Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology—defined here simply as the use of mathematics in cancer research—complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.

The pace and unpredictability of evolution are critically relevant in a variety of modern challenges: combating drug resistance in pathogens and cancer, understanding how species respond to environmental perturbations like climate change, and developing artificial selection approaches for agriculture. Great progress has been made in quantitative modeling of evolution using fitness landscapes, allowing a degree of prediction for future evolutionary histories. Yet fine-grained control of the speed and the distributions of these trajectories remains elusive. We propose an approach to achieve this using ideas originally developed in a completely different context -counterdiabatic driving to control the behavior of quantum states for applications like quantum computing and manipulating ultra-cold atoms. Implementing these ideas for the first time in a biological context, we show how a set of external control parameters (i.e. varying drug concentrations / types, temperature, nutrients) can guide the probability distribution of genotypes in a population along a specified path and time interval. This level of control, allowing empirical optimization of evolutionary speed and trajectories, has myriad potential applications, from enhancing adaptive therapies for diseases, to the development of thermotolerant crops in preparation for climate change, to accelerating bioengineering methods built on evolutionary models, like directed evolution of biomolecules.The quest to control evolutionary processes in areas like agriculture and medicine predates our understanding of evolution itself. Recent years have seen growing research efforts toward this goal, driven by rapid progress in quantifying genetic changes across a population 1-3 as well as a global rise in challenging problems like therapeutic drug resistance 4-6 . New approaches that have arisen in response include prospective therapies that steer evolution of pathogens toward maximized drug sensitivity 7, 8 , typically requiring multiple rounds of selective pressures and subsequent evolution under them. Since we cannot predict the exact progression of mutations that occur in the course of the treatment, the best we can hope for is to achieve control over probability distributions of evolutionary outcomes. However, our lack of precise control over the timing of these outcomes poses a major practical impediment to engineering the course of evolution. This naturally raises a question: Rather than being at the mercy of evolution's unpredictability and pace, what if we could simultaneously control the speed and the distribution of genotypes over time?Controlling an inherently stochastic process like evolution has close parallels to problems in other disciplines.Quantum information protocols crucially depend on coherent control over the time evolution of quantum states under external driving 9, 10 , in many cases requiring that a system remain in an instantaneous ground state of a time-varying Hamiltonian in applications like cold atom transport 11 and quantum adiabatic computat...

DISCLAIMER: This article does not represent the official recommendation of the Cleveland Clinic or CaseWestern Reserve University School of Medicine, nor has it yet been peer reviewed. We are releasing it early, pre-peer review, to allow for quick dissemination/vetting by the scientific/clinical community given the necessity for rapid conservation of personal protective equipment (PPE) during this dire global situation. We welcome feedback from the community.Personal protective equipment (PPE), including face shields, surgical masks, and N95 respirators, is crucially important to the safety of both patients and medical personnel, particularly in the event of an infectious pandemic. As the incidence of Coronavirus Disease (COVID-19) increases exponentially in the United States and worldwide, healthcare provider demand for these necessities is currently outpacing supply. As such, strategies to extend the lifespan of the supply of medical equipment as safely as possible are critically important. In the midst of the current pandemic, there has been a concerted effort to identify viable ways to conserve PPE, including decontamination after use. Some hospitals have already begun using UV-C light to decontaminate N95 respirators and other PPE, but many lack the space or equipment to implement existing protocols. In this study, we outline a procedure by which PPE may be decontaminated using ultraviolet (UV) radiation in biosafety cabinets (BSCs), a common element of many academic, public health, and hospital laboratories, and discuss the dose ranges needed for effective decontamination of critical PPE. We further discuss obstacles to this approach including the possibility that the UV radiation levels vary within BSCs. Effective decontamination of N95 respirator masks or surgical masks requires UV-C doses of greater than 1 Jcm −2 , which would take a minimum of 4.3 hours per side when placing the N95 at the bottom of the BSCs tested in this study. Elevating the N95 mask by 48 cm (so that it lies 19 cm from the top of the BSC) would enable the delivery of germicidal doses of UV-C in 62 minutes per side. Effective decontamination of face shields likely requires a much lower UV-C dose, and may be achieved by placing the face shields at the bottom of the BSC for 20 minutes per side. Our results are intended to provide support to healthcare organizations looking for alternative methods to extend their reserves of PPE. We recognize that institutions will require robust quality control processes to guarantee the efficacy of any implemented decontamination protocol. We also recognize that in certain situations such institutional resources may not be available; while we subscribe to the general principle that some degree of decontamination is preferable to re-use without decontamination, we would strongly advise that in such cases at least some degree of on-site verification of UV dose delivery be performed.