Second order ancillary: A differential view from continuity

Second order approximate ancillaries have evolved as the primary ingredient for recent likelihood development in statistical inference. This uses quantile functions rather than the equivalent distribution functions, and the intrinsic ancillary contour is given explicitly as the plug-in estimate of the vector quantile function. The derivation uses a Taylor expansion of the full quantile function, and the linear term gives a tangent to the observed ancillary contour. For the scalar parameter case, there is a vector field that integrates to give the ancillary contours, but for the vector case, there are multiple vector fields and the Frobenius conditions for mutual consistency may not hold. We demonstrate, however, that the conditions hold in a restricted way and that this verifies the second order ancillary contours in moderate deviations. The methodology can generate an appropriate exact ancillary when such exists or an approximate ancillary for the numerical or Monte Carlo calculation of $p$-values and confidence quantiles. Examples are given, including nonlinear regression and several enigmatic examples from the literature.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ248 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Topological soliton-polaritons in 1D systems of light and fermionic matter

Quantum nonlinear optics is a quickly growing field with large technological promise, at the same time involving complex and novel many-body phenomena. In the usual scenario, optical nonlinearities originate from the interactions between polaritons, which are hybrid quasi-particles mixing matter and light degrees of freedom. Here we introduce a type of polariton which is intrinsically nonlinear and emerges as the natural quasi-particle in presence quantum degenerate fermionic matter. It is a composite object made of a fermion trapped inside an optical soliton forming a topological defect in a spontaneously formed crystalline structure. Each of these soliton-polaritons carries a $\textbf{Z}_2$ topological quantum number, as they create a domain wall between two crystalline regions with opposite dimerization so that the fermion is trapped in an interphase state. These composite objects are formally equivalent to those appearing in the Su-Schrieffer-Heeger (SSH) model for electrons coupled to lattice phonons.Comment: Edited version. 6+7 pages, 3 figure

CD28 and T cell antigen receptor signal transduction coordinately regulate interleukin 2 gene expression in response to superantigen stimulation.

Activation of an immune response requires intercellular contact between T lymphocytes and antigen-presenting cells (APC). Interaction of the T cell antigen receptor (TCR) with antigen in the context of major histocompatibility molecules mediates signal transduction, but T cell activation appears to require the induction of a second costimulatory signal transduction pathway. Recent studies suggest that interaction of CD28 with B7 on APC might deliver such a costimulatory signal. To investigate the role of CD28 signal transduction during APC-dependent T cell activation, we have used Staphylococcal enterotoxins (SEs) presented by a B7-positive APC. We used anti-B7 monoclonal antibodies and a mutant interleukin 2 (IL-2) promoter construct, unresponsive to CD28-generated signals, in transient transfection assays to examine the contribution of the CD28-B7 interaction to IL-2 gene activation. These studies indicate that the CD28-regulated signal transduction pathway is activated during SE stimulation of T cells and plays an important role in SE induction of IL-2 gene expression through its influence upon the CD28-responsive element contained within the IL-2 gene promoter. This effect is particularly profound in the activation of the IL-2 gene in peripheral blood T cells

In situ analysis of neuronal dynamics and positional cues in the patterning of nerve connections

