Detecting periodicity in experimental data using linear modeling techniques

Fourier spectral estimates and, to a lesser extent, the autocorrelation function are the primary tools to detect periodicities in experimental data in the physical and biological sciences. We propose a new method which is more reliable than traditional techniques, and is able to make clear identification of periodic behavior when traditional techniques do not. This technique is based on an information theoretic reduction of linear (autoregressive) models so that only the essential features of an autoregressive model are retained. These models we call reduced autoregressive models (RARM). The essential features of reduced autoregressive models include any periodicity present in the data. We provide theoretical and numerical evidence from both experimental and artificial data, to demonstrate that this technique will reliably detect periodicities if and only if they are present in the data. There are strong information theoretic arguments to support the statement that RARM detects periodicities if they are present. Surrogate data techniques are used to ensure the converse. Furthermore, our calculations demonstrate that RARM is more robust, more accurate, and more sensitive, than traditional spectral techniques.Comment: 10 pages (revtex) and 6 figures. To appear in Phys Rev E. Modified styl

Scattering and absorption of ultracold atoms by nanotubes

We investigate theoretically how cold atoms, including Bose-Einstein condensates, are scattered from, or absorbed by nanotubes with a view to analysing recent experiments. In particular we consider the role of potential strength, quantum reflection, atomic interactions and tube vibrations on atom loss rates. Lifshitz theory calculations deliver a significantly stronger scattering potential than that found in experiment and we discuss possible reasons for this. We find that the scattering potential for dielectric tubes can be calculated to a good approximation using a modified pairwise summation approach, which is efficient and easily extendable to arbitrary geometries. Quantum reflection of atoms from a nanotube may become a significant factor at low temperatures, especially for non-metallic tubes. Interatomic interactions are shown to increase the rate at which atoms are lost to the nanotube and lead to non-trivial dynamics. Thermal nanotube vibrations do not significantly increase loss rates or reduce condensate fractions, but lower frequency oscillations can dramatically heat the cloud.Comment: 7 pages, 4 figure

Emergence of overwintered larvae of eye-spotted bud moth, Spilonota ocellana (Lepidoptera: Tortricidae) in relation to temperature and apple tree phenology at Summerland, British Columbia

We recorded daily appearance of overwintered larvae of eye-spotted bud moth (ESBM), Spilonota ocellana (Denis & Schiffermüller) in spring 1992, 1994, and 1996 in an unsprayed apple orchard at Summerland, British Columbia, to relate larval emergence to degree-day (DD) accumulation and apple phenology. In all years the first larva was found between mid-March and early April, and none appeared after late April. Median emergence of larvae occurred when McIntosh apple trees were at early, tight-cluster stage of fruit-bud development. Larval head capsule measurements showed that ESBM usually overwinter as fifth and sixth instars, with a small proportion (≤6%) as fourth instar larvae. In the laboratory we monitored emergence of non-diapausing overwintered larvae from apple branches incubated at 8.8, 9.4, 12.9, 15.0, 18.0, and 20.9ºC. A least-squares linear regression described emergence over this temperature range relatively accurately (r2 = 0.57, P < 0.05) and a base temperature for emergence (Tb = 1.0ºC ± 0.6) was extrapolated from this regression. Regression analysis indicated median emergence should require 154.6 ± 6.7 DD above 1ºC (DD 1ºC). Using daily airtemperature maxima and minima and 1 March to start accumulating DD1ºC, the error between predicted and observed days to median emergence in the field was -6.7 ± 3.1 d; the regression model predicted early in every case. Using observed larval appearance on apples (1992, 1994, & 1996) and an iterative process, we determined that a combination of 6ºC as the Tb and 1 January as a date to start accumulating DD6ºC, minimized the coefficient of variation for the three-year mean DD 6ºC accumulations (82.7 ± 3.5 DD 6ºC) required for 50% of the larvae to appear in the field. While this latter DD index described observed emergence of larvae accurately, and its use may help improve management of ESBM, it should be validated using independent data before growers use it routinely

Difference score correlations in relationship research: A conceptual primer

The practice of computing correlations between “difference” or “discrepancy” scores and an outcome variable is common in many areas of social science. Relationship researchers most commonly use difference scores to index the (dis)similarity of members of two-person relationships. Using an intuitive, graphical approach—and avoiding formulas and pointing fingers—we illustrate problems with using difference score correlations in relationship research, suggest ways to ensure that difference score correlations are maximally informative, and briefly review alternatives to difference score correlations in studying similarity, accuracy, and related constructs.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73008/1/j.1475-6811.1999.tb00206.x.pd

Inactivation of Kell blood group antigens by 2-aminoethylisothiouronium bromide

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75007/1/j.1365-2141.1982.tb07295.x.pd

Zeros of 6j Symbols:Atoms:Nuclei and Bosons

The same 6j symbols that explains the absence of a certain atomic state in LS coupling also explain the absence of certain states for a system of bosons and also for certain nuclear states in jj coupling

Analytic Treatment of Positronium Spin Splittings in Light-Front QED

We study the QED bound-state problem in a light-front hamiltonian approach. Starting with a bare cutoff QED Hamiltonian, $H_{_{B}}$, with matrix elements between free states of drastically different energies removed, we perform a similarity transformation that removes the matrix elements between free states with energy differences between the bare cutoff, $\Lambda$, and effective cutoff, \lam (\lam < \Lam). This generates effective interactions in the renormalized Hamiltonian, $H_{_{R}}$. These effective interactions are derived to order $\alpha$ in this work, with $\alpha \ll 1$. $H_{_{R}}$ is renormalized by requiring it to satisfy coupling coherence. A nonrelativistic limit of the theory is taken, and the resulting Hamiltonian is studied using bound-state perturbation theory (BSPT). The effective cutoff, \lam^2, is fixed, and the limit, 0 \longleftarrow m^2 \alpha^2\ll \lam^2 \ll m^2 \alpha \longrightarrow \infty, is taken. This upper bound on \lam^2 places the effects of low-energy (energy transfer below \lam) emission in the effective interactions in the $| e {\overline e} >$ sector. This lower bound on \lam^2 insures that the nonperturbative scale of interest is not removed by the similarity transformation. As an explicit example of the general formalism introduced, we show that the Hamiltonian renormalized to $O(\alpha)$ reproduces the exact spectrum of spin splittings, with degeneracies dictated by rotational symmetry, for the ground state through $O(\alpha^4)$. The entire calculation is performed analytically, and gives the well known singlet-triplet ground state spin splitting of positronium, $7/6 \alpha^2 Ryd$. We discuss remaining corrections other than the spin splittings and how they can be treated in calculating the spectrum with higher precision.Comment: 46 pages, latex, 3 Postscript figures included, section on remaining corrections added, title changed, error in older version corrected, cutoff placed in a windo

Addition theorems for spin spherical harmonics. II Results

Based on the results of part I, we obtain the general form of the addition theorem for spin spherical harmonics and give explicit results in the cases involving one spin-$s'$ and one spin-$s$ spherical harmonics with $s',s=1/2$, 1, 3/2, and $|s'-s|=0$, 1. We obtain also a fully general addition theorem for one scalar and one tensor spherical harmonic of arbitrary rank. A variety of bilocal sums of ordinary and spin spherical harmonics are given in explicit form, including a general explicit expression for bilocal spherical harmonics