Evolutionary Inference for Function-valued Traits: Gaussian Process Regression on Phylogenies

Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated due to phylogenetic relationships. In this paper we give a flexible statistical model for such data, by combining assumptions from phylogenetics with Gaussian processes. We describe its use as a nonparametric Bayesian prior distribution, both for prediction (placing posterior distributions on ancestral functions) and model selection (comparing rates of evolution across a phylogeny, or identifying the most likely phylogenies consistent with the observed data). Our work is integrative, extending the popular phylogenetic Brownian Motion and Ornstein-Uhlenbeck models to functional data and Bayesian inference, and extending Gaussian Process regression to phylogenies. We provide a brief illustration of the application of our method.Comment: 7 pages, 1 figur

Relationships between class size and teaching: a multi-method analysis of English infant schools

Research and debate on class size differences has focused on relations with achievement, and there is little relevant research on what mediating classroom processes might be involved. In this article we investigate connections between class size and teaching interactions. We adopt a multimethod approach, integrating qualitative in formation from teachers' end-of-year accounts and data from case studies with quantitative information from time-allocation estimates and systematic observations. Our data come from a longitudinal study of two cohorts of more than 10,000 children altogether for 3 years after enrollment in English infant schools (aged 4-7 years). Our results show, overall, that in smaller classes there is more individualized teacher support for learning. We interpret the results in the context of teacher time allocation, research on effective teaching, and post-Vygotskian approaches to teaching. It is suggested that direct models of teacher influences on pupils need to be adapted to allow for class size as a contextual factor that influences both teachers and pupils

Atomic resolved material displacement on graphite surfaces by scanning tunnelling microscopy

Atomic scale modifications and subsequent atomic resolution imaging has been achieved on the highly oriented pyrolytic graphite surface in air. Application of short pulse voltages, above a minimum threshold voltage of 3.5 V, across the tunneling gap results in the displacement of a layer or more of atoms to form a hole and create a neighboring mound or ‘‘nanodot’’ from the displaced atoms. We have found a correlation between the hole and ‘‘nanodot’’ volume at the atomic level and observe an asymmetric displacement of material in all cases of feature creation. Nanofeatures as small as four carbon atoms at beta sites have been created. Our experimental observations are consistent with the modification process depending on the gradient in the electric field induced by the rise time of the bias pulse voltage and not the pulse duration. Interesting faceting behavior has also been observed around some hole edges. Tip bias pulsing sometimes induced a tip, and not a surface modification, resulting in a change in the observed tunneling image

Topology of Cell-Aggregated Planar Graphs

We present new algorithm for growth of non-clustered planar graphs by aggregation of cells with given distribution of size and constraint of connectivity k=3 per node. The emergent graph structures are controlled by two parameters--chemical potential of the cell aggregation and the width of the cell size distribution. We compute several statistical properties of these graphs--fractal dimension of the perimeter, distribution of shortest paths between pairs of nodes and topological betweenness of nodes and links. We show how these topological properties depend on the control parameters of the aggregation process and discuss their relevance for the conduction of current in self-assembled nanopatterns.Comment: 8 pages, 5 figure

The Enigmatic Radio Afterglow of GRB 991216

We present wide-band radio observations spanning from 1.4 GHz to 350 GHz of the afterglow of GRB 991216, taken from 1 to 80 days after the burst. The optical and X-ray afterglow of this burst were fairly typical and are explained by a jet fireball. In contrast, the radio light curve is unusual in two respects: (a) the radio light curve does not show the usual rise to maximum flux on timescales of weeks and instead appears to be declining already on day 1 and (b) the power law indices show significant steepening from the radio through the X-ray bands. We show that the standard fireball model, in which the afterglow is from a forward shock, is unable to account for (b) and we conclude that the bulk of the radio emission must arise from a different source. We consider two models, neither of which can be ruled out with the existing data. In the first (conventional) model, the early radio emission is attributed to emission from the reverse shock as in the case of GRB 990123. We predict that the prompt optical emission would have been as bright (or brighter) than 8th magnitude. In the second (exotic) model, the radio emission originates from the forward shock of an isotropically energetic fireball (10^54 erg) expanding into a tenuous medium (10^-4 cm^-3). The resulting fireball would remain relativistic for months and is potentially resolvable with VLBI techniques. Finally, we note that the near-IR bump of the afterglow is similar to that seen in GRB 971214 and no fireball model can explain this bump.Comment: ApJ, submitte

Measure of the path integral in lattice gauge theory

We show how to construct the measure of the path integral in lattice gauge theory. This measure contains a factor beyond the standard Haar measure. Such factor becomes relevant for the calculation of a single transition amplitude (in contrast to the calculation of ratios of amplitudes). Single amplitudes are required for computation of the partition function and the free energy. For U(1) lattice gauge theory, we present a numerical simulation of the transition amplitude comparing the path integral with the evolution in terms of the Hamiltonian, showing good agreement.Comment: 5 pages, 2 figure

A Nonconvex Singular Stochastic Control Problem and its Related Optimal Stopping Boundaries

