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In this preliminary report, two optimization approaches, gradient descent with automatic differentiation and particle swarm optimization, are presented, applied, and compared in an effort to leverage dynamic information collected during contrast-enhanced medical imaging of tumors to estimate four blood flow parameters: perfusion, permeability surface area product, volume of the plasma, and volume of the interstitial space. Using Fick’s law on a simple two-compartment model, the resulting PDEs are numerically integrated using a collocation method for a set of boundary and initial conditions and known values of the parameters, and the resulting tracer concentrations were spatially integrated to generate truth data of signal intensity as a function of time only. After using physical constraints on the boundaries to recover reasonable estimates for two of the parameters, the two optimization approaches are used in an attempt to recover estimates for the remaining two parameters. The resulting efficacy and efficiency of the two optimization approaches are compared.

As we aim to prepare students to tackle increasingly complex problems in the real world, we believe that extracurricular contests can provide a fun, low-stakes environment to practice mathematical and interdisciplinary modelling skills. In this chapter, we discuss the value of providing such experiences for students and provide an overview of a popular international competition. We then describe rural and urban variations of a local modelling competition designed to provide instant feedback and foster social interaction among student modelers. After offering some thoughts on developing appropriate problems for these competitions, we close by sharing some informal feedback from students and faculty who have participated in these competitions.

In its December 2019 edition, the \textit{Notices of the American Mathematical Society} published an essay critical of the use of diversity statements in academic hiring. The publication of this essay prompted many responses, including three public letters circulated within the mathematical sciences community. Each letter was signed by hundreds of people and was published online, also by the American Mathematical Society. We report on a study of the signatories' demographics, which we infer using a crowdsourcing approach. Letter A highlights diversity and social justice. The pool of signatories contains relatively more individuals inferred to be women and/or members of underrepresented ethnic groups. Moreover, this pool is diverse with respect to the levels of professional security and types of academic institutions represented. Letter B does not comment on diversity, but rather, asks for discussion and debate. This letter was signed by a strong majority of individuals inferred to be white men in professionally secure positions at highly research intensive universities. Letter C speaks out specifically against diversity statements, calling them "a mistake," and claiming that their usage during early stages of faculty hiring "diminishes mathematical achievement." Individuals who signed both Letters B and C, that is, signatories who both privilege debate and oppose diversity statements, are overwhelmingly inferred to be tenured white men at highly research intensive universities. Our empirical results are consistent with theories of power drawn from the social sciences., 21 pages, 2 tables, 2 figures; minor textual edits made to previous version

The article of record as published may be found at http://dx.doi.org/10.1093/comnet/cnx040 Productive learning environments strike a balance between student motivation and the necessary learning outcomes associated with a particular course. This article explores one way to achieve such a balance and discusses some of the subtle benefits that spring from that balance. We designed a network science course that achieves course objectives and at the same time allows students to develop, test, and monitor a network of their own choosing. Rather than use canned networks, we introduce a set of assignments called the Network Profile Summary in which students continually apply newly learned course concepts to their selected networks and are therefore able to realize the utility and place of these concepts. This course design fosters student motivation and encourages independent learning. Under this pedagogical paradigm, students began to see coursework, concepts and feedback as productive and globally meaningful rather than corrective and locally meaningful. U.S. Department of Defense

The field of differential equations is rich with applications that can be used to motivate and facilitate learning. This paper presents a variety of ways a modeling-focus can be adopted, based on the desired learning outcomes of an individual course. We offer an overview of the implementation of this approach within a specific course and identify several modeling scenarios that can be used either to introduce and motivate a lesson topic or to allow students to apply recently acquired skills to a meaningful problem. While using applications has clear benefits for our students, many of whom go on to pursue engineering degrees, adding these components to a course can be challenging, so this paper also addresses some logistical approaches to folding these applications into a course with success. Student feedback is also provided as evidence of the value of adopting such an approach.

Many recent cancer treatments focus on preventing angiogenesis, the process by which a tumor promotes the growth of large and efficient capillary beds for the increased nourishment required to support the tumor's rapid growth[l]. To measure the efficacy of these treatments in a timely fashion, there is an interest in using data from dynamic sequences of contrast-enhanced medical imaging, such as MRI and CT, to measure blood flow parameters such as perfusion, permeability-surface-area product, and the relative volumes of the plasma and extracellular-extravascular space. Starting with a two compartment model presented by the radiology community[2], this work challenges the application of a simplification to this problem, which was originally developed to model capillary reuptake[3]. While the primary result of this work is the demonstration of the inaccuracy of this simplification, the remainder of the paper is dedicated to presenting alternative methods for calculating the perfusion and plasma volume coefficients. These methods are applied to model data sets based on real patient data, and preliminary results are presented.