience increased world- view defense among participants who consumed a placebo but not among participants who consumed a glucose drink. Glucose might reduce defensiveness after mortality salience by increasing the effectiveness of the self-controlled suppression of death-related thought, by providing resources to cope with mortality salience and reducing its threatening nature, or by distancing the individual from actual physical death

Selection into Mixed Marriages: Evidence from North Carolina, 1894-1906

Using a novel dataset from agricultural censuses and geological sources, I examine the selec- tion into mixed marriages between whites and Cherokee Indians in North Carolina during the late nineteenth century. I find that the well-documented wealth advantage of Cherokee Indian households containing white husbands is driven mostly by positive selection. Thus, once family fixed effects are controlled for, the observed intermarriage premium is completely eliminated. (JEL D03, N31, O12.

Speeding up low-mass planetary microlensing simulations and modelling: the Caustic Region Of INfluence

Extensive simulations of planetary microlensing are necessary both before and after a survey is conducted: before to design and optimize the survey and after to understand its detection efficiency. The major bottleneck in such computations is the computation of lightcurves. However, for low-mass planets most of these computations are wasteful, as most lightcurves do not contain detectable planetary signatures. In this paper I develop a parameterization of the binary microlens that is conducive to avoiding lightcurve computations. I empirically find analytic expressions describing the limits of the parameter space that contain the vast majority of low-mass planet detections. Through a large scale simulation I measure the (in)completeness of the parameterization and the speed-up it is possible to achieve. For Earth-mass planets in a wide range of orbits it is possible to speed up simulations by a factor of ${\sim} 30$-$125$ (depending on the survey's annual duty-cycle) at the cost of missing ${\sim} 1$ percent of detections (which is actually a smaller loss than for the arbitrary parameter limits typically applied in microlensing simulations). The benefits of the parameterization probably outweigh the costs for planets below $100M_{\oplus}$. For planets at the sensitivity limit of AFTA-WFIRST, simulation speed-ups of a factor ${\sim} 1000$ or more are possible.Comment: 9 pages, 8 figures, 3 table