Recently developed imaging techniques permit individual cells to be uniquely labeled and followed over time as development proceeds in intact vertebrate embryos. Small groups of cells in the developing eye rudiment of the frog Xenopus have been labeled with the vital dyes DiI, lysinated fluorescein dextran (LFD) or lysinated rhodamine dextran (LRD). Individual optic axons and their growth cones were clearly visible in the intact living animal using confocal microscopy or epifluorescence microscopy with a low light level video camera and computer-based video image enhancement. To follow the dynamics of single optic nerve fiber terminal arborizations, small groups of cells, or even single retinal ganglion cells, were labeled with DiI, and the resulting labeled optic nerve fibers were imaged using a confocal microscope. The images show a profound alteration in morphology from day to day, demonstrating that optic nerve terminal arborizations are dynamic structures constantly extending and retracting branches. To follow the topography of the developing projection and analyze the cues that guide its formation, small groups of eyebud cells from LFD- and LRD-labeled donor embryos were grafted to an unlabeled host in either a location equivalent to that from which they had been removed (homotopic grafts) or a non-equivalent location (heterotopic grafts). Axons from homotopic grafts projected to the tectum as expected from the adult topography of the retinotectal projection. Dorsoventral topography was present from the time that the optic nerve fibers were observable in the tectum, in agreement with previous work. Nasotemporal topography was subtle or absent for the first few days, and then slowly refined. The importance of positional cues was tested by performing heterotopic eyebud grafts, in which the labeled eyebud cells are grafted to inappropriate places in the host eyebud. The heterotopic grafts appeared to integrate with the ectopic site in the eyebud in a functional manner. They should, therefore, project to the tectum together with their new neighbors if neighbor interactions or activity-based cues were of primary importance in the initial patterning of the map. However, the experiments showed that the axons from heterotopic grafts always behaved in a fashion appropriate to their position of origin in the donor, regardless of their final position in the host. These observations indicate that small groups of eyebud cells (as small as a single cell) possess positional information that plays a dominant role in guiding the optic nerve fibers to their target sites in the tectum

Vehicle Steering control: A model of learning

A hierarchy of strategies were postulated to describe the process of learning steering control. Vehicle motion and steering control data were recorded for twelve novices who drove an instrumented car twice a week during and after a driver training course. Car-driver describing functions were calculated, the probable control structure determined, and the driver-alone transfer function modelled. The data suggested that the largest changes in steering control with learning were in the way the driver used the lateral position cue

Higher Accuracy for Bayesian and Frequentist Inference: Large Sample Theory for Small Sample Likelihood

Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual evaluation of such $p$-values is by simulations, and such simulations do verify that the global distribution of the $p$-values is uniform(0, 1), to high accuracy in repeated sampling. The derivation of the $p$-values, however, asserts a stronger statement, that they have a uniform(0, 1) distribution conditionally, given identified precision information provided by the data. We take a simple regression example that involves exact precision information and use large sample techniques to extract highly accurate information as to the statistical position of the data point with respect to the parameter: specifically, we examine various $p$-values and Bayesian posterior survivor $s$-values for validity. With observed data we numerically evaluate the various $p$-values and $s$-values, and we also record the related general formulas. We then assess the numerical values for accuracy using Markov chain Monte Carlo (McMC) methods. We also propose some third-order likelihood-based procedures for obtaining means and variances of Bayesian posterior distributions, again followed by McMC assessment. Finally we propose some adaptive McMC methods to improve the simulation acceptance rates. All these methods are based on asymptotic analysis that derives from the effect of additional data. And the methods use simple calculations based on familiar maximizing values and related informations. The example illustrates the general formulas and the ease of calculations, while the McMC assessments demonstrate the numerical validity of the $p$-values as percentage position of a data point. The example, however, is very simple and transparent, and thus gives little indication that in a wide generality of models the formulas do accurately separate information for almost any parameter of interest, and then do give accurate $p$-value determinations from that information. As illustration an enigmatic problem in the literature is discussed and simulations are recorded; various examples in the literature are cited.Comment: Published in at http://dx.doi.org/10.1214/07-STS240 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Is HIV short-sighted? Insights from a multistrain nested model

An important component of pathogen evolution at the population level is evolution within hosts. Unless evolution within hosts is very slow compared to the duration of infection, the composition of pathogen genotypes within a host is likely to change during the course of an infection, thus altering the composition of genotypes available for transmission as infection progresses. We develop a nested modeling approach that allows us to follow the evolution of pathogens at the epidemiological level by explicitly considering within-host evolutionary dynamics of multiple competing strains and the timing of transmission. We use the framework to investigate the impact of short-sighted within-host evolution on the evolution of virulence of human immunodeficiency virus (HIV), and find that the topology of the within-host adaptive landscape determines how virulence evolves at the epidemiological level. If viral reproduction rates increase significantly during the course of infection, the viral population will evolve a high level of virulence even though this will reduce the transmission potential of the virus. However, if reproduction rates increase more modestly, as data suggest, our model predicts that HIV virulence will be only marginally higher than the level that maximizes the transmission potential of the virus