Center for Statistical Sciences Seminar
Abstract:
We present an expectation-maximization algorithm for a simultaneous truth and performance level estimation of the
latent ground truth (i.e., gold standard) in medical images. We consider a collection of segmentations and compute a
probabilistic estimate of the true segmentation target, along with a measure of the performance level represented. The
probabilistic estimate of the true segmentation is formed by optimally combining repeated segmentations and weighting the
segmentations iteratively to derive the estimated performance level. Spatial correlation structures are incorporated using
a Markov random field model. Automated segmentations may then be compared against the estimated composite ground truth
using several two-sample validation metrics. We construct parametrically the corresponding receiver operating characteristic
curve, Dice similarity coefficient and mutual information. The performances of such metrics are investigated via
Monte-Carlo simulations.
* This investigation was based on joint work with Professors Simon K. Warfield, William M. Wells and Ron Kikinis of Harvard
Medical School and Massachusetts Institute of Technology. Funding sources included NSF ITR 0426558, a research grant from
CIMIT, RG347A2/2 from the NMSS, NIH grants R01LM007861, R01GM074068, R03CA126466, R01EB008015, R01RR021885, P30HD018655,
U41RR019703, and P41RR013218.
Lefschetz Center for Dynamical Systems Seminar
Abstract: The growth and form of a soft solid pose a range of problems that combine aspects of geometry and physics. I will discuss two examples of growth and form in the plant world motivated by qualitative and quantitative biological observations in the common Lily: (i) the shape of a freely growing pollen tube, and (ii) the undulating fringes on a leaf or petal. In each case, we will see how a combination of physical experiments, mathematical models and computations allow us to unravel the basis for the diversity and complexity of form and sharpens the search for structure.
Center for Fluid Mechanics Seminar
Abstract: Like miners wearing headlamps, active sensory systems?such as the echolocating bat and weakly electric fish?have the advantage of not relying on extrinsic energy sources for sensory stimulation. Such systems, however, are under a basic biophysical constraint: spherical spreading losses on the outbound leg of the signal, and the same on the return, join to form fourth-power fall off with distance. To double the range that an object is detected at, this relationship implies a or 16-fold increase in emission power is needed. Perhaps related to this observation, at standard hunting velocities both the bat and weakly electric fish sense prey with less than half a second to spare before collision in the absence of a course correction. Reflecting this "just-in-time" sensory system, both animals exhibit remarkable maneuverability. In this talk, I'll discuss some of the unique sensory and mechanical abilities of weakly electric fish, how these abilities are closely intertwined in short-range systems, and some robotics work we have done on artificial electrosense and propulsion systems inspired by the fish.
Stochastic Systems Seminar
Abstract: We introduce the concept of instant independence for certain anticipating stochastic processes and take the class of instantly independent stochastic processes as a counterpart of adapted stochastic processes for the Ito theory of stochastic integration. Then we define the stochastic integral of a stochastic process which is a linear combination of the products of instantly independent and adapted stochastic processes. The crucial idea is to use the right endpoints of subintervals as the evaluation points for the instantly independent factors, while the left endpoints of subintervals are used for the adapted factors. We prove a special case of Ito's formula for this new stochastic integral and present some simple examples of stochastic differential equations involving the new stochastic integral.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Scientific Computing Seminar
Abstract: Unsteady incompressible viscous flows of a fluid enclosed in a cylindrical container with an open top surface are discussed. These moving free-surface flows are generated by the steady rotation of the solid bottom end-wall. Such type of flows belongs to a group of recirculating lid-driven cavity flows with geometrical axisymmetry. The top surface of the cylindrical cavity is left open so that the free surface can freely deformed. The Reynolds regime corresponds to unsteady transitional flows with some incursions in the fully laminar regime. The approach taken here revealed new nonaxisymmetric flow states that are investigated based on a fully three-dimensional solution of the Navier-Stokes equations for the free-surface cylindrical swirling flow, without resorting to any symmetry property unlike all other results available in the literature. Theses solutions are obtained through direct numerical simulations based on a highly-accurate Legendre spectral element method combined with a moving-grid technique.
PDE Seminar
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: I discuss my ongoing work in creating a computer system that plays the role of musical accompanist in a non-improvisatory composition for soloist and ensemble. This application simulates a concerto-like setting for a live soloist, allowing the soloist to {\em lead} an interactive real-time audio synthesis of the accompanying ensemble, ranging from single piano to full orchestra. An accompanist must synthesize a number of different sources of information. First of all, the accompanist must perform a real-time analysis of the soloist's acoustic signal enabling the accompanist to ``hear'' the soloist. The accompaniment must also understand the basic template for musical performance that is described in the musical score, (notes, rhythms, etc.) thereby allowing the system to ``sight-read'' (perform with no training) credibly. However, the accompanist must also be able to improve over successive rehearsals, much as live musicians do; thus the accompanist must be capable of learning from training data. I will describe the modeling approach of my baseline system, provide a live demonstration of the robustness of the system, as well as documenting a number of examples with members of our Jacobs School of Music. I will also discuss current directions in improving the system, including source separation and modeling of musical timing.