The number of dense arrangements

AbstractConsider arrangements of N elements of two kinds, A and B, such that any segment of length m contains at least k type A elements. We evaluate the number of such arrangements

Gambling Teams and Waiting Times for Patterns in Two-State Markov Chains

Methods using gambling teams and martingales are developed and applied to find formulas for the expected value and the generating function of the waiting time until one observes an element of a finite collection of patterns in a sequence which is generated by a two-state first or higher order Markov chain

A ferromagnet with a glass transition

We introduce a finite-connectivity ferromagnetic model with a three-spin interaction which has a crystalline (ferromagnetic) phase as well as a glass phase. The model is not frustrated, it has a ferromagnetic equilibrium phase at low temperature which is not reached dynamically in a quench from the high-temperature phase. Instead it shows a glass transition which can be studied in detail by a one step replica-symmetry broken calculation. This spin model exhibits the main properties of the structural glass transition at a solvable mean-field level.Comment: 7 pages, 2 figures, uses epl.cls (included

Observations of Comet 9P/Tempel 1 with the Keck 1 HIRES Instrument During Deep Impact

We report high-spectral resolution observations of comet 9P/Tempel 1 before, during and after the impact on 4 July 2005 UT of the Deep Impact spacecraft with the comet. These observations were obtained with the HIRES instrument on Keck 1. We observed brightening of both the dust and gas, but at different rates. We report the behavior of OH, NH, CN, C$_{3}$, CH, NH$_{2}$ and C$_{2}$ gas. From our observations, we determined a CN outflow velocity of at least 0.51 km sec$^{-1}$. The dust color did not change substantially. To date, we see no new species in our spectra, nor do we see any evidence of prompt emission. From our observations, the interior material released by the impact looks the same as the material released from the surface by ambient cometary activity. However, further processing of the data may uncover subtle differences in the material that is released as well as the time evolution of this material.Comment: 22 pages, 5 figures (1 color, landscape). Accepted for publication in Icaru

Toward an Unsteady Aerodynamic ROM for Multiple Mach Regimes

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97065/1/AIAA2012-1708.pd

On the chromatic number of random geometric graphs

Given independent random points X_1,...,X_n\in\eR^d with common probability distribution $\nu$, and a positive distance $r=r(n)>0$, we construct a random geometric graph $G_n$ with vertex set $\{1,...,n\}$ where distinct $i$ and $j$ are adjacent when \norm{X_i-X_j}\leq r. Here \norm{.} may be any norm on \eR^d, and $\nu$ may be any probability distribution on \eR^d with a bounded density function. We consider the chromatic number $\chi(G_n)$ of $G_n$ and its relation to the clique number $\omega(G_n)$ as $n \to \infty$. Both McDiarmid and Penrose considered the range of $r$ when $r \ll (\frac{\ln n}{n})^{1/d}$ and the range when $r \gg (\frac{\ln n}{n})^{1/d}$, and their results showed a dramatic difference between these two cases. Here we sharpen and extend the earlier results, and in particular we consider the `phase change' range when $r \sim (\frac{t\ln n}{n})^{1/d}$ with $t>0$ a fixed constant. Both McDiarmid and Penrose asked for the behaviour of the chromatic number in this range. We determine constants $c(t)$ such that $\frac{\chi(G_n)}{nr^d}\to c(t)$ almost surely. Further, we find a "sharp threshold" (except for less interesting choices of the norm when the unit ball tiles $d$-space): there is a constant $t_0>0$ such that if $t \leq t_0$ then $\frac{\chi(G_n)}{\omega(G_n)}$ tends to 1 almost surely, but if $t > t_0$ then $\frac{\chi(G_n)}{\omega(G_n)}$ tends to a limit $>1$ almost surely.Comment: 56 pages, to appear in Combinatorica. Some typos correcte

Higher algebraic KK-groups and D\mathcal D-split sequences

In this paper, we use $\mathcal D$-split sequences and derived equivalences to provide formulas for calculation of higher algebraic $K$-groups (or mod-$p$ $K$-groups) of certain matrix subrings which cover tiled orders, rings related to chains of Glaz-Vasconcelos ideals, and some other classes of rings. In our results, we do not assume any homological requirements on rings and ideals under investigation, and therefore extend sharply many existing results of this type in the algebraic $K$-theory literature to a more general context.Comment: 20 page

Nonparametric methods for analyzing replication origins in genomewide data

Due to the advent of high-throughput genomic technology, it has become possible to monitor cellular activities on a genomewide basis. With these new methods, scientists can begin to address important biological questions. One such question involves the identification of replication origins, which are regions in the chromosomes where DNA replication is initiated. One hypothesis is that their locations are nonrandom throughout the genome. In this article, we analyze data from a recent yeast study in which candidate replication origins were profiled using cDNA microarrays to test this hypothesis. We find no evidence for such clustering.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47937/1/10142_2004_Article_122.pd

A Latent Variable Partial Least Squares Path Modeling Approach to Regional Association and Polygenic Effect with Applications to a Human Obesity Study

Genetic association studies are now routinely used to identify single nucleotide polymorphisms (SNPs) linked with human diseases or traits through single SNP-single trait tests. Here we introduced partial least squares path modeling (PLSPM) for association between single or multiple SNPs and a latent trait that can involve single or multiple correlated measurement(s). Furthermore, the framework naturally provides estimators of polygenic effect by appropriately weighting trait-attributing alleles. We conducted computer simulations to assess the performance via multiple SNPs and human obesity-related traits as measured by body mass index (BMI), waist and hip circumferences. Our results showed that the associate statistics had type I error rates close to nominal level and were powerful for a range of effect and sample sizes. When applied to 12 candidate regions in data (N = 2,417) from the European Prospective Investigation of Cancer (EPIC)-Norfolk study, a region in FTO was found to have stronger association (rs7204609∼rs9939881 at the first intron P = 4.29×10−7) than single SNP analysis (all with P>10−4) and a latent quantitative phenotype was obtained using a subset sample of EPIC-Norfolk (N = 12,559). We believe our method is appropriate for assessment of regional association and polygenic effect on a single or multiple traits

Stationary relativistic jets

In this paper we describe a simple numerical approach which allows to study the structure of steady-state axisymmetric relativistic jets using one-dimensional time-dependent simulations. It is based on the fact that for narrow jets with vz≈cvz≈c the steady-state equations of relativistic magnetohydrodynamics can be accurately approximated by the one-dimensional time-dependent equations after the substitution z=ctz=ct. Since only the time-dependent codes are now publicly available this is a valuable and efficient alternative to the development of a high-specialised code for the time-independent equations. The approach is also much cheaper and more robust compared to the relaxation method. We tested this technique against numerical and analytical solutions found in literature as well as solutions we obtained using the relaxation method and found it sufficiently accurate. In the process, we discovered the reason for the failure of the self-similar analytical model of the jet reconfinement in relatively flat atmospheres and elucidated the nature of radial oscillations of steady-state jets