In this thesis, we present different approaches to tying knots using robots by enforcing different types of constraints. We attack the problem from three different directions; mechanical design, motion planning with simple control strategies, and...
For ordinary knots in R 3 , there are no degree one Vassiliev invariants. For virtual knots, however, the space of degree one Vassiliev invariants is infinite dimensional. We introduce a sequence of three degree one Vassiliev invariants of virtual...
Cell growth and division are coordinated to keep homeostasis of cell size. The components of the core machinery are conserved in a wide range of cell types. Fission yeast (S. pombe) has been an important model organism to study cell size control...
Identifying the determinants of reproductive success in small-scale societies is critical for understanding how natural selection has shaped human evolution and behavior. The available evidence suggests that status-accruing behaviors such as...
There are no Vassiliev invariants of degree one for classical knots. A. Henrich proved the existence of a sequence of three Vassiliev invariants of degree one for virtual knots. The invariants get stronger and stronger, and the final invariant is...
One of the most distinctive aspects of humans as a species is our propensity to form complex social networks made up of intense, non-reproductive bonds with non-kin. Navigating these networks presents a considerable cognitive challenge that is...
Lowest order charged particle motion in the Earth''s magnetosphere can be explained using simple adiabatic theory. However, nonadiabatic theory is required to explain particle behavior in cases such as when the particle's gyroradius is large...
For a local field K, we study the affine buildings Ξ n and Δ n naturally associated to SL n ( K ) and Sp n ( K ), respectively. Since Sp n ( K ) is a subgroup of SL 2 n ( K ), we investigate properties of a natural embedding of Δ n in Ξ 2 n ....
I consider the problem of extending certain invariants of subsets of natural numbers to their equivalents for subsets of larger cardinals. The two specific questions I will address are the extension of the off-branch number [Special characters...
Topological graph theory. Aperiodicity. Paths and cycles (Graph theory)
The condition ""every cycle has an entry"" first appeared in the literature in Kumjian, Pask, and Raeburn's paper on Cuntz-Krieger algebras of directed graphs, where it was called Condition (L). It provides a necessary condition for simplicity of...
Goldman and Turaev constructed a Lie bialgebra structure on the free Z-module generated by free homotopy classes of loops on an oriented surface. Turaev conjectured that the cobracket of A is zero if and only if A is a power of a simple class. Chas...
The field of proteomics aims to identify and quantify the protein contents of a biological sample. The mass spectrometer is the instrument of choice to characterize these proteins. In the typical proteomics experiment, mass spectra are collected...