Cryo-electron microscopy (cryo-EM) is a technique for discovering the 3D structures of small molecules. To perform this 3D reconstruction a large number of 2D images taken from unknown microscope positions must be correctly positioned back in 3D space. Although these microscope positions are unknown, the common lines of intersection of the image planes can be detected and used in 3D reconstruction. A major difficulty in this process is large amounts of noise in the common line data.
The set of all noiseless common lines forms a semi-algebraic set (a set defined by polynomial equalities and inequalities). We define and describe the geometry of this set, and briefly discuss applications.
Bryan Daniels
In physical systems, boundaries in parameter space that separate different large-scale behavior correspond to phase transitions, where small changes in microscopic parameters lead to drastic changes in macroscopic observables. We use fine-grained data about conflict in a macaque society to ask whether this social system is located near a phase transition. We find using two models (an equilibrium Ising model and a dynamic branching process model) that the system is near but below a transition, indicating that aggression dissipates quickly enough to avoid becoming typically widespread, but not so quickly that large fights are impossible. A relation between thermodynamics and
information theory shows that being near the transition implies that it is easier for an observer of fight sizes to infer changes in
individual proclivities to fight. More generally, this points to the
possibility of quantifying a system’s collective behavior by measuring the degree to which information can percolate among different spatial scales.
Discovery Building, Orchard View Room
Bryan Daniels, David Dynerman