Extending the Latent Multinomial Model with Complex Error Processes and Dynamic Markov Bases

The latent multinomial model (LMM) model of Link et al. (2010) provided a general framework for modelling mark-recapture data with potential errors in identification. Key to this approach was a Markov chain Monte Carlo (MCMC) scheme for sampling possible configurations of the counts true capture histories that could have generated the observed data. This MCMC algorithm used vectors from a basis for the kernel of the linear map between the true and observed counts to move between the possible configurations of the true data. Schofield and Bonner (2015) showed that a strict basis was sufficient for some models of the errors, including the model presented by Link et al. (2010), but a larger set called a Markov basis may be required for more complex models. We address two further challenges with this approach: 1) that models with more complex error mechanisms do not fit easily within the LMM and 2) that the Markov basis can be difficult or impossible to compute for even moderate sized studies. We address these issues by extending the LMM to separately model the capture/demographic process and the error process and by developing a new MCMC sampling scheme using dynamic Markov bases. Our work is motivated by a study of Queen snakes (Regina septemvittata) in Kentucky, USA, and we use simulation to compare the use of PIT tags, with perfect identification, and brands, which are prone to error, when estimating survival rates

Symmetric quivers, invariant theory, and saturation theorems for the classical groups

Let G denote either a special orthogonal group or a symplectic group defined over the complex numbers. We prove the following saturation result for G: given dominant weights \lambda^1, ..., \lambda^r such that the tensor product V_{N\lambda^1} \otimes ... \otimes V_{N\lambda^r} contains nonzero G-invariants for some N \ge 1, we show that the tensor product V_{2\lambda^1} \otimes ... \otimes V_{2\lambda^r} also contains nonzero G-invariants. This extends results of Kapovich-Millson and Belkale-Kumar and complements similar results for the general linear group due to Knutson-Tao and Derksen-Weyman. Our techniques involve the invariant theory of quivers equipped with an involution and the generic representation theory of certain quivers with relations.Comment: 29 pages, no figures; v2: updated Theorem 2.4 to odd characteristic, added Remark 3.9, added references, corrected some definitions and typo

Exact location of dopants below the Si(001):H surface from scanning tunnelling microscopy and density functional theory

Control of dopants in silicon remains the most important approach to tailoring the properties of electronic materials for integrated circuits, with Group V impurities the most important n-type dopants. At the same time, silicon is finding new applications in coherent quantum devices, thanks to the magnetically quiet environment it provides for the impurity orbitals. The ionization energies and the shape of the dopant orbitals depend on the surfaces and interfaces with which they interact. The location of the dopant and local environment effects will therefore determine the functionality of both future quantum information processors and next-generation semiconductor devices. Here we match observed dopant wavefunctions from low-temperature scanning tunnelling microscopy (STM) to images simulated from first-principles density functional theory (DFT) calculations. By this combination of experiment and theory we precisely determine the substitutional sites of neutral As dopants between 5 and 15A below the Si(001):H surface. In the process we gain a full understanding of the interaction of the donor-electron state with the surface, and hence of the transition between the bulk dopant (with its delocalised hydrogenic orbital) and the previously studied dopants in the surface layer.Comment: 12 pages; accepted for publication in Phys. Rev.

Atmospheric mercury in the Latrobe Valley, Australia : case study June 2013

Gaseous elemental mercury observations were conducted at Churchill, Victoria, in Australia from April to July, 2013, using a Tekran 2537 analyzer. A strong diurnal variation with daytime average values of 1.2–1.3 ng m–3 and nighttime average values of 1.6–1.8 ng m–3 was observed. These values are significantly higher than the Southern Hemisphere average of 0.85–1.05 ng m–3. Churchill is in the Latrobe Valley, approximately 150 km East of Melbourne, where approximately 80% of Victoria’s electricity is generated from low-rank brown coal from four major power stations: Loy Yang A, Loy Yang B, Hazelwood, and Yallourn. These aging generators do not have any sulfur, nitrogen oxide, or mercury air pollution controls. Mercury emitted in the 2015–2016 year in the Latrobe Valley is estimated to have had an externalized health cost of $AUD88 million. Air pollution mercury simulations were conducted using the Weather Research and Forecast model with Chemistry at 3 × 3 km resolution. Electrical power generation emissions were added using mercury emissions created from the National Energy Market’s 5-min energy distribution data. The strong diurnal cycle in the observed mercury was well simulated (R2 ¼ .49 and P value ¼ 0.00) when soil mercury emissions arising from several years of wet and dry deposition in a radius around the power generators was included in the model, as has been observed around aging lignite coal power generators elsewhere. These results indicate that long-term air and soil sampling in power generation regions, even after the closure of coal fired power stations, will have important implications to understanding the airborne mercury emissions sources. Copyright: © 2021 The Author(s). **Please note that there are multiple authors for this article therefore only the name of the first 5 including Federation University Australia affiliate “Melita Keywood” is provided in this record*

Impacts of a Recurrent Resuspension Event and Variable Phytoplankton Community Composition On Remote Sensing Reflectance

In order to characterize the impact of turbidity plumes on optical and biological dynamics, a suite of environmental parameters were measured in southern Lake Michigan during the springtime recurrent sediment plume. In-water measurements of inherent optical properties (IOPs) were entered into the Hydrolight 4.2 radiative transfer model and the output was compared with measured apparent optical properties (AOPs) across a wide range of optical conditions. Hydrolight output and measured underwater light fields were then used to clarify the effects of the sediment plume on primary production, phytoplankton community composition, and nearshore remote sensing ocean color algorithms. Our results show that the sediment plume had a negligible effect on the spectral light environment and phytoplankton physiology. The plume did not significantly alter the spectral quality of available light and did not lead to light limited phytoplankton populations compared to non-plume conditions. Further, the suspended sediment in the plume did not seriously impact the performance of ocean color algorithms. We evaluated several currently employed chlorophyll algorithms and demonstrated that the main factor compromising the efficacy of these algorithms was the composition of phytoplankton populations. As phycobilin-containing algae became the dominant species, chlorophyll algorithms that use traditional blue/green reflectance ratios were compromised due to the high absorption of green light by phycobilin pigments. This is a notable difficulty in coastal areas, which have highly variable phytoplankton composition and are often dominated by sharp fronts of phycobilin and non-phycobilin containing algae

Bismuth trichloride as a molecular precursor for silicon doping

Dopant impurity species can be incorporated into the silicon (001) surface via the adsorption and dissociation of simple precursor molecules. Examples include phosphine (PH3), arsine (AsH3), and diborane (B2H6) for the incorporation of phosphorus, arsenic, and boron, respectively. Through exploitation of precursor surface chemistry, the spatial locations of these incorporated dopants can be controlled at the atomic scale via the patterning of a hydrogen lithographic resist layer using scanning tunneling microscopy (STM). There is strong interest in the spatial control of bismuth atoms incorporated into silicon for quantum technological applications; however, there is currently no known precursor for the incorporation of bismuth that is compatible with this STM-based lithographic method. Here, we explore the precursor chemistry (adsorption, diffusion, and dissociation) of bismuth trichloride (BiCl3) on Si(001). We show atomic-resolution STM images of BiCl3 exposed Si(001) surfaces at low coverage and combine this with density functional theory calculations to produce a model of the surface processes and the observed features. Our results show that, at room temperature, BiCl3 completely dissociates to produce bismuth ad-atoms, ad-dimers, and surface-bound chlorine, and we explain how BiCl3 is a strong candidate for a bismuth precursor compound compatible with lithographic patterning at the sub-nanometer scale