AbstractThe purpose of my talk is to give a progress report on a Masamu research program, the elephant demography project.  The elephant project has morphed over time, and during the past couple of years turned its focus to the topic of demographic stochasticity.  Demographic stochasticity is a property of population growth that results from dealing…

Abstract This talk presents a historical overview of several important developments in harmonic analysis, emphasizing how foundational questions led to major advances in modern mathematics. Beginning with classical Hardy spaces, Lebesgue spaces, and the Hilbert transform, we review the role of the M. Riesz theorem and the correspondence between analytic and real-variable function spaces. We…

Abstract Controllability is a fundamental concept in control theory concerned with the ability to steer a dynamical system toward a desired target state using admissible controls. We begin with the classical controllability theory of finite-dimensional systems, highlighting the Kalman rank condition and its role in characterizing exact controllability. We then move to infinite-dimensional systems, where…

Abstract Heart disease and its associated comorbidities represent a leading global cause of morbidity and mortality.Yet the physiological signatures preceding clinical diagnosis remain poorly characterized. The mechanistic links between short-term changes in physiological state and long-term multimorbidity progression are similarly understudied. Early detection of disease-preceding signals could meaningfully improve diagnostic lead time enabling a fundamental shift from reactive diagnosis…

Abstract Quantilized mean-field game models involve quantiles of the population’s distribution. We study a class of such games with a capacity for ranking games, where the performance of each agent is evaluated based on its terminal state relative to the population’s quantile value. This evaluation criteria is designed to select the top performing agents. We…