Abstract. Equivalences are known between problems of singular stochastic control (SSC) with convex performance criteria and related questions of optimal stopping; see, for example, Karatzas and Shreve [SIAM J. Control Optim., 22 (1984), pp. 856–877]. The aim of this paper is to inves-tigate how far connections of this type generalize to a nonconvex problem of purchasing electricity. Where the classical equivalence breaks down we provide alternative connections to optimal stopping problems. We consider a nonconvex infinite time horizon SSC problem whose state consists of an un-controlled diffusion representing a real-valued commodity price, and a controlled increasing bounded process representing an inventory. We analyze the geometry of the action and inaction regions by characterizing their (optimal) boundaries. Unlike the case of convex SSC problems we find that the optimal boundaries may be both reflecting and repelling and it is natural to interpret the problem as one of SSC with discretionary stopping

Measuring the Hausdorff Dimension of Quantum Mechanical Paths

We measure the propagator length in imaginary time quantum mechanics by Monte Carlo simulation on a lattice and extract the Hausdorff dimension $d_{H}$. We find that all local potentials fall into the same universality class giving $d_{H}=2$ like the free motion. A velocity dependent action ($S \propto \int dt \mid \vec{v} \mid^{\alpha}$) in the path integral (e.g. electrons moving in solids, or Brueckner's theory of nuclear matter) yields $d_{H}=\frac{\alpha }{\alpha - 1}$ if $\alpha > 2$ and $d_{H}=2$ if $\alpha \leq 2$. We discuss the relevance of fractal pathes in solid state physics and in $QFT$, in particular for the Wilson loop in $QCD$.Comment: uuencoded and compressed shell archive file. 8 pages with 7 figure

High resolution observations of the L1551 bipolar outflow

The nearby dark cloud Lynds 1551 contains one of the closest examples of a well-collimated bipolar molecular outflow. This source has the largest angular size of any known outflow and was the first bipolar outflow to be detected. The outflow originates from a low-luminosity young stellar object, IRS-5. Optical and radio continuum observations show the presence of a highly collimated, ionized stellar wind orginating from close to IRS-5 and aligned with the molecular outflow. However, we have little information on the actual mechanism that generates the stellar wind and collimates it into opposed jets. The Very Large Array (VLA) observations indicate that the winds originate within 10(15) cm of IRS-5, unfortunately at a size scale difficult to resolve. For these reasons, observations of the structure and dynamics of the hypersonic molecular gas may provide valuable information on the origin and evolution of these outflows. In addition, the study of the impact of the outflowing gas on the surrounding molecular material is essential to understand the consequence these outflows have on the evolution and star formation history of the entire cloud. Moriarty-Schieven et al. (1986) obtained a oversampled map of the CO emission of a portion of both the blueshifted and redshifted outflows in LI551 using Five College Radio Astronomy Observatory 14 m telescope. The oversampled maps have been reconstructed to an effective angular resolution of 20 arcsec using a maximum entropy algorithm. A continuation of the study of Moriarty-Schieven et al. is presented. The entire L1551 outflow has now been mapped at 12 arcsec sampling requiring roughly 4000 spectra. This data has been constructed to 20 arcsec resolution to provide the first high resolution picture of the entire L1551 outflow. This new data has shown that the blueshifted lobe is more extended than previously thought and has expanded downstream sufficiently to break out of the dense molecular cloud, but the redshifted outflow is still confined within the molecular cloud. Details of the structure and kinematics of the high velocity gas are used to test the various models of the origin and evolution of outflows

Opioid analgesia and the somatosensory memory of neonatal surgical injury in the adult rat

Background Nociceptive input during early development can produce somatosensory memory that influences future pain response. Hind-paw incision during the 1st postnatal week in the rat enhances re-incision hyperalgesia in adulthood. We now evaluate its modulation by neonatal analgesia. Methods Neonatal rats [Postnatal Day 3 (P3)] received saline, intrathecal morphine 0.1 mg kg−1 (IT), subcutaneous morphine 1 mg kg−1 (SC), or sciatic levobupivacaine block (LA) before and after plantar hind-paw incision (three×2 hourly injections). Six weeks later, behavioural thresholds and electromyography (EMG) measures of re-incision hyperalgesia were compared with an age-matched adult-only incision (IN) group. Morphine effects on spontaneous (conditioned place preference) and evoked (EMG sensitivity) pain after adult incision were compared with prior neonatal incision and saline or morphine groups. The acute neonatal effects of incision and analgesia on behavioural hyperalgesia at P3 were also evaluated. Results Adult re-incision hyperalgesia was not prevented by neonatal peri-incision morphine (saline, IT, and SC groups > IN; P<0.05–0.01). Neonatal sciatic block, but not morphine, prevented the enhanced re-incision reflex sensitivity in adulthood (LA < saline and morphine groups, P<0.01; LA vs IN, not significant). Morphine efficacy in adulthood was altered after morphine alone in the neonatal period, but not when administered with neonatal incision. Morphine prevented the acute incision-induced hyperalgesia in neonatal rats, but only sciatic block had a preventive analgesic effect at 24 h. Conclusions Long-term effects after neonatal injury highlight the need for preventive strategies. Despite effective analgesia at the time of neonatal incision, morphine as a sole analgesic did not alter the somatosensory memory of early-life surgical injury