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Graphical models and likelihood ratios can be used by forensic scientists to compare support given by evidence to propositions put forward by competing parties during court proceedings. Such models can also be used to evaluate support for activity-level propositions, i.e. propositions that refer to the nature of activities associated with evidence and how this evidence came to be at a crime scene. Graphical methods can be used to show explicitly different scenarios that might explain the evidence in a case and to distinguish between evidence requiring evaluation by a jury and quantifiable evidence from the crime scene. Such visual representations can be helpful for forensic practitioners, the police and lawyers who may need to assess the value that different pieces of evidence make to their arguments in a case. In this paper we demonstrate for the first time how chain event graphs can be applied to a criminal case involving drug trafficking. We show how different types of evidence (i.e. expert judgement and data collected from a crime scene) can be combined using a chain event graph and show how the hierarchical model deriving from the graph can be used to evaluate the degree of support for different activity-level propositions in the case. We also develop a modification of the standard chain event graph to simplify their use in forensic applications.

We compare three graphical methods for displaying evidence in a legal case: Wigmore Charts, Bayesian Networks and Chain Event Graphs. We find that these methods are aimed at three distinct audiences, respectively lawyers, forensic scientists and the police. The methods are illustrated using part of the evidence in the case of the murder of Meredith Kercher. More specifically, we focus on representing the list of propositions, evidence, testimony and facts given in the first trial against Raffaele Sollecito and Amanda Knox with these graphical methodologies.

In pharmaceutical therapeutic design or toxicology, accurately predicting the permeation of chemicals through human epithelial tissues is crucial, where permeation is significantly influenced by the tissue's cellular architecture. Current mathematical models for multi-layered epithelium such as the oral mucosa only use simplistic 'bricks and mortar' geometries and therefore do not account for the complex cellular architecture of these tissues at the microscale level, such as the extensive plasma membrane convolutions that define the extracellular spaces between cells. Chemicals often permeate tissues via this paracellular route, meaning that permeation is underestimated. To address this, measurements of human buccal mucosal tissue were conducted to ascertain the width and tortuosity of extracellular spaces across the epithelium. Using mechanistic mathematical modelling, we show that the convoluted geometry of extracellular spaces significantly impacts chemical permeation and that this can be approximated, provided that extracellular tortuosity is accounted for. We next developed an advanced physically-relevant in silico model of oral mucosal chemical permeation using partial differential equations, fitted to chemical permeation in vitro assays on tissue-engineered human oral mucosa. Tissue geometries were measured and captured in silico, and permeation examined and predicted for chemicals with different physicochemical properties. The effect of altering the extracellular space to mimic permeation enhancers was also assessed by perturbing the in silico model. This novel in vitro-in silico approach has the potential to expedite pharmaceutical innovation for testing oromucosal chemical permeation, providing a more accurate, physiologically-relevant model which can reduce animal testing with early screening based on chemical properties.

Recent computational studies have predicted many new ternary nitrides, revealing synthetic opportunities in this underexplored phase space. However, synthesizing new ternary nitrides is difficult, in part because intermediate and product phases often have high cohesive energies that inhibit diffusion. Here, we report the synthesis of two new phases, calcium zirconium nitride (CaZrN$_2$) and calcium hafnium nitride (CaHfN$_2$), by solid state metathesis reactions between Ca$_3$N$_2$ and $M$Cl$_4$ ($M$ = Zr, Hf). Although the reaction nominally proceeds to the target phases in a 1:1 ratio of the precursors via Ca$_3$N$_2$ + $M$Cl$_4$ $\rightarrow$ Ca$M$N$_2$ + 2 CaCl$_2$, reactions prepared this way result in Ca-poor materials (Ca$_xM_{2-x}$N$_2$, $x<1$). A small excess of Ca$_3$N$_2$ (ca. 20 mol\%) is needed to yield stoichiometric Ca$M$N$_2$, as confirmed by high-resolution synchrotron powder X-ray diffraction. In situ synchrotron X-ray diffraction studies reveal that nominally stoichiometric reactions produce Zr$^{3+}$ intermediates early in the reaction pathway, and the excess Ca$_3$N$_2$ is needed to reoxidize Zr$^{3+}$ intermediates back to the Zr$^{4+}$ oxidation state of CaZrN$_2$. Analysis of computationally-derived chemical potential diagrams rationalizes this synthetic approach and its contrast from the synthesis of MgZrN$_2$. These findings additionally highlight the utility of in situ diffraction studies and computational thermochemistry to provide mechanistic guidance for synthesis.

