The need for speed : Maximizing random walks speed on fixed environments

We study nearest neighbor random walks on fixed environments of $\mathbb{Z}$ composed of two point types : $(1/2,1/2)$ and $(p,1-p)$ for $p>1/2$. We show that for every environment with density of $p$ drifts bounded by $\lambda$ we have $\limsup_{n\rightarrow\infty}\frac{X_n}{n}\leq (2p-1)\lambda$, where $X_n$ is a random walk on the environment. In addition up to some integer effect the environment which gives the best speed is given by equally spaced drifts

Recommended Core Measures for Evaluating the Patient-Centered Medical Home: Cost, Utilization, and Clinical Quality

Outlines the process of the Patient-Centered Medical Home Evaluators' Collaborative for identifying core standardized measures and their recommended principles and measures for evaluating cost and utilization and clinical quality

Integrating genomics and phylogenetics in understanding the history of Trichinella species

In 2004, funding was received by Washington University’s Genome Sequencing Center through NHGRI, to completely sequence several nematode genomes as part of a holistic effort to advance our understanding of the human genome and evolution within the Metazoa. Trichinella spiralis was among this group of worms because of its strategic location at the base of the phylum Nematoda, and the belief that extant species represented an ancient divergent event that occurred as early as the Paleozoic. At the same time, a concerted effort was put forth to solidify the phylogeny of extant species of Trichinella based upon molecular analyses of a multi-gene system to understand the history of the genus and thereby enhance utilization of the forthcoming sequence data. Since the inception of this research, several findings have emerged: (1) the size of T. spiralis genome estimated by flow cytometry (71.3 Mb) is substantially smaller than originally predicted (270 Mb); (2) to date, a subset of the total of 3,534,683 sequences have been assembled into a 59.3 Mb unique sequence; (3) 19% of the assembled sequence is comprised of repetitive elements; and (4) sequence data are predicated upon extant T. spiralis which probably diverged as little as 20 million years ago. Thus, the utility of the T. spiralis genome as representative of an archaic species must be tempered with the knowledge that encapsulated and non-encapsulated clades probably separated during the mid-Miocene as temperate ecosystems changed

Isoperimetry in two-dimensional percolation

We consider the unique infinite connected component of supercritical bond percolation on the square lattice and study the geometric properties of isoperimetric sets, i.e., sets with minimal boundary for a given volume. For almost every realization of the infinite connected component we prove that, as the volume of the isoperimetric set tends to infinity, its asymptotic shape can be characterized by an isoperimetric problem in the plane with respect to a particular norm. As an application we then show that the anchored isoperimetric profile with respect to a given point as well as the Cheeger constant of the giant component in finite boxes scale to deterministic quantities. This settles a conjecture of Itai Benjamini for the plane.Comment: 40 pages, 2 figs; version to appear in Commun. Pure Appl. Mat

Dryland pasture and crop conditions as seen by HCMM

The author has identified the following significant results. The soil moisture difference between the flight lines was partly due to water-holding capacity differences of the two soil types. Fields along the east flight line were in clay; while along the west flight line, the soil was sandy loam which holds less moisture. Due to differences in the amount of green material, the pastures were wetter than the wheat fields. Most of the pastures average from 40-80% green material, while wheat averages from 90-100% green material. A large amount of green material transpired more water and depleted the soil water content faster than dead vegetation. Visicorder data found temperature differences between the rangeland and winter wheat fields. Pasture had a larger percentage of dead material with different thermal properties than live vegetation, and surface temperature was primarily dependent on insolation. Dead material transpired less, but warms up faster than wheat fields