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Abstract: Phase I clinical trials explore the toxicity of new therapeutic agents. Phase II trials seek to establish some sign of efficacy. But practical applications vary creating a suite of statistical expressions for these trials’ goals and objectives. There is now a robust statistical literature on these topics. We review the development of adaptive dose selection procedures in early phase clinical trials. We will show how a suite of modern approaches developed out of classical stochastic approximation, random walks and optimal design theory. Critical effects that design choices have on analysis procedures are described. We focus on the distinguishing concepts and goals behind the various approaches.

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Meet and greet with refreshments at 1:00 pm. Talk is at 1:30 pm

ABSTRACT: A large part of stochastic portfolio theory, as initiated by Robert Fernholz in the 1990s, is concerned with construction of practical equity portfolios that can beat the stock market index by active rule-based trading. The truly remarkable part of the theory is that it requires no probabilistic modeling on the future behavior of stock prices. There is a Monge-Kantorovich optimal transport problem that naturally arises in the construction of such portfolios. This transport problem is a multiplicative analog of the well-studied quadratic Kantorovich- Wasserstein transport with equally striking properties. We will see aspects of this transport problem from theoretical uses such as defining gradient flows in a non-metric setting to practical uses such as in determining the right frequency of trading. Interesting probability theory comes in as we consider entropic relaxation of this problem giving rise to multiplicative Schrodinger bridges.

PIMS - UVic Distinguished Lecture

Meet and Greet at 3:00, talk at 3:30

Understanding how environmental randomness affects evolution is of fundamental importance for biology. The presence of temporal or spatial randomness significantly affects the competition dynamics in populations and gives rise to some counterintuitive observations. In this talk, I will present some recent results on the evolutionary dynamics in systems where spatial and temporal randomness affects division and/or death parameters of cells. Of particular interest are the dynamics of non-selected mutants, whose rates come from the same distribution as those of wild type cells. Temporal and spatial types of randomness possess fundamentally different properties. Under temporal randomness, depending on the exact formulation of the update rules, minority mutants can be advantageous, disadvantageous, or neutral. In contrast to this, under spatial randomness, minority mutants are always advantageous. Applications to biomedical problems, including biofilms and cancer, are discussed.

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Coffee and Tea Meet and Greet is at 2:30, talk starts shortly after.

Abstract
New single-cell technologies such as single-cell RNA-seq and high-dimensional flow cytometry enable the unprecedented interrogation of single-cell phenotypes (and functions) under various biological conditions. A common statistical problem is the discovery and characterization of such cell phenotypes from single-cell data and their relationship to clinical outcomes including response to cancer immunotherapy or protection after vaccination. During this talk, I will present some statistical methodology we have developed to analyze high-dimensional single-cell data. I will illustrate these novel approaches using several datasets that we have recently generated to characterize immune responses in the context of vaccination and immunotherapy.

The Provost's Distinguished Women Scholar Lecture is supported by the Provost’s Distinguished Women Scholars Lecture Committee and the Pacific Institute for the Mathematical Sciences.

• Tea reception 6:00-6:30pm
• Public talk 6:30-9:00pm

Abstract

New kinds of data are giving rise to exciting new opportunities in public health. The recent revolution in DNA sequencing means that for the first time, we can read the sequences of viruses and bacteria that cause human disease. This allows us to track their evolution through time, and even to track how they are spreading through communities and environments. However, the best ways to control infectious disease do not leap off the pages of these data. Instead, we need to build ways to model and understand these rich sources of data, and we need to connect the information we gain to our efforts in public health. These tasks require new mathematics. In my group, we have developed a way to connect the DNA sequences from bacterial infections to 'outbreak stories' -- who infected whom and when. We combine genomic data, locations and clinical histories, allowing us to estimate how the infection spreads in a community. I will describe how the method works and some of its applications for public health, and I will give a broader picture of some of the coming challenges that healthcare brings to the mathematical sciences.

The Provost's Distinguished Women Scholar Lecture is supported by the Provost’s Distinguished Women Scholars Lecture Committee and the Pacific Institute for the Mathematical Sciences.

• Tea reception 3:00-3:20pm
• Academic Seminar 3:20-4:20pm

Abstract

Improvements in sequencing technology mean that we have rich data on how infections evolve and spread. In this talk I will describe two settings where this calls for new mathematics. Trees -- in the sense of graphs with no cycles -- are a cornerstone of how we understand these data. Trees can represent patterns of ancestry through time, showing evolutionary stories that are supported by data and revealing how consistent models are with data. In the first part of the talk, I will describe a metric on trees that is based on polynomial representations of trees. Since each tree has a unique polynomial, comparing the coefficients yields a suite of tree comparison tools. We illustrate these with data from cetacean evolution and infectious disease. In the second part of the talk, I will describe how we can use trees, together with a type of colouring, to do Bayesian inference of who infected whom in an infectious disease outbreak. I will apply this tool to data from tuberculosis infections.

PIMS Distinguished Lecture

Join us for refreshments at a meet and greet at 3:00 pm, the talk will follow at 3:30 pm.

ABSTRACT: Optimization and optimal dynamical control are used to investigate the accuracy of analytical estimates for solutions of some basic nonlinear partial differential equations of mathematical hydrodynamics. Even though many mathematical estimates are demonstrably sharp, the result of a sequence of applications of such estimates need not be, leaving uncertainty in the precision of the ultimate result of the analysis. We examine the classical analysis bounding enstrophy and palinstrophy amplification in Burgers’ and the Navier-Stokes equations and discover that the best known instantaneous growth rates estimates for these quantities are indeed sharp. Integrating the estimates in time may (as in the 2D Navier-Stokes case) but does not always (as in the Burgers case) produce sharp estimates in which case optimal control techniques must be brought to bear to determine the actual extreme behavior of the nonlinear dynamics. The question for the 3D Navier-Stokes equations remains unresolved although work is in progress to apply these tools to address it. The most recent work reported here is joint with Diego Ayala and Thilo Simon, Journal of Fluid Mechanics 837, 839–857 (2018).

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