Lee Segel one of the greatest applied mathematicians of our time passed away on January 31, 2005. His obituary (SIAM News, 03-10-2005) read "With his death, the applied mathematics community lost one of its finest practitioners, and the theoretical biology community lost a true pioneer who was still a leader at the cutting edge of so many subjects. And most importantly, the world community lost a true mensch, a compassionate and loving individual who inspired so many with his brilliance, his enthusiasm, his sense of humor, and his concern for others." Lee Segel was an extraordinary mentor of women and his former students include many leaders in the field of mathematical biology. In this talk through a series of examples, I will illustrate my experiences with women mathematicians at the undergraduate, graduate and postdoctoral level as they engaged in research in mathematical biology. I will discuss their research as a prelude to the lecture of one of the most outstanding mathematical biologist, Trachette Jackson who chose to become a mathematician through the encouragement and support of the late Joaquin Bustoz Jr.
Conformational diseases result from the failure of a specific protein to fold into its correct functional state. The misfolded proteins can lead to the toxic aggregation of proteins. In some cases, misfolded proteins interact with bystanders proteins (unfolded and native folded proteins), eliciting a misfolded phenotype. These bystander polypeptides would follow their normal physiological pathways in absence of misfolded proteins. In some conformational diseases, evidence suggests that bystander protein disappearance occurs through direct or indirect interaction with misfolded proteins, resulting in a transformation into aggregate-prone misfolded protein. Protein aggregation in conformational diseases often displays a threshold phenomenon characterized by a sudden shift between nontoxic and toxic levels of protein aggregates. We propose a general mechanism of bystander and misfolded protein interaction to investigate how the threshold phenomenon in protein aggregation is triggered in conformational diseases. Using a continuous flow reactor model of the endoplasmic reticulum, we derived the conditions necessary to produce threshold phenomena. Our results indicate that slight changes in the ratio of misfolded to bystander basal protein concentrations can trigger the threshold phenomena in protein aggregation. Our model proposes a general mechanism for the loss of function observed in certain conformational diseases. We also identify the conditions necessary to trigger the observed threshold phenomena in protein aggregation. Understanding the conditions necessary for the aggregation threshold phenomena is an important step towards developing therapeutic strategies targeting the modulation of conformational diseases.
Nonlinear partial differential equations arise in stochastic optimal control via dynamic programming equations. In many cases, solutions of these equations aid in the design of optimal controls. We discuss a class of equations where the associated control processes are "singular" with respect to the time variable. These equations arise in models for spacecraft control, financial models that incorporate transaction costs, and in models of queueing systems.
A new way to model the dynamics of malaria transmission that takes into consideration the demography of the transmitting vector will be presented. Model results indicate the existence of nontrivial disease free and endemic steady state solutions which can be driven to instability via a Hopf bifurcation as a parameter is varied in parameter space. The model therefore captures natural occurring oscillations known to occur in the dynamics of mosquito populations and these oscillations lead to oscillations in the dynamics of malaria transmission without recourse to external seasonal forcing, a way that has been used in the past to obtain such oscillations. Possible reasons why it has been difficult to eradicate malaria will also be discussed. The discovery of these natural occurring oscillatory dynamics present a plausible framework for developing and implementing control strategies. These will be discussed.
In the 2002 film by Gurinder Chadha, character Jesminder 'Jess' Bhamra states "No one can cross a ball or bend it like Beckham" in a reference to the international soccer star's ability to cause the ball to swerve. French researchers Guillaume Dupeux, Anne Le Goff, David Quere and Christophe Clanet published a paper earlier this year in the New Journal of Physics detailing both experimental and mathematical analyses of a spinning ball in a fluid to show that it must follow a spiral. In this talk, we give an overview of their discussion by reviewing the Navier-Stokes equation in a Serret-Frenet coordinate system. This talk is dedicated to the memory of Angela Grant and her love of mathematics in sports.