PACM Colloquium

PACM Colloquium: Stochastic Models in Robotics and Structural Biology

Many stochastic problems of interest in engineering and science involve random rigid-body motions. In this talk, a variety of stochastic phenomena that evolve on the group of rigid-body motions will be discussed together with tools from harmonic analysis and Lie theory to solve the associated equations. These include mobile robot path planning, statistical mechanics of DNA, and problems in image processing. Current work on multi-robot team diagnosis and repair, information fusion, and self-replicating robots will also be discussed.

PACM Colloquium: Recent progress in object recognition and symmetry detection in digital images

I will survey developments in the application of invariants of various types, including differential invariant signatures and joint invariant histograms, for object recognition and symmetry detection in digital images.  Recent applications, including automated jigsaw puzzle assembly and cancer detection, will be presented.

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PACM Colloquium: How Far Are We From Having a Satisfactory Theory of Clustering?

Unsupervised learning is widely recognized as one of the most important challenges facing machine learning nowadays. However, unlike supervised learning, our current theoretical understanding of those tasks, and in particular of clustering, is very rudimentary. Although hundreds of clustering papers are being published every year, there is hardly any work reasoning about clustering independently of any particular algorithm, objective function, or generative data model.

PACM Colloquium: Equiangular lines and spherical codes in Euclidean spaces

A family of lines through the origin in Euclidean space is called equiangular if any pair of lines defines the same angle. The problem of estimating the maximum cardinality of such a family in $\mathbb{R}^n$ was extensively studied for the last 70 years. Answering a question of Lemmens and Seidel from 1973, in this talk we show that for every fixed angle $\theta$ and sufficiently large $n$ there are at most $2n-2$ lines in $\mathbb{R}^n$ with common angle $\theta$. Moreover, this is achievable only when $\theta =\arccos\frac{1}{3}$.

PACM Colloquium: Survival and Schooling Hydrodynamics

The aqueous environment of natural swimmers mediates magnificent patterns of schooling as well as their escape and attack routines. We study the fluid mechanics of single and multiple swimmers through simulations that rely on state of the art multi-resolution vortex methods. Stochastic optimisation and  machine learning algorithms are used to find optimal shapes and motions for single and synchronised patterns for multiple swimmers.

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