Exact Likelihoods for N-mixture models with Time-to-Detection Data

This paper is concerned with the formulation of $N$-mixture models for estimating the abundance and probability of detection of a species from binary response, count and time-to-detection data. A modelling framework, which encompasses time-to-first-detection within the context of detection/non-detection and time-to-each-detection and time-to-first-detection within the context of count data, is introduced. Two observation processes which depend on whether or not double counting is assumed to occur are also considered. The main focus of the paper is on the derivation of explicit forms for the likelihoods associated with each of the proposed models. Closed-form expressions for the likelihoods associated with time-to-detection data are new and are developed from the theory of order statistics. A key finding of the study is that, based on the assumption of no double counting, the likelihoods associated with times-to-detection together with count data are the product of the likelihood for the counts alone and a term which depends on the detection probability parameter. This result demonstrates that, in this case, recording times-to-detection could well improve precision in estimation over recording counts alone. In contrast, for the double counting protocol with exponential arrival times, no information was found to be gained by recording times-to-detection in addition to the count data. An R package and an accompanying vignette are also introduced in order to complement the algebraic results and to demonstrate the use of the models in practice.Comment: 21 pages, 1 figur

The beta function of the multichannel Kondo model

The beta function of the multichannel Kondo model is calculated exactly in the limit of large spin N and channel number M=gamma*N, with constant gamma. There are no corrections in any finite order of 1/N. One zero is found at a finite coupling strength, showing directly the Non--Fermi liquid behavior of the model. This renormalization group flow allows to introduce a variational principle for the entropy, to obtain the low temperature thermodynamics. Such in particular the low temperature thermodynamics of the non--crossing approximation to the Kondo model becomes accessible.Comment: 4 page

Counting chirps : acoustic monitoring of cryptic frogs

Funding for the frog survey was received from the National Geographic Society/Waitt Grants Program (No. W184-11). The EPSRC and NERC helped to fund this research through a PhD grant (No. EP/1000917/1) to D.L.B. R.A. and G.J.M. acknowledge initiative funding from the National Research Foundation of South Africa.1 .  Global amphibian declines have resulted in a vital need for monitoring programmes that follow population trends. Monitoring using advertisement calls is ideal as choruses are undisturbed during data collection. However, methods currently employed by managers frequently rely on trained observers, and/or do not provide density data on which to base trends. 2 .  This study explores the utility of monitoring using acoustic spatially explicit capture-recapture (aSECR) with time of arrival (ToA) and signal strength (SS) as a quantitative monitoring technique to measure call density of a threatened but visually cryptic anuran, the Cape peninsula moss frog Arthroleptella lightfooti. 3 .  The relationships between temporal and environmental variables (date, rainfall, temperature) and A. lightfooti call density at three study sites on the Cape peninsula, South Africa were examined. Acoustic data, collected from an array of six microphones over four months during the winter breeding season, provided a time series of call density estimates. 4 .  Model selection indicated that call density was primarily associated with seasonality fitted as a quadratic function. Call density peaked mid-breeding season. At the main study site, the lowest recorded mean call density (0·160 calls m-2 min-1) occurred in May and reached its peak mid-July (1·259 calls m-2 min-1). The sites differed in call density, but also the effective sampling area. 5 .  Synthesis and applications.The monitoring technique, acoustic spatially explicit capture–recapture (aSCR), quantitatively estimates call density without disturbing the calling animals or their environment, while time of arrival (ToA) and signal strength (SS) significantly add to the accuracy of call localisation, which in turn increases precision of call density estimates without the need for specialist field staff. This technique appears ideally suited to aid the monitoring of visually cryptic, acoustically active species.Publisher PDFPeer reviewe

Kinks in the Kondo problem

We find the exact quasiparticle spectrum for the continuum Kondo problem of $k$ species of electrons coupled to an impurity of spin $S$. In this description, the impurity becomes an immobile quasiparticle sitting on the boundary. The particles are ``kinks'', which can be thought of as field configurations interpolating between adjacent wells of a potential with $k+1$ degenerate minima. For the overscreened case $k>2S$, the boundary has this kink structure as well, which explains the non-integer number of boundary states previously observed. Using simple arguments along with the consistency requirements of an integrable theory, we find the exact elastic $S$-matrix for the quasiparticles scattering among themselves and off of the boundary. This allows the calculation of the exact free energy, which agrees with the known Bethe ansatz solution.Comment: 9 pages +1 figur

Measurements of the 12C/13C ratio in Planetary Nebulae and implications for stellar evolution

