# Seminars & Events for PACM/Applied Mathematics Colloquium

##### Collective motion and decision-making in animal groups

Animal groups such as bird flocks, insect swarms and fish schools are spectacular, ecologically important and sometimes devastating features of the biology of various species. Outbreaks of the desert locust, for example, can invade approximately one fifth of the Earth's land surface and are estimated to affect the livelihood of one in ten people on the planet. Using a combined theoretical and experimental approach involving insect and vertebrate groups I will address how, and why, individuals move in unison and investigate the principals of information transfer in these groups, particularly focusing on leadership and collective consensus decision-making.

##### New Insights into Semidefinite Programming for Combinatorial Optimization

Beginning with the seminal work of Goemans and Williamson on Max-Cut, semidefinite programming (SDP) has firmly established itself as an important ingredient in the toolkit for designing approximation algorithms for NP-hard problems. Algorithms designed using this approach produce configurations of vectors in high dimensions which are then converted into actual solutions.

##### Did the great masters 'cheat' using optics? Computer vision and graphics addresses a bold theory in art history

In 2001, artist David Hockney and scientist Charles Falco stunned the art world with a controversial theory that, if correct, would profoundly alter our view of the development of image making. They claimed that as early as 1420, Renaissance artists employed optical devices such as concave mirrors to project images onto their canvases, which they then traced or painted over. In this way, the theory attempts to explain the newfound heightened naturalism or "opticality" of painters such as Jan van Eyck, Robert Campin, Hans Holbein the Younger, and many others.

##### Closing the optimality gap using affinity propagation

An important problem in science and engineering is how to find and associate constituent patterns or motifs in large amounts of high-dimensional data. Examples include the identification and modeling of object parts in images, and the detection and association of RNA motifs that regulate tissue-dependent gene splicing in mammals. One approach is to identify a subset of representative data exemplars that are used to summarize and model the data. This is an NP-hard problem that is traditionally solved approximately by randomly choosing an initial subset of data points and then iteratively refining it. I'll describe a method called 'affinity propagation', which takes as input measures of similarity between pairs of data points.

##### Branched Polymers

A branched polymer is a finite, connected set of non-overlapping unit balls in space. The powerful "dimension reduction" theorem of Brydges and Imbrie permits computation of the volume of the space of branched polymers of size N in dimensions 2 or 3. We will show how these and some related computations can be done using elementary calculus and combinatorics. New results include methods for random generation, asymptotic diameter in 3-space, and a combinatorial proof of the notorious "random flight" problem of Rayleigh and Spitzer. Joint work with Rick Kenyon (Brown).

##### A worldwide web of images

In this talk we'll explore the emerging potential of computer vision to transform the way we think about the interconnectedness of digital imagery and the Web, and how these relate to our physical environment. We'll begin with an introduction to the foundations of "3D computer vision," a bag of tricks which has been developing steadily for three decades, combining classical photogrammetry with machine vision. We'll then dive specifically into Photosynth, based on a combination of the Photo Tourism project (a collaboration between Microsoft Research and the University of Washington) and Seadragon, a multiresolution networked platform allowing one to play with arbitrarily many arbitrary large visual objects using only constant-time and constant-bandwidth operations.

##### Mathematical and Computational Challenges in Shear Stiffness Imaging of Tissue: Can cancerous and benign lesions be distinguished?

For centuries doctors have palpated tissue to detect abnormalities. We target imaging the stiffness the doctor feels in the palpation exam, including imaging deeper than what can be felt in this exam and distinguishing between benign and cancerous lesions. Current applications include breast and prostate cancer. Current experimentalists with whom we collaborate are: Dr. Richard Ehman, Mayo Clinic; Mathias Fink, ESPCI, Paris; and Dr. Kevin Parker at the University of Rochester. We describe the challenges and opportunities for imaging, including mathematical modeling and algorithmic development, with the data from the individual experiments

##### Airplane boarding and space-time geometry

It is hard to think of a process that is more boring than boarding an airplane. In the hope of relieving, or at least shortening, some of the pain, airlines have devised various boarding strategies such as back-to-front, window to aisle, boarding by zones or even unassigned seating. In the talk we will try to overturn the negative image that airplane boarding has and will try to portray it as a very exciting process which is modeled via space-time (a.k.a Lorentzian) geometry with a touch of random matrix theory. Using the model we will try to figure out what are the better strategies. If time permits, we will use insights from the airplane borading process to suggest an interpretation for Einstein's law of motion in which god plays the ultimate dice game. The talk is entirely self contained. Partly based on joint works with D.

##### Active and Semi-Supervised Learning Theory

Science is arguably the pinnacle of human intellectual achievement, yet the scientific discovery process itself remains an art. Human intuition and experience is still the driving force of the high-level discovery process: we determine which hypotheses and theories to entertain, which experiments to conduct, how data should be interpreted, when hypotheses should be abandoned, and so on. Meanwhile machines are limited to low-level tasks such as gathering and processing data. A grand challenge for scientific discovery in the 21st century is to devise machines that directly participate in the high-level discovery process. Towards this grand challenge, we must formally characterize the limits of machine learning.