Discrete Conformal and Harmonic Maps for Surface Analysis
DateTuesday, February 26, 2019 - 12:30pm
AbstractConformal and harmonic maps have many nice properties, many due to the fact that they are solutions of elliptic PDE. We will briefly describe some applications and potential applications of conformal and harmonic mappings of domains and surfaces. We will also describe some techniques of discretizing these mappings in a way that preserves some geometric structure. The eventual goal is to have a robust theory of discrete mappings that maintain nice geometric properties to enable efficient computation and robustness of approximation. We will draw some connections between discrete geometry (e.g., Delaunay triangulations) and numerical analysis (e.g., finite element methods).
An Autonomous Model of the Mammalian Cell Cycle
DateTuesday, February 26, 2019 - 4:00pm
AbstractA mathematical model for the mammalian cell cycle is developed that considers the cycle as a sequence of tasks that must be successfully completed in order. Each task is the result of a relatively long process (“integrate”) whose completion triggers a relatively rapid response (“fire”). The model contrasts with previous ones in several ways. It is autonomous, with the cycle driven by growth factors and not any externally imposed “growth” clock. It accounts for the fact that cell cycle progression is not merely driven by cascading waves of cell cycle controllers, but rather must of necessity be coupled to the successful completion of essential tasks. The tasks considered are the most essential ones for the cell cycle: passage of the restriction point, licensing of origins, firing of origins and completion of DNA replication, nuclear envelope breakdown, kinetochore attachment, passage of the spindle checkpoint, and mitosis. Primary cell cycle controllers considered are Cyclin D1 (in complex with CDK4/6), APCCdh1, CDC25A, SCF, RPA, MPF, and APCCdc20. While there is no shortage of prime candidates for “master regulators” of the cell cycle, the selections made here were dictated by the need to relate cell cycle tasks to integrate-and-fire processes, and the necessity for mechanisms to detect successful completion of tasks. Biologists have not reached a consensus regarding certain key aspects of cell cycle control, and some of these issues are considered from the mathematical modeling perspective. Does licensing of origins occur in M or in G1? Is absence of Cdt1 in S phase truly the primary mechanism of preventing relicensing and rereplication in mammalian cells? If not, what is the primary mechanism, and could it be related to nuclear envelope breakdown? How is the firing of origins regulated during S phase? Could it be regulated by the same mechanism used for arresting S phase in the case of DNA damage? Does the primary regulator triggering entry into S phase, CDC25A, peak at the G1-S transition, or does it continue to rise until M? Generally, how does the cell cycle prevent tasks from occurring at the wrong time, and does it make sense to assume that the main mechanism is “absence” (near-zero levels) of certain cell cycle controllers? We discuss how the biological literature provides conflicting answers to these questions, but how certain answers seem far more reasonable in the context of a mathematical model.
Intelligent Optical Networks: Sisyphean Myth or Next Generation?
DateThursday, February 28, 2019 - 12:30pm
AbstractAlmost since the very first fiber optic communication system was realized in a lab, researchers have been imagining the creation of an automated, switched ‘intelligent’ optical network able to move data with the expansive capacity of the optical spectrum. Multiple attempts at this have wrecked upon the rocky shores of the physics behind optical transmission. Optical systems today are largely ‘fat pipes’ that carry large volumes data but lack any intelligent switching capability. Software tools aid network operators in configuring system and remote controls are able to automate simple tasks. With 5G wireless and other software defined networking (SDN) applications driving greater automation at higher speeds and lower latency, there is more need for intelligence in the optical layer than ever before. Machine learning and other advanced algorithms have gained interest as a potential pathway to better predicting and controlling the complex physical systems that comprise an optical network. We will describe some of the sisyphean efforts to realize intelligent optical networks and the state of the art today. New approaches that involve machine learning will be reviewed and we will identify promising areas going forward. Bio: Dr. Dan Kilper is a research professor and Director of the Center for Integrated Access Networks (CIAN) in the College of Optical Sciences at the University of Arizona, Tucson. He holds a joint appointment in Electrical and Computer Engineering at the University of Arizona and an adjunct faculty position in Electrical Engineering at Columbia University. He received a PhD in Physics from the University of Michigan in 1996. From 2000-2013, he was a member of technical staff at Bell Labs. He received the Bell Labs President's Gold Medal Award for his work on physical layer control that enabled the first continental scale transparent network. He is recognized internationally as a pioneer in physical layer monitoring and control including its use in software defined networks for metro, data centers, and 5G wireless applications. He holds seven patents and authored five book chapters and more than one hundred fifty peer-reviewed publications.