A mathematical model is used to investigate the effectiveness of the chemotherapy drug Topotecan against neuroblastoma. Optimal control theory is applied to minimize the tumor volume and the amount of drug utilized. The model incorporates a state constraint that requires the level of circulating neutrophils (white blood cells that form an integral part of the immune system) to remain above an acceptable value. The treatment schedule is designed to simultaneously satisfy this constraint and achieve the best results in fighting the tumor. Existence and uniqueness of the solution of the optimality system, which is the state system coupled with the adjoint system, is established. Numerical simulations are given to demonstrate the behavior of the tumor and the immune system components represented in the model.

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Abstract. In this paper, we look at a model depicting the relationship of cancer cells in different development stages with immune cells and a cell cycle specific chemotherapy drug. The model includes a constant delay in the mitotic phase. By applying optimal control theory, we seek to minimize the cost associated with the chemotherapy drug and to minimize the number of tumor cells. Global existence of a solution has been shown for this model and existence of an optimal control has also been proven. Optimality conditions and characterization of the control are discussed.

Several studies have shown that the use of active learning strategies can help improve student success and persistence in STEM-related fields. Despite this, widespread adoption of active learning strategies is not yet a reality as institutional change can be difficult to enact. Accordingly, it is important to understand how departments in institutions of higher education can initiate and sustain meaningful change. We use interview data collected from two institutions to examine how leaders at two universities contributed to the initiation, implementation, and sustainability of active learning in undergraduate calculus and precalculus courses. At each institution, we spoke to 27 stakeholders involved in changes (including administrators, department chairs, course coordinators, instructors, and students). Our results show that the success of these changes rested on the ability of leaders to stimulate significant cultural shifts within the mathematics department. We use communities of transformation theory and the four-frame model of organization change in STEM departments in order to better understand how leaders enabled such cultural shifts. Our study highlights actions leaders may take to support efforts at improving education by normalizing the use of active learning strategies and provides potential reasons for the efficacy of such actions. These results underscore the importance of establishing flexible, distributed leadership models that attend to the cultural and operational norms of a department. Such results may inform leaders at other institutions looking to improve education in their STEM departments.

Diffuse midline gliomas (DMG) harbouring H3K27M mutation are paediatric tumours with a dismal outcome. Recently, a new subtype of midline gliomas has been described with similar features to DMG, including loss of H3K27 trimethylation, but lacking the canonical H3K27M mutation (H3-WT). Here, we report a cohort of five H3-WT tumours profiled by whole-genome sequencing, RNA sequencing and DNA methylation profiling and combine their analysis with previously published cases. We show that these tumours have recurrent and mutually exclusive mutations in either ACVR1 or EGFR and are characterised by high expression of EZHIP associated to its promoter hypomethylation. Affected patients share a similar poor prognosis as patients with H3K27M DMG. Global molecular analysis of H3-WT and H3K27M DMG reveal distinct transcriptome and methylome profiles including differential methylation of homeobox genes involved in development and cellular differentiation. Patients have distinct clinical features, with a trend demonstrating ACVR1 mutations occurring in H3-WT tumours at an older age. This in-depth exploration of H3-WT tumours further characterises this novel DMG, H3K27-altered sub-group, characterised by a specific immunohistochemistry profile with H3K27me3 loss, wild-type H3K27M and positive EZHIP. It also gives new insights into the possible mechanism and pathway regulation in these tumours, potentially opening new therapeutic avenues for these tumours which have no known effective treatment. This study has been retrospectively registered on clinicaltrial.gov on 8 November 2017 under the registration number NCT03336931 (https://clinicaltrials.gov/ct2/show/NCT03336931).