A long-standing problem in rigidity theory is to characterize the graphs which are minimally
generically rigid in $3$-space. The results of Cauchy, Dehn, and Alexandrov give one …

Semi-cyclic 4-polytopes were introduced in (12). In Chapter 2, we present the results from
this paper. In particular, a complete facial description of the semi-cyclic 4-polytopes is given. …

Among the d-polytopes with v vertices, the neighbourly polytopes have the greatest number
of facets. This maximum property of neighbourly polytopes has prompted researchers to …

A significant range of geometric structures whose rigidity has been explored, for both
practical and theoretical purposes, are formed by modifying generically isostatic triangulated …

In this research, we investigate, refine, and implement algorithmic tools that allow us to
answer decision questions about regular languages. We provide a thorough presentation of …

The investigation of many real-world applications involves mathematical models that consist
of systems of ordinary differential equations (ODEs). This thesis mainly focuses on the …

A periodic framework is a simple infinite graph CG, together with a realization of its vertices
Cp in Rd such that the resulting framework is invariant under a set L of d linearly independent …

This interdisciplinary project explores “predictive policing”, a blanket term given to a number
of crime prediction algorithms and tools used by police departments across the globe in an …

Differential equations are involved in many felds. Often these cannot be solved exactly, so
they must be approximated. To do this, we derive a fourth order finite difference scheme for …

… • Wendy Finbow-Singh and Walter Whiteley described inductive constructions on
modified … • Walter Whiteley reports: ”Wendy Finbow-Singh and I have applied the inductive …