Seminars and Colloquiums
Week of January 17, 2011
Professor Michael Frazier, Wednesday
Dr. Ronald Mahler, Lockheed Martin, Thursday
If you are interested in giving or arranging a talk for one of our seminars or colloquiums,
please review our calendar.
If you have questions, or a date you would like to confirm, please contact Dr. Fernando Schwartz.
Wednesday, January 19
TIME: 3:35 pm
ROOM: Ayres 114
SPEAKER: Professor Michael Frazier
TITLE: "Estimates for Green's functions of Schrodinger operators via Neumann series"
ABSTRACT: We consider an integral operator with a nonnegative kernel, on a measure space. Under certain conditions, we obtain upper and lower estimates of the same type for the kernel of the Neumann series of the operator. Applying these results leads to estimates for the Green's function for certain time-independent Schrodinger operators. These estimates in turn yield solvability conditions for certain inhomogeneous Schrodinger equations, and for a nonlinear equation of Riccati type.
Thursday, January 20
TIME: 3:35 pm
ROOM: Ayres 405
SPEAKER: Dr. Ronald Mahler, Lockheed Martin
TITLE: "Abstract Statistics Successfully Applied to Practice: Random Set Bayes Filters"
ABSTRACT: "Multitarget tracking" refers to the problem of estimating the number, positions, velocities, identities, etc. of multiple entities moving as a joint dynamical system. Two new multitarget tracking algorithms--the PHD and CPHD filters--have attracted considerable international interest since 2000. Well over 300 research publications devoted to them have appeared since that time. In part this is because these filters:
( are based on explicit statistical sensor and motion models;
( detect and track targets in relatively dense clutter;
( avoid traditional measurement-to-track association;
( estimate target number directly from the measurements;
( are very fast when implemented using Gaussian-mixture techniques;
( outperform bottom-up traditional approaches in many cases.
They are based on a fundamentally new paradigm: first- and second-order multitarget statistical moments, based on a top-down point process (random finite set) formulation of Bayes filtering theory. This talk provides an overview of their applications, implementations, and theoretical foundations.