We present the results of a study aimed at determining the 12C/13C ratio in two samples of planetary nebuale (PNe) by means of mm-wave observations of 12CO and 13CO. The first group includes six PNe which have been observed in the 3He+ hyperfine transition; the other group consists of 23 nebulae with rich molecular envelopes. We have determined the isotopic ratio in 14 objects and the results indicate a range of values between 9 and 23. In particular, three PNe have ratios well below the value predicted by standard evolutionary models (about 20), indicating that some extra-mixing process has occurred in these stars. We briefly discuss the implications of our results for standard and nonstandard stellar nucleosynthesis.Comment: 8 pages, LaTeX, 1 Postscript figure. to appear in The Primordial Nuclei and Their Galactic Evolution, eds. N. Prantzos, M. Tosi, R. von Steiger (Kluwer: Dordrecht

The Effective Particle-Hole Interaction and the Optical Response of Simple Metal Clusters

Following Sham and Rice [L. J. Sham, T. M. Rice, Phys. Rev. 144 (1966) 708] the correlated motion of particle-hole pairs is studied, starting from the general two-particle Greens function. In this way we derive a matrix equation for eigenvalues and wave functions, respectively, of the general type of collective excitation of a N-particle system. The interplay between excitons and plasmons is fully described by this new set of equations. As a by-product we obtain - at least a-posteriori - a justification for the use of the TDLDA for simple-metal clusters.Comment: RevTeX, 15 pages, 5 figures in uufiles format, 1 figure avaible from [email protected]

On the Corrections to Dashen's Theorem

The electromagnetic corrections to the masses of the pseudoscalar mesons $\pi$ and $K$ are considered. We calculate in chiral perturbation theory the contributions which arise from resonances within a photon loop at order $O(e^2 m_q)$. Within this approach we find rather moderate deviations to Dashen's theorem.Comment: 14 pages, sligthly enlarged version; a numerical error is corrected and the embedding of the figures is improved. The complete paper, including figures, is also available via anonymous ftp at ftp://www-ttp.physik.uni-karlsruhe.de/ , or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints/; to be published in Phys.Rev.

A general framework for animal density estimation from acoustic detections across a fixed microphone array

Acoustic monitoring can be an efficient, cheap, non‐invasive alternative to physical trapping of individuals. Spatially explicit capture–recapture (SECR) methods have been proposed to estimate calling animal abundance and density from data collected by a fixed array of microphones. However, these methods make some assumptions that are unlikely to hold in many situations, and the consequences of violating these are yet to be investigated. We generalize existing acoustic SECR methodology, enabling these methods to be used in a much wider variety of situations. We incorporate time‐of‐arrival (TOA) data collected by the microphone array, increasing the precision of calling animal density estimates. We use our method to estimate calling male density of the Cape Peninsula Moss Frog Arthroleptella lightfooti. Our method gives rise to an estimator of calling animal density that has negligible bias, and 95% confidence intervals with appropriate coverage. We show that using TOA information can substantially improve estimate precision. Our analysis of the A. lightfooti data provides the first statistically rigorous estimate of calling male density for an anuran population using a microphone array. This method fills a methodological gap in the monitoring of frog populations and is applicable to acoustic monitoring of other species that call or vocalize

First-trimester or second-trimester screening, or both, for Down's syndrome

BACKGROUND: It is uncertain how best to screen pregnant women for the presence of fetal Down's syndrome: to perform first-trimester screening, to perform second-trimester screening, or to use strategies incorporating measurements in both trimesters.METHODS: Women with singleton pregnancies underwent first-trimester combined screening (measurement of nuchal translucency, pregnancy-associated plasma protein A [PAPP-A], and the free beta subunit of human chorionic gonadotropin at 10 weeks 3 days through 13 weeks 6 days of gestation) and second-trimester quadruple screening (measurement of alpha-fetoprotein, total human chorionic gonadotropin, unconjugated estriol, and inhibin A at 15 through 18 weeks of gestation). We compared the results of stepwise sequential screening (risk results provided after each test), fully integrated screening (single risk result provided), and serum integrated screening (identical to fully integrated screening, but without nuchal translucency).RESULTS: First-trimester screening was performed in 38,167 patients; 117 had a fetus with Down's syndrome. At a 5 percent false positive rate, the rates of detection of Down's syndrome were as follows: with first-trimester combined screening, 87 percent, 85 percent, and 82 percent for measurements performed at 11, 12, and 13 weeks, respectively; with second-trimester quadruple screening, 81 percent; with stepwise sequential screening, 95 percent; with serum integrated screening, 88 percent; and with fully integrated screening with first-trimester measurements performed at 11 weeks, 96 percent. Paired comparisons found significant differences between the tests, except for the comparison between serum integrated screening and combined screening.CONCLUSIONS: First-trimester combined screening at 11 weeks of gestation is better than second-trimester quadruple screening but at 13 weeks has results similar to second-trimester quadruple screening. Both stepwise sequential screening and fully integrated screening have high rates of detection of Down's syndrome, with low false positive rates