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We define the bisector energy E(P) of a set P in R-2 to be the number of quadruples (a, b, c, d) is an element of P-4 such that a, b determine the same perpendicular bisector as c, d. Equivalently, E(P) is the number of isosceles trapezoids determined by P ...
We study the structure of planar point sets that determine a small number of distinct distances. Specifically, we show that if a set of n points determines o(n) distinct distances, then no line contains Omega(n (7/8)) points of and no circle contains Omega ...
We present a new formulation of a shape space containing all continuously defined 2D spline curves up to a similarity transform of a reference shape. We are able to measure a distance between an arbitrary curve and the shape space itself. Our contribution ...
Common single-nucleotide variation in the host accounts for 25% of the variability in the plasma levels of HIV during the clinical latency stage (viral load set point). However, the role of rare variants and copy number variants remains relatively unexplor ...
This thesis addresses the design of optimization-based control laws for the case where convergence to a desired set-point, minimization of an arbitrary performance index, or a combination of the two, is the desired objective. The results are developed with ...
Given a finite n-element set X, a family of subsets F subset of 2(X) is said to separate X if any two elements of X are separated by at least one member of F. It is shown that if vertical bar F vertical bar > 2(n-1), then one can select vertical bar log n ...
The plasma response to resonant magnetic perturbations (RMPs) in ASDEX Upgrade is modeled with the non-linear resistive MHD code JOREK, using input profiles that match those of the experiments as closely as possible. The RMP configuration for which edge lo ...
Recent theoretical work predicts intrinsic toroidal rotation in the tokamak edge to depend strongly on the normalized major radial position of the X-point. With this motivation, we conducted a series of Ohmic L-mode shots on the Tokamak a Configuration Var ...
Three-dimensional non-axisymmetric magnetic fields are purposely applied to toroidally symmetric fusion plasmas in order to modify transport of heat and particle fluxes to the plasma-facing components (PFCs), and specifically to control and suppress edge l ...
Given a collection of n opaque unit disks in the plane, we want to find a stacking order for them that maximizes their visible perimeter, the total length of all pieces of their boundaries visible from above. We prove that if the centers of the disks form ...