Determining the dimension of iterative Hessian transformation

The central mean subspace (CMS) and iterative Hessian transformation (IHT) have been introduced recently for dimension reduction when the conditional mean is of interest. Suppose that X is a vector-valued predictor and Y is a scalar response. The basic problem is to find a lower-dimensional predictor \eta^TX such that E(Y|X)=E(Y|\eta^TX). The CMS defines the inferential object for this problem and IHT provides an estimating procedure. Compared with other methods, IHT requires fewer assumptions and has been shown to perform well when the additional assumptions required by those methods fail. In this paper we give an asymptotic analysis of IHT and provide stepwise asymptotic hypothesis tests to determine the dimension of the CMS, as estimated by IHT. Here, the original IHT method has been modified to be invariant under location and scale transformations. To provide empirical support for our asymptotic results, we will present a series of simulation studies. These agree well with the theory. The method is applied to analyze an ozone data set.Comment: Published at http://dx.doi.org/10.1214/009053604000000661 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optical contamination screening of materials with a high-finesse Fabry-Perot cavity resonated continuously at 1.06-µm wavelength in vacuum

An optical-loss measurement system based on a resonant Fabry Perot cavity at 1.06µm in vacuum has been developed for independent monitoring of the cavity total loss and the optical absorption loss. Maintenance of cavity resonance over a one-month period allows the assessment of long-term degradation of the cavity optics in the presence of outgassing materials, with sensitivities of 5 ppm yr for total cavity loss and 2 ppm yr for cavity absorption loss. Test results for light-emitting diodes, Kapton-insulated cable assemblies, and Vac-seal epoxy adhesive are given. Scaling of these results to the optical performance requirements of LIGO is discussed

Evolving Bacterial Envelopes and Plasticity of TLR2-Dependent Responses: Basic Research and Translational Opportunities.

Innate immune mechanisms that follow early recognition of microbes influence the nature and magnitude of subsequent adaptive immune responses. Early detection of microbes depends on pattern recognition receptors that sense pathogen-associated molecular patterns or microbial-associated molecular patterns (PAMPS or MAMPs, respectively). The bacterial envelope contains MAMPs that include membrane proteins, lipopeptides, glycopolymers, and other pro-inflammatory molecules. Bacteria are selected by environmental pressures resulting in quantitative or qualitative changes in their envelope structures that often promote evasion of host immune responses and therefore, infection. However, recent studies have shown that slight, adaptive changes in MAMPs on the bacterial cell wall may result in their ability to induce the secretion not only of pro-inflammatory cytokines but also of anti-inflammatory cytokines. This effect can fine-tune the subsequent response to microbes expressing these MAMPs and lead to the establishment of a commensal state within the host rather than infectious disease. In this review, we will examine the plasticity of Toll-like receptor (TLR) 2 signaling as evidence of evolving MAMPs, using the better-characterized TLR4 as a template. We will review the role of differential dimerization of TLR2 and the arrangement of signaling complexes and co-receptors in determining the capacity of the host to recognize an array of TLR2 ligands and generate different immune responses to these ligands. Last, we will assess briefly how this plasticity may expand the array of interactions between microbes and immune systems beyond the traditional disease-causing paradigm

Making Wireless Sensor Network Simulators Cooperate

CONE

Preparation, Characterization and Reactivity of (3-Methylpentadienyl)iron(1+) Cations

The title cations (9 and 12) were prepared by dehydration of (3-methyl-2,4-pentadien-1-ol)Fe(CO)2L+ complexes. The structure of the (CO)2PPh3-ligated 12 was determined by single-crystal X-ray analysis. Reaction of carbon and heteroatom nucleophiles to (3-methylpentadienyl)Fe(CO)3+ cations 9 and 12 proceeds either via attack at the dienyl terminus to give (3-methyl-1,3Z-diene)iron complexes or via attack at the internal carbon, followed by carbon monoxide insertion and reductive elimination to afford 3-methyl-4-substituted cyclohexenones. Cyclohexenone formation was found to be prevalent for addition of stabilized nucleophiles with strongly dissociated counterions to cation 9 (L = CO). Reaction of cation 9 with sodium bis[(−)-8-phenylmenthyl] malonate gave a single diastereomeric cyclohexenone

Asymptotic expansions for harmonic functions at conical boundary points

We prove three theorems about the asymptotic behavior of solutions $u$ to the homogeneous Dirichlet problem for the Laplace equation at boundary points with tangent cones. First, under very mild hypotheses, we show that the doubling index of $u$ either has a unique finite limit, or goes to infinity; in other words, there is a well-defined order of vanishing. Second, under more quantitative hypotheses, we prove that if the order of vanishing of $u$ is finite at a boundary point $0$, then locally $u(x) = |x|^m \psi(x/|x|) + o(|x|^m)$, where $|x|^m \psi(x/|x|)$ is a homogeneous harmonic function on the tangent cone. Finally, we construct a convex domain in three dimensions where such an expansion fails at a boundary point, showing that some quantitative hypotheses are necessary in general. The assumptions in all of the results only involve regularity at a single point, and in particular are much weaker than what is necessary for unique continuation, monotonicity of Almgren's frequency, Carleman estimates, or other related techniques

From ab initio quantum mechanics to molecular neurobiology: A cation-pi binding site in the nicotinic receptor

The nicotinic acetylcholine receptor is the prototype ligand-gated ion channel. A number of aromatic amino acids have been identified as contributing to the agonist binding site, suggesting that cation-pi interactions may be involved in binding the quaternary ammonium group of the agonist, acetylcholine. Here we show a compelling correlation between: (i) ab initio quantum mechanical predictions of cation-pi binding abilities and (ii) EC50 values for acetylcholine at the receptor for a series of tryptophan derivatives that were incorporated into the receptor by using the in vivo nonsense-suppression method for unnatural amino acid incorporation. Such a correlation is seen at one, and only one, of the aromatic residues-tryptophan-149 of the alpha subunit. This finding indicates that, on binding, the cationic, quaternary ammonium group of acetylcholine makes van der Waals contact with the indole side chain of alpha tryptophan-149, providing the most precise structural information to date on this receptor. Consistent with this model, a tethered quaternary ammonium group emanating from position alpha 149 produces a constitutively active receptor