No description available.

No description available.

This paper is a collection of corrections and related thoughts for Bevil's thesis The Welsh Crwth, Its History and Its Genealogy.

Combinatorics on words explore words – often called strings in the com- puter science community, or monoids in mathematics – and their structural properties. One of the most studied question deals with repetitions which are a form of redundancy. The thesis focuses on estimating the maximum number of distinct squares in a string of length n. Our approach is to study the combinatorial properties of these overlapping structures, nested systems, and obtain insights into the intricate patterns that squares create. Determin- ing the maximum number of repetitions in a string is of interest in different fields such as biology and computer science. For example, the question arrises when one tries to bound the number of repetitions in a gene or in a computer file to be data compressed. Specific strings containing many repetitions are often of interest for additional combinatorial properties. After a brief review of earlier results and an introduction to the question of bounding the maxi- mum number of distinct squares, we present the combinatorial insights and techniques used to obtain the main result of the thesis: a strengthening of the universal upper bound obtained by Fraenkel and Simpson in 1998. / Thesis / Doctor of Philosophy (PhD)

This thesis concerns flat knots and their properties. We study various invariants of flat knots, such as the crossing number, the u-polynomial, the flat arrow polynomial, the flat Jones-Krushkal polynomial, the based matrices, and the φ-invariant. We also examine the behavior of these invariants under connected sum and cabling. We give a matrix-based algorithm to calculate the flat Jones-Krushkal polynomial. We take a special interest in certain subclasses of flat knots, such as almost classical flat knots, checkerboard colorable flat knots, and slice flat knots. We explore how the invariants can be used to obstruct a flat knot from being almost classical, checkerboard colorable, or slice. We show that any minimal crossing diagram of a composite flat knot is a con- nected sum, and we introduce a skein formula for the constant term of the flat arrow polynomial. A companion project to this thesis is the interactive website, FlatKnotInfo. It provides a curated dataset of examples and invariants of flat knots. It also features a tool for searching flat knots and another tool that crossreferences flat knots with virtual knots. FlatKnotInfo was used to develop many of the results in this thesis, and we hope others find it useful for their research on flat knots. The Python code for calculating based matrices and flat Jones-Krushkal polynomials is included in an appendix. / Dissertation / Doctor of Philosophy (PhD)

In the absence of treatment following strokes, both humans and model organisms demonstrate partial improvements in motor function. Several endogenous mechanisms, such as cortical reorganization, are hypothesized to cause this spontaneous biological recovery. Reorganization of the motor cortex occurs within a time sensitive period and involves both proximal and distal sites of the intact brain. Despite these advancements, whether the same or different cells are used in the reorganized cortex after stroke remains unknown. In order to identify the motor networks involved in recovery, our lab has begun using the inducible Arc-CreERᵀ²:Rosa-YFPᶠᐟᶠ mice. In conjunction with the bimanual string-pulling task, this inducible model allows for the labelling of active cells throughout stroke recovery; either pre, 2 days post-stroke (dps) and 2 weeks post-stroke (wps). Behavioural deficits on the string-pull task were observed at 2 dps and accompanied by a decrease in active cells in the ipsilesional secondary motor (M2) cortex of stroke mice. By 2 wps, stroke mice had partial recovery of motor function with no differences in active cells in the ipsilesional M2. Interestingly, ~40% of cell in the motor cortex of sham and stroke mice were activated more than once while performing the string-pull task until 2 wps. Deeplabcut kinematic analysis of the string-pull task was also unable to identify differences in motor performance between stroke and sham mice. In addition, irrelevant of stroke injuries, only 60% of cells co-expressed the pan-neuronal marker NeuN after surgeries. Together these findings suggest that 40% of cells are reactivated up to 2 weeks post-stroke during the performance of a motor task, despite the acute decreases in active cells in the ipsilesional M2 of stroke mice. DeepLabCut kinematic results also highlight the need to redefine kinematic outcomes to better assess the full spectrum of stroke deficits.

No description available.

No description available.

No description available.

No description available.