Blueshifts - or, more accurately, blue asymmetries - in broad emission lines such as CIV $\lambda$1550 are common in luminous quasars and correlate with fundamental properties such as Eddington ratio and broad absorption line (BAL) characteristics. However, the formation of these blueshifts is still not understood, and neither is their physical connection to the BAL phenomenon or accretion disc. In this work, we present Monte Carlo radiative transfer and photoionization simulations using parametrized biconical disc-wind models. We take advantage of the azimuthal symmetry of a quasar and show that we can reproduce CIV blueshifts provided that (i) the disc-midplane is optically thick out to radii beyond the line formation region, so that the receding wind bicone is obscured; and (ii) the system is viewed from relatively low (that is, more face-on) inclinations ($\lesssim40^\circ$). We show that CIV emission line blueshifts and BALs can form in the same wind structure. The velocity profile of the wind has a significant impact on the location of the line formation region and the resulting line profile, suggesting that the shape of the emission lines can be used as a probe of wind-driving physics. While we are successful at producing blueshifts/blue asymmetries in outflows, we struggle to match the detailed shape or skew of the observed emission line profiles. In addition, our models produce redshifted emission-line asymmetries for certain viewing angles. We discuss our work in the context of the CIV $\lambda$1550 emission blueshift versus equivalent-width space and explore the implications for quasar disc wind physics., Comment: 20 pages, 12 figures + 1 appendix. Supplementary material, simulation data and plotting scripts available at: https://github.com/jhmatthews/blueshifts

Resource adequacy studies typically use standard metrics such as Loss of Load Expectation and Expected Energy Unserved to quantify the risk of supply shortfalls. This paper critiques present approaches to adequacy assessment and capacity procurement in terms of their relevance to decision maker interests, before demonstrating alternatives including risk-averse metrics and visualisations of wider risk profile. This is illustrated with results for a Great Britain example, in which the risk profile varies substantially with the installed capacity of wind generation. This paper goes beyond previous literature through its critical discussion of how current practices reflect decision maker interests; and how decision making can be improved using a broader range of outputs available from standard models., Comment: 23 pages, 4 figures

In active galactic nuclei, the relationship between UV and X-ray luminosity is well studied (often characterised by $\alpha_\text{ox}$) but often with heterogeneous samples. We have parametrized the intrinsic distribution of X-ray luminosity, $L_\text{X}$, for the optically-selected sample of SDSS quasars in the Stripe 82 and XXL fields across redshifts 0.5-3.5. We make use of the available XMM observations and a custom pipeline to produce Bayesian sensitivity curves that are used to derive the intrinsic X-ray distribution in a hierarchical Bayesian framework. We find that the X-ray luminosity distribution is well described by a Gaussian function in ${\log_{10}}L_\text{X}$ space with a mean that is dependent on the monochromatic 2500A UV luminosity, $L_{2500}$. We also observe some redshift dependence of the distribution. The mean of the $L_\text{X}$ distribution increases with redshift while the width decreases. This weak but significant redshift dependence leads to $L_{2500}$-$L_\text{X}$ and $L_{2500}$-$\alpha_\text{ox}$ relations that evolve with redshift, and we produce a redshift- and $L_{2500}$-dependent $\alpha_\text{ox}$ equation. The increasing average black hole mass with redshift in our sample points to black hole mass as a potential driver of the redshift evolution., Comment: 16 pages, 13 figures. Submitted to MNRAS

In many stochastic service systems, decision-makers find themselves making a sequence of decisions, with the number of decisions being unpredictable. To enhance these decisions, it is crucial to uncover the causal impact these decisions have through careful analysis of observational data from the system. However, these decisions are not made independently, as they are shaped by previous decisions and outcomes. This phenomenon is called sequential bias and violates a key assumption in causal inference that one person's decision does not interfere with the potential outcomes of another. To address this issue, we establish a connection between sequential bias and the subfield of causal inference known as dynamic treatment regimes. We expand these frameworks to account for the random number of decisions by modeling the decision-making process as a marked point process. Consequently, we can define and identify causal effects to quantify sequential bias. Moreover, we propose estimators and explore their properties, including double robustness and semiparametric efficiency. In a case study of 27,831 encounters with a large academic emergency department, we use our approach to demonstrate that the decision to route a patient to an area for low acuity patients has a significant impact on the care of future patients.