Rational weak mixing in infinite measure spaces

Rational weak mixing is a measure theoretic version of Krickeberg's strong ratio mixing property for infinite measure preserving transformations. It requires "{\tt density}" ratio convergence for every pair of measurable sets in a dense hereditary ring. Rational weak mixing implies weak rational ergodicity and (spectral) weak mixing. It is enjoyed for example by Markov shifts with Orey's strong ratio limit property. The power, subsequence version of the property is generic.Comment: Typos in the definitions of "rational weak mixing" and "weak rational ergodicity" (p.5) are correcte

Empirical testing of algorithms for variable-sized label placement

We report an empirical comparison of different heuristic techniques for variable-sized point-feature label placement.Engineering and Applied Science

Classification of time series by shapelet transformation

Time-series classification (TSC) problems present a specific challenge for classification algorithms: how to measure similarity between series. A \emph{shapelet} is a time-series subsequence that allows for TSC based on local, phase-independent similarity in shape. Shapelet-based classification uses the similarity between a shapelet and a series as a discriminatory feature. One benefit of the shapelet approach is that shapelets are comprehensible, and can offer insight into the problem domain. The original shapelet-based classifier embeds the shapelet-discovery algorithm in a decision tree, and uses information gain to assess the quality of candidates, finding a new shapelet at each node of the tree through an enumerative search. Subsequent research has focused mainly on techniques to speed up the search. We examine how best to use the shapelet primitive to construct classifiers. We propose a single-scan shapelet algorithm that finds the best $k$ shapelets, which are used to produce a transformed dataset, where each of the $k$ features represent the distance between a time series and a shapelet. The primary advantages over the embedded approach are that the transformed data can be used in conjunction with any classifier, and that there is no recursive search for shapelets. We demonstrate that the transformed data, in conjunction with more complex classifiers, gives greater accuracy than the embedded shapelet tree. We also evaluate three similarity measures that produce equivalent results to information gain in less time. Finally, we show that by conducting post-transform clustering of shapelets, we can enhance the interpretability of the transformed data. We conduct our experiments on 29 datasets: 17 from the UCR repository, and 12 we provide ourselve

The Grizzly, April 19, 2007

Airband a Success • Omega Chi Blood Drive • Hillel Holocaust Discussion • Letter to the Editor • What Dreams May Come • Ivory-billed Woodpecker Not Extinct! • Fiber Facts • Earth-Shattering Drumming • Opinions: No Child Left Behind? Really?; Gitmo on Strike • Bears Win 11th in a Row; Coach McGowan Earns 200th Victory • Women\u27s Lacrosse Hangs Tough with #4 Gettysburghttps://digitalcommons.ursinus.edu/grizzlynews/1738/thumbnail.jp

A multi-layer extension of the stochastic heat equation

Motivated by recent developments on solvable directed polymer models, we define a 'multi-layer' extension of the stochastic heat equation involving non-intersecting Brownian motions.Comment: v4: substantially extended and revised versio

The Grizzly, February 15, 2007

Darfur Fast Week Kickoff • United Men of Color Reception • The Peter Pan Project • CoSA Kickoff a Success • Power of Purple • Preview of The Laramie Project • Nutrition Tips • Inside Look at New Member Education • Opinions: Black History Month; Our Long-Awaited Greek Column • Heartbreak at Hopkins • Guntli Leading Rebounder • Senior Day Basketball Double-Headerhttps://digitalcommons.ursinus.edu/grizzlynews/1731/thumbnail.jp

The Very Short Period M Dwarf Binary SDSS J001641-000925

We present follow-up observations and analysis of the recently discovered short period low-mass eclipsing binary, SDSS J001641-000925. With an orbital period of 0.19856 days, this system has one of the shortest known periods for an M dwarf binary system. Medium-resolution spectroscopy and multi-band photometry for the system are presented. Markov chain Monte Carlo modeling of the light curves and radial velocities yields estimated masses for the stars of M1 = 0.54 +/- 0.07 Msun and M2 = 0.34 +/- 0.04 Msun, and radii of R1 = 0.68 +/- 0.03 Rsun and R2 = 0.58 +/- 0.03 Rsun respectively. This solution places both components above the critical Roche overfill limit, providing strong evidence that SDSS J001641-000925 is the first verified M-dwarf contact binary system. Within the follow-up spectroscopy we find signatures of non-solid body rotation velocities, which we interpret as evidence for mass transfer or loss within the system. In addition, our photometry samples the system over 9 years, and we find strong evidence for period decay at the rate of dP/dt ~8 s/yr. Both of these signatures raise the intriguing possibility that the system is in over-contact, and actively losing angular momentum, likely through mass loss. This places SDSS J001641-000925 as not just the first M-dwarf over-contact binary, but one of the few systems of any spectral type known to be actively undergoing coalescence. Further study SDSS J001641-000925 is on-going to verify the nature of the system, which may prove to be a unique astrophysical laboratory.Comment: 11 figures, ApJ Accepte