Push is Fast on Sparse Random Graphs

We consider the classical push broadcast process on a large class of sparse random multigraphs that includes random power law graphs and multigraphs. Our analysis shows that for every $\varepsilon>0$, whp $O(\log n)$ rounds are sufficient to inform all but an $\varepsilon$-fraction of the vertices. It is not hard to see that, e.g. for random power law graphs, the push process needs whp $n^{\Omega(1)}$ rounds to inform all vertices. Fountoulakis, Panagiotou and Sauerwald proved that for random graphs that have power law degree sequences with $\beta>3$, the push-pull protocol needs $\Omega(\log n)$ to inform all but $\varepsilon n$ vertices whp. Our result demonstrates that, for such random graphs, the pull mechanism does not (asymptotically) improve the running time. This is surprising as it is known that, on random power law graphs with $2<\beta<3$, push-pull is exponentially faster than pull

Smoothing ℓ1\ell_1-penalized estimators for high-dimensional time-course data

When a series of (related) linear models has to be estimated it is often appropriate to combine the different data-sets to construct more efficient estimators. We use $\ell_1$-penalized estimators like the Lasso or the Adaptive Lasso which can simultaneously do parameter estimation and model selection. We show that for a time-course of high-dimensional linear models the convergence rates of the Lasso and of the Adaptive Lasso can be improved by combining the different time-points in a suitable way. Moreover, the Adaptive Lasso still enjoys oracle properties and consistent variable selection. The finite sample properties of the proposed methods are illustrated on simulated data and on a real problem of motif finding in DNA sequences.Comment: Published in at http://dx.doi.org/10.1214/07-EJS103 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Discussion: One-step sparse estimates in nonconcave penalized likelihood models

Discussion of ``One-step sparse estimates in nonconcave penalized likelihood models'' [arXiv:0808.1012]Comment: Published in at http://dx.doi.org/10.1214/07-AOS0316A the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bridge trisections in rational surfaces

We study smooth isotopy classes of complex curves in complex surfaces from the perspective of the theory of bridge trisections, with a special focus on curves in $\mathbb{CP}^2$ and $\mathbb{CP}^1\times\mathbb{CP}^1$. We are especially interested in bridge trisections and trisections that are as simple as possible, which we call "efficient". We show that any curve in $\mathbb{CP}^2$ or $\mathbb{CP}^1\times\mathbb{CP}^1$ admits an efficient bridge trisection. Because bridge trisections and trisections are nicely related via branched covering operations, we are able to give many examples of complex surfaces that admit efficient trisections. Among these are hypersurfaces in $\mathbb{CP}^3$, the elliptic surfaces $E(n)$, the Horikawa surfaces $H(n)$, and complete intersections of hypersurfaces in $\mathbb{CP}^N$. As a corollary, we observe that, in many cases, manifolds that are homeomorphic but not diffeomorphic have the same trisection genus, which is consistent with the conjecture that trisection genus is additive under connected sum. We give many trisection diagrams to illustrate our examples.Comment: 46 pages, 28 color figure

A New Method for Exposing Deposit Feeders to Contaminated Sediments for Food Chain Studies

(excerpt) The ubiquity and refractory nature of certain organic compounds, such as chlorinated pesticides and polychlorinated biphenyls (PCB\u27s), results in their accumulation in aquatic sediments (Holdrinet et al. 1978, Peck et al. 1980, Wang et al. 1979). Their continuous release from this reservoir through physico-chemical and biogenic processes to the overlying water column results in the accumulation of xenobiotic compounds in the food chain

Intraspecific Variation in Taxonomic Characteristics of the Mayfly \u3ci\u3ePotamanthus Myops\u3c/i\u3e (Walsh)

Data collected from an ecological study of the mayfly Potamanthus rnyops (Walsh) in Michigan showed intraspecific variability in taxonomic characteristics that have been employed by previous investigators for species separation. Nymphal dorsal maculation patterns varied considerably within a single population. Also, the ratio of mandibular tusk length to head length increased with successive nymphal instars. Certain adult taxonomic characteristics, particularly relative male imago eye size and distance of separation, were either too poorly defined or too variable to be conclusive in species identification

Notes on the Life History of \u3ci\u3ePotamanthus Myops\u3c/i\u3e in Southeastern Michigan (Ephemeroptera: Potamanthidae)

Naiads of the mayfly Potamanthus myops were collected six times over a one year period from the Huron River to obtain some information on their natural history. Contrary to other Ephemeroidea, myops was never collected below the substrate surface, but was usually found on the underside of stones. The immature mayflies were measured and their length plotted for each collection period. The results support the hypothesis that the majority of myops requires two years to mature

A Modified Method for Reading Midges (Diptera: Chironomidae)

A small scale rearing chamber that provides a continuous source of different life stages of Glyptotendipes barbipes Staeger for bioassay studies was developed. A modified glass aquarium containing a substrate of shredded paper hand towels and artificial medium was employed. The amount of protein fed to the larvae can be used to trigger peak emergence, oviposition, and the rate of maturation. Fifty-three egg masses were sampled and 68% were fertile. Ninety-five percent of these hatched and 85% emerged as adults

Effects of Salmon Spawning Activity on Macroinvertebrates in a Small Michigan Stream

Density and composition of macroinvertebrate populations were examined prior to and during the migration and spawning of coho and chinook salmon in a small stream in Michigan. Data gathered from bottom samples indicated that disruption of substrate in the experimental area resulted in a significant decrease in the numbers and species of the macroinvertebrate community. This reduction of invertebrates can create a severe stress on native trout populations