Hydrogen lithography has been used to template phosphine-based surface chemistry to fabricate atomic-scale devices, a process we abbreviate as atomic precision advanced manufacturing (APAM). Here, we use mid-infrared variable angle spectroscopic ellipsometry (IR-VASE) to characterize single-nanometer thickness phosphorus dopant layers (δ-layers) in silicon made using APAM compatible processes. A large Drude response is directly attributable to the δ-layer and can be used for nondestructive monitoring of the condition of the APAM layer when integrating additional processing steps. The carrier density and mobility extracted from our room temperature IR-VASE measurements are consistent with cryogenic magneto-transport measurements, showing that APAM δ-layers function at room temperature. Finally, the permittivity extracted from these measurements shows that the doping in the APAM δ-layers is so large that their low-frequency in-plane response is reminiscent of a silicide. However, there is no indication of a plasma resonance, likely due to reduced dimensionality and/or low scattering lifetime.

In a singularly perturbed limit, we analyse the existence and linear stability of steady-state hotspot solutions for an extension of the 1-D three-component reaction-diffusion (RD) system formulated and studied numerically in Jones et. al. [Math. Models. Meth. Appl. Sci., 20, Suppl., (2010)], which models urban crime with police intervention. In our extended RD model, the field variables are the attractiveness field for burglary, the criminal population density and the police population density. Our model includes a scalar parameter that determines the strength of the police drift towards maxima of the attractiveness field. For a special choice of this parameter, we recover the ‘cops-on-the-dots’ policing strategy of Jones et. al., where the police mimic the drift of the criminals towards maxima of the attractiveness field. For our extended model, the method of matched asymptotic expansions is used to construct 1-D steady-state hotspot patterns as well as to derive nonlocal eigenvalue problems (NLEPs) that characterise the linear stability of these hotspot steady states to ${\cal O}$ (1) timescale instabilities. For a cops-on-the-dots policing strategy, we prove that a multi-hotspot steady state is linearly stable to synchronous perturbations of the hotspot amplitudes. Alternatively, for asynchronous perturbations of the hotspot amplitudes, a hybrid analytical–numerical method is used to construct linear stability phase diagrams in the police vs. criminal diffusivity parameter space. In one particular region of these phase diagrams, the hotspot steady states are shown to be unstable to asynchronous oscillatory instabilities in the hotspot amplitudes that arise from a Hopf bifurcation. Within the context of our model, this provides a parameter range where the effect of a cops-on-the-dots policing strategy is to only displace crime temporally between neighbouring spatial regions. Our hybrid approach to study the NLEPs combines rigorous spectral results with a numerical parameterisation of any Hopf bifurcation threshold. For the cops-on-the-dots policing strategy, our linear stability predictions for steady-state hotspot patterns are confirmed from full numerical PDE simulations of the three-component RD system.

Domestic dogs display complex roaming behaviours, which need to be captured to more realistically model the spread of rabies. We have previously shown that roaming behaviours of domestic dogs can be categorised as stay-at-home, roamer and explorer in the Northern Peninsular Area (NPA), Queensland, Australia. These roaming behaviours are likely to cause heterogeneous contact rates that influence the speed or pattern of rabies spread in a dog population. The aim of this study was to define contact spatial kernels using the overlap of individual dog utilisation distributions to describe the daily probability of contact between pairs of dogs exhibiting these three a priori roaming behaviours. We further aimed to determine if the kernels lead to different predicted rabies outbreaks (outbreak duration and number of rabid dogs) by incorporating the spatial kernels into a previously developed rabies spread model for the NPA. Spatial kernels created with both dogs in a pair being explorers or one dog explorer and one dog roamer (who roamed away from their residence) produced short but large outbreaks compared with spatial kernels with at least one stay-at-home dog. Outputs from this model incorporating heterogeneous contacts demonstrate how roaming behaviours influence disease spread in domestic dog populations.

We introduce a Bayesian approach to conduct inferential analyses on dyadic data while accounting for interdependencies between observations through a set of additive and multiplicative effects (AME). The AME model is built on a generalized linear modeling framework and is thus flexible enough to be applied to a variety of contexts. We contrast the AME model to two prominent approaches in the literature: the latent space model (LSM) and the exponential random graph model (ERGM). Relative to these approaches, we show that the AME approach is (a) to be easy to implement; (b) interpretable in a general linear model framework; (c) computationally straightforward; (d) not prone to degeneracy; (e) captures first-, second-, and third-order network dependencies; and (f) notably outperforms ERGMs and LSMs on a variety of metrics and in an out-of-sample context. In summary, AME offers a straightforward way to undertake nuanced, principled inferential network analysis for a wide range of social science questions.