The immune response to Mycobacterium tuberculosis (Mtb) infection is the formation of multicellular lesions, or granolomas, in the lung of the individual. However, the structure of the granulomas and the spatial distribution of the immune cells within is not well understood. In this paper we develop a mathematical model investigating the early and initial immune response to Mtb. The model consists of coupled reaction-diffusion-advection partial differential equations governing the dynamics of the relevant macrophage and bacteria populations and a bacteria-produced chemokine. Our novel application of mathematical concepts of internal states and internal velocity allows us to begin to study this unique immunological structure. Volume changes resulting from proliferation and death terms generate a velocity field by which all cells are transported within the forming granuloma. We present numerical results for two distinct infection outcomes: controlled and uncontrolled granuloma growth. Using a simplified model we are able to analytically determine conditions under which the bacteria population decreases, representing early clearance of infection, or grows, representing the initial stages of granuloma formation.

Abstract. The use of different mathematical tools to study biological processes is necessary to capture effects occurring at different scales. Here we study as an example the immune response to infection with the bacteria Mycobacterium tuberculosis, the causative agent of tuberculosis (TB). Immune responses are both global (lymph nodes, blood, and spleen) as well as local (site of infection) in nature. Interestingly, the immune response in TB at the site of infection results in the formation of spherical structures comprised of cells, bacteria, and effector molecules known as granulomas. In this work, we use four different mathematical tools to explore both the global immune response as well as the more local one (granuloma formation) and compare and contrast results obtained using these methods. Applying a range of approaches from continuous deterministic models to discrete stochastic ones allows us to make predictions and suggest hypotheses about the underlying biology that might otherwise go unnoticed. The tools developed and applied here are also applicable in other settings such as tumor modeling.

The tumour suppressor gene, p53, plays an important role in tumour development. Under low levels of oxygen (hypoxia), cells expressing wild-type p53 undergo programmed cell death (apoptosis), whereas cells expressing mutations in the p53 gene may survive and express angiogenic growth factors that stimulate tumour vascularization. Given that cells expressing mutations in the p53 gene have been observed in many forms of human tumour, it is important to understand how both wild-type and mutant cells react to hypoxic conditions. In this paper a mathematical model is presented to investigate the effects of alternating periods of hypoxia and normoxia (normal oxygen levels) on a population of wild-type and mutant p53 tumour cells. The model consists of three coupled ordinary differential equations that describe the densities of the two cell types and the oxygen concentration and, as such, may describe the growth of avascular tumours in vitro and/or in vivo. Numerical and analytical techniques are used to determine how changes in the system parameters influence the time at which mutant cells become dominant within the population. A feedback mechanism, which switches off the oxygen supply when the total cell density exceeds a threshold value, is introduced into the model to investigate the impact that vessel collapse (and the associated hypoxia) has on the time at which the mutant cells become dominant within vascular tumours growing in vivo. Using the model we can predict the time it takes for a subpopulation of mutant p53 tumour cells to become the dominant population within either an avascular tumour or a localized region of a vascular tumour. Based on independent experimental results, our model suggests that the mutant population becomes dominant more quickly in vivo than in vitro (12 days vs 17 days).

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Previous studies have focused on the biases and feedback loops that occur in predictive policing algorithms. These studies show how systemically and institutionally biased data leads to these feedback loops when predictive policing algorithms are applied in real life.We take a step back, and show that the choice in algorithm can be embedded in a specific criminological theory, and that the choice of a model on its own even without biased data can create biased feedback loops. By synthesizing "historical" data, in which we control the relationships between crimes, location and time, we show that the current predictive policing algorithms create biased feedback loops even with completely random data. We then review the process of creation and deployment of these predictive systems, and highlight when good practices, such as fitting a model to data, "go bad" within the context of larger system development and deployment. Using best practices from previous work on assessing and mitigating the impact of new technologies, we highlight where the design of these algorithms has broken down. The study also found that multidisciplinary analysis of such systems is vital for uncovering these issues and shows that any study of equitable AI should involve a systematic and holistic analysis of their design rationalities. CCS Concepts: • Applied computing → Law, social and behavioral sciences; • Software and its engineering → Designing software; • Theory of computation → Models of computation.

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As many domains employ ever more complex systems-of-systems, capturing provenance among component systems is increasingly important. Applications such as intrusion detection, load balancing, traffic routing, and insider threat detection all involve monitoring and analyzing the data provenance. Implicit in these applications is the assumption that "good" provenance is captured (e.g. complete provenance graphs, or one full path). When attempting to provide "good" provenance for a complex system of systems, it is necessary to know "how hard" the provenance-enabling will be and the likely quality of the provenance to be produced. In this work, we provide analytical results and simulation tools to assist in the scoping of the provenance enabling process. We provide use cases of complex systems-of-systems within which users wish to capture provenance. We describe the parameters that must be taken into account when undertaking the provenance-enabling of a system of systems. We provide a tool that models the interactions and types of capture agents involved in a complex systems-of-systems, including the set of known and unknown systems in the environment. The tool provides an estimation of quantity and type of capture agents that will need to be deployed for provenance-enablement in a complex system that is not completely known.

In many laboratories during an undergraduate science education, students are given a set of procedures to follow to obtain a pre‐determined outcome. Often students give little thought to the underlying scientific principles and lack a true understanding of the experimental protocol. Not only does this laboratory format not represent ‘real’ science, it leaves students unprepared for the often unpredictable and intimidating nature of experimental design. Here we have chosen classic biochemical experiments paired with computational modeling approaches to help students navigate the process of designing an experiment, from initial planning to hypothesis development to data analysis. Students can use the modeling mechanisms to help predict experimental outcomes and gain a better understanding of scientific